BARK FACTOR EQUATIONS FOR NORTHERN HARDWOODS INMICHI6AN

BY EiARY Vi FOWIpoundR NEMAH Ei HUSSAIN DAYID J COHEN ~D DpoundpoundPAK KHATRY-cHHpoundTRI

1999

Bark Factor Equations For Northern Hardwoods

in Michigan

by

Gary W Fowler Nemah G Hussain

David J Cohen and Deepak Khatry-Chhetri

1999

Forest Information Leaflet Forest Management Division

Michigan Department of Natural Resources and

School of Natural Resources and Environment The University of Michigan

NUMBER - 1-99

FORESTRY INFORMATION LEAFLET FOREST MANAGEMENT DIVISION

MICHIGAN DEPARTMENT OF NATURAL RESOURCES

SUBJECT - BARK FACTORS

DATE 31 October 99

TITLE BARK FACTOR EQUATIONS FOR NORTHERN HARDWOODS IN MICHIGAN

AUTHORS- Gary W Fowler Professor of Biometrics School of Natural Resources and Environment University of Michigan Nemah G Hussain Timber Sales Program Leader Forest Management Division Michigan Department of Natural Resources and David j Cohen and Deepak Khatry-Chhetri bull PhD graduate students School of Natural Resources and Environment University of Michigan

BACKGROUND

Bark factor (BF) is the ratio of diameter inside bark (Dill) to diameter outside bark (DOB) at a

given tree height Even though bark factor does increase with height for many species a constant

bark factor usually determin~d at breast height has been assumed in many cases for all tree

heights for many species Thus the use of a constant bark factor for all tree heights will usually

lead to underestimates of most tree and log solid wood volumes and overestimates of bark volume

for many species

Bark factor equations have been developed for aspen (Fowler and Hussain 1987b Fowler

1991) jack pine (Fowler and Hussain 1991 Fowler 1993) and red pine (Fowler and Hussain 1987a

Fowler and Damschroder 1988) in Michigan where hark factor was regressed on tree height (TH)

In all cases there was a very strong relationship hetween BF and TH Bark factor equations were

also developed for oaks (Fowler et al 1997) and paper birch (Fowler and Hussain 1997) in

Michigan where BF was regressed on TH and DOB These relationships were relatively weak with

the relationship to DOB being somewhat stronger

middotCurrent position Research Associate Carnegie Department of Plant Biology Stanford University

bark factor hardwoodsnorthern hardwoods -1shy

-2shy

PURPOSE

The purpose of this paper is to present bark factor equations for northern hardwood tree

species in Michigan and show how the prediction equations may be used

METHODS AND MATERIALS

As part of a larger study to develop new volume equations for hardwoods in Michigan felled

tree measurements were made on a total of 568 notthern hardwood trees from 15 hardwood stands

in Michigan (1) 369 trees from 9 stands in the Upper Peninsula (1 5 and 3 stands from the Copper

Country Escanaba River and Superior state forests respectively) and (2) 199 trees from 6 stands in

the Lower Peninsula (4 and 2 stands from the Mackinaw and Pere Marquette state forests

respectively) The numbers of trees measured hy species are shown below

No of Trees Measured Species

UP LP Michigan

Sugar Maple (SM) Red Maple (RM) Basswood (BW) White Ash (WA) Black Cherry (BC) American Beech (AB) Yellow Birch (YB) American elm (AE)

161

92 5-+ 38

7 6

II 0

87 46

7 21 20 17 0

248 138 61 59 27 23 11

All trees were measured during May-August 1995

Dffi and DOB were measured to the nearest 00 I in at stump height which varied from 2-40

in except for one unusual tree that had a stump hctght of 95 in the top of each 83-ft bolt (100-in

stick) or other nominal bolt length varying fr(lrn 6-16 ft cut out of the stem of each tree to an

approximate 36-in diameter top limit (ie ~tcrnwoot) and at the bottom and top of each 83-ft

bolt or other nominal bolt length varying from 7-16 ft cut out of limbs and top forks of each tree to

an approximate 36-in diameter top limit (ie topwood) DBH was measured to the nearest 01 in

-3shy

and bark thickness at DBH height was measured to the nearest 001 inch DBH height was 45 ft

from the ground except for trees forked below 45 ft where DBH height was approximately 45 ft

above the fork DBH varied from 38-242 in with a mean of 93 in for the data set of 568 trees

Stemwood

The prediction data set included 528 trees distributed by state forest and species as described

above This yielded 1488 829 398 410 178 131 66 and 6 bark factor measurements for SM

RM BW W A BC AB YB and AE respectively There were a total of 3506 bark factor

measurements for the 568 trees

The mean minimum and maximum DBH in in and merchantable height (MH) in ft for the

trees of each species are shown below MH is the height of the tree from the ground to an

approximate 36-in merchantable diameter top limit

No of DBH MH Species Trees x Min-Max x Min -Max

SM 248 92 38-242 3438 858-6367 RM 138 79 85-179 3395 850-5875 BW 61 118 46-218 4192 867-7225 WA 59 89 43-207 4171 867-8200 BC 27 99 70-161 3867 1708-5883 AB 23 116 51-189 3445 875-5042 YB 11 124 90-183 3488 1833-4392 AE 1 120 3608

The following table shows the mean minimum and maximum BF tree height to

measurement in ft (TH) and DOB at TH for the set of bark factor measurements for each species

Bark Factor Equations For Northern Hardwoods

in Michigan

by

Gary W Fowler Nemah G Hussain

David J Cohen and Deepak Khatry-Chhetri

1999

Forest Information Leaflet Forest Management Division

Michigan Department of Natural Resources and

School of Natural Resources and Environment The University of Michigan

NUMBER - 1-99

FORESTRY INFORMATION LEAFLET FOREST MANAGEMENT DIVISION

MICHIGAN DEPARTMENT OF NATURAL RESOURCES

SUBJECT - BARK FACTORS

DATE 31 October 99

TITLE BARK FACTOR EQUATIONS FOR NORTHERN HARDWOODS IN MICHIGAN

AUTHORS- Gary W Fowler Professor of Biometrics School of Natural Resources and Environment University of Michigan Nemah G Hussain Timber Sales Program Leader Forest Management Division Michigan Department of Natural Resources and David j Cohen and Deepak Khatry-Chhetri bull PhD graduate students School of Natural Resources and Environment University of Michigan

BACKGROUND

Bark factor (BF) is the ratio of diameter inside bark (Dill) to diameter outside bark (DOB) at a

given tree height Even though bark factor does increase with height for many species a constant

bark factor usually determin~d at breast height has been assumed in many cases for all tree

heights for many species Thus the use of a constant bark factor for all tree heights will usually

lead to underestimates of most tree and log solid wood volumes and overestimates of bark volume

for many species

Bark factor equations have been developed for aspen (Fowler and Hussain 1987b Fowler

1991) jack pine (Fowler and Hussain 1991 Fowler 1993) and red pine (Fowler and Hussain 1987a

Fowler and Damschroder 1988) in Michigan where hark factor was regressed on tree height (TH)

In all cases there was a very strong relationship hetween BF and TH Bark factor equations were

also developed for oaks (Fowler et al 1997) and paper birch (Fowler and Hussain 1997) in

Michigan where BF was regressed on TH and DOB These relationships were relatively weak with

the relationship to DOB being somewhat stronger

middotCurrent position Research Associate Carnegie Department of Plant Biology Stanford University

bark factor hardwoodsnorthern hardwoods -1shy

-2shy

PURPOSE

The purpose of this paper is to present bark factor equations for northern hardwood tree

species in Michigan and show how the prediction equations may be used

METHODS AND MATERIALS

As part of a larger study to develop new volume equations for hardwoods in Michigan felled

tree measurements were made on a total of 568 notthern hardwood trees from 15 hardwood stands

in Michigan (1) 369 trees from 9 stands in the Upper Peninsula (1 5 and 3 stands from the Copper

Country Escanaba River and Superior state forests respectively) and (2) 199 trees from 6 stands in

the Lower Peninsula (4 and 2 stands from the Mackinaw and Pere Marquette state forests

respectively) The numbers of trees measured hy species are shown below

No of Trees Measured Species

UP LP Michigan

Sugar Maple (SM) Red Maple (RM) Basswood (BW) White Ash (WA) Black Cherry (BC) American Beech (AB) Yellow Birch (YB) American elm (AE)

161

92 5-+ 38

7 6

II 0

87 46

7 21 20 17 0

248 138 61 59 27 23 11

All trees were measured during May-August 1995

Dffi and DOB were measured to the nearest 00 I in at stump height which varied from 2-40

in except for one unusual tree that had a stump hctght of 95 in the top of each 83-ft bolt (100-in

stick) or other nominal bolt length varying fr(lrn 6-16 ft cut out of the stem of each tree to an

approximate 36-in diameter top limit (ie ~tcrnwoot) and at the bottom and top of each 83-ft

bolt or other nominal bolt length varying from 7-16 ft cut out of limbs and top forks of each tree to

an approximate 36-in diameter top limit (ie topwood) DBH was measured to the nearest 01 in

-3shy

and bark thickness at DBH height was measured to the nearest 001 inch DBH height was 45 ft

from the ground except for trees forked below 45 ft where DBH height was approximately 45 ft

above the fork DBH varied from 38-242 in with a mean of 93 in for the data set of 568 trees

Stemwood

The prediction data set included 528 trees distributed by state forest and species as described

above This yielded 1488 829 398 410 178 131 66 and 6 bark factor measurements for SM

RM BW W A BC AB YB and AE respectively There were a total of 3506 bark factor

measurements for the 568 trees

The mean minimum and maximum DBH in in and merchantable height (MH) in ft for the

trees of each species are shown below MH is the height of the tree from the ground to an

approximate 36-in merchantable diameter top limit

No of DBH MH Species Trees x Min-Max x Min -Max

SM 248 92 38-242 3438 858-6367 RM 138 79 85-179 3395 850-5875 BW 61 118 46-218 4192 867-7225 WA 59 89 43-207 4171 867-8200 BC 27 99 70-161 3867 1708-5883 AB 23 116 51-189 3445 875-5042 YB 11 124 90-183 3488 1833-4392 AE 1 120 3608

The following table shows the mean minimum and maximum BF tree height to

measurement in ft (TH) and DOB at TH for the set of bark factor measurements for each species

NUMBER - 1-99

FORESTRY INFORMATION LEAFLET FOREST MANAGEMENT DIVISION

MICHIGAN DEPARTMENT OF NATURAL RESOURCES

SUBJECT - BARK FACTORS

DATE 31 October 99

TITLE BARK FACTOR EQUATIONS FOR NORTHERN HARDWOODS IN MICHIGAN

AUTHORS- Gary W Fowler Professor of Biometrics School of Natural Resources and Environment University of Michigan Nemah G Hussain Timber Sales Program Leader Forest Management Division Michigan Department of Natural Resources and David j Cohen and Deepak Khatry-Chhetri bull PhD graduate students School of Natural Resources and Environment University of Michigan

BACKGROUND

Bark factor (BF) is the ratio of diameter inside bark (Dill) to diameter outside bark (DOB) at a

given tree height Even though bark factor does increase with height for many species a constant

bark factor usually determin~d at breast height has been assumed in many cases for all tree

heights for many species Thus the use of a constant bark factor for all tree heights will usually

lead to underestimates of most tree and log solid wood volumes and overestimates of bark volume

for many species

Bark factor equations have been developed for aspen (Fowler and Hussain 1987b Fowler

1991) jack pine (Fowler and Hussain 1991 Fowler 1993) and red pine (Fowler and Hussain 1987a

Fowler and Damschroder 1988) in Michigan where hark factor was regressed on tree height (TH)

In all cases there was a very strong relationship hetween BF and TH Bark factor equations were

also developed for oaks (Fowler et al 1997) and paper birch (Fowler and Hussain 1997) in

Michigan where BF was regressed on TH and DOB These relationships were relatively weak with

the relationship to DOB being somewhat stronger

middotCurrent position Research Associate Carnegie Department of Plant Biology Stanford University

bark factor hardwoodsnorthern hardwoods -1shy

-2shy

PURPOSE

The purpose of this paper is to present bark factor equations for northern hardwood tree

species in Michigan and show how the prediction equations may be used

METHODS AND MATERIALS

As part of a larger study to develop new volume equations for hardwoods in Michigan felled

tree measurements were made on a total of 568 notthern hardwood trees from 15 hardwood stands

in Michigan (1) 369 trees from 9 stands in the Upper Peninsula (1 5 and 3 stands from the Copper

Country Escanaba River and Superior state forests respectively) and (2) 199 trees from 6 stands in

the Lower Peninsula (4 and 2 stands from the Mackinaw and Pere Marquette state forests

respectively) The numbers of trees measured hy species are shown below

No of Trees Measured Species

UP LP Michigan

Sugar Maple (SM) Red Maple (RM) Basswood (BW) White Ash (WA) Black Cherry (BC) American Beech (AB) Yellow Birch (YB) American elm (AE)

161

92 5-+ 38

7 6

II 0

87 46

7 21 20 17 0

248 138 61 59 27 23 11

All trees were measured during May-August 1995

Dffi and DOB were measured to the nearest 00 I in at stump height which varied from 2-40

in except for one unusual tree that had a stump hctght of 95 in the top of each 83-ft bolt (100-in

stick) or other nominal bolt length varying fr(lrn 6-16 ft cut out of the stem of each tree to an

approximate 36-in diameter top limit (ie ~tcrnwoot) and at the bottom and top of each 83-ft

bolt or other nominal bolt length varying from 7-16 ft cut out of limbs and top forks of each tree to

an approximate 36-in diameter top limit (ie topwood) DBH was measured to the nearest 01 in

-3shy

and bark thickness at DBH height was measured to the nearest 001 inch DBH height was 45 ft

from the ground except for trees forked below 45 ft where DBH height was approximately 45 ft

above the fork DBH varied from 38-242 in with a mean of 93 in for the data set of 568 trees

Stemwood

The prediction data set included 528 trees distributed by state forest and species as described

above This yielded 1488 829 398 410 178 131 66 and 6 bark factor measurements for SM

RM BW W A BC AB YB and AE respectively There were a total of 3506 bark factor

measurements for the 568 trees

The mean minimum and maximum DBH in in and merchantable height (MH) in ft for the

trees of each species are shown below MH is the height of the tree from the ground to an

approximate 36-in merchantable diameter top limit

No of DBH MH Species Trees x Min-Max x Min -Max

SM 248 92 38-242 3438 858-6367 RM 138 79 85-179 3395 850-5875 BW 61 118 46-218 4192 867-7225 WA 59 89 43-207 4171 867-8200 BC 27 99 70-161 3867 1708-5883 AB 23 116 51-189 3445 875-5042 YB 11 124 90-183 3488 1833-4392 AE 1 120 3608

The following table shows the mean minimum and maximum BF tree height to

measurement in ft (TH) and DOB at TH for the set of bark factor measurements for each species

-2shy

PURPOSE

The purpose of this paper is to present bark factor equations for northern hardwood tree

species in Michigan and show how the prediction equations may be used

METHODS AND MATERIALS

As part of a larger study to develop new volume equations for hardwoods in Michigan felled

tree measurements were made on a total of 568 notthern hardwood trees from 15 hardwood stands

in Michigan (1) 369 trees from 9 stands in the Upper Peninsula (1 5 and 3 stands from the Copper

Country Escanaba River and Superior state forests respectively) and (2) 199 trees from 6 stands in

the Lower Peninsula (4 and 2 stands from the Mackinaw and Pere Marquette state forests

respectively) The numbers of trees measured hy species are shown below

No of Trees Measured Species

UP LP Michigan

Sugar Maple (SM) Red Maple (RM) Basswood (BW) White Ash (WA) Black Cherry (BC) American Beech (AB) Yellow Birch (YB) American elm (AE)

161

92 5-+ 38

7 6

II 0

87 46

7 21 20 17 0

248 138 61 59 27 23 11

All trees were measured during May-August 1995

Dffi and DOB were measured to the nearest 00 I in at stump height which varied from 2-40

in except for one unusual tree that had a stump hctght of 95 in the top of each 83-ft bolt (100-in

stick) or other nominal bolt length varying fr(lrn 6-16 ft cut out of the stem of each tree to an

approximate 36-in diameter top limit (ie ~tcrnwoot) and at the bottom and top of each 83-ft

bolt or other nominal bolt length varying from 7-16 ft cut out of limbs and top forks of each tree to

an approximate 36-in diameter top limit (ie topwood) DBH was measured to the nearest 01 in

-3shy

and bark thickness at DBH height was measured to the nearest 001 inch DBH height was 45 ft

from the ground except for trees forked below 45 ft where DBH height was approximately 45 ft

above the fork DBH varied from 38-242 in with a mean of 93 in for the data set of 568 trees

Stemwood

The prediction data set included 528 trees distributed by state forest and species as described

above This yielded 1488 829 398 410 178 131 66 and 6 bark factor measurements for SM

RM BW W A BC AB YB and AE respectively There were a total of 3506 bark factor

measurements for the 568 trees

The mean minimum and maximum DBH in in and merchantable height (MH) in ft for the

trees of each species are shown below MH is the height of the tree from the ground to an

approximate 36-in merchantable diameter top limit

No of DBH MH Species Trees x Min-Max x Min -Max

SM 248 92 38-242 3438 858-6367 RM 138 79 85-179 3395 850-5875 BW 61 118 46-218 4192 867-7225 WA 59 89 43-207 4171 867-8200 BC 27 99 70-161 3867 1708-5883 AB 23 116 51-189 3445 875-5042 YB 11 124 90-183 3488 1833-4392 AE 1 120 3608

The following table shows the mean minimum and maximum BF tree height to

measurement in ft (TH) and DOB at TH for the set of bark factor measurements for each species

-3shy

and bark thickness at DBH height was measured to the nearest 001 inch DBH height was 45 ft

from the ground except for trees forked below 45 ft where DBH height was approximately 45 ft

above the fork DBH varied from 38-242 in with a mean of 93 in for the data set of 568 trees

Stemwood

The prediction data set included 528 trees distributed by state forest and species as described

above This yielded 1488 829 398 410 178 131 66 and 6 bark factor measurements for SM

RM BW W A BC AB YB and AE respectively There were a total of 3506 bark factor

measurements for the 568 trees

The mean minimum and maximum DBH in in and merchantable height (MH) in ft for the

trees of each species are shown below MH is the height of the tree from the ground to an

approximate 36-in merchantable diameter top limit

No of DBH MH Species Trees x Min-Max x Min -Max

SM 248 92 38-242 3438 858-6367 RM 138 79 85-179 3395 850-5875 BW 61 118 46-218 4192 867-7225 WA 59 89 43-207 4171 867-8200 BC 27 99 70-161 3867 1708-5883 AB 23 116 51-189 3445 875-5042 YB 11 124 90-183 3488 1833-4392 AE 1 120 3608

The following table shows the mean minimum and maximum BF tree height to

measurement in ft (TH) and DOB at TH for the set of bark factor measurements for each species

-4shy

No ofBF BF TH DOB atTH Species Measurements X Min-Max X Min-Max X Min -Max

SM 1488 0976 0890-0997 1718 025-6367 834 259-2550 RM 829 0980 0876-0998 1711 017-5875 693 277-1968 BW 398 0970 0917-0999 2114 025-7225 1040 351-2342 WA 410 0932 0844-0994 2115 017-8200 792 306-2511 BC 178 0965 0927-0994 1837 033-5883 811 315-1903 AB 131 0995 0960-0999 1684 017-5042 1077 320-2276 YB 66 0991 0979-0998 1660 050-4392 1033 350-2005 AE 6 0964 0956-0977 1658 067-3608 1133 874-1521

Top wood

The prediction data set included the following numbers of trees with topwood and associated

bark factor measurements by species

Species

SM RM BW WA BC AB YB AE

Total

No of Trees

61 18 8

13 9 5 7 0

121

No of Measurements

342 74 38 75 32 44 26 0

631

The mean minimum and maximum DBH in in MH in ft and number of topwood sticks for

the trees of each species are shown below

No of DBH MH No of To2wood Sticks Species Trees x Min-Max x Min-Max x Min-Max

SM 61 135 68-242 3579 925-6367 37 1-13 RM 18 117 75-179 3669 933-5058 27 1-12 BW 8 153 107-187 4240 2567-5192 30 1-7 WA 13 128 61-207 4708 1742-8200 37 1-12625 BC 9 122 101-161 3897 1708-5883 23 1-4 AB 5 166 132-189 2518 1792-3433 62 3-1025 YB 7 138 94-183 3518 1833-4392 21 1-4 AE 0 -shy

-5shy

The following table shows the mean minimum and maximum BF and DOB at the BF

measurement point for the set of bark factor measurements for each species

No ofBF BF DOBSpecies Measurements X Min-Max X Min -Max

SM 342 0977 0 913-0998 671 290-1706 RM 74 0981 0907-0997 566 258-1324 BW 38 0962 0945-0991 777 376-1113 WA 75 0935 0886-0990 627 336-1318 BC 32 0974 0951-0991 631 340-1116 AB 44 0994 0984-0999 796 398-1326 YB 26 0989 0979-0994 621 344-1034 AE 0

RESULTS

The best prediction equations based on simplicity meeting the assumptions of normality and

homogeneity and having among the smallest standard errors of the estimate ( sybullx) and the largest

coefficients of determination ( R 2 ) were

Stem wood Red Maple (n=829)

p

1

(1) BF=0996730-0002397bullDOB 0164 0014339 lt0001

1

(2) BF = 0972344 + 0003554 bullIn TH 0106 0014828 lt0001

1

(3) BF = 0989060-0001923bull DOB+0002002 bullIn TH 0191 0014112 lt0001

White Ash (n=410)

1

(4) BF=0922166+0001198bullDOB 0032 0023334 lt000 1

1

(5) BF = 0937036 + 0000805 bull TH- 0009279 bull In TH 0121 0022265 lt000 1

II

(6) BF = 0922785 + 0001429 bull DOB+0000838 bull TH 0161 0021780 lt0001

- 0008356 bull In TH

-6shy

Sugar Maple (n=l488)

R2 sybullx p

A

(7) BF =0988318-0001497 bull DOB 0165 0013699 lt0001 A

(8) BF =0970865 + 0002264 bullIn TH 0046 0014645 lt0001

A

(9) BF =0985763-0001396 bull DOB+0000779 bullIn TH 0170 0013665 lt0001

Basswood (n=398)

A

(10) BF =0974486-0000403bull DOB 0016 0013026 0012 A

(11) BF =0970312 + 0000072 bull TH- 0000631bull In TH 0008 0013097 0214

A

(12) BF =0975340-0000409 bull DOB+0000052 bull TH 0018 0013048 0070

- 0000770 bull In TH

Black Cherry (n=178)

A

(13) BF =0971912 -0000841bull DOB 0027 0014924 0029 A

(14) BF =0954777 + 0004557 bullIn TH 0197 0013561 lt0001

A

(15) BF =0942909 + 0001075 bull DOB+0005950 bull In TH 0222 0013381 lt0001

Yellow Birch (n=66)

A

(16) BF =0987390 + 0000307 bull DOB 0106 0003544 0008

A

(17) BF =0990354- 0000111bull TH + 0000885 bull In TH 0036 0003710 0317

A

(18) BF =0984658 + 0000400 bull DOB- 0000060 bull TH 0143 0003527 0022

+ 0001192 bullIn TH

American Beech (n=131)

(19) BF =1027382- 0103065DOB- 00090 12 bull In DOB 0159 0004220 lt0001

A (20) BF =0994075-0000047 bullTH + 000089( bullIn TH 0034 0004524 0111

A (21) BF =1020317- 0097775DOB- Ootl7 l77 bull In DOB 0240 0004043 lt0001

+ 0000014 bull TH+0000841bull1n TH

-7shy

American Elm (n=6)

R2 sybullx p

(22) II

BF = 0925851 + 0003400 bull DOB 0908 0002658 0003

(23) II

BF = 0975815 -0000058bull TH -0004696bullln TH 0968 0001801 0006

(24) II

BF = 0987215-0000786 bull DOB- 0000073 bull TH 0970 0002132 0044

- 0005707 bull In TH

Prediction Equations 1 4 7 10 13 16 19 and 22 for RM WA SM BW BC YB AB and AE

respectively yield the following estimated bark factors

PredictionoEquations l -+ 7 10 13 16 19 and 22

II

DOB BF (in) RM WA SM BW BC YB AB AE

30 0990 0926 0984 0973 0969 0988 0983 0936 40 0987 0927 0982 0973 0969 0989 0989 0939 50 0985 0928 0981 0972 0968 0989 0992 0943 60 0982 0929 0979 0972 0967 0989 0994 0946 70 0980 0931 0978 0972 0966 0990 0995 0950 80 0978 0932 0976 0971 0965 0990 0996 0953 90 0975 0933 0975 0971 0964 0990 0996 0956

100 0973 0934 0973 0970 0964 0990 0996 0960 110 0970 0935 0972 0970 0963 0991 0996 0963 120 0968 0937 0970 0970 0962 0991 0996 0967 130 0966 0938 0969 0969 0961 0991 0996 0970 140 0963 0939 0967 0968 0960 0992 0996 0973 150 0961 0940 0966 0968 0959 0992 0996 0977 160 0958 0941 0964 0968 0958 0992 0996 0980 170 0956 0943 0963 0968 0958 0993 0996 0984 180 0954 0944 0961 0967 0956 0993 0996 0987 190 0951 0945 0960 0967 0956 0993 0995 0990 200 0949 0946 0958 0966 0955 0994 0995 0994 210 0946 0947 0957 OlJ(J6 0954 0994 0995 220 0944 0949 0955 () lt)(l(J 0953 0994 0995 230 0942 0950 0954 () l)(J) 0953 0994 0995 240 0939 0951 0952 ( )l)(J) 0952 0995 0994 250 0937 0952 0951 ())J~ 0951 0995 0994

-8shy

Prediction Equations 2 5 8 11 14 17 20 and 23 for RM WA SM BW BC YB AB and AE

respectively yield the following estimated bark factors

Prediction Equations 2 5 8 11 14 17 20 and 23

TH BF (ft) RM WA SM BW BC YB AB AE

025 0970 0950 0971 0971 0948 0989 0993 0982 05 0971 0944 0971 0971 0952 0990 0993 0979 10 0973 0939 0972 0970 0955 0990 0994 0976 20 0974 0932 0972 0970 0958 0991 0995 0972 30 0975 0929 0972 0970 0960 0991 0995 0970 45 0977 0927 0973 0970 0962 0991 0995 0968 85 0979 0924 0974 0970 0965 0991 0996 0965

170 0981 0924 0976 0970 0968 0991 0996 0962 255 0984 0928 0978 0970 0970 0990 0996 0959 340 0986 0932 0980 0971 0971 0990 0996 0957 425 0988 0936 0982 0971 0972 0989 0995 0956 510 0989 0942 0984 0972 0973 0988 0995 0954 595 0991 0947 0986 0972 0973 0987 0995 0953 680 0993 0953 0988 0973 0974 0987 0995 0952 765 0995 0958 0990 0973 0975 0986 0994 0951

The ranges of predicted BF values for DOB from 30 to 250 in based on Equations 1 4 7 10 13

16 19 and 22 are 0053 0026 0033 0009 0018 0007 0011 and 0058 for RM WA SM

BW BC YB AB and AE respectively Note that no bark factors are given for DQB210 in for

AE because the estimated values are greater than one This is due to the small sample size (ie one

tree with 6 measurements) and the largest DOB being no larger than 1521 inches The ranges of

predicted BF values forTH from 025 to 765 ft based on Equations 2 5 8 11 14 17 20 and 23

are 0025 0034 0019 0003 0027 0005 0003 and 0031 for RM WA SM BW BC YB AB

and AE respectively Because of these moderate to small ranges the low R 2 values of the

prediction equations and some of the prediction equations not being significant at a= 005 you

might argue that the mean bark factor yields an adequate prediction model for each species

-9shy

- 829 (25) RM BF = BF =I BFJ829 =0980 0015671

i=l

- 410 26) WA BF = BF = I BFJ410 = 0932 0023692

i=l

1488 (27) SM BF = BF = L Bfi1488 = 0976 0014991

i=1

398 (28) BW BF = BF = L Bfi 398 = 0970 0013115

i=1

178 (29) BC BF = BF = L Bfi179 = 0965 0015086

i=1

66 (30) YB BF = BF = L BFi66 = 0991 0003720

i=1

131 (31) AB BF = BF = L Bfi131 = 0995 0004566

i=1

6 (32) AE BF = BF =L BFJ6 =0964 0007831

i=1

See the above two tables to find where Equations 25-32 over- and underestimate related to

Equations 1-24-57-8 lO-ll 13-14 16-17 19-20 and 22-23 respectively

Prediction Equations 1 4 7 10 13 16 and 22 are significantly different (Bartletts x 2 -test

for equal variances Plt0005 F-test for equal slopes Plt0001) Prediction Equations 2 8 and 14

are significantly different (Bartletts i-test for equal variances Plt010 F-test for equal slopes

PltOOO 1) Prediction Equations 5 11 17 20 and 23 are significantly different (Bartletts i -test

for equal variances Plt0005 F-test for equal slopes Plt0001) Prediction Equations 27-32 related

to mean bark factors are also significantly different (Bartletts x 2 -test for equal variances Plt0005

F-test for equal means Plt0001) All Bonferroni pairwise comparisons of means are significantly

-10shy

different (Plt0003) except for (RM AE) (SM AE) (BW AE) (BC AE) and (YB AB) Note that

the sample size for AE is only 6

Topwood R2 psybullx n

1

(33) RM BF = 1006791 - 0004569 bull DOB 0245 0016815 lt0001 74 1

(34) WA BF = 0936727 - 0000206 bull DOB 0000 0023230 0866 75 1

(35) SM BF = 0995302-0002757 bull DOB 0201 0013598 lt0001 342 1

(36) BW BF = 0979121-0002155bull DOB 0135 0010484 0023 38 1

(37) BC BF = 0977830-0000604 bull DOB 0017 0009709 0478 32

1

(38) YB BF = 0987032 + 0000281 bull DOB 0012 0004606 0593 26 1

(39) AB BF = 1038966-0131661DOB 0463 0002353 lt0001 44

-0012832bulllnDOB

Prediction Equations 33-39 for RM W A SM BW BC YB and AB respectively yield the

following estimated bark factors

Prediction Equations 33-39

DOB 1

BF (in) RM WA SM BW BC YB AB

30 0993 0936 0987 0973 0976 0988 0981 40 0989 0936 0984 0971 0975 0988 0988 50 0984 0936 0982 0968 0975 0988 0992 60 0979 0935 0979 0966 0974 0989 0994 70 0975 0935 0976 0964 0974 0989 0995 80 0970 0935 0973 0962 0973 0989 0996 90 0966 0935 0970 0960 0972 0990 0996

100 0961 0935 0968 0958 0972 0990 0996 110 0957 0934 0965 0955 0971 0990 0996 120 0952 0934 0962 0953 0971 0990 0996 130 0947 0934 0959 0951 0970 0991 0996 140 0943 0934 0957 0949 0969 0991 OQ96 150 0938 0934 0954 0947 0969 0991 0995 160 0934 0933 0951 0945 0968 0992 0995 170 0929 0933 0948 0942 0968 0992 0995 180 0924 0933 0946 0940 0967 0992 0995 190 0920 0933 0943 0938 0966 0992 0994 200 0915 0933 0940 0936 0966 0993 0994

-11shy

The ranges of predicted BF values for DOB from 30 to 200 in are 0078 0003 0047 0037

0010 0005 and 0015 for RM WA SM BW BC YB and AB respectively Because of these

moderate to small ranges the low R 2 values of the prediction equations the moderate sample sizes

and some of the prediction equations not being significant at a=005 you might argue that the mean

bark factor yields an adequate prediction model (except possibly for RM)

74 (40) RM BF = BF =I BFi74 = 0981 0019213

i=l 75

(41) WA BF = BF =I B~75 = 0935 0023077 i=l 342

(42) SM BF = BF = I B~ 342 = 0977 0015190 i=l 38

(43) BW BF = BF =I BFi38 =0962 0011118 i=l

32 (44) BC BF = BF =I BFi32 = 0974 0009633

i=l

26 (45) YB BF = BF =I Bfi 26 = 0989 0004540

i=l

44 (46) AB BF=BF= I BFi44=0995 0003135

i=l

See the above table to find where Equations 40-46 over- and underestimate reflected to Equations

33-39 respectively

Prediction Equations 33-38 are significant y different (Bartletts 12 -test for equal variances

Plt0005 F-test for equal slopes P=OOOl) Prediction Equations 40-46 related to mean bark factors

are also significantly different (Bartletts -test for equal variances Plt0005 F-test for equal

-12shy

means PltOOOl) All Bonferroni pairwise comparisons of means are significantly different

(Plt005) except for (RM SM) (RM BC) (RM YB) (SM BC) and (YB AB)

Pooled prediction equations

The stemwood and topwood BF prediction equations with DOB as the independent variable

were compared for each of the species except for AB where the independent variables were 1DOB

and ln DOB The resulting P-values are as follows

Bartletts z2 -test F-test for Equal Species for Equal Variances Regression Coefficients

RM P=005+ P=OOOl WA P=01 P=0267 SM P=0862 PltOOOl BW P=OOlJ-+ P=0120 BC P=0005 P=0854 YB P=0106 P=0954 AB PltOOOI P=0942

Bonferroni level of significance a=OOS7=0007

The above results indicate that the two equations for WA BW BC YB and AB can be pooled

while some prediction accuracy will be lost if the two equations for RM and SM are pooled (See the

two equations shown for each species earlier in this paper) Note that there is no lopwood for the

one AE tree in the data set Therefore the pooled equation is the stemwood equation for AE

The pooled prediction equations are

R2 sybullx p n

A

(47) RM BF =0997087 -0002476bull DOB 0166 0014604 lt0001 903

A

(48) WA BF =0924553 + 0001003 bull DOB 0021 0023385 0001 485

A

(49) SM BF =0988615-0001568 bull DOB (Jl64 0013748 lt0001 1830

A

(50) BW BF =0972865-0000320 bull DOB 00 lO 0013085 0040 436

A

(51) BC BF =0974512 -0001028bull DOB 0041 0014455 0003 210

A

(52) YB BF =0986997 + 0000334 bull DOB 0107 0003825 0001 92

-13shy

R2 sybullx p n

1

(53) AB BF =1028314- 0105996DOB 0201 0003819 lt0001 175

- 0009288 bull In DOB

Prediction equations 47-53 for RM WA SM BW BC YB and AB respectively yield the

following estimated bark factors

Prediction Equations 47-53

1

DOB BF (in) RM WA SM BW BC YB AB

30 0990 0928 0984 0972 0971 0988 0983 40 0987 0929 0982 0972 0970 0988 0989 50 0985 0930 0981 0971 0969 0989 0992 60 0982 0931 0979 0971 0968 0989 0994 70 0980 0932 0978 0971 0967 0989 0995 80 0977 0933 0976 0970 0966 0989 0996 90 0975 0934 0975 0970 0965 0990 0996

100 0972 0935 0973 0969 0964 0990 0996 110 0970 0936 0971 0969 0963 0991 0996 120 0967 0937 0970 0969 0962 0991 0996 130 0965 0938 0968 0968 0961 0991 0996 140 0962 0939 0967 0968 0960 0992 0996 150 0960 0940 0965 0968 0959 0992 0996 160 0957 0941 0964 0968 0958 0992 0996 170 0955 0942 0962 0967 0957 0993 0996 180 0953 0943 0960 0967 0956 0993 0996 190 0950 0944 0959 0967 0955 0993 0995 200 0948 0945 0957 0966 0954 0994 0995 210 0945 0946 0956 0966 0953 0994 0995 220 0943 0947 0954 0966 0952 0994 0995 230 0940 0948 0953 0966 0951 0995 0995 240 0938 0949 0951 0965 0950 0995 0994 250 0935 0950 0949 0965 0949 0995 0994

Note that the pooled BF estimates for each species are close to those of Equations 1 4 7 10

13 16 and 19 for stemwood This makes sense since the stemwood sample sizes were considerably

larger than the topwood sample sizes for each species For topwood the pooled BF estimates for

YB and AB are very close to Equations 38 and 39 respectively for topwood However there are

some larger differences for the other species over the range of DOB from 30-200 inches

-14shy

bull RM - Pooled BF estimates are lower than those of Equation 33 for DOB lt 50 in and higher for DOB ~ 50 in (from 0003 lower to 0033 higher)

bull WA - Pooled BF estimates are lower than those of Equation 34 for DOB lt 100 in and higher for DOB gt 100 in (from 0008 lower to 0012 higher)

bull SM - Pooled BF estimates are lower than those of Equation 35 for DOB lt 60 in and higher for DOB gt 60 in (from 0003 lower to 0017 higher)

bull BW - Pooled BF estimates are lower than those of Equation 36 for DOB lt 40 in and higher for DOB ~ 40 in (from 0001 lower to 0030 higher)

bull BC - Pooled BF estimates are lower than those of Equation 37 for all values of DOB (from 0005 to 0012lower)

The ranges of the pooled predicted BF values for DOB from 30 to 250 in are 0055 0022 0035

0007 0022 0007 and 0013 for RM WA SM BW BC YB and AB respectively Because of

these moderate to small ranges the low R2 values of the prediction equations and some of the

prediction equations not being significant you might argue that the mean bark factor yields an

adequate prediction model

The stemwood and topwood mean BFs were compared for each of the species The resulting

P-values are as follows

Species Bartletts zLtest

for Equal Variances F-test for Equal

Regression Coefficients

RM 0013 0681 WA 0770 0202 SM 0775 0287 BW 0196 0004 BC 0004 0001 YB 0222 0055 AB 0005 0542

Bonferroni level of significance a PC =00057 =0007

The above results indicate that the two means for RM W A SM YB and AB can be pooled while

some prediction accuracy will be lost if the two means for BW and BC are pooled (See the two

means shown for each species earlier in the paper) Note that there is no topwood for the one AE

tree in the data set Therefore the pooled mean is the stemwood mean for AE

-15shy

The pooled mean bark factors are

903 (54) RM middot BF = BF = L Bfl 903 = 0980 0015980

i=1

485 (55) WA BF = BF = L Bfl485 = 0932 0023614

i=1

1830 (56) SM BF= BF= L Bfl1830 = 0976 0015029

i=1

436 (57) BW BF = BF = L Bfl436 = 0970 0013134

i=l

210 (58) BC BF = BF = L Bfl210 = 0966 0014725

i=l

92 (59) YB BF = BF = L BFi92 = 0990 0004025

i=l

175 (60) AB BF = BF = L BF)l75 = 0995 0004248

i=1

See the table based on Equations 47-53 to see where Equations 54-60 under- and overestimate

respectively

Bark thickness

For the stemwood data set (n=3506) BT was significantly different for the eight different

species (Bartletts x2 -test for equal variances PltOOOl F-test for equal means PltOOOl) All

Bonferroni pairwise comparisons of means are significantly different except for (RM YB) (RM

AE) (WA AE) (SM AE) (BW AE) (BC AE) (YB AB) and (BW BC) Note that the sample

size for AE is only 6

Average minimum and maximum BTs and Pearsons correlations of BT with DOB DBH

and TH are shown below for the eight species

-16shy

BT BTDOB BTDBH BTTHSpecies nx Min-Max r p r p r p

RM 0077 0005-0525 0678 lt0001 0484 lt0001 -0369 lt0001 829 WA 0263 0012-1760 0632 lt0001 0428 lt0001 -0329 lt0001 410 SM 0113 0008-0672 0794 lt0001 0685 lt0001 -0293 lt0001 1488 BW 0158 0005-0525 0738 lt0001 0633 lt0001 -0192 lt0001 398 BC 0145 0012-0438 0653 lt0001 0169 0024 -0683 lt0001 178 YB 0046 0020-0115 0448 lt0001 0234 0058 -0383 0002 66 AB 0024 0005-0395 0236 0007 0067 0448 -0229 0009 131 AE 0195 0170-0228 -0511 0300 0405 0425 6

AE data consists of six measurements from one tree

BT was significantly positively related to DOB for all species except for AE where there was a

negative relation that was not significant BT was significantly positively related to DBH for all

species except for YB and AB where the positive relations were not significant BT was

significantly negatively related to TH for all species except for AE where there was a positive

relationship that was not significant

Average BTs for various DOB and TH classes for the eight species are as follows

DOB Class BT (in) RM WA SM BW BC YB AB AE

~400

401 to 800 801 to 1200 1201 to 1600

gt1600

0017 0054 0134 0239 0236

0091 0220 0321 0394 0468

0024 0060 0141 0225 0324

0032 0093 0150 0119 0268

0058 0101 0192 0252 0199

0020 0032 0048 0060 0058

0022 0019 0019 0020 0048

0200 0170

THClass BT (ft) RM WA SM BW BC YB AB AE

~050 0134 0208 0146 0114 0263 0038 0036 051 to 450 0110 0338 0161 0199 0192 0057 0038 0180 451 to 1000 0080 0296 0105 0165 0169 0047 0021 1001 to 2000 0065 0278 010(1 0153 0140 0049 0016 0210 2001 to 3000 0060 0250 0094 0146 0102 0041 0016 0200 3001 to 4000 0045 0220 0089 0134 0087 0037 0014 0190 4001 to 5000 0038 0220 0062 0153 0061 0025 0015

~5000 0016 0159 0047 0136 0038 0016

-17shy

In general BT is smallest for AB followed by YB RM SM BC BW and AE in increasing order

with BT for WA being the largest In general BT increases with DOB and decreases with TH

Most of the anomalies are due to small sample sizes

For the topwood data set (n=631) BT was significantly different for the seven different

species (Bartletts -test for equal variances PltOOOl F-test for equal means PltOOOl) All

Bonferroni pairwise comparisons of means are significantly different except for (RM SM) (RM

BC) (RM YB) (SM BC) (BC YB) and (YB AB)

Average minimum and maximum BTs and Pearsons correlations of BT with DOB and DBH

are shown below for the seven species

Species x

BT

Min- Max

BT DOB p r

BTDBH p n

RM WA SM BW BC YB AB

0064 0203 0086 0150 0083 0034 0019

0008-0385 0022-0458 0005-0362 0018-0262 0018-0175 Ool5-0075 0008-0038

06SO 0723 0768 0813 0723 0464 0051

lt0001 lt0001 lt0001 lt0001 lt0001

0017 0744

0549 0360 0440 0588 0380 0216 0661

lt0001 0002

lt0001 lt0001

0032 0290

lt0001

74 75

342 38 32 26 44

BT was significantly positively related to DOB for all species except for AB and to DBH for all

species except for YB

Average BTs for various DOB classes for the seven species are as follows

DOB Class BT (in) RM WA S~t BW BC YB AB

500 OQl8 0126 oltH) 0054 0051 0024 0021 501 to 700 0073 0212 () t)(J 0105 0086 0032 0019 701 to 900 0152 0281 () Ill 0170 0115 0057 0015 901 to 1100 0158 0255 () 177 0193 0114 0043 0020

111 to 1300 0122 0345 0222 0205 0135 0026

-18shy

In general BT is smallest for AB followed by YB BC RM SM and BW in increasing order

with BT for W A being the largest In general BT increases with DOB Most of the anomalies are

due to small sample sizes

Comparison with other BF equations

Fowler (1993) showed that while there were significant species differences between BF

equations for aspen jack pine and red pine there was a very strong relationship between BF and

tree height for each species (ie R 2 gt097 for each species) BF was a function of TH and In TH

showing that BF increased with TH to some maximum and then decreased for larger THs with the

steepness of the decrease depending on the species For all three species BF was not strongly

related to DBH or DOB at a given TH

For paper birch (Fowler and Hussain 1997) BF significantly increased with DOB at TH

(R2 =0219) and significantly decreased with In TH (R2 =0166) for stemwood while BF

significantly increased with DOB for topwood ( R 2 =0218) BF was much more variable than for

aspen red pine and jack pine

Fowler et al (1997) showed that black oak (BO) red oak (RO) and white oak (WO) have BPs

that are quite variable and prediction equations with the same independent variables as for paper

birch with the direction of the relations reversed For stemwood BF decreased with DOB at TH

( R 2 =0270 0418 and 0014 for BO RO and WO respectively) and increased with In TH ( R 2 =

0190 0275 and 0011 for BO RO and WO respectively) For topwood BF decreased with DOB

(R2=0366 0457 and 0100 for BO RO and WO respectively) These prediction equations were

significant but they were only moderately strong at best being only somewhat stronger in general

than the prediction equations for paper birch The prediction equations based on DOB were

-19shy

somewhat stronger than the prediction equations based on In TH The BF equations were

significantly different for the three species and for topwood versus stemwood except for RO

This study shows that the eight northern hardwood species have BFs that are quite variable

with some species having prediction equations with the same independent variables as for paper

birch and the three oak species while other species had different independent variables For

stemwood BF decreased with DOB at TH for RM SM BW and BC increased with In DOB at TH

for W A YB and AE and increased and then somewhat decreased with 1DOB and In DOB as the

independent variables for AB BF increased with In TH for RM SM and BC decreased and then

increased with TH and In TH for WA and BW increased and then decreased with TH and In TH for

YB AB and AE The prediction equations for AE are very suspect as they were based on only six

BF measurements from one tree For topwood BF decreased with DOB for RM WA SM BW

and BC increased with DOB for YB and increased and somewhat decreased with 1DOB and

In DOB for AB All prediction equations for stemwood were significant except for the TH

equations for BW and YB For topwood only the prediction equations for RM SM BW and AB

were significant In general all prediction equations were only moderately strong at best and some

of them were very weak The BF equations were significantly different for most species while the

stemwood and topwood BF equations were not significantly different except for RM and SM

GUIDELINES FOR USERS

We recommend use of the following equations for northern hardwoods when accurate

estimates of bark factors are desired

Stemwood

bull Red maple I

(1) BF =0996730-0002397 bull DOB I

(2) BF =0972344 + 0003554 bull In TH

-20shy

bull White ash 1

(3) BF = 0922166 +0001198bull DOB 1

(4) BF = 0937036 + 0000805 bull TH- 0009279 bullIn TH

bull- Sugar maple 1

(5) BF=0988318-0001497bullDOB 1

(6) BF = 0970865 + 0002264 bullIn TH

bull Basswood 1

(7) BF = 0974486-0000403 bull DOB 1

(8) BF = 0970312 + 0000072 bull TH- 0000631bullln TH

bull Black cherry 1

(9) BF = 0971912 -0000841bull DOB 1

(lO) BF = 0954777 + 0004557 bullIn TH

bull Yell ow birch 1

(11) BF = 0987390 + 0000307 bull DOB 1

(12) BF = 0990354-0000111bull TH+0000885bullln TH

bull American beech 1

(l3) BF = l027382-0l03065DOB -0009012bullln DOB

1

(14) BF = 0994075-0000047 bull TH+0000896 bullIn TH

bull American elm 1

(l5) BF =0925851 + 0003400 bull DOB 1

(16) BF = 0975815-0000058 bull TH- 0()()4696bullln TH

Use Equations 1 3 5 7 9 11 13 and 15 if DOBis measured Use Equations 2 4 6 8 10 12 14

and 16 when only THis measured

Topwood 1

(l7) RM BF = 1006791-0004569 bull DOB 1

(18) WA BF = 0936727 -0000206bull DOB 1

(l9) SM BF = 0995302-0002757 bull DOB

-21shy

(20) BW BF = 0979121-0002155 bull DOB

(21) BC BF = 0977830- 0000604 bull DOB

(22) YB BF = 0987032 + 0000281bull DOB

(23) AB BF = 1038966- 0131661DOB - 0012832 bullln DOB

The equation for stemwood and topwood pooled could be used if DOB is measured with moderate

loss in accuracy for RM and SM and little loss in accuracy for the other five species The pooled

equations in general will be more accurate for stemwood compared to topwood especially for RM

and SM

(24) RM BF == 0997087 -0002476bull DOB

1

(25) WA BF = 0924553 + 000 I 003 bull DOB

(26) SM BF=0988615-0001568bullDOB

(27) BW BF = 0972865-0000320 bull DOB

(28) BC BF=0974512-0001028bullDOB

(29) YB BF = 0986997 + 0000334 bull DOB

(30) AB BF = 1028314- 0105996DOB- 0009288 bullIn DOB

There is no pooled equation for AE as there was no topwood for the one AE tree in the data set

For reasonable accuracy in many situations the following constants could be used for bark

factors

DOB Class Stemwood BF (in) RM WA St-1 BW BC YB AB AE

DOBs50 0988 0927 09S~ 0973 0969 0989 0988 0939 50ltDOBsl00 0979 0931 0977 0971 0966 0990 0995 0951 l00ltDOBs150 0967 0937 0970 0969 0962 0991 0996 0968 150ltDOBs200 0955 0943 0962 0967 0957 0993 0996 0985

DOBgt200 0943 0949 0954 0965 0953 0994 0995 0994

-22shy

DOB Class ToEwoodBF (in) RM WA SM BW BC YB AB

DOBS50 0989 0936 0984 0971 0975 0988 0987 50ltD0BSl00 0970 0935 0973 0962 0973 0989 0995 100ltD0BS150 0947 0934 0959 0951 0970 0991 0996 150ltD0BS200 0924 0933 0946 0940 0967 0992 0995

008gt200 0902 0932 0932 0930 0964 0993 0993

TH Stemwood BF (ft) RM WA SM BW BC YB AB AE

THS05 0970 0947 0971 0971 0950 0990 0993 0980 05ltTHS45 0974 0932 olJn 0970 0959 0991 0995 0972

45ltTHS 100 0978 0925 0974 0970 0964 0991 0996 0966 100ltTHS200 0980 0924 0gt76 0970 0967 0991 0996 0963 200ltTHS300 0984 0928 0gt7S 0970 0970 0990 0996 0959 300ltTHS400 0986 0932 OltJSO 0971 0971 0990 0996 0957 400ltTHS500 0988 0937 () l)S~ 0971 0972 0989 0995 0955

THgt500 0992 0950 07 0974 0974 0987 0995 0952

The following constants for bark factor could be used for simplicity with moderately

approximate results especially for a large number of treessticks

Species Stem wood Top wood Stemwood and Topwood

RM 0980 0981 0980 WA 0932 0935 0932 SM 0976 0977 0976 BW 0970 0962 0970 BC 0965 0974 0966 YB 0991 0989 0990 AB 0995 0995 0995 AE 0964 0964

The above constants would be more accurate for those species that did not have significant

prediction equations andor small sample sizes B~ cry careful with using any of the results of this

study outside the range of the data set for each species Since the results for AE are based on six

stemwood measurements from one tree they arc of course very suspect

-23shy

Use of prediction equations

The prediction equations can be used to estimate BF at any DOB andor TH Since

BF=DIBDOB DIB can be estimated as DIB=BFbull DOB and DOB can be estimated as

DOB=DIBBF Past DOB and DOB growth can be estimated from past DIB growth as follows

Past DOB Growth=Past DIB GrowthBF

and

Past DOB=Present DOB -Past DOB Growth

where past DIB growth might be obtained with an increment borer

Specific uses of the prediction equations include (1) estimation of the solid wood and bark

volume of standing trees (2) estimation of bark volume or peeled volume from unpeeled volume

of felled tree sections (3) growth studies and (4) estimating tree form (eg Girard Form Class)

See Husch et al ( 1982) for a detailed discussion on bark factors

-24- LITERATURE CITED middot

Fowler G W 1991 An aspen bark factor equation for Michigan North J Appl For 8(1) 12-15

Fowler G W 1993 A jack pine bark factor equation for Michigan North J Appl For 10(2) 86-89

Fowler G W and L J Damschroder 1988 A red pine bark factor equation for Michigan North J Appl For 5(1) 28-30

Fowler G W and N G Hussain 1987a Bark factor equation for red pine Michigan DNR For Infor Leaflet 1-87 2 p

Fowler G W and N G Hussain 1987b Bark factor equation for aspen Michigan DNR For Infor Leaflet 2-87 2 p

Fowler G W and N G Hussain 1991 Bark factor equation for jack pine in Michigan Michigan DNR For Infor Leaflet 1-91 5 p

Fowler G W and N G Hussain 1997 Bark factor equations for paper birch in Michigan Michigan DNR For Infor Leaflet 1-97 12 p

Fowler G W N G Hussain D J Cohen and D Khatry-Chhetri 1997 Bark factor equations for oak in Michigan Michigan DNR For Infor Leaflet 2-97 15 p

Husch B C I Miller and T W Beers 1982 Forest Mensuration John Wiley and Sons Inc NY 402 p

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Ken Alto

Kim Dufresne

Tim Tennis

lonst Manbullpmeut DWisioa 15 Resource Mana1ement Units

bullJfectble l2519bull

bull -Resource Jf~nt Unit OJke

1 -Raource Jf~nt Unit BOUIIdariea

1 -CountyBouruiiJrfea

-6shy

Sugar Maple (n=l488)

R2 sybullx p

A

(7) BF =0988318-0001497 bull DOB 0165 0013699 lt0001 A

(8) BF =0970865 + 0002264 bullIn TH 0046 0014645 lt0001

A

(9) BF =0985763-0001396 bull DOB+0000779 bullIn TH 0170 0013665 lt0001

Basswood (n=398)

A

(10) BF =0974486-0000403bull DOB 0016 0013026 0012 A

(11) BF =0970312 + 0000072 bull TH- 0000631bull In TH 0008 0013097 0214

A

(12) BF =0975340-0000409 bull DOB+0000052 bull TH 0018 0013048 0070

- 0000770 bull In TH

Black Cherry (n=178)

A

(13) BF =0971912 -0000841bull DOB 0027 0014924 0029 A

(14) BF =0954777 + 0004557 bullIn TH 0197 0013561 lt0001

A

(15) BF =0942909 + 0001075 bull DOB+0005950 bull In TH 0222 0013381 lt0001

Yellow Birch (n=66)

A

(16) BF =0987390 + 0000307 bull DOB 0106 0003544 0008

A

(17) BF =0990354- 0000111bull TH + 0000885 bull In TH 0036 0003710 0317

A

(18) BF =0984658 + 0000400 bull DOB- 0000060 bull TH 0143 0003527 0022

+ 0001192 bullIn TH

American Beech (n=131)

(19) BF =1027382- 0103065DOB- 00090 12 bull In DOB 0159 0004220 lt0001

A (20) BF =0994075-0000047 bullTH + 000089( bullIn TH 0034 0004524 0111

A (21) BF =1020317- 0097775DOB- Ootl7 l77 bull In DOB 0240 0004043 lt0001

+ 0000014 bull TH+0000841bull1n TH

-7shy

American Elm (n=6)

R2 sybullx p

(22) II

BF = 0925851 + 0003400 bull DOB 0908 0002658 0003

(23) II

BF = 0975815 -0000058bull TH -0004696bullln TH 0968 0001801 0006

(24) II

BF = 0987215-0000786 bull DOB- 0000073 bull TH 0970 0002132 0044

- 0005707 bull In TH

Prediction Equations 1 4 7 10 13 16 19 and 22 for RM WA SM BW BC YB AB and AE

respectively yield the following estimated bark factors

PredictionoEquations l -+ 7 10 13 16 19 and 22

II

DOB BF (in) RM WA SM BW BC YB AB AE

30 0990 0926 0984 0973 0969 0988 0983 0936 40 0987 0927 0982 0973 0969 0989 0989 0939 50 0985 0928 0981 0972 0968 0989 0992 0943 60 0982 0929 0979 0972 0967 0989 0994 0946 70 0980 0931 0978 0972 0966 0990 0995 0950 80 0978 0932 0976 0971 0965 0990 0996 0953 90 0975 0933 0975 0971 0964 0990 0996 0956

100 0973 0934 0973 0970 0964 0990 0996 0960 110 0970 0935 0972 0970 0963 0991 0996 0963 120 0968 0937 0970 0970 0962 0991 0996 0967 130 0966 0938 0969 0969 0961 0991 0996 0970 140 0963 0939 0967 0968 0960 0992 0996 0973 150 0961 0940 0966 0968 0959 0992 0996 0977 160 0958 0941 0964 0968 0958 0992 0996 0980 170 0956 0943 0963 0968 0958 0993 0996 0984 180 0954 0944 0961 0967 0956 0993 0996 0987 190 0951 0945 0960 0967 0956 0993 0995 0990 200 0949 0946 0958 0966 0955 0994 0995 0994 210 0946 0947 0957 OlJ(J6 0954 0994 0995 220 0944 0949 0955 () lt)(l(J 0953 0994 0995 230 0942 0950 0954 () l)(J) 0953 0994 0995 240 0939 0951 0952 ( )l)(J) 0952 0995 0994 250 0937 0952 0951 ())J~ 0951 0995 0994

-8shy

Prediction Equations 2 5 8 11 14 17 20 and 23 for RM WA SM BW BC YB AB and AE

respectively yield the following estimated bark factors

Prediction Equations 2 5 8 11 14 17 20 and 23

TH BF (ft) RM WA SM BW BC YB AB AE

025 0970 0950 0971 0971 0948 0989 0993 0982 05 0971 0944 0971 0971 0952 0990 0993 0979 10 0973 0939 0972 0970 0955 0990 0994 0976 20 0974 0932 0972 0970 0958 0991 0995 0972 30 0975 0929 0972 0970 0960 0991 0995 0970 45 0977 0927 0973 0970 0962 0991 0995 0968 85 0979 0924 0974 0970 0965 0991 0996 0965

170 0981 0924 0976 0970 0968 0991 0996 0962 255 0984 0928 0978 0970 0970 0990 0996 0959 340 0986 0932 0980 0971 0971 0990 0996 0957 425 0988 0936 0982 0971 0972 0989 0995 0956 510 0989 0942 0984 0972 0973 0988 0995 0954 595 0991 0947 0986 0972 0973 0987 0995 0953 680 0993 0953 0988 0973 0974 0987 0995 0952 765 0995 0958 0990 0973 0975 0986 0994 0951

The ranges of predicted BF values for DOB from 30 to 250 in based on Equations 1 4 7 10 13

16 19 and 22 are 0053 0026 0033 0009 0018 0007 0011 and 0058 for RM WA SM

BW BC YB AB and AE respectively Note that no bark factors are given for DQB210 in for

AE because the estimated values are greater than one This is due to the small sample size (ie one

tree with 6 measurements) and the largest DOB being no larger than 1521 inches The ranges of

predicted BF values forTH from 025 to 765 ft based on Equations 2 5 8 11 14 17 20 and 23

are 0025 0034 0019 0003 0027 0005 0003 and 0031 for RM WA SM BW BC YB AB

and AE respectively Because of these moderate to small ranges the low R 2 values of the

prediction equations and some of the prediction equations not being significant at a= 005 you

might argue that the mean bark factor yields an adequate prediction model for each species

-9shy

- 829 (25) RM BF = BF =I BFJ829 =0980 0015671

i=l

- 410 26) WA BF = BF = I BFJ410 = 0932 0023692

i=l

1488 (27) SM BF = BF = L Bfi1488 = 0976 0014991

i=1

398 (28) BW BF = BF = L Bfi 398 = 0970 0013115

i=1

178 (29) BC BF = BF = L Bfi179 = 0965 0015086

i=1

66 (30) YB BF = BF = L BFi66 = 0991 0003720

i=1

131 (31) AB BF = BF = L Bfi131 = 0995 0004566

i=1

6 (32) AE BF = BF =L BFJ6 =0964 0007831

i=1

See the above two tables to find where Equations 25-32 over- and underestimate related to

Equations 1-24-57-8 lO-ll 13-14 16-17 19-20 and 22-23 respectively

Prediction Equations 1 4 7 10 13 16 and 22 are significantly different (Bartletts x 2 -test

for equal variances Plt0005 F-test for equal slopes Plt0001) Prediction Equations 2 8 and 14

are significantly different (Bartletts i-test for equal variances Plt010 F-test for equal slopes

PltOOO 1) Prediction Equations 5 11 17 20 and 23 are significantly different (Bartletts i -test

for equal variances Plt0005 F-test for equal slopes Plt0001) Prediction Equations 27-32 related

to mean bark factors are also significantly different (Bartletts x 2 -test for equal variances Plt0005

F-test for equal means Plt0001) All Bonferroni pairwise comparisons of means are significantly

-10shy

different (Plt0003) except for (RM AE) (SM AE) (BW AE) (BC AE) and (YB AB) Note that

the sample size for AE is only 6

Topwood R2 psybullx n

1

(33) RM BF = 1006791 - 0004569 bull DOB 0245 0016815 lt0001 74 1

(34) WA BF = 0936727 - 0000206 bull DOB 0000 0023230 0866 75 1

(35) SM BF = 0995302-0002757 bull DOB 0201 0013598 lt0001 342 1

(36) BW BF = 0979121-0002155bull DOB 0135 0010484 0023 38 1

(37) BC BF = 0977830-0000604 bull DOB 0017 0009709 0478 32

1

(38) YB BF = 0987032 + 0000281 bull DOB 0012 0004606 0593 26 1

(39) AB BF = 1038966-0131661DOB 0463 0002353 lt0001 44

-0012832bulllnDOB

Prediction Equations 33-39 for RM W A SM BW BC YB and AB respectively yield the

following estimated bark factors

Prediction Equations 33-39

DOB 1

BF (in) RM WA SM BW BC YB AB

30 0993 0936 0987 0973 0976 0988 0981 40 0989 0936 0984 0971 0975 0988 0988 50 0984 0936 0982 0968 0975 0988 0992 60 0979 0935 0979 0966 0974 0989 0994 70 0975 0935 0976 0964 0974 0989 0995 80 0970 0935 0973 0962 0973 0989 0996 90 0966 0935 0970 0960 0972 0990 0996

100 0961 0935 0968 0958 0972 0990 0996 110 0957 0934 0965 0955 0971 0990 0996 120 0952 0934 0962 0953 0971 0990 0996 130 0947 0934 0959 0951 0970 0991 0996 140 0943 0934 0957 0949 0969 0991 OQ96 150 0938 0934 0954 0947 0969 0991 0995 160 0934 0933 0951 0945 0968 0992 0995 170 0929 0933 0948 0942 0968 0992 0995 180 0924 0933 0946 0940 0967 0992 0995 190 0920 0933 0943 0938 0966 0992 0994 200 0915 0933 0940 0936 0966 0993 0994

-11shy

The ranges of predicted BF values for DOB from 30 to 200 in are 0078 0003 0047 0037

0010 0005 and 0015 for RM WA SM BW BC YB and AB respectively Because of these

moderate to small ranges the low R 2 values of the prediction equations the moderate sample sizes

and some of the prediction equations not being significant at a=005 you might argue that the mean

bark factor yields an adequate prediction model (except possibly for RM)

74 (40) RM BF = BF =I BFi74 = 0981 0019213

i=l 75

(41) WA BF = BF =I B~75 = 0935 0023077 i=l 342

(42) SM BF = BF = I B~ 342 = 0977 0015190 i=l 38

(43) BW BF = BF =I BFi38 =0962 0011118 i=l

32 (44) BC BF = BF =I BFi32 = 0974 0009633

i=l

26 (45) YB BF = BF =I Bfi 26 = 0989 0004540

i=l

44 (46) AB BF=BF= I BFi44=0995 0003135

i=l

See the above table to find where Equations 40-46 over- and underestimate reflected to Equations

33-39 respectively

Prediction Equations 33-38 are significant y different (Bartletts 12 -test for equal variances

Plt0005 F-test for equal slopes P=OOOl) Prediction Equations 40-46 related to mean bark factors

are also significantly different (Bartletts -test for equal variances Plt0005 F-test for equal

-12shy

means PltOOOl) All Bonferroni pairwise comparisons of means are significantly different

(Plt005) except for (RM SM) (RM BC) (RM YB) (SM BC) and (YB AB)

Pooled prediction equations

The stemwood and topwood BF prediction equations with DOB as the independent variable

were compared for each of the species except for AB where the independent variables were 1DOB

and ln DOB The resulting P-values are as follows

Bartletts z2 -test F-test for Equal Species for Equal Variances Regression Coefficients

RM P=005+ P=OOOl WA P=01 P=0267 SM P=0862 PltOOOl BW P=OOlJ-+ P=0120 BC P=0005 P=0854 YB P=0106 P=0954 AB PltOOOI P=0942

Bonferroni level of significance a=OOS7=0007

The above results indicate that the two equations for WA BW BC YB and AB can be pooled

while some prediction accuracy will be lost if the two equations for RM and SM are pooled (See the

two equations shown for each species earlier in this paper) Note that there is no lopwood for the

one AE tree in the data set Therefore the pooled equation is the stemwood equation for AE

The pooled prediction equations are

R2 sybullx p n

A

(47) RM BF =0997087 -0002476bull DOB 0166 0014604 lt0001 903

A

(48) WA BF =0924553 + 0001003 bull DOB 0021 0023385 0001 485

A

(49) SM BF =0988615-0001568 bull DOB (Jl64 0013748 lt0001 1830

A

(50) BW BF =0972865-0000320 bull DOB 00 lO 0013085 0040 436

A

(51) BC BF =0974512 -0001028bull DOB 0041 0014455 0003 210

A

(52) YB BF =0986997 + 0000334 bull DOB 0107 0003825 0001 92

-13shy

R2 sybullx p n

1

(53) AB BF =1028314- 0105996DOB 0201 0003819 lt0001 175

- 0009288 bull In DOB

Prediction equations 47-53 for RM WA SM BW BC YB and AB respectively yield the

following estimated bark factors

Prediction Equations 47-53

1

DOB BF (in) RM WA SM BW BC YB AB

30 0990 0928 0984 0972 0971 0988 0983 40 0987 0929 0982 0972 0970 0988 0989 50 0985 0930 0981 0971 0969 0989 0992 60 0982 0931 0979 0971 0968 0989 0994 70 0980 0932 0978 0971 0967 0989 0995 80 0977 0933 0976 0970 0966 0989 0996 90 0975 0934 0975 0970 0965 0990 0996

100 0972 0935 0973 0969 0964 0990 0996 110 0970 0936 0971 0969 0963 0991 0996 120 0967 0937 0970 0969 0962 0991 0996 130 0965 0938 0968 0968 0961 0991 0996 140 0962 0939 0967 0968 0960 0992 0996 150 0960 0940 0965 0968 0959 0992 0996 160 0957 0941 0964 0968 0958 0992 0996 170 0955 0942 0962 0967 0957 0993 0996 180 0953 0943 0960 0967 0956 0993 0996 190 0950 0944 0959 0967 0955 0993 0995 200 0948 0945 0957 0966 0954 0994 0995 210 0945 0946 0956 0966 0953 0994 0995 220 0943 0947 0954 0966 0952 0994 0995 230 0940 0948 0953 0966 0951 0995 0995 240 0938 0949 0951 0965 0950 0995 0994 250 0935 0950 0949 0965 0949 0995 0994

Note that the pooled BF estimates for each species are close to those of Equations 1 4 7 10

13 16 and 19 for stemwood This makes sense since the stemwood sample sizes were considerably

larger than the topwood sample sizes for each species For topwood the pooled BF estimates for

YB and AB are very close to Equations 38 and 39 respectively for topwood However there are

some larger differences for the other species over the range of DOB from 30-200 inches

-14shy

bull RM - Pooled BF estimates are lower than those of Equation 33 for DOB lt 50 in and higher for DOB ~ 50 in (from 0003 lower to 0033 higher)

bull WA - Pooled BF estimates are lower than those of Equation 34 for DOB lt 100 in and higher for DOB gt 100 in (from 0008 lower to 0012 higher)

bull SM - Pooled BF estimates are lower than those of Equation 35 for DOB lt 60 in and higher for DOB gt 60 in (from 0003 lower to 0017 higher)

bull BW - Pooled BF estimates are lower than those of Equation 36 for DOB lt 40 in and higher for DOB ~ 40 in (from 0001 lower to 0030 higher)

bull BC - Pooled BF estimates are lower than those of Equation 37 for all values of DOB (from 0005 to 0012lower)

The ranges of the pooled predicted BF values for DOB from 30 to 250 in are 0055 0022 0035

0007 0022 0007 and 0013 for RM WA SM BW BC YB and AB respectively Because of

these moderate to small ranges the low R2 values of the prediction equations and some of the

prediction equations not being significant you might argue that the mean bark factor yields an

adequate prediction model

The stemwood and topwood mean BFs were compared for each of the species The resulting

P-values are as follows

Species Bartletts zLtest

for Equal Variances F-test for Equal

Regression Coefficients

RM 0013 0681 WA 0770 0202 SM 0775 0287 BW 0196 0004 BC 0004 0001 YB 0222 0055 AB 0005 0542

Bonferroni level of significance a PC =00057 =0007

The above results indicate that the two means for RM W A SM YB and AB can be pooled while

some prediction accuracy will be lost if the two means for BW and BC are pooled (See the two

means shown for each species earlier in the paper) Note that there is no topwood for the one AE

tree in the data set Therefore the pooled mean is the stemwood mean for AE

-15shy

The pooled mean bark factors are

903 (54) RM middot BF = BF = L Bfl 903 = 0980 0015980

i=1

485 (55) WA BF = BF = L Bfl485 = 0932 0023614

i=1

1830 (56) SM BF= BF= L Bfl1830 = 0976 0015029

i=1

436 (57) BW BF = BF = L Bfl436 = 0970 0013134

i=l

210 (58) BC BF = BF = L Bfl210 = 0966 0014725

i=l

92 (59) YB BF = BF = L BFi92 = 0990 0004025

i=l

175 (60) AB BF = BF = L BF)l75 = 0995 0004248

i=1

See the table based on Equations 47-53 to see where Equations 54-60 under- and overestimate

respectively

Bark thickness

For the stemwood data set (n=3506) BT was significantly different for the eight different

species (Bartletts x2 -test for equal variances PltOOOl F-test for equal means PltOOOl) All

Bonferroni pairwise comparisons of means are significantly different except for (RM YB) (RM

AE) (WA AE) (SM AE) (BW AE) (BC AE) (YB AB) and (BW BC) Note that the sample

size for AE is only 6

Average minimum and maximum BTs and Pearsons correlations of BT with DOB DBH

and TH are shown below for the eight species

-16shy

BT BTDOB BTDBH BTTHSpecies nx Min-Max r p r p r p

RM 0077 0005-0525 0678 lt0001 0484 lt0001 -0369 lt0001 829 WA 0263 0012-1760 0632 lt0001 0428 lt0001 -0329 lt0001 410 SM 0113 0008-0672 0794 lt0001 0685 lt0001 -0293 lt0001 1488 BW 0158 0005-0525 0738 lt0001 0633 lt0001 -0192 lt0001 398 BC 0145 0012-0438 0653 lt0001 0169 0024 -0683 lt0001 178 YB 0046 0020-0115 0448 lt0001 0234 0058 -0383 0002 66 AB 0024 0005-0395 0236 0007 0067 0448 -0229 0009 131 AE 0195 0170-0228 -0511 0300 0405 0425 6

AE data consists of six measurements from one tree

BT was significantly positively related to DOB for all species except for AE where there was a

negative relation that was not significant BT was significantly positively related to DBH for all

species except for YB and AB where the positive relations were not significant BT was

significantly negatively related to TH for all species except for AE where there was a positive

relationship that was not significant

Average BTs for various DOB and TH classes for the eight species are as follows

DOB Class BT (in) RM WA SM BW BC YB AB AE

~400

401 to 800 801 to 1200 1201 to 1600

gt1600

0017 0054 0134 0239 0236

0091 0220 0321 0394 0468

0024 0060 0141 0225 0324

0032 0093 0150 0119 0268

0058 0101 0192 0252 0199

0020 0032 0048 0060 0058

0022 0019 0019 0020 0048

0200 0170

THClass BT (ft) RM WA SM BW BC YB AB AE

~050 0134 0208 0146 0114 0263 0038 0036 051 to 450 0110 0338 0161 0199 0192 0057 0038 0180 451 to 1000 0080 0296 0105 0165 0169 0047 0021 1001 to 2000 0065 0278 010(1 0153 0140 0049 0016 0210 2001 to 3000 0060 0250 0094 0146 0102 0041 0016 0200 3001 to 4000 0045 0220 0089 0134 0087 0037 0014 0190 4001 to 5000 0038 0220 0062 0153 0061 0025 0015

~5000 0016 0159 0047 0136 0038 0016

-17shy

In general BT is smallest for AB followed by YB RM SM BC BW and AE in increasing order

with BT for WA being the largest In general BT increases with DOB and decreases with TH

Most of the anomalies are due to small sample sizes

For the topwood data set (n=631) BT was significantly different for the seven different

species (Bartletts -test for equal variances PltOOOl F-test for equal means PltOOOl) All

Bonferroni pairwise comparisons of means are significantly different except for (RM SM) (RM

BC) (RM YB) (SM BC) (BC YB) and (YB AB)

Average minimum and maximum BTs and Pearsons correlations of BT with DOB and DBH

are shown below for the seven species

Species x

BT

Min- Max

BT DOB p r

BTDBH p n

RM WA SM BW BC YB AB

0064 0203 0086 0150 0083 0034 0019

0008-0385 0022-0458 0005-0362 0018-0262 0018-0175 Ool5-0075 0008-0038

06SO 0723 0768 0813 0723 0464 0051

lt0001 lt0001 lt0001 lt0001 lt0001

0017 0744

0549 0360 0440 0588 0380 0216 0661

lt0001 0002

lt0001 lt0001

0032 0290

lt0001

74 75

342 38 32 26 44

BT was significantly positively related to DOB for all species except for AB and to DBH for all

species except for YB

Average BTs for various DOB classes for the seven species are as follows

DOB Class BT (in) RM WA S~t BW BC YB AB

500 OQl8 0126 oltH) 0054 0051 0024 0021 501 to 700 0073 0212 () t)(J 0105 0086 0032 0019 701 to 900 0152 0281 () Ill 0170 0115 0057 0015 901 to 1100 0158 0255 () 177 0193 0114 0043 0020

111 to 1300 0122 0345 0222 0205 0135 0026

-18shy

In general BT is smallest for AB followed by YB BC RM SM and BW in increasing order

with BT for W A being the largest In general BT increases with DOB Most of the anomalies are

due to small sample sizes

Comparison with other BF equations

Fowler (1993) showed that while there were significant species differences between BF

equations for aspen jack pine and red pine there was a very strong relationship between BF and

tree height for each species (ie R 2 gt097 for each species) BF was a function of TH and In TH

showing that BF increased with TH to some maximum and then decreased for larger THs with the

steepness of the decrease depending on the species For all three species BF was not strongly

related to DBH or DOB at a given TH

For paper birch (Fowler and Hussain 1997) BF significantly increased with DOB at TH

(R2 =0219) and significantly decreased with In TH (R2 =0166) for stemwood while BF

significantly increased with DOB for topwood ( R 2 =0218) BF was much more variable than for

aspen red pine and jack pine

Fowler et al (1997) showed that black oak (BO) red oak (RO) and white oak (WO) have BPs

that are quite variable and prediction equations with the same independent variables as for paper

birch with the direction of the relations reversed For stemwood BF decreased with DOB at TH

( R 2 =0270 0418 and 0014 for BO RO and WO respectively) and increased with In TH ( R 2 =

0190 0275 and 0011 for BO RO and WO respectively) For topwood BF decreased with DOB

(R2=0366 0457 and 0100 for BO RO and WO respectively) These prediction equations were

significant but they were only moderately strong at best being only somewhat stronger in general

than the prediction equations for paper birch The prediction equations based on DOB were

-19shy

somewhat stronger than the prediction equations based on In TH The BF equations were

significantly different for the three species and for topwood versus stemwood except for RO

This study shows that the eight northern hardwood species have BFs that are quite variable

with some species having prediction equations with the same independent variables as for paper

birch and the three oak species while other species had different independent variables For

stemwood BF decreased with DOB at TH for RM SM BW and BC increased with In DOB at TH

for W A YB and AE and increased and then somewhat decreased with 1DOB and In DOB as the

independent variables for AB BF increased with In TH for RM SM and BC decreased and then

increased with TH and In TH for WA and BW increased and then decreased with TH and In TH for

YB AB and AE The prediction equations for AE are very suspect as they were based on only six

BF measurements from one tree For topwood BF decreased with DOB for RM WA SM BW

and BC increased with DOB for YB and increased and somewhat decreased with 1DOB and

In DOB for AB All prediction equations for stemwood were significant except for the TH

equations for BW and YB For topwood only the prediction equations for RM SM BW and AB

were significant In general all prediction equations were only moderately strong at best and some

of them were very weak The BF equations were significantly different for most species while the

stemwood and topwood BF equations were not significantly different except for RM and SM

GUIDELINES FOR USERS

We recommend use of the following equations for northern hardwoods when accurate

estimates of bark factors are desired

Stemwood

bull Red maple I

(1) BF =0996730-0002397 bull DOB I

(2) BF =0972344 + 0003554 bull In TH

-20shy

bull White ash 1

(3) BF = 0922166 +0001198bull DOB 1

(4) BF = 0937036 + 0000805 bull TH- 0009279 bullIn TH

bull- Sugar maple 1

(5) BF=0988318-0001497bullDOB 1

(6) BF = 0970865 + 0002264 bullIn TH

bull Basswood 1

(7) BF = 0974486-0000403 bull DOB 1

(8) BF = 0970312 + 0000072 bull TH- 0000631bullln TH

bull Black cherry 1

(9) BF = 0971912 -0000841bull DOB 1

(lO) BF = 0954777 + 0004557 bullIn TH

bull Yell ow birch 1

(11) BF = 0987390 + 0000307 bull DOB 1

(12) BF = 0990354-0000111bull TH+0000885bullln TH

bull American beech 1

(l3) BF = l027382-0l03065DOB -0009012bullln DOB

1

(14) BF = 0994075-0000047 bull TH+0000896 bullIn TH

bull American elm 1

(l5) BF =0925851 + 0003400 bull DOB 1

(16) BF = 0975815-0000058 bull TH- 0()()4696bullln TH

Use Equations 1 3 5 7 9 11 13 and 15 if DOBis measured Use Equations 2 4 6 8 10 12 14

and 16 when only THis measured

Topwood 1

(l7) RM BF = 1006791-0004569 bull DOB 1

(18) WA BF = 0936727 -0000206bull DOB 1

(l9) SM BF = 0995302-0002757 bull DOB

-21shy

(20) BW BF = 0979121-0002155 bull DOB

(21) BC BF = 0977830- 0000604 bull DOB

(22) YB BF = 0987032 + 0000281bull DOB

(23) AB BF = 1038966- 0131661DOB - 0012832 bullln DOB

The equation for stemwood and topwood pooled could be used if DOB is measured with moderate

loss in accuracy for RM and SM and little loss in accuracy for the other five species The pooled

equations in general will be more accurate for stemwood compared to topwood especially for RM

and SM

(24) RM BF == 0997087 -0002476bull DOB

1

(25) WA BF = 0924553 + 000 I 003 bull DOB

(26) SM BF=0988615-0001568bullDOB

(27) BW BF = 0972865-0000320 bull DOB

(28) BC BF=0974512-0001028bullDOB

(29) YB BF = 0986997 + 0000334 bull DOB

(30) AB BF = 1028314- 0105996DOB- 0009288 bullIn DOB

There is no pooled equation for AE as there was no topwood for the one AE tree in the data set

For reasonable accuracy in many situations the following constants could be used for bark

factors

DOB Class Stemwood BF (in) RM WA St-1 BW BC YB AB AE

DOBs50 0988 0927 09S~ 0973 0969 0989 0988 0939 50ltDOBsl00 0979 0931 0977 0971 0966 0990 0995 0951 l00ltDOBs150 0967 0937 0970 0969 0962 0991 0996 0968 150ltDOBs200 0955 0943 0962 0967 0957 0993 0996 0985

DOBgt200 0943 0949 0954 0965 0953 0994 0995 0994

-22shy

DOB Class ToEwoodBF (in) RM WA SM BW BC YB AB

DOBS50 0989 0936 0984 0971 0975 0988 0987 50ltD0BSl00 0970 0935 0973 0962 0973 0989 0995 100ltD0BS150 0947 0934 0959 0951 0970 0991 0996 150ltD0BS200 0924 0933 0946 0940 0967 0992 0995

008gt200 0902 0932 0932 0930 0964 0993 0993

TH Stemwood BF (ft) RM WA SM BW BC YB AB AE

THS05 0970 0947 0971 0971 0950 0990 0993 0980 05ltTHS45 0974 0932 olJn 0970 0959 0991 0995 0972

45ltTHS 100 0978 0925 0974 0970 0964 0991 0996 0966 100ltTHS200 0980 0924 0gt76 0970 0967 0991 0996 0963 200ltTHS300 0984 0928 0gt7S 0970 0970 0990 0996 0959 300ltTHS400 0986 0932 OltJSO 0971 0971 0990 0996 0957 400ltTHS500 0988 0937 () l)S~ 0971 0972 0989 0995 0955

THgt500 0992 0950 07 0974 0974 0987 0995 0952

The following constants for bark factor could be used for simplicity with moderately

approximate results especially for a large number of treessticks

Species Stem wood Top wood Stemwood and Topwood

RM 0980 0981 0980 WA 0932 0935 0932 SM 0976 0977 0976 BW 0970 0962 0970 BC 0965 0974 0966 YB 0991 0989 0990 AB 0995 0995 0995 AE 0964 0964

The above constants would be more accurate for those species that did not have significant

prediction equations andor small sample sizes B~ cry careful with using any of the results of this

study outside the range of the data set for each species Since the results for AE are based on six

stemwood measurements from one tree they arc of course very suspect

-23shy

Use of prediction equations

The prediction equations can be used to estimate BF at any DOB andor TH Since

BF=DIBDOB DIB can be estimated as DIB=BFbull DOB and DOB can be estimated as

DOB=DIBBF Past DOB and DOB growth can be estimated from past DIB growth as follows

Past DOB Growth=Past DIB GrowthBF

and

Past DOB=Present DOB -Past DOB Growth

where past DIB growth might be obtained with an increment borer

Specific uses of the prediction equations include (1) estimation of the solid wood and bark

volume of standing trees (2) estimation of bark volume or peeled volume from unpeeled volume

of felled tree sections (3) growth studies and (4) estimating tree form (eg Girard Form Class)

See Husch et al ( 1982) for a detailed discussion on bark factors

-24- LITERATURE CITED middot

Fowler G W 1991 An aspen bark factor equation for Michigan North J Appl For 8(1) 12-15

Fowler G W 1993 A jack pine bark factor equation for Michigan North J Appl For 10(2) 86-89

Fowler G W and L J Damschroder 1988 A red pine bark factor equation for Michigan North J Appl For 5(1) 28-30

Fowler G W and N G Hussain 1987a Bark factor equation for red pine Michigan DNR For Infor Leaflet 1-87 2 p

Fowler G W and N G Hussain 1987b Bark factor equation for aspen Michigan DNR For Infor Leaflet 2-87 2 p

Fowler G W and N G Hussain 1991 Bark factor equation for jack pine in Michigan Michigan DNR For Infor Leaflet 1-91 5 p

Fowler G W and N G Hussain 1997 Bark factor equations for paper birch in Michigan Michigan DNR For Infor Leaflet 1-97 12 p

Fowler G W N G Hussain D J Cohen and D Khatry-Chhetri 1997 Bark factor equations for oak in Michigan Michigan DNR For Infor Leaflet 2-97 15 p

Husch B C I Miller and T W Beers 1982 Forest Mensuration John Wiley and Sons Inc NY 402 p

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Ken Alto

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Tim Tennis

lonst Manbullpmeut DWisioa 15 Resource Mana1ement Units

bullJfectble l2519bull

bull -Resource Jf~nt Unit OJke

1 -Raource Jf~nt Unit BOUIIdariea

1 -CountyBouruiiJrfea

-7shy

American Elm (n=6)

R2 sybullx p

(22) II

BF = 0925851 + 0003400 bull DOB 0908 0002658 0003

(23) II

BF = 0975815 -0000058bull TH -0004696bullln TH 0968 0001801 0006

(24) II

BF = 0987215-0000786 bull DOB- 0000073 bull TH 0970 0002132 0044

- 0005707 bull In TH

Prediction Equations 1 4 7 10 13 16 19 and 22 for RM WA SM BW BC YB AB and AE

respectively yield the following estimated bark factors

PredictionoEquations l -+ 7 10 13 16 19 and 22

II

DOB BF (in) RM WA SM BW BC YB AB AE

30 0990 0926 0984 0973 0969 0988 0983 0936 40 0987 0927 0982 0973 0969 0989 0989 0939 50 0985 0928 0981 0972 0968 0989 0992 0943 60 0982 0929 0979 0972 0967 0989 0994 0946 70 0980 0931 0978 0972 0966 0990 0995 0950 80 0978 0932 0976 0971 0965 0990 0996 0953 90 0975 0933 0975 0971 0964 0990 0996 0956

100 0973 0934 0973 0970 0964 0990 0996 0960 110 0970 0935 0972 0970 0963 0991 0996 0963 120 0968 0937 0970 0970 0962 0991 0996 0967 130 0966 0938 0969 0969 0961 0991 0996 0970 140 0963 0939 0967 0968 0960 0992 0996 0973 150 0961 0940 0966 0968 0959 0992 0996 0977 160 0958 0941 0964 0968 0958 0992 0996 0980 170 0956 0943 0963 0968 0958 0993 0996 0984 180 0954 0944 0961 0967 0956 0993 0996 0987 190 0951 0945 0960 0967 0956 0993 0995 0990 200 0949 0946 0958 0966 0955 0994 0995 0994 210 0946 0947 0957 OlJ(J6 0954 0994 0995 220 0944 0949 0955 () lt)(l(J 0953 0994 0995 230 0942 0950 0954 () l)(J) 0953 0994 0995 240 0939 0951 0952 ( )l)(J) 0952 0995 0994 250 0937 0952 0951 ())J~ 0951 0995 0994

-8shy

Prediction Equations 2 5 8 11 14 17 20 and 23 for RM WA SM BW BC YB AB and AE

respectively yield the following estimated bark factors

Prediction Equations 2 5 8 11 14 17 20 and 23

TH BF (ft) RM WA SM BW BC YB AB AE

025 0970 0950 0971 0971 0948 0989 0993 0982 05 0971 0944 0971 0971 0952 0990 0993 0979 10 0973 0939 0972 0970 0955 0990 0994 0976 20 0974 0932 0972 0970 0958 0991 0995 0972 30 0975 0929 0972 0970 0960 0991 0995 0970 45 0977 0927 0973 0970 0962 0991 0995 0968 85 0979 0924 0974 0970 0965 0991 0996 0965

170 0981 0924 0976 0970 0968 0991 0996 0962 255 0984 0928 0978 0970 0970 0990 0996 0959 340 0986 0932 0980 0971 0971 0990 0996 0957 425 0988 0936 0982 0971 0972 0989 0995 0956 510 0989 0942 0984 0972 0973 0988 0995 0954 595 0991 0947 0986 0972 0973 0987 0995 0953 680 0993 0953 0988 0973 0974 0987 0995 0952 765 0995 0958 0990 0973 0975 0986 0994 0951

The ranges of predicted BF values for DOB from 30 to 250 in based on Equations 1 4 7 10 13

16 19 and 22 are 0053 0026 0033 0009 0018 0007 0011 and 0058 for RM WA SM

BW BC YB AB and AE respectively Note that no bark factors are given for DQB210 in for

AE because the estimated values are greater than one This is due to the small sample size (ie one

tree with 6 measurements) and the largest DOB being no larger than 1521 inches The ranges of

predicted BF values forTH from 025 to 765 ft based on Equations 2 5 8 11 14 17 20 and 23

are 0025 0034 0019 0003 0027 0005 0003 and 0031 for RM WA SM BW BC YB AB

and AE respectively Because of these moderate to small ranges the low R 2 values of the

prediction equations and some of the prediction equations not being significant at a= 005 you

might argue that the mean bark factor yields an adequate prediction model for each species

-9shy

- 829 (25) RM BF = BF =I BFJ829 =0980 0015671

i=l

- 410 26) WA BF = BF = I BFJ410 = 0932 0023692

i=l

1488 (27) SM BF = BF = L Bfi1488 = 0976 0014991

i=1

398 (28) BW BF = BF = L Bfi 398 = 0970 0013115

i=1

178 (29) BC BF = BF = L Bfi179 = 0965 0015086

i=1

66 (30) YB BF = BF = L BFi66 = 0991 0003720

i=1

131 (31) AB BF = BF = L Bfi131 = 0995 0004566

i=1

6 (32) AE BF = BF =L BFJ6 =0964 0007831

i=1

See the above two tables to find where Equations 25-32 over- and underestimate related to

Equations 1-24-57-8 lO-ll 13-14 16-17 19-20 and 22-23 respectively

Prediction Equations 1 4 7 10 13 16 and 22 are significantly different (Bartletts x 2 -test

for equal variances Plt0005 F-test for equal slopes Plt0001) Prediction Equations 2 8 and 14

are significantly different (Bartletts i-test for equal variances Plt010 F-test for equal slopes

PltOOO 1) Prediction Equations 5 11 17 20 and 23 are significantly different (Bartletts i -test

for equal variances Plt0005 F-test for equal slopes Plt0001) Prediction Equations 27-32 related

to mean bark factors are also significantly different (Bartletts x 2 -test for equal variances Plt0005

F-test for equal means Plt0001) All Bonferroni pairwise comparisons of means are significantly

-10shy

different (Plt0003) except for (RM AE) (SM AE) (BW AE) (BC AE) and (YB AB) Note that

the sample size for AE is only 6

Topwood R2 psybullx n

1

(33) RM BF = 1006791 - 0004569 bull DOB 0245 0016815 lt0001 74 1

(34) WA BF = 0936727 - 0000206 bull DOB 0000 0023230 0866 75 1

(35) SM BF = 0995302-0002757 bull DOB 0201 0013598 lt0001 342 1

(36) BW BF = 0979121-0002155bull DOB 0135 0010484 0023 38 1

(37) BC BF = 0977830-0000604 bull DOB 0017 0009709 0478 32

1

(38) YB BF = 0987032 + 0000281 bull DOB 0012 0004606 0593 26 1

(39) AB BF = 1038966-0131661DOB 0463 0002353 lt0001 44

-0012832bulllnDOB

Prediction Equations 33-39 for RM W A SM BW BC YB and AB respectively yield the

following estimated bark factors

Prediction Equations 33-39

DOB 1

BF (in) RM WA SM BW BC YB AB

30 0993 0936 0987 0973 0976 0988 0981 40 0989 0936 0984 0971 0975 0988 0988 50 0984 0936 0982 0968 0975 0988 0992 60 0979 0935 0979 0966 0974 0989 0994 70 0975 0935 0976 0964 0974 0989 0995 80 0970 0935 0973 0962 0973 0989 0996 90 0966 0935 0970 0960 0972 0990 0996

100 0961 0935 0968 0958 0972 0990 0996 110 0957 0934 0965 0955 0971 0990 0996 120 0952 0934 0962 0953 0971 0990 0996 130 0947 0934 0959 0951 0970 0991 0996 140 0943 0934 0957 0949 0969 0991 OQ96 150 0938 0934 0954 0947 0969 0991 0995 160 0934 0933 0951 0945 0968 0992 0995 170 0929 0933 0948 0942 0968 0992 0995 180 0924 0933 0946 0940 0967 0992 0995 190 0920 0933 0943 0938 0966 0992 0994 200 0915 0933 0940 0936 0966 0993 0994

-11shy

The ranges of predicted BF values for DOB from 30 to 200 in are 0078 0003 0047 0037

0010 0005 and 0015 for RM WA SM BW BC YB and AB respectively Because of these

moderate to small ranges the low R 2 values of the prediction equations the moderate sample sizes

and some of the prediction equations not being significant at a=005 you might argue that the mean

bark factor yields an adequate prediction model (except possibly for RM)

74 (40) RM BF = BF =I BFi74 = 0981 0019213

i=l 75

(41) WA BF = BF =I B~75 = 0935 0023077 i=l 342

(42) SM BF = BF = I B~ 342 = 0977 0015190 i=l 38

(43) BW BF = BF =I BFi38 =0962 0011118 i=l

32 (44) BC BF = BF =I BFi32 = 0974 0009633

i=l

26 (45) YB BF = BF =I Bfi 26 = 0989 0004540

i=l

44 (46) AB BF=BF= I BFi44=0995 0003135

i=l

See the above table to find where Equations 40-46 over- and underestimate reflected to Equations

33-39 respectively

Prediction Equations 33-38 are significant y different (Bartletts 12 -test for equal variances

Plt0005 F-test for equal slopes P=OOOl) Prediction Equations 40-46 related to mean bark factors

are also significantly different (Bartletts -test for equal variances Plt0005 F-test for equal

-12shy

means PltOOOl) All Bonferroni pairwise comparisons of means are significantly different

(Plt005) except for (RM SM) (RM BC) (RM YB) (SM BC) and (YB AB)

Pooled prediction equations

The stemwood and topwood BF prediction equations with DOB as the independent variable

were compared for each of the species except for AB where the independent variables were 1DOB

and ln DOB The resulting P-values are as follows

Bartletts z2 -test F-test for Equal Species for Equal Variances Regression Coefficients

RM P=005+ P=OOOl WA P=01 P=0267 SM P=0862 PltOOOl BW P=OOlJ-+ P=0120 BC P=0005 P=0854 YB P=0106 P=0954 AB PltOOOI P=0942

Bonferroni level of significance a=OOS7=0007

The above results indicate that the two equations for WA BW BC YB and AB can be pooled

while some prediction accuracy will be lost if the two equations for RM and SM are pooled (See the

two equations shown for each species earlier in this paper) Note that there is no lopwood for the

one AE tree in the data set Therefore the pooled equation is the stemwood equation for AE

The pooled prediction equations are

R2 sybullx p n

A

(47) RM BF =0997087 -0002476bull DOB 0166 0014604 lt0001 903

A

(48) WA BF =0924553 + 0001003 bull DOB 0021 0023385 0001 485

A

(49) SM BF =0988615-0001568 bull DOB (Jl64 0013748 lt0001 1830

A

(50) BW BF =0972865-0000320 bull DOB 00 lO 0013085 0040 436

A

(51) BC BF =0974512 -0001028bull DOB 0041 0014455 0003 210

A

(52) YB BF =0986997 + 0000334 bull DOB 0107 0003825 0001 92

-13shy

R2 sybullx p n

1

(53) AB BF =1028314- 0105996DOB 0201 0003819 lt0001 175

- 0009288 bull In DOB

Prediction equations 47-53 for RM WA SM BW BC YB and AB respectively yield the

following estimated bark factors

Prediction Equations 47-53

1

DOB BF (in) RM WA SM BW BC YB AB

30 0990 0928 0984 0972 0971 0988 0983 40 0987 0929 0982 0972 0970 0988 0989 50 0985 0930 0981 0971 0969 0989 0992 60 0982 0931 0979 0971 0968 0989 0994 70 0980 0932 0978 0971 0967 0989 0995 80 0977 0933 0976 0970 0966 0989 0996 90 0975 0934 0975 0970 0965 0990 0996

100 0972 0935 0973 0969 0964 0990 0996 110 0970 0936 0971 0969 0963 0991 0996 120 0967 0937 0970 0969 0962 0991 0996 130 0965 0938 0968 0968 0961 0991 0996 140 0962 0939 0967 0968 0960 0992 0996 150 0960 0940 0965 0968 0959 0992 0996 160 0957 0941 0964 0968 0958 0992 0996 170 0955 0942 0962 0967 0957 0993 0996 180 0953 0943 0960 0967 0956 0993 0996 190 0950 0944 0959 0967 0955 0993 0995 200 0948 0945 0957 0966 0954 0994 0995 210 0945 0946 0956 0966 0953 0994 0995 220 0943 0947 0954 0966 0952 0994 0995 230 0940 0948 0953 0966 0951 0995 0995 240 0938 0949 0951 0965 0950 0995 0994 250 0935 0950 0949 0965 0949 0995 0994

Note that the pooled BF estimates for each species are close to those of Equations 1 4 7 10

13 16 and 19 for stemwood This makes sense since the stemwood sample sizes were considerably

larger than the topwood sample sizes for each species For topwood the pooled BF estimates for

YB and AB are very close to Equations 38 and 39 respectively for topwood However there are

some larger differences for the other species over the range of DOB from 30-200 inches

-14shy

bull RM - Pooled BF estimates are lower than those of Equation 33 for DOB lt 50 in and higher for DOB ~ 50 in (from 0003 lower to 0033 higher)

bull WA - Pooled BF estimates are lower than those of Equation 34 for DOB lt 100 in and higher for DOB gt 100 in (from 0008 lower to 0012 higher)

bull SM - Pooled BF estimates are lower than those of Equation 35 for DOB lt 60 in and higher for DOB gt 60 in (from 0003 lower to 0017 higher)

bull BW - Pooled BF estimates are lower than those of Equation 36 for DOB lt 40 in and higher for DOB ~ 40 in (from 0001 lower to 0030 higher)

bull BC - Pooled BF estimates are lower than those of Equation 37 for all values of DOB (from 0005 to 0012lower)

The ranges of the pooled predicted BF values for DOB from 30 to 250 in are 0055 0022 0035

0007 0022 0007 and 0013 for RM WA SM BW BC YB and AB respectively Because of

these moderate to small ranges the low R2 values of the prediction equations and some of the

prediction equations not being significant you might argue that the mean bark factor yields an

adequate prediction model

The stemwood and topwood mean BFs were compared for each of the species The resulting

P-values are as follows

Species Bartletts zLtest

for Equal Variances F-test for Equal

Regression Coefficients

RM 0013 0681 WA 0770 0202 SM 0775 0287 BW 0196 0004 BC 0004 0001 YB 0222 0055 AB 0005 0542

Bonferroni level of significance a PC =00057 =0007

The above results indicate that the two means for RM W A SM YB and AB can be pooled while

some prediction accuracy will be lost if the two means for BW and BC are pooled (See the two

means shown for each species earlier in the paper) Note that there is no topwood for the one AE

tree in the data set Therefore the pooled mean is the stemwood mean for AE

-15shy

The pooled mean bark factors are

903 (54) RM middot BF = BF = L Bfl 903 = 0980 0015980

i=1

485 (55) WA BF = BF = L Bfl485 = 0932 0023614

i=1

1830 (56) SM BF= BF= L Bfl1830 = 0976 0015029

i=1

436 (57) BW BF = BF = L Bfl436 = 0970 0013134

i=l

210 (58) BC BF = BF = L Bfl210 = 0966 0014725

i=l

92 (59) YB BF = BF = L BFi92 = 0990 0004025

i=l

175 (60) AB BF = BF = L BF)l75 = 0995 0004248

i=1

See the table based on Equations 47-53 to see where Equations 54-60 under- and overestimate

respectively

Bark thickness

For the stemwood data set (n=3506) BT was significantly different for the eight different

species (Bartletts x2 -test for equal variances PltOOOl F-test for equal means PltOOOl) All

Bonferroni pairwise comparisons of means are significantly different except for (RM YB) (RM

AE) (WA AE) (SM AE) (BW AE) (BC AE) (YB AB) and (BW BC) Note that the sample

size for AE is only 6

Average minimum and maximum BTs and Pearsons correlations of BT with DOB DBH

and TH are shown below for the eight species

-16shy

BT BTDOB BTDBH BTTHSpecies nx Min-Max r p r p r p

RM 0077 0005-0525 0678 lt0001 0484 lt0001 -0369 lt0001 829 WA 0263 0012-1760 0632 lt0001 0428 lt0001 -0329 lt0001 410 SM 0113 0008-0672 0794 lt0001 0685 lt0001 -0293 lt0001 1488 BW 0158 0005-0525 0738 lt0001 0633 lt0001 -0192 lt0001 398 BC 0145 0012-0438 0653 lt0001 0169 0024 -0683 lt0001 178 YB 0046 0020-0115 0448 lt0001 0234 0058 -0383 0002 66 AB 0024 0005-0395 0236 0007 0067 0448 -0229 0009 131 AE 0195 0170-0228 -0511 0300 0405 0425 6

AE data consists of six measurements from one tree

BT was significantly positively related to DOB for all species except for AE where there was a

negative relation that was not significant BT was significantly positively related to DBH for all

species except for YB and AB where the positive relations were not significant BT was

significantly negatively related to TH for all species except for AE where there was a positive

relationship that was not significant

Average BTs for various DOB and TH classes for the eight species are as follows

DOB Class BT (in) RM WA SM BW BC YB AB AE

~400

401 to 800 801 to 1200 1201 to 1600

gt1600

0017 0054 0134 0239 0236

0091 0220 0321 0394 0468

0024 0060 0141 0225 0324

0032 0093 0150 0119 0268

0058 0101 0192 0252 0199

0020 0032 0048 0060 0058

0022 0019 0019 0020 0048

0200 0170

THClass BT (ft) RM WA SM BW BC YB AB AE

~050 0134 0208 0146 0114 0263 0038 0036 051 to 450 0110 0338 0161 0199 0192 0057 0038 0180 451 to 1000 0080 0296 0105 0165 0169 0047 0021 1001 to 2000 0065 0278 010(1 0153 0140 0049 0016 0210 2001 to 3000 0060 0250 0094 0146 0102 0041 0016 0200 3001 to 4000 0045 0220 0089 0134 0087 0037 0014 0190 4001 to 5000 0038 0220 0062 0153 0061 0025 0015

~5000 0016 0159 0047 0136 0038 0016

-17shy

In general BT is smallest for AB followed by YB RM SM BC BW and AE in increasing order

with BT for WA being the largest In general BT increases with DOB and decreases with TH

Most of the anomalies are due to small sample sizes

For the topwood data set (n=631) BT was significantly different for the seven different

species (Bartletts -test for equal variances PltOOOl F-test for equal means PltOOOl) All

Bonferroni pairwise comparisons of means are significantly different except for (RM SM) (RM

BC) (RM YB) (SM BC) (BC YB) and (YB AB)

Average minimum and maximum BTs and Pearsons correlations of BT with DOB and DBH

are shown below for the seven species

Species x

BT

Min- Max

BT DOB p r

BTDBH p n

RM WA SM BW BC YB AB

0064 0203 0086 0150 0083 0034 0019

0008-0385 0022-0458 0005-0362 0018-0262 0018-0175 Ool5-0075 0008-0038

06SO 0723 0768 0813 0723 0464 0051

lt0001 lt0001 lt0001 lt0001 lt0001

0017 0744

0549 0360 0440 0588 0380 0216 0661

lt0001 0002

lt0001 lt0001

0032 0290

lt0001

74 75

342 38 32 26 44

BT was significantly positively related to DOB for all species except for AB and to DBH for all

species except for YB

Average BTs for various DOB classes for the seven species are as follows

DOB Class BT (in) RM WA S~t BW BC YB AB

500 OQl8 0126 oltH) 0054 0051 0024 0021 501 to 700 0073 0212 () t)(J 0105 0086 0032 0019 701 to 900 0152 0281 () Ill 0170 0115 0057 0015 901 to 1100 0158 0255 () 177 0193 0114 0043 0020

111 to 1300 0122 0345 0222 0205 0135 0026

-18shy

In general BT is smallest for AB followed by YB BC RM SM and BW in increasing order

with BT for W A being the largest In general BT increases with DOB Most of the anomalies are

due to small sample sizes

Comparison with other BF equations

Fowler (1993) showed that while there were significant species differences between BF

equations for aspen jack pine and red pine there was a very strong relationship between BF and

tree height for each species (ie R 2 gt097 for each species) BF was a function of TH and In TH

showing that BF increased with TH to some maximum and then decreased for larger THs with the

steepness of the decrease depending on the species For all three species BF was not strongly

related to DBH or DOB at a given TH

For paper birch (Fowler and Hussain 1997) BF significantly increased with DOB at TH

(R2 =0219) and significantly decreased with In TH (R2 =0166) for stemwood while BF

significantly increased with DOB for topwood ( R 2 =0218) BF was much more variable than for

aspen red pine and jack pine

Fowler et al (1997) showed that black oak (BO) red oak (RO) and white oak (WO) have BPs

that are quite variable and prediction equations with the same independent variables as for paper

birch with the direction of the relations reversed For stemwood BF decreased with DOB at TH

( R 2 =0270 0418 and 0014 for BO RO and WO respectively) and increased with In TH ( R 2 =

0190 0275 and 0011 for BO RO and WO respectively) For topwood BF decreased with DOB

(R2=0366 0457 and 0100 for BO RO and WO respectively) These prediction equations were

significant but they were only moderately strong at best being only somewhat stronger in general

than the prediction equations for paper birch The prediction equations based on DOB were

-19shy

somewhat stronger than the prediction equations based on In TH The BF equations were

significantly different for the three species and for topwood versus stemwood except for RO

This study shows that the eight northern hardwood species have BFs that are quite variable

with some species having prediction equations with the same independent variables as for paper

birch and the three oak species while other species had different independent variables For

stemwood BF decreased with DOB at TH for RM SM BW and BC increased with In DOB at TH

for W A YB and AE and increased and then somewhat decreased with 1DOB and In DOB as the

independent variables for AB BF increased with In TH for RM SM and BC decreased and then

increased with TH and In TH for WA and BW increased and then decreased with TH and In TH for

YB AB and AE The prediction equations for AE are very suspect as they were based on only six

BF measurements from one tree For topwood BF decreased with DOB for RM WA SM BW

and BC increased with DOB for YB and increased and somewhat decreased with 1DOB and

In DOB for AB All prediction equations for stemwood were significant except for the TH

equations for BW and YB For topwood only the prediction equations for RM SM BW and AB

were significant In general all prediction equations were only moderately strong at best and some

of them were very weak The BF equations were significantly different for most species while the

stemwood and topwood BF equations were not significantly different except for RM and SM

GUIDELINES FOR USERS

We recommend use of the following equations for northern hardwoods when accurate

estimates of bark factors are desired

Stemwood

bull Red maple I

(1) BF =0996730-0002397 bull DOB I

(2) BF =0972344 + 0003554 bull In TH

-20shy

bull White ash 1

(3) BF = 0922166 +0001198bull DOB 1

(4) BF = 0937036 + 0000805 bull TH- 0009279 bullIn TH

bull- Sugar maple 1

(5) BF=0988318-0001497bullDOB 1

(6) BF = 0970865 + 0002264 bullIn TH

bull Basswood 1

(7) BF = 0974486-0000403 bull DOB 1

(8) BF = 0970312 + 0000072 bull TH- 0000631bullln TH

bull Black cherry 1

(9) BF = 0971912 -0000841bull DOB 1

(lO) BF = 0954777 + 0004557 bullIn TH

bull Yell ow birch 1

(11) BF = 0987390 + 0000307 bull DOB 1

(12) BF = 0990354-0000111bull TH+0000885bullln TH

bull American beech 1

(l3) BF = l027382-0l03065DOB -0009012bullln DOB

1

(14) BF = 0994075-0000047 bull TH+0000896 bullIn TH

bull American elm 1

(l5) BF =0925851 + 0003400 bull DOB 1

(16) BF = 0975815-0000058 bull TH- 0()()4696bullln TH

Use Equations 1 3 5 7 9 11 13 and 15 if DOBis measured Use Equations 2 4 6 8 10 12 14

and 16 when only THis measured

Topwood 1

(l7) RM BF = 1006791-0004569 bull DOB 1

(18) WA BF = 0936727 -0000206bull DOB 1

(l9) SM BF = 0995302-0002757 bull DOB

-21shy

(20) BW BF = 0979121-0002155 bull DOB

(21) BC BF = 0977830- 0000604 bull DOB

(22) YB BF = 0987032 + 0000281bull DOB

(23) AB BF = 1038966- 0131661DOB - 0012832 bullln DOB

The equation for stemwood and topwood pooled could be used if DOB is measured with moderate

loss in accuracy for RM and SM and little loss in accuracy for the other five species The pooled

equations in general will be more accurate for stemwood compared to topwood especially for RM

and SM

(24) RM BF == 0997087 -0002476bull DOB

1

(25) WA BF = 0924553 + 000 I 003 bull DOB

(26) SM BF=0988615-0001568bullDOB

(27) BW BF = 0972865-0000320 bull DOB

(28) BC BF=0974512-0001028bullDOB

(29) YB BF = 0986997 + 0000334 bull DOB

(30) AB BF = 1028314- 0105996DOB- 0009288 bullIn DOB

There is no pooled equation for AE as there was no topwood for the one AE tree in the data set

For reasonable accuracy in many situations the following constants could be used for bark

factors

DOB Class Stemwood BF (in) RM WA St-1 BW BC YB AB AE

DOBs50 0988 0927 09S~ 0973 0969 0989 0988 0939 50ltDOBsl00 0979 0931 0977 0971 0966 0990 0995 0951 l00ltDOBs150 0967 0937 0970 0969 0962 0991 0996 0968 150ltDOBs200 0955 0943 0962 0967 0957 0993 0996 0985

DOBgt200 0943 0949 0954 0965 0953 0994 0995 0994

-22shy

DOB Class ToEwoodBF (in) RM WA SM BW BC YB AB

DOBS50 0989 0936 0984 0971 0975 0988 0987 50ltD0BSl00 0970 0935 0973 0962 0973 0989 0995 100ltD0BS150 0947 0934 0959 0951 0970 0991 0996 150ltD0BS200 0924 0933 0946 0940 0967 0992 0995

008gt200 0902 0932 0932 0930 0964 0993 0993

TH Stemwood BF (ft) RM WA SM BW BC YB AB AE

THS05 0970 0947 0971 0971 0950 0990 0993 0980 05ltTHS45 0974 0932 olJn 0970 0959 0991 0995 0972

45ltTHS 100 0978 0925 0974 0970 0964 0991 0996 0966 100ltTHS200 0980 0924 0gt76 0970 0967 0991 0996 0963 200ltTHS300 0984 0928 0gt7S 0970 0970 0990 0996 0959 300ltTHS400 0986 0932 OltJSO 0971 0971 0990 0996 0957 400ltTHS500 0988 0937 () l)S~ 0971 0972 0989 0995 0955

THgt500 0992 0950 07 0974 0974 0987 0995 0952

The following constants for bark factor could be used for simplicity with moderately

approximate results especially for a large number of treessticks

Species Stem wood Top wood Stemwood and Topwood

RM 0980 0981 0980 WA 0932 0935 0932 SM 0976 0977 0976 BW 0970 0962 0970 BC 0965 0974 0966 YB 0991 0989 0990 AB 0995 0995 0995 AE 0964 0964

The above constants would be more accurate for those species that did not have significant

prediction equations andor small sample sizes B~ cry careful with using any of the results of this

study outside the range of the data set for each species Since the results for AE are based on six

stemwood measurements from one tree they arc of course very suspect

-23shy

Use of prediction equations

The prediction equations can be used to estimate BF at any DOB andor TH Since

BF=DIBDOB DIB can be estimated as DIB=BFbull DOB and DOB can be estimated as

DOB=DIBBF Past DOB and DOB growth can be estimated from past DIB growth as follows

Past DOB Growth=Past DIB GrowthBF

and

Past DOB=Present DOB -Past DOB Growth

where past DIB growth might be obtained with an increment borer

Specific uses of the prediction equations include (1) estimation of the solid wood and bark

volume of standing trees (2) estimation of bark volume or peeled volume from unpeeled volume

of felled tree sections (3) growth studies and (4) estimating tree form (eg Girard Form Class)

See Husch et al ( 1982) for a detailed discussion on bark factors

-24- LITERATURE CITED middot

Fowler G W 1991 An aspen bark factor equation for Michigan North J Appl For 8(1) 12-15

Fowler G W 1993 A jack pine bark factor equation for Michigan North J Appl For 10(2) 86-89

Fowler G W and L J Damschroder 1988 A red pine bark factor equation for Michigan North J Appl For 5(1) 28-30

Fowler G W and N G Hussain 1987a Bark factor equation for red pine Michigan DNR For Infor Leaflet 1-87 2 p

Fowler G W and N G Hussain 1987b Bark factor equation for aspen Michigan DNR For Infor Leaflet 2-87 2 p

Fowler G W and N G Hussain 1991 Bark factor equation for jack pine in Michigan Michigan DNR For Infor Leaflet 1-91 5 p

Fowler G W and N G Hussain 1997 Bark factor equations for paper birch in Michigan Michigan DNR For Infor Leaflet 1-97 12 p

Fowler G W N G Hussain D J Cohen and D Khatry-Chhetri 1997 Bark factor equations for oak in Michigan Michigan DNR For Infor Leaflet 2-97 15 p

Husch B C I Miller and T W Beers 1982 Forest Mensuration John Wiley and Sons Inc NY 402 p

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lonst Manbullpmeut DWisioa 15 Resource Mana1ement Units

bullJfectble l2519bull

bull -Resource Jf~nt Unit OJke

1 -Raource Jf~nt Unit BOUIIdariea

1 -CountyBouruiiJrfea

-8shy

Prediction Equations 2 5 8 11 14 17 20 and 23 for RM WA SM BW BC YB AB and AE

respectively yield the following estimated bark factors

Prediction Equations 2 5 8 11 14 17 20 and 23

TH BF (ft) RM WA SM BW BC YB AB AE

025 0970 0950 0971 0971 0948 0989 0993 0982 05 0971 0944 0971 0971 0952 0990 0993 0979 10 0973 0939 0972 0970 0955 0990 0994 0976 20 0974 0932 0972 0970 0958 0991 0995 0972 30 0975 0929 0972 0970 0960 0991 0995 0970 45 0977 0927 0973 0970 0962 0991 0995 0968 85 0979 0924 0974 0970 0965 0991 0996 0965

170 0981 0924 0976 0970 0968 0991 0996 0962 255 0984 0928 0978 0970 0970 0990 0996 0959 340 0986 0932 0980 0971 0971 0990 0996 0957 425 0988 0936 0982 0971 0972 0989 0995 0956 510 0989 0942 0984 0972 0973 0988 0995 0954 595 0991 0947 0986 0972 0973 0987 0995 0953 680 0993 0953 0988 0973 0974 0987 0995 0952 765 0995 0958 0990 0973 0975 0986 0994 0951

The ranges of predicted BF values for DOB from 30 to 250 in based on Equations 1 4 7 10 13

16 19 and 22 are 0053 0026 0033 0009 0018 0007 0011 and 0058 for RM WA SM

BW BC YB AB and AE respectively Note that no bark factors are given for DQB210 in for

AE because the estimated values are greater than one This is due to the small sample size (ie one

tree with 6 measurements) and the largest DOB being no larger than 1521 inches The ranges of

predicted BF values forTH from 025 to 765 ft based on Equations 2 5 8 11 14 17 20 and 23

are 0025 0034 0019 0003 0027 0005 0003 and 0031 for RM WA SM BW BC YB AB

and AE respectively Because of these moderate to small ranges the low R 2 values of the

prediction equations and some of the prediction equations not being significant at a= 005 you

might argue that the mean bark factor yields an adequate prediction model for each species

-9shy

- 829 (25) RM BF = BF =I BFJ829 =0980 0015671

i=l

- 410 26) WA BF = BF = I BFJ410 = 0932 0023692

i=l

1488 (27) SM BF = BF = L Bfi1488 = 0976 0014991

i=1

398 (28) BW BF = BF = L Bfi 398 = 0970 0013115

i=1

178 (29) BC BF = BF = L Bfi179 = 0965 0015086

i=1

66 (30) YB BF = BF = L BFi66 = 0991 0003720

i=1

131 (31) AB BF = BF = L Bfi131 = 0995 0004566

i=1

6 (32) AE BF = BF =L BFJ6 =0964 0007831

i=1

See the above two tables to find where Equations 25-32 over- and underestimate related to

Equations 1-24-57-8 lO-ll 13-14 16-17 19-20 and 22-23 respectively

Prediction Equations 1 4 7 10 13 16 and 22 are significantly different (Bartletts x 2 -test

for equal variances Plt0005 F-test for equal slopes Plt0001) Prediction Equations 2 8 and 14

are significantly different (Bartletts i-test for equal variances Plt010 F-test for equal slopes

PltOOO 1) Prediction Equations 5 11 17 20 and 23 are significantly different (Bartletts i -test

for equal variances Plt0005 F-test for equal slopes Plt0001) Prediction Equations 27-32 related

to mean bark factors are also significantly different (Bartletts x 2 -test for equal variances Plt0005

F-test for equal means Plt0001) All Bonferroni pairwise comparisons of means are significantly

-10shy

different (Plt0003) except for (RM AE) (SM AE) (BW AE) (BC AE) and (YB AB) Note that

the sample size for AE is only 6

Topwood R2 psybullx n

1

(33) RM BF = 1006791 - 0004569 bull DOB 0245 0016815 lt0001 74 1

(34) WA BF = 0936727 - 0000206 bull DOB 0000 0023230 0866 75 1

(35) SM BF = 0995302-0002757 bull DOB 0201 0013598 lt0001 342 1

(36) BW BF = 0979121-0002155bull DOB 0135 0010484 0023 38 1

(37) BC BF = 0977830-0000604 bull DOB 0017 0009709 0478 32

1

(38) YB BF = 0987032 + 0000281 bull DOB 0012 0004606 0593 26 1

(39) AB BF = 1038966-0131661DOB 0463 0002353 lt0001 44

-0012832bulllnDOB

Prediction Equations 33-39 for RM W A SM BW BC YB and AB respectively yield the

following estimated bark factors

Prediction Equations 33-39

DOB 1

BF (in) RM WA SM BW BC YB AB

30 0993 0936 0987 0973 0976 0988 0981 40 0989 0936 0984 0971 0975 0988 0988 50 0984 0936 0982 0968 0975 0988 0992 60 0979 0935 0979 0966 0974 0989 0994 70 0975 0935 0976 0964 0974 0989 0995 80 0970 0935 0973 0962 0973 0989 0996 90 0966 0935 0970 0960 0972 0990 0996

100 0961 0935 0968 0958 0972 0990 0996 110 0957 0934 0965 0955 0971 0990 0996 120 0952 0934 0962 0953 0971 0990 0996 130 0947 0934 0959 0951 0970 0991 0996 140 0943 0934 0957 0949 0969 0991 OQ96 150 0938 0934 0954 0947 0969 0991 0995 160 0934 0933 0951 0945 0968 0992 0995 170 0929 0933 0948 0942 0968 0992 0995 180 0924 0933 0946 0940 0967 0992 0995 190 0920 0933 0943 0938 0966 0992 0994 200 0915 0933 0940 0936 0966 0993 0994

-11shy

The ranges of predicted BF values for DOB from 30 to 200 in are 0078 0003 0047 0037

0010 0005 and 0015 for RM WA SM BW BC YB and AB respectively Because of these

moderate to small ranges the low R 2 values of the prediction equations the moderate sample sizes

and some of the prediction equations not being significant at a=005 you might argue that the mean

bark factor yields an adequate prediction model (except possibly for RM)

74 (40) RM BF = BF =I BFi74 = 0981 0019213

i=l 75

(41) WA BF = BF =I B~75 = 0935 0023077 i=l 342

(42) SM BF = BF = I B~ 342 = 0977 0015190 i=l 38

(43) BW BF = BF =I BFi38 =0962 0011118 i=l

32 (44) BC BF = BF =I BFi32 = 0974 0009633

i=l

26 (45) YB BF = BF =I Bfi 26 = 0989 0004540

i=l

44 (46) AB BF=BF= I BFi44=0995 0003135

i=l

See the above table to find where Equations 40-46 over- and underestimate reflected to Equations

33-39 respectively

Prediction Equations 33-38 are significant y different (Bartletts 12 -test for equal variances

Plt0005 F-test for equal slopes P=OOOl) Prediction Equations 40-46 related to mean bark factors

are also significantly different (Bartletts -test for equal variances Plt0005 F-test for equal

-12shy

means PltOOOl) All Bonferroni pairwise comparisons of means are significantly different

(Plt005) except for (RM SM) (RM BC) (RM YB) (SM BC) and (YB AB)

Pooled prediction equations

The stemwood and topwood BF prediction equations with DOB as the independent variable

were compared for each of the species except for AB where the independent variables were 1DOB

and ln DOB The resulting P-values are as follows

Bartletts z2 -test F-test for Equal Species for Equal Variances Regression Coefficients

RM P=005+ P=OOOl WA P=01 P=0267 SM P=0862 PltOOOl BW P=OOlJ-+ P=0120 BC P=0005 P=0854 YB P=0106 P=0954 AB PltOOOI P=0942

Bonferroni level of significance a=OOS7=0007

The above results indicate that the two equations for WA BW BC YB and AB can be pooled

while some prediction accuracy will be lost if the two equations for RM and SM are pooled (See the

two equations shown for each species earlier in this paper) Note that there is no lopwood for the

one AE tree in the data set Therefore the pooled equation is the stemwood equation for AE

The pooled prediction equations are

R2 sybullx p n

A

(47) RM BF =0997087 -0002476bull DOB 0166 0014604 lt0001 903

A

(48) WA BF =0924553 + 0001003 bull DOB 0021 0023385 0001 485

A

(49) SM BF =0988615-0001568 bull DOB (Jl64 0013748 lt0001 1830

A

(50) BW BF =0972865-0000320 bull DOB 00 lO 0013085 0040 436

A

(51) BC BF =0974512 -0001028bull DOB 0041 0014455 0003 210

A

(52) YB BF =0986997 + 0000334 bull DOB 0107 0003825 0001 92

-13shy

R2 sybullx p n

1

(53) AB BF =1028314- 0105996DOB 0201 0003819 lt0001 175

- 0009288 bull In DOB

Prediction equations 47-53 for RM WA SM BW BC YB and AB respectively yield the

following estimated bark factors

Prediction Equations 47-53

1

DOB BF (in) RM WA SM BW BC YB AB

30 0990 0928 0984 0972 0971 0988 0983 40 0987 0929 0982 0972 0970 0988 0989 50 0985 0930 0981 0971 0969 0989 0992 60 0982 0931 0979 0971 0968 0989 0994 70 0980 0932 0978 0971 0967 0989 0995 80 0977 0933 0976 0970 0966 0989 0996 90 0975 0934 0975 0970 0965 0990 0996

100 0972 0935 0973 0969 0964 0990 0996 110 0970 0936 0971 0969 0963 0991 0996 120 0967 0937 0970 0969 0962 0991 0996 130 0965 0938 0968 0968 0961 0991 0996 140 0962 0939 0967 0968 0960 0992 0996 150 0960 0940 0965 0968 0959 0992 0996 160 0957 0941 0964 0968 0958 0992 0996 170 0955 0942 0962 0967 0957 0993 0996 180 0953 0943 0960 0967 0956 0993 0996 190 0950 0944 0959 0967 0955 0993 0995 200 0948 0945 0957 0966 0954 0994 0995 210 0945 0946 0956 0966 0953 0994 0995 220 0943 0947 0954 0966 0952 0994 0995 230 0940 0948 0953 0966 0951 0995 0995 240 0938 0949 0951 0965 0950 0995 0994 250 0935 0950 0949 0965 0949 0995 0994

Note that the pooled BF estimates for each species are close to those of Equations 1 4 7 10

13 16 and 19 for stemwood This makes sense since the stemwood sample sizes were considerably

larger than the topwood sample sizes for each species For topwood the pooled BF estimates for

YB and AB are very close to Equations 38 and 39 respectively for topwood However there are

some larger differences for the other species over the range of DOB from 30-200 inches

-14shy

bull RM - Pooled BF estimates are lower than those of Equation 33 for DOB lt 50 in and higher for DOB ~ 50 in (from 0003 lower to 0033 higher)

bull WA - Pooled BF estimates are lower than those of Equation 34 for DOB lt 100 in and higher for DOB gt 100 in (from 0008 lower to 0012 higher)

bull SM - Pooled BF estimates are lower than those of Equation 35 for DOB lt 60 in and higher for DOB gt 60 in (from 0003 lower to 0017 higher)

bull BW - Pooled BF estimates are lower than those of Equation 36 for DOB lt 40 in and higher for DOB ~ 40 in (from 0001 lower to 0030 higher)

bull BC - Pooled BF estimates are lower than those of Equation 37 for all values of DOB (from 0005 to 0012lower)

The ranges of the pooled predicted BF values for DOB from 30 to 250 in are 0055 0022 0035

0007 0022 0007 and 0013 for RM WA SM BW BC YB and AB respectively Because of

these moderate to small ranges the low R2 values of the prediction equations and some of the

prediction equations not being significant you might argue that the mean bark factor yields an

adequate prediction model

The stemwood and topwood mean BFs were compared for each of the species The resulting

P-values are as follows

Species Bartletts zLtest

for Equal Variances F-test for Equal

Regression Coefficients

RM 0013 0681 WA 0770 0202 SM 0775 0287 BW 0196 0004 BC 0004 0001 YB 0222 0055 AB 0005 0542

Bonferroni level of significance a PC =00057 =0007

The above results indicate that the two means for RM W A SM YB and AB can be pooled while

some prediction accuracy will be lost if the two means for BW and BC are pooled (See the two

means shown for each species earlier in the paper) Note that there is no topwood for the one AE

tree in the data set Therefore the pooled mean is the stemwood mean for AE

-15shy

The pooled mean bark factors are

903 (54) RM middot BF = BF = L Bfl 903 = 0980 0015980

i=1

485 (55) WA BF = BF = L Bfl485 = 0932 0023614

i=1

1830 (56) SM BF= BF= L Bfl1830 = 0976 0015029

i=1

436 (57) BW BF = BF = L Bfl436 = 0970 0013134

i=l

210 (58) BC BF = BF = L Bfl210 = 0966 0014725

i=l

92 (59) YB BF = BF = L BFi92 = 0990 0004025

i=l

175 (60) AB BF = BF = L BF)l75 = 0995 0004248

i=1

See the table based on Equations 47-53 to see where Equations 54-60 under- and overestimate

respectively

Bark thickness

For the stemwood data set (n=3506) BT was significantly different for the eight different

species (Bartletts x2 -test for equal variances PltOOOl F-test for equal means PltOOOl) All

Bonferroni pairwise comparisons of means are significantly different except for (RM YB) (RM

AE) (WA AE) (SM AE) (BW AE) (BC AE) (YB AB) and (BW BC) Note that the sample

size for AE is only 6

Average minimum and maximum BTs and Pearsons correlations of BT with DOB DBH

and TH are shown below for the eight species

-16shy

BT BTDOB BTDBH BTTHSpecies nx Min-Max r p r p r p

RM 0077 0005-0525 0678 lt0001 0484 lt0001 -0369 lt0001 829 WA 0263 0012-1760 0632 lt0001 0428 lt0001 -0329 lt0001 410 SM 0113 0008-0672 0794 lt0001 0685 lt0001 -0293 lt0001 1488 BW 0158 0005-0525 0738 lt0001 0633 lt0001 -0192 lt0001 398 BC 0145 0012-0438 0653 lt0001 0169 0024 -0683 lt0001 178 YB 0046 0020-0115 0448 lt0001 0234 0058 -0383 0002 66 AB 0024 0005-0395 0236 0007 0067 0448 -0229 0009 131 AE 0195 0170-0228 -0511 0300 0405 0425 6

AE data consists of six measurements from one tree

BT was significantly positively related to DOB for all species except for AE where there was a

negative relation that was not significant BT was significantly positively related to DBH for all

species except for YB and AB where the positive relations were not significant BT was

significantly negatively related to TH for all species except for AE where there was a positive

relationship that was not significant

Average BTs for various DOB and TH classes for the eight species are as follows

DOB Class BT (in) RM WA SM BW BC YB AB AE

~400

401 to 800 801 to 1200 1201 to 1600

gt1600

0017 0054 0134 0239 0236

0091 0220 0321 0394 0468

0024 0060 0141 0225 0324

0032 0093 0150 0119 0268

0058 0101 0192 0252 0199

0020 0032 0048 0060 0058

0022 0019 0019 0020 0048

0200 0170

THClass BT (ft) RM WA SM BW BC YB AB AE

~050 0134 0208 0146 0114 0263 0038 0036 051 to 450 0110 0338 0161 0199 0192 0057 0038 0180 451 to 1000 0080 0296 0105 0165 0169 0047 0021 1001 to 2000 0065 0278 010(1 0153 0140 0049 0016 0210 2001 to 3000 0060 0250 0094 0146 0102 0041 0016 0200 3001 to 4000 0045 0220 0089 0134 0087 0037 0014 0190 4001 to 5000 0038 0220 0062 0153 0061 0025 0015

~5000 0016 0159 0047 0136 0038 0016

-17shy

In general BT is smallest for AB followed by YB RM SM BC BW and AE in increasing order

with BT for WA being the largest In general BT increases with DOB and decreases with TH

Most of the anomalies are due to small sample sizes

For the topwood data set (n=631) BT was significantly different for the seven different

species (Bartletts -test for equal variances PltOOOl F-test for equal means PltOOOl) All

Bonferroni pairwise comparisons of means are significantly different except for (RM SM) (RM

BC) (RM YB) (SM BC) (BC YB) and (YB AB)

Average minimum and maximum BTs and Pearsons correlations of BT with DOB and DBH

are shown below for the seven species

Species x

BT

Min- Max

BT DOB p r

BTDBH p n

RM WA SM BW BC YB AB

0064 0203 0086 0150 0083 0034 0019

0008-0385 0022-0458 0005-0362 0018-0262 0018-0175 Ool5-0075 0008-0038

06SO 0723 0768 0813 0723 0464 0051

lt0001 lt0001 lt0001 lt0001 lt0001

0017 0744

0549 0360 0440 0588 0380 0216 0661

lt0001 0002

lt0001 lt0001

0032 0290

lt0001

74 75

342 38 32 26 44

BT was significantly positively related to DOB for all species except for AB and to DBH for all

species except for YB

Average BTs for various DOB classes for the seven species are as follows

DOB Class BT (in) RM WA S~t BW BC YB AB

500 OQl8 0126 oltH) 0054 0051 0024 0021 501 to 700 0073 0212 () t)(J 0105 0086 0032 0019 701 to 900 0152 0281 () Ill 0170 0115 0057 0015 901 to 1100 0158 0255 () 177 0193 0114 0043 0020

111 to 1300 0122 0345 0222 0205 0135 0026

-18shy

In general BT is smallest for AB followed by YB BC RM SM and BW in increasing order

with BT for W A being the largest In general BT increases with DOB Most of the anomalies are

due to small sample sizes

Comparison with other BF equations

Fowler (1993) showed that while there were significant species differences between BF

equations for aspen jack pine and red pine there was a very strong relationship between BF and

tree height for each species (ie R 2 gt097 for each species) BF was a function of TH and In TH

showing that BF increased with TH to some maximum and then decreased for larger THs with the

steepness of the decrease depending on the species For all three species BF was not strongly

related to DBH or DOB at a given TH

For paper birch (Fowler and Hussain 1997) BF significantly increased with DOB at TH

(R2 =0219) and significantly decreased with In TH (R2 =0166) for stemwood while BF

significantly increased with DOB for topwood ( R 2 =0218) BF was much more variable than for

aspen red pine and jack pine

Fowler et al (1997) showed that black oak (BO) red oak (RO) and white oak (WO) have BPs

that are quite variable and prediction equations with the same independent variables as for paper

birch with the direction of the relations reversed For stemwood BF decreased with DOB at TH

( R 2 =0270 0418 and 0014 for BO RO and WO respectively) and increased with In TH ( R 2 =

0190 0275 and 0011 for BO RO and WO respectively) For topwood BF decreased with DOB

(R2=0366 0457 and 0100 for BO RO and WO respectively) These prediction equations were

significant but they were only moderately strong at best being only somewhat stronger in general

than the prediction equations for paper birch The prediction equations based on DOB were

-19shy

somewhat stronger than the prediction equations based on In TH The BF equations were

significantly different for the three species and for topwood versus stemwood except for RO

This study shows that the eight northern hardwood species have BFs that are quite variable

with some species having prediction equations with the same independent variables as for paper

birch and the three oak species while other species had different independent variables For

stemwood BF decreased with DOB at TH for RM SM BW and BC increased with In DOB at TH

for W A YB and AE and increased and then somewhat decreased with 1DOB and In DOB as the

independent variables for AB BF increased with In TH for RM SM and BC decreased and then

increased with TH and In TH for WA and BW increased and then decreased with TH and In TH for

YB AB and AE The prediction equations for AE are very suspect as they were based on only six

BF measurements from one tree For topwood BF decreased with DOB for RM WA SM BW

and BC increased with DOB for YB and increased and somewhat decreased with 1DOB and

In DOB for AB All prediction equations for stemwood were significant except for the TH

equations for BW and YB For topwood only the prediction equations for RM SM BW and AB

were significant In general all prediction equations were only moderately strong at best and some

of them were very weak The BF equations were significantly different for most species while the

stemwood and topwood BF equations were not significantly different except for RM and SM

GUIDELINES FOR USERS

We recommend use of the following equations for northern hardwoods when accurate

estimates of bark factors are desired

Stemwood

bull Red maple I

(1) BF =0996730-0002397 bull DOB I

(2) BF =0972344 + 0003554 bull In TH

-20shy

bull White ash 1

(3) BF = 0922166 +0001198bull DOB 1

(4) BF = 0937036 + 0000805 bull TH- 0009279 bullIn TH

bull- Sugar maple 1

(5) BF=0988318-0001497bullDOB 1

(6) BF = 0970865 + 0002264 bullIn TH

bull Basswood 1

(7) BF = 0974486-0000403 bull DOB 1

(8) BF = 0970312 + 0000072 bull TH- 0000631bullln TH

bull Black cherry 1

(9) BF = 0971912 -0000841bull DOB 1

(lO) BF = 0954777 + 0004557 bullIn TH

bull Yell ow birch 1

(11) BF = 0987390 + 0000307 bull DOB 1

(12) BF = 0990354-0000111bull TH+0000885bullln TH

bull American beech 1

(l3) BF = l027382-0l03065DOB -0009012bullln DOB

1

(14) BF = 0994075-0000047 bull TH+0000896 bullIn TH

bull American elm 1

(l5) BF =0925851 + 0003400 bull DOB 1

(16) BF = 0975815-0000058 bull TH- 0()()4696bullln TH

Use Equations 1 3 5 7 9 11 13 and 15 if DOBis measured Use Equations 2 4 6 8 10 12 14

and 16 when only THis measured

Topwood 1

(l7) RM BF = 1006791-0004569 bull DOB 1

(18) WA BF = 0936727 -0000206bull DOB 1

(l9) SM BF = 0995302-0002757 bull DOB

-21shy

(20) BW BF = 0979121-0002155 bull DOB

(21) BC BF = 0977830- 0000604 bull DOB

(22) YB BF = 0987032 + 0000281bull DOB

(23) AB BF = 1038966- 0131661DOB - 0012832 bullln DOB

The equation for stemwood and topwood pooled could be used if DOB is measured with moderate

loss in accuracy for RM and SM and little loss in accuracy for the other five species The pooled

equations in general will be more accurate for stemwood compared to topwood especially for RM

and SM

(24) RM BF == 0997087 -0002476bull DOB

1

(25) WA BF = 0924553 + 000 I 003 bull DOB

(26) SM BF=0988615-0001568bullDOB

(27) BW BF = 0972865-0000320 bull DOB

(28) BC BF=0974512-0001028bullDOB

(29) YB BF = 0986997 + 0000334 bull DOB

(30) AB BF = 1028314- 0105996DOB- 0009288 bullIn DOB

There is no pooled equation for AE as there was no topwood for the one AE tree in the data set

For reasonable accuracy in many situations the following constants could be used for bark

factors

DOB Class Stemwood BF (in) RM WA St-1 BW BC YB AB AE

DOBs50 0988 0927 09S~ 0973 0969 0989 0988 0939 50ltDOBsl00 0979 0931 0977 0971 0966 0990 0995 0951 l00ltDOBs150 0967 0937 0970 0969 0962 0991 0996 0968 150ltDOBs200 0955 0943 0962 0967 0957 0993 0996 0985

DOBgt200 0943 0949 0954 0965 0953 0994 0995 0994

-22shy

DOB Class ToEwoodBF (in) RM WA SM BW BC YB AB

DOBS50 0989 0936 0984 0971 0975 0988 0987 50ltD0BSl00 0970 0935 0973 0962 0973 0989 0995 100ltD0BS150 0947 0934 0959 0951 0970 0991 0996 150ltD0BS200 0924 0933 0946 0940 0967 0992 0995

008gt200 0902 0932 0932 0930 0964 0993 0993

TH Stemwood BF (ft) RM WA SM BW BC YB AB AE

THS05 0970 0947 0971 0971 0950 0990 0993 0980 05ltTHS45 0974 0932 olJn 0970 0959 0991 0995 0972

45ltTHS 100 0978 0925 0974 0970 0964 0991 0996 0966 100ltTHS200 0980 0924 0gt76 0970 0967 0991 0996 0963 200ltTHS300 0984 0928 0gt7S 0970 0970 0990 0996 0959 300ltTHS400 0986 0932 OltJSO 0971 0971 0990 0996 0957 400ltTHS500 0988 0937 () l)S~ 0971 0972 0989 0995 0955

THgt500 0992 0950 07 0974 0974 0987 0995 0952

The following constants for bark factor could be used for simplicity with moderately

approximate results especially for a large number of treessticks

Species Stem wood Top wood Stemwood and Topwood

RM 0980 0981 0980 WA 0932 0935 0932 SM 0976 0977 0976 BW 0970 0962 0970 BC 0965 0974 0966 YB 0991 0989 0990 AB 0995 0995 0995 AE 0964 0964

The above constants would be more accurate for those species that did not have significant

prediction equations andor small sample sizes B~ cry careful with using any of the results of this

study outside the range of the data set for each species Since the results for AE are based on six

stemwood measurements from one tree they arc of course very suspect

-23shy

Use of prediction equations

The prediction equations can be used to estimate BF at any DOB andor TH Since

BF=DIBDOB DIB can be estimated as DIB=BFbull DOB and DOB can be estimated as

DOB=DIBBF Past DOB and DOB growth can be estimated from past DIB growth as follows

Past DOB Growth=Past DIB GrowthBF

and

Past DOB=Present DOB -Past DOB Growth

where past DIB growth might be obtained with an increment borer

Specific uses of the prediction equations include (1) estimation of the solid wood and bark

volume of standing trees (2) estimation of bark volume or peeled volume from unpeeled volume

of felled tree sections (3) growth studies and (4) estimating tree form (eg Girard Form Class)

See Husch et al ( 1982) for a detailed discussion on bark factors

-24- LITERATURE CITED middot

Fowler G W 1991 An aspen bark factor equation for Michigan North J Appl For 8(1) 12-15

Fowler G W 1993 A jack pine bark factor equation for Michigan North J Appl For 10(2) 86-89

Fowler G W and L J Damschroder 1988 A red pine bark factor equation for Michigan North J Appl For 5(1) 28-30

Fowler G W and N G Hussain 1987a Bark factor equation for red pine Michigan DNR For Infor Leaflet 1-87 2 p

Fowler G W and N G Hussain 1987b Bark factor equation for aspen Michigan DNR For Infor Leaflet 2-87 2 p

Fowler G W and N G Hussain 1991 Bark factor equation for jack pine in Michigan Michigan DNR For Infor Leaflet 1-91 5 p

Fowler G W and N G Hussain 1997 Bark factor equations for paper birch in Michigan Michigan DNR For Infor Leaflet 1-97 12 p

Fowler G W N G Hussain D J Cohen and D Khatry-Chhetri 1997 Bark factor equations for oak in Michigan Michigan DNR For Infor Leaflet 2-97 15 p

Husch B C I Miller and T W Beers 1982 Forest Mensuration John Wiley and Sons Inc NY 402 p

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lonst Manbullpmeut DWisioa 15 Resource Mana1ement Units

bullJfectble l2519bull

bull -Resource Jf~nt Unit OJke

1 -Raource Jf~nt Unit BOUIIdariea

1 -CountyBouruiiJrfea

-9shy

- 829 (25) RM BF = BF =I BFJ829 =0980 0015671

i=l

- 410 26) WA BF = BF = I BFJ410 = 0932 0023692

i=l

1488 (27) SM BF = BF = L Bfi1488 = 0976 0014991

i=1

398 (28) BW BF = BF = L Bfi 398 = 0970 0013115

i=1

178 (29) BC BF = BF = L Bfi179 = 0965 0015086

i=1

66 (30) YB BF = BF = L BFi66 = 0991 0003720

i=1

131 (31) AB BF = BF = L Bfi131 = 0995 0004566

i=1

6 (32) AE BF = BF =L BFJ6 =0964 0007831

i=1

See the above two tables to find where Equations 25-32 over- and underestimate related to

Equations 1-24-57-8 lO-ll 13-14 16-17 19-20 and 22-23 respectively

Prediction Equations 1 4 7 10 13 16 and 22 are significantly different (Bartletts x 2 -test

for equal variances Plt0005 F-test for equal slopes Plt0001) Prediction Equations 2 8 and 14

are significantly different (Bartletts i-test for equal variances Plt010 F-test for equal slopes

PltOOO 1) Prediction Equations 5 11 17 20 and 23 are significantly different (Bartletts i -test

for equal variances Plt0005 F-test for equal slopes Plt0001) Prediction Equations 27-32 related

to mean bark factors are also significantly different (Bartletts x 2 -test for equal variances Plt0005

F-test for equal means Plt0001) All Bonferroni pairwise comparisons of means are significantly

-10shy

different (Plt0003) except for (RM AE) (SM AE) (BW AE) (BC AE) and (YB AB) Note that

the sample size for AE is only 6

Topwood R2 psybullx n

1

(33) RM BF = 1006791 - 0004569 bull DOB 0245 0016815 lt0001 74 1

(34) WA BF = 0936727 - 0000206 bull DOB 0000 0023230 0866 75 1

(35) SM BF = 0995302-0002757 bull DOB 0201 0013598 lt0001 342 1

(36) BW BF = 0979121-0002155bull DOB 0135 0010484 0023 38 1

(37) BC BF = 0977830-0000604 bull DOB 0017 0009709 0478 32

1

(38) YB BF = 0987032 + 0000281 bull DOB 0012 0004606 0593 26 1

(39) AB BF = 1038966-0131661DOB 0463 0002353 lt0001 44

-0012832bulllnDOB

Prediction Equations 33-39 for RM W A SM BW BC YB and AB respectively yield the

following estimated bark factors

Prediction Equations 33-39

DOB 1

BF (in) RM WA SM BW BC YB AB

30 0993 0936 0987 0973 0976 0988 0981 40 0989 0936 0984 0971 0975 0988 0988 50 0984 0936 0982 0968 0975 0988 0992 60 0979 0935 0979 0966 0974 0989 0994 70 0975 0935 0976 0964 0974 0989 0995 80 0970 0935 0973 0962 0973 0989 0996 90 0966 0935 0970 0960 0972 0990 0996

100 0961 0935 0968 0958 0972 0990 0996 110 0957 0934 0965 0955 0971 0990 0996 120 0952 0934 0962 0953 0971 0990 0996 130 0947 0934 0959 0951 0970 0991 0996 140 0943 0934 0957 0949 0969 0991 OQ96 150 0938 0934 0954 0947 0969 0991 0995 160 0934 0933 0951 0945 0968 0992 0995 170 0929 0933 0948 0942 0968 0992 0995 180 0924 0933 0946 0940 0967 0992 0995 190 0920 0933 0943 0938 0966 0992 0994 200 0915 0933 0940 0936 0966 0993 0994

-11shy

The ranges of predicted BF values for DOB from 30 to 200 in are 0078 0003 0047 0037

0010 0005 and 0015 for RM WA SM BW BC YB and AB respectively Because of these

moderate to small ranges the low R 2 values of the prediction equations the moderate sample sizes

and some of the prediction equations not being significant at a=005 you might argue that the mean

bark factor yields an adequate prediction model (except possibly for RM)

74 (40) RM BF = BF =I BFi74 = 0981 0019213

i=l 75

(41) WA BF = BF =I B~75 = 0935 0023077 i=l 342

(42) SM BF = BF = I B~ 342 = 0977 0015190 i=l 38

(43) BW BF = BF =I BFi38 =0962 0011118 i=l

32 (44) BC BF = BF =I BFi32 = 0974 0009633

i=l

26 (45) YB BF = BF =I Bfi 26 = 0989 0004540

i=l

44 (46) AB BF=BF= I BFi44=0995 0003135

i=l

See the above table to find where Equations 40-46 over- and underestimate reflected to Equations

33-39 respectively

Prediction Equations 33-38 are significant y different (Bartletts 12 -test for equal variances

Plt0005 F-test for equal slopes P=OOOl) Prediction Equations 40-46 related to mean bark factors

are also significantly different (Bartletts -test for equal variances Plt0005 F-test for equal

-12shy

means PltOOOl) All Bonferroni pairwise comparisons of means are significantly different

(Plt005) except for (RM SM) (RM BC) (RM YB) (SM BC) and (YB AB)

Pooled prediction equations

The stemwood and topwood BF prediction equations with DOB as the independent variable

were compared for each of the species except for AB where the independent variables were 1DOB

and ln DOB The resulting P-values are as follows

Bartletts z2 -test F-test for Equal Species for Equal Variances Regression Coefficients

RM P=005+ P=OOOl WA P=01 P=0267 SM P=0862 PltOOOl BW P=OOlJ-+ P=0120 BC P=0005 P=0854 YB P=0106 P=0954 AB PltOOOI P=0942

Bonferroni level of significance a=OOS7=0007

The above results indicate that the two equations for WA BW BC YB and AB can be pooled

while some prediction accuracy will be lost if the two equations for RM and SM are pooled (See the

two equations shown for each species earlier in this paper) Note that there is no lopwood for the

one AE tree in the data set Therefore the pooled equation is the stemwood equation for AE

The pooled prediction equations are

R2 sybullx p n

A

(47) RM BF =0997087 -0002476bull DOB 0166 0014604 lt0001 903

A

(48) WA BF =0924553 + 0001003 bull DOB 0021 0023385 0001 485

A

(49) SM BF =0988615-0001568 bull DOB (Jl64 0013748 lt0001 1830

A

(50) BW BF =0972865-0000320 bull DOB 00 lO 0013085 0040 436

A

(51) BC BF =0974512 -0001028bull DOB 0041 0014455 0003 210

A

(52) YB BF =0986997 + 0000334 bull DOB 0107 0003825 0001 92

-13shy

R2 sybullx p n

1

(53) AB BF =1028314- 0105996DOB 0201 0003819 lt0001 175

- 0009288 bull In DOB

Prediction equations 47-53 for RM WA SM BW BC YB and AB respectively yield the

following estimated bark factors

Prediction Equations 47-53

1

DOB BF (in) RM WA SM BW BC YB AB

30 0990 0928 0984 0972 0971 0988 0983 40 0987 0929 0982 0972 0970 0988 0989 50 0985 0930 0981 0971 0969 0989 0992 60 0982 0931 0979 0971 0968 0989 0994 70 0980 0932 0978 0971 0967 0989 0995 80 0977 0933 0976 0970 0966 0989 0996 90 0975 0934 0975 0970 0965 0990 0996

100 0972 0935 0973 0969 0964 0990 0996 110 0970 0936 0971 0969 0963 0991 0996 120 0967 0937 0970 0969 0962 0991 0996 130 0965 0938 0968 0968 0961 0991 0996 140 0962 0939 0967 0968 0960 0992 0996 150 0960 0940 0965 0968 0959 0992 0996 160 0957 0941 0964 0968 0958 0992 0996 170 0955 0942 0962 0967 0957 0993 0996 180 0953 0943 0960 0967 0956 0993 0996 190 0950 0944 0959 0967 0955 0993 0995 200 0948 0945 0957 0966 0954 0994 0995 210 0945 0946 0956 0966 0953 0994 0995 220 0943 0947 0954 0966 0952 0994 0995 230 0940 0948 0953 0966 0951 0995 0995 240 0938 0949 0951 0965 0950 0995 0994 250 0935 0950 0949 0965 0949 0995 0994

Note that the pooled BF estimates for each species are close to those of Equations 1 4 7 10

13 16 and 19 for stemwood This makes sense since the stemwood sample sizes were considerably

larger than the topwood sample sizes for each species For topwood the pooled BF estimates for

YB and AB are very close to Equations 38 and 39 respectively for topwood However there are

some larger differences for the other species over the range of DOB from 30-200 inches

-14shy

bull RM - Pooled BF estimates are lower than those of Equation 33 for DOB lt 50 in and higher for DOB ~ 50 in (from 0003 lower to 0033 higher)

bull WA - Pooled BF estimates are lower than those of Equation 34 for DOB lt 100 in and higher for DOB gt 100 in (from 0008 lower to 0012 higher)

bull SM - Pooled BF estimates are lower than those of Equation 35 for DOB lt 60 in and higher for DOB gt 60 in (from 0003 lower to 0017 higher)

bull BW - Pooled BF estimates are lower than those of Equation 36 for DOB lt 40 in and higher for DOB ~ 40 in (from 0001 lower to 0030 higher)

bull BC - Pooled BF estimates are lower than those of Equation 37 for all values of DOB (from 0005 to 0012lower)

The ranges of the pooled predicted BF values for DOB from 30 to 250 in are 0055 0022 0035

0007 0022 0007 and 0013 for RM WA SM BW BC YB and AB respectively Because of

these moderate to small ranges the low R2 values of the prediction equations and some of the

prediction equations not being significant you might argue that the mean bark factor yields an

adequate prediction model

The stemwood and topwood mean BFs were compared for each of the species The resulting

P-values are as follows

Species Bartletts zLtest

for Equal Variances F-test for Equal

Regression Coefficients

RM 0013 0681 WA 0770 0202 SM 0775 0287 BW 0196 0004 BC 0004 0001 YB 0222 0055 AB 0005 0542

Bonferroni level of significance a PC =00057 =0007

The above results indicate that the two means for RM W A SM YB and AB can be pooled while

some prediction accuracy will be lost if the two means for BW and BC are pooled (See the two

means shown for each species earlier in the paper) Note that there is no topwood for the one AE

tree in the data set Therefore the pooled mean is the stemwood mean for AE

-15shy

The pooled mean bark factors are

903 (54) RM middot BF = BF = L Bfl 903 = 0980 0015980

i=1

485 (55) WA BF = BF = L Bfl485 = 0932 0023614

i=1

1830 (56) SM BF= BF= L Bfl1830 = 0976 0015029

i=1

436 (57) BW BF = BF = L Bfl436 = 0970 0013134

i=l

210 (58) BC BF = BF = L Bfl210 = 0966 0014725

i=l

92 (59) YB BF = BF = L BFi92 = 0990 0004025

i=l

175 (60) AB BF = BF = L BF)l75 = 0995 0004248

i=1

See the table based on Equations 47-53 to see where Equations 54-60 under- and overestimate

respectively

Bark thickness

For the stemwood data set (n=3506) BT was significantly different for the eight different

species (Bartletts x2 -test for equal variances PltOOOl F-test for equal means PltOOOl) All

Bonferroni pairwise comparisons of means are significantly different except for (RM YB) (RM

AE) (WA AE) (SM AE) (BW AE) (BC AE) (YB AB) and (BW BC) Note that the sample

size for AE is only 6

Average minimum and maximum BTs and Pearsons correlations of BT with DOB DBH

and TH are shown below for the eight species

-16shy

BT BTDOB BTDBH BTTHSpecies nx Min-Max r p r p r p

RM 0077 0005-0525 0678 lt0001 0484 lt0001 -0369 lt0001 829 WA 0263 0012-1760 0632 lt0001 0428 lt0001 -0329 lt0001 410 SM 0113 0008-0672 0794 lt0001 0685 lt0001 -0293 lt0001 1488 BW 0158 0005-0525 0738 lt0001 0633 lt0001 -0192 lt0001 398 BC 0145 0012-0438 0653 lt0001 0169 0024 -0683 lt0001 178 YB 0046 0020-0115 0448 lt0001 0234 0058 -0383 0002 66 AB 0024 0005-0395 0236 0007 0067 0448 -0229 0009 131 AE 0195 0170-0228 -0511 0300 0405 0425 6

AE data consists of six measurements from one tree

BT was significantly positively related to DOB for all species except for AE where there was a

negative relation that was not significant BT was significantly positively related to DBH for all

species except for YB and AB where the positive relations were not significant BT was

significantly negatively related to TH for all species except for AE where there was a positive

relationship that was not significant

Average BTs for various DOB and TH classes for the eight species are as follows

DOB Class BT (in) RM WA SM BW BC YB AB AE

~400

401 to 800 801 to 1200 1201 to 1600

gt1600

0017 0054 0134 0239 0236

0091 0220 0321 0394 0468

0024 0060 0141 0225 0324

0032 0093 0150 0119 0268

0058 0101 0192 0252 0199

0020 0032 0048 0060 0058

0022 0019 0019 0020 0048

0200 0170

THClass BT (ft) RM WA SM BW BC YB AB AE

~050 0134 0208 0146 0114 0263 0038 0036 051 to 450 0110 0338 0161 0199 0192 0057 0038 0180 451 to 1000 0080 0296 0105 0165 0169 0047 0021 1001 to 2000 0065 0278 010(1 0153 0140 0049 0016 0210 2001 to 3000 0060 0250 0094 0146 0102 0041 0016 0200 3001 to 4000 0045 0220 0089 0134 0087 0037 0014 0190 4001 to 5000 0038 0220 0062 0153 0061 0025 0015

~5000 0016 0159 0047 0136 0038 0016

-17shy

In general BT is smallest for AB followed by YB RM SM BC BW and AE in increasing order

with BT for WA being the largest In general BT increases with DOB and decreases with TH

Most of the anomalies are due to small sample sizes

For the topwood data set (n=631) BT was significantly different for the seven different

species (Bartletts -test for equal variances PltOOOl F-test for equal means PltOOOl) All

Bonferroni pairwise comparisons of means are significantly different except for (RM SM) (RM

BC) (RM YB) (SM BC) (BC YB) and (YB AB)

Average minimum and maximum BTs and Pearsons correlations of BT with DOB and DBH

are shown below for the seven species

Species x

BT

Min- Max

BT DOB p r

BTDBH p n

RM WA SM BW BC YB AB

0064 0203 0086 0150 0083 0034 0019

0008-0385 0022-0458 0005-0362 0018-0262 0018-0175 Ool5-0075 0008-0038

06SO 0723 0768 0813 0723 0464 0051

lt0001 lt0001 lt0001 lt0001 lt0001

0017 0744

0549 0360 0440 0588 0380 0216 0661

lt0001 0002

lt0001 lt0001

0032 0290

lt0001

74 75

342 38 32 26 44

BT was significantly positively related to DOB for all species except for AB and to DBH for all

species except for YB

Average BTs for various DOB classes for the seven species are as follows

DOB Class BT (in) RM WA S~t BW BC YB AB

500 OQl8 0126 oltH) 0054 0051 0024 0021 501 to 700 0073 0212 () t)(J 0105 0086 0032 0019 701 to 900 0152 0281 () Ill 0170 0115 0057 0015 901 to 1100 0158 0255 () 177 0193 0114 0043 0020

111 to 1300 0122 0345 0222 0205 0135 0026

-18shy

In general BT is smallest for AB followed by YB BC RM SM and BW in increasing order

with BT for W A being the largest In general BT increases with DOB Most of the anomalies are

due to small sample sizes

Comparison with other BF equations

Fowler (1993) showed that while there were significant species differences between BF

equations for aspen jack pine and red pine there was a very strong relationship between BF and

tree height for each species (ie R 2 gt097 for each species) BF was a function of TH and In TH

showing that BF increased with TH to some maximum and then decreased for larger THs with the

steepness of the decrease depending on the species For all three species BF was not strongly

related to DBH or DOB at a given TH

For paper birch (Fowler and Hussain 1997) BF significantly increased with DOB at TH

(R2 =0219) and significantly decreased with In TH (R2 =0166) for stemwood while BF

significantly increased with DOB for topwood ( R 2 =0218) BF was much more variable than for

aspen red pine and jack pine

Fowler et al (1997) showed that black oak (BO) red oak (RO) and white oak (WO) have BPs

that are quite variable and prediction equations with the same independent variables as for paper

birch with the direction of the relations reversed For stemwood BF decreased with DOB at TH

( R 2 =0270 0418 and 0014 for BO RO and WO respectively) and increased with In TH ( R 2 =

0190 0275 and 0011 for BO RO and WO respectively) For topwood BF decreased with DOB

(R2=0366 0457 and 0100 for BO RO and WO respectively) These prediction equations were

significant but they were only moderately strong at best being only somewhat stronger in general

than the prediction equations for paper birch The prediction equations based on DOB were

-19shy

somewhat stronger than the prediction equations based on In TH The BF equations were

significantly different for the three species and for topwood versus stemwood except for RO

This study shows that the eight northern hardwood species have BFs that are quite variable

with some species having prediction equations with the same independent variables as for paper

birch and the three oak species while other species had different independent variables For

stemwood BF decreased with DOB at TH for RM SM BW and BC increased with In DOB at TH

for W A YB and AE and increased and then somewhat decreased with 1DOB and In DOB as the

independent variables for AB BF increased with In TH for RM SM and BC decreased and then

increased with TH and In TH for WA and BW increased and then decreased with TH and In TH for

YB AB and AE The prediction equations for AE are very suspect as they were based on only six

BF measurements from one tree For topwood BF decreased with DOB for RM WA SM BW

and BC increased with DOB for YB and increased and somewhat decreased with 1DOB and

In DOB for AB All prediction equations for stemwood were significant except for the TH

equations for BW and YB For topwood only the prediction equations for RM SM BW and AB

were significant In general all prediction equations were only moderately strong at best and some

of them were very weak The BF equations were significantly different for most species while the

stemwood and topwood BF equations were not significantly different except for RM and SM

GUIDELINES FOR USERS

We recommend use of the following equations for northern hardwoods when accurate

estimates of bark factors are desired

Stemwood

bull Red maple I

(1) BF =0996730-0002397 bull DOB I

(2) BF =0972344 + 0003554 bull In TH

-20shy

bull White ash 1

(3) BF = 0922166 +0001198bull DOB 1

(4) BF = 0937036 + 0000805 bull TH- 0009279 bullIn TH

bull- Sugar maple 1

(5) BF=0988318-0001497bullDOB 1

(6) BF = 0970865 + 0002264 bullIn TH

bull Basswood 1

(7) BF = 0974486-0000403 bull DOB 1

(8) BF = 0970312 + 0000072 bull TH- 0000631bullln TH

bull Black cherry 1

(9) BF = 0971912 -0000841bull DOB 1

(lO) BF = 0954777 + 0004557 bullIn TH

bull Yell ow birch 1

(11) BF = 0987390 + 0000307 bull DOB 1

(12) BF = 0990354-0000111bull TH+0000885bullln TH

bull American beech 1

(l3) BF = l027382-0l03065DOB -0009012bullln DOB

1

(14) BF = 0994075-0000047 bull TH+0000896 bullIn TH

bull American elm 1

(l5) BF =0925851 + 0003400 bull DOB 1

(16) BF = 0975815-0000058 bull TH- 0()()4696bullln TH

Use Equations 1 3 5 7 9 11 13 and 15 if DOBis measured Use Equations 2 4 6 8 10 12 14

and 16 when only THis measured

Topwood 1

(l7) RM BF = 1006791-0004569 bull DOB 1

(18) WA BF = 0936727 -0000206bull DOB 1

(l9) SM BF = 0995302-0002757 bull DOB

-21shy

(20) BW BF = 0979121-0002155 bull DOB

(21) BC BF = 0977830- 0000604 bull DOB

(22) YB BF = 0987032 + 0000281bull DOB

(23) AB BF = 1038966- 0131661DOB - 0012832 bullln DOB

The equation for stemwood and topwood pooled could be used if DOB is measured with moderate

loss in accuracy for RM and SM and little loss in accuracy for the other five species The pooled

equations in general will be more accurate for stemwood compared to topwood especially for RM

and SM

(24) RM BF == 0997087 -0002476bull DOB

1

(25) WA BF = 0924553 + 000 I 003 bull DOB

(26) SM BF=0988615-0001568bullDOB

(27) BW BF = 0972865-0000320 bull DOB

(28) BC BF=0974512-0001028bullDOB

(29) YB BF = 0986997 + 0000334 bull DOB

(30) AB BF = 1028314- 0105996DOB- 0009288 bullIn DOB

There is no pooled equation for AE as there was no topwood for the one AE tree in the data set

For reasonable accuracy in many situations the following constants could be used for bark

factors

DOB Class Stemwood BF (in) RM WA St-1 BW BC YB AB AE

DOBs50 0988 0927 09S~ 0973 0969 0989 0988 0939 50ltDOBsl00 0979 0931 0977 0971 0966 0990 0995 0951 l00ltDOBs150 0967 0937 0970 0969 0962 0991 0996 0968 150ltDOBs200 0955 0943 0962 0967 0957 0993 0996 0985

DOBgt200 0943 0949 0954 0965 0953 0994 0995 0994

-22shy

DOB Class ToEwoodBF (in) RM WA SM BW BC YB AB

DOBS50 0989 0936 0984 0971 0975 0988 0987 50ltD0BSl00 0970 0935 0973 0962 0973 0989 0995 100ltD0BS150 0947 0934 0959 0951 0970 0991 0996 150ltD0BS200 0924 0933 0946 0940 0967 0992 0995

008gt200 0902 0932 0932 0930 0964 0993 0993

TH Stemwood BF (ft) RM WA SM BW BC YB AB AE

THS05 0970 0947 0971 0971 0950 0990 0993 0980 05ltTHS45 0974 0932 olJn 0970 0959 0991 0995 0972

45ltTHS 100 0978 0925 0974 0970 0964 0991 0996 0966 100ltTHS200 0980 0924 0gt76 0970 0967 0991 0996 0963 200ltTHS300 0984 0928 0gt7S 0970 0970 0990 0996 0959 300ltTHS400 0986 0932 OltJSO 0971 0971 0990 0996 0957 400ltTHS500 0988 0937 () l)S~ 0971 0972 0989 0995 0955

THgt500 0992 0950 07 0974 0974 0987 0995 0952

The following constants for bark factor could be used for simplicity with moderately

approximate results especially for a large number of treessticks

Species Stem wood Top wood Stemwood and Topwood

RM 0980 0981 0980 WA 0932 0935 0932 SM 0976 0977 0976 BW 0970 0962 0970 BC 0965 0974 0966 YB 0991 0989 0990 AB 0995 0995 0995 AE 0964 0964

The above constants would be more accurate for those species that did not have significant

prediction equations andor small sample sizes B~ cry careful with using any of the results of this

study outside the range of the data set for each species Since the results for AE are based on six

stemwood measurements from one tree they arc of course very suspect

-23shy

Use of prediction equations

The prediction equations can be used to estimate BF at any DOB andor TH Since

BF=DIBDOB DIB can be estimated as DIB=BFbull DOB and DOB can be estimated as

DOB=DIBBF Past DOB and DOB growth can be estimated from past DIB growth as follows

Past DOB Growth=Past DIB GrowthBF

and

Past DOB=Present DOB -Past DOB Growth

where past DIB growth might be obtained with an increment borer

Specific uses of the prediction equations include (1) estimation of the solid wood and bark

volume of standing trees (2) estimation of bark volume or peeled volume from unpeeled volume

of felled tree sections (3) growth studies and (4) estimating tree form (eg Girard Form Class)

See Husch et al ( 1982) for a detailed discussion on bark factors

-24- LITERATURE CITED middot

Fowler G W 1991 An aspen bark factor equation for Michigan North J Appl For 8(1) 12-15

Fowler G W 1993 A jack pine bark factor equation for Michigan North J Appl For 10(2) 86-89

Fowler G W and L J Damschroder 1988 A red pine bark factor equation for Michigan North J Appl For 5(1) 28-30

Fowler G W and N G Hussain 1987a Bark factor equation for red pine Michigan DNR For Infor Leaflet 1-87 2 p

Fowler G W and N G Hussain 1987b Bark factor equation for aspen Michigan DNR For Infor Leaflet 2-87 2 p

Fowler G W and N G Hussain 1991 Bark factor equation for jack pine in Michigan Michigan DNR For Infor Leaflet 1-91 5 p

Fowler G W and N G Hussain 1997 Bark factor equations for paper birch in Michigan Michigan DNR For Infor Leaflet 1-97 12 p

Fowler G W N G Hussain D J Cohen and D Khatry-Chhetri 1997 Bark factor equations for oak in Michigan Michigan DNR For Infor Leaflet 2-97 15 p

Husch B C I Miller and T W Beers 1982 Forest Mensuration John Wiley and Sons Inc NY 402 p

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-10shy

different (Plt0003) except for (RM AE) (SM AE) (BW AE) (BC AE) and (YB AB) Note that

the sample size for AE is only 6

Topwood R2 psybullx n

1

(33) RM BF = 1006791 - 0004569 bull DOB 0245 0016815 lt0001 74 1

(34) WA BF = 0936727 - 0000206 bull DOB 0000 0023230 0866 75 1

(35) SM BF = 0995302-0002757 bull DOB 0201 0013598 lt0001 342 1

(36) BW BF = 0979121-0002155bull DOB 0135 0010484 0023 38 1

(37) BC BF = 0977830-0000604 bull DOB 0017 0009709 0478 32

1

(38) YB BF = 0987032 + 0000281 bull DOB 0012 0004606 0593 26 1

(39) AB BF = 1038966-0131661DOB 0463 0002353 lt0001 44

-0012832bulllnDOB

Prediction Equations 33-39 for RM W A SM BW BC YB and AB respectively yield the

following estimated bark factors

Prediction Equations 33-39

DOB 1

BF (in) RM WA SM BW BC YB AB

30 0993 0936 0987 0973 0976 0988 0981 40 0989 0936 0984 0971 0975 0988 0988 50 0984 0936 0982 0968 0975 0988 0992 60 0979 0935 0979 0966 0974 0989 0994 70 0975 0935 0976 0964 0974 0989 0995 80 0970 0935 0973 0962 0973 0989 0996 90 0966 0935 0970 0960 0972 0990 0996

100 0961 0935 0968 0958 0972 0990 0996 110 0957 0934 0965 0955 0971 0990 0996 120 0952 0934 0962 0953 0971 0990 0996 130 0947 0934 0959 0951 0970 0991 0996 140 0943 0934 0957 0949 0969 0991 OQ96 150 0938 0934 0954 0947 0969 0991 0995 160 0934 0933 0951 0945 0968 0992 0995 170 0929 0933 0948 0942 0968 0992 0995 180 0924 0933 0946 0940 0967 0992 0995 190 0920 0933 0943 0938 0966 0992 0994 200 0915 0933 0940 0936 0966 0993 0994

-11shy

The ranges of predicted BF values for DOB from 30 to 200 in are 0078 0003 0047 0037

0010 0005 and 0015 for RM WA SM BW BC YB and AB respectively Because of these

moderate to small ranges the low R 2 values of the prediction equations the moderate sample sizes

and some of the prediction equations not being significant at a=005 you might argue that the mean

bark factor yields an adequate prediction model (except possibly for RM)

74 (40) RM BF = BF =I BFi74 = 0981 0019213

i=l 75

(41) WA BF = BF =I B~75 = 0935 0023077 i=l 342

(42) SM BF = BF = I B~ 342 = 0977 0015190 i=l 38

(43) BW BF = BF =I BFi38 =0962 0011118 i=l

32 (44) BC BF = BF =I BFi32 = 0974 0009633

i=l

26 (45) YB BF = BF =I Bfi 26 = 0989 0004540

i=l

44 (46) AB BF=BF= I BFi44=0995 0003135

i=l

See the above table to find where Equations 40-46 over- and underestimate reflected to Equations

33-39 respectively

Prediction Equations 33-38 are significant y different (Bartletts 12 -test for equal variances

Plt0005 F-test for equal slopes P=OOOl) Prediction Equations 40-46 related to mean bark factors

are also significantly different (Bartletts -test for equal variances Plt0005 F-test for equal

-12shy

means PltOOOl) All Bonferroni pairwise comparisons of means are significantly different

(Plt005) except for (RM SM) (RM BC) (RM YB) (SM BC) and (YB AB)

Pooled prediction equations

The stemwood and topwood BF prediction equations with DOB as the independent variable

were compared for each of the species except for AB where the independent variables were 1DOB

and ln DOB The resulting P-values are as follows

Bartletts z2 -test F-test for Equal Species for Equal Variances Regression Coefficients

RM P=005+ P=OOOl WA P=01 P=0267 SM P=0862 PltOOOl BW P=OOlJ-+ P=0120 BC P=0005 P=0854 YB P=0106 P=0954 AB PltOOOI P=0942

Bonferroni level of significance a=OOS7=0007

The above results indicate that the two equations for WA BW BC YB and AB can be pooled

while some prediction accuracy will be lost if the two equations for RM and SM are pooled (See the

two equations shown for each species earlier in this paper) Note that there is no lopwood for the

one AE tree in the data set Therefore the pooled equation is the stemwood equation for AE

The pooled prediction equations are

R2 sybullx p n

A

(47) RM BF =0997087 -0002476bull DOB 0166 0014604 lt0001 903

A

(48) WA BF =0924553 + 0001003 bull DOB 0021 0023385 0001 485

A

(49) SM BF =0988615-0001568 bull DOB (Jl64 0013748 lt0001 1830

A

(50) BW BF =0972865-0000320 bull DOB 00 lO 0013085 0040 436

A

(51) BC BF =0974512 -0001028bull DOB 0041 0014455 0003 210

A

(52) YB BF =0986997 + 0000334 bull DOB 0107 0003825 0001 92

-13shy

R2 sybullx p n

1

(53) AB BF =1028314- 0105996DOB 0201 0003819 lt0001 175

- 0009288 bull In DOB

Prediction equations 47-53 for RM WA SM BW BC YB and AB respectively yield the

following estimated bark factors

Prediction Equations 47-53

1

DOB BF (in) RM WA SM BW BC YB AB

30 0990 0928 0984 0972 0971 0988 0983 40 0987 0929 0982 0972 0970 0988 0989 50 0985 0930 0981 0971 0969 0989 0992 60 0982 0931 0979 0971 0968 0989 0994 70 0980 0932 0978 0971 0967 0989 0995 80 0977 0933 0976 0970 0966 0989 0996 90 0975 0934 0975 0970 0965 0990 0996

100 0972 0935 0973 0969 0964 0990 0996 110 0970 0936 0971 0969 0963 0991 0996 120 0967 0937 0970 0969 0962 0991 0996 130 0965 0938 0968 0968 0961 0991 0996 140 0962 0939 0967 0968 0960 0992 0996 150 0960 0940 0965 0968 0959 0992 0996 160 0957 0941 0964 0968 0958 0992 0996 170 0955 0942 0962 0967 0957 0993 0996 180 0953 0943 0960 0967 0956 0993 0996 190 0950 0944 0959 0967 0955 0993 0995 200 0948 0945 0957 0966 0954 0994 0995 210 0945 0946 0956 0966 0953 0994 0995 220 0943 0947 0954 0966 0952 0994 0995 230 0940 0948 0953 0966 0951 0995 0995 240 0938 0949 0951 0965 0950 0995 0994 250 0935 0950 0949 0965 0949 0995 0994

Note that the pooled BF estimates for each species are close to those of Equations 1 4 7 10

13 16 and 19 for stemwood This makes sense since the stemwood sample sizes were considerably

larger than the topwood sample sizes for each species For topwood the pooled BF estimates for

YB and AB are very close to Equations 38 and 39 respectively for topwood However there are

some larger differences for the other species over the range of DOB from 30-200 inches

-14shy

bull RM - Pooled BF estimates are lower than those of Equation 33 for DOB lt 50 in and higher for DOB ~ 50 in (from 0003 lower to 0033 higher)

bull WA - Pooled BF estimates are lower than those of Equation 34 for DOB lt 100 in and higher for DOB gt 100 in (from 0008 lower to 0012 higher)

bull SM - Pooled BF estimates are lower than those of Equation 35 for DOB lt 60 in and higher for DOB gt 60 in (from 0003 lower to 0017 higher)

bull BW - Pooled BF estimates are lower than those of Equation 36 for DOB lt 40 in and higher for DOB ~ 40 in (from 0001 lower to 0030 higher)

bull BC - Pooled BF estimates are lower than those of Equation 37 for all values of DOB (from 0005 to 0012lower)

The ranges of the pooled predicted BF values for DOB from 30 to 250 in are 0055 0022 0035

0007 0022 0007 and 0013 for RM WA SM BW BC YB and AB respectively Because of

these moderate to small ranges the low R2 values of the prediction equations and some of the

prediction equations not being significant you might argue that the mean bark factor yields an

adequate prediction model

The stemwood and topwood mean BFs were compared for each of the species The resulting

P-values are as follows

Species Bartletts zLtest

for Equal Variances F-test for Equal

Regression Coefficients

RM 0013 0681 WA 0770 0202 SM 0775 0287 BW 0196 0004 BC 0004 0001 YB 0222 0055 AB 0005 0542

Bonferroni level of significance a PC =00057 =0007

The above results indicate that the two means for RM W A SM YB and AB can be pooled while

some prediction accuracy will be lost if the two means for BW and BC are pooled (See the two

means shown for each species earlier in the paper) Note that there is no topwood for the one AE

tree in the data set Therefore the pooled mean is the stemwood mean for AE

-15shy

The pooled mean bark factors are

903 (54) RM middot BF = BF = L Bfl 903 = 0980 0015980

i=1

485 (55) WA BF = BF = L Bfl485 = 0932 0023614

i=1

1830 (56) SM BF= BF= L Bfl1830 = 0976 0015029

i=1

436 (57) BW BF = BF = L Bfl436 = 0970 0013134

i=l

210 (58) BC BF = BF = L Bfl210 = 0966 0014725

i=l

92 (59) YB BF = BF = L BFi92 = 0990 0004025

i=l

175 (60) AB BF = BF = L BF)l75 = 0995 0004248

i=1

See the table based on Equations 47-53 to see where Equations 54-60 under- and overestimate

respectively

Bark thickness

For the stemwood data set (n=3506) BT was significantly different for the eight different

species (Bartletts x2 -test for equal variances PltOOOl F-test for equal means PltOOOl) All

Bonferroni pairwise comparisons of means are significantly different except for (RM YB) (RM

AE) (WA AE) (SM AE) (BW AE) (BC AE) (YB AB) and (BW BC) Note that the sample

size for AE is only 6

Average minimum and maximum BTs and Pearsons correlations of BT with DOB DBH

and TH are shown below for the eight species

-16shy

BT BTDOB BTDBH BTTHSpecies nx Min-Max r p r p r p

RM 0077 0005-0525 0678 lt0001 0484 lt0001 -0369 lt0001 829 WA 0263 0012-1760 0632 lt0001 0428 lt0001 -0329 lt0001 410 SM 0113 0008-0672 0794 lt0001 0685 lt0001 -0293 lt0001 1488 BW 0158 0005-0525 0738 lt0001 0633 lt0001 -0192 lt0001 398 BC 0145 0012-0438 0653 lt0001 0169 0024 -0683 lt0001 178 YB 0046 0020-0115 0448 lt0001 0234 0058 -0383 0002 66 AB 0024 0005-0395 0236 0007 0067 0448 -0229 0009 131 AE 0195 0170-0228 -0511 0300 0405 0425 6

AE data consists of six measurements from one tree

BT was significantly positively related to DOB for all species except for AE where there was a

negative relation that was not significant BT was significantly positively related to DBH for all

species except for YB and AB where the positive relations were not significant BT was

significantly negatively related to TH for all species except for AE where there was a positive

relationship that was not significant

Average BTs for various DOB and TH classes for the eight species are as follows

DOB Class BT (in) RM WA SM BW BC YB AB AE

~400

401 to 800 801 to 1200 1201 to 1600

gt1600

0017 0054 0134 0239 0236

0091 0220 0321 0394 0468

0024 0060 0141 0225 0324

0032 0093 0150 0119 0268

0058 0101 0192 0252 0199

0020 0032 0048 0060 0058

0022 0019 0019 0020 0048

0200 0170

THClass BT (ft) RM WA SM BW BC YB AB AE

~050 0134 0208 0146 0114 0263 0038 0036 051 to 450 0110 0338 0161 0199 0192 0057 0038 0180 451 to 1000 0080 0296 0105 0165 0169 0047 0021 1001 to 2000 0065 0278 010(1 0153 0140 0049 0016 0210 2001 to 3000 0060 0250 0094 0146 0102 0041 0016 0200 3001 to 4000 0045 0220 0089 0134 0087 0037 0014 0190 4001 to 5000 0038 0220 0062 0153 0061 0025 0015

~5000 0016 0159 0047 0136 0038 0016

-17shy

In general BT is smallest for AB followed by YB RM SM BC BW and AE in increasing order

with BT for WA being the largest In general BT increases with DOB and decreases with TH

Most of the anomalies are due to small sample sizes

For the topwood data set (n=631) BT was significantly different for the seven different

species (Bartletts -test for equal variances PltOOOl F-test for equal means PltOOOl) All

Bonferroni pairwise comparisons of means are significantly different except for (RM SM) (RM

BC) (RM YB) (SM BC) (BC YB) and (YB AB)

Average minimum and maximum BTs and Pearsons correlations of BT with DOB and DBH

are shown below for the seven species

Species x

BT

Min- Max

BT DOB p r

BTDBH p n

RM WA SM BW BC YB AB

0064 0203 0086 0150 0083 0034 0019

0008-0385 0022-0458 0005-0362 0018-0262 0018-0175 Ool5-0075 0008-0038

06SO 0723 0768 0813 0723 0464 0051

lt0001 lt0001 lt0001 lt0001 lt0001

0017 0744

0549 0360 0440 0588 0380 0216 0661

lt0001 0002

lt0001 lt0001

0032 0290

lt0001

74 75

342 38 32 26 44

BT was significantly positively related to DOB for all species except for AB and to DBH for all

species except for YB

Average BTs for various DOB classes for the seven species are as follows

DOB Class BT (in) RM WA S~t BW BC YB AB

500 OQl8 0126 oltH) 0054 0051 0024 0021 501 to 700 0073 0212 () t)(J 0105 0086 0032 0019 701 to 900 0152 0281 () Ill 0170 0115 0057 0015 901 to 1100 0158 0255 () 177 0193 0114 0043 0020

111 to 1300 0122 0345 0222 0205 0135 0026

-18shy

In general BT is smallest for AB followed by YB BC RM SM and BW in increasing order

with BT for W A being the largest In general BT increases with DOB Most of the anomalies are

due to small sample sizes

Comparison with other BF equations

Fowler (1993) showed that while there were significant species differences between BF

equations for aspen jack pine and red pine there was a very strong relationship between BF and

tree height for each species (ie R 2 gt097 for each species) BF was a function of TH and In TH

showing that BF increased with TH to some maximum and then decreased for larger THs with the

steepness of the decrease depending on the species For all three species BF was not strongly

related to DBH or DOB at a given TH

For paper birch (Fowler and Hussain 1997) BF significantly increased with DOB at TH

(R2 =0219) and significantly decreased with In TH (R2 =0166) for stemwood while BF

significantly increased with DOB for topwood ( R 2 =0218) BF was much more variable than for

aspen red pine and jack pine

Fowler et al (1997) showed that black oak (BO) red oak (RO) and white oak (WO) have BPs

that are quite variable and prediction equations with the same independent variables as for paper

birch with the direction of the relations reversed For stemwood BF decreased with DOB at TH

( R 2 =0270 0418 and 0014 for BO RO and WO respectively) and increased with In TH ( R 2 =

0190 0275 and 0011 for BO RO and WO respectively) For topwood BF decreased with DOB

(R2=0366 0457 and 0100 for BO RO and WO respectively) These prediction equations were

significant but they were only moderately strong at best being only somewhat stronger in general

than the prediction equations for paper birch The prediction equations based on DOB were

-19shy

somewhat stronger than the prediction equations based on In TH The BF equations were

significantly different for the three species and for topwood versus stemwood except for RO

This study shows that the eight northern hardwood species have BFs that are quite variable

with some species having prediction equations with the same independent variables as for paper

birch and the three oak species while other species had different independent variables For

stemwood BF decreased with DOB at TH for RM SM BW and BC increased with In DOB at TH

for W A YB and AE and increased and then somewhat decreased with 1DOB and In DOB as the

independent variables for AB BF increased with In TH for RM SM and BC decreased and then

increased with TH and In TH for WA and BW increased and then decreased with TH and In TH for

YB AB and AE The prediction equations for AE are very suspect as they were based on only six

BF measurements from one tree For topwood BF decreased with DOB for RM WA SM BW

and BC increased with DOB for YB and increased and somewhat decreased with 1DOB and

In DOB for AB All prediction equations for stemwood were significant except for the TH

equations for BW and YB For topwood only the prediction equations for RM SM BW and AB

were significant In general all prediction equations were only moderately strong at best and some

of them were very weak The BF equations were significantly different for most species while the

stemwood and topwood BF equations were not significantly different except for RM and SM

GUIDELINES FOR USERS

We recommend use of the following equations for northern hardwoods when accurate

estimates of bark factors are desired

Stemwood

bull Red maple I

(1) BF =0996730-0002397 bull DOB I

(2) BF =0972344 + 0003554 bull In TH

-20shy

bull White ash 1

(3) BF = 0922166 +0001198bull DOB 1

(4) BF = 0937036 + 0000805 bull TH- 0009279 bullIn TH

bull- Sugar maple 1

(5) BF=0988318-0001497bullDOB 1

(6) BF = 0970865 + 0002264 bullIn TH

bull Basswood 1

(7) BF = 0974486-0000403 bull DOB 1

(8) BF = 0970312 + 0000072 bull TH- 0000631bullln TH

bull Black cherry 1

(9) BF = 0971912 -0000841bull DOB 1

(lO) BF = 0954777 + 0004557 bullIn TH

bull Yell ow birch 1

(11) BF = 0987390 + 0000307 bull DOB 1

(12) BF = 0990354-0000111bull TH+0000885bullln TH

bull American beech 1

(l3) BF = l027382-0l03065DOB -0009012bullln DOB

1

(14) BF = 0994075-0000047 bull TH+0000896 bullIn TH

bull American elm 1

(l5) BF =0925851 + 0003400 bull DOB 1

(16) BF = 0975815-0000058 bull TH- 0()()4696bullln TH

Use Equations 1 3 5 7 9 11 13 and 15 if DOBis measured Use Equations 2 4 6 8 10 12 14

and 16 when only THis measured

Topwood 1

(l7) RM BF = 1006791-0004569 bull DOB 1

(18) WA BF = 0936727 -0000206bull DOB 1

(l9) SM BF = 0995302-0002757 bull DOB

-21shy

(20) BW BF = 0979121-0002155 bull DOB

(21) BC BF = 0977830- 0000604 bull DOB

(22) YB BF = 0987032 + 0000281bull DOB

(23) AB BF = 1038966- 0131661DOB - 0012832 bullln DOB

The equation for stemwood and topwood pooled could be used if DOB is measured with moderate

loss in accuracy for RM and SM and little loss in accuracy for the other five species The pooled

equations in general will be more accurate for stemwood compared to topwood especially for RM

and SM

(24) RM BF == 0997087 -0002476bull DOB

1

(25) WA BF = 0924553 + 000 I 003 bull DOB

(26) SM BF=0988615-0001568bullDOB

(27) BW BF = 0972865-0000320 bull DOB

(28) BC BF=0974512-0001028bullDOB

(29) YB BF = 0986997 + 0000334 bull DOB

(30) AB BF = 1028314- 0105996DOB- 0009288 bullIn DOB

There is no pooled equation for AE as there was no topwood for the one AE tree in the data set

For reasonable accuracy in many situations the following constants could be used for bark

factors

DOB Class Stemwood BF (in) RM WA St-1 BW BC YB AB AE

DOBs50 0988 0927 09S~ 0973 0969 0989 0988 0939 50ltDOBsl00 0979 0931 0977 0971 0966 0990 0995 0951 l00ltDOBs150 0967 0937 0970 0969 0962 0991 0996 0968 150ltDOBs200 0955 0943 0962 0967 0957 0993 0996 0985

DOBgt200 0943 0949 0954 0965 0953 0994 0995 0994

-22shy

DOB Class ToEwoodBF (in) RM WA SM BW BC YB AB

DOBS50 0989 0936 0984 0971 0975 0988 0987 50ltD0BSl00 0970 0935 0973 0962 0973 0989 0995 100ltD0BS150 0947 0934 0959 0951 0970 0991 0996 150ltD0BS200 0924 0933 0946 0940 0967 0992 0995

008gt200 0902 0932 0932 0930 0964 0993 0993

TH Stemwood BF (ft) RM WA SM BW BC YB AB AE

THS05 0970 0947 0971 0971 0950 0990 0993 0980 05ltTHS45 0974 0932 olJn 0970 0959 0991 0995 0972

45ltTHS 100 0978 0925 0974 0970 0964 0991 0996 0966 100ltTHS200 0980 0924 0gt76 0970 0967 0991 0996 0963 200ltTHS300 0984 0928 0gt7S 0970 0970 0990 0996 0959 300ltTHS400 0986 0932 OltJSO 0971 0971 0990 0996 0957 400ltTHS500 0988 0937 () l)S~ 0971 0972 0989 0995 0955

THgt500 0992 0950 07 0974 0974 0987 0995 0952

The following constants for bark factor could be used for simplicity with moderately

approximate results especially for a large number of treessticks

Species Stem wood Top wood Stemwood and Topwood

RM 0980 0981 0980 WA 0932 0935 0932 SM 0976 0977 0976 BW 0970 0962 0970 BC 0965 0974 0966 YB 0991 0989 0990 AB 0995 0995 0995 AE 0964 0964

The above constants would be more accurate for those species that did not have significant

prediction equations andor small sample sizes B~ cry careful with using any of the results of this

study outside the range of the data set for each species Since the results for AE are based on six

stemwood measurements from one tree they arc of course very suspect

-23shy

Use of prediction equations

The prediction equations can be used to estimate BF at any DOB andor TH Since

BF=DIBDOB DIB can be estimated as DIB=BFbull DOB and DOB can be estimated as

DOB=DIBBF Past DOB and DOB growth can be estimated from past DIB growth as follows

Past DOB Growth=Past DIB GrowthBF

and

Past DOB=Present DOB -Past DOB Growth

where past DIB growth might be obtained with an increment borer

Specific uses of the prediction equations include (1) estimation of the solid wood and bark

volume of standing trees (2) estimation of bark volume or peeled volume from unpeeled volume

of felled tree sections (3) growth studies and (4) estimating tree form (eg Girard Form Class)

See Husch et al ( 1982) for a detailed discussion on bark factors

-24- LITERATURE CITED middot

Fowler G W 1991 An aspen bark factor equation for Michigan North J Appl For 8(1) 12-15

Fowler G W 1993 A jack pine bark factor equation for Michigan North J Appl For 10(2) 86-89

Fowler G W and L J Damschroder 1988 A red pine bark factor equation for Michigan North J Appl For 5(1) 28-30

Fowler G W and N G Hussain 1987a Bark factor equation for red pine Michigan DNR For Infor Leaflet 1-87 2 p

Fowler G W and N G Hussain 1987b Bark factor equation for aspen Michigan DNR For Infor Leaflet 2-87 2 p

Fowler G W and N G Hussain 1991 Bark factor equation for jack pine in Michigan Michigan DNR For Infor Leaflet 1-91 5 p

Fowler G W and N G Hussain 1997 Bark factor equations for paper birch in Michigan Michigan DNR For Infor Leaflet 1-97 12 p

Fowler G W N G Hussain D J Cohen and D Khatry-Chhetri 1997 Bark factor equations for oak in Michigan Michigan DNR For Infor Leaflet 2-97 15 p

Husch B C I Miller and T W Beers 1982 Forest Mensuration John Wiley and Sons Inc NY 402 p

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-11shy

The ranges of predicted BF values for DOB from 30 to 200 in are 0078 0003 0047 0037

0010 0005 and 0015 for RM WA SM BW BC YB and AB respectively Because of these

moderate to small ranges the low R 2 values of the prediction equations the moderate sample sizes

and some of the prediction equations not being significant at a=005 you might argue that the mean

bark factor yields an adequate prediction model (except possibly for RM)

74 (40) RM BF = BF =I BFi74 = 0981 0019213

i=l 75

(41) WA BF = BF =I B~75 = 0935 0023077 i=l 342

(42) SM BF = BF = I B~ 342 = 0977 0015190 i=l 38

(43) BW BF = BF =I BFi38 =0962 0011118 i=l

32 (44) BC BF = BF =I BFi32 = 0974 0009633

i=l

26 (45) YB BF = BF =I Bfi 26 = 0989 0004540

i=l

44 (46) AB BF=BF= I BFi44=0995 0003135

i=l

See the above table to find where Equations 40-46 over- and underestimate reflected to Equations

33-39 respectively

Prediction Equations 33-38 are significant y different (Bartletts 12 -test for equal variances

Plt0005 F-test for equal slopes P=OOOl) Prediction Equations 40-46 related to mean bark factors

are also significantly different (Bartletts -test for equal variances Plt0005 F-test for equal

-12shy

means PltOOOl) All Bonferroni pairwise comparisons of means are significantly different

(Plt005) except for (RM SM) (RM BC) (RM YB) (SM BC) and (YB AB)

Pooled prediction equations

The stemwood and topwood BF prediction equations with DOB as the independent variable

were compared for each of the species except for AB where the independent variables were 1DOB

and ln DOB The resulting P-values are as follows

Bartletts z2 -test F-test for Equal Species for Equal Variances Regression Coefficients

RM P=005+ P=OOOl WA P=01 P=0267 SM P=0862 PltOOOl BW P=OOlJ-+ P=0120 BC P=0005 P=0854 YB P=0106 P=0954 AB PltOOOI P=0942

Bonferroni level of significance a=OOS7=0007

The above results indicate that the two equations for WA BW BC YB and AB can be pooled

while some prediction accuracy will be lost if the two equations for RM and SM are pooled (See the

two equations shown for each species earlier in this paper) Note that there is no lopwood for the

one AE tree in the data set Therefore the pooled equation is the stemwood equation for AE

The pooled prediction equations are

R2 sybullx p n

A

(47) RM BF =0997087 -0002476bull DOB 0166 0014604 lt0001 903

A

(48) WA BF =0924553 + 0001003 bull DOB 0021 0023385 0001 485

A

(49) SM BF =0988615-0001568 bull DOB (Jl64 0013748 lt0001 1830

A

(50) BW BF =0972865-0000320 bull DOB 00 lO 0013085 0040 436

A

(51) BC BF =0974512 -0001028bull DOB 0041 0014455 0003 210

A

(52) YB BF =0986997 + 0000334 bull DOB 0107 0003825 0001 92

-13shy

R2 sybullx p n

1

(53) AB BF =1028314- 0105996DOB 0201 0003819 lt0001 175

- 0009288 bull In DOB

Prediction equations 47-53 for RM WA SM BW BC YB and AB respectively yield the

following estimated bark factors

Prediction Equations 47-53

1

DOB BF (in) RM WA SM BW BC YB AB

30 0990 0928 0984 0972 0971 0988 0983 40 0987 0929 0982 0972 0970 0988 0989 50 0985 0930 0981 0971 0969 0989 0992 60 0982 0931 0979 0971 0968 0989 0994 70 0980 0932 0978 0971 0967 0989 0995 80 0977 0933 0976 0970 0966 0989 0996 90 0975 0934 0975 0970 0965 0990 0996

100 0972 0935 0973 0969 0964 0990 0996 110 0970 0936 0971 0969 0963 0991 0996 120 0967 0937 0970 0969 0962 0991 0996 130 0965 0938 0968 0968 0961 0991 0996 140 0962 0939 0967 0968 0960 0992 0996 150 0960 0940 0965 0968 0959 0992 0996 160 0957 0941 0964 0968 0958 0992 0996 170 0955 0942 0962 0967 0957 0993 0996 180 0953 0943 0960 0967 0956 0993 0996 190 0950 0944 0959 0967 0955 0993 0995 200 0948 0945 0957 0966 0954 0994 0995 210 0945 0946 0956 0966 0953 0994 0995 220 0943 0947 0954 0966 0952 0994 0995 230 0940 0948 0953 0966 0951 0995 0995 240 0938 0949 0951 0965 0950 0995 0994 250 0935 0950 0949 0965 0949 0995 0994

Note that the pooled BF estimates for each species are close to those of Equations 1 4 7 10

13 16 and 19 for stemwood This makes sense since the stemwood sample sizes were considerably

larger than the topwood sample sizes for each species For topwood the pooled BF estimates for

YB and AB are very close to Equations 38 and 39 respectively for topwood However there are

some larger differences for the other species over the range of DOB from 30-200 inches

-14shy

bull RM - Pooled BF estimates are lower than those of Equation 33 for DOB lt 50 in and higher for DOB ~ 50 in (from 0003 lower to 0033 higher)

bull WA - Pooled BF estimates are lower than those of Equation 34 for DOB lt 100 in and higher for DOB gt 100 in (from 0008 lower to 0012 higher)

bull SM - Pooled BF estimates are lower than those of Equation 35 for DOB lt 60 in and higher for DOB gt 60 in (from 0003 lower to 0017 higher)

bull BW - Pooled BF estimates are lower than those of Equation 36 for DOB lt 40 in and higher for DOB ~ 40 in (from 0001 lower to 0030 higher)

bull BC - Pooled BF estimates are lower than those of Equation 37 for all values of DOB (from 0005 to 0012lower)

The ranges of the pooled predicted BF values for DOB from 30 to 250 in are 0055 0022 0035

0007 0022 0007 and 0013 for RM WA SM BW BC YB and AB respectively Because of

these moderate to small ranges the low R2 values of the prediction equations and some of the

prediction equations not being significant you might argue that the mean bark factor yields an

adequate prediction model

The stemwood and topwood mean BFs were compared for each of the species The resulting

P-values are as follows

Species Bartletts zLtest

for Equal Variances F-test for Equal

Regression Coefficients

RM 0013 0681 WA 0770 0202 SM 0775 0287 BW 0196 0004 BC 0004 0001 YB 0222 0055 AB 0005 0542

Bonferroni level of significance a PC =00057 =0007

The above results indicate that the two means for RM W A SM YB and AB can be pooled while

some prediction accuracy will be lost if the two means for BW and BC are pooled (See the two

means shown for each species earlier in the paper) Note that there is no topwood for the one AE

tree in the data set Therefore the pooled mean is the stemwood mean for AE

-15shy

The pooled mean bark factors are

903 (54) RM middot BF = BF = L Bfl 903 = 0980 0015980

i=1

485 (55) WA BF = BF = L Bfl485 = 0932 0023614

i=1

1830 (56) SM BF= BF= L Bfl1830 = 0976 0015029

i=1

436 (57) BW BF = BF = L Bfl436 = 0970 0013134

i=l

210 (58) BC BF = BF = L Bfl210 = 0966 0014725

i=l

92 (59) YB BF = BF = L BFi92 = 0990 0004025

i=l

175 (60) AB BF = BF = L BF)l75 = 0995 0004248

i=1

See the table based on Equations 47-53 to see where Equations 54-60 under- and overestimate

respectively

Bark thickness

For the stemwood data set (n=3506) BT was significantly different for the eight different

species (Bartletts x2 -test for equal variances PltOOOl F-test for equal means PltOOOl) All

Bonferroni pairwise comparisons of means are significantly different except for (RM YB) (RM

AE) (WA AE) (SM AE) (BW AE) (BC AE) (YB AB) and (BW BC) Note that the sample

size for AE is only 6

Average minimum and maximum BTs and Pearsons correlations of BT with DOB DBH

and TH are shown below for the eight species

-16shy

BT BTDOB BTDBH BTTHSpecies nx Min-Max r p r p r p

RM 0077 0005-0525 0678 lt0001 0484 lt0001 -0369 lt0001 829 WA 0263 0012-1760 0632 lt0001 0428 lt0001 -0329 lt0001 410 SM 0113 0008-0672 0794 lt0001 0685 lt0001 -0293 lt0001 1488 BW 0158 0005-0525 0738 lt0001 0633 lt0001 -0192 lt0001 398 BC 0145 0012-0438 0653 lt0001 0169 0024 -0683 lt0001 178 YB 0046 0020-0115 0448 lt0001 0234 0058 -0383 0002 66 AB 0024 0005-0395 0236 0007 0067 0448 -0229 0009 131 AE 0195 0170-0228 -0511 0300 0405 0425 6

AE data consists of six measurements from one tree

BT was significantly positively related to DOB for all species except for AE where there was a

negative relation that was not significant BT was significantly positively related to DBH for all

species except for YB and AB where the positive relations were not significant BT was

significantly negatively related to TH for all species except for AE where there was a positive

relationship that was not significant

Average BTs for various DOB and TH classes for the eight species are as follows

DOB Class BT (in) RM WA SM BW BC YB AB AE

~400

401 to 800 801 to 1200 1201 to 1600

gt1600

0017 0054 0134 0239 0236

0091 0220 0321 0394 0468

0024 0060 0141 0225 0324

0032 0093 0150 0119 0268

0058 0101 0192 0252 0199

0020 0032 0048 0060 0058

0022 0019 0019 0020 0048

0200 0170

THClass BT (ft) RM WA SM BW BC YB AB AE

~050 0134 0208 0146 0114 0263 0038 0036 051 to 450 0110 0338 0161 0199 0192 0057 0038 0180 451 to 1000 0080 0296 0105 0165 0169 0047 0021 1001 to 2000 0065 0278 010(1 0153 0140 0049 0016 0210 2001 to 3000 0060 0250 0094 0146 0102 0041 0016 0200 3001 to 4000 0045 0220 0089 0134 0087 0037 0014 0190 4001 to 5000 0038 0220 0062 0153 0061 0025 0015

~5000 0016 0159 0047 0136 0038 0016

-17shy

In general BT is smallest for AB followed by YB RM SM BC BW and AE in increasing order

with BT for WA being the largest In general BT increases with DOB and decreases with TH

Most of the anomalies are due to small sample sizes

For the topwood data set (n=631) BT was significantly different for the seven different

species (Bartletts -test for equal variances PltOOOl F-test for equal means PltOOOl) All

Bonferroni pairwise comparisons of means are significantly different except for (RM SM) (RM

BC) (RM YB) (SM BC) (BC YB) and (YB AB)

Average minimum and maximum BTs and Pearsons correlations of BT with DOB and DBH

are shown below for the seven species

Species x

BT

Min- Max

BT DOB p r

BTDBH p n

RM WA SM BW BC YB AB

0064 0203 0086 0150 0083 0034 0019

0008-0385 0022-0458 0005-0362 0018-0262 0018-0175 Ool5-0075 0008-0038

06SO 0723 0768 0813 0723 0464 0051

lt0001 lt0001 lt0001 lt0001 lt0001

0017 0744

0549 0360 0440 0588 0380 0216 0661

lt0001 0002

lt0001 lt0001

0032 0290

lt0001

74 75

342 38 32 26 44

BT was significantly positively related to DOB for all species except for AB and to DBH for all

species except for YB

Average BTs for various DOB classes for the seven species are as follows

DOB Class BT (in) RM WA S~t BW BC YB AB

500 OQl8 0126 oltH) 0054 0051 0024 0021 501 to 700 0073 0212 () t)(J 0105 0086 0032 0019 701 to 900 0152 0281 () Ill 0170 0115 0057 0015 901 to 1100 0158 0255 () 177 0193 0114 0043 0020

111 to 1300 0122 0345 0222 0205 0135 0026

-18shy

In general BT is smallest for AB followed by YB BC RM SM and BW in increasing order

with BT for W A being the largest In general BT increases with DOB Most of the anomalies are

due to small sample sizes

Comparison with other BF equations

Fowler (1993) showed that while there were significant species differences between BF

equations for aspen jack pine and red pine there was a very strong relationship between BF and

tree height for each species (ie R 2 gt097 for each species) BF was a function of TH and In TH

showing that BF increased with TH to some maximum and then decreased for larger THs with the

steepness of the decrease depending on the species For all three species BF was not strongly

related to DBH or DOB at a given TH

For paper birch (Fowler and Hussain 1997) BF significantly increased with DOB at TH

(R2 =0219) and significantly decreased with In TH (R2 =0166) for stemwood while BF

significantly increased with DOB for topwood ( R 2 =0218) BF was much more variable than for

aspen red pine and jack pine

Fowler et al (1997) showed that black oak (BO) red oak (RO) and white oak (WO) have BPs

that are quite variable and prediction equations with the same independent variables as for paper

birch with the direction of the relations reversed For stemwood BF decreased with DOB at TH

( R 2 =0270 0418 and 0014 for BO RO and WO respectively) and increased with In TH ( R 2 =

0190 0275 and 0011 for BO RO and WO respectively) For topwood BF decreased with DOB

(R2=0366 0457 and 0100 for BO RO and WO respectively) These prediction equations were

significant but they were only moderately strong at best being only somewhat stronger in general

than the prediction equations for paper birch The prediction equations based on DOB were

-19shy

somewhat stronger than the prediction equations based on In TH The BF equations were

significantly different for the three species and for topwood versus stemwood except for RO

This study shows that the eight northern hardwood species have BFs that are quite variable

with some species having prediction equations with the same independent variables as for paper

birch and the three oak species while other species had different independent variables For

stemwood BF decreased with DOB at TH for RM SM BW and BC increased with In DOB at TH

for W A YB and AE and increased and then somewhat decreased with 1DOB and In DOB as the

independent variables for AB BF increased with In TH for RM SM and BC decreased and then

increased with TH and In TH for WA and BW increased and then decreased with TH and In TH for

YB AB and AE The prediction equations for AE are very suspect as they were based on only six

BF measurements from one tree For topwood BF decreased with DOB for RM WA SM BW

and BC increased with DOB for YB and increased and somewhat decreased with 1DOB and

In DOB for AB All prediction equations for stemwood were significant except for the TH

equations for BW and YB For topwood only the prediction equations for RM SM BW and AB

were significant In general all prediction equations were only moderately strong at best and some

of them were very weak The BF equations were significantly different for most species while the

stemwood and topwood BF equations were not significantly different except for RM and SM

GUIDELINES FOR USERS

We recommend use of the following equations for northern hardwoods when accurate

estimates of bark factors are desired

Stemwood

bull Red maple I

(1) BF =0996730-0002397 bull DOB I

(2) BF =0972344 + 0003554 bull In TH

-20shy

bull White ash 1

(3) BF = 0922166 +0001198bull DOB 1

(4) BF = 0937036 + 0000805 bull TH- 0009279 bullIn TH

bull- Sugar maple 1

(5) BF=0988318-0001497bullDOB 1

(6) BF = 0970865 + 0002264 bullIn TH

bull Basswood 1

(7) BF = 0974486-0000403 bull DOB 1

(8) BF = 0970312 + 0000072 bull TH- 0000631bullln TH

bull Black cherry 1

(9) BF = 0971912 -0000841bull DOB 1

(lO) BF = 0954777 + 0004557 bullIn TH

bull Yell ow birch 1

(11) BF = 0987390 + 0000307 bull DOB 1

(12) BF = 0990354-0000111bull TH+0000885bullln TH

bull American beech 1

(l3) BF = l027382-0l03065DOB -0009012bullln DOB

1

(14) BF = 0994075-0000047 bull TH+0000896 bullIn TH

bull American elm 1

(l5) BF =0925851 + 0003400 bull DOB 1

(16) BF = 0975815-0000058 bull TH- 0()()4696bullln TH

Use Equations 1 3 5 7 9 11 13 and 15 if DOBis measured Use Equations 2 4 6 8 10 12 14

and 16 when only THis measured

Topwood 1

(l7) RM BF = 1006791-0004569 bull DOB 1

(18) WA BF = 0936727 -0000206bull DOB 1

(l9) SM BF = 0995302-0002757 bull DOB

-21shy

(20) BW BF = 0979121-0002155 bull DOB

(21) BC BF = 0977830- 0000604 bull DOB

(22) YB BF = 0987032 + 0000281bull DOB

(23) AB BF = 1038966- 0131661DOB - 0012832 bullln DOB

The equation for stemwood and topwood pooled could be used if DOB is measured with moderate

loss in accuracy for RM and SM and little loss in accuracy for the other five species The pooled

equations in general will be more accurate for stemwood compared to topwood especially for RM

and SM

(24) RM BF == 0997087 -0002476bull DOB

1

(25) WA BF = 0924553 + 000 I 003 bull DOB

(26) SM BF=0988615-0001568bullDOB

(27) BW BF = 0972865-0000320 bull DOB

(28) BC BF=0974512-0001028bullDOB

(29) YB BF = 0986997 + 0000334 bull DOB

(30) AB BF = 1028314- 0105996DOB- 0009288 bullIn DOB

There is no pooled equation for AE as there was no topwood for the one AE tree in the data set

For reasonable accuracy in many situations the following constants could be used for bark

factors

DOB Class Stemwood BF (in) RM WA St-1 BW BC YB AB AE

DOBs50 0988 0927 09S~ 0973 0969 0989 0988 0939 50ltDOBsl00 0979 0931 0977 0971 0966 0990 0995 0951 l00ltDOBs150 0967 0937 0970 0969 0962 0991 0996 0968 150ltDOBs200 0955 0943 0962 0967 0957 0993 0996 0985

DOBgt200 0943 0949 0954 0965 0953 0994 0995 0994

-22shy

DOB Class ToEwoodBF (in) RM WA SM BW BC YB AB

DOBS50 0989 0936 0984 0971 0975 0988 0987 50ltD0BSl00 0970 0935 0973 0962 0973 0989 0995 100ltD0BS150 0947 0934 0959 0951 0970 0991 0996 150ltD0BS200 0924 0933 0946 0940 0967 0992 0995

008gt200 0902 0932 0932 0930 0964 0993 0993

TH Stemwood BF (ft) RM WA SM BW BC YB AB AE

THS05 0970 0947 0971 0971 0950 0990 0993 0980 05ltTHS45 0974 0932 olJn 0970 0959 0991 0995 0972

45ltTHS 100 0978 0925 0974 0970 0964 0991 0996 0966 100ltTHS200 0980 0924 0gt76 0970 0967 0991 0996 0963 200ltTHS300 0984 0928 0gt7S 0970 0970 0990 0996 0959 300ltTHS400 0986 0932 OltJSO 0971 0971 0990 0996 0957 400ltTHS500 0988 0937 () l)S~ 0971 0972 0989 0995 0955

THgt500 0992 0950 07 0974 0974 0987 0995 0952

The following constants for bark factor could be used for simplicity with moderately

approximate results especially for a large number of treessticks

Species Stem wood Top wood Stemwood and Topwood

RM 0980 0981 0980 WA 0932 0935 0932 SM 0976 0977 0976 BW 0970 0962 0970 BC 0965 0974 0966 YB 0991 0989 0990 AB 0995 0995 0995 AE 0964 0964

The above constants would be more accurate for those species that did not have significant

prediction equations andor small sample sizes B~ cry careful with using any of the results of this

study outside the range of the data set for each species Since the results for AE are based on six

stemwood measurements from one tree they arc of course very suspect

-23shy

Use of prediction equations

The prediction equations can be used to estimate BF at any DOB andor TH Since

BF=DIBDOB DIB can be estimated as DIB=BFbull DOB and DOB can be estimated as

DOB=DIBBF Past DOB and DOB growth can be estimated from past DIB growth as follows

Past DOB Growth=Past DIB GrowthBF

and

Past DOB=Present DOB -Past DOB Growth

where past DIB growth might be obtained with an increment borer

Specific uses of the prediction equations include (1) estimation of the solid wood and bark

volume of standing trees (2) estimation of bark volume or peeled volume from unpeeled volume

of felled tree sections (3) growth studies and (4) estimating tree form (eg Girard Form Class)

See Husch et al ( 1982) for a detailed discussion on bark factors

-24- LITERATURE CITED middot

Fowler G W 1991 An aspen bark factor equation for Michigan North J Appl For 8(1) 12-15

Fowler G W 1993 A jack pine bark factor equation for Michigan North J Appl For 10(2) 86-89

Fowler G W and L J Damschroder 1988 A red pine bark factor equation for Michigan North J Appl For 5(1) 28-30

Fowler G W and N G Hussain 1987a Bark factor equation for red pine Michigan DNR For Infor Leaflet 1-87 2 p

Fowler G W and N G Hussain 1987b Bark factor equation for aspen Michigan DNR For Infor Leaflet 2-87 2 p

Fowler G W and N G Hussain 1991 Bark factor equation for jack pine in Michigan Michigan DNR For Infor Leaflet 1-91 5 p

Fowler G W and N G Hussain 1997 Bark factor equations for paper birch in Michigan Michigan DNR For Infor Leaflet 1-97 12 p

Fowler G W N G Hussain D J Cohen and D Khatry-Chhetri 1997 Bark factor equations for oak in Michigan Michigan DNR For Infor Leaflet 2-97 15 p

Husch B C I Miller and T W Beers 1982 Forest Mensuration John Wiley and Sons Inc NY 402 p

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lonst Manbullpmeut DWisioa 15 Resource Mana1ement Units

bullJfectble l2519bull

bull -Resource Jf~nt Unit OJke

1 -Raource Jf~nt Unit BOUIIdariea

1 -CountyBouruiiJrfea

-12shy

means PltOOOl) All Bonferroni pairwise comparisons of means are significantly different

(Plt005) except for (RM SM) (RM BC) (RM YB) (SM BC) and (YB AB)

Pooled prediction equations

The stemwood and topwood BF prediction equations with DOB as the independent variable

were compared for each of the species except for AB where the independent variables were 1DOB

and ln DOB The resulting P-values are as follows

Bartletts z2 -test F-test for Equal Species for Equal Variances Regression Coefficients

RM P=005+ P=OOOl WA P=01 P=0267 SM P=0862 PltOOOl BW P=OOlJ-+ P=0120 BC P=0005 P=0854 YB P=0106 P=0954 AB PltOOOI P=0942

Bonferroni level of significance a=OOS7=0007

The above results indicate that the two equations for WA BW BC YB and AB can be pooled

while some prediction accuracy will be lost if the two equations for RM and SM are pooled (See the

two equations shown for each species earlier in this paper) Note that there is no lopwood for the

one AE tree in the data set Therefore the pooled equation is the stemwood equation for AE

The pooled prediction equations are

R2 sybullx p n

A

(47) RM BF =0997087 -0002476bull DOB 0166 0014604 lt0001 903

A

(48) WA BF =0924553 + 0001003 bull DOB 0021 0023385 0001 485

A

(49) SM BF =0988615-0001568 bull DOB (Jl64 0013748 lt0001 1830

A

(50) BW BF =0972865-0000320 bull DOB 00 lO 0013085 0040 436

A

(51) BC BF =0974512 -0001028bull DOB 0041 0014455 0003 210

A

(52) YB BF =0986997 + 0000334 bull DOB 0107 0003825 0001 92

-13shy

R2 sybullx p n

1

(53) AB BF =1028314- 0105996DOB 0201 0003819 lt0001 175

- 0009288 bull In DOB

Prediction equations 47-53 for RM WA SM BW BC YB and AB respectively yield the

following estimated bark factors

Prediction Equations 47-53

1

DOB BF (in) RM WA SM BW BC YB AB

30 0990 0928 0984 0972 0971 0988 0983 40 0987 0929 0982 0972 0970 0988 0989 50 0985 0930 0981 0971 0969 0989 0992 60 0982 0931 0979 0971 0968 0989 0994 70 0980 0932 0978 0971 0967 0989 0995 80 0977 0933 0976 0970 0966 0989 0996 90 0975 0934 0975 0970 0965 0990 0996

100 0972 0935 0973 0969 0964 0990 0996 110 0970 0936 0971 0969 0963 0991 0996 120 0967 0937 0970 0969 0962 0991 0996 130 0965 0938 0968 0968 0961 0991 0996 140 0962 0939 0967 0968 0960 0992 0996 150 0960 0940 0965 0968 0959 0992 0996 160 0957 0941 0964 0968 0958 0992 0996 170 0955 0942 0962 0967 0957 0993 0996 180 0953 0943 0960 0967 0956 0993 0996 190 0950 0944 0959 0967 0955 0993 0995 200 0948 0945 0957 0966 0954 0994 0995 210 0945 0946 0956 0966 0953 0994 0995 220 0943 0947 0954 0966 0952 0994 0995 230 0940 0948 0953 0966 0951 0995 0995 240 0938 0949 0951 0965 0950 0995 0994 250 0935 0950 0949 0965 0949 0995 0994

Note that the pooled BF estimates for each species are close to those of Equations 1 4 7 10

13 16 and 19 for stemwood This makes sense since the stemwood sample sizes were considerably

larger than the topwood sample sizes for each species For topwood the pooled BF estimates for

YB and AB are very close to Equations 38 and 39 respectively for topwood However there are

some larger differences for the other species over the range of DOB from 30-200 inches

-14shy

bull RM - Pooled BF estimates are lower than those of Equation 33 for DOB lt 50 in and higher for DOB ~ 50 in (from 0003 lower to 0033 higher)

bull WA - Pooled BF estimates are lower than those of Equation 34 for DOB lt 100 in and higher for DOB gt 100 in (from 0008 lower to 0012 higher)

bull SM - Pooled BF estimates are lower than those of Equation 35 for DOB lt 60 in and higher for DOB gt 60 in (from 0003 lower to 0017 higher)

bull BW - Pooled BF estimates are lower than those of Equation 36 for DOB lt 40 in and higher for DOB ~ 40 in (from 0001 lower to 0030 higher)

bull BC - Pooled BF estimates are lower than those of Equation 37 for all values of DOB (from 0005 to 0012lower)

The ranges of the pooled predicted BF values for DOB from 30 to 250 in are 0055 0022 0035

0007 0022 0007 and 0013 for RM WA SM BW BC YB and AB respectively Because of

these moderate to small ranges the low R2 values of the prediction equations and some of the

prediction equations not being significant you might argue that the mean bark factor yields an

adequate prediction model

The stemwood and topwood mean BFs were compared for each of the species The resulting

P-values are as follows

Species Bartletts zLtest

for Equal Variances F-test for Equal

Regression Coefficients

RM 0013 0681 WA 0770 0202 SM 0775 0287 BW 0196 0004 BC 0004 0001 YB 0222 0055 AB 0005 0542

Bonferroni level of significance a PC =00057 =0007

The above results indicate that the two means for RM W A SM YB and AB can be pooled while

some prediction accuracy will be lost if the two means for BW and BC are pooled (See the two

means shown for each species earlier in the paper) Note that there is no topwood for the one AE

tree in the data set Therefore the pooled mean is the stemwood mean for AE

-15shy

The pooled mean bark factors are

903 (54) RM middot BF = BF = L Bfl 903 = 0980 0015980

i=1

485 (55) WA BF = BF = L Bfl485 = 0932 0023614

i=1

1830 (56) SM BF= BF= L Bfl1830 = 0976 0015029

i=1

436 (57) BW BF = BF = L Bfl436 = 0970 0013134

i=l

210 (58) BC BF = BF = L Bfl210 = 0966 0014725

i=l

92 (59) YB BF = BF = L BFi92 = 0990 0004025

i=l

175 (60) AB BF = BF = L BF)l75 = 0995 0004248

i=1

See the table based on Equations 47-53 to see where Equations 54-60 under- and overestimate

respectively

Bark thickness

For the stemwood data set (n=3506) BT was significantly different for the eight different

species (Bartletts x2 -test for equal variances PltOOOl F-test for equal means PltOOOl) All

Bonferroni pairwise comparisons of means are significantly different except for (RM YB) (RM

AE) (WA AE) (SM AE) (BW AE) (BC AE) (YB AB) and (BW BC) Note that the sample

size for AE is only 6

Average minimum and maximum BTs and Pearsons correlations of BT with DOB DBH

and TH are shown below for the eight species

-16shy

BT BTDOB BTDBH BTTHSpecies nx Min-Max r p r p r p

RM 0077 0005-0525 0678 lt0001 0484 lt0001 -0369 lt0001 829 WA 0263 0012-1760 0632 lt0001 0428 lt0001 -0329 lt0001 410 SM 0113 0008-0672 0794 lt0001 0685 lt0001 -0293 lt0001 1488 BW 0158 0005-0525 0738 lt0001 0633 lt0001 -0192 lt0001 398 BC 0145 0012-0438 0653 lt0001 0169 0024 -0683 lt0001 178 YB 0046 0020-0115 0448 lt0001 0234 0058 -0383 0002 66 AB 0024 0005-0395 0236 0007 0067 0448 -0229 0009 131 AE 0195 0170-0228 -0511 0300 0405 0425 6

AE data consists of six measurements from one tree

BT was significantly positively related to DOB for all species except for AE where there was a

negative relation that was not significant BT was significantly positively related to DBH for all

species except for YB and AB where the positive relations were not significant BT was

significantly negatively related to TH for all species except for AE where there was a positive

relationship that was not significant

Average BTs for various DOB and TH classes for the eight species are as follows

DOB Class BT (in) RM WA SM BW BC YB AB AE

~400

401 to 800 801 to 1200 1201 to 1600

gt1600

0017 0054 0134 0239 0236

0091 0220 0321 0394 0468

0024 0060 0141 0225 0324

0032 0093 0150 0119 0268

0058 0101 0192 0252 0199

0020 0032 0048 0060 0058

0022 0019 0019 0020 0048

0200 0170

THClass BT (ft) RM WA SM BW BC YB AB AE

~050 0134 0208 0146 0114 0263 0038 0036 051 to 450 0110 0338 0161 0199 0192 0057 0038 0180 451 to 1000 0080 0296 0105 0165 0169 0047 0021 1001 to 2000 0065 0278 010(1 0153 0140 0049 0016 0210 2001 to 3000 0060 0250 0094 0146 0102 0041 0016 0200 3001 to 4000 0045 0220 0089 0134 0087 0037 0014 0190 4001 to 5000 0038 0220 0062 0153 0061 0025 0015

~5000 0016 0159 0047 0136 0038 0016

-17shy

In general BT is smallest for AB followed by YB RM SM BC BW and AE in increasing order

with BT for WA being the largest In general BT increases with DOB and decreases with TH

Most of the anomalies are due to small sample sizes

For the topwood data set (n=631) BT was significantly different for the seven different

species (Bartletts -test for equal variances PltOOOl F-test for equal means PltOOOl) All

Bonferroni pairwise comparisons of means are significantly different except for (RM SM) (RM

BC) (RM YB) (SM BC) (BC YB) and (YB AB)

Average minimum and maximum BTs and Pearsons correlations of BT with DOB and DBH

are shown below for the seven species

Species x

BT

Min- Max

BT DOB p r

BTDBH p n

RM WA SM BW BC YB AB

0064 0203 0086 0150 0083 0034 0019

0008-0385 0022-0458 0005-0362 0018-0262 0018-0175 Ool5-0075 0008-0038

06SO 0723 0768 0813 0723 0464 0051

lt0001 lt0001 lt0001 lt0001 lt0001

0017 0744

0549 0360 0440 0588 0380 0216 0661

lt0001 0002

lt0001 lt0001

0032 0290

lt0001

74 75

342 38 32 26 44

BT was significantly positively related to DOB for all species except for AB and to DBH for all

species except for YB

Average BTs for various DOB classes for the seven species are as follows

DOB Class BT (in) RM WA S~t BW BC YB AB

500 OQl8 0126 oltH) 0054 0051 0024 0021 501 to 700 0073 0212 () t)(J 0105 0086 0032 0019 701 to 900 0152 0281 () Ill 0170 0115 0057 0015 901 to 1100 0158 0255 () 177 0193 0114 0043 0020

111 to 1300 0122 0345 0222 0205 0135 0026

-18shy

In general BT is smallest for AB followed by YB BC RM SM and BW in increasing order

with BT for W A being the largest In general BT increases with DOB Most of the anomalies are

due to small sample sizes

Comparison with other BF equations

Fowler (1993) showed that while there were significant species differences between BF

equations for aspen jack pine and red pine there was a very strong relationship between BF and

tree height for each species (ie R 2 gt097 for each species) BF was a function of TH and In TH

showing that BF increased with TH to some maximum and then decreased for larger THs with the

steepness of the decrease depending on the species For all three species BF was not strongly

related to DBH or DOB at a given TH

For paper birch (Fowler and Hussain 1997) BF significantly increased with DOB at TH

(R2 =0219) and significantly decreased with In TH (R2 =0166) for stemwood while BF

significantly increased with DOB for topwood ( R 2 =0218) BF was much more variable than for

aspen red pine and jack pine

Fowler et al (1997) showed that black oak (BO) red oak (RO) and white oak (WO) have BPs

that are quite variable and prediction equations with the same independent variables as for paper

birch with the direction of the relations reversed For stemwood BF decreased with DOB at TH

( R 2 =0270 0418 and 0014 for BO RO and WO respectively) and increased with In TH ( R 2 =

0190 0275 and 0011 for BO RO and WO respectively) For topwood BF decreased with DOB

(R2=0366 0457 and 0100 for BO RO and WO respectively) These prediction equations were

significant but they were only moderately strong at best being only somewhat stronger in general

than the prediction equations for paper birch The prediction equations based on DOB were

-19shy

somewhat stronger than the prediction equations based on In TH The BF equations were

significantly different for the three species and for topwood versus stemwood except for RO

This study shows that the eight northern hardwood species have BFs that are quite variable

with some species having prediction equations with the same independent variables as for paper

birch and the three oak species while other species had different independent variables For

stemwood BF decreased with DOB at TH for RM SM BW and BC increased with In DOB at TH

for W A YB and AE and increased and then somewhat decreased with 1DOB and In DOB as the

independent variables for AB BF increased with In TH for RM SM and BC decreased and then

increased with TH and In TH for WA and BW increased and then decreased with TH and In TH for

YB AB and AE The prediction equations for AE are very suspect as they were based on only six

BF measurements from one tree For topwood BF decreased with DOB for RM WA SM BW

and BC increased with DOB for YB and increased and somewhat decreased with 1DOB and

In DOB for AB All prediction equations for stemwood were significant except for the TH

equations for BW and YB For topwood only the prediction equations for RM SM BW and AB

were significant In general all prediction equations were only moderately strong at best and some

of them were very weak The BF equations were significantly different for most species while the

stemwood and topwood BF equations were not significantly different except for RM and SM

GUIDELINES FOR USERS

We recommend use of the following equations for northern hardwoods when accurate

estimates of bark factors are desired

Stemwood

bull Red maple I

(1) BF =0996730-0002397 bull DOB I

(2) BF =0972344 + 0003554 bull In TH

-20shy

bull White ash 1

(3) BF = 0922166 +0001198bull DOB 1

(4) BF = 0937036 + 0000805 bull TH- 0009279 bullIn TH

bull- Sugar maple 1

(5) BF=0988318-0001497bullDOB 1

(6) BF = 0970865 + 0002264 bullIn TH

bull Basswood 1

(7) BF = 0974486-0000403 bull DOB 1

(8) BF = 0970312 + 0000072 bull TH- 0000631bullln TH

bull Black cherry 1

(9) BF = 0971912 -0000841bull DOB 1

(lO) BF = 0954777 + 0004557 bullIn TH

bull Yell ow birch 1

(11) BF = 0987390 + 0000307 bull DOB 1

(12) BF = 0990354-0000111bull TH+0000885bullln TH

bull American beech 1

(l3) BF = l027382-0l03065DOB -0009012bullln DOB

1

(14) BF = 0994075-0000047 bull TH+0000896 bullIn TH

bull American elm 1

(l5) BF =0925851 + 0003400 bull DOB 1

(16) BF = 0975815-0000058 bull TH- 0()()4696bullln TH

Use Equations 1 3 5 7 9 11 13 and 15 if DOBis measured Use Equations 2 4 6 8 10 12 14

and 16 when only THis measured

Topwood 1

(l7) RM BF = 1006791-0004569 bull DOB 1

(18) WA BF = 0936727 -0000206bull DOB 1

(l9) SM BF = 0995302-0002757 bull DOB

-21shy

(20) BW BF = 0979121-0002155 bull DOB

(21) BC BF = 0977830- 0000604 bull DOB

(22) YB BF = 0987032 + 0000281bull DOB

(23) AB BF = 1038966- 0131661DOB - 0012832 bullln DOB

The equation for stemwood and topwood pooled could be used if DOB is measured with moderate

loss in accuracy for RM and SM and little loss in accuracy for the other five species The pooled

equations in general will be more accurate for stemwood compared to topwood especially for RM

and SM

(24) RM BF == 0997087 -0002476bull DOB

1

(25) WA BF = 0924553 + 000 I 003 bull DOB

(26) SM BF=0988615-0001568bullDOB

(27) BW BF = 0972865-0000320 bull DOB

(28) BC BF=0974512-0001028bullDOB

(29) YB BF = 0986997 + 0000334 bull DOB

(30) AB BF = 1028314- 0105996DOB- 0009288 bullIn DOB

There is no pooled equation for AE as there was no topwood for the one AE tree in the data set

For reasonable accuracy in many situations the following constants could be used for bark

factors

DOB Class Stemwood BF (in) RM WA St-1 BW BC YB AB AE

DOBs50 0988 0927 09S~ 0973 0969 0989 0988 0939 50ltDOBsl00 0979 0931 0977 0971 0966 0990 0995 0951 l00ltDOBs150 0967 0937 0970 0969 0962 0991 0996 0968 150ltDOBs200 0955 0943 0962 0967 0957 0993 0996 0985

DOBgt200 0943 0949 0954 0965 0953 0994 0995 0994

-22shy

DOB Class ToEwoodBF (in) RM WA SM BW BC YB AB

DOBS50 0989 0936 0984 0971 0975 0988 0987 50ltD0BSl00 0970 0935 0973 0962 0973 0989 0995 100ltD0BS150 0947 0934 0959 0951 0970 0991 0996 150ltD0BS200 0924 0933 0946 0940 0967 0992 0995

008gt200 0902 0932 0932 0930 0964 0993 0993

TH Stemwood BF (ft) RM WA SM BW BC YB AB AE

THS05 0970 0947 0971 0971 0950 0990 0993 0980 05ltTHS45 0974 0932 olJn 0970 0959 0991 0995 0972

45ltTHS 100 0978 0925 0974 0970 0964 0991 0996 0966 100ltTHS200 0980 0924 0gt76 0970 0967 0991 0996 0963 200ltTHS300 0984 0928 0gt7S 0970 0970 0990 0996 0959 300ltTHS400 0986 0932 OltJSO 0971 0971 0990 0996 0957 400ltTHS500 0988 0937 () l)S~ 0971 0972 0989 0995 0955

THgt500 0992 0950 07 0974 0974 0987 0995 0952

The following constants for bark factor could be used for simplicity with moderately

approximate results especially for a large number of treessticks

Species Stem wood Top wood Stemwood and Topwood

RM 0980 0981 0980 WA 0932 0935 0932 SM 0976 0977 0976 BW 0970 0962 0970 BC 0965 0974 0966 YB 0991 0989 0990 AB 0995 0995 0995 AE 0964 0964

The above constants would be more accurate for those species that did not have significant

prediction equations andor small sample sizes B~ cry careful with using any of the results of this

study outside the range of the data set for each species Since the results for AE are based on six

stemwood measurements from one tree they arc of course very suspect

-23shy

Use of prediction equations

The prediction equations can be used to estimate BF at any DOB andor TH Since

BF=DIBDOB DIB can be estimated as DIB=BFbull DOB and DOB can be estimated as

DOB=DIBBF Past DOB and DOB growth can be estimated from past DIB growth as follows

Past DOB Growth=Past DIB GrowthBF

and

Past DOB=Present DOB -Past DOB Growth

where past DIB growth might be obtained with an increment borer

Specific uses of the prediction equations include (1) estimation of the solid wood and bark

volume of standing trees (2) estimation of bark volume or peeled volume from unpeeled volume

of felled tree sections (3) growth studies and (4) estimating tree form (eg Girard Form Class)

See Husch et al ( 1982) for a detailed discussion on bark factors

-24- LITERATURE CITED middot

Fowler G W 1991 An aspen bark factor equation for Michigan North J Appl For 8(1) 12-15

Fowler G W 1993 A jack pine bark factor equation for Michigan North J Appl For 10(2) 86-89

Fowler G W and L J Damschroder 1988 A red pine bark factor equation for Michigan North J Appl For 5(1) 28-30

Fowler G W and N G Hussain 1987a Bark factor equation for red pine Michigan DNR For Infor Leaflet 1-87 2 p

Fowler G W and N G Hussain 1987b Bark factor equation for aspen Michigan DNR For Infor Leaflet 2-87 2 p

Fowler G W and N G Hussain 1991 Bark factor equation for jack pine in Michigan Michigan DNR For Infor Leaflet 1-91 5 p

Fowler G W and N G Hussain 1997 Bark factor equations for paper birch in Michigan Michigan DNR For Infor Leaflet 1-97 12 p

Fowler G W N G Hussain D J Cohen and D Khatry-Chhetri 1997 Bark factor equations for oak in Michigan Michigan DNR For Infor Leaflet 2-97 15 p

Husch B C I Miller and T W Beers 1982 Forest Mensuration John Wiley and Sons Inc NY 402 p

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lonst Manbullpmeut DWisioa 15 Resource Mana1ement Units

bullJfectble l2519bull

bull -Resource Jf~nt Unit OJke

1 -Raource Jf~nt Unit BOUIIdariea

1 -CountyBouruiiJrfea

-13shy

R2 sybullx p n

1

(53) AB BF =1028314- 0105996DOB 0201 0003819 lt0001 175

- 0009288 bull In DOB

Prediction equations 47-53 for RM WA SM BW BC YB and AB respectively yield the

following estimated bark factors

Prediction Equations 47-53

1

DOB BF (in) RM WA SM BW BC YB AB

30 0990 0928 0984 0972 0971 0988 0983 40 0987 0929 0982 0972 0970 0988 0989 50 0985 0930 0981 0971 0969 0989 0992 60 0982 0931 0979 0971 0968 0989 0994 70 0980 0932 0978 0971 0967 0989 0995 80 0977 0933 0976 0970 0966 0989 0996 90 0975 0934 0975 0970 0965 0990 0996

100 0972 0935 0973 0969 0964 0990 0996 110 0970 0936 0971 0969 0963 0991 0996 120 0967 0937 0970 0969 0962 0991 0996 130 0965 0938 0968 0968 0961 0991 0996 140 0962 0939 0967 0968 0960 0992 0996 150 0960 0940 0965 0968 0959 0992 0996 160 0957 0941 0964 0968 0958 0992 0996 170 0955 0942 0962 0967 0957 0993 0996 180 0953 0943 0960 0967 0956 0993 0996 190 0950 0944 0959 0967 0955 0993 0995 200 0948 0945 0957 0966 0954 0994 0995 210 0945 0946 0956 0966 0953 0994 0995 220 0943 0947 0954 0966 0952 0994 0995 230 0940 0948 0953 0966 0951 0995 0995 240 0938 0949 0951 0965 0950 0995 0994 250 0935 0950 0949 0965 0949 0995 0994

Note that the pooled BF estimates for each species are close to those of Equations 1 4 7 10

13 16 and 19 for stemwood This makes sense since the stemwood sample sizes were considerably

larger than the topwood sample sizes for each species For topwood the pooled BF estimates for

YB and AB are very close to Equations 38 and 39 respectively for topwood However there are

some larger differences for the other species over the range of DOB from 30-200 inches

-14shy

bull RM - Pooled BF estimates are lower than those of Equation 33 for DOB lt 50 in and higher for DOB ~ 50 in (from 0003 lower to 0033 higher)

bull WA - Pooled BF estimates are lower than those of Equation 34 for DOB lt 100 in and higher for DOB gt 100 in (from 0008 lower to 0012 higher)

bull SM - Pooled BF estimates are lower than those of Equation 35 for DOB lt 60 in and higher for DOB gt 60 in (from 0003 lower to 0017 higher)

bull BW - Pooled BF estimates are lower than those of Equation 36 for DOB lt 40 in and higher for DOB ~ 40 in (from 0001 lower to 0030 higher)

bull BC - Pooled BF estimates are lower than those of Equation 37 for all values of DOB (from 0005 to 0012lower)

The ranges of the pooled predicted BF values for DOB from 30 to 250 in are 0055 0022 0035

0007 0022 0007 and 0013 for RM WA SM BW BC YB and AB respectively Because of

these moderate to small ranges the low R2 values of the prediction equations and some of the

prediction equations not being significant you might argue that the mean bark factor yields an

adequate prediction model

The stemwood and topwood mean BFs were compared for each of the species The resulting

P-values are as follows

Species Bartletts zLtest

for Equal Variances F-test for Equal

Regression Coefficients

RM 0013 0681 WA 0770 0202 SM 0775 0287 BW 0196 0004 BC 0004 0001 YB 0222 0055 AB 0005 0542

Bonferroni level of significance a PC =00057 =0007

The above results indicate that the two means for RM W A SM YB and AB can be pooled while

some prediction accuracy will be lost if the two means for BW and BC are pooled (See the two

means shown for each species earlier in the paper) Note that there is no topwood for the one AE

tree in the data set Therefore the pooled mean is the stemwood mean for AE

-15shy

The pooled mean bark factors are

903 (54) RM middot BF = BF = L Bfl 903 = 0980 0015980

i=1

485 (55) WA BF = BF = L Bfl485 = 0932 0023614

i=1

1830 (56) SM BF= BF= L Bfl1830 = 0976 0015029

i=1

436 (57) BW BF = BF = L Bfl436 = 0970 0013134

i=l

210 (58) BC BF = BF = L Bfl210 = 0966 0014725

i=l

92 (59) YB BF = BF = L BFi92 = 0990 0004025

i=l

175 (60) AB BF = BF = L BF)l75 = 0995 0004248

i=1

See the table based on Equations 47-53 to see where Equations 54-60 under- and overestimate

respectively

Bark thickness

For the stemwood data set (n=3506) BT was significantly different for the eight different

species (Bartletts x2 -test for equal variances PltOOOl F-test for equal means PltOOOl) All

Bonferroni pairwise comparisons of means are significantly different except for (RM YB) (RM

AE) (WA AE) (SM AE) (BW AE) (BC AE) (YB AB) and (BW BC) Note that the sample

size for AE is only 6

Average minimum and maximum BTs and Pearsons correlations of BT with DOB DBH

and TH are shown below for the eight species

-16shy

BT BTDOB BTDBH BTTHSpecies nx Min-Max r p r p r p

RM 0077 0005-0525 0678 lt0001 0484 lt0001 -0369 lt0001 829 WA 0263 0012-1760 0632 lt0001 0428 lt0001 -0329 lt0001 410 SM 0113 0008-0672 0794 lt0001 0685 lt0001 -0293 lt0001 1488 BW 0158 0005-0525 0738 lt0001 0633 lt0001 -0192 lt0001 398 BC 0145 0012-0438 0653 lt0001 0169 0024 -0683 lt0001 178 YB 0046 0020-0115 0448 lt0001 0234 0058 -0383 0002 66 AB 0024 0005-0395 0236 0007 0067 0448 -0229 0009 131 AE 0195 0170-0228 -0511 0300 0405 0425 6

AE data consists of six measurements from one tree

BT was significantly positively related to DOB for all species except for AE where there was a

negative relation that was not significant BT was significantly positively related to DBH for all

species except for YB and AB where the positive relations were not significant BT was

significantly negatively related to TH for all species except for AE where there was a positive

relationship that was not significant

Average BTs for various DOB and TH classes for the eight species are as follows

DOB Class BT (in) RM WA SM BW BC YB AB AE

~400

401 to 800 801 to 1200 1201 to 1600

gt1600

0017 0054 0134 0239 0236

0091 0220 0321 0394 0468

0024 0060 0141 0225 0324

0032 0093 0150 0119 0268

0058 0101 0192 0252 0199

0020 0032 0048 0060 0058

0022 0019 0019 0020 0048

0200 0170

THClass BT (ft) RM WA SM BW BC YB AB AE

~050 0134 0208 0146 0114 0263 0038 0036 051 to 450 0110 0338 0161 0199 0192 0057 0038 0180 451 to 1000 0080 0296 0105 0165 0169 0047 0021 1001 to 2000 0065 0278 010(1 0153 0140 0049 0016 0210 2001 to 3000 0060 0250 0094 0146 0102 0041 0016 0200 3001 to 4000 0045 0220 0089 0134 0087 0037 0014 0190 4001 to 5000 0038 0220 0062 0153 0061 0025 0015

~5000 0016 0159 0047 0136 0038 0016

-17shy

In general BT is smallest for AB followed by YB RM SM BC BW and AE in increasing order

with BT for WA being the largest In general BT increases with DOB and decreases with TH

Most of the anomalies are due to small sample sizes

For the topwood data set (n=631) BT was significantly different for the seven different

species (Bartletts -test for equal variances PltOOOl F-test for equal means PltOOOl) All

Bonferroni pairwise comparisons of means are significantly different except for (RM SM) (RM

BC) (RM YB) (SM BC) (BC YB) and (YB AB)

Average minimum and maximum BTs and Pearsons correlations of BT with DOB and DBH

are shown below for the seven species

Species x

BT

Min- Max

BT DOB p r

BTDBH p n

RM WA SM BW BC YB AB

0064 0203 0086 0150 0083 0034 0019

0008-0385 0022-0458 0005-0362 0018-0262 0018-0175 Ool5-0075 0008-0038

06SO 0723 0768 0813 0723 0464 0051

lt0001 lt0001 lt0001 lt0001 lt0001

0017 0744

0549 0360 0440 0588 0380 0216 0661

lt0001 0002

lt0001 lt0001

0032 0290

lt0001

74 75

342 38 32 26 44

BT was significantly positively related to DOB for all species except for AB and to DBH for all

species except for YB

Average BTs for various DOB classes for the seven species are as follows

DOB Class BT (in) RM WA S~t BW BC YB AB

500 OQl8 0126 oltH) 0054 0051 0024 0021 501 to 700 0073 0212 () t)(J 0105 0086 0032 0019 701 to 900 0152 0281 () Ill 0170 0115 0057 0015 901 to 1100 0158 0255 () 177 0193 0114 0043 0020

111 to 1300 0122 0345 0222 0205 0135 0026

-18shy

In general BT is smallest for AB followed by YB BC RM SM and BW in increasing order

with BT for W A being the largest In general BT increases with DOB Most of the anomalies are

due to small sample sizes

Comparison with other BF equations

Fowler (1993) showed that while there were significant species differences between BF

equations for aspen jack pine and red pine there was a very strong relationship between BF and

tree height for each species (ie R 2 gt097 for each species) BF was a function of TH and In TH

showing that BF increased with TH to some maximum and then decreased for larger THs with the

steepness of the decrease depending on the species For all three species BF was not strongly

related to DBH or DOB at a given TH

For paper birch (Fowler and Hussain 1997) BF significantly increased with DOB at TH

(R2 =0219) and significantly decreased with In TH (R2 =0166) for stemwood while BF

significantly increased with DOB for topwood ( R 2 =0218) BF was much more variable than for

aspen red pine and jack pine

Fowler et al (1997) showed that black oak (BO) red oak (RO) and white oak (WO) have BPs

that are quite variable and prediction equations with the same independent variables as for paper

birch with the direction of the relations reversed For stemwood BF decreased with DOB at TH

( R 2 =0270 0418 and 0014 for BO RO and WO respectively) and increased with In TH ( R 2 =

0190 0275 and 0011 for BO RO and WO respectively) For topwood BF decreased with DOB

(R2=0366 0457 and 0100 for BO RO and WO respectively) These prediction equations were

significant but they were only moderately strong at best being only somewhat stronger in general

than the prediction equations for paper birch The prediction equations based on DOB were

-19shy

somewhat stronger than the prediction equations based on In TH The BF equations were

significantly different for the three species and for topwood versus stemwood except for RO

This study shows that the eight northern hardwood species have BFs that are quite variable

with some species having prediction equations with the same independent variables as for paper

birch and the three oak species while other species had different independent variables For

stemwood BF decreased with DOB at TH for RM SM BW and BC increased with In DOB at TH

for W A YB and AE and increased and then somewhat decreased with 1DOB and In DOB as the

independent variables for AB BF increased with In TH for RM SM and BC decreased and then

increased with TH and In TH for WA and BW increased and then decreased with TH and In TH for

YB AB and AE The prediction equations for AE are very suspect as they were based on only six

BF measurements from one tree For topwood BF decreased with DOB for RM WA SM BW

and BC increased with DOB for YB and increased and somewhat decreased with 1DOB and

In DOB for AB All prediction equations for stemwood were significant except for the TH

equations for BW and YB For topwood only the prediction equations for RM SM BW and AB

were significant In general all prediction equations were only moderately strong at best and some

of them were very weak The BF equations were significantly different for most species while the

stemwood and topwood BF equations were not significantly different except for RM and SM

GUIDELINES FOR USERS

We recommend use of the following equations for northern hardwoods when accurate

estimates of bark factors are desired

Stemwood

bull Red maple I

(1) BF =0996730-0002397 bull DOB I

(2) BF =0972344 + 0003554 bull In TH

-20shy

bull White ash 1

(3) BF = 0922166 +0001198bull DOB 1

(4) BF = 0937036 + 0000805 bull TH- 0009279 bullIn TH

bull- Sugar maple 1

(5) BF=0988318-0001497bullDOB 1

(6) BF = 0970865 + 0002264 bullIn TH

bull Basswood 1

(7) BF = 0974486-0000403 bull DOB 1

(8) BF = 0970312 + 0000072 bull TH- 0000631bullln TH

bull Black cherry 1

(9) BF = 0971912 -0000841bull DOB 1

(lO) BF = 0954777 + 0004557 bullIn TH

bull Yell ow birch 1

(11) BF = 0987390 + 0000307 bull DOB 1

(12) BF = 0990354-0000111bull TH+0000885bullln TH

bull American beech 1

(l3) BF = l027382-0l03065DOB -0009012bullln DOB

1

(14) BF = 0994075-0000047 bull TH+0000896 bullIn TH

bull American elm 1

(l5) BF =0925851 + 0003400 bull DOB 1

(16) BF = 0975815-0000058 bull TH- 0()()4696bullln TH

Use Equations 1 3 5 7 9 11 13 and 15 if DOBis measured Use Equations 2 4 6 8 10 12 14

and 16 when only THis measured

Topwood 1

(l7) RM BF = 1006791-0004569 bull DOB 1

(18) WA BF = 0936727 -0000206bull DOB 1

(l9) SM BF = 0995302-0002757 bull DOB

-21shy

(20) BW BF = 0979121-0002155 bull DOB

(21) BC BF = 0977830- 0000604 bull DOB

(22) YB BF = 0987032 + 0000281bull DOB

(23) AB BF = 1038966- 0131661DOB - 0012832 bullln DOB

The equation for stemwood and topwood pooled could be used if DOB is measured with moderate

loss in accuracy for RM and SM and little loss in accuracy for the other five species The pooled

equations in general will be more accurate for stemwood compared to topwood especially for RM

and SM

(24) RM BF == 0997087 -0002476bull DOB

1

(25) WA BF = 0924553 + 000 I 003 bull DOB

(26) SM BF=0988615-0001568bullDOB

(27) BW BF = 0972865-0000320 bull DOB

(28) BC BF=0974512-0001028bullDOB

(29) YB BF = 0986997 + 0000334 bull DOB

(30) AB BF = 1028314- 0105996DOB- 0009288 bullIn DOB

There is no pooled equation for AE as there was no topwood for the one AE tree in the data set

For reasonable accuracy in many situations the following constants could be used for bark

factors

DOB Class Stemwood BF (in) RM WA St-1 BW BC YB AB AE

DOBs50 0988 0927 09S~ 0973 0969 0989 0988 0939 50ltDOBsl00 0979 0931 0977 0971 0966 0990 0995 0951 l00ltDOBs150 0967 0937 0970 0969 0962 0991 0996 0968 150ltDOBs200 0955 0943 0962 0967 0957 0993 0996 0985

DOBgt200 0943 0949 0954 0965 0953 0994 0995 0994

-22shy

DOB Class ToEwoodBF (in) RM WA SM BW BC YB AB

DOBS50 0989 0936 0984 0971 0975 0988 0987 50ltD0BSl00 0970 0935 0973 0962 0973 0989 0995 100ltD0BS150 0947 0934 0959 0951 0970 0991 0996 150ltD0BS200 0924 0933 0946 0940 0967 0992 0995

008gt200 0902 0932 0932 0930 0964 0993 0993

TH Stemwood BF (ft) RM WA SM BW BC YB AB AE

THS05 0970 0947 0971 0971 0950 0990 0993 0980 05ltTHS45 0974 0932 olJn 0970 0959 0991 0995 0972

45ltTHS 100 0978 0925 0974 0970 0964 0991 0996 0966 100ltTHS200 0980 0924 0gt76 0970 0967 0991 0996 0963 200ltTHS300 0984 0928 0gt7S 0970 0970 0990 0996 0959 300ltTHS400 0986 0932 OltJSO 0971 0971 0990 0996 0957 400ltTHS500 0988 0937 () l)S~ 0971 0972 0989 0995 0955

THgt500 0992 0950 07 0974 0974 0987 0995 0952

The following constants for bark factor could be used for simplicity with moderately

approximate results especially for a large number of treessticks

Species Stem wood Top wood Stemwood and Topwood

RM 0980 0981 0980 WA 0932 0935 0932 SM 0976 0977 0976 BW 0970 0962 0970 BC 0965 0974 0966 YB 0991 0989 0990 AB 0995 0995 0995 AE 0964 0964

The above constants would be more accurate for those species that did not have significant

prediction equations andor small sample sizes B~ cry careful with using any of the results of this

study outside the range of the data set for each species Since the results for AE are based on six

stemwood measurements from one tree they arc of course very suspect

-23shy

Use of prediction equations

The prediction equations can be used to estimate BF at any DOB andor TH Since

BF=DIBDOB DIB can be estimated as DIB=BFbull DOB and DOB can be estimated as

DOB=DIBBF Past DOB and DOB growth can be estimated from past DIB growth as follows

Past DOB Growth=Past DIB GrowthBF

and

Past DOB=Present DOB -Past DOB Growth

where past DIB growth might be obtained with an increment borer

Specific uses of the prediction equations include (1) estimation of the solid wood and bark

volume of standing trees (2) estimation of bark volume or peeled volume from unpeeled volume

of felled tree sections (3) growth studies and (4) estimating tree form (eg Girard Form Class)

See Husch et al ( 1982) for a detailed discussion on bark factors

-24- LITERATURE CITED middot

Fowler G W 1991 An aspen bark factor equation for Michigan North J Appl For 8(1) 12-15

Fowler G W 1993 A jack pine bark factor equation for Michigan North J Appl For 10(2) 86-89

Fowler G W and L J Damschroder 1988 A red pine bark factor equation for Michigan North J Appl For 5(1) 28-30

Fowler G W and N G Hussain 1987a Bark factor equation for red pine Michigan DNR For Infor Leaflet 1-87 2 p

Fowler G W and N G Hussain 1987b Bark factor equation for aspen Michigan DNR For Infor Leaflet 2-87 2 p

Fowler G W and N G Hussain 1991 Bark factor equation for jack pine in Michigan Michigan DNR For Infor Leaflet 1-91 5 p

Fowler G W and N G Hussain 1997 Bark factor equations for paper birch in Michigan Michigan DNR For Infor Leaflet 1-97 12 p

Fowler G W N G Hussain D J Cohen and D Khatry-Chhetri 1997 Bark factor equations for oak in Michigan Michigan DNR For Infor Leaflet 2-97 15 p

Husch B C I Miller and T W Beers 1982 Forest Mensuration John Wiley and Sons Inc NY 402 p

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Ken Alto

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lonst Manbullpmeut DWisioa 15 Resource Mana1ement Units

bullJfectble l2519bull

bull -Resource Jf~nt Unit OJke

1 -Raource Jf~nt Unit BOUIIdariea

1 -CountyBouruiiJrfea

-14shy

bull RM - Pooled BF estimates are lower than those of Equation 33 for DOB lt 50 in and higher for DOB ~ 50 in (from 0003 lower to 0033 higher)

bull WA - Pooled BF estimates are lower than those of Equation 34 for DOB lt 100 in and higher for DOB gt 100 in (from 0008 lower to 0012 higher)

bull SM - Pooled BF estimates are lower than those of Equation 35 for DOB lt 60 in and higher for DOB gt 60 in (from 0003 lower to 0017 higher)

bull BW - Pooled BF estimates are lower than those of Equation 36 for DOB lt 40 in and higher for DOB ~ 40 in (from 0001 lower to 0030 higher)

bull BC - Pooled BF estimates are lower than those of Equation 37 for all values of DOB (from 0005 to 0012lower)

The ranges of the pooled predicted BF values for DOB from 30 to 250 in are 0055 0022 0035

0007 0022 0007 and 0013 for RM WA SM BW BC YB and AB respectively Because of

these moderate to small ranges the low R2 values of the prediction equations and some of the

prediction equations not being significant you might argue that the mean bark factor yields an

adequate prediction model

The stemwood and topwood mean BFs were compared for each of the species The resulting

P-values are as follows

Species Bartletts zLtest

for Equal Variances F-test for Equal

Regression Coefficients

RM 0013 0681 WA 0770 0202 SM 0775 0287 BW 0196 0004 BC 0004 0001 YB 0222 0055 AB 0005 0542

Bonferroni level of significance a PC =00057 =0007

The above results indicate that the two means for RM W A SM YB and AB can be pooled while

some prediction accuracy will be lost if the two means for BW and BC are pooled (See the two

means shown for each species earlier in the paper) Note that there is no topwood for the one AE

tree in the data set Therefore the pooled mean is the stemwood mean for AE

-15shy

The pooled mean bark factors are

903 (54) RM middot BF = BF = L Bfl 903 = 0980 0015980

i=1

485 (55) WA BF = BF = L Bfl485 = 0932 0023614

i=1

1830 (56) SM BF= BF= L Bfl1830 = 0976 0015029

i=1

436 (57) BW BF = BF = L Bfl436 = 0970 0013134

i=l

210 (58) BC BF = BF = L Bfl210 = 0966 0014725

i=l

92 (59) YB BF = BF = L BFi92 = 0990 0004025

i=l

175 (60) AB BF = BF = L BF)l75 = 0995 0004248

i=1

See the table based on Equations 47-53 to see where Equations 54-60 under- and overestimate

respectively

Bark thickness

For the stemwood data set (n=3506) BT was significantly different for the eight different

species (Bartletts x2 -test for equal variances PltOOOl F-test for equal means PltOOOl) All

Bonferroni pairwise comparisons of means are significantly different except for (RM YB) (RM

AE) (WA AE) (SM AE) (BW AE) (BC AE) (YB AB) and (BW BC) Note that the sample

size for AE is only 6

Average minimum and maximum BTs and Pearsons correlations of BT with DOB DBH

and TH are shown below for the eight species

-16shy

BT BTDOB BTDBH BTTHSpecies nx Min-Max r p r p r p

RM 0077 0005-0525 0678 lt0001 0484 lt0001 -0369 lt0001 829 WA 0263 0012-1760 0632 lt0001 0428 lt0001 -0329 lt0001 410 SM 0113 0008-0672 0794 lt0001 0685 lt0001 -0293 lt0001 1488 BW 0158 0005-0525 0738 lt0001 0633 lt0001 -0192 lt0001 398 BC 0145 0012-0438 0653 lt0001 0169 0024 -0683 lt0001 178 YB 0046 0020-0115 0448 lt0001 0234 0058 -0383 0002 66 AB 0024 0005-0395 0236 0007 0067 0448 -0229 0009 131 AE 0195 0170-0228 -0511 0300 0405 0425 6

AE data consists of six measurements from one tree

BT was significantly positively related to DOB for all species except for AE where there was a

negative relation that was not significant BT was significantly positively related to DBH for all

species except for YB and AB where the positive relations were not significant BT was

significantly negatively related to TH for all species except for AE where there was a positive

relationship that was not significant

Average BTs for various DOB and TH classes for the eight species are as follows

DOB Class BT (in) RM WA SM BW BC YB AB AE

~400

401 to 800 801 to 1200 1201 to 1600

gt1600

0017 0054 0134 0239 0236

0091 0220 0321 0394 0468

0024 0060 0141 0225 0324

0032 0093 0150 0119 0268

0058 0101 0192 0252 0199

0020 0032 0048 0060 0058

0022 0019 0019 0020 0048

0200 0170

THClass BT (ft) RM WA SM BW BC YB AB AE

~050 0134 0208 0146 0114 0263 0038 0036 051 to 450 0110 0338 0161 0199 0192 0057 0038 0180 451 to 1000 0080 0296 0105 0165 0169 0047 0021 1001 to 2000 0065 0278 010(1 0153 0140 0049 0016 0210 2001 to 3000 0060 0250 0094 0146 0102 0041 0016 0200 3001 to 4000 0045 0220 0089 0134 0087 0037 0014 0190 4001 to 5000 0038 0220 0062 0153 0061 0025 0015

~5000 0016 0159 0047 0136 0038 0016

-17shy

In general BT is smallest for AB followed by YB RM SM BC BW and AE in increasing order

with BT for WA being the largest In general BT increases with DOB and decreases with TH

Most of the anomalies are due to small sample sizes

For the topwood data set (n=631) BT was significantly different for the seven different

species (Bartletts -test for equal variances PltOOOl F-test for equal means PltOOOl) All

Bonferroni pairwise comparisons of means are significantly different except for (RM SM) (RM

BC) (RM YB) (SM BC) (BC YB) and (YB AB)

Average minimum and maximum BTs and Pearsons correlations of BT with DOB and DBH

are shown below for the seven species

Species x

BT

Min- Max

BT DOB p r

BTDBH p n

RM WA SM BW BC YB AB

0064 0203 0086 0150 0083 0034 0019

0008-0385 0022-0458 0005-0362 0018-0262 0018-0175 Ool5-0075 0008-0038

06SO 0723 0768 0813 0723 0464 0051

lt0001 lt0001 lt0001 lt0001 lt0001

0017 0744

0549 0360 0440 0588 0380 0216 0661

lt0001 0002

lt0001 lt0001

0032 0290

lt0001

74 75

342 38 32 26 44

BT was significantly positively related to DOB for all species except for AB and to DBH for all

species except for YB

Average BTs for various DOB classes for the seven species are as follows

DOB Class BT (in) RM WA S~t BW BC YB AB

500 OQl8 0126 oltH) 0054 0051 0024 0021 501 to 700 0073 0212 () t)(J 0105 0086 0032 0019 701 to 900 0152 0281 () Ill 0170 0115 0057 0015 901 to 1100 0158 0255 () 177 0193 0114 0043 0020

111 to 1300 0122 0345 0222 0205 0135 0026

-18shy

In general BT is smallest for AB followed by YB BC RM SM and BW in increasing order

with BT for W A being the largest In general BT increases with DOB Most of the anomalies are

due to small sample sizes

Comparison with other BF equations

Fowler (1993) showed that while there were significant species differences between BF

equations for aspen jack pine and red pine there was a very strong relationship between BF and

tree height for each species (ie R 2 gt097 for each species) BF was a function of TH and In TH

showing that BF increased with TH to some maximum and then decreased for larger THs with the

steepness of the decrease depending on the species For all three species BF was not strongly

related to DBH or DOB at a given TH

For paper birch (Fowler and Hussain 1997) BF significantly increased with DOB at TH

(R2 =0219) and significantly decreased with In TH (R2 =0166) for stemwood while BF

significantly increased with DOB for topwood ( R 2 =0218) BF was much more variable than for

aspen red pine and jack pine

Fowler et al (1997) showed that black oak (BO) red oak (RO) and white oak (WO) have BPs

that are quite variable and prediction equations with the same independent variables as for paper

birch with the direction of the relations reversed For stemwood BF decreased with DOB at TH

( R 2 =0270 0418 and 0014 for BO RO and WO respectively) and increased with In TH ( R 2 =

0190 0275 and 0011 for BO RO and WO respectively) For topwood BF decreased with DOB

(R2=0366 0457 and 0100 for BO RO and WO respectively) These prediction equations were

significant but they were only moderately strong at best being only somewhat stronger in general

than the prediction equations for paper birch The prediction equations based on DOB were

-19shy

somewhat stronger than the prediction equations based on In TH The BF equations were

significantly different for the three species and for topwood versus stemwood except for RO

This study shows that the eight northern hardwood species have BFs that are quite variable

with some species having prediction equations with the same independent variables as for paper

birch and the three oak species while other species had different independent variables For

stemwood BF decreased with DOB at TH for RM SM BW and BC increased with In DOB at TH

for W A YB and AE and increased and then somewhat decreased with 1DOB and In DOB as the

independent variables for AB BF increased with In TH for RM SM and BC decreased and then

increased with TH and In TH for WA and BW increased and then decreased with TH and In TH for

YB AB and AE The prediction equations for AE are very suspect as they were based on only six

BF measurements from one tree For topwood BF decreased with DOB for RM WA SM BW

and BC increased with DOB for YB and increased and somewhat decreased with 1DOB and

In DOB for AB All prediction equations for stemwood were significant except for the TH

equations for BW and YB For topwood only the prediction equations for RM SM BW and AB

were significant In general all prediction equations were only moderately strong at best and some

of them were very weak The BF equations were significantly different for most species while the

stemwood and topwood BF equations were not significantly different except for RM and SM

GUIDELINES FOR USERS

We recommend use of the following equations for northern hardwoods when accurate

estimates of bark factors are desired

Stemwood

bull Red maple I

(1) BF =0996730-0002397 bull DOB I

(2) BF =0972344 + 0003554 bull In TH

-20shy

bull White ash 1

(3) BF = 0922166 +0001198bull DOB 1

(4) BF = 0937036 + 0000805 bull TH- 0009279 bullIn TH

bull- Sugar maple 1

(5) BF=0988318-0001497bullDOB 1

(6) BF = 0970865 + 0002264 bullIn TH

bull Basswood 1

(7) BF = 0974486-0000403 bull DOB 1

(8) BF = 0970312 + 0000072 bull TH- 0000631bullln TH

bull Black cherry 1

(9) BF = 0971912 -0000841bull DOB 1

(lO) BF = 0954777 + 0004557 bullIn TH

bull Yell ow birch 1

(11) BF = 0987390 + 0000307 bull DOB 1

(12) BF = 0990354-0000111bull TH+0000885bullln TH

bull American beech 1

(l3) BF = l027382-0l03065DOB -0009012bullln DOB

1

(14) BF = 0994075-0000047 bull TH+0000896 bullIn TH

bull American elm 1

(l5) BF =0925851 + 0003400 bull DOB 1

(16) BF = 0975815-0000058 bull TH- 0()()4696bullln TH

Use Equations 1 3 5 7 9 11 13 and 15 if DOBis measured Use Equations 2 4 6 8 10 12 14

and 16 when only THis measured

Topwood 1

(l7) RM BF = 1006791-0004569 bull DOB 1

(18) WA BF = 0936727 -0000206bull DOB 1

(l9) SM BF = 0995302-0002757 bull DOB

-21shy

(20) BW BF = 0979121-0002155 bull DOB

(21) BC BF = 0977830- 0000604 bull DOB

(22) YB BF = 0987032 + 0000281bull DOB

(23) AB BF = 1038966- 0131661DOB - 0012832 bullln DOB

The equation for stemwood and topwood pooled could be used if DOB is measured with moderate

loss in accuracy for RM and SM and little loss in accuracy for the other five species The pooled

equations in general will be more accurate for stemwood compared to topwood especially for RM

and SM

(24) RM BF == 0997087 -0002476bull DOB

1

(25) WA BF = 0924553 + 000 I 003 bull DOB

(26) SM BF=0988615-0001568bullDOB

(27) BW BF = 0972865-0000320 bull DOB

(28) BC BF=0974512-0001028bullDOB

(29) YB BF = 0986997 + 0000334 bull DOB

(30) AB BF = 1028314- 0105996DOB- 0009288 bullIn DOB

There is no pooled equation for AE as there was no topwood for the one AE tree in the data set

For reasonable accuracy in many situations the following constants could be used for bark

factors

DOB Class Stemwood BF (in) RM WA St-1 BW BC YB AB AE

DOBs50 0988 0927 09S~ 0973 0969 0989 0988 0939 50ltDOBsl00 0979 0931 0977 0971 0966 0990 0995 0951 l00ltDOBs150 0967 0937 0970 0969 0962 0991 0996 0968 150ltDOBs200 0955 0943 0962 0967 0957 0993 0996 0985

DOBgt200 0943 0949 0954 0965 0953 0994 0995 0994

-22shy

DOB Class ToEwoodBF (in) RM WA SM BW BC YB AB

DOBS50 0989 0936 0984 0971 0975 0988 0987 50ltD0BSl00 0970 0935 0973 0962 0973 0989 0995 100ltD0BS150 0947 0934 0959 0951 0970 0991 0996 150ltD0BS200 0924 0933 0946 0940 0967 0992 0995

008gt200 0902 0932 0932 0930 0964 0993 0993

TH Stemwood BF (ft) RM WA SM BW BC YB AB AE

THS05 0970 0947 0971 0971 0950 0990 0993 0980 05ltTHS45 0974 0932 olJn 0970 0959 0991 0995 0972

45ltTHS 100 0978 0925 0974 0970 0964 0991 0996 0966 100ltTHS200 0980 0924 0gt76 0970 0967 0991 0996 0963 200ltTHS300 0984 0928 0gt7S 0970 0970 0990 0996 0959 300ltTHS400 0986 0932 OltJSO 0971 0971 0990 0996 0957 400ltTHS500 0988 0937 () l)S~ 0971 0972 0989 0995 0955

THgt500 0992 0950 07 0974 0974 0987 0995 0952

The following constants for bark factor could be used for simplicity with moderately

approximate results especially for a large number of treessticks

Species Stem wood Top wood Stemwood and Topwood

RM 0980 0981 0980 WA 0932 0935 0932 SM 0976 0977 0976 BW 0970 0962 0970 BC 0965 0974 0966 YB 0991 0989 0990 AB 0995 0995 0995 AE 0964 0964

The above constants would be more accurate for those species that did not have significant

prediction equations andor small sample sizes B~ cry careful with using any of the results of this

study outside the range of the data set for each species Since the results for AE are based on six

stemwood measurements from one tree they arc of course very suspect

-23shy

Use of prediction equations

The prediction equations can be used to estimate BF at any DOB andor TH Since

BF=DIBDOB DIB can be estimated as DIB=BFbull DOB and DOB can be estimated as

DOB=DIBBF Past DOB and DOB growth can be estimated from past DIB growth as follows

Past DOB Growth=Past DIB GrowthBF

and

Past DOB=Present DOB -Past DOB Growth

where past DIB growth might be obtained with an increment borer

Specific uses of the prediction equations include (1) estimation of the solid wood and bark

volume of standing trees (2) estimation of bark volume or peeled volume from unpeeled volume

of felled tree sections (3) growth studies and (4) estimating tree form (eg Girard Form Class)

See Husch et al ( 1982) for a detailed discussion on bark factors

-24- LITERATURE CITED middot

Fowler G W 1991 An aspen bark factor equation for Michigan North J Appl For 8(1) 12-15

Fowler G W 1993 A jack pine bark factor equation for Michigan North J Appl For 10(2) 86-89

Fowler G W and L J Damschroder 1988 A red pine bark factor equation for Michigan North J Appl For 5(1) 28-30

Fowler G W and N G Hussain 1987a Bark factor equation for red pine Michigan DNR For Infor Leaflet 1-87 2 p

Fowler G W and N G Hussain 1987b Bark factor equation for aspen Michigan DNR For Infor Leaflet 2-87 2 p

Fowler G W and N G Hussain 1991 Bark factor equation for jack pine in Michigan Michigan DNR For Infor Leaflet 1-91 5 p

Fowler G W and N G Hussain 1997 Bark factor equations for paper birch in Michigan Michigan DNR For Infor Leaflet 1-97 12 p

Fowler G W N G Hussain D J Cohen and D Khatry-Chhetri 1997 Bark factor equations for oak in Michigan Michigan DNR For Infor Leaflet 2-97 15 p

Husch B C I Miller and T W Beers 1982 Forest Mensuration John Wiley and Sons Inc NY 402 p

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(_0____

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Joe Fields

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Don Torchia

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Ken Alto

Kim Dufresne

Tim Tennis

lonst Manbullpmeut DWisioa 15 Resource Mana1ement Units

bullJfectble l2519bull

bull -Resource Jf~nt Unit OJke

1 -Raource Jf~nt Unit BOUIIdariea

1 -CountyBouruiiJrfea

-15shy

The pooled mean bark factors are

903 (54) RM middot BF = BF = L Bfl 903 = 0980 0015980

i=1

485 (55) WA BF = BF = L Bfl485 = 0932 0023614

i=1

1830 (56) SM BF= BF= L Bfl1830 = 0976 0015029

i=1

436 (57) BW BF = BF = L Bfl436 = 0970 0013134

i=l

210 (58) BC BF = BF = L Bfl210 = 0966 0014725

i=l

92 (59) YB BF = BF = L BFi92 = 0990 0004025

i=l

175 (60) AB BF = BF = L BF)l75 = 0995 0004248

i=1

See the table based on Equations 47-53 to see where Equations 54-60 under- and overestimate

respectively

Bark thickness

For the stemwood data set (n=3506) BT was significantly different for the eight different

species (Bartletts x2 -test for equal variances PltOOOl F-test for equal means PltOOOl) All

Bonferroni pairwise comparisons of means are significantly different except for (RM YB) (RM

AE) (WA AE) (SM AE) (BW AE) (BC AE) (YB AB) and (BW BC) Note that the sample

size for AE is only 6

Average minimum and maximum BTs and Pearsons correlations of BT with DOB DBH

and TH are shown below for the eight species

-16shy

BT BTDOB BTDBH BTTHSpecies nx Min-Max r p r p r p

RM 0077 0005-0525 0678 lt0001 0484 lt0001 -0369 lt0001 829 WA 0263 0012-1760 0632 lt0001 0428 lt0001 -0329 lt0001 410 SM 0113 0008-0672 0794 lt0001 0685 lt0001 -0293 lt0001 1488 BW 0158 0005-0525 0738 lt0001 0633 lt0001 -0192 lt0001 398 BC 0145 0012-0438 0653 lt0001 0169 0024 -0683 lt0001 178 YB 0046 0020-0115 0448 lt0001 0234 0058 -0383 0002 66 AB 0024 0005-0395 0236 0007 0067 0448 -0229 0009 131 AE 0195 0170-0228 -0511 0300 0405 0425 6

AE data consists of six measurements from one tree

BT was significantly positively related to DOB for all species except for AE where there was a

negative relation that was not significant BT was significantly positively related to DBH for all

species except for YB and AB where the positive relations were not significant BT was

significantly negatively related to TH for all species except for AE where there was a positive

relationship that was not significant

Average BTs for various DOB and TH classes for the eight species are as follows

DOB Class BT (in) RM WA SM BW BC YB AB AE

~400

401 to 800 801 to 1200 1201 to 1600

gt1600

0017 0054 0134 0239 0236

0091 0220 0321 0394 0468

0024 0060 0141 0225 0324

0032 0093 0150 0119 0268

0058 0101 0192 0252 0199

0020 0032 0048 0060 0058

0022 0019 0019 0020 0048

0200 0170

THClass BT (ft) RM WA SM BW BC YB AB AE

~050 0134 0208 0146 0114 0263 0038 0036 051 to 450 0110 0338 0161 0199 0192 0057 0038 0180 451 to 1000 0080 0296 0105 0165 0169 0047 0021 1001 to 2000 0065 0278 010(1 0153 0140 0049 0016 0210 2001 to 3000 0060 0250 0094 0146 0102 0041 0016 0200 3001 to 4000 0045 0220 0089 0134 0087 0037 0014 0190 4001 to 5000 0038 0220 0062 0153 0061 0025 0015

~5000 0016 0159 0047 0136 0038 0016

-17shy

In general BT is smallest for AB followed by YB RM SM BC BW and AE in increasing order

with BT for WA being the largest In general BT increases with DOB and decreases with TH

Most of the anomalies are due to small sample sizes

For the topwood data set (n=631) BT was significantly different for the seven different

species (Bartletts -test for equal variances PltOOOl F-test for equal means PltOOOl) All

Bonferroni pairwise comparisons of means are significantly different except for (RM SM) (RM

BC) (RM YB) (SM BC) (BC YB) and (YB AB)

Average minimum and maximum BTs and Pearsons correlations of BT with DOB and DBH

are shown below for the seven species

Species x

BT

Min- Max

BT DOB p r

BTDBH p n

RM WA SM BW BC YB AB

0064 0203 0086 0150 0083 0034 0019

0008-0385 0022-0458 0005-0362 0018-0262 0018-0175 Ool5-0075 0008-0038

06SO 0723 0768 0813 0723 0464 0051

lt0001 lt0001 lt0001 lt0001 lt0001

0017 0744

0549 0360 0440 0588 0380 0216 0661

lt0001 0002

lt0001 lt0001

0032 0290

lt0001

74 75

342 38 32 26 44

BT was significantly positively related to DOB for all species except for AB and to DBH for all

species except for YB

Average BTs for various DOB classes for the seven species are as follows

DOB Class BT (in) RM WA S~t BW BC YB AB

500 OQl8 0126 oltH) 0054 0051 0024 0021 501 to 700 0073 0212 () t)(J 0105 0086 0032 0019 701 to 900 0152 0281 () Ill 0170 0115 0057 0015 901 to 1100 0158 0255 () 177 0193 0114 0043 0020

111 to 1300 0122 0345 0222 0205 0135 0026

-18shy

In general BT is smallest for AB followed by YB BC RM SM and BW in increasing order

with BT for W A being the largest In general BT increases with DOB Most of the anomalies are

due to small sample sizes

Comparison with other BF equations

Fowler (1993) showed that while there were significant species differences between BF

equations for aspen jack pine and red pine there was a very strong relationship between BF and

tree height for each species (ie R 2 gt097 for each species) BF was a function of TH and In TH

showing that BF increased with TH to some maximum and then decreased for larger THs with the

steepness of the decrease depending on the species For all three species BF was not strongly

related to DBH or DOB at a given TH

For paper birch (Fowler and Hussain 1997) BF significantly increased with DOB at TH

(R2 =0219) and significantly decreased with In TH (R2 =0166) for stemwood while BF

significantly increased with DOB for topwood ( R 2 =0218) BF was much more variable than for

aspen red pine and jack pine

Fowler et al (1997) showed that black oak (BO) red oak (RO) and white oak (WO) have BPs

that are quite variable and prediction equations with the same independent variables as for paper

birch with the direction of the relations reversed For stemwood BF decreased with DOB at TH

( R 2 =0270 0418 and 0014 for BO RO and WO respectively) and increased with In TH ( R 2 =

0190 0275 and 0011 for BO RO and WO respectively) For topwood BF decreased with DOB

(R2=0366 0457 and 0100 for BO RO and WO respectively) These prediction equations were

significant but they were only moderately strong at best being only somewhat stronger in general

than the prediction equations for paper birch The prediction equations based on DOB were

-19shy

somewhat stronger than the prediction equations based on In TH The BF equations were

significantly different for the three species and for topwood versus stemwood except for RO

This study shows that the eight northern hardwood species have BFs that are quite variable

with some species having prediction equations with the same independent variables as for paper

birch and the three oak species while other species had different independent variables For

stemwood BF decreased with DOB at TH for RM SM BW and BC increased with In DOB at TH

for W A YB and AE and increased and then somewhat decreased with 1DOB and In DOB as the

independent variables for AB BF increased with In TH for RM SM and BC decreased and then

increased with TH and In TH for WA and BW increased and then decreased with TH and In TH for

YB AB and AE The prediction equations for AE are very suspect as they were based on only six

BF measurements from one tree For topwood BF decreased with DOB for RM WA SM BW

and BC increased with DOB for YB and increased and somewhat decreased with 1DOB and

In DOB for AB All prediction equations for stemwood were significant except for the TH

equations for BW and YB For topwood only the prediction equations for RM SM BW and AB

were significant In general all prediction equations were only moderately strong at best and some

of them were very weak The BF equations were significantly different for most species while the

stemwood and topwood BF equations were not significantly different except for RM and SM

GUIDELINES FOR USERS

We recommend use of the following equations for northern hardwoods when accurate

estimates of bark factors are desired

Stemwood

bull Red maple I

(1) BF =0996730-0002397 bull DOB I

(2) BF =0972344 + 0003554 bull In TH

-20shy

bull White ash 1

(3) BF = 0922166 +0001198bull DOB 1

(4) BF = 0937036 + 0000805 bull TH- 0009279 bullIn TH

bull- Sugar maple 1

(5) BF=0988318-0001497bullDOB 1

(6) BF = 0970865 + 0002264 bullIn TH

bull Basswood 1

(7) BF = 0974486-0000403 bull DOB 1

(8) BF = 0970312 + 0000072 bull TH- 0000631bullln TH

bull Black cherry 1

(9) BF = 0971912 -0000841bull DOB 1

(lO) BF = 0954777 + 0004557 bullIn TH

bull Yell ow birch 1

(11) BF = 0987390 + 0000307 bull DOB 1

(12) BF = 0990354-0000111bull TH+0000885bullln TH

bull American beech 1

(l3) BF = l027382-0l03065DOB -0009012bullln DOB

1

(14) BF = 0994075-0000047 bull TH+0000896 bullIn TH

bull American elm 1

(l5) BF =0925851 + 0003400 bull DOB 1

(16) BF = 0975815-0000058 bull TH- 0()()4696bullln TH

Use Equations 1 3 5 7 9 11 13 and 15 if DOBis measured Use Equations 2 4 6 8 10 12 14

and 16 when only THis measured

Topwood 1

(l7) RM BF = 1006791-0004569 bull DOB 1

(18) WA BF = 0936727 -0000206bull DOB 1

(l9) SM BF = 0995302-0002757 bull DOB

-21shy

(20) BW BF = 0979121-0002155 bull DOB

(21) BC BF = 0977830- 0000604 bull DOB

(22) YB BF = 0987032 + 0000281bull DOB

(23) AB BF = 1038966- 0131661DOB - 0012832 bullln DOB

The equation for stemwood and topwood pooled could be used if DOB is measured with moderate

loss in accuracy for RM and SM and little loss in accuracy for the other five species The pooled

equations in general will be more accurate for stemwood compared to topwood especially for RM

and SM

(24) RM BF == 0997087 -0002476bull DOB

1

(25) WA BF = 0924553 + 000 I 003 bull DOB

(26) SM BF=0988615-0001568bullDOB

(27) BW BF = 0972865-0000320 bull DOB

(28) BC BF=0974512-0001028bullDOB

(29) YB BF = 0986997 + 0000334 bull DOB

(30) AB BF = 1028314- 0105996DOB- 0009288 bullIn DOB

There is no pooled equation for AE as there was no topwood for the one AE tree in the data set

For reasonable accuracy in many situations the following constants could be used for bark

factors

DOB Class Stemwood BF (in) RM WA St-1 BW BC YB AB AE

DOBs50 0988 0927 09S~ 0973 0969 0989 0988 0939 50ltDOBsl00 0979 0931 0977 0971 0966 0990 0995 0951 l00ltDOBs150 0967 0937 0970 0969 0962 0991 0996 0968 150ltDOBs200 0955 0943 0962 0967 0957 0993 0996 0985

DOBgt200 0943 0949 0954 0965 0953 0994 0995 0994

-22shy

DOB Class ToEwoodBF (in) RM WA SM BW BC YB AB

DOBS50 0989 0936 0984 0971 0975 0988 0987 50ltD0BSl00 0970 0935 0973 0962 0973 0989 0995 100ltD0BS150 0947 0934 0959 0951 0970 0991 0996 150ltD0BS200 0924 0933 0946 0940 0967 0992 0995

008gt200 0902 0932 0932 0930 0964 0993 0993

TH Stemwood BF (ft) RM WA SM BW BC YB AB AE

THS05 0970 0947 0971 0971 0950 0990 0993 0980 05ltTHS45 0974 0932 olJn 0970 0959 0991 0995 0972

45ltTHS 100 0978 0925 0974 0970 0964 0991 0996 0966 100ltTHS200 0980 0924 0gt76 0970 0967 0991 0996 0963 200ltTHS300 0984 0928 0gt7S 0970 0970 0990 0996 0959 300ltTHS400 0986 0932 OltJSO 0971 0971 0990 0996 0957 400ltTHS500 0988 0937 () l)S~ 0971 0972 0989 0995 0955

THgt500 0992 0950 07 0974 0974 0987 0995 0952

The following constants for bark factor could be used for simplicity with moderately

approximate results especially for a large number of treessticks

Species Stem wood Top wood Stemwood and Topwood

RM 0980 0981 0980 WA 0932 0935 0932 SM 0976 0977 0976 BW 0970 0962 0970 BC 0965 0974 0966 YB 0991 0989 0990 AB 0995 0995 0995 AE 0964 0964

The above constants would be more accurate for those species that did not have significant

prediction equations andor small sample sizes B~ cry careful with using any of the results of this

study outside the range of the data set for each species Since the results for AE are based on six

stemwood measurements from one tree they arc of course very suspect

-23shy

Use of prediction equations

The prediction equations can be used to estimate BF at any DOB andor TH Since

BF=DIBDOB DIB can be estimated as DIB=BFbull DOB and DOB can be estimated as

DOB=DIBBF Past DOB and DOB growth can be estimated from past DIB growth as follows

Past DOB Growth=Past DIB GrowthBF

and

Past DOB=Present DOB -Past DOB Growth

where past DIB growth might be obtained with an increment borer

Specific uses of the prediction equations include (1) estimation of the solid wood and bark

volume of standing trees (2) estimation of bark volume or peeled volume from unpeeled volume

of felled tree sections (3) growth studies and (4) estimating tree form (eg Girard Form Class)

See Husch et al ( 1982) for a detailed discussion on bark factors

-24- LITERATURE CITED middot

Fowler G W 1991 An aspen bark factor equation for Michigan North J Appl For 8(1) 12-15

Fowler G W 1993 A jack pine bark factor equation for Michigan North J Appl For 10(2) 86-89

Fowler G W and L J Damschroder 1988 A red pine bark factor equation for Michigan North J Appl For 5(1) 28-30

Fowler G W and N G Hussain 1987a Bark factor equation for red pine Michigan DNR For Infor Leaflet 1-87 2 p

Fowler G W and N G Hussain 1987b Bark factor equation for aspen Michigan DNR For Infor Leaflet 2-87 2 p

Fowler G W and N G Hussain 1991 Bark factor equation for jack pine in Michigan Michigan DNR For Infor Leaflet 1-91 5 p

Fowler G W and N G Hussain 1997 Bark factor equations for paper birch in Michigan Michigan DNR For Infor Leaflet 1-97 12 p

Fowler G W N G Hussain D J Cohen and D Khatry-Chhetri 1997 Bark factor equations for oak in Michigan Michigan DNR For Infor Leaflet 2-97 15 p

Husch B C I Miller and T W Beers 1982 Forest Mensuration John Wiley and Sons Inc NY 402 p

~ FOREST MANAGEMENT DIVISION John M Robertsoa 51~ 373-1275 DMSION OFFICE PO Box 30452 Lansing MI 48909-7952

Brian Hutchins 517 275-5211 Forest Fire ExJ)Ciinent Station 1337 E Robinson Lake Rd Box 68 Roscommon MI 48653 Rich Mergener 906 341-2518 Wyman N~ Rt No 2 Box 2004 Manistique MI 49854 Rich Mergener 810 229-9152 State Forest Tree Improvement Center 4631 Bishop Lake Rd Howell MI 48843

Mike Palada 906~ 228-6561 Marquette Office 1990 Us-41 South MUQuette Ml 49855 Bill Maid ~906 249-1497 Marguctte Warehouse amp Repair ShoP 110 Foid Rd Marquette MI 49855

Edwin Moore s17 732-4481 Gaylord Warehouse amp Repair Shop 540 S Otsego Ave PO Box 596 Gaylord MI 49734

Marty Nelson

Debbie Begalle

Dennis Nezich

Bill Brondyke

Gilbert Joy Dean Reid

(_0____

Jeff Stampfly

Dayle Garlock

Bill ONeill

Joe Jarecki Dennis Vitton

Joe Fields

Courtney Borgondy

Susan Thiel

Don Torchia

(906) 353-6651 (906) 288-3321 (906) 224-2771 (906) 875-6622 (906) 563-9248 (906) 246-3245 (906) 786-2354 (906) 753-6317 (906) 346-920 1 (906) 485-1031 (906) 249-1497 (906) 293-3293 (906) 635-5281 (906) 477-6048 (906) 297-2581 (906) 452-6227 (906) 499-3346 (906) 341-2518

616 775-9727 517 826-3211 517 275-5151

(517) 785-425 1 (517) 354-7822 (517) 733-8775 (517) 731-5806 (616) 533-8341 (616) 238-9314 (616) 539-8564 (517) 983-4101 (616) 775-9727 (616) 745-4651 (616) 824-3591 (616) 734-5840 (616) 861-5636 (616) 922-5280 (616) 258-2711 (616) 325-4611 (517) 426-9205 (5 17) 539-6411 (5 I 7) 846-4104 (5 I 7) 687-7771 (517) 348-6371 (517) 736-8336 (517) 826-3211 (517) 275-4622 (517) 422-2897 (517) 345-0472

BARAGA FOREST MANAGEMENT UNIT 427 US-41 North Baraga MI 49908 Twm Lakes Fteld Office Rt I Box 234 Toivola MI 49965 Wakefield Field Office 1405 East US-2 Wakefield Ml49968

CRYSTAL FALLS FOREST MANAGEMENT UNIT 1420 US-2 West Crystal Falls Ml49920 Norway Fteld Office Os-2 West PO Box 126 Norway MI 49870 Felch Field Office PO Box 188 Felch MI 49831

ESCANABA FOREST MANAGEMENT UNIT 6833 Hwy 2 41 amp M-35 Gladstone MI 49837 Stephenson F1eld Office West 5420 River Road Stephenson MI 49887

GWINN FOREST MANAGEMENT UNIT 410 West M-35 Gwinn MI 49841 lshpemmg Field Ofttce 1985 US 41 Hwy West Ishpeming MI 49849

Marquette Field Office 110 Ford Road Marquette Ml 49855 NEWBERRY FOREST MANAGEMENT UNIT Box 428 5666 M 123 S Newberry MI 49868 SAULT STE MARIE FOREST MANAGEMENT UNIT Box 798 200 I Ashmun Sault Ste Marie Ml 49783

Naubinway Field Office PO Box 287 US 2 Naubinway MI 49762 Detour Field Office PO Box 92 Ml34 Detour MI4972S

SHINGLETON FOREST MANAGEMENT UNIT M-28 West PO Box 67 Shingleton Ml49884 Seney Fteld Office Comer ofM-77 amp M-28 PO Box 72 Seney MI 49883 Wyman Nursery Rt No 2 Box 2004 Manistique MI498S4

ay o tce I est M- ox ay o Cadillac Office 8015 Mackinaw Trail Cadillac Ml 49601 Mio Office 191 S Mt Tom Rd Box 939 Mio MI 48647 Roscommon Office 8717 N Roscommon Rd Box 128 Roscommon Ml 48653

ATLANTA FOREST MANAGEMENT UNIT 13501 M-33 Atlanta Ml49709 Alpena Field Office 4343 M-32 West Alpena Ml49707 Onaway Field Office Hwy M-211 Box 32 Onaway Ml49765

GAYLORD FOREST MANAGEMENT UNIT 1732 West M-32 Box 667 Gaylord Ml49734 BeUaJre Fteld office 70 I E Cayuga St PO Box 278 Bellaire Ml 49615 Indian River Field Office PO Box 10 6984 Wilson Indian River Ml49749 Pellston Field Office 304 Stimson Box 126 Pellston Ml49769

PIGEON RIVER COUNTRY FOREST MANAGEMENT UNIT 9966 Twin Lakes Rd Vanderbilt Ml 49795 CADILLAC FOREST MANAGEMENT UNIT 8015 Mackinaw Trail Cadillac MI 49601

Baldwm Fteld Office Route 2 Box 2810 Baldwin Ml49304 Manton Field Office 521 N Michigan Manton Ml49663 Evart Field Office 951 W 7th Street Evart Ml 49631 Oceana Field Office 1757 E Hayes Rd M-20 Shelby Ml49455

TRAVERSE CITY FOREST MANAGEMENT UNIT 970 Emerson Traverse City Ml49686 Kalkaska Fteld Office 2089 N B~rch St Kalkaska MI 49646 Platte River Field Office 15210 US 31 Hwy Beulah Ml49617

GLADWIN FOREST MANAGEMENT UNIT 801 N Silverleaf PO Box 337 Gladwin M148624 Harrison Field Office 708 N First St Harrison Ml 48625 Standish Field Office 527 N M76 Box 447 Standish MI 48658 Sanford Field Office 118 W Saginaw MI 48657

GRAYLING FOREST MANAGEMENT UNIT 1955 Nl-75 BL Grayling MI 49738 Lmcoln F1eld Office 408 Mam St PO Box 122 Lincoln MI 48742 Mio Field Office 191 S Mt Tom Rd Box 939 Mio MI 48647

ROSCOMMON FOREST MANAGEMENT UNIT Box 218 Roscommon MI 48653 Houghton Liike F1eld Office 180 S Harrtson Rd Houghton Lake Ml48629 West Branch Field Office 2389 South M-76 West Branch MI 48661

Ken Alto

Kim Dufresne

Tim Tennis

lonst Manbullpmeut DWisioa 15 Resource Mana1ement Units

bullJfectble l2519bull

bull -Resource Jf~nt Unit OJke

1 -Raource Jf~nt Unit BOUIIdariea

1 -CountyBouruiiJrfea

-16shy

BT BTDOB BTDBH BTTHSpecies nx Min-Max r p r p r p

RM 0077 0005-0525 0678 lt0001 0484 lt0001 -0369 lt0001 829 WA 0263 0012-1760 0632 lt0001 0428 lt0001 -0329 lt0001 410 SM 0113 0008-0672 0794 lt0001 0685 lt0001 -0293 lt0001 1488 BW 0158 0005-0525 0738 lt0001 0633 lt0001 -0192 lt0001 398 BC 0145 0012-0438 0653 lt0001 0169 0024 -0683 lt0001 178 YB 0046 0020-0115 0448 lt0001 0234 0058 -0383 0002 66 AB 0024 0005-0395 0236 0007 0067 0448 -0229 0009 131 AE 0195 0170-0228 -0511 0300 0405 0425 6

AE data consists of six measurements from one tree

BT was significantly positively related to DOB for all species except for AE where there was a

negative relation that was not significant BT was significantly positively related to DBH for all

species except for YB and AB where the positive relations were not significant BT was

significantly negatively related to TH for all species except for AE where there was a positive

relationship that was not significant

Average BTs for various DOB and TH classes for the eight species are as follows

DOB Class BT (in) RM WA SM BW BC YB AB AE

~400

401 to 800 801 to 1200 1201 to 1600

gt1600

0017 0054 0134 0239 0236

0091 0220 0321 0394 0468

0024 0060 0141 0225 0324

0032 0093 0150 0119 0268

0058 0101 0192 0252 0199

0020 0032 0048 0060 0058

0022 0019 0019 0020 0048

0200 0170

THClass BT (ft) RM WA SM BW BC YB AB AE

~050 0134 0208 0146 0114 0263 0038 0036 051 to 450 0110 0338 0161 0199 0192 0057 0038 0180 451 to 1000 0080 0296 0105 0165 0169 0047 0021 1001 to 2000 0065 0278 010(1 0153 0140 0049 0016 0210 2001 to 3000 0060 0250 0094 0146 0102 0041 0016 0200 3001 to 4000 0045 0220 0089 0134 0087 0037 0014 0190 4001 to 5000 0038 0220 0062 0153 0061 0025 0015

~5000 0016 0159 0047 0136 0038 0016

-17shy

In general BT is smallest for AB followed by YB RM SM BC BW and AE in increasing order

with BT for WA being the largest In general BT increases with DOB and decreases with TH

Most of the anomalies are due to small sample sizes

For the topwood data set (n=631) BT was significantly different for the seven different

species (Bartletts -test for equal variances PltOOOl F-test for equal means PltOOOl) All

Bonferroni pairwise comparisons of means are significantly different except for (RM SM) (RM

BC) (RM YB) (SM BC) (BC YB) and (YB AB)

Average minimum and maximum BTs and Pearsons correlations of BT with DOB and DBH

are shown below for the seven species

Species x

BT

Min- Max

BT DOB p r

BTDBH p n

RM WA SM BW BC YB AB

0064 0203 0086 0150 0083 0034 0019

0008-0385 0022-0458 0005-0362 0018-0262 0018-0175 Ool5-0075 0008-0038

06SO 0723 0768 0813 0723 0464 0051

lt0001 lt0001 lt0001 lt0001 lt0001

0017 0744

0549 0360 0440 0588 0380 0216 0661

lt0001 0002

lt0001 lt0001

0032 0290

lt0001

74 75

342 38 32 26 44

BT was significantly positively related to DOB for all species except for AB and to DBH for all

species except for YB

Average BTs for various DOB classes for the seven species are as follows

DOB Class BT (in) RM WA S~t BW BC YB AB

500 OQl8 0126 oltH) 0054 0051 0024 0021 501 to 700 0073 0212 () t)(J 0105 0086 0032 0019 701 to 900 0152 0281 () Ill 0170 0115 0057 0015 901 to 1100 0158 0255 () 177 0193 0114 0043 0020

111 to 1300 0122 0345 0222 0205 0135 0026

-18shy

In general BT is smallest for AB followed by YB BC RM SM and BW in increasing order

with BT for W A being the largest In general BT increases with DOB Most of the anomalies are

due to small sample sizes

Comparison with other BF equations

Fowler (1993) showed that while there were significant species differences between BF

equations for aspen jack pine and red pine there was a very strong relationship between BF and

tree height for each species (ie R 2 gt097 for each species) BF was a function of TH and In TH

showing that BF increased with TH to some maximum and then decreased for larger THs with the

steepness of the decrease depending on the species For all three species BF was not strongly

related to DBH or DOB at a given TH

For paper birch (Fowler and Hussain 1997) BF significantly increased with DOB at TH

(R2 =0219) and significantly decreased with In TH (R2 =0166) for stemwood while BF

significantly increased with DOB for topwood ( R 2 =0218) BF was much more variable than for

aspen red pine and jack pine

Fowler et al (1997) showed that black oak (BO) red oak (RO) and white oak (WO) have BPs

that are quite variable and prediction equations with the same independent variables as for paper

birch with the direction of the relations reversed For stemwood BF decreased with DOB at TH

( R 2 =0270 0418 and 0014 for BO RO and WO respectively) and increased with In TH ( R 2 =

0190 0275 and 0011 for BO RO and WO respectively) For topwood BF decreased with DOB

(R2=0366 0457 and 0100 for BO RO and WO respectively) These prediction equations were

significant but they were only moderately strong at best being only somewhat stronger in general

than the prediction equations for paper birch The prediction equations based on DOB were

-19shy

somewhat stronger than the prediction equations based on In TH The BF equations were

significantly different for the three species and for topwood versus stemwood except for RO

This study shows that the eight northern hardwood species have BFs that are quite variable

with some species having prediction equations with the same independent variables as for paper

birch and the three oak species while other species had different independent variables For

stemwood BF decreased with DOB at TH for RM SM BW and BC increased with In DOB at TH

for W A YB and AE and increased and then somewhat decreased with 1DOB and In DOB as the

independent variables for AB BF increased with In TH for RM SM and BC decreased and then

increased with TH and In TH for WA and BW increased and then decreased with TH and In TH for

YB AB and AE The prediction equations for AE are very suspect as they were based on only six

BF measurements from one tree For topwood BF decreased with DOB for RM WA SM BW

and BC increased with DOB for YB and increased and somewhat decreased with 1DOB and

In DOB for AB All prediction equations for stemwood were significant except for the TH

equations for BW and YB For topwood only the prediction equations for RM SM BW and AB

were significant In general all prediction equations were only moderately strong at best and some

of them were very weak The BF equations were significantly different for most species while the

stemwood and topwood BF equations were not significantly different except for RM and SM

GUIDELINES FOR USERS

We recommend use of the following equations for northern hardwoods when accurate

estimates of bark factors are desired

Stemwood

bull Red maple I

(1) BF =0996730-0002397 bull DOB I

(2) BF =0972344 + 0003554 bull In TH

-20shy

bull White ash 1

(3) BF = 0922166 +0001198bull DOB 1

(4) BF = 0937036 + 0000805 bull TH- 0009279 bullIn TH

bull- Sugar maple 1

(5) BF=0988318-0001497bullDOB 1

(6) BF = 0970865 + 0002264 bullIn TH

bull Basswood 1

(7) BF = 0974486-0000403 bull DOB 1

(8) BF = 0970312 + 0000072 bull TH- 0000631bullln TH

bull Black cherry 1

(9) BF = 0971912 -0000841bull DOB 1

(lO) BF = 0954777 + 0004557 bullIn TH

bull Yell ow birch 1

(11) BF = 0987390 + 0000307 bull DOB 1

(12) BF = 0990354-0000111bull TH+0000885bullln TH

bull American beech 1

(l3) BF = l027382-0l03065DOB -0009012bullln DOB

1

(14) BF = 0994075-0000047 bull TH+0000896 bullIn TH

bull American elm 1

(l5) BF =0925851 + 0003400 bull DOB 1

(16) BF = 0975815-0000058 bull TH- 0()()4696bullln TH

Use Equations 1 3 5 7 9 11 13 and 15 if DOBis measured Use Equations 2 4 6 8 10 12 14

and 16 when only THis measured

Topwood 1

(l7) RM BF = 1006791-0004569 bull DOB 1

(18) WA BF = 0936727 -0000206bull DOB 1

(l9) SM BF = 0995302-0002757 bull DOB

-21shy

(20) BW BF = 0979121-0002155 bull DOB

(21) BC BF = 0977830- 0000604 bull DOB

(22) YB BF = 0987032 + 0000281bull DOB

(23) AB BF = 1038966- 0131661DOB - 0012832 bullln DOB

The equation for stemwood and topwood pooled could be used if DOB is measured with moderate

loss in accuracy for RM and SM and little loss in accuracy for the other five species The pooled

equations in general will be more accurate for stemwood compared to topwood especially for RM

and SM

(24) RM BF == 0997087 -0002476bull DOB

1

(25) WA BF = 0924553 + 000 I 003 bull DOB

(26) SM BF=0988615-0001568bullDOB

(27) BW BF = 0972865-0000320 bull DOB

(28) BC BF=0974512-0001028bullDOB

(29) YB BF = 0986997 + 0000334 bull DOB

(30) AB BF = 1028314- 0105996DOB- 0009288 bullIn DOB

There is no pooled equation for AE as there was no topwood for the one AE tree in the data set

For reasonable accuracy in many situations the following constants could be used for bark

factors

DOB Class Stemwood BF (in) RM WA St-1 BW BC YB AB AE

DOBs50 0988 0927 09S~ 0973 0969 0989 0988 0939 50ltDOBsl00 0979 0931 0977 0971 0966 0990 0995 0951 l00ltDOBs150 0967 0937 0970 0969 0962 0991 0996 0968 150ltDOBs200 0955 0943 0962 0967 0957 0993 0996 0985

DOBgt200 0943 0949 0954 0965 0953 0994 0995 0994

-22shy

DOB Class ToEwoodBF (in) RM WA SM BW BC YB AB

DOBS50 0989 0936 0984 0971 0975 0988 0987 50ltD0BSl00 0970 0935 0973 0962 0973 0989 0995 100ltD0BS150 0947 0934 0959 0951 0970 0991 0996 150ltD0BS200 0924 0933 0946 0940 0967 0992 0995

008gt200 0902 0932 0932 0930 0964 0993 0993

TH Stemwood BF (ft) RM WA SM BW BC YB AB AE

THS05 0970 0947 0971 0971 0950 0990 0993 0980 05ltTHS45 0974 0932 olJn 0970 0959 0991 0995 0972

45ltTHS 100 0978 0925 0974 0970 0964 0991 0996 0966 100ltTHS200 0980 0924 0gt76 0970 0967 0991 0996 0963 200ltTHS300 0984 0928 0gt7S 0970 0970 0990 0996 0959 300ltTHS400 0986 0932 OltJSO 0971 0971 0990 0996 0957 400ltTHS500 0988 0937 () l)S~ 0971 0972 0989 0995 0955

THgt500 0992 0950 07 0974 0974 0987 0995 0952

The following constants for bark factor could be used for simplicity with moderately

approximate results especially for a large number of treessticks

Species Stem wood Top wood Stemwood and Topwood

RM 0980 0981 0980 WA 0932 0935 0932 SM 0976 0977 0976 BW 0970 0962 0970 BC 0965 0974 0966 YB 0991 0989 0990 AB 0995 0995 0995 AE 0964 0964

The above constants would be more accurate for those species that did not have significant

prediction equations andor small sample sizes B~ cry careful with using any of the results of this

study outside the range of the data set for each species Since the results for AE are based on six

stemwood measurements from one tree they arc of course very suspect

-23shy

Use of prediction equations

The prediction equations can be used to estimate BF at any DOB andor TH Since

BF=DIBDOB DIB can be estimated as DIB=BFbull DOB and DOB can be estimated as

DOB=DIBBF Past DOB and DOB growth can be estimated from past DIB growth as follows

Past DOB Growth=Past DIB GrowthBF

and

Past DOB=Present DOB -Past DOB Growth

where past DIB growth might be obtained with an increment borer

Specific uses of the prediction equations include (1) estimation of the solid wood and bark

volume of standing trees (2) estimation of bark volume or peeled volume from unpeeled volume

of felled tree sections (3) growth studies and (4) estimating tree form (eg Girard Form Class)

See Husch et al ( 1982) for a detailed discussion on bark factors

-24- LITERATURE CITED middot

Fowler G W 1991 An aspen bark factor equation for Michigan North J Appl For 8(1) 12-15

Fowler G W 1993 A jack pine bark factor equation for Michigan North J Appl For 10(2) 86-89

Fowler G W and L J Damschroder 1988 A red pine bark factor equation for Michigan North J Appl For 5(1) 28-30

Fowler G W and N G Hussain 1987a Bark factor equation for red pine Michigan DNR For Infor Leaflet 1-87 2 p

Fowler G W and N G Hussain 1987b Bark factor equation for aspen Michigan DNR For Infor Leaflet 2-87 2 p

Fowler G W and N G Hussain 1991 Bark factor equation for jack pine in Michigan Michigan DNR For Infor Leaflet 1-91 5 p

Fowler G W and N G Hussain 1997 Bark factor equations for paper birch in Michigan Michigan DNR For Infor Leaflet 1-97 12 p

Fowler G W N G Hussain D J Cohen and D Khatry-Chhetri 1997 Bark factor equations for oak in Michigan Michigan DNR For Infor Leaflet 2-97 15 p

Husch B C I Miller and T W Beers 1982 Forest Mensuration John Wiley and Sons Inc NY 402 p

~ FOREST MANAGEMENT DIVISION John M Robertsoa 51~ 373-1275 DMSION OFFICE PO Box 30452 Lansing MI 48909-7952

Brian Hutchins 517 275-5211 Forest Fire ExJ)Ciinent Station 1337 E Robinson Lake Rd Box 68 Roscommon MI 48653 Rich Mergener 906 341-2518 Wyman N~ Rt No 2 Box 2004 Manistique MI 49854 Rich Mergener 810 229-9152 State Forest Tree Improvement Center 4631 Bishop Lake Rd Howell MI 48843

Mike Palada 906~ 228-6561 Marquette Office 1990 Us-41 South MUQuette Ml 49855 Bill Maid ~906 249-1497 Marguctte Warehouse amp Repair ShoP 110 Foid Rd Marquette MI 49855

Edwin Moore s17 732-4481 Gaylord Warehouse amp Repair Shop 540 S Otsego Ave PO Box 596 Gaylord MI 49734

Marty Nelson

Debbie Begalle

Dennis Nezich

Bill Brondyke

Gilbert Joy Dean Reid

(_0____

Jeff Stampfly

Dayle Garlock

Bill ONeill

Joe Jarecki Dennis Vitton

Joe Fields

Courtney Borgondy

Susan Thiel

Don Torchia

(906) 353-6651 (906) 288-3321 (906) 224-2771 (906) 875-6622 (906) 563-9248 (906) 246-3245 (906) 786-2354 (906) 753-6317 (906) 346-920 1 (906) 485-1031 (906) 249-1497 (906) 293-3293 (906) 635-5281 (906) 477-6048 (906) 297-2581 (906) 452-6227 (906) 499-3346 (906) 341-2518

616 775-9727 517 826-3211 517 275-5151

(517) 785-425 1 (517) 354-7822 (517) 733-8775 (517) 731-5806 (616) 533-8341 (616) 238-9314 (616) 539-8564 (517) 983-4101 (616) 775-9727 (616) 745-4651 (616) 824-3591 (616) 734-5840 (616) 861-5636 (616) 922-5280 (616) 258-2711 (616) 325-4611 (517) 426-9205 (5 17) 539-6411 (5 I 7) 846-4104 (5 I 7) 687-7771 (517) 348-6371 (517) 736-8336 (517) 826-3211 (517) 275-4622 (517) 422-2897 (517) 345-0472

BARAGA FOREST MANAGEMENT UNIT 427 US-41 North Baraga MI 49908 Twm Lakes Fteld Office Rt I Box 234 Toivola MI 49965 Wakefield Field Office 1405 East US-2 Wakefield Ml49968

CRYSTAL FALLS FOREST MANAGEMENT UNIT 1420 US-2 West Crystal Falls Ml49920 Norway Fteld Office Os-2 West PO Box 126 Norway MI 49870 Felch Field Office PO Box 188 Felch MI 49831

ESCANABA FOREST MANAGEMENT UNIT 6833 Hwy 2 41 amp M-35 Gladstone MI 49837 Stephenson F1eld Office West 5420 River Road Stephenson MI 49887

GWINN FOREST MANAGEMENT UNIT 410 West M-35 Gwinn MI 49841 lshpemmg Field Ofttce 1985 US 41 Hwy West Ishpeming MI 49849

Marquette Field Office 110 Ford Road Marquette Ml 49855 NEWBERRY FOREST MANAGEMENT UNIT Box 428 5666 M 123 S Newberry MI 49868 SAULT STE MARIE FOREST MANAGEMENT UNIT Box 798 200 I Ashmun Sault Ste Marie Ml 49783

Naubinway Field Office PO Box 287 US 2 Naubinway MI 49762 Detour Field Office PO Box 92 Ml34 Detour MI4972S

SHINGLETON FOREST MANAGEMENT UNIT M-28 West PO Box 67 Shingleton Ml49884 Seney Fteld Office Comer ofM-77 amp M-28 PO Box 72 Seney MI 49883 Wyman Nursery Rt No 2 Box 2004 Manistique MI498S4

ay o tce I est M- ox ay o Cadillac Office 8015 Mackinaw Trail Cadillac Ml 49601 Mio Office 191 S Mt Tom Rd Box 939 Mio MI 48647 Roscommon Office 8717 N Roscommon Rd Box 128 Roscommon Ml 48653

ATLANTA FOREST MANAGEMENT UNIT 13501 M-33 Atlanta Ml49709 Alpena Field Office 4343 M-32 West Alpena Ml49707 Onaway Field Office Hwy M-211 Box 32 Onaway Ml49765

GAYLORD FOREST MANAGEMENT UNIT 1732 West M-32 Box 667 Gaylord Ml49734 BeUaJre Fteld office 70 I E Cayuga St PO Box 278 Bellaire Ml 49615 Indian River Field Office PO Box 10 6984 Wilson Indian River Ml49749 Pellston Field Office 304 Stimson Box 126 Pellston Ml49769

PIGEON RIVER COUNTRY FOREST MANAGEMENT UNIT 9966 Twin Lakes Rd Vanderbilt Ml 49795 CADILLAC FOREST MANAGEMENT UNIT 8015 Mackinaw Trail Cadillac MI 49601

Baldwm Fteld Office Route 2 Box 2810 Baldwin Ml49304 Manton Field Office 521 N Michigan Manton Ml49663 Evart Field Office 951 W 7th Street Evart Ml 49631 Oceana Field Office 1757 E Hayes Rd M-20 Shelby Ml49455

TRAVERSE CITY FOREST MANAGEMENT UNIT 970 Emerson Traverse City Ml49686 Kalkaska Fteld Office 2089 N B~rch St Kalkaska MI 49646 Platte River Field Office 15210 US 31 Hwy Beulah Ml49617

GLADWIN FOREST MANAGEMENT UNIT 801 N Silverleaf PO Box 337 Gladwin M148624 Harrison Field Office 708 N First St Harrison Ml 48625 Standish Field Office 527 N M76 Box 447 Standish MI 48658 Sanford Field Office 118 W Saginaw MI 48657

GRAYLING FOREST MANAGEMENT UNIT 1955 Nl-75 BL Grayling MI 49738 Lmcoln F1eld Office 408 Mam St PO Box 122 Lincoln MI 48742 Mio Field Office 191 S Mt Tom Rd Box 939 Mio MI 48647

ROSCOMMON FOREST MANAGEMENT UNIT Box 218 Roscommon MI 48653 Houghton Liike F1eld Office 180 S Harrtson Rd Houghton Lake Ml48629 West Branch Field Office 2389 South M-76 West Branch MI 48661

Ken Alto

Kim Dufresne

Tim Tennis

lonst Manbullpmeut DWisioa 15 Resource Mana1ement Units

bullJfectble l2519bull

bull -Resource Jf~nt Unit OJke

1 -Raource Jf~nt Unit BOUIIdariea

1 -CountyBouruiiJrfea

-17shy

In general BT is smallest for AB followed by YB RM SM BC BW and AE in increasing order

with BT for WA being the largest In general BT increases with DOB and decreases with TH

Most of the anomalies are due to small sample sizes

For the topwood data set (n=631) BT was significantly different for the seven different

species (Bartletts -test for equal variances PltOOOl F-test for equal means PltOOOl) All

Bonferroni pairwise comparisons of means are significantly different except for (RM SM) (RM

BC) (RM YB) (SM BC) (BC YB) and (YB AB)

Average minimum and maximum BTs and Pearsons correlations of BT with DOB and DBH

are shown below for the seven species

Species x

BT

Min- Max

BT DOB p r

BTDBH p n

RM WA SM BW BC YB AB

0064 0203 0086 0150 0083 0034 0019

0008-0385 0022-0458 0005-0362 0018-0262 0018-0175 Ool5-0075 0008-0038

06SO 0723 0768 0813 0723 0464 0051

lt0001 lt0001 lt0001 lt0001 lt0001

0017 0744

0549 0360 0440 0588 0380 0216 0661

lt0001 0002

lt0001 lt0001

0032 0290

lt0001

74 75

342 38 32 26 44

BT was significantly positively related to DOB for all species except for AB and to DBH for all

species except for YB

Average BTs for various DOB classes for the seven species are as follows

DOB Class BT (in) RM WA S~t BW BC YB AB

500 OQl8 0126 oltH) 0054 0051 0024 0021 501 to 700 0073 0212 () t)(J 0105 0086 0032 0019 701 to 900 0152 0281 () Ill 0170 0115 0057 0015 901 to 1100 0158 0255 () 177 0193 0114 0043 0020

111 to 1300 0122 0345 0222 0205 0135 0026

-18shy

In general BT is smallest for AB followed by YB BC RM SM and BW in increasing order

with BT for W A being the largest In general BT increases with DOB Most of the anomalies are

due to small sample sizes

Comparison with other BF equations

Fowler (1993) showed that while there were significant species differences between BF

equations for aspen jack pine and red pine there was a very strong relationship between BF and

tree height for each species (ie R 2 gt097 for each species) BF was a function of TH and In TH

showing that BF increased with TH to some maximum and then decreased for larger THs with the

steepness of the decrease depending on the species For all three species BF was not strongly

related to DBH or DOB at a given TH

For paper birch (Fowler and Hussain 1997) BF significantly increased with DOB at TH

(R2 =0219) and significantly decreased with In TH (R2 =0166) for stemwood while BF

significantly increased with DOB for topwood ( R 2 =0218) BF was much more variable than for

aspen red pine and jack pine

Fowler et al (1997) showed that black oak (BO) red oak (RO) and white oak (WO) have BPs

that are quite variable and prediction equations with the same independent variables as for paper

birch with the direction of the relations reversed For stemwood BF decreased with DOB at TH

( R 2 =0270 0418 and 0014 for BO RO and WO respectively) and increased with In TH ( R 2 =

0190 0275 and 0011 for BO RO and WO respectively) For topwood BF decreased with DOB

(R2=0366 0457 and 0100 for BO RO and WO respectively) These prediction equations were

significant but they were only moderately strong at best being only somewhat stronger in general

than the prediction equations for paper birch The prediction equations based on DOB were

-19shy

somewhat stronger than the prediction equations based on In TH The BF equations were

significantly different for the three species and for topwood versus stemwood except for RO

This study shows that the eight northern hardwood species have BFs that are quite variable

with some species having prediction equations with the same independent variables as for paper

birch and the three oak species while other species had different independent variables For

stemwood BF decreased with DOB at TH for RM SM BW and BC increased with In DOB at TH

for W A YB and AE and increased and then somewhat decreased with 1DOB and In DOB as the

independent variables for AB BF increased with In TH for RM SM and BC decreased and then

increased with TH and In TH for WA and BW increased and then decreased with TH and In TH for

YB AB and AE The prediction equations for AE are very suspect as they were based on only six

BF measurements from one tree For topwood BF decreased with DOB for RM WA SM BW

and BC increased with DOB for YB and increased and somewhat decreased with 1DOB and

In DOB for AB All prediction equations for stemwood were significant except for the TH

equations for BW and YB For topwood only the prediction equations for RM SM BW and AB

were significant In general all prediction equations were only moderately strong at best and some

of them were very weak The BF equations were significantly different for most species while the

stemwood and topwood BF equations were not significantly different except for RM and SM

GUIDELINES FOR USERS

We recommend use of the following equations for northern hardwoods when accurate

estimates of bark factors are desired

Stemwood

bull Red maple I

(1) BF =0996730-0002397 bull DOB I

(2) BF =0972344 + 0003554 bull In TH

-20shy

bull White ash 1

(3) BF = 0922166 +0001198bull DOB 1

(4) BF = 0937036 + 0000805 bull TH- 0009279 bullIn TH

bull- Sugar maple 1

(5) BF=0988318-0001497bullDOB 1

(6) BF = 0970865 + 0002264 bullIn TH

bull Basswood 1

(7) BF = 0974486-0000403 bull DOB 1

(8) BF = 0970312 + 0000072 bull TH- 0000631bullln TH

bull Black cherry 1

(9) BF = 0971912 -0000841bull DOB 1

(lO) BF = 0954777 + 0004557 bullIn TH

bull Yell ow birch 1

(11) BF = 0987390 + 0000307 bull DOB 1

(12) BF = 0990354-0000111bull TH+0000885bullln TH

bull American beech 1

(l3) BF = l027382-0l03065DOB -0009012bullln DOB

1

(14) BF = 0994075-0000047 bull TH+0000896 bullIn TH

bull American elm 1

(l5) BF =0925851 + 0003400 bull DOB 1

(16) BF = 0975815-0000058 bull TH- 0()()4696bullln TH

Use Equations 1 3 5 7 9 11 13 and 15 if DOBis measured Use Equations 2 4 6 8 10 12 14

and 16 when only THis measured

Topwood 1

(l7) RM BF = 1006791-0004569 bull DOB 1

(18) WA BF = 0936727 -0000206bull DOB 1

(l9) SM BF = 0995302-0002757 bull DOB

-21shy

(20) BW BF = 0979121-0002155 bull DOB

(21) BC BF = 0977830- 0000604 bull DOB

(22) YB BF = 0987032 + 0000281bull DOB

(23) AB BF = 1038966- 0131661DOB - 0012832 bullln DOB

The equation for stemwood and topwood pooled could be used if DOB is measured with moderate

loss in accuracy for RM and SM and little loss in accuracy for the other five species The pooled

equations in general will be more accurate for stemwood compared to topwood especially for RM

and SM

(24) RM BF == 0997087 -0002476bull DOB

1

(25) WA BF = 0924553 + 000 I 003 bull DOB

(26) SM BF=0988615-0001568bullDOB

(27) BW BF = 0972865-0000320 bull DOB

(28) BC BF=0974512-0001028bullDOB

(29) YB BF = 0986997 + 0000334 bull DOB

(30) AB BF = 1028314- 0105996DOB- 0009288 bullIn DOB

There is no pooled equation for AE as there was no topwood for the one AE tree in the data set

For reasonable accuracy in many situations the following constants could be used for bark

factors

DOB Class Stemwood BF (in) RM WA St-1 BW BC YB AB AE

DOBs50 0988 0927 09S~ 0973 0969 0989 0988 0939 50ltDOBsl00 0979 0931 0977 0971 0966 0990 0995 0951 l00ltDOBs150 0967 0937 0970 0969 0962 0991 0996 0968 150ltDOBs200 0955 0943 0962 0967 0957 0993 0996 0985

DOBgt200 0943 0949 0954 0965 0953 0994 0995 0994

-22shy

DOB Class ToEwoodBF (in) RM WA SM BW BC YB AB

DOBS50 0989 0936 0984 0971 0975 0988 0987 50ltD0BSl00 0970 0935 0973 0962 0973 0989 0995 100ltD0BS150 0947 0934 0959 0951 0970 0991 0996 150ltD0BS200 0924 0933 0946 0940 0967 0992 0995

008gt200 0902 0932 0932 0930 0964 0993 0993

TH Stemwood BF (ft) RM WA SM BW BC YB AB AE

THS05 0970 0947 0971 0971 0950 0990 0993 0980 05ltTHS45 0974 0932 olJn 0970 0959 0991 0995 0972

45ltTHS 100 0978 0925 0974 0970 0964 0991 0996 0966 100ltTHS200 0980 0924 0gt76 0970 0967 0991 0996 0963 200ltTHS300 0984 0928 0gt7S 0970 0970 0990 0996 0959 300ltTHS400 0986 0932 OltJSO 0971 0971 0990 0996 0957 400ltTHS500 0988 0937 () l)S~ 0971 0972 0989 0995 0955

THgt500 0992 0950 07 0974 0974 0987 0995 0952

The following constants for bark factor could be used for simplicity with moderately

approximate results especially for a large number of treessticks

Species Stem wood Top wood Stemwood and Topwood

RM 0980 0981 0980 WA 0932 0935 0932 SM 0976 0977 0976 BW 0970 0962 0970 BC 0965 0974 0966 YB 0991 0989 0990 AB 0995 0995 0995 AE 0964 0964

The above constants would be more accurate for those species that did not have significant

prediction equations andor small sample sizes B~ cry careful with using any of the results of this

study outside the range of the data set for each species Since the results for AE are based on six

stemwood measurements from one tree they arc of course very suspect

-23shy

Use of prediction equations

The prediction equations can be used to estimate BF at any DOB andor TH Since

BF=DIBDOB DIB can be estimated as DIB=BFbull DOB and DOB can be estimated as

DOB=DIBBF Past DOB and DOB growth can be estimated from past DIB growth as follows

Past DOB Growth=Past DIB GrowthBF

and

Past DOB=Present DOB -Past DOB Growth

where past DIB growth might be obtained with an increment borer

Specific uses of the prediction equations include (1) estimation of the solid wood and bark

volume of standing trees (2) estimation of bark volume or peeled volume from unpeeled volume

of felled tree sections (3) growth studies and (4) estimating tree form (eg Girard Form Class)

See Husch et al ( 1982) for a detailed discussion on bark factors

-24- LITERATURE CITED middot

Fowler G W 1991 An aspen bark factor equation for Michigan North J Appl For 8(1) 12-15

Fowler G W 1993 A jack pine bark factor equation for Michigan North J Appl For 10(2) 86-89

Fowler G W and L J Damschroder 1988 A red pine bark factor equation for Michigan North J Appl For 5(1) 28-30

Fowler G W and N G Hussain 1987a Bark factor equation for red pine Michigan DNR For Infor Leaflet 1-87 2 p

Fowler G W and N G Hussain 1987b Bark factor equation for aspen Michigan DNR For Infor Leaflet 2-87 2 p

Fowler G W and N G Hussain 1991 Bark factor equation for jack pine in Michigan Michigan DNR For Infor Leaflet 1-91 5 p

Fowler G W and N G Hussain 1997 Bark factor equations for paper birch in Michigan Michigan DNR For Infor Leaflet 1-97 12 p

Fowler G W N G Hussain D J Cohen and D Khatry-Chhetri 1997 Bark factor equations for oak in Michigan Michigan DNR For Infor Leaflet 2-97 15 p

Husch B C I Miller and T W Beers 1982 Forest Mensuration John Wiley and Sons Inc NY 402 p

~ FOREST MANAGEMENT DIVISION John M Robertsoa 51~ 373-1275 DMSION OFFICE PO Box 30452 Lansing MI 48909-7952

Brian Hutchins 517 275-5211 Forest Fire ExJ)Ciinent Station 1337 E Robinson Lake Rd Box 68 Roscommon MI 48653 Rich Mergener 906 341-2518 Wyman N~ Rt No 2 Box 2004 Manistique MI 49854 Rich Mergener 810 229-9152 State Forest Tree Improvement Center 4631 Bishop Lake Rd Howell MI 48843

Mike Palada 906~ 228-6561 Marquette Office 1990 Us-41 South MUQuette Ml 49855 Bill Maid ~906 249-1497 Marguctte Warehouse amp Repair ShoP 110 Foid Rd Marquette MI 49855

Edwin Moore s17 732-4481 Gaylord Warehouse amp Repair Shop 540 S Otsego Ave PO Box 596 Gaylord MI 49734

Marty Nelson

Debbie Begalle

Dennis Nezich

Bill Brondyke

Gilbert Joy Dean Reid

(_0____

Jeff Stampfly

Dayle Garlock

Bill ONeill

Joe Jarecki Dennis Vitton

Joe Fields

Courtney Borgondy

Susan Thiel

Don Torchia

(906) 353-6651 (906) 288-3321 (906) 224-2771 (906) 875-6622 (906) 563-9248 (906) 246-3245 (906) 786-2354 (906) 753-6317 (906) 346-920 1 (906) 485-1031 (906) 249-1497 (906) 293-3293 (906) 635-5281 (906) 477-6048 (906) 297-2581 (906) 452-6227 (906) 499-3346 (906) 341-2518

616 775-9727 517 826-3211 517 275-5151

(517) 785-425 1 (517) 354-7822 (517) 733-8775 (517) 731-5806 (616) 533-8341 (616) 238-9314 (616) 539-8564 (517) 983-4101 (616) 775-9727 (616) 745-4651 (616) 824-3591 (616) 734-5840 (616) 861-5636 (616) 922-5280 (616) 258-2711 (616) 325-4611 (517) 426-9205 (5 17) 539-6411 (5 I 7) 846-4104 (5 I 7) 687-7771 (517) 348-6371 (517) 736-8336 (517) 826-3211 (517) 275-4622 (517) 422-2897 (517) 345-0472

BARAGA FOREST MANAGEMENT UNIT 427 US-41 North Baraga MI 49908 Twm Lakes Fteld Office Rt I Box 234 Toivola MI 49965 Wakefield Field Office 1405 East US-2 Wakefield Ml49968

CRYSTAL FALLS FOREST MANAGEMENT UNIT 1420 US-2 West Crystal Falls Ml49920 Norway Fteld Office Os-2 West PO Box 126 Norway MI 49870 Felch Field Office PO Box 188 Felch MI 49831

ESCANABA FOREST MANAGEMENT UNIT 6833 Hwy 2 41 amp M-35 Gladstone MI 49837 Stephenson F1eld Office West 5420 River Road Stephenson MI 49887

GWINN FOREST MANAGEMENT UNIT 410 West M-35 Gwinn MI 49841 lshpemmg Field Ofttce 1985 US 41 Hwy West Ishpeming MI 49849

Marquette Field Office 110 Ford Road Marquette Ml 49855 NEWBERRY FOREST MANAGEMENT UNIT Box 428 5666 M 123 S Newberry MI 49868 SAULT STE MARIE FOREST MANAGEMENT UNIT Box 798 200 I Ashmun Sault Ste Marie Ml 49783

Naubinway Field Office PO Box 287 US 2 Naubinway MI 49762 Detour Field Office PO Box 92 Ml34 Detour MI4972S

SHINGLETON FOREST MANAGEMENT UNIT M-28 West PO Box 67 Shingleton Ml49884 Seney Fteld Office Comer ofM-77 amp M-28 PO Box 72 Seney MI 49883 Wyman Nursery Rt No 2 Box 2004 Manistique MI498S4

ay o tce I est M- ox ay o Cadillac Office 8015 Mackinaw Trail Cadillac Ml 49601 Mio Office 191 S Mt Tom Rd Box 939 Mio MI 48647 Roscommon Office 8717 N Roscommon Rd Box 128 Roscommon Ml 48653

ATLANTA FOREST MANAGEMENT UNIT 13501 M-33 Atlanta Ml49709 Alpena Field Office 4343 M-32 West Alpena Ml49707 Onaway Field Office Hwy M-211 Box 32 Onaway Ml49765

GAYLORD FOREST MANAGEMENT UNIT 1732 West M-32 Box 667 Gaylord Ml49734 BeUaJre Fteld office 70 I E Cayuga St PO Box 278 Bellaire Ml 49615 Indian River Field Office PO Box 10 6984 Wilson Indian River Ml49749 Pellston Field Office 304 Stimson Box 126 Pellston Ml49769

PIGEON RIVER COUNTRY FOREST MANAGEMENT UNIT 9966 Twin Lakes Rd Vanderbilt Ml 49795 CADILLAC FOREST MANAGEMENT UNIT 8015 Mackinaw Trail Cadillac MI 49601

Baldwm Fteld Office Route 2 Box 2810 Baldwin Ml49304 Manton Field Office 521 N Michigan Manton Ml49663 Evart Field Office 951 W 7th Street Evart Ml 49631 Oceana Field Office 1757 E Hayes Rd M-20 Shelby Ml49455

TRAVERSE CITY FOREST MANAGEMENT UNIT 970 Emerson Traverse City Ml49686 Kalkaska Fteld Office 2089 N B~rch St Kalkaska MI 49646 Platte River Field Office 15210 US 31 Hwy Beulah Ml49617

GLADWIN FOREST MANAGEMENT UNIT 801 N Silverleaf PO Box 337 Gladwin M148624 Harrison Field Office 708 N First St Harrison Ml 48625 Standish Field Office 527 N M76 Box 447 Standish MI 48658 Sanford Field Office 118 W Saginaw MI 48657

GRAYLING FOREST MANAGEMENT UNIT 1955 Nl-75 BL Grayling MI 49738 Lmcoln F1eld Office 408 Mam St PO Box 122 Lincoln MI 48742 Mio Field Office 191 S Mt Tom Rd Box 939 Mio MI 48647

ROSCOMMON FOREST MANAGEMENT UNIT Box 218 Roscommon MI 48653 Houghton Liike F1eld Office 180 S Harrtson Rd Houghton Lake Ml48629 West Branch Field Office 2389 South M-76 West Branch MI 48661

Ken Alto

Kim Dufresne

Tim Tennis

lonst Manbullpmeut DWisioa 15 Resource Mana1ement Units

bullJfectble l2519bull

bull -Resource Jf~nt Unit OJke

1 -Raource Jf~nt Unit BOUIIdariea

1 -CountyBouruiiJrfea

-18shy

In general BT is smallest for AB followed by YB BC RM SM and BW in increasing order

with BT for W A being the largest In general BT increases with DOB Most of the anomalies are

due to small sample sizes

Comparison with other BF equations

Fowler (1993) showed that while there were significant species differences between BF

equations for aspen jack pine and red pine there was a very strong relationship between BF and

tree height for each species (ie R 2 gt097 for each species) BF was a function of TH and In TH

showing that BF increased with TH to some maximum and then decreased for larger THs with the

steepness of the decrease depending on the species For all three species BF was not strongly

related to DBH or DOB at a given TH

For paper birch (Fowler and Hussain 1997) BF significantly increased with DOB at TH

(R2 =0219) and significantly decreased with In TH (R2 =0166) for stemwood while BF

significantly increased with DOB for topwood ( R 2 =0218) BF was much more variable than for

aspen red pine and jack pine

Fowler et al (1997) showed that black oak (BO) red oak (RO) and white oak (WO) have BPs

that are quite variable and prediction equations with the same independent variables as for paper

birch with the direction of the relations reversed For stemwood BF decreased with DOB at TH

( R 2 =0270 0418 and 0014 for BO RO and WO respectively) and increased with In TH ( R 2 =

0190 0275 and 0011 for BO RO and WO respectively) For topwood BF decreased with DOB

(R2=0366 0457 and 0100 for BO RO and WO respectively) These prediction equations were

significant but they were only moderately strong at best being only somewhat stronger in general

than the prediction equations for paper birch The prediction equations based on DOB were

-19shy

somewhat stronger than the prediction equations based on In TH The BF equations were

significantly different for the three species and for topwood versus stemwood except for RO

This study shows that the eight northern hardwood species have BFs that are quite variable

with some species having prediction equations with the same independent variables as for paper

birch and the three oak species while other species had different independent variables For

stemwood BF decreased with DOB at TH for RM SM BW and BC increased with In DOB at TH

for W A YB and AE and increased and then somewhat decreased with 1DOB and In DOB as the

independent variables for AB BF increased with In TH for RM SM and BC decreased and then

increased with TH and In TH for WA and BW increased and then decreased with TH and In TH for

YB AB and AE The prediction equations for AE are very suspect as they were based on only six

BF measurements from one tree For topwood BF decreased with DOB for RM WA SM BW

and BC increased with DOB for YB and increased and somewhat decreased with 1DOB and

In DOB for AB All prediction equations for stemwood were significant except for the TH

equations for BW and YB For topwood only the prediction equations for RM SM BW and AB

were significant In general all prediction equations were only moderately strong at best and some

of them were very weak The BF equations were significantly different for most species while the

stemwood and topwood BF equations were not significantly different except for RM and SM

GUIDELINES FOR USERS

We recommend use of the following equations for northern hardwoods when accurate

estimates of bark factors are desired

Stemwood

bull Red maple I

(1) BF =0996730-0002397 bull DOB I

(2) BF =0972344 + 0003554 bull In TH

-20shy

bull White ash 1

(3) BF = 0922166 +0001198bull DOB 1

(4) BF = 0937036 + 0000805 bull TH- 0009279 bullIn TH

bull- Sugar maple 1

(5) BF=0988318-0001497bullDOB 1

(6) BF = 0970865 + 0002264 bullIn TH

bull Basswood 1

(7) BF = 0974486-0000403 bull DOB 1

(8) BF = 0970312 + 0000072 bull TH- 0000631bullln TH

bull Black cherry 1

(9) BF = 0971912 -0000841bull DOB 1

(lO) BF = 0954777 + 0004557 bullIn TH

bull Yell ow birch 1

(11) BF = 0987390 + 0000307 bull DOB 1

(12) BF = 0990354-0000111bull TH+0000885bullln TH

bull American beech 1

(l3) BF = l027382-0l03065DOB -0009012bullln DOB

1

(14) BF = 0994075-0000047 bull TH+0000896 bullIn TH

bull American elm 1

(l5) BF =0925851 + 0003400 bull DOB 1

(16) BF = 0975815-0000058 bull TH- 0()()4696bullln TH

Use Equations 1 3 5 7 9 11 13 and 15 if DOBis measured Use Equations 2 4 6 8 10 12 14

and 16 when only THis measured

Topwood 1

(l7) RM BF = 1006791-0004569 bull DOB 1

(18) WA BF = 0936727 -0000206bull DOB 1

(l9) SM BF = 0995302-0002757 bull DOB

-21shy

(20) BW BF = 0979121-0002155 bull DOB

(21) BC BF = 0977830- 0000604 bull DOB

(22) YB BF = 0987032 + 0000281bull DOB

(23) AB BF = 1038966- 0131661DOB - 0012832 bullln DOB

The equation for stemwood and topwood pooled could be used if DOB is measured with moderate

loss in accuracy for RM and SM and little loss in accuracy for the other five species The pooled

equations in general will be more accurate for stemwood compared to topwood especially for RM

and SM

(24) RM BF == 0997087 -0002476bull DOB

1

(25) WA BF = 0924553 + 000 I 003 bull DOB

(26) SM BF=0988615-0001568bullDOB

(27) BW BF = 0972865-0000320 bull DOB

(28) BC BF=0974512-0001028bullDOB

(29) YB BF = 0986997 + 0000334 bull DOB

(30) AB BF = 1028314- 0105996DOB- 0009288 bullIn DOB

There is no pooled equation for AE as there was no topwood for the one AE tree in the data set

For reasonable accuracy in many situations the following constants could be used for bark

factors

DOB Class Stemwood BF (in) RM WA St-1 BW BC YB AB AE

DOBs50 0988 0927 09S~ 0973 0969 0989 0988 0939 50ltDOBsl00 0979 0931 0977 0971 0966 0990 0995 0951 l00ltDOBs150 0967 0937 0970 0969 0962 0991 0996 0968 150ltDOBs200 0955 0943 0962 0967 0957 0993 0996 0985

DOBgt200 0943 0949 0954 0965 0953 0994 0995 0994

-22shy

DOB Class ToEwoodBF (in) RM WA SM BW BC YB AB

DOBS50 0989 0936 0984 0971 0975 0988 0987 50ltD0BSl00 0970 0935 0973 0962 0973 0989 0995 100ltD0BS150 0947 0934 0959 0951 0970 0991 0996 150ltD0BS200 0924 0933 0946 0940 0967 0992 0995

008gt200 0902 0932 0932 0930 0964 0993 0993

TH Stemwood BF (ft) RM WA SM BW BC YB AB AE

THS05 0970 0947 0971 0971 0950 0990 0993 0980 05ltTHS45 0974 0932 olJn 0970 0959 0991 0995 0972

45ltTHS 100 0978 0925 0974 0970 0964 0991 0996 0966 100ltTHS200 0980 0924 0gt76 0970 0967 0991 0996 0963 200ltTHS300 0984 0928 0gt7S 0970 0970 0990 0996 0959 300ltTHS400 0986 0932 OltJSO 0971 0971 0990 0996 0957 400ltTHS500 0988 0937 () l)S~ 0971 0972 0989 0995 0955

THgt500 0992 0950 07 0974 0974 0987 0995 0952

The following constants for bark factor could be used for simplicity with moderately

approximate results especially for a large number of treessticks

Species Stem wood Top wood Stemwood and Topwood

RM 0980 0981 0980 WA 0932 0935 0932 SM 0976 0977 0976 BW 0970 0962 0970 BC 0965 0974 0966 YB 0991 0989 0990 AB 0995 0995 0995 AE 0964 0964

The above constants would be more accurate for those species that did not have significant

prediction equations andor small sample sizes B~ cry careful with using any of the results of this

study outside the range of the data set for each species Since the results for AE are based on six

stemwood measurements from one tree they arc of course very suspect

-23shy

Use of prediction equations

The prediction equations can be used to estimate BF at any DOB andor TH Since

BF=DIBDOB DIB can be estimated as DIB=BFbull DOB and DOB can be estimated as

DOB=DIBBF Past DOB and DOB growth can be estimated from past DIB growth as follows

Past DOB Growth=Past DIB GrowthBF

and

Past DOB=Present DOB -Past DOB Growth

where past DIB growth might be obtained with an increment borer

Specific uses of the prediction equations include (1) estimation of the solid wood and bark

volume of standing trees (2) estimation of bark volume or peeled volume from unpeeled volume

of felled tree sections (3) growth studies and (4) estimating tree form (eg Girard Form Class)

See Husch et al ( 1982) for a detailed discussion on bark factors

-24- LITERATURE CITED middot

Fowler G W 1991 An aspen bark factor equation for Michigan North J Appl For 8(1) 12-15

Fowler G W 1993 A jack pine bark factor equation for Michigan North J Appl For 10(2) 86-89

Fowler G W and L J Damschroder 1988 A red pine bark factor equation for Michigan North J Appl For 5(1) 28-30

Fowler G W and N G Hussain 1987a Bark factor equation for red pine Michigan DNR For Infor Leaflet 1-87 2 p

Fowler G W and N G Hussain 1987b Bark factor equation for aspen Michigan DNR For Infor Leaflet 2-87 2 p

Fowler G W and N G Hussain 1991 Bark factor equation for jack pine in Michigan Michigan DNR For Infor Leaflet 1-91 5 p

Fowler G W and N G Hussain 1997 Bark factor equations for paper birch in Michigan Michigan DNR For Infor Leaflet 1-97 12 p

Fowler G W N G Hussain D J Cohen and D Khatry-Chhetri 1997 Bark factor equations for oak in Michigan Michigan DNR For Infor Leaflet 2-97 15 p

Husch B C I Miller and T W Beers 1982 Forest Mensuration John Wiley and Sons Inc NY 402 p

~ FOREST MANAGEMENT DIVISION John M Robertsoa 51~ 373-1275 DMSION OFFICE PO Box 30452 Lansing MI 48909-7952

Brian Hutchins 517 275-5211 Forest Fire ExJ)Ciinent Station 1337 E Robinson Lake Rd Box 68 Roscommon MI 48653 Rich Mergener 906 341-2518 Wyman N~ Rt No 2 Box 2004 Manistique MI 49854 Rich Mergener 810 229-9152 State Forest Tree Improvement Center 4631 Bishop Lake Rd Howell MI 48843

Mike Palada 906~ 228-6561 Marquette Office 1990 Us-41 South MUQuette Ml 49855 Bill Maid ~906 249-1497 Marguctte Warehouse amp Repair ShoP 110 Foid Rd Marquette MI 49855

Edwin Moore s17 732-4481 Gaylord Warehouse amp Repair Shop 540 S Otsego Ave PO Box 596 Gaylord MI 49734

Marty Nelson

Debbie Begalle

Dennis Nezich

Bill Brondyke

Gilbert Joy Dean Reid

(_0____

Jeff Stampfly

Dayle Garlock

Bill ONeill

Joe Jarecki Dennis Vitton

Joe Fields

Courtney Borgondy

Susan Thiel

Don Torchia

(906) 353-6651 (906) 288-3321 (906) 224-2771 (906) 875-6622 (906) 563-9248 (906) 246-3245 (906) 786-2354 (906) 753-6317 (906) 346-920 1 (906) 485-1031 (906) 249-1497 (906) 293-3293 (906) 635-5281 (906) 477-6048 (906) 297-2581 (906) 452-6227 (906) 499-3346 (906) 341-2518

616 775-9727 517 826-3211 517 275-5151

(517) 785-425 1 (517) 354-7822 (517) 733-8775 (517) 731-5806 (616) 533-8341 (616) 238-9314 (616) 539-8564 (517) 983-4101 (616) 775-9727 (616) 745-4651 (616) 824-3591 (616) 734-5840 (616) 861-5636 (616) 922-5280 (616) 258-2711 (616) 325-4611 (517) 426-9205 (5 17) 539-6411 (5 I 7) 846-4104 (5 I 7) 687-7771 (517) 348-6371 (517) 736-8336 (517) 826-3211 (517) 275-4622 (517) 422-2897 (517) 345-0472

BARAGA FOREST MANAGEMENT UNIT 427 US-41 North Baraga MI 49908 Twm Lakes Fteld Office Rt I Box 234 Toivola MI 49965 Wakefield Field Office 1405 East US-2 Wakefield Ml49968

CRYSTAL FALLS FOREST MANAGEMENT UNIT 1420 US-2 West Crystal Falls Ml49920 Norway Fteld Office Os-2 West PO Box 126 Norway MI 49870 Felch Field Office PO Box 188 Felch MI 49831

ESCANABA FOREST MANAGEMENT UNIT 6833 Hwy 2 41 amp M-35 Gladstone MI 49837 Stephenson F1eld Office West 5420 River Road Stephenson MI 49887

GWINN FOREST MANAGEMENT UNIT 410 West M-35 Gwinn MI 49841 lshpemmg Field Ofttce 1985 US 41 Hwy West Ishpeming MI 49849

Marquette Field Office 110 Ford Road Marquette Ml 49855 NEWBERRY FOREST MANAGEMENT UNIT Box 428 5666 M 123 S Newberry MI 49868 SAULT STE MARIE FOREST MANAGEMENT UNIT Box 798 200 I Ashmun Sault Ste Marie Ml 49783

Naubinway Field Office PO Box 287 US 2 Naubinway MI 49762 Detour Field Office PO Box 92 Ml34 Detour MI4972S

SHINGLETON FOREST MANAGEMENT UNIT M-28 West PO Box 67 Shingleton Ml49884 Seney Fteld Office Comer ofM-77 amp M-28 PO Box 72 Seney MI 49883 Wyman Nursery Rt No 2 Box 2004 Manistique MI498S4

ay o tce I est M- ox ay o Cadillac Office 8015 Mackinaw Trail Cadillac Ml 49601 Mio Office 191 S Mt Tom Rd Box 939 Mio MI 48647 Roscommon Office 8717 N Roscommon Rd Box 128 Roscommon Ml 48653

ATLANTA FOREST MANAGEMENT UNIT 13501 M-33 Atlanta Ml49709 Alpena Field Office 4343 M-32 West Alpena Ml49707 Onaway Field Office Hwy M-211 Box 32 Onaway Ml49765

GAYLORD FOREST MANAGEMENT UNIT 1732 West M-32 Box 667 Gaylord Ml49734 BeUaJre Fteld office 70 I E Cayuga St PO Box 278 Bellaire Ml 49615 Indian River Field Office PO Box 10 6984 Wilson Indian River Ml49749 Pellston Field Office 304 Stimson Box 126 Pellston Ml49769

PIGEON RIVER COUNTRY FOREST MANAGEMENT UNIT 9966 Twin Lakes Rd Vanderbilt Ml 49795 CADILLAC FOREST MANAGEMENT UNIT 8015 Mackinaw Trail Cadillac MI 49601

Baldwm Fteld Office Route 2 Box 2810 Baldwin Ml49304 Manton Field Office 521 N Michigan Manton Ml49663 Evart Field Office 951 W 7th Street Evart Ml 49631 Oceana Field Office 1757 E Hayes Rd M-20 Shelby Ml49455

TRAVERSE CITY FOREST MANAGEMENT UNIT 970 Emerson Traverse City Ml49686 Kalkaska Fteld Office 2089 N B~rch St Kalkaska MI 49646 Platte River Field Office 15210 US 31 Hwy Beulah Ml49617

GLADWIN FOREST MANAGEMENT UNIT 801 N Silverleaf PO Box 337 Gladwin M148624 Harrison Field Office 708 N First St Harrison Ml 48625 Standish Field Office 527 N M76 Box 447 Standish MI 48658 Sanford Field Office 118 W Saginaw MI 48657

GRAYLING FOREST MANAGEMENT UNIT 1955 Nl-75 BL Grayling MI 49738 Lmcoln F1eld Office 408 Mam St PO Box 122 Lincoln MI 48742 Mio Field Office 191 S Mt Tom Rd Box 939 Mio MI 48647

ROSCOMMON FOREST MANAGEMENT UNIT Box 218 Roscommon MI 48653 Houghton Liike F1eld Office 180 S Harrtson Rd Houghton Lake Ml48629 West Branch Field Office 2389 South M-76 West Branch MI 48661

Ken Alto

Kim Dufresne

Tim Tennis

lonst Manbullpmeut DWisioa 15 Resource Mana1ement Units

bullJfectble l2519bull

bull -Resource Jf~nt Unit OJke

1 -Raource Jf~nt Unit BOUIIdariea

1 -CountyBouruiiJrfea

-19shy

somewhat stronger than the prediction equations based on In TH The BF equations were

significantly different for the three species and for topwood versus stemwood except for RO

This study shows that the eight northern hardwood species have BFs that are quite variable

with some species having prediction equations with the same independent variables as for paper

birch and the three oak species while other species had different independent variables For

stemwood BF decreased with DOB at TH for RM SM BW and BC increased with In DOB at TH

for W A YB and AE and increased and then somewhat decreased with 1DOB and In DOB as the

independent variables for AB BF increased with In TH for RM SM and BC decreased and then

increased with TH and In TH for WA and BW increased and then decreased with TH and In TH for

YB AB and AE The prediction equations for AE are very suspect as they were based on only six

BF measurements from one tree For topwood BF decreased with DOB for RM WA SM BW

and BC increased with DOB for YB and increased and somewhat decreased with 1DOB and

In DOB for AB All prediction equations for stemwood were significant except for the TH

equations for BW and YB For topwood only the prediction equations for RM SM BW and AB

were significant In general all prediction equations were only moderately strong at best and some

of them were very weak The BF equations were significantly different for most species while the

stemwood and topwood BF equations were not significantly different except for RM and SM

GUIDELINES FOR USERS

We recommend use of the following equations for northern hardwoods when accurate

estimates of bark factors are desired

Stemwood

bull Red maple I

(1) BF =0996730-0002397 bull DOB I

(2) BF =0972344 + 0003554 bull In TH

-20shy

bull White ash 1

(3) BF = 0922166 +0001198bull DOB 1

(4) BF = 0937036 + 0000805 bull TH- 0009279 bullIn TH

bull- Sugar maple 1

(5) BF=0988318-0001497bullDOB 1

(6) BF = 0970865 + 0002264 bullIn TH

bull Basswood 1

(7) BF = 0974486-0000403 bull DOB 1

(8) BF = 0970312 + 0000072 bull TH- 0000631bullln TH

bull Black cherry 1

(9) BF = 0971912 -0000841bull DOB 1

(lO) BF = 0954777 + 0004557 bullIn TH

bull Yell ow birch 1

(11) BF = 0987390 + 0000307 bull DOB 1

(12) BF = 0990354-0000111bull TH+0000885bullln TH

bull American beech 1

(l3) BF = l027382-0l03065DOB -0009012bullln DOB

1

(14) BF = 0994075-0000047 bull TH+0000896 bullIn TH

bull American elm 1

(l5) BF =0925851 + 0003400 bull DOB 1

(16) BF = 0975815-0000058 bull TH- 0()()4696bullln TH

Use Equations 1 3 5 7 9 11 13 and 15 if DOBis measured Use Equations 2 4 6 8 10 12 14

and 16 when only THis measured

Topwood 1

(l7) RM BF = 1006791-0004569 bull DOB 1

(18) WA BF = 0936727 -0000206bull DOB 1

(l9) SM BF = 0995302-0002757 bull DOB

-21shy

(20) BW BF = 0979121-0002155 bull DOB

(21) BC BF = 0977830- 0000604 bull DOB

(22) YB BF = 0987032 + 0000281bull DOB

(23) AB BF = 1038966- 0131661DOB - 0012832 bullln DOB

The equation for stemwood and topwood pooled could be used if DOB is measured with moderate

loss in accuracy for RM and SM and little loss in accuracy for the other five species The pooled

equations in general will be more accurate for stemwood compared to topwood especially for RM

and SM

(24) RM BF == 0997087 -0002476bull DOB

1

(25) WA BF = 0924553 + 000 I 003 bull DOB

(26) SM BF=0988615-0001568bullDOB

(27) BW BF = 0972865-0000320 bull DOB

(28) BC BF=0974512-0001028bullDOB

(29) YB BF = 0986997 + 0000334 bull DOB

(30) AB BF = 1028314- 0105996DOB- 0009288 bullIn DOB

There is no pooled equation for AE as there was no topwood for the one AE tree in the data set

For reasonable accuracy in many situations the following constants could be used for bark

factors

DOB Class Stemwood BF (in) RM WA St-1 BW BC YB AB AE

DOBs50 0988 0927 09S~ 0973 0969 0989 0988 0939 50ltDOBsl00 0979 0931 0977 0971 0966 0990 0995 0951 l00ltDOBs150 0967 0937 0970 0969 0962 0991 0996 0968 150ltDOBs200 0955 0943 0962 0967 0957 0993 0996 0985

DOBgt200 0943 0949 0954 0965 0953 0994 0995 0994

-22shy

DOB Class ToEwoodBF (in) RM WA SM BW BC YB AB

DOBS50 0989 0936 0984 0971 0975 0988 0987 50ltD0BSl00 0970 0935 0973 0962 0973 0989 0995 100ltD0BS150 0947 0934 0959 0951 0970 0991 0996 150ltD0BS200 0924 0933 0946 0940 0967 0992 0995

008gt200 0902 0932 0932 0930 0964 0993 0993

TH Stemwood BF (ft) RM WA SM BW BC YB AB AE

THS05 0970 0947 0971 0971 0950 0990 0993 0980 05ltTHS45 0974 0932 olJn 0970 0959 0991 0995 0972

45ltTHS 100 0978 0925 0974 0970 0964 0991 0996 0966 100ltTHS200 0980 0924 0gt76 0970 0967 0991 0996 0963 200ltTHS300 0984 0928 0gt7S 0970 0970 0990 0996 0959 300ltTHS400 0986 0932 OltJSO 0971 0971 0990 0996 0957 400ltTHS500 0988 0937 () l)S~ 0971 0972 0989 0995 0955

THgt500 0992 0950 07 0974 0974 0987 0995 0952

The following constants for bark factor could be used for simplicity with moderately

approximate results especially for a large number of treessticks

Species Stem wood Top wood Stemwood and Topwood

RM 0980 0981 0980 WA 0932 0935 0932 SM 0976 0977 0976 BW 0970 0962 0970 BC 0965 0974 0966 YB 0991 0989 0990 AB 0995 0995 0995 AE 0964 0964

The above constants would be more accurate for those species that did not have significant

prediction equations andor small sample sizes B~ cry careful with using any of the results of this

study outside the range of the data set for each species Since the results for AE are based on six

stemwood measurements from one tree they arc of course very suspect

-23shy

Use of prediction equations

The prediction equations can be used to estimate BF at any DOB andor TH Since

BF=DIBDOB DIB can be estimated as DIB=BFbull DOB and DOB can be estimated as

DOB=DIBBF Past DOB and DOB growth can be estimated from past DIB growth as follows

Past DOB Growth=Past DIB GrowthBF

and

Past DOB=Present DOB -Past DOB Growth

where past DIB growth might be obtained with an increment borer

Specific uses of the prediction equations include (1) estimation of the solid wood and bark

volume of standing trees (2) estimation of bark volume or peeled volume from unpeeled volume

of felled tree sections (3) growth studies and (4) estimating tree form (eg Girard Form Class)

See Husch et al ( 1982) for a detailed discussion on bark factors

-24- LITERATURE CITED middot

Fowler G W 1991 An aspen bark factor equation for Michigan North J Appl For 8(1) 12-15

Fowler G W 1993 A jack pine bark factor equation for Michigan North J Appl For 10(2) 86-89

Fowler G W and L J Damschroder 1988 A red pine bark factor equation for Michigan North J Appl For 5(1) 28-30

Fowler G W and N G Hussain 1987a Bark factor equation for red pine Michigan DNR For Infor Leaflet 1-87 2 p

Fowler G W and N G Hussain 1987b Bark factor equation for aspen Michigan DNR For Infor Leaflet 2-87 2 p

Fowler G W and N G Hussain 1991 Bark factor equation for jack pine in Michigan Michigan DNR For Infor Leaflet 1-91 5 p

Fowler G W and N G Hussain 1997 Bark factor equations for paper birch in Michigan Michigan DNR For Infor Leaflet 1-97 12 p

Fowler G W N G Hussain D J Cohen and D Khatry-Chhetri 1997 Bark factor equations for oak in Michigan Michigan DNR For Infor Leaflet 2-97 15 p

Husch B C I Miller and T W Beers 1982 Forest Mensuration John Wiley and Sons Inc NY 402 p

~ FOREST MANAGEMENT DIVISION John M Robertsoa 51~ 373-1275 DMSION OFFICE PO Box 30452 Lansing MI 48909-7952

Brian Hutchins 517 275-5211 Forest Fire ExJ)Ciinent Station 1337 E Robinson Lake Rd Box 68 Roscommon MI 48653 Rich Mergener 906 341-2518 Wyman N~ Rt No 2 Box 2004 Manistique MI 49854 Rich Mergener 810 229-9152 State Forest Tree Improvement Center 4631 Bishop Lake Rd Howell MI 48843

Mike Palada 906~ 228-6561 Marquette Office 1990 Us-41 South MUQuette Ml 49855 Bill Maid ~906 249-1497 Marguctte Warehouse amp Repair ShoP 110 Foid Rd Marquette MI 49855

Edwin Moore s17 732-4481 Gaylord Warehouse amp Repair Shop 540 S Otsego Ave PO Box 596 Gaylord MI 49734

Marty Nelson

Debbie Begalle

Dennis Nezich

Bill Brondyke

Gilbert Joy Dean Reid

(_0____

Jeff Stampfly

Dayle Garlock

Bill ONeill

Joe Jarecki Dennis Vitton

Joe Fields

Courtney Borgondy

Susan Thiel

Don Torchia

(906) 353-6651 (906) 288-3321 (906) 224-2771 (906) 875-6622 (906) 563-9248 (906) 246-3245 (906) 786-2354 (906) 753-6317 (906) 346-920 1 (906) 485-1031 (906) 249-1497 (906) 293-3293 (906) 635-5281 (906) 477-6048 (906) 297-2581 (906) 452-6227 (906) 499-3346 (906) 341-2518

616 775-9727 517 826-3211 517 275-5151

(517) 785-425 1 (517) 354-7822 (517) 733-8775 (517) 731-5806 (616) 533-8341 (616) 238-9314 (616) 539-8564 (517) 983-4101 (616) 775-9727 (616) 745-4651 (616) 824-3591 (616) 734-5840 (616) 861-5636 (616) 922-5280 (616) 258-2711 (616) 325-4611 (517) 426-9205 (5 17) 539-6411 (5 I 7) 846-4104 (5 I 7) 687-7771 (517) 348-6371 (517) 736-8336 (517) 826-3211 (517) 275-4622 (517) 422-2897 (517) 345-0472

BARAGA FOREST MANAGEMENT UNIT 427 US-41 North Baraga MI 49908 Twm Lakes Fteld Office Rt I Box 234 Toivola MI 49965 Wakefield Field Office 1405 East US-2 Wakefield Ml49968

CRYSTAL FALLS FOREST MANAGEMENT UNIT 1420 US-2 West Crystal Falls Ml49920 Norway Fteld Office Os-2 West PO Box 126 Norway MI 49870 Felch Field Office PO Box 188 Felch MI 49831

ESCANABA FOREST MANAGEMENT UNIT 6833 Hwy 2 41 amp M-35 Gladstone MI 49837 Stephenson F1eld Office West 5420 River Road Stephenson MI 49887

GWINN FOREST MANAGEMENT UNIT 410 West M-35 Gwinn MI 49841 lshpemmg Field Ofttce 1985 US 41 Hwy West Ishpeming MI 49849

Marquette Field Office 110 Ford Road Marquette Ml 49855 NEWBERRY FOREST MANAGEMENT UNIT Box 428 5666 M 123 S Newberry MI 49868 SAULT STE MARIE FOREST MANAGEMENT UNIT Box 798 200 I Ashmun Sault Ste Marie Ml 49783

Naubinway Field Office PO Box 287 US 2 Naubinway MI 49762 Detour Field Office PO Box 92 Ml34 Detour MI4972S

SHINGLETON FOREST MANAGEMENT UNIT M-28 West PO Box 67 Shingleton Ml49884 Seney Fteld Office Comer ofM-77 amp M-28 PO Box 72 Seney MI 49883 Wyman Nursery Rt No 2 Box 2004 Manistique MI498S4

ay o tce I est M- ox ay o Cadillac Office 8015 Mackinaw Trail Cadillac Ml 49601 Mio Office 191 S Mt Tom Rd Box 939 Mio MI 48647 Roscommon Office 8717 N Roscommon Rd Box 128 Roscommon Ml 48653

ATLANTA FOREST MANAGEMENT UNIT 13501 M-33 Atlanta Ml49709 Alpena Field Office 4343 M-32 West Alpena Ml49707 Onaway Field Office Hwy M-211 Box 32 Onaway Ml49765

GAYLORD FOREST MANAGEMENT UNIT 1732 West M-32 Box 667 Gaylord Ml49734 BeUaJre Fteld office 70 I E Cayuga St PO Box 278 Bellaire Ml 49615 Indian River Field Office PO Box 10 6984 Wilson Indian River Ml49749 Pellston Field Office 304 Stimson Box 126 Pellston Ml49769

PIGEON RIVER COUNTRY FOREST MANAGEMENT UNIT 9966 Twin Lakes Rd Vanderbilt Ml 49795 CADILLAC FOREST MANAGEMENT UNIT 8015 Mackinaw Trail Cadillac MI 49601

Baldwm Fteld Office Route 2 Box 2810 Baldwin Ml49304 Manton Field Office 521 N Michigan Manton Ml49663 Evart Field Office 951 W 7th Street Evart Ml 49631 Oceana Field Office 1757 E Hayes Rd M-20 Shelby Ml49455

TRAVERSE CITY FOREST MANAGEMENT UNIT 970 Emerson Traverse City Ml49686 Kalkaska Fteld Office 2089 N B~rch St Kalkaska MI 49646 Platte River Field Office 15210 US 31 Hwy Beulah Ml49617

GLADWIN FOREST MANAGEMENT UNIT 801 N Silverleaf PO Box 337 Gladwin M148624 Harrison Field Office 708 N First St Harrison Ml 48625 Standish Field Office 527 N M76 Box 447 Standish MI 48658 Sanford Field Office 118 W Saginaw MI 48657

GRAYLING FOREST MANAGEMENT UNIT 1955 Nl-75 BL Grayling MI 49738 Lmcoln F1eld Office 408 Mam St PO Box 122 Lincoln MI 48742 Mio Field Office 191 S Mt Tom Rd Box 939 Mio MI 48647

ROSCOMMON FOREST MANAGEMENT UNIT Box 218 Roscommon MI 48653 Houghton Liike F1eld Office 180 S Harrtson Rd Houghton Lake Ml48629 West Branch Field Office 2389 South M-76 West Branch MI 48661

Ken Alto

Kim Dufresne

Tim Tennis

lonst Manbullpmeut DWisioa 15 Resource Mana1ement Units

bullJfectble l2519bull

bull -Resource Jf~nt Unit OJke

1 -Raource Jf~nt Unit BOUIIdariea

1 -CountyBouruiiJrfea

-20shy

bull White ash 1

(3) BF = 0922166 +0001198bull DOB 1

(4) BF = 0937036 + 0000805 bull TH- 0009279 bullIn TH

bull- Sugar maple 1

(5) BF=0988318-0001497bullDOB 1

(6) BF = 0970865 + 0002264 bullIn TH

bull Basswood 1

(7) BF = 0974486-0000403 bull DOB 1

(8) BF = 0970312 + 0000072 bull TH- 0000631bullln TH

bull Black cherry 1

(9) BF = 0971912 -0000841bull DOB 1

(lO) BF = 0954777 + 0004557 bullIn TH

bull Yell ow birch 1

(11) BF = 0987390 + 0000307 bull DOB 1

(12) BF = 0990354-0000111bull TH+0000885bullln TH

bull American beech 1

(l3) BF = l027382-0l03065DOB -0009012bullln DOB

1

(14) BF = 0994075-0000047 bull TH+0000896 bullIn TH

bull American elm 1

(l5) BF =0925851 + 0003400 bull DOB 1

(16) BF = 0975815-0000058 bull TH- 0()()4696bullln TH

Use Equations 1 3 5 7 9 11 13 and 15 if DOBis measured Use Equations 2 4 6 8 10 12 14

and 16 when only THis measured

Topwood 1

(l7) RM BF = 1006791-0004569 bull DOB 1

(18) WA BF = 0936727 -0000206bull DOB 1

(l9) SM BF = 0995302-0002757 bull DOB

-21shy

(20) BW BF = 0979121-0002155 bull DOB

(21) BC BF = 0977830- 0000604 bull DOB

(22) YB BF = 0987032 + 0000281bull DOB

(23) AB BF = 1038966- 0131661DOB - 0012832 bullln DOB

The equation for stemwood and topwood pooled could be used if DOB is measured with moderate

loss in accuracy for RM and SM and little loss in accuracy for the other five species The pooled

equations in general will be more accurate for stemwood compared to topwood especially for RM

and SM

(24) RM BF == 0997087 -0002476bull DOB

1

(25) WA BF = 0924553 + 000 I 003 bull DOB

(26) SM BF=0988615-0001568bullDOB

(27) BW BF = 0972865-0000320 bull DOB

(28) BC BF=0974512-0001028bullDOB

(29) YB BF = 0986997 + 0000334 bull DOB

(30) AB BF = 1028314- 0105996DOB- 0009288 bullIn DOB

There is no pooled equation for AE as there was no topwood for the one AE tree in the data set

For reasonable accuracy in many situations the following constants could be used for bark

factors

DOB Class Stemwood BF (in) RM WA St-1 BW BC YB AB AE

DOBs50 0988 0927 09S~ 0973 0969 0989 0988 0939 50ltDOBsl00 0979 0931 0977 0971 0966 0990 0995 0951 l00ltDOBs150 0967 0937 0970 0969 0962 0991 0996 0968 150ltDOBs200 0955 0943 0962 0967 0957 0993 0996 0985

DOBgt200 0943 0949 0954 0965 0953 0994 0995 0994

-22shy

DOB Class ToEwoodBF (in) RM WA SM BW BC YB AB

DOBS50 0989 0936 0984 0971 0975 0988 0987 50ltD0BSl00 0970 0935 0973 0962 0973 0989 0995 100ltD0BS150 0947 0934 0959 0951 0970 0991 0996 150ltD0BS200 0924 0933 0946 0940 0967 0992 0995

008gt200 0902 0932 0932 0930 0964 0993 0993

TH Stemwood BF (ft) RM WA SM BW BC YB AB AE

THS05 0970 0947 0971 0971 0950 0990 0993 0980 05ltTHS45 0974 0932 olJn 0970 0959 0991 0995 0972

45ltTHS 100 0978 0925 0974 0970 0964 0991 0996 0966 100ltTHS200 0980 0924 0gt76 0970 0967 0991 0996 0963 200ltTHS300 0984 0928 0gt7S 0970 0970 0990 0996 0959 300ltTHS400 0986 0932 OltJSO 0971 0971 0990 0996 0957 400ltTHS500 0988 0937 () l)S~ 0971 0972 0989 0995 0955

THgt500 0992 0950 07 0974 0974 0987 0995 0952

The following constants for bark factor could be used for simplicity with moderately

approximate results especially for a large number of treessticks

Species Stem wood Top wood Stemwood and Topwood

RM 0980 0981 0980 WA 0932 0935 0932 SM 0976 0977 0976 BW 0970 0962 0970 BC 0965 0974 0966 YB 0991 0989 0990 AB 0995 0995 0995 AE 0964 0964

The above constants would be more accurate for those species that did not have significant

prediction equations andor small sample sizes B~ cry careful with using any of the results of this

study outside the range of the data set for each species Since the results for AE are based on six

stemwood measurements from one tree they arc of course very suspect

-23shy

Use of prediction equations

The prediction equations can be used to estimate BF at any DOB andor TH Since

BF=DIBDOB DIB can be estimated as DIB=BFbull DOB and DOB can be estimated as

DOB=DIBBF Past DOB and DOB growth can be estimated from past DIB growth as follows

Past DOB Growth=Past DIB GrowthBF

and

Past DOB=Present DOB -Past DOB Growth

where past DIB growth might be obtained with an increment borer

Specific uses of the prediction equations include (1) estimation of the solid wood and bark

volume of standing trees (2) estimation of bark volume or peeled volume from unpeeled volume

of felled tree sections (3) growth studies and (4) estimating tree form (eg Girard Form Class)

See Husch et al ( 1982) for a detailed discussion on bark factors

-24- LITERATURE CITED middot

Fowler G W 1991 An aspen bark factor equation for Michigan North J Appl For 8(1) 12-15

Fowler G W 1993 A jack pine bark factor equation for Michigan North J Appl For 10(2) 86-89

Fowler G W and L J Damschroder 1988 A red pine bark factor equation for Michigan North J Appl For 5(1) 28-30

Fowler G W and N G Hussain 1987a Bark factor equation for red pine Michigan DNR For Infor Leaflet 1-87 2 p

Fowler G W and N G Hussain 1987b Bark factor equation for aspen Michigan DNR For Infor Leaflet 2-87 2 p

Fowler G W and N G Hussain 1991 Bark factor equation for jack pine in Michigan Michigan DNR For Infor Leaflet 1-91 5 p

Fowler G W and N G Hussain 1997 Bark factor equations for paper birch in Michigan Michigan DNR For Infor Leaflet 1-97 12 p

Fowler G W N G Hussain D J Cohen and D Khatry-Chhetri 1997 Bark factor equations for oak in Michigan Michigan DNR For Infor Leaflet 2-97 15 p

Husch B C I Miller and T W Beers 1982 Forest Mensuration John Wiley and Sons Inc NY 402 p

~ FOREST MANAGEMENT DIVISION John M Robertsoa 51~ 373-1275 DMSION OFFICE PO Box 30452 Lansing MI 48909-7952

Brian Hutchins 517 275-5211 Forest Fire ExJ)Ciinent Station 1337 E Robinson Lake Rd Box 68 Roscommon MI 48653 Rich Mergener 906 341-2518 Wyman N~ Rt No 2 Box 2004 Manistique MI 49854 Rich Mergener 810 229-9152 State Forest Tree Improvement Center 4631 Bishop Lake Rd Howell MI 48843

Mike Palada 906~ 228-6561 Marquette Office 1990 Us-41 South MUQuette Ml 49855 Bill Maid ~906 249-1497 Marguctte Warehouse amp Repair ShoP 110 Foid Rd Marquette MI 49855

Edwin Moore s17 732-4481 Gaylord Warehouse amp Repair Shop 540 S Otsego Ave PO Box 596 Gaylord MI 49734

Marty Nelson

Debbie Begalle

Dennis Nezich

Bill Brondyke

Gilbert Joy Dean Reid

(_0____

Jeff Stampfly

Dayle Garlock

Bill ONeill

Joe Jarecki Dennis Vitton

Joe Fields

Courtney Borgondy

Susan Thiel

Don Torchia

(906) 353-6651 (906) 288-3321 (906) 224-2771 (906) 875-6622 (906) 563-9248 (906) 246-3245 (906) 786-2354 (906) 753-6317 (906) 346-920 1 (906) 485-1031 (906) 249-1497 (906) 293-3293 (906) 635-5281 (906) 477-6048 (906) 297-2581 (906) 452-6227 (906) 499-3346 (906) 341-2518

616 775-9727 517 826-3211 517 275-5151

(517) 785-425 1 (517) 354-7822 (517) 733-8775 (517) 731-5806 (616) 533-8341 (616) 238-9314 (616) 539-8564 (517) 983-4101 (616) 775-9727 (616) 745-4651 (616) 824-3591 (616) 734-5840 (616) 861-5636 (616) 922-5280 (616) 258-2711 (616) 325-4611 (517) 426-9205 (5 17) 539-6411 (5 I 7) 846-4104 (5 I 7) 687-7771 (517) 348-6371 (517) 736-8336 (517) 826-3211 (517) 275-4622 (517) 422-2897 (517) 345-0472

BARAGA FOREST MANAGEMENT UNIT 427 US-41 North Baraga MI 49908 Twm Lakes Fteld Office Rt I Box 234 Toivola MI 49965 Wakefield Field Office 1405 East US-2 Wakefield Ml49968

CRYSTAL FALLS FOREST MANAGEMENT UNIT 1420 US-2 West Crystal Falls Ml49920 Norway Fteld Office Os-2 West PO Box 126 Norway MI 49870 Felch Field Office PO Box 188 Felch MI 49831

ESCANABA FOREST MANAGEMENT UNIT 6833 Hwy 2 41 amp M-35 Gladstone MI 49837 Stephenson F1eld Office West 5420 River Road Stephenson MI 49887

GWINN FOREST MANAGEMENT UNIT 410 West M-35 Gwinn MI 49841 lshpemmg Field Ofttce 1985 US 41 Hwy West Ishpeming MI 49849

Marquette Field Office 110 Ford Road Marquette Ml 49855 NEWBERRY FOREST MANAGEMENT UNIT Box 428 5666 M 123 S Newberry MI 49868 SAULT STE MARIE FOREST MANAGEMENT UNIT Box 798 200 I Ashmun Sault Ste Marie Ml 49783

Naubinway Field Office PO Box 287 US 2 Naubinway MI 49762 Detour Field Office PO Box 92 Ml34 Detour MI4972S

SHINGLETON FOREST MANAGEMENT UNIT M-28 West PO Box 67 Shingleton Ml49884 Seney Fteld Office Comer ofM-77 amp M-28 PO Box 72 Seney MI 49883 Wyman Nursery Rt No 2 Box 2004 Manistique MI498S4

ay o tce I est M- ox ay o Cadillac Office 8015 Mackinaw Trail Cadillac Ml 49601 Mio Office 191 S Mt Tom Rd Box 939 Mio MI 48647 Roscommon Office 8717 N Roscommon Rd Box 128 Roscommon Ml 48653

ATLANTA FOREST MANAGEMENT UNIT 13501 M-33 Atlanta Ml49709 Alpena Field Office 4343 M-32 West Alpena Ml49707 Onaway Field Office Hwy M-211 Box 32 Onaway Ml49765

GAYLORD FOREST MANAGEMENT UNIT 1732 West M-32 Box 667 Gaylord Ml49734 BeUaJre Fteld office 70 I E Cayuga St PO Box 278 Bellaire Ml 49615 Indian River Field Office PO Box 10 6984 Wilson Indian River Ml49749 Pellston Field Office 304 Stimson Box 126 Pellston Ml49769

PIGEON RIVER COUNTRY FOREST MANAGEMENT UNIT 9966 Twin Lakes Rd Vanderbilt Ml 49795 CADILLAC FOREST MANAGEMENT UNIT 8015 Mackinaw Trail Cadillac MI 49601

Baldwm Fteld Office Route 2 Box 2810 Baldwin Ml49304 Manton Field Office 521 N Michigan Manton Ml49663 Evart Field Office 951 W 7th Street Evart Ml 49631 Oceana Field Office 1757 E Hayes Rd M-20 Shelby Ml49455

TRAVERSE CITY FOREST MANAGEMENT UNIT 970 Emerson Traverse City Ml49686 Kalkaska Fteld Office 2089 N B~rch St Kalkaska MI 49646 Platte River Field Office 15210 US 31 Hwy Beulah Ml49617

GLADWIN FOREST MANAGEMENT UNIT 801 N Silverleaf PO Box 337 Gladwin M148624 Harrison Field Office 708 N First St Harrison Ml 48625 Standish Field Office 527 N M76 Box 447 Standish MI 48658 Sanford Field Office 118 W Saginaw MI 48657

GRAYLING FOREST MANAGEMENT UNIT 1955 Nl-75 BL Grayling MI 49738 Lmcoln F1eld Office 408 Mam St PO Box 122 Lincoln MI 48742 Mio Field Office 191 S Mt Tom Rd Box 939 Mio MI 48647

ROSCOMMON FOREST MANAGEMENT UNIT Box 218 Roscommon MI 48653 Houghton Liike F1eld Office 180 S Harrtson Rd Houghton Lake Ml48629 West Branch Field Office 2389 South M-76 West Branch MI 48661

Ken Alto

Kim Dufresne

Tim Tennis

lonst Manbullpmeut DWisioa 15 Resource Mana1ement Units

bullJfectble l2519bull

bull -Resource Jf~nt Unit OJke

1 -Raource Jf~nt Unit BOUIIdariea

1 -CountyBouruiiJrfea

-21shy

(20) BW BF = 0979121-0002155 bull DOB

(21) BC BF = 0977830- 0000604 bull DOB

(22) YB BF = 0987032 + 0000281bull DOB

(23) AB BF = 1038966- 0131661DOB - 0012832 bullln DOB

The equation for stemwood and topwood pooled could be used if DOB is measured with moderate

loss in accuracy for RM and SM and little loss in accuracy for the other five species The pooled

equations in general will be more accurate for stemwood compared to topwood especially for RM

and SM

(24) RM BF == 0997087 -0002476bull DOB

1

(25) WA BF = 0924553 + 000 I 003 bull DOB

(26) SM BF=0988615-0001568bullDOB

(27) BW BF = 0972865-0000320 bull DOB

(28) BC BF=0974512-0001028bullDOB

(29) YB BF = 0986997 + 0000334 bull DOB

(30) AB BF = 1028314- 0105996DOB- 0009288 bullIn DOB

There is no pooled equation for AE as there was no topwood for the one AE tree in the data set

For reasonable accuracy in many situations the following constants could be used for bark

factors

DOB Class Stemwood BF (in) RM WA St-1 BW BC YB AB AE

DOBs50 0988 0927 09S~ 0973 0969 0989 0988 0939 50ltDOBsl00 0979 0931 0977 0971 0966 0990 0995 0951 l00ltDOBs150 0967 0937 0970 0969 0962 0991 0996 0968 150ltDOBs200 0955 0943 0962 0967 0957 0993 0996 0985

DOBgt200 0943 0949 0954 0965 0953 0994 0995 0994

-22shy

DOB Class ToEwoodBF (in) RM WA SM BW BC YB AB

DOBS50 0989 0936 0984 0971 0975 0988 0987 50ltD0BSl00 0970 0935 0973 0962 0973 0989 0995 100ltD0BS150 0947 0934 0959 0951 0970 0991 0996 150ltD0BS200 0924 0933 0946 0940 0967 0992 0995

008gt200 0902 0932 0932 0930 0964 0993 0993

TH Stemwood BF (ft) RM WA SM BW BC YB AB AE

THS05 0970 0947 0971 0971 0950 0990 0993 0980 05ltTHS45 0974 0932 olJn 0970 0959 0991 0995 0972

45ltTHS 100 0978 0925 0974 0970 0964 0991 0996 0966 100ltTHS200 0980 0924 0gt76 0970 0967 0991 0996 0963 200ltTHS300 0984 0928 0gt7S 0970 0970 0990 0996 0959 300ltTHS400 0986 0932 OltJSO 0971 0971 0990 0996 0957 400ltTHS500 0988 0937 () l)S~ 0971 0972 0989 0995 0955

THgt500 0992 0950 07 0974 0974 0987 0995 0952

The following constants for bark factor could be used for simplicity with moderately

approximate results especially for a large number of treessticks

Species Stem wood Top wood Stemwood and Topwood

RM 0980 0981 0980 WA 0932 0935 0932 SM 0976 0977 0976 BW 0970 0962 0970 BC 0965 0974 0966 YB 0991 0989 0990 AB 0995 0995 0995 AE 0964 0964

The above constants would be more accurate for those species that did not have significant

prediction equations andor small sample sizes B~ cry careful with using any of the results of this

study outside the range of the data set for each species Since the results for AE are based on six

stemwood measurements from one tree they arc of course very suspect

-23shy

Use of prediction equations

The prediction equations can be used to estimate BF at any DOB andor TH Since

BF=DIBDOB DIB can be estimated as DIB=BFbull DOB and DOB can be estimated as

DOB=DIBBF Past DOB and DOB growth can be estimated from past DIB growth as follows

Past DOB Growth=Past DIB GrowthBF

and

Past DOB=Present DOB -Past DOB Growth

where past DIB growth might be obtained with an increment borer

Specific uses of the prediction equations include (1) estimation of the solid wood and bark

volume of standing trees (2) estimation of bark volume or peeled volume from unpeeled volume

of felled tree sections (3) growth studies and (4) estimating tree form (eg Girard Form Class)

See Husch et al ( 1982) for a detailed discussion on bark factors

-24- LITERATURE CITED middot

Fowler G W 1991 An aspen bark factor equation for Michigan North J Appl For 8(1) 12-15

Fowler G W 1993 A jack pine bark factor equation for Michigan North J Appl For 10(2) 86-89

Fowler G W and L J Damschroder 1988 A red pine bark factor equation for Michigan North J Appl For 5(1) 28-30

Fowler G W and N G Hussain 1987a Bark factor equation for red pine Michigan DNR For Infor Leaflet 1-87 2 p

Fowler G W and N G Hussain 1987b Bark factor equation for aspen Michigan DNR For Infor Leaflet 2-87 2 p

Fowler G W and N G Hussain 1991 Bark factor equation for jack pine in Michigan Michigan DNR For Infor Leaflet 1-91 5 p

Fowler G W and N G Hussain 1997 Bark factor equations for paper birch in Michigan Michigan DNR For Infor Leaflet 1-97 12 p

Fowler G W N G Hussain D J Cohen and D Khatry-Chhetri 1997 Bark factor equations for oak in Michigan Michigan DNR For Infor Leaflet 2-97 15 p

Husch B C I Miller and T W Beers 1982 Forest Mensuration John Wiley and Sons Inc NY 402 p

~ FOREST MANAGEMENT DIVISION John M Robertsoa 51~ 373-1275 DMSION OFFICE PO Box 30452 Lansing MI 48909-7952

Brian Hutchins 517 275-5211 Forest Fire ExJ)Ciinent Station 1337 E Robinson Lake Rd Box 68 Roscommon MI 48653 Rich Mergener 906 341-2518 Wyman N~ Rt No 2 Box 2004 Manistique MI 49854 Rich Mergener 810 229-9152 State Forest Tree Improvement Center 4631 Bishop Lake Rd Howell MI 48843

Mike Palada 906~ 228-6561 Marquette Office 1990 Us-41 South MUQuette Ml 49855 Bill Maid ~906 249-1497 Marguctte Warehouse amp Repair ShoP 110 Foid Rd Marquette MI 49855

Edwin Moore s17 732-4481 Gaylord Warehouse amp Repair Shop 540 S Otsego Ave PO Box 596 Gaylord MI 49734

Marty Nelson

Debbie Begalle

Dennis Nezich

Bill Brondyke

Gilbert Joy Dean Reid

(_0____

Jeff Stampfly

Dayle Garlock

Bill ONeill

Joe Jarecki Dennis Vitton

Joe Fields

Courtney Borgondy

Susan Thiel

Don Torchia

(906) 353-6651 (906) 288-3321 (906) 224-2771 (906) 875-6622 (906) 563-9248 (906) 246-3245 (906) 786-2354 (906) 753-6317 (906) 346-920 1 (906) 485-1031 (906) 249-1497 (906) 293-3293 (906) 635-5281 (906) 477-6048 (906) 297-2581 (906) 452-6227 (906) 499-3346 (906) 341-2518

616 775-9727 517 826-3211 517 275-5151

(517) 785-425 1 (517) 354-7822 (517) 733-8775 (517) 731-5806 (616) 533-8341 (616) 238-9314 (616) 539-8564 (517) 983-4101 (616) 775-9727 (616) 745-4651 (616) 824-3591 (616) 734-5840 (616) 861-5636 (616) 922-5280 (616) 258-2711 (616) 325-4611 (517) 426-9205 (5 17) 539-6411 (5 I 7) 846-4104 (5 I 7) 687-7771 (517) 348-6371 (517) 736-8336 (517) 826-3211 (517) 275-4622 (517) 422-2897 (517) 345-0472

BARAGA FOREST MANAGEMENT UNIT 427 US-41 North Baraga MI 49908 Twm Lakes Fteld Office Rt I Box 234 Toivola MI 49965 Wakefield Field Office 1405 East US-2 Wakefield Ml49968

CRYSTAL FALLS FOREST MANAGEMENT UNIT 1420 US-2 West Crystal Falls Ml49920 Norway Fteld Office Os-2 West PO Box 126 Norway MI 49870 Felch Field Office PO Box 188 Felch MI 49831

ESCANABA FOREST MANAGEMENT UNIT 6833 Hwy 2 41 amp M-35 Gladstone MI 49837 Stephenson F1eld Office West 5420 River Road Stephenson MI 49887

GWINN FOREST MANAGEMENT UNIT 410 West M-35 Gwinn MI 49841 lshpemmg Field Ofttce 1985 US 41 Hwy West Ishpeming MI 49849

Marquette Field Office 110 Ford Road Marquette Ml 49855 NEWBERRY FOREST MANAGEMENT UNIT Box 428 5666 M 123 S Newberry MI 49868 SAULT STE MARIE FOREST MANAGEMENT UNIT Box 798 200 I Ashmun Sault Ste Marie Ml 49783

Naubinway Field Office PO Box 287 US 2 Naubinway MI 49762 Detour Field Office PO Box 92 Ml34 Detour MI4972S

SHINGLETON FOREST MANAGEMENT UNIT M-28 West PO Box 67 Shingleton Ml49884 Seney Fteld Office Comer ofM-77 amp M-28 PO Box 72 Seney MI 49883 Wyman Nursery Rt No 2 Box 2004 Manistique MI498S4

ay o tce I est M- ox ay o Cadillac Office 8015 Mackinaw Trail Cadillac Ml 49601 Mio Office 191 S Mt Tom Rd Box 939 Mio MI 48647 Roscommon Office 8717 N Roscommon Rd Box 128 Roscommon Ml 48653

ATLANTA FOREST MANAGEMENT UNIT 13501 M-33 Atlanta Ml49709 Alpena Field Office 4343 M-32 West Alpena Ml49707 Onaway Field Office Hwy M-211 Box 32 Onaway Ml49765

GAYLORD FOREST MANAGEMENT UNIT 1732 West M-32 Box 667 Gaylord Ml49734 BeUaJre Fteld office 70 I E Cayuga St PO Box 278 Bellaire Ml 49615 Indian River Field Office PO Box 10 6984 Wilson Indian River Ml49749 Pellston Field Office 304 Stimson Box 126 Pellston Ml49769

PIGEON RIVER COUNTRY FOREST MANAGEMENT UNIT 9966 Twin Lakes Rd Vanderbilt Ml 49795 CADILLAC FOREST MANAGEMENT UNIT 8015 Mackinaw Trail Cadillac MI 49601

Baldwm Fteld Office Route 2 Box 2810 Baldwin Ml49304 Manton Field Office 521 N Michigan Manton Ml49663 Evart Field Office 951 W 7th Street Evart Ml 49631 Oceana Field Office 1757 E Hayes Rd M-20 Shelby Ml49455

TRAVERSE CITY FOREST MANAGEMENT UNIT 970 Emerson Traverse City Ml49686 Kalkaska Fteld Office 2089 N B~rch St Kalkaska MI 49646 Platte River Field Office 15210 US 31 Hwy Beulah Ml49617

GLADWIN FOREST MANAGEMENT UNIT 801 N Silverleaf PO Box 337 Gladwin M148624 Harrison Field Office 708 N First St Harrison Ml 48625 Standish Field Office 527 N M76 Box 447 Standish MI 48658 Sanford Field Office 118 W Saginaw MI 48657

GRAYLING FOREST MANAGEMENT UNIT 1955 Nl-75 BL Grayling MI 49738 Lmcoln F1eld Office 408 Mam St PO Box 122 Lincoln MI 48742 Mio Field Office 191 S Mt Tom Rd Box 939 Mio MI 48647

ROSCOMMON FOREST MANAGEMENT UNIT Box 218 Roscommon MI 48653 Houghton Liike F1eld Office 180 S Harrtson Rd Houghton Lake Ml48629 West Branch Field Office 2389 South M-76 West Branch MI 48661

Ken Alto

Kim Dufresne

Tim Tennis

lonst Manbullpmeut DWisioa 15 Resource Mana1ement Units

bullJfectble l2519bull

bull -Resource Jf~nt Unit OJke

1 -Raource Jf~nt Unit BOUIIdariea

1 -CountyBouruiiJrfea

-22shy

DOB Class ToEwoodBF (in) RM WA SM BW BC YB AB

DOBS50 0989 0936 0984 0971 0975 0988 0987 50ltD0BSl00 0970 0935 0973 0962 0973 0989 0995 100ltD0BS150 0947 0934 0959 0951 0970 0991 0996 150ltD0BS200 0924 0933 0946 0940 0967 0992 0995

008gt200 0902 0932 0932 0930 0964 0993 0993

TH Stemwood BF (ft) RM WA SM BW BC YB AB AE

THS05 0970 0947 0971 0971 0950 0990 0993 0980 05ltTHS45 0974 0932 olJn 0970 0959 0991 0995 0972

45ltTHS 100 0978 0925 0974 0970 0964 0991 0996 0966 100ltTHS200 0980 0924 0gt76 0970 0967 0991 0996 0963 200ltTHS300 0984 0928 0gt7S 0970 0970 0990 0996 0959 300ltTHS400 0986 0932 OltJSO 0971 0971 0990 0996 0957 400ltTHS500 0988 0937 () l)S~ 0971 0972 0989 0995 0955

THgt500 0992 0950 07 0974 0974 0987 0995 0952

The following constants for bark factor could be used for simplicity with moderately

approximate results especially for a large number of treessticks

Species Stem wood Top wood Stemwood and Topwood

RM 0980 0981 0980 WA 0932 0935 0932 SM 0976 0977 0976 BW 0970 0962 0970 BC 0965 0974 0966 YB 0991 0989 0990 AB 0995 0995 0995 AE 0964 0964

The above constants would be more accurate for those species that did not have significant

prediction equations andor small sample sizes B~ cry careful with using any of the results of this

study outside the range of the data set for each species Since the results for AE are based on six

stemwood measurements from one tree they arc of course very suspect

-23shy

Use of prediction equations

The prediction equations can be used to estimate BF at any DOB andor TH Since

BF=DIBDOB DIB can be estimated as DIB=BFbull DOB and DOB can be estimated as

DOB=DIBBF Past DOB and DOB growth can be estimated from past DIB growth as follows

Past DOB Growth=Past DIB GrowthBF

and

Past DOB=Present DOB -Past DOB Growth

where past DIB growth might be obtained with an increment borer

Specific uses of the prediction equations include (1) estimation of the solid wood and bark

volume of standing trees (2) estimation of bark volume or peeled volume from unpeeled volume

of felled tree sections (3) growth studies and (4) estimating tree form (eg Girard Form Class)

See Husch et al ( 1982) for a detailed discussion on bark factors

-24- LITERATURE CITED middot

Fowler G W 1991 An aspen bark factor equation for Michigan North J Appl For 8(1) 12-15

Fowler G W 1993 A jack pine bark factor equation for Michigan North J Appl For 10(2) 86-89

Fowler G W and L J Damschroder 1988 A red pine bark factor equation for Michigan North J Appl For 5(1) 28-30

Fowler G W and N G Hussain 1987a Bark factor equation for red pine Michigan DNR For Infor Leaflet 1-87 2 p

Fowler G W and N G Hussain 1987b Bark factor equation for aspen Michigan DNR For Infor Leaflet 2-87 2 p

Fowler G W and N G Hussain 1991 Bark factor equation for jack pine in Michigan Michigan DNR For Infor Leaflet 1-91 5 p

Fowler G W and N G Hussain 1997 Bark factor equations for paper birch in Michigan Michigan DNR For Infor Leaflet 1-97 12 p

Fowler G W N G Hussain D J Cohen and D Khatry-Chhetri 1997 Bark factor equations for oak in Michigan Michigan DNR For Infor Leaflet 2-97 15 p

Husch B C I Miller and T W Beers 1982 Forest Mensuration John Wiley and Sons Inc NY 402 p

~ FOREST MANAGEMENT DIVISION John M Robertsoa 51~ 373-1275 DMSION OFFICE PO Box 30452 Lansing MI 48909-7952

Brian Hutchins 517 275-5211 Forest Fire ExJ)Ciinent Station 1337 E Robinson Lake Rd Box 68 Roscommon MI 48653 Rich Mergener 906 341-2518 Wyman N~ Rt No 2 Box 2004 Manistique MI 49854 Rich Mergener 810 229-9152 State Forest Tree Improvement Center 4631 Bishop Lake Rd Howell MI 48843

Mike Palada 906~ 228-6561 Marquette Office 1990 Us-41 South MUQuette Ml 49855 Bill Maid ~906 249-1497 Marguctte Warehouse amp Repair ShoP 110 Foid Rd Marquette MI 49855

Edwin Moore s17 732-4481 Gaylord Warehouse amp Repair Shop 540 S Otsego Ave PO Box 596 Gaylord MI 49734

Marty Nelson

Debbie Begalle

Dennis Nezich

Bill Brondyke

Gilbert Joy Dean Reid

(_0____

Jeff Stampfly

Dayle Garlock

Bill ONeill

Joe Jarecki Dennis Vitton

Joe Fields

Courtney Borgondy

Susan Thiel

Don Torchia

(906) 353-6651 (906) 288-3321 (906) 224-2771 (906) 875-6622 (906) 563-9248 (906) 246-3245 (906) 786-2354 (906) 753-6317 (906) 346-920 1 (906) 485-1031 (906) 249-1497 (906) 293-3293 (906) 635-5281 (906) 477-6048 (906) 297-2581 (906) 452-6227 (906) 499-3346 (906) 341-2518

616 775-9727 517 826-3211 517 275-5151

(517) 785-425 1 (517) 354-7822 (517) 733-8775 (517) 731-5806 (616) 533-8341 (616) 238-9314 (616) 539-8564 (517) 983-4101 (616) 775-9727 (616) 745-4651 (616) 824-3591 (616) 734-5840 (616) 861-5636 (616) 922-5280 (616) 258-2711 (616) 325-4611 (517) 426-9205 (5 17) 539-6411 (5 I 7) 846-4104 (5 I 7) 687-7771 (517) 348-6371 (517) 736-8336 (517) 826-3211 (517) 275-4622 (517) 422-2897 (517) 345-0472

BARAGA FOREST MANAGEMENT UNIT 427 US-41 North Baraga MI 49908 Twm Lakes Fteld Office Rt I Box 234 Toivola MI 49965 Wakefield Field Office 1405 East US-2 Wakefield Ml49968

CRYSTAL FALLS FOREST MANAGEMENT UNIT 1420 US-2 West Crystal Falls Ml49920 Norway Fteld Office Os-2 West PO Box 126 Norway MI 49870 Felch Field Office PO Box 188 Felch MI 49831

ESCANABA FOREST MANAGEMENT UNIT 6833 Hwy 2 41 amp M-35 Gladstone MI 49837 Stephenson F1eld Office West 5420 River Road Stephenson MI 49887

GWINN FOREST MANAGEMENT UNIT 410 West M-35 Gwinn MI 49841 lshpemmg Field Ofttce 1985 US 41 Hwy West Ishpeming MI 49849

Marquette Field Office 110 Ford Road Marquette Ml 49855 NEWBERRY FOREST MANAGEMENT UNIT Box 428 5666 M 123 S Newberry MI 49868 SAULT STE MARIE FOREST MANAGEMENT UNIT Box 798 200 I Ashmun Sault Ste Marie Ml 49783

Naubinway Field Office PO Box 287 US 2 Naubinway MI 49762 Detour Field Office PO Box 92 Ml34 Detour MI4972S

SHINGLETON FOREST MANAGEMENT UNIT M-28 West PO Box 67 Shingleton Ml49884 Seney Fteld Office Comer ofM-77 amp M-28 PO Box 72 Seney MI 49883 Wyman Nursery Rt No 2 Box 2004 Manistique MI498S4

ay o tce I est M- ox ay o Cadillac Office 8015 Mackinaw Trail Cadillac Ml 49601 Mio Office 191 S Mt Tom Rd Box 939 Mio MI 48647 Roscommon Office 8717 N Roscommon Rd Box 128 Roscommon Ml 48653

ATLANTA FOREST MANAGEMENT UNIT 13501 M-33 Atlanta Ml49709 Alpena Field Office 4343 M-32 West Alpena Ml49707 Onaway Field Office Hwy M-211 Box 32 Onaway Ml49765

GAYLORD FOREST MANAGEMENT UNIT 1732 West M-32 Box 667 Gaylord Ml49734 BeUaJre Fteld office 70 I E Cayuga St PO Box 278 Bellaire Ml 49615 Indian River Field Office PO Box 10 6984 Wilson Indian River Ml49749 Pellston Field Office 304 Stimson Box 126 Pellston Ml49769

PIGEON RIVER COUNTRY FOREST MANAGEMENT UNIT 9966 Twin Lakes Rd Vanderbilt Ml 49795 CADILLAC FOREST MANAGEMENT UNIT 8015 Mackinaw Trail Cadillac MI 49601

Baldwm Fteld Office Route 2 Box 2810 Baldwin Ml49304 Manton Field Office 521 N Michigan Manton Ml49663 Evart Field Office 951 W 7th Street Evart Ml 49631 Oceana Field Office 1757 E Hayes Rd M-20 Shelby Ml49455

TRAVERSE CITY FOREST MANAGEMENT UNIT 970 Emerson Traverse City Ml49686 Kalkaska Fteld Office 2089 N B~rch St Kalkaska MI 49646 Platte River Field Office 15210 US 31 Hwy Beulah Ml49617

GLADWIN FOREST MANAGEMENT UNIT 801 N Silverleaf PO Box 337 Gladwin M148624 Harrison Field Office 708 N First St Harrison Ml 48625 Standish Field Office 527 N M76 Box 447 Standish MI 48658 Sanford Field Office 118 W Saginaw MI 48657

GRAYLING FOREST MANAGEMENT UNIT 1955 Nl-75 BL Grayling MI 49738 Lmcoln F1eld Office 408 Mam St PO Box 122 Lincoln MI 48742 Mio Field Office 191 S Mt Tom Rd Box 939 Mio MI 48647

ROSCOMMON FOREST MANAGEMENT UNIT Box 218 Roscommon MI 48653 Houghton Liike F1eld Office 180 S Harrtson Rd Houghton Lake Ml48629 West Branch Field Office 2389 South M-76 West Branch MI 48661

Ken Alto

Kim Dufresne

Tim Tennis

lonst Manbullpmeut DWisioa 15 Resource Mana1ement Units

bullJfectble l2519bull

bull -Resource Jf~nt Unit OJke

1 -Raource Jf~nt Unit BOUIIdariea

1 -CountyBouruiiJrfea

-23shy

Use of prediction equations

The prediction equations can be used to estimate BF at any DOB andor TH Since

BF=DIBDOB DIB can be estimated as DIB=BFbull DOB and DOB can be estimated as

DOB=DIBBF Past DOB and DOB growth can be estimated from past DIB growth as follows

Past DOB Growth=Past DIB GrowthBF

and

Past DOB=Present DOB -Past DOB Growth

where past DIB growth might be obtained with an increment borer

Specific uses of the prediction equations include (1) estimation of the solid wood and bark

volume of standing trees (2) estimation of bark volume or peeled volume from unpeeled volume

of felled tree sections (3) growth studies and (4) estimating tree form (eg Girard Form Class)

See Husch et al ( 1982) for a detailed discussion on bark factors

-24- LITERATURE CITED middot

Fowler G W 1991 An aspen bark factor equation for Michigan North J Appl For 8(1) 12-15

Fowler G W 1993 A jack pine bark factor equation for Michigan North J Appl For 10(2) 86-89

Fowler G W and L J Damschroder 1988 A red pine bark factor equation for Michigan North J Appl For 5(1) 28-30

Fowler G W and N G Hussain 1987a Bark factor equation for red pine Michigan DNR For Infor Leaflet 1-87 2 p

Fowler G W and N G Hussain 1987b Bark factor equation for aspen Michigan DNR For Infor Leaflet 2-87 2 p

Fowler G W and N G Hussain 1991 Bark factor equation for jack pine in Michigan Michigan DNR For Infor Leaflet 1-91 5 p

Fowler G W and N G Hussain 1997 Bark factor equations for paper birch in Michigan Michigan DNR For Infor Leaflet 1-97 12 p

Fowler G W N G Hussain D J Cohen and D Khatry-Chhetri 1997 Bark factor equations for oak in Michigan Michigan DNR For Infor Leaflet 2-97 15 p

Husch B C I Miller and T W Beers 1982 Forest Mensuration John Wiley and Sons Inc NY 402 p

~ FOREST MANAGEMENT DIVISION John M Robertsoa 51~ 373-1275 DMSION OFFICE PO Box 30452 Lansing MI 48909-7952

Brian Hutchins 517 275-5211 Forest Fire ExJ)Ciinent Station 1337 E Robinson Lake Rd Box 68 Roscommon MI 48653 Rich Mergener 906 341-2518 Wyman N~ Rt No 2 Box 2004 Manistique MI 49854 Rich Mergener 810 229-9152 State Forest Tree Improvement Center 4631 Bishop Lake Rd Howell MI 48843

Mike Palada 906~ 228-6561 Marquette Office 1990 Us-41 South MUQuette Ml 49855 Bill Maid ~906 249-1497 Marguctte Warehouse amp Repair ShoP 110 Foid Rd Marquette MI 49855

Edwin Moore s17 732-4481 Gaylord Warehouse amp Repair Shop 540 S Otsego Ave PO Box 596 Gaylord MI 49734

Marty Nelson

Debbie Begalle

Dennis Nezich

Bill Brondyke

Gilbert Joy Dean Reid

(_0____

Jeff Stampfly

Dayle Garlock

Bill ONeill

Joe Jarecki Dennis Vitton

Joe Fields

Courtney Borgondy

Susan Thiel

Don Torchia

(906) 353-6651 (906) 288-3321 (906) 224-2771 (906) 875-6622 (906) 563-9248 (906) 246-3245 (906) 786-2354 (906) 753-6317 (906) 346-920 1 (906) 485-1031 (906) 249-1497 (906) 293-3293 (906) 635-5281 (906) 477-6048 (906) 297-2581 (906) 452-6227 (906) 499-3346 (906) 341-2518

616 775-9727 517 826-3211 517 275-5151

(517) 785-425 1 (517) 354-7822 (517) 733-8775 (517) 731-5806 (616) 533-8341 (616) 238-9314 (616) 539-8564 (517) 983-4101 (616) 775-9727 (616) 745-4651 (616) 824-3591 (616) 734-5840 (616) 861-5636 (616) 922-5280 (616) 258-2711 (616) 325-4611 (517) 426-9205 (5 17) 539-6411 (5 I 7) 846-4104 (5 I 7) 687-7771 (517) 348-6371 (517) 736-8336 (517) 826-3211 (517) 275-4622 (517) 422-2897 (517) 345-0472

BARAGA FOREST MANAGEMENT UNIT 427 US-41 North Baraga MI 49908 Twm Lakes Fteld Office Rt I Box 234 Toivola MI 49965 Wakefield Field Office 1405 East US-2 Wakefield Ml49968

CRYSTAL FALLS FOREST MANAGEMENT UNIT 1420 US-2 West Crystal Falls Ml49920 Norway Fteld Office Os-2 West PO Box 126 Norway MI 49870 Felch Field Office PO Box 188 Felch MI 49831

ESCANABA FOREST MANAGEMENT UNIT 6833 Hwy 2 41 amp M-35 Gladstone MI 49837 Stephenson F1eld Office West 5420 River Road Stephenson MI 49887

GWINN FOREST MANAGEMENT UNIT 410 West M-35 Gwinn MI 49841 lshpemmg Field Ofttce 1985 US 41 Hwy West Ishpeming MI 49849

Marquette Field Office 110 Ford Road Marquette Ml 49855 NEWBERRY FOREST MANAGEMENT UNIT Box 428 5666 M 123 S Newberry MI 49868 SAULT STE MARIE FOREST MANAGEMENT UNIT Box 798 200 I Ashmun Sault Ste Marie Ml 49783

Naubinway Field Office PO Box 287 US 2 Naubinway MI 49762 Detour Field Office PO Box 92 Ml34 Detour MI4972S

SHINGLETON FOREST MANAGEMENT UNIT M-28 West PO Box 67 Shingleton Ml49884 Seney Fteld Office Comer ofM-77 amp M-28 PO Box 72 Seney MI 49883 Wyman Nursery Rt No 2 Box 2004 Manistique MI498S4

ay o tce I est M- ox ay o Cadillac Office 8015 Mackinaw Trail Cadillac Ml 49601 Mio Office 191 S Mt Tom Rd Box 939 Mio MI 48647 Roscommon Office 8717 N Roscommon Rd Box 128 Roscommon Ml 48653

ATLANTA FOREST MANAGEMENT UNIT 13501 M-33 Atlanta Ml49709 Alpena Field Office 4343 M-32 West Alpena Ml49707 Onaway Field Office Hwy M-211 Box 32 Onaway Ml49765

GAYLORD FOREST MANAGEMENT UNIT 1732 West M-32 Box 667 Gaylord Ml49734 BeUaJre Fteld office 70 I E Cayuga St PO Box 278 Bellaire Ml 49615 Indian River Field Office PO Box 10 6984 Wilson Indian River Ml49749 Pellston Field Office 304 Stimson Box 126 Pellston Ml49769

PIGEON RIVER COUNTRY FOREST MANAGEMENT UNIT 9966 Twin Lakes Rd Vanderbilt Ml 49795 CADILLAC FOREST MANAGEMENT UNIT 8015 Mackinaw Trail Cadillac MI 49601

Baldwm Fteld Office Route 2 Box 2810 Baldwin Ml49304 Manton Field Office 521 N Michigan Manton Ml49663 Evart Field Office 951 W 7th Street Evart Ml 49631 Oceana Field Office 1757 E Hayes Rd M-20 Shelby Ml49455

TRAVERSE CITY FOREST MANAGEMENT UNIT 970 Emerson Traverse City Ml49686 Kalkaska Fteld Office 2089 N B~rch St Kalkaska MI 49646 Platte River Field Office 15210 US 31 Hwy Beulah Ml49617

GLADWIN FOREST MANAGEMENT UNIT 801 N Silverleaf PO Box 337 Gladwin M148624 Harrison Field Office 708 N First St Harrison Ml 48625 Standish Field Office 527 N M76 Box 447 Standish MI 48658 Sanford Field Office 118 W Saginaw MI 48657

GRAYLING FOREST MANAGEMENT UNIT 1955 Nl-75 BL Grayling MI 49738 Lmcoln F1eld Office 408 Mam St PO Box 122 Lincoln MI 48742 Mio Field Office 191 S Mt Tom Rd Box 939 Mio MI 48647

ROSCOMMON FOREST MANAGEMENT UNIT Box 218 Roscommon MI 48653 Houghton Liike F1eld Office 180 S Harrtson Rd Houghton Lake Ml48629 West Branch Field Office 2389 South M-76 West Branch MI 48661

Ken Alto

Kim Dufresne

Tim Tennis

lonst Manbullpmeut DWisioa 15 Resource Mana1ement Units

bullJfectble l2519bull

bull -Resource Jf~nt Unit OJke

1 -Raource Jf~nt Unit BOUIIdariea

1 -CountyBouruiiJrfea

-24- LITERATURE CITED middot

Fowler G W 1991 An aspen bark factor equation for Michigan North J Appl For 8(1) 12-15

Fowler G W 1993 A jack pine bark factor equation for Michigan North J Appl For 10(2) 86-89

Fowler G W and L J Damschroder 1988 A red pine bark factor equation for Michigan North J Appl For 5(1) 28-30

Fowler G W and N G Hussain 1987a Bark factor equation for red pine Michigan DNR For Infor Leaflet 1-87 2 p

Fowler G W and N G Hussain 1987b Bark factor equation for aspen Michigan DNR For Infor Leaflet 2-87 2 p

Fowler G W and N G Hussain 1991 Bark factor equation for jack pine in Michigan Michigan DNR For Infor Leaflet 1-91 5 p

Fowler G W and N G Hussain 1997 Bark factor equations for paper birch in Michigan Michigan DNR For Infor Leaflet 1-97 12 p

Fowler G W N G Hussain D J Cohen and D Khatry-Chhetri 1997 Bark factor equations for oak in Michigan Michigan DNR For Infor Leaflet 2-97 15 p

Husch B C I Miller and T W Beers 1982 Forest Mensuration John Wiley and Sons Inc NY 402 p

~ FOREST MANAGEMENT DIVISION John M Robertsoa 51~ 373-1275 DMSION OFFICE PO Box 30452 Lansing MI 48909-7952

Brian Hutchins 517 275-5211 Forest Fire ExJ)Ciinent Station 1337 E Robinson Lake Rd Box 68 Roscommon MI 48653 Rich Mergener 906 341-2518 Wyman N~ Rt No 2 Box 2004 Manistique MI 49854 Rich Mergener 810 229-9152 State Forest Tree Improvement Center 4631 Bishop Lake Rd Howell MI 48843

Mike Palada 906~ 228-6561 Marquette Office 1990 Us-41 South MUQuette Ml 49855 Bill Maid ~906 249-1497 Marguctte Warehouse amp Repair ShoP 110 Foid Rd Marquette MI 49855

Edwin Moore s17 732-4481 Gaylord Warehouse amp Repair Shop 540 S Otsego Ave PO Box 596 Gaylord MI 49734

Marty Nelson

Debbie Begalle

Dennis Nezich

Bill Brondyke

Gilbert Joy Dean Reid

(_0____

Jeff Stampfly

Dayle Garlock

Bill ONeill

Joe Jarecki Dennis Vitton

Joe Fields

Courtney Borgondy

Susan Thiel

Don Torchia

(906) 353-6651 (906) 288-3321 (906) 224-2771 (906) 875-6622 (906) 563-9248 (906) 246-3245 (906) 786-2354 (906) 753-6317 (906) 346-920 1 (906) 485-1031 (906) 249-1497 (906) 293-3293 (906) 635-5281 (906) 477-6048 (906) 297-2581 (906) 452-6227 (906) 499-3346 (906) 341-2518

616 775-9727 517 826-3211 517 275-5151

(517) 785-425 1 (517) 354-7822 (517) 733-8775 (517) 731-5806 (616) 533-8341 (616) 238-9314 (616) 539-8564 (517) 983-4101 (616) 775-9727 (616) 745-4651 (616) 824-3591 (616) 734-5840 (616) 861-5636 (616) 922-5280 (616) 258-2711 (616) 325-4611 (517) 426-9205 (5 17) 539-6411 (5 I 7) 846-4104 (5 I 7) 687-7771 (517) 348-6371 (517) 736-8336 (517) 826-3211 (517) 275-4622 (517) 422-2897 (517) 345-0472

BARAGA FOREST MANAGEMENT UNIT 427 US-41 North Baraga MI 49908 Twm Lakes Fteld Office Rt I Box 234 Toivola MI 49965 Wakefield Field Office 1405 East US-2 Wakefield Ml49968

CRYSTAL FALLS FOREST MANAGEMENT UNIT 1420 US-2 West Crystal Falls Ml49920 Norway Fteld Office Os-2 West PO Box 126 Norway MI 49870 Felch Field Office PO Box 188 Felch MI 49831

ESCANABA FOREST MANAGEMENT UNIT 6833 Hwy 2 41 amp M-35 Gladstone MI 49837 Stephenson F1eld Office West 5420 River Road Stephenson MI 49887

GWINN FOREST MANAGEMENT UNIT 410 West M-35 Gwinn MI 49841 lshpemmg Field Ofttce 1985 US 41 Hwy West Ishpeming MI 49849

Marquette Field Office 110 Ford Road Marquette Ml 49855 NEWBERRY FOREST MANAGEMENT UNIT Box 428 5666 M 123 S Newberry MI 49868 SAULT STE MARIE FOREST MANAGEMENT UNIT Box 798 200 I Ashmun Sault Ste Marie Ml 49783

Naubinway Field Office PO Box 287 US 2 Naubinway MI 49762 Detour Field Office PO Box 92 Ml34 Detour MI4972S

SHINGLETON FOREST MANAGEMENT UNIT M-28 West PO Box 67 Shingleton Ml49884 Seney Fteld Office Comer ofM-77 amp M-28 PO Box 72 Seney MI 49883 Wyman Nursery Rt No 2 Box 2004 Manistique MI498S4

ay o tce I est M- ox ay o Cadillac Office 8015 Mackinaw Trail Cadillac Ml 49601 Mio Office 191 S Mt Tom Rd Box 939 Mio MI 48647 Roscommon Office 8717 N Roscommon Rd Box 128 Roscommon Ml 48653

ATLANTA FOREST MANAGEMENT UNIT 13501 M-33 Atlanta Ml49709 Alpena Field Office 4343 M-32 West Alpena Ml49707 Onaway Field Office Hwy M-211 Box 32 Onaway Ml49765

GAYLORD FOREST MANAGEMENT UNIT 1732 West M-32 Box 667 Gaylord Ml49734 BeUaJre Fteld office 70 I E Cayuga St PO Box 278 Bellaire Ml 49615 Indian River Field Office PO Box 10 6984 Wilson Indian River Ml49749 Pellston Field Office 304 Stimson Box 126 Pellston Ml49769

PIGEON RIVER COUNTRY FOREST MANAGEMENT UNIT 9966 Twin Lakes Rd Vanderbilt Ml 49795 CADILLAC FOREST MANAGEMENT UNIT 8015 Mackinaw Trail Cadillac MI 49601

Baldwm Fteld Office Route 2 Box 2810 Baldwin Ml49304 Manton Field Office 521 N Michigan Manton Ml49663 Evart Field Office 951 W 7th Street Evart Ml 49631 Oceana Field Office 1757 E Hayes Rd M-20 Shelby Ml49455

TRAVERSE CITY FOREST MANAGEMENT UNIT 970 Emerson Traverse City Ml49686 Kalkaska Fteld Office 2089 N B~rch St Kalkaska MI 49646 Platte River Field Office 15210 US 31 Hwy Beulah Ml49617

GLADWIN FOREST MANAGEMENT UNIT 801 N Silverleaf PO Box 337 Gladwin M148624 Harrison Field Office 708 N First St Harrison Ml 48625 Standish Field Office 527 N M76 Box 447 Standish MI 48658 Sanford Field Office 118 W Saginaw MI 48657

GRAYLING FOREST MANAGEMENT UNIT 1955 Nl-75 BL Grayling MI 49738 Lmcoln F1eld Office 408 Mam St PO Box 122 Lincoln MI 48742 Mio Field Office 191 S Mt Tom Rd Box 939 Mio MI 48647

ROSCOMMON FOREST MANAGEMENT UNIT Box 218 Roscommon MI 48653 Houghton Liike F1eld Office 180 S Harrtson Rd Houghton Lake Ml48629 West Branch Field Office 2389 South M-76 West Branch MI 48661

Ken Alto

Kim Dufresne

Tim Tennis

lonst Manbullpmeut DWisioa 15 Resource Mana1ement Units

bullJfectble l2519bull

bull -Resource Jf~nt Unit OJke

1 -Raource Jf~nt Unit BOUIIdariea

1 -CountyBouruiiJrfea

~ FOREST MANAGEMENT DIVISION John M Robertsoa 51~ 373-1275 DMSION OFFICE PO Box 30452 Lansing MI 48909-7952

Brian Hutchins 517 275-5211 Forest Fire ExJ)Ciinent Station 1337 E Robinson Lake Rd Box 68 Roscommon MI 48653 Rich Mergener 906 341-2518 Wyman N~ Rt No 2 Box 2004 Manistique MI 49854 Rich Mergener 810 229-9152 State Forest Tree Improvement Center 4631 Bishop Lake Rd Howell MI 48843

Mike Palada 906~ 228-6561 Marquette Office 1990 Us-41 South MUQuette Ml 49855 Bill Maid ~906 249-1497 Marguctte Warehouse amp Repair ShoP 110 Foid Rd Marquette MI 49855

Edwin Moore s17 732-4481 Gaylord Warehouse amp Repair Shop 540 S Otsego Ave PO Box 596 Gaylord MI 49734

Marty Nelson

Debbie Begalle

Dennis Nezich

Bill Brondyke

Gilbert Joy Dean Reid

(_0____

Jeff Stampfly

Dayle Garlock

Bill ONeill

Joe Jarecki Dennis Vitton

Joe Fields

Courtney Borgondy

Susan Thiel

Don Torchia

(906) 353-6651 (906) 288-3321 (906) 224-2771 (906) 875-6622 (906) 563-9248 (906) 246-3245 (906) 786-2354 (906) 753-6317 (906) 346-920 1 (906) 485-1031 (906) 249-1497 (906) 293-3293 (906) 635-5281 (906) 477-6048 (906) 297-2581 (906) 452-6227 (906) 499-3346 (906) 341-2518

616 775-9727 517 826-3211 517 275-5151

(517) 785-425 1 (517) 354-7822 (517) 733-8775 (517) 731-5806 (616) 533-8341 (616) 238-9314 (616) 539-8564 (517) 983-4101 (616) 775-9727 (616) 745-4651 (616) 824-3591 (616) 734-5840 (616) 861-5636 (616) 922-5280 (616) 258-2711 (616) 325-4611 (517) 426-9205 (5 17) 539-6411 (5 I 7) 846-4104 (5 I 7) 687-7771 (517) 348-6371 (517) 736-8336 (517) 826-3211 (517) 275-4622 (517) 422-2897 (517) 345-0472

BARAGA FOREST MANAGEMENT UNIT 427 US-41 North Baraga MI 49908 Twm Lakes Fteld Office Rt I Box 234 Toivola MI 49965 Wakefield Field Office 1405 East US-2 Wakefield Ml49968

CRYSTAL FALLS FOREST MANAGEMENT UNIT 1420 US-2 West Crystal Falls Ml49920 Norway Fteld Office Os-2 West PO Box 126 Norway MI 49870 Felch Field Office PO Box 188 Felch MI 49831

ESCANABA FOREST MANAGEMENT UNIT 6833 Hwy 2 41 amp M-35 Gladstone MI 49837 Stephenson F1eld Office West 5420 River Road Stephenson MI 49887

GWINN FOREST MANAGEMENT UNIT 410 West M-35 Gwinn MI 49841 lshpemmg Field Ofttce 1985 US 41 Hwy West Ishpeming MI 49849

Marquette Field Office 110 Ford Road Marquette Ml 49855 NEWBERRY FOREST MANAGEMENT UNIT Box 428 5666 M 123 S Newberry MI 49868 SAULT STE MARIE FOREST MANAGEMENT UNIT Box 798 200 I Ashmun Sault Ste Marie Ml 49783

Naubinway Field Office PO Box 287 US 2 Naubinway MI 49762 Detour Field Office PO Box 92 Ml34 Detour MI4972S

SHINGLETON FOREST MANAGEMENT UNIT M-28 West PO Box 67 Shingleton Ml49884 Seney Fteld Office Comer ofM-77 amp M-28 PO Box 72 Seney MI 49883 Wyman Nursery Rt No 2 Box 2004 Manistique MI498S4

ay o tce I est M- ox ay o Cadillac Office 8015 Mackinaw Trail Cadillac Ml 49601 Mio Office 191 S Mt Tom Rd Box 939 Mio MI 48647 Roscommon Office 8717 N Roscommon Rd Box 128 Roscommon Ml 48653

ATLANTA FOREST MANAGEMENT UNIT 13501 M-33 Atlanta Ml49709 Alpena Field Office 4343 M-32 West Alpena Ml49707 Onaway Field Office Hwy M-211 Box 32 Onaway Ml49765

GAYLORD FOREST MANAGEMENT UNIT 1732 West M-32 Box 667 Gaylord Ml49734 BeUaJre Fteld office 70 I E Cayuga St PO Box 278 Bellaire Ml 49615 Indian River Field Office PO Box 10 6984 Wilson Indian River Ml49749 Pellston Field Office 304 Stimson Box 126 Pellston Ml49769

PIGEON RIVER COUNTRY FOREST MANAGEMENT UNIT 9966 Twin Lakes Rd Vanderbilt Ml 49795 CADILLAC FOREST MANAGEMENT UNIT 8015 Mackinaw Trail Cadillac MI 49601

Baldwm Fteld Office Route 2 Box 2810 Baldwin Ml49304 Manton Field Office 521 N Michigan Manton Ml49663 Evart Field Office 951 W 7th Street Evart Ml 49631 Oceana Field Office 1757 E Hayes Rd M-20 Shelby Ml49455

TRAVERSE CITY FOREST MANAGEMENT UNIT 970 Emerson Traverse City Ml49686 Kalkaska Fteld Office 2089 N B~rch St Kalkaska MI 49646 Platte River Field Office 15210 US 31 Hwy Beulah Ml49617

GLADWIN FOREST MANAGEMENT UNIT 801 N Silverleaf PO Box 337 Gladwin M148624 Harrison Field Office 708 N First St Harrison Ml 48625 Standish Field Office 527 N M76 Box 447 Standish MI 48658 Sanford Field Office 118 W Saginaw MI 48657

GRAYLING FOREST MANAGEMENT UNIT 1955 Nl-75 BL Grayling MI 49738 Lmcoln F1eld Office 408 Mam St PO Box 122 Lincoln MI 48742 Mio Field Office 191 S Mt Tom Rd Box 939 Mio MI 48647

ROSCOMMON FOREST MANAGEMENT UNIT Box 218 Roscommon MI 48653 Houghton Liike F1eld Office 180 S Harrtson Rd Houghton Lake Ml48629 West Branch Field Office 2389 South M-76 West Branch MI 48661

Ken Alto

Kim Dufresne

Tim Tennis

lonst Manbullpmeut DWisioa 15 Resource Mana1ement Units

bullJfectble l2519bull

bull -Resource Jf~nt Unit OJke

1 -Raource Jf~nt Unit BOUIIdariea

1 -CountyBouruiiJrfea

lonst Manbullpmeut DWisioa 15 Resource Mana1ement Units

bullJfectble l2519bull

bull -Resource Jf~nt Unit OJke

1 -Raource Jf~nt Unit BOUIIdariea

1 -CountyBouruiiJrfea