modeling branch characteristics in douglas-fir & western hemlock

Modeling Branch Characteristics In Douglas-fir

& Western Hemlock

Cast of Characters

• Dr. Gero Becker– Professor, Univ. of Freiburg, Germany, Visiting Scholar, SMC

• Dr. David Briggs– Professor UW CFR, Director, SMC

• Dr. Olav Hoibo– Associate Professor, Agric. Univ. Norway, Visiting Scholar, SMC

• Eric Turnblom– Assistant Professor, UW CFR, Silviculture Project Leader, SMC

Branches Respond Too!

Outline

I. Number & Diameter of BH Branches: SMC ProtocolA. Type I Douglas-fir: PCT Effect on Average BH Branches in a

Stand

B. Type I Douglas-fir: PCT Effect on BH Branches of Individual Trees

C. Type I Western Hemlock: PCT Effect, status

D. Type III: Effect of Initial Spacing, status

II. PNW/Germany Cross-Comparison of DF Branch Diameter

III. Vertical Branch Profiles: DF & WH• Live/dead transition

• Branch/Stem Growth Dynamic

I. Number & Diameter of BH Branches

• Douglas-fir branch protocol

• Type I and Type III Installations

• Taken on height trees on each plot (~42 trees)

• First whorl above BH – Diameter of largest branch in the whorl

– Total # branches in whorl >= 1/2 diameter of largest branch

– Total # branches in half-internode above & below the whorl that are >= 1/2 diameter of largest whorl branch

A. Effect of PCT on Douglas-fir: Stand Level Models

• Sample– 19 Type I installations

– 57 plots ISPA, ISPA/2, ISPA/4

– 2397 trees

• Site Index is Flewelling (2001)

A. Effect of PCT on Douglas-fir: Stand Level Modeling Method

a. Factorial Treatment Structure• 4 levels of Flewelling Site Index

• 3 levels of stand density (stems/acre)

• Covariates: Crown length, crown ratio Mean height, HT_40, mean height above BH Total age, BH age QMD, relative density

b. Plots with crown base < BH, > BH, and combined• No differences found with crown base below vs above BH

• Elapsed time since crown receded above BH is too short

1. Effect of PCT on Total BH Branch Count of Type I Douglas-fir Stands: Results

• as stems per acre increases total BH branch count decreases

• more shade on BH branches in denser stands

• 250 & 550 spa classes are not significantly different

• 125 spa class is significantly different 0

1

2

3

4

5

6

7

8

9

10

125 250 550

Stems per Acre Class#

BH B

ranc

hes

1. Effect of PCT on Total BH Branch Count of Type I Douglas-fir Stands: Results

• Site classes I, II, & III are not significantly different

• Site IV is significantly lower

• fewer resources to produce and maintain branches

• Also, total BH branch count– Decreases as average crown

length of stand increases (more shade on BH branches ?)

– Decreases as total stand age increases (self pruning?)

0

1

2

3

4

5

6

7

8

9

10

I III II IV

Site Index (Flewelling 2001)#

BH B

ranc

hes

2. Effect of PCT on BH Nodal Branch Count of Type I Douglas-fir Stands: Results

0

1

2

3

4

5

6

7

8

9

10

I III II IV

Site Index (Flewelling, 2001)# B

H No

dal B

ranc

hes

• Site classes II & III are not significantly different

• Site classes II & IV are not significantly different

• Highest site class has about 1 more nodal branch (more resources for nodal branch production & survival?)

3. Effect of PCT on BH Internodal Branch Count of Type I Douglas-fir Stands: Results

• Site classes II, & III are not significantly different

• Site III, I, & IV are not significantly different

• Site IV low due to fewer resources for production & survival of internodal branches

• Site I low due to competition and shading by more numerous nodal branches

• Also, BH internodal branch count– Decreases as average crown length of

stand increases (more shade on BH internodal branches ?)

– Decreases as total stand age increases (self pruning of internodals?)

0

1

2

3

4

5

6

7

8

9

10

II III I IV

Site Index (Flewelling, 2001)#

Inte

rnod

al B

H Br

anch

es

4. Effect of PCT on BH Branch Count of Type I Douglas-fir Stands: Regression Models

C T 1.0

b0 b1(CL) b2(SPA )b3 (SPA 2 )b4(AGE)b5 (SI30 )b6 (SI302 )

Total = f (ave crown length, stems/acre, total age, site index)

Internodal = f (ave crown length, total age, site index)

)()()()()( 2305304

23210 SIbSIbAGEbAGEbCLbbCI

Nodal = Total - Internodal

5. Effect of PCT on Largest BH Branch Diameter of Type I Douglas-fir Stands: Regression Models

• All significantly different

• Lower stand density has larger BH branches (more space, less shade on BH, longer lived faster growing branches)

• Also, largest BH branch diameter– Increases as QMD increases

(bigger tree allometry?)

– Decreases as total stand age increases (point of maximum branch diameter becomes embedded inside the stem

0

0.2

0.4

0.6

0.8

1

1.2

1.4

125 250 550

Spems per AcreLa

rges

t BH

Bran

ch D

iam

eter

6. Effect of PCT on Largest BH Branch Diameter of Type I Douglas-fir Stands: Regression Model

D B 1.0

b0 b1(SPA )b2 (SPA 2 ) b3(QMD) b4(AGE) b5(AGE2 )

Average for Stand = f(QMD, total age, stems per acre)

B. Effect of PCT on Douglas-fir: Individual Tree Modeling Method

a. Allometry with orthogonal quadratic polynomials for each of the 57 plots• Largest BH branch diameter vs other tree size measures: DBH best • Branch counts vs other tree size measures: DBH best

b. ANCOVA of 57 sets of coefficients• 4 levels of Flewelling Site Index• 3 levels of stand density (stems/acre)• Covariates:

Crown length, crown ratio Mean height, HT_40, mean height above BH Total age, BH age QMD, relative density

c. Plots with crown base < BH, > BH, and combined• No differences found with crown base below vs above BH• Elapsed time since crown receded above BH is too short

d. Regression

1. Effect of PCT on BH Branch Counts of Douglas-fir Trees: Regression Model

Total = f(DBH, stems per acre, total age, site index, crown length)

Internodal: use stand level model = f(total age, site index, crown length)

)()()()()( 2305304

23210 SIbSIbAGEbAGEbCLbbCI

Nodal

= Total - Internodal

)(

)()()()()()(

0.1

0

23063054

23210

DBHb

SIzSIzAGEzSPAzSPAzCLzzCTi

2. Effect of PCT on Largest BH Branch Diameter of Douglas-fir Trees: Regression Model

DBi 1.0

z0 z1(SPA ) z2 (SPA 2 ) z4 (AGE) z5(AGE2 )

DBH

b0 b1(SPA ) b2 (QMD) b3(QMD2 ) b4 (AGE )b5 (CL)

Individual Tree Largest BH Branch Diameter = f(DBH; stems per acre, total age, QMD, crown length)

3. Conclusion: PCT of Douglas fir (Type I)

• Stand level variables (red) greatly improved individual tree model predictions!

• O. Hoibo has also found this in his crown profile research

• Status:– Article in review with Forest Science

• Future– Can we relate the BH results to the rest of the tree

– Can we develop a QC tool & prediction system that can be related to log grades/sorts

C. Effect of PCT & Planting Density: W. Hemlock Protocol & Plans

• Type I and Type III Installations

• Taken on height trees on each plot (~42 trees)

• 3 foot zone centered on BH – Diameter of largest branch

– Total # branches >= 1/2 diameter of largest branch

• Started in 00/01 Field Season

• Preliminary analysis after 01/02 season

3 ft

D. Effect of Planting Density: Douglas-fir

• Type III

• Data for 98/99, 99/00, 00/01, 01/02 seasons

• Preliminary work with 98/99 data– 8 installations; 6 plots each

– small trees on wider spacings tend to have larger branches than same age, larger trees on denser spacings

– another aspect of crossover effect?

• Will begin analysis this winter/spring

II. PNW/Germany Cross-Comparison of DF Branch Diameter

Objectives:

Determine differences between branch diameter profile characteristics between two geographically disparate (Germany/PNW U.S.) Douglas-fir data sets

Gain insights into “best” modeling approach for future branch diameter modeling

Available Data

• German data set– 4 plots: density ranges 150 -300 SPA; sites range 100 -140 ft@50

yr;

total ages range 32 -41 years

– 42 trees: DBH ranges 9.4 -16.1 in.; total heights range 62 -89 ft;

HCB ranges 25.6 -47.6 ft.

• SMC ‘Crown Study’ data set – 66 plots: density ranges 80 -600 SPA; sites range 80 -140 ft@50 yr;

total ages range 9 -36 years

– 562 trees: DBH ranges 1.0 -18.3 in.; total heights range 7.4 -104.7 ft;

HCB ranges 0 -67.1 ft.

Testing Equations

• Wobst/Becker Equation:

• Maguire, et al. (1999) Equation:

BD (3.0 aRDFT)d e( b.RDFT )

a f (DBH, Ht, HOD, DOH,HCB,CR,D2 H)

b f (a), d is a parameter

BD (1CW 2 )WC

W 1 Z0.5

C 3Z 4

Z h / CL, h is height above crown base

Branch Diameter Profile Comparison

• Upper curve (red) is Wobst/Becker model

• Lower curve (maeve) is Maguire et al.

• Upper is for live/dead branches, lower is for live only

0.1 0.2 0.3 0.4RELDIS

20

30

40

BDWB

BDM

Residual Patterns

Wobst/Becker Maguire, et al.

0.1 0.2 0.3 0.4 0.5

RELDIS

-30

-20

-10

0

10B

D

W

B

_

R

0.1 0.2 0.3 0.4 0.5

RELDIS

-30

-20

-10

0

10

B

D

M

_

R

Residuals Comparison

On average, Maguire et al. predicts larger branches, but ...

-30 -20 -10 0 10

BDM_R

BDM_R

-30 -20 -10 0 10

BDWB_R

BDWB_

-30 -20 -10 0 10

BDM_R

B

D

W

B

_

R

Future Plans

• Use both models to predict branch diameters on trees in the SMC data set

• Determine which modeling approach / equation form is “best”

• Report results at IUFRO conference 2002

III. Vertical Branch/Knot Profiles: DF• Douglas-fir Sample

– SMC Type I

– High Site, Medium Site

– ISPA , ISPA/2

– Similar age & ISPA

– 1 tree from each septile of DBH distribution (28 total trees)

– 7 trees x 4 plots = 28 trees

– Whorl 3, 6, 9, … 21 from top = 7 whorls/tree

A. Transition from Live to Dead Knot: DF

• Branch Measurements– Azimuth

– Horizontal distance from cambium to

• Pith

• Live/dead transition

– Knot diameter at• Live/dead transition

• Cambium

• 1 branch diameter distance from stem surface (outside bark)

– All branches

• Data collected & analysis underway

B. Relationship Between Stem & Branch Diameter Growth

• Measure– Smallest, median & largest of

the 7 tree sample from each plot

– Whorl # 6, 12, 18 from top

– Annual ring widths of stem cross-section

– Annual ring widths of smallest, median, & largest branch in each

• Data collected & analysis underway

C. Vertical Branch/Knot Profiles: W. Hemlock

• Sample– Medium Site Type I Hemlock

– ISPA & ISPA/2

– 1 tree/septile of DBH distribution = 14 total trees

– 3 foot sections @ mid-live crown, live crown base, midway from crown base to ground, and at BH

• Transition from sound (live) to unsound (dead) knot– Sound knot length from pith

– Knot diameter (max) at transition – Largest 5 and next to smallest branch = 6 total

• Ring growth of stem & branch: all stem sections (4/tree)– Ring widths of stem

– Ring widths of largest, median, & smallest branch

• Samples collected: Anyone want a job?

The End