efficiency of alternative forest inventory methods in ... · efficiency of alternative forest...

ORIGINAL PAPER

Efficiency of alternative forest inventory methods in partiallyharvested stands

Ben Rice • Aaron R. Weiskittel • Robert G. Wagner

Received: 12 September 2012 / Revised: 26 July 2013 / Accepted: 22 November 2013 / Published online: 19 January 2014

� Springer-Verlag Berlin Heidelberg 2014

Abstract Forest inventory is vital to all aspects of forest

management and inventory methods can vary greatly in

their accuracy, precision, efficiency and cost. In Maine,

much of the forestland base has been managed using partial

harvesting methods over the past two decades. These par-

tial harvesting methods generally produce highly hetero-

geneous stand structures and composition. Consequently, it

is currently unclear which inventory methods are best

given the distinct spatial and structural heterogeneity that is

created. We compared efficiency and stand-level inventory

estimates using horizontal point, fixed area and horizontal

line sampling measurement methods in 16 partially har-

vested stands across northern and central Maine. Some

stand-level variables were sensitive to measurement

method (e.g., volume, quadratic mean diameter and small

stem density and basal area), while others were less sen-

sitive (e.g., overall basal area and stem density). Efficiency,

defined as a combination of precision of volume estimates

and measurement time, varied among measurement meth-

ods at lower stand basal area values but was similar at

higher basal area, with the exception of the fixed area

method. Overall, horizontal line sampling proved to be a

viable method in post-partial harvest stand conditions. Our

results illustrate the trade-offs between precision and time

costs involved in several measurement methods under a

range of heterogeneous stand conditions.

Keywords Mensuration � Variable radius sampling �Horizontal line sampling � Partial harvesting �Big BAF

Introduction

Forest planning and management to achieve a range of

economic, ecological and social outcomes are dependent

upon high-quality forest inventory data. Forest mensuration

field techniques are the foundation of any attempt to

develop, implement and assess forest management prac-

tices, but these methods can vary substantially in the

accuracy, precision and costs of producing estimates of

forest inventory parameters. The three primary components

of forest inventory are as follows: (1) sampling method, (2)

sampling intensity and (3) measurement method. The

approach to these components should ideally be deter-

mined by available resources (i.e., time and money) and the

desired precision and accuracy. In practice, institutional

and individual knowledge, skills, history and preferences

play a large role in developing and executing forest

inventories. Even in the absence of these biases, deter-

mining the appropriate combination of sampling method,

sampling intensity and measurement method may be

challenging, particularly in novel stand types.

Measurement methods available for forest inventories

generally fall into two broad categories, area-based and

tree-based methods. Area-based methods involve delin-

eating some area or areas within a stand in which all or a

subset of trees are measured. There are a number of vari-

ations to this approach that involves fixed area plots of

differing shapes and sizes. Fixed area plots remain widely

used, particularly for research and continuous forest

inventory (CFI) purposes, such as in the sampling scheme

Communicated by G. Kandler.

B. Rice (&) � A. R. Weiskittel � R. G. Wagner

School of Forest Resources, University of Maine,

5755 Nutting Hall, Orono, ME, USA

e-mail: ben.rice@maine.edu

123

Eur J Forest Res (2014) 133:261–272

DOI 10.1007/s10342-013-0756-4

currently being used by the USDA Forest Service’s Forest

Inventory and Analysis (FIA) Program (USDA Forest

Service 2007). Other types of fixed area methods have been

largely abandoned in favor of tree-based methods. For

example, strip cruising was once a widely used method in

the United States but has largely fallen out of favor (Iles

2003, p. 334).

Tree-based methods include numerous variants of

probability proportional to size (pps) methods and related

approaches involving probability proportional to prediction

(3-P). The pps methods are also known as plotless, variable

radius, angle-count sampling or Bitterlich methods (Bell

and Dilworth 2002, p. 181; Bitterlich 1984). Variable

radius sampling includes horizontal and vertical methods

(Grosenbaugh 1958). While vertical variable radius tech-

niques (i.e., probability proportional to height) have

received much attention in the literature, their practical

application remains limited (Ducey and Kershaw 2011).

The use of horizontal variable radius plot sampling, also

known as horizontal point sampling, is widely used in

operational forest inventory in North America (Iles 2003,

p. 495). In this approach, plots are based on the area pro-

jected around a tree rather than the area around a sampling

point. The projected area around an individual tree

increases with diameter and is inversely related to the

selection angle used. If a tree’s projected area (also known

as the inclusion zone) overlaps with the sampling point, the

tree is considered ‘‘in.’’

Horizontal line sampling is a similar method but as the

name suggests lines are employed as sampling units rather

than points. Typically, trees are sighted perpendicular to

the sampling line. Horizontal line sampling, while less

widely used than horizontal point sampling, is a potential

alternative in measuring heterogeneous stands. Horizontal

line sampling covers more stand area than a comparable

horizontal point sampling method, increasing the proba-

bility that all substand patterns are sampled adequately

(Barrett and Allen 1966). There are two primary differ-

ences between horizontal point and line sampling. The

shape of inclusion zones is rectangular in horizontal line

sampling compared to the circular inclusion zones in hor-

izontal point sampling. Also simple tree counts in the more

commonly used horizontal point sampling yield basal area

per unit area, whereas counts in horizontal line sampling

yield diameter per unit area.

Choice of gauge angle, or more commonly expressed as

basal area factor (BAF), in variable radius sampling, which

controls the number of trees sampled per plot (i.e., sam-

pling intensity), is analogous to the choice of plot size in

fixed area sampling. The BAF selection has been shown to

influence stand-level estimation of basal area and stem

density (Brooks and Wiant 2004). The precision of stand-

level attribute estimates must be balanced with the cost.

For example, stands containing larger, more widely scat-

tered trees are generally more efficiently inventoried using

larger plots (Mesavage and Grosenbaugh 1956), which

calls for use of a smaller BAF in the case of variable radius

sampling. Problems arise though when the number of

sample trees is so low as to greatly increase variability and

conversely high tree counts can lead to errors due to missed

trees (Beers and Miller 1964).

Variable radius methods are frequently combined with

double sampling. The increased efficiency of double sam-

pling is well known (Dahl et al. 2008), although not prac-

ticed universally. Typically in double sampling, the majority

of ‘‘in’’ trees (often referred to as ‘‘BA trees’’) are either

counted to simply estimate the basal area or diameters may

also be measured to estimate the stand diameter distribution.

A subset of these ‘‘in’’ trees (often referred to as ‘‘VBAR

trees’’) is measured more intensively to estimate the rela-

tionship between basal area and volume, often referred to as

the volume–basal area ratio (VBAR). Generally, this

approach involves measuring heights of every so many trees

or every so many plots. Volume estimates are generally only

needed for 25–35 % of trees (Shiver and Borders 1996,

p. 216). An increasingly popular variation on variable radius

methods with double sampling is the big BAF method

(Marshall et al. 2004). This method allows a large number of

trees to be used in determining the basal area per unit area

with a smaller BAF (maintaining low variance) while

reducing the number of trees to be measured by using a

larger BAF (i.e., big BAF) and decreasing the travel distance

between the sampling point and measurement trees (Des-

marais 2002). This method also avoids potential bias in tree

selection and the frequent oversampling involved in

choosing every so many trees or plots. BAF values to select

VBAR trees using the big BAF method have been recom-

mended between 5.11 and 11.15 BAF in a study of Appa-

lachian hardwood stands (Brooks 2006).

Given the wide variety of measurement methods avail-

able, it is unfortunate that the choice of methods appears to

frequently be driven by local or agency preferences

(Gambill et al. 1985). Quantitative comparison of inven-

tory methods provides a sound basis for choosing a method

based on stand conditions and desired accuracy, precision

and efficiency. Following the introduction of variable

radius sampling in North America, there were numerous

publications comparing various aspects of variable radius

and fixed area methods, but the nature of these studies and

the computing power available at the time led primarily to

case studies that are limited in their inference to a wider

range of stand conditions. Many contemporary studies of

forest inventory methods are conducted using computer

simulations (e.g., Becker and Nichols 2011; Marquardt

et al. 2010). While this approach yields important results

that contribute to the field of mensuration and operational

262 Eur J Forest Res (2014) 133:261–272

123

forest inventory, there is a need to conduct real-world

stand-level studies that incorporate the variability and

challenges inherent in fieldwork. On the other hand, such

research can be labor intensive, and the studies that have

focused on mensuration at the stand level usually have a

low number of sample stands (e.g., Avery and Newton

1965; Brooks and McGill 2004; Lindemuth 2007). Addi-

tionally, the breadth of sampling methods tested varies

greatly, and some methods are seldom addressed in the

literature. For example, efficiency studies of horizontal line

sampling are limited despite the fact that this method has

been available since the 1950s (Strand 1958).

Forest inventory methods in heterogeneous stands

present a growing issue in the state of Maine, USA. Over

the past 20 years, harvesting techniques in the state have

undergone a significant shift, from a heavy reliance on

clear-cut harvesting to a predominance of partial harvest-

ing. Currently, partial harvesting is the dominant harvest

method, representing approximately 97 % of the area

harvested in Maine’s forest between 2006 and 2010 (Maine

Forest Service 2011). Using this approach, logging opera-

tions create non-permanent trails and timber may or may

not be partially removed between these trails. Thus, a stand

with at least two or three distinct conditions is created,

which challenges the identification of a stand as an area

containing trees with like characteristics, in terms of age,

size and species (Bell 2000). Such heterogeneous stands

continue to be created, and it is therefore important that

land managers be able to assess the volume of timber in

such stands for the purposes of timber sales, wood supply

projections and land transactions (Borders et al. 2008). In

addition, there has been no previous effort to assess the

precision or efficiency of inventory methods in Maine’s

partially harvested stands. In order to assess the current

condition of Maine’s forestlands and plan for the future, it

is vital that we understand how inventory methods perform

in partially harvested stands. Therefore, our objective was

to compare horizontal point, fixed area and horizontal line

measurement methods in partially harvested stands across

northern and central Maine. The specific objectives were to

(1) quantify the efficiency, comprised of the precision and

measurement time, of these measurement methods in par-

tially harvested stands, and (2) compare stand-level

inventory estimates generated by these measurement

methods.

Methods

Study area

The study area was located in the state of Maine, which

lies within the Acadian forest, a transitional mixed conifer

and hardwood forest type located between northern

hardwood forests to the south and west and boreal

coniferous forests to the north (Loo and Ives 2003). The

fieldwork for this study was conducted in partially har-

vested stands across 1.65 million ha in northern and

central Maine (Fig. 1). Common softwood species within

the study area include: balsam fir (Abies balsamea (L.) P.

Mill.); red spruce (Picea rubens Sarg.); eastern white pine

(Pinus strobus L.); northern white-cedar (Thuja occiden-

talis L.) and eastern hemlock (Tsuga canadensis (L.)

Carr.). Common hardwood species include red maple

(Acer rubrum L.); sugar maple (Acer saccharum Marsh.);

yellow birch (Betula alleghaniensis Britt.); paper birch

(Betula papyrifera Marsh.); American beech (Fagus

grandifolia Ehrh.); bigtooth aspen (Populus grandidentata

Michx.) and trembling aspen (Populus tremuloides

Michx.). The study area lies within Maine’s northern and

central climatic zones. Precipitation in both zones is well

distributed throughout the year, with an annual average

between 95.5 and 110.0 cm (Briggs and Lemin 1992).

Stands were chosen with the assistance of the Maine

Image Analysis Laboratory (MIAL). Previous work by the

MIAL has described landscape-level harvest patterns

across northern Maine using remotely sensed data (e.g., Jin

and Sader 2006; Simons 2009). For our study, the MIAL

generated a list of 250 stands that according to their ana-

lysis had received one partial harvest with \70 % canopy

removal between 1988 and 2007. We randomly selected

stands from among these and conducted site visits to verify

stand conditions. We rejected stands that were extremely

mesic (i.e., spruce bogs), had active logging operations

during the site visit, and/or appeared to contain

\6.89 m2 ha-1 (\30 ft2 acre-1) of basal area. We selected

16 stands for inclusion across the study area, which ranged

in size from 9 to 310 ha. Fifteen of the stands had been

partially harvested between 1988 and 2007, while the

remaining stand was apparently harvested earlier than this.

We chose to retain this stand to provide a more complete

range of possible stand conditions. Overall, stand condi-

tions were quite variable in terms of stand composition and

structure (Table 1).

Data collection

Sampling was conducted in the summer of 2010 and 2011.

Inventory plots were placed on a systematic grid in each

stand. The number of plots in each stand ranged from 12 to

39, varying based on stand size and shape. To minimize

potential bias related to the order of methods tested, the

order of measurement methods was randomly varied from

plot to plot. Horizontal point sampling methods were

conducted at each plot, horizontal line sampling at every

third and fixed area at every fifth plot (Table 2).

Eur J Forest Res (2014) 133:261–272 263

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Circular plots of 0.04 ha were used for the fixed area

method, a plot size commonly used in forest inventory work

in the United States (Avery and Newton 1965; Brooks and

McGill 2004). Fixed area plots of 0.04 ha have been shown

to provide accurate estimates with little gains in accuracy at

larger sizes (Becker and Nichols 2011). The walkthrough

method was used for trees located near the stand boundary

to reduce edge bias for all measurement methods (Ducey

et al. 2004). Trees were selected for all variable radius

methods using an American scale Spiegel Relaskop (Rela-

skop-Technik Vertriebsges.m.b.H, Salzburg, Austria). For

horizontal point sampling methods, three different BAFs

(BAFs in customary units are noted as BAFe) were used: 2.3

BAF (10 BAFe), 4.6 BAF (20 BAFe) and 18.4 BAF (80

BAFe). Horizontal line sampling was conducted following

the basic methods of Beers and Miller (1976). At each

horizontal line sampling point, a 21.34 m line was estab-

lished. The first-line segment of 10.67 m was established

along a randomly selected azimuth, and a second 10.67 m

segment was oriented to an azimuth 120� less than the

randomly selected azimuth. Trees were viewed at right

angles perpendicular to the line, selecting ‘‘in’’ trees as in

variable radius point sampling (Beers and Miller 1976).

When the stand boundary was encountered, the bounce-

back method was employed (Gregoire and Valentine 2008,

p. 299; Iles 2003, p. 419). Using this method, if the stand

boundary is encountered, the line stops at the boundary and

is retraced until reaching the full line segment length.

For each ‘‘in’’ tree[1.37 m height and[5 cm diameter

at breast height (DBH; breast height at 1.37 m), we

recorded species and measured DBH to the nearest

0.25 cm. For VBAR trees, height to the nearest 0.3 m and

Fig. 1 Map of study area in

northern and central Maine,

USA. Study area denoted in

dotted portion

264 Eur J Forest Res (2014) 133:261–272

123

height to crown base to the nearest 0.3 m were measured

using a Haglof ultrasonic hypsometer (Haglof Inc., Madi-

son, MS). Height to crown base was determined using the

‘‘uncompacted crown method’’ wherein the height to the

lowest live foliage is measured (USDA Forest Service

2007). Distance measurements for apparently borderline

trees in all methods were made using a Haglof hypsometer

and was double-checked with a tape using appropriate

slope corrections as needed.

To assess the efficiency of each method, the plot mea-

surement time for each measurement method was recorded.

Time was recorded for the selection and measurement of

VBAR and BA trees (Table 1). The travel time between

sampling points within a stand, inter-unit time (Alton et al.

1958) was not recorded. We felt that the variation among

workers and among stand conditions would lead to high

variability that could mask the differences among sampling

methods.

Overall, a total of 437 plots in 16 stands were measured

and used in our analysis. From these, we calculated stand-

level inventory estimates for each method, including basal

area, VBAR, density (trees per hectare) total stand volume

per ha, quadratic mean diameter (QMD) and efficiency.

Total volume was estimated using the species-specific

equations of Honer (1967). Various metrics of efficiency

have been used (Avery and Newton 1965; Barrett and

Carter 1968; Lindemuth 2007). We chose the approach

originally proposed by Mesavage and Grosenbaugh (1956):

Efficiency = Volume% SE2 � Total time ð1Þ

where the volume percent standard error (SE) is the

combined basal area and VBAR standard errors calculated

using Bruce’s method (Bell and Dilworth 2002, p. 235),

and total time is the time needed to inventory a stand under

a given measurement method. Note that this metric of

efficiency is somewhat counterintuitive; that is, higher

efficiency is associated with lower values. This approach to

efficiency is typically standardized to some baseline

measurement method (e.g., Dahl et al. 2008; Kenning

et al. 2005):

Relative efficiency

¼ Volume% SE2 � Total time

Baseline volume% SE2 � Baseline total time

ð2Þ

In the interest of providing a more comprehensive com-

parison of measurement methods, we used raw efficiency

values rather than relative efficiency values.

Analytical approach

All analyses were conducted using the R statistical software

(R Development Core Team 2011), and we relied on the nlme

package for analysis of mixed models (Pinheiro et al. 2011).

Table 1 Summary of raw stand and plot attributes for 16 sampled

stands in northern and central Maine

Mean SD Range

Stand (n = 16) values for all methods

Area (ha) 69.3 74.8 9.3–310.8

Density (TPH) 1,018 366 67–2,331

Basal area (m2 ha-1) 18.23 5.62 5.03–35.08

QMD (cm) 15.80 3.54 10.76–30.83

Efficiency 423.92 451.83 98.28–2,579.03

Area harvested (%) 65.11 25.83 0.00–100.00

Hardwood composition (%) 73.28 20.14 34.54–100.00

Plot (n = 437) values

Horizontal point samples per

stand

27 6 12–39

Plot sampling time by method

10 BAFe (s) 537 343 14–2,945

20 BAFe (s) 279 194 1–1,472

80 BAFe (s) 152 141 9–1,304

Big BAF (s) 359 235 22–2,045

Fixed (s) 2,298 1,485 64–7,113

Line (s) 858 450 59–3,437

Table 2 Overview of methods evaluated

Method Description VBAR tree selection Sampling frequency

10 BAFe HPS using 2.29 BAF Every 5th tree Each sampling point

20 BAFe HPS using 4.59 BAF Every 5th tree Each sampling point

80 BAFe HPS using 18.43 BAF Every tree Each sampling point

Big BAF HPS using 4.59 BAF Selected with 18.43 BAF Each sampling point

Fixed Circular 0.04 ha (0.1 acre) plot Every 5th tree 1/5 of sampling points

Line HLS using 6.38 BAFa (28BAFe) on 21.34 m line Every 5th tree 1/3 of sampling points

The methods include horizontal point sampling (HPS) with three basal area factors (BAF), fixed area sampling and horizontal line sampling

(HLS)a Gauge constant k = 0.05. Note that BAF actually varies with tree diameter in horizontal line sampling but in the interest of familiarity we have

chosen to report the BAF associated with horizontal point sampling

Eur J Forest Res (2014) 133:261–272 265

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For the analysis of efficiency and the individual components

of efficiency (time and volume standard error), mixed models

were used to account for both the fixed effects of measurement

method and stand basal area and the random effects associated

with variability among stands, resulting in a general analysis

of covariance (ANCOVA) equation:

Yij ¼/j þMj � BAj þ di þ eij ð3Þ

where Yij is the attribute of interest (i.e., efficiency value,

stand measurement time or volume standard error), aj is the

intercept of the jth measurement method, Mj is the slope of

the line for the jth measurement method, BAj is stand mean

basal area (m2 ha-1) for the jth measurement method, di is

the random variable associated with the ith stand assumed

to be N(0, rd2), and eij is the residual error assumed to be

N(0, re2). Analyses were performed similarly, excluding the

stand mean basal area, for all stand-level inventory values

(basal area, basal area coefficient of variation (CV),

density, QMD and volume):

Yij ¼/j þMj þ di þ eij ð4Þ

Average values for each measurement method were cal-

culated using the lsmeans package in R (DiRienzo 2010).

Post hoc tests were performed using Tukey’s method for

multiple comparisons with a statistical significance level of

p B 0.05.

Results

Overall, all of the ANCOVA models for the analysis of

efficiency and its components fit well, with the fixed effects

accounting for 66.4, 55.2 and 49.5 % of the variation for

the volume standard error, time and efficiency, respec-

tively. In analysis of the efficiency data, inclusion of ran-

dom effects increased the R2 from 49.5 to 57.0 %. The root

mean square error (RMSE) for the analysis of efficiency

was 338.48 (unitless), 7.10 % for the volume standard error

model and 46.44 min for the time model.

Efficiency

Results of the mixed model indicated statistical signifi-

cance for the measurement method (p \ 0.0001) and for

the interaction of measurement method and basal area

(p = 0.0008). Decreased efficiency values (higher effi-

ciency) were observed in the horizontal line sampling and

fixed area methods with increasing basal area (Fig. 2). At

lower basal area values, all of the horizontal point sampling

methods were more efficient than both the horizontal line

and fixed area methods, while with increasing basal area,

the horizontal line method becomes comparable to the

horizontal point methods (Fig. 3). For example, the hori-

zontal line and 10 BAFe methods were indistinguishable,

Fig. 2 Fitted regression lines displaying the interaction of method and basal area with a efficiency, b stand measurement time and c volume

standard error. The vertical lines at the bottom of the x-axis represent observed values

266 Eur J Forest Res (2014) 133:261–272

123

with overlapping 95 % confidence intervals, at basal areas

between 17 and 18 m2 ha-1.

Components of efficiency

As mentioned above, the efficiency metric is composed of

two elements, volume percent standard error and time.

Measurement method influenced the estimate of volume

percent standard error (p \ 0.0001), and there was a sig-

nificant interaction between method and basal area

(p \ 0.0001). Volume percent standard error was higher in

the 80 BAFe, horizontal line sampling and fixed area

methods (Fig. 2). There was also an interaction between

method and basal area for all methods, resulting in an

inverse relationship between basal area and volume stan-

dard error for all methods tested. Similarly for measure-

ment time, there was a significant effect of measurement

method (p \ 0.0001) and an interaction between method

and basal area (p = 0.0009). Both the 80 BAFe horizontal

point sampling and horizontal line sampling methods were

relatively unaffected by basal area (Fig. 2).

Basal area

We did not detect any difference in stand-level basal area

estimates among measurement methods (p = 0.5907),

although the percent of basal area in small stems (\12.7 cm)

did vary by method (p = 0.0342). The 80 BAFe method

resulted in lower estimates (range 4.3–5.1 %) of percent

basal area in small trees than all other methods (Table 3) but

the difference was only statistically significant when com-

pared to the fixed area method with an estimated difference

of 5.1 % (95 % CI 0.2–10.1). Estimates of the basal area

coefficient of variation (CV) differed by method

(p \ 0.0001) with the 80 BAFe method producing a higher

estimate than all other methods (between 52.2 and 67.4 %)

with the greatest difference between the 80 BAFe and the

fixed area method, 67.4 % (95 % CI 44.4–90.4).

Density

The estimates of average number of stems per ha did not

differ among methods (p = 0.6465), but the percent of small

Fig. 3 Predicted efficiency

values and 95 % confidence

intervals, illustrating efficiency

value trends throughout the

range of basal area in partially

harvested stands

Table 3 Stand-level least square estimates (mean ± SE) by measurement method for 16 partially harvested stands in northern and central Maine

10 BAFe 20 BAFe 80 BAFe Big BAF Fixed Line

Basal area (m2 ha-1) 17.33a (1.48) 18.64a (1.50) 18.86a (1.48) * 17.97a (1.48) 17.44a (1.48)

Basal area \12.7 cm (% of

total)

20.15a,b (2.52) 20.81a,b (2.54) 15.82a (2.52) * 20.94b (2.52) 20.39a,b (2.52)

QMD (cm) 15.15a (0.86) 15.10a (0.88) 17.97b (0.86) * 15.23a (0.86) 15.39a (0.86)

Basal area CV (%) 57.21a (7.23) 63.47a (7.41) 115.67b (7.23) * 48.25a (7.23) 59.61a (7.23)

Stems (number ha-1) 990.44a (96.37) 1,071.22a (97.37) 943.20a (96.37) * 1,037.01a (96.37) 987.63a (96.37)

Stems \12.7 cm (% of total) 64.81a (4.03) 65.93a (4.10) 49.15b (4.03) * 65.35a (4.03) 64.10a (4.03)

Volume (m3 ha-1) 112.41a,b (10.69) 119.72a,b (10.80) 125.97b (10.69) 125.73b (10.80) 86.32c (10.69) 98.83a,c (10.69)

Different letters among methods indicate statistically significant differences at p B 0.05

* Values derived from 20 BAFe

Eur J Forest Res (2014) 133:261–272 267

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stems did vary among methods (p = 0.0001; Table 3). In

terms of small stems, the 80 BAFe horizontal point sampling

method underestimated the percent of small stems relative to

the other methods tested by 14.96–16.78 %.

QMD

Measurement methods differed in estimation of stand

QMD (p = 0.0007), with 80 BAFe providing QMD esti-

mates, between 2.58 and 2.87 cm higher compared to all

other methods (Table 3). The largest difference was

between the 80 BAFe and the 20 BAFe methods, 2.87 cm

(95 % CI 0.69–5.05).

Volume estimates

Not surprisingly, volume estimates varied among methods

(p = 0.0001). The fixed area method provided the lowest

estimated volume and 80 BAFe the highest. The difference

between these methods was 39.65 m3 ha-1 (95 % CI

17.99–60.84). The fixed area method resulted in lower

volume estimates compared to all other methods tested

(range 26.09–39.65 m3 ha-1) with the exception of the line

method. The horizontal line and fixed area methods pro-

duced volume estimates that were not different from each

other, but both were significantly lower than the 80 BAFe

and big BAF methods (range 26.90–39.65 m3 ha-1). These

volume differences were attributed to both differences in

stand basal area estimates in small stems and also slight

differences among methods in estimates of VBAR (data

not shown).

Discussion

Poor forest inventory can contribute to suboptimal forest

management decisions, resulting in significant financial

losses (Borders et al. 2008). With this in mind, forest

inventories need to be designed and conducted to optimize

a balance of relevant quality data while minimizing costs.

Due to the inherent variability in forested systems and the

subjective nature of balancing competing values, there is

no single approach that predictably serves both purposes

across a range of stand conditions.

Based on the results of this work in partially harvested

stands in northern and central Maine, there are some gen-

eralizations that can be made. Most importantly, our results

showed that measurement methods can vary greatly in the

estimation of specific stand variables (e.g., volume, QMD

and small stem density and basal area), while others may

vary little (e.g., overall basal area and stem density) under

rather heterogeneous forest stand conditions.

Fixed area

Fixed area methods are relatively time consuming even at

low sampling intensity, but the inefficiency of the fixed

area method across a wide range of conditions encountered

in the partially harvested stands sampled for this research

was largely expected. One of the most time consuming

elements in fixed area sampling is establishment of plot

boundaries (Alton et al. 1958). Our results indicated that

even when using time saving technology (such as an

ultrasonic hypsometer), fixed area sampling is still more

time consuming than most of the variable radius methods

tested.

On the other hand, there may be alternatives that offer

increased efficiency. For example, other studies have found

that rectangular plots may perform better than circular

(Marquardt et al. 2010). One of the additional challenges

associated with fixed area plot sampling is inaccurate

characterization of the plot (i.e., missing stems) due to

either crew error in tallying the stems within the plot or

errors in establishing plot boundaries. Bias due to non-

detection is possible even with small plots and the problem

increases with larger plots (Kenning et al. 2005). Even in

the absence of such field errors, fixed area sampling may

not deliver the desired accuracy and precision. For exam-

ple, it was found that horizontal line sampling yields better

stand-level estimates than fixed area sampling particularly

in larger diameter classes even at a lower sampling inten-

sity (Schreuder et al. 1992). Also, horizontal point sam-

pling has been shown to be more efficient for estimation of

basal area than fixed area sampling (Matern 1972). Fixed

area plots do have a role in certain types of forest data

acquisition. Fixed area plots continue to be the preferred

method in repeated measurement schemes.

Horizontal point sampling

All horizontal point sampling measurement methods tested

were more efficient than the fixed area method across the

range of basal areas observed, which was consistent with

previous work (Dahl et al. 2008; Matern 1972). Generally,

there is a clear time savings with horizontal point sampling

over fixed area plot sampling, which has been long

appreciated in the literature (Matern 1972; Shanks 1954).

Interestingly, the 10 BAFe method did not perform better

than the fixed method with respect to time, which reflects

the poor visibility in these stands, the high number of stems

measured and the time involved in checking a large number

of borderline trees.

The efficiency of the horizontal point methods tested

was relatively invariant with only slight increases in effi-

ciency (decreases in the efficiency value) with increasing

basal area. We did not observe substantial differences in

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123

overall efficiency among any of the horizontal point sam-

pling methods tested, which reflects the trade-off between

time and precision (Fig. 2). The 10 BAFe method required

the most time and there were modest differences in mea-

surement time between the big BAF and 20 BAFe methods.

Selecting BA and VBAR trees on the same angle gauge

sweep would have likely increased the efficiency of the big

BAF method by further decreasing the plot measurement

time. Not surprisingly, 80 BAFe took the least amount of

time and had lower precision of volume estimates, which

was expected given the low number of trees measured and

the high variability between plots. The volume standard

error for the 20 BAFe and big BAF methods was surpris-

ingly similar. Given the benefits of the big BAF method,

such as decreased travel time between plot center and

VBAR trees and a reduction in possible crew bias in tree

selection, we believe this method should receive closer

consideration in operational forest inventory.

Numerous studies have been conducted comparing

BAFs in various timber types. Use of a large BAF is often

associated with decreased accuracy (Becker and Nichols

2011). Generally, there is an increase in basal area esti-

mates with increasing BAF (Brooks 2006; Lindemuth

2007), which at some point leads to substantial overesti-

mation of basal area (Becker and Nichols 2011; Wiant

et al. 1984) and possibly general instability in stand-level

estimates (Brooks and McGill 2004). We did not note this

trend in our analysis, but we may not have used a wide

enough range of BAFs. However, our results indicate that

higher BAF (lower tree counts) resulted in overall increa-

ses in estimation of basal area variability. Lindemuth

(2007) also noted such increasing variability among plots

with decreasing tree counts per plot. In the present study,

variability of basal area estimates, represented by the CV,

was significantly higher for 80 BAFe than all other methods

tested. This correlation between BAF and CV has been

previously noted in the literature (Becker and Nichols

2011).

On the other hand, it has been observed that use of a

relatively small BAF may lead to underestimates of basal

area (Wiant et al. 1984), which has been attributed to field

errors, namely undercounting trees. In theory, with perfect

detection the use of smaller BAF should lead to smaller

standard error and estimates should remain unbiased (Ducey

et al. 2002). In our study, we were not under the production

pressures experienced in operational forest inventory and

therefore were able to take the time and care to minimize

field sampling errors. We would expect such undercounting

errors to be higher in operational situations. Nonetheless,

smaller BAFs decrease overall efficiency by increasing the

number of trees measured and can lead to significant time

expenditure in checking borderline trees. We observed a

sharp increase in time expenditure for the 10 BAFe method

with increasing basal area. In Appalachian hardwood stands,

it was shown that 2.29 BAF (10 BAFe) and lower are only

justified in larger stands with relatively low CV (Gambill

et al. 1985), which are conditions not common in the partially

harvested stands that we sampled. Consequently, we rec-

ommend against the use of the 2.29 BAF (10 BAFe), par-

ticularly in partially harvested stands where visibility is often

poor. Such recommendations are not new, as Wiant et al.

(1984) recommended a BAF of 4.59 or 9.18 (20 BAFe or 40

BAFe) in sawtimber in the eastern United States.

Horizontal line sampling

Despite the widespread adoption of horizontal point sam-

pling in North America, horizontal line sampling has not

been widely used in operational forest mensuration. In the

heterogeneous stands used in this study, we found that

horizontal line sampling was less efficient at lower basal

areas and just as efficient as horizontal point sampling

methods in stands with higher basal areas. Horizontal line

sampling provided volume estimates equivalent to 10

BAFe, 20 BAFe and fixed area methods, but lower than big

BAF and 80 BAFe methods. The volume percent standard

error of horizontal line sampling was higher than horizontal

point sampling at lower basal areas, but showed an inverse

relationship with basal area. In previous studies, horizontal

line sampling has proven to be equivalent or superior to

horizontal point sampling in various respects (e.g., Rıos

et al. 2000; Schreuder et al. 1987). Time expenditure for

the horizontal line method was relatively consistent across

a range of stand conditions. As with the fixed area method,

there is a fixed time investment in establishment and layout

of the sampling lines. This fixed time investment likely

contributes to differing assessments of efficiency in hori-

zontal line sampling methods in the literature, as field

conditions can substantially increase or decrease plot

measurement times. For example, in a measurement com-

parison study working in plantation stands, horizontal line

sampling using a large factor prism was found to be more

efficient than both horizontal point sampling and fixed area

plots (Rıos et al. 2000).

Horizontal line sampling has been used to some extent

with permanent sampling plots in Taiwan (Yang 1983), but

we are unaware of the regular operational use of horizontal

line sampling elsewhere in the world. Because horizontal

line sampling is not widely used in operational forest

inventory, there may be concerns over the accuracy and

precision of stand-level estimates. Our results showed that

in heterogeneous stands, horizontal line sampling provided

estimates of basal area, basal area CV, density, QMD and

volume that did not differ from those derived from the

horizontal point sampling typically used in the region (i.e.,

10 and 20 BAFe). Several other studies have addressed the

Eur J Forest Res (2014) 133:261–272 269

123

issue of accuracy and precision of horizontal line sampling

compared to the more widely used horizontal point sam-

pling. For example, in a plantation setting where horizontal

point and line methods were compared, no differences in

accuracy were found (Rıos et al. 2000). A pilot study in

Taiwan compared horizontal line sampling, fixed area plots

and a complete census on 14.25 ha (Yang 1983). With an

appropriate angle gauge, horizontal line sampling provided

volume estimates within 3.6 % of the complete census and

more accurate than fixed area sampling. In a simulation

study, Schreuder et al. (1987) found that horizontal line

sampling performed better in estimating total basal area

than horizontal point sampling. Lindemuth (2007) noted

that horizontal line sampling provided somewhat lower

estimates of basal area than fixed or horizontal point

sampling methods, which we did not observe. Using a

modified horizontal line sampling method, Kenning et al.

(2005) found that basal area was occasionally underesti-

mated (one of six stands) when compared to fixed area

estimates. On the other hand, Marquardt et al. (2010)

determined that horizontal line sampling did not perform

particularly well when estimating trees per ha or basal area

in simulated riparian zone sampling. They hypothesized

that longer lines using a larger BAF may have improved

results, an issue which we address below. Previous work

has observed that variability, estimated by CV, is similar

for horizontal point and line methods (Barrett and Allen

1966). Despite the acceptable performance of the hori-

zontal line sampling, there has not been extensive work on

developing guidelines to address the balance of cost,

accuracy and precision in horizontal line sampling.

The sampling intensity of the horizontal line sampling

method remains an understudied issue in terms of appro-

priate number of sampling lines, length of individual lines

and the appropriate angle gauge to use in a given stand

type. Beers and Miller (1976) recommend a line length of

1–2 chains (20.12–40.14 m). Lindemuth (2007), using 1

and 16 chain (20.12 and 321.95 m) lines, determined that

basal area estimates were unaffected by line length. Sch-

reuder et al. (1987) utilized an approximate equivalent of a

6 BAF prism with no mention of line length in a simulation

study. In comparing sampling methods for snags, Kenning

et al. (2005) used two chain (40.14 m) lines with a BAF of

4.59 (20 BAFe) in a modified horizontal line sampling

scheme (Ducey et al. 2002). Using this method, the overall

efficiency of basal area estimates, accounting for sampling

time and estimated CV, was better than fixed area sampling

in five of six stands when using a two-man crew and two of

six stands when using a one-man crew (Kenning et al.

2005). According to their analysis, the required sample size

using 2 chain-modified lines would be about 40 % the

number of 0.02 ha plots to achieve the same allowable

error in estimation of basal error. Furthermore, the crew

measurement time would also be significantly less,

approximately 23 % less, for the modified horizontal line

sampling. We found that sampling one-third the number of

points sampled using the horizontal point sampling meth-

ods resulted in slightly fewer measured trees on average

compared to the 20 BAFe method.

In the case of partially harvested stands in Maine, we

foresee several advantages to horizontal line sampling

compared to horizontal point sampling. Primarily, hori-

zontal line sampling allows the forest inventory crews to

sample a wider range of the within stand variability while

visiting a fewer number of points. With horizontal point

sampling and fixed area sampling, there is potential for

under- or overestimates of stand values based solely on the

chance that a majority of plots fall within harvested or

unharvested portions of a stand. This possibility may be

particularly problematic when sampling intensity is low.

Secondly, bias in sampling location selection is signifi-

cantly reduced, particularly when using a randomly ori-

ented line. Finally, the horizontal line method allows, with

little additional effort, estimation of any linear feature, such

as roads, streams, planting failures or in our case the per-

cent area in different stand conditions (i.e., trails and

unharvested areas).

Implications and conclusions

No single measurement method is suitable for all possible

stand conditions (Lowell 1997). However, there are several

attributes that forest mensurationists should keep in mind

when designing a forest inventory. First, spatial patterns

and diameter distributions strongly influence sampling

precision (Matern 1972). Measurement method selection is

intertwined with sampling intensity and the spatial

arrangement of the sample trees. The choice of BAF in

variable radius sampling, whether line or point, is certainly

important in precision and efficiency of estimates. Gambill

et al. (1985) related the optimum BAF to volume CV, plot

cruise time, desired probability level, tract size and

allowable sampling error. As noted previously, we would

recommend against the widespread use of any particular

BAF without regard to stand conditions. Additionally, we

believe that selection of VBAR trees using the big BAF

method has the potential to increase efficiency and in

highly heterogeneous stands, such as partially harvested,

horizontal line sampling may also be useful.

With the increasing pressures on forests to supply a

range of goods and services to a growing global population

with a decreasing forestland base, being able to accurately,

precisely and efficiently sample forest conditions is critical.

Forest researchers and practitioners should strive to better

understand the stand-level factors affecting the ability to

270 Eur J Forest Res (2014) 133:261–272

123

describe and quantify forest conditions. As noted earlier,

mensuration field studies incorporating multiple stands are

exceedingly rare and many field studies have had a fairly

limited scope (e.g., Brooks and McGill 2004; Lindemuth

2007). Even simulations may be based on relatively small

areas or from simulated stand structures (e.g., Schreuder

et al. 1987). Furthermore, simulation studies are also lim-

ited by the inability to examine sampling costs in a realistic

setting (Marquardt et al. 2010). Such studies may be lim-

ited in their scope of inference and make it difficult to

predict accuracy, precision and efficiency in applied set-

tings. There are certainly limitations to field based

research. Our study, for example, would have benefited

from collection of more detailed stand and plot-level data

to allow a more in-depth exploration of optimal sampling

effort both in terms of the combination of number of

sampling plots (points or lines) and BAF. On the other

hand, a plot-level analysis would require location infor-

mation for all trees, which would have been cost prohibi-

tive. With these limitations and strengths in mind,

researchers should strive to better integrate theoretical and

simulation studies with field trials.

Despite any shortcomings of the present research project

or any other, it is clear that mensuration must be responsive

to challenges within applied forestry (Temesgen et al.

2007) and the challenges raised by heterogeneous condi-

tions like Maine’s partially harvested stands are substantial.

Further research is needed to examine underutilized

approaches such as horizontal line sampling and sector

sampling (Smith et al. 2008) in such heterogeneous stands.

In particular, we need a better understanding of the balance

between accuracy, precision and cost under a wide range of

stand conditions.

Acknowledgments This research was funded by the Northeastern

States Research Cooperative, University of Maine School of Forest

Resources and University of Maine Cooperative Forestry Research

Unit (CFRU). Member organizations of the CFRU also provided the

field sites for this research. Kasey Legaard and Erin Simons-Legaard

of the University of Maine Image Analysis Laboratory (MIAL) pro-

vided key technical support for this project. This work was supported

by the Maine Agricultural and Forestry Research Station at the

University of Maine (Maine Agricultural and Forest Experiment

Station Publication Number 3290).

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