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: [email protected]
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
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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
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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
268 Eur J Forest Res (2014) 133:261–272
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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