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 practices, 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 determined 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, determining 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 delineating some area or areas within a stand in which all or a subset of trees are measured. There are a number of variations 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 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 techniques (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 projected 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 probability that all substand patterns are sampled adequately (Barrett and Allen 1966). There are two primary differences between horizontal point and line sampling. The shape of inclusion zones is rectangular in horizontal line sampling compared to the circular inclusion zones in horizontal 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., sampling 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 scattered 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 sampling is well known (Dahl et al. 2008), although not practiced 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 relationship 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 (Desmarais 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 recommended between 5.11 and 11.15 BAF in a study of Appalachian hardwood stands (Brooks 2006).

Given the wide variety of measurement methods available, 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 inventory 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 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). Additionally, 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 harvesting. 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 operations 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 partially 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 harvested 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 occidentalis 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).

Fig. 1
figure 1

Map of study area in northern and central Maine, USA. Study area denoted in dotted portion

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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 analysis 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 conditions were quite variable in terms of stand composition and structure (Table 1).

Table 1 Summary of raw stand and plot attributes for 16 sampled stands in northern and central Maine
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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).

Table 2 Overview of methods evaluated
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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 (Relaskop-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 established. 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 height to crown base to the nearest 0.3 m were measured using a Haglof ultrasonic hypsometer (Haglof Inc., Madison, 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 measurement 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):

$${\text{Efficiency = Volume}}\% \;{\text{SE}}^{2} \times {\text{Total}}\;{\text{time}}$$
(1)

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):

$${\text{Relative}}\;{\text{efficiency}} = \frac{{ {\text{Volume}}\% \;{\text{SE}}^{2} \times {\text{Total}}\;{\text{time}}}}{{{\text{Baseline}}\;{\text{volume}}\% \;{\text{SE}}^{2} \times {\text{Baseline}}\;{\text{total}}\;{\text{time}}}}$$
(2)

In the interest of providing a more comprehensive comparison 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). 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:

$$Y_{ij} =\, \propto_{j} + M_{j} \times \overline{\text{BA}}_{j} + \delta_{i} + \varepsilon_{ij}$$
(3)

where Y ij is the attribute of interest (i.e., efficiency value, stand measurement time or volume standard error), α j is the intercept of the jth measurement method, M j is the slope of the line for the jth measurement method, \(\overline{\text{BA}}_{j}\) is stand mean basal area (m2 ha−1) for the jth measurement method, δ i is the random variable associated with the ith stand assumed to be N(0, σ 2 δ ), and ε ij is the residual error assumed to be N(0, σ 2 ε ). 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):

$$Y_{ij} =\, \propto_{j} + M_{j} + \delta_{i} + \varepsilon_{ij}$$
(4)

Average values for each measurement method were calculated 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 ≤ 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, respectively. In analysis of the efficiency data, inclusion of random effects increased the R 2 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 significance for the measurement method (p < 0.0001) and for the interaction of measurement method and basal area (p = 0.0008). Decreased efficiency values (higher efficiency) 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 horizontal line and 10 BAFe methods were indistinguishable, with overlapping 95 % confidence intervals, at basal areas between 17 and 18 m2 ha−1.

Fig. 2
figure 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

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Fig. 3
figure 3

Predicted efficiency values and 95 % confidence intervals, illustrating efficiency value trends throughout the range of basal area in partially harvested stands

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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 significant 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 standard error for all methods tested. Similarly for measurement 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 compared 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).

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

The estimates of average number of stems per ha did not differ among methods (p = 0.6465), but the percent of small 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 estimates, 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 produced 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 generalizations 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 example, 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 intensity (Schreuder et al. 1992). Also, horizontal point sampling 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 efficiency (decreases in the efficiency value) with increasing basal area. We did not observe substantial differences in overall efficiency among any of the horizontal point sampling 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 measurement 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 surprisingly 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 estimates with increasing BAF (Brooks 2006; Lindemuth 2007), which at some point leads to substantial overestimation 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 increases 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 recommend against the use of the 2.29 BAF (10 BAFe), particularly 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 sampling 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., Ríos 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 horizontal line sampling methods in the literature, as field conditions can substantially increase or decrease plot measurement times. For example, in a measurement comparison 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 (Ríos 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 issue of accuracy and precision of horizontal line sampling compared to the more widely used horizontal point sampling. For example, in a plantation setting where horizontal point and line methods were compared, no differences in accuracy were found (Ríos 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 underestimated (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 horizontal 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 appropriate 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. Schreuder 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 methods 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, horizontal 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 significantly reduced, particularly when using a randomly oriented 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 percent 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 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 limited by the inability to examine sampling costs in a realistic setting (Marquardt et al. 2010). Such studies may be limited in their scope of inference and make it difficult to predict accuracy, precision and efficiency in applied settings. 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 information for all trees, which would have been cost prohibitive. 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 conditions 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.