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Evaluation of sampling strategies to estimate crown biomass

Evaluation of sampling strategies to estimate crown biomass Background: Depending on tree and site characteristics crown biomass accounts for a significant portion of the total aboveground biomass in the tree. Crown biomass estimation is useful for different purposes including evaluating the economic feasibility of crown utilization for energy production or forest products, fuel load assessments and fire management strategies, and wildfire modeling. However, crown biomass is difficult to predict because of the variability within and among species and sites. Thus the allometric equations used for predicting crown biomass should be based on data collected with precise and unbiased sampling strategies. In this study, we evaluate the performance different sampling strategies to estimate crown biomass and to evaluate the effect of sample size in estimating crown biomass. Methods: Using data collected from 20 destructively sampled trees, we evaluated 11 different sampling strategies using six evaluation statistics: bias, relative bias, root mean square error (RMSE), relative RMSE, amount of biomass sampled, and relative biomass sampled. We also evaluated the performance of the selected sampling strategies when different numbers of branches (3, 6, 9, and 12) are selected from each tree. Tree specific log linear model with branch diameter and branch length as covariates was used to obtain individual branch biomass. Results: Compared to all other methods stratified sampling with probability proportional to size estimation technique produced better results when three or six branches per tree were sampled. However, the systematic sampling with ratio estimation technique was the best when at least nine branches per tree were sampled. Under the stratified sampling strategy, selecting unequal number of branches per stratum produced approximately similar results to simple random sampling, but it further decreased RMSE when information on branch diameter is used in the design and estimation phases. Conclusions: Use of auxiliary information in design or estimation phase reduces the RMSE produced by a sampling strategy. However, this is attained by having to sample larger amount of biomass. Based on our finding we would recommend sampling nine branches per tree to be reasonably efficient and limit the amount of fieldwork. Keywords: Aboveground biomass; Crown; Sampling strategies; Pacific Northwest * Correspondence: Hailemariam.Temesgen@oregonstate.edu Department of Forest Engineering, Resources, and Management, College of Forestry, Oregon State University, 280 Peavy Hall, Corvallis, OR 97331, USA Full list of author information is available at the end of the article © 2015 Poudel et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. Poudel et al. Forest Ecosystems (2015) 2:1 Page 2 of 11 Background The common understanding among researchers and The global issue of climate change and an increasing practitioners is that an accurate carbon stock estimate interest in the reduction of fossil fuel carbon dioxide requires improved and consistent methods for tree and emissions by using forest biomass for energy produc- component biomass estimation (Hansen 2002; Zhou and tion has increased the importance of forest biomass Hemstrom 2009). quantification in recent years. Different national and Crown biomass is the oven dry weight of the entire international reports have presented the amount of crown, including the leading shoot above the last- carbon sequestered by forest ecosystems. For example, formed whorl, excluding the main bole (Hepp and the Intergovernmental Panel on Climate Change reports Brister 1982). The components of crown biomass are that forests contain about 80% of aboveground and 40% wood, bark, and foliage weights. Crown biomass of belowground carbon stock (IPCC 2007). Addition- accounts for a significant portion of total tree biomass ally, it is reported that the amount of carbon stored in but the amount and its distribution vary by tree and dry wood is approximately 50% by weight (Brown 1986; site characteristics. Using the data from two Alaskan Paladinic et al. 2009; Sedjo and Sohngen 2012). Picea mariana ecosystems, Barney et al. (1978) re- Biomass, in general, includes both above and below ported that foliage comprised 17% to 37% of the total ground living and dead mass of trees, shrubs, vines, and tree mass for the lowland stands and 17% to 50% of the roots. However, most of the researches on biomass total tree mass in the upland stands. Total bole mass estimation have focused on aboveground biomass ranged from 11% to 58% in lowland stands and 21% because of the difficulty in collecting belowground data to 61% in the upland stands. In a study to determine (Lu 2006). The amount of biomass in a forest is influ- the patterns of biomass allocation in dominant and enced by various site factors such as stand density and suppressed loblolly pine (Pinus taeda), Naidu et al. site productivity; soil characteristics such as texture (1998) found that the dominant trees allocated 24.5% and moisture content; and tree characteristics such of biomass to the crown (13.2% in branch and 11.3% in as species and age. On the other hand, distribution needle) and the suppressed trees allocated 12.3% (6.7% of crown biomass affects the carbon cycle, soil nutrient in branch and 5.6% in needle). Kuyaha et al. (2013) allocation, fuel accumulation, and wildlife habitat found that crown biomass formed up to 26% (22% in environments in terrestrial ecosystems and it governs branch and 4% in needle) of aboveground biomass in the potential of carbon emission due to deforestation farmed eucalyptus species. In assessing the importance (Lu 2005). The major components of aboveground tree of crown dimensions to improve tropical tree biomass biomass are merchantable stem biomass (bole including estimate, Goodman et al. (2013) found the trees in bark and wood), stump biomass, foliage biomass, and their study to have nearly half of the total aboveground branches/top biomass (Zhou and Hemstrom 2009). tree biomass in branches (44% ± 2%). The common biomass estimation approach selects Estimates of crown biomass for each stand condition some trees, which are representative of the populations is necessary to understand nutrient depletion and for of interest, for destructive sampling and weighs their evaluating the economic feasibility of crown utilization components. Regression models are then fit to relate for energy production or forest products (Hepp and some easily measurable attributes, such as diameter at Brister 1982). Furthermore, estimates of crown biomass breast height and total tree height, with tree (or compo- aid in fuel load assessments and fire management strat- nent) biomass. The amount of biomass distributed in egies (He et al. 2013) because it is one of the important different components is dependent on species and their input variables in most wildfire models (Saatchi et al. geographic location (Pooreter et al. 2012), management 2007). Much of the focus in estimating crown biomass practices (Tumwebaze et al. 2013) and tree size and has been in the form of regression models and in the selection of predictor variables rather than in the stand density (Jenkins et al. 2003). Ritchie et al. (2013) found that for the given DBH and crown ratio, thinned methods of sample selection. In addition, comparisons stands had more foliage biomass but slightly less branch of sampling strategies have been carried out mainly for foliar biomass sampling rather than the total crown biomass than unthinned stands. Similarly, the contribu- tion of component biomass to the total aboveground (branch wood, bark, and foliage) biomass. Thus, the biomass varies by tree size (de-Miguel et al. 2014b). evaluation of different sampling designs and sample size in estimating crown biomass is an important Henry et al. (2011) found differences in biomass due to floristic composition, tree species and growth strategies aspect of aboveground biomass estimation. for the tree species within a given climatic zone. Thus, Common sampling strategies used in aboveground the component biomass estimations, for example branch biomass estimation include simple random sampling, or crown biomass, bole biomass, and bark biomass, are systematic sampling, stratified random sampling, and important to account for the variability within the tree. randomized branch sampling. The suitability of a technique Poudel et al. Forest Ecosystems (2015) 2:1 Page 3 of 11 is determined by the availability of funds, required accuracy, with ratio estimation as the most efficient estimate of structure and composition of vegetation, and desired individual tree foliage biomass. de-Miguel et al. (2014a) specificity of estimation (Catchpole and Wheeler 1992). developed generalized, calibratable, mixed-effects meta- Additionally, the amount of time a particular technique models for large-scale biomass prediction. One of their takes to implement in the field is also important. The objectives was to investigate and demonstrate how the simple random sampling is generally used as the basis biomass prediction differed when calibration trees were to evaluate the performance of other sampling designs selected using different sampling strategies. They found (e.g. Snowdon 1986; Temesgen 2003). that a stratified sampling was better compared to the Gregoire et al. (1995) have proposed a number of sam- simple random sampling. Thus there is no strong rationale pling procedures (randomized branch sampling, import- to support one method as being superior to another. ance sampling, control-variate sampling, two-stage and Crown biomass is difficult to predict because of the vari- three-stage sampling) that can be used to estimate foliage ability within and among species and various sites. A good and other characteristics of individual trees. The random- allometric equation for predicting aboveground biomass ized branch sampling (RBS) was originally introduced by should be based on data collected with an appropriate Jessen (1955) to determine the fruit count on orchard (precise and unbiased) sampling method. In this context, trees. Valentine and Hilton (1977) used this method to the objective of this study was to evaluate different obtain estimates of leaf counts, foliar area, and foliar mass sampling strategies to estimate crown biomass. We also of mature Quercus species. Good et al. (2001) have evaluated how the performance of different methods was employed RBS with importance sampling for estimating affected when different number of branches (3, 6, 9, and tree component biomass. Since the sample is accumulated 12) per tree was sampled in estimating crown biomass. sequentially along the path, RBS does not require locating and counting the total number of branches beforehand. Methods However, Chiric et al. (2014) posed some doubts on the ef- Study area fectiveness of RBS in sampling big trees or trees with ir- This study was conducted in the McDonald-Dunn regular forms. According to Valentine and Hilton (1977), Forest, an approximately 4,550 ha property, managed by the the accuracy of RBS is largely dependent on the probabil- Oregon StateUniversityin the westernofthe edge of ity assignment and the time required to take RBS samples the Willamette Valley in Oregon and on the eastern depends on the size of the trees and experience of those foothills of the Coast Range (123°15' W, 44°35' N, 120 m taking the samples. elevation). The forest consists predominantly of the Swank and Schreuder (1974) compared stratified two- Douglas-fir (Pseudotsuga menziesii (Mirbel) Franco) and a phase sampling, two-phase sampling with a regression small Grand fir (Abies grandis (Dougl. ex D. Don) Lindl.) estimator, and two-phase sampling with a ratio-of-means and has a wide range of overstory age-class distribution estimator. They found the stratified two-phase sampling with majority of the stands less than 80 years old and as the most precise and appropriate method for estimat- some stands that are 80 to 120 years old. The forest ing surface area and biomass for a young eastern white receives approximately 110 cm of annual rainfall and aver- pine forest. Temesgen (2003) found that stratified age annual temperature ranges from 6°C to 17°C. random sampling produced the lowest mean squared error value in comparing five sampling designs to quan- Data tify tree leaf area. Stratification in branch biomass Twenty sample trees (11 Douglas-fir and 9 Grand fir) sampling can be done in many different ways. Snowdon were subjectively selected from stands of different ages (1986) showed improved accuracy of estimates by strati- for destructive sampling avoiding the trees with obvious fication based on crown position compared to those defects and trees close to stand edges. The field work obtained by simple random sampling, especially at low was carried out between the first week of July and third sampling intensities. Their findings suggest that stratifi- week of September 2012. Trees that were forked below cation by whorl was slightly but not significantly inferior breast height and with damaged tops were not included to stratification based on crown position or branch in sampling. Tree level attributes including total height, diameter. Another approach used in selecting branches height to the base of first live branch, crown width, and for estimating crown biomass is to divide the bole into main stem diameter at 0.15, 0.76, 1.37, and 2.40 m above sections and pile up the branches from each section into ground, and every 1.22 m afterwards were recorded. The different size classes and randomly select a number of branches were divided into four diameter classes (1.3 cm branches proportional to the total number of branches in class = 0–2.5 cm, 3.8 cm class = 2.6–5.1 cm, 6.4 cm class = each size class (e.g. Harrison et al. 2009, Devine et al. 5.2–7.6 cm, 8.9 cm class = 7.7–10.2 cm). For all first order 2013). In an evaluation of ten different sampling strategies, branches, height to- and diameter- at branch base were Temesgen et al. (2011) found that systematic sampling measured. Poudel et al. Forest Ecosystems (2015) 2:1 Page 4 of 11 For the first and every third branch, when proceeding the best fit (Adj-R = 0.93), therefore was used to predict from the base, in each diameter class, length and weight individual branch biomass within each tree. of both live and dead branches were recorded. From those selected branches, four branches per diameter ln y ¼ β þ β ln BD þ β ln BL þ ε ð2Þ ij ij ij ij 0i 1i 2i class were weighed with and without foliage. The nee- dles were removed in the field to obtain the green where y , BD and BL are oven dry weight (kg) of branch ij ij ij weight of foliage and branch wood with bark. Two of (wood, bark, and foliage combined), branch diameter th th these four branches were taken to the lab, keeping (cm), and branch length (m) of the j branch on i tree branch and foliage in separate paper bags, for drying. respectively; β ‘s are regression parameters to be esti- ij The branches were chipped in to small pieces to exped- mated; ln(·) is the natural logarithm; and ε ‘s are the ran- ij ite the drying process and placed in a kiln for drying at dom error. The full model included other variables such 105°C. The oven dry weight was recorded by tracking as height to the base of the branch, crown width and the weight lost by each sample until no further weight crown length, but were dropped because they were not was lost. Table 1 presents the tree and branch level sum- statistically significant (p-value > 0.05). Lengths for the rd mary of the felled-tree data used in this study. 2/3 branches (not measured in the field) were obtained by fitting the following log linear model (Adj-R =0.74): Individual branch biomass ln BL ¼ β þ β ln BD þ β ln RBD þ ε ð3Þ ij ij ij ij Kershaw and Maguire (1995) developed a tree specific 0i 1i 2i log linear model (Equation 1) using branch diameter where BD , BL , and ε are same as defined in Equation 2 ij ij ij (BD) and depth into the crown (DINC: the distance and RBD is the relative branch depth (relative position of ij from tip to the base of the branch) as covariates to esti- th th the subject branch from the crown base) of j branch in i mate branch foliage biomass. Temesgen et al. (2011) tree and is computed as follows (Ishii and Wilson 2001): successfully used this model in comparing sampling strategies for tree foliage biomass estimation. total tree height−height to the base of subject branch RBD ¼ total tree height−height to the base of lowest live branch The RBD is 1.0 for the first live branch. The logarith- ln y ¼ β þ β ln BD þ β ln DINC ij ij ij 0i 1i 2i mic regressions are reported to result in a negative bias þ ε ð1Þ ij when data are back transformed to arithmetic scale. The commonly used remedy to this is to multiply the back MSE transformed results by a correction factor exp , This model was modified by replacing DINC with branch length (Equation 2). The modified model provided where MSE is the mean squared error obtained by the Table 1 Summary of felled-tree and branch-level attributes used in this study Variable n Mean SD Minimum Maximum Tree data DBH (cm) 62.8 27.0 23.9 114.0 Height (m) 34.6 10.3 18.3 46.5 Crown base height (m) 10.2 6.3 0.8 23.7 Crown length (m) 24.4 6.2 12.2 34.4 Crown width (m) 8.6 2.4 5.2 13.4 Branch data Diameter (cm) 3464 3.7 2.1 0.8 10.4 Length (m) 1178 2.8 1.6 0.1 10.2 Total green weight (kg) 1102 4.14 5.61 0.05 46.99 Green weight of branch wood (kg) 326 3.98 5.61 0.05 38.01 Green foliage weight (kg) 264 1.80 1.84 0.05 9.71 Total dry weight (kg) 128 3.44 4.08 0.12 18.40 Dry weight of branch wood (kg) 128 2.68 3.49 0.07 15.37 Dry foliage weight (kg) 128 0.76 0.79 0.04 4.58 Poudel et al. Forest Ecosystems (2015) 2:1 Page 5 of 11 least-squares regression. However, there are conflicting selection, first a random starting point between 1 and total remarks about the correction factor itself. For example number of branches was randomly chosen, the interval Beauchamp and Olson (1973) and Flewelling and then is added obtaining exactly n (sample size) branches. Pienaar (1981) suggested that this correction factor was Then the numbers are divided by the sample size and still biased because the sample variance is consistent rounded to the nearest whole number to get the selected but it is biased for finite sample sizes. We did not use samples. the correction factor in our study. The trend in the Methods 6–11 belonged to different stratified sampling relationship between crown biomass and branch diameter strategies. The stratified sampling method divides the popu- and length was similar but the variability in biomass lation into subpopulations of size n ,where n is the h h increased with increasing branch length (Figure 1). All number of elements in stratum h. The total crown length statistical procedures were performed using statistical was divided into three sections having equal number of software R (R Core Team 2014). branches as three strata. In methods 6 (STR) and 7 (STR- RAT), n/3 branches were randomly selected with equal Methods for crown biomass sampling probability, where n is the sample size. Again, the difference We evaluated 11 sampling methods to select branches for between these two methods lies in the estimation of total estimating crown biomass. The 11 sampling strategies crown biomass. STR method uses the SRS estimation tech- belonged to three main categories: simple random nique while STR-RAT method uses the ratio estimation sampling, systematic sampling, and stratified sampling. technique to obtain the total crown biomass. Method 8 Methods 1 and 2 are based on simple random sampling (STR-PPS), stratified sampling with PPS, selected branches (SRS) strategy. In each of these methods, each branch was in each stratum with probability proportional to the square chosen randomly such that each individual branch has of branch diameter. Total crown biomass in this method equal probability of selection at any stage of selection. The was obtained by summing the stratum total crown biomass difference in these methods is in the estimation of total calculated using Horvitz-Thompson unequal probability tree biomass: method 1 uses SRS estimator while method estimator (Horvitz and Thompson 1952). 2 (SRS-RAT) uses the ratio estimator with squared branch Methods 9–11 (stratified, unequal) are based on the idea diameter as auxiliary information. Method 1 is also the that the distribution of crown biomass in different strata basis for comparing the performance of other methods. depends on the relative position of the branches in the tree. Method 3, probability proportional to size (PPS), uses Ishii and McDowell (2001) found that mean branch branch size as auxiliary information in sample selection. volume increased from upper- to lower-crown. For a given Total crown biomass in this method was calculated using density, biomass (oven dry weight) is the function of Horvitz-Thompson estimator (Horvitz and Thompson volume. Therefore, the stratified sampling method was 1952). Methods 4 (SYS) and 5 (SYS-RAT) are systematic modified to incorporate the variability of biomass distribu- sampling with similar design phase but different estima- tion within a tree. Trees were first divided into three sec- tion phase. Method 4 uses the SRS estimator while tions having equal number of branches. Then, 4, 3, and 2 method 5 uses the ratio estimator. The fractional inter- branches from the lower, middle, and upper section of the val systematic sample selection procedure was used in trees were selected respectively. This corresponds that the the systematic selection of the branches because it number of branches selected in each section is propor- ensures the equal probability of selection for all the tional to the observed biomass in that section of the tree. branches (Temesgen et al. 2011). The interval was Because stratification based on crown length resulted in determined based on the total number of branches the biased estimation of crown biomass, the balanced in each tree. In fractional interval systematic sample stratification method was applied. The total number of Figure 1 Scatterplot of dry biomass (kg) against branch diameter (a) and branch length (b) by species (DF = Douglas-fir, GF = Grand fir). Poudel et al. Forest Ecosystems (2015) 2:1 Page 6 of 11 Table 2 Summary of methods used for crown biomass estimation in this study Methods Equations for total crown biomass Selection probability Inclusion probability Simple random sampling 1 1 n SRS ^ τ ¼ NB y i i ij n NB NB i i j¼1 NB y X ij j¼1 2 1 n ^ X SRS-RAT τ ¼ BD i n ij NB NB i i BD ij j¼1 j¼1 X 2 y BD ij ij PPS PPS ^ τ ¼ π ¼ X π ¼ 1− 1−π i PPS ij ij NB ij ij BD j∈S ij j¼1 Systematic sampling 1 n n SYS τ ¼ NB y i i n ij NB NB i i j¼1 NB y X ij j¼1 2 n n ^ X SYS-RAT τ ¼ BD i n ij NB NB i i BD ij j¼1 j¼1 Stratified sampling H n XX 2 BD N ij n ih h STR τ ¼ y X n ijh NB N h ih BD h¼1 j¼1 ij j¼1 X X H n ih y 2 n ijh h BD h¼1 j¼1 ij n STR-RAT τ ¼ X X X H n NB N h ih ih 2 2 BD BD n ijh ij h¼1 j¼1 h j¼1 XX 2 y BD ijh ijh STR−PPS STR-PPS ^ τ ¼ X π ¼ 1− 1−π ij iSðÞ TR−PPS ðÞ STR−PPS NB ij ih ijh BD h¼1 j∈S h ijh j¼1 th th th th Notation: ^ τ is the estimated total crown biomass for i tree; y is the oven dry weight of j branch on i tree; NB is the number of branches on i tree; n is ij i th th th number of branches sampled; N is the number of branches in h stratum on i tree; and n is the number of branches sampled in h stratum. ih h branches selected in each tree (nine) was determined based sampling with equal number of branches per stratum. on the amount of biomass sampled. Total crown biomass Methods 9–11 were based on selecting nine branches in in each stratum was computed using the SRS estimation each tree. Table 2 summarizes the inclusion probability, technique in method 9 (Un-STR), PPS in method 10 (Un- selection probability, and the estimator of the total crown PPS), and ratio estimation in method 11 (Un-STRRAT). biomass in each of the sampling strategies evaluated in Total crown biomass in each tree was computed by sum- this study. ming the crown biomass in each stratum. The unequal branch selection strategy was also evaluated using similar Evaluation of sampling strategies evaluation statistics used for the other eight methods. We evaluated the performance of 11 sampling strategies to Performances of first eight methods were evaluated by estimate crown biomass using the following six statistics selecting four different sample sizes (3, 6, 9, and 12) in estimated from 5,000 iterations. These measures were suc- each tree. These sample sizes were chosen for the ease of cessfully used to evaluate the performance of sampling strat- distributing samples into three different strata in stratified egies to estimate foliage biomass in Temesgen et al. (2011). Table 3 Average bias (kg) produced by different sampling methods and sample sizes based on 5,000 simulations Sampling strategies Sample size SRS SRS-RAT PPS SYS SYS-RAT STR STR-RAT STR-PPS 3 0.237 −4.091 −0.158 0.433 −9.320 −0.659 −3.554 −0.104 6 0.215 −1.711 0.010 0.139 −1.922 0.399 −1.387 −0.101 9 −0.081 −0.937 −0.068 0.133 0.166 0.191 −0.857 −0.094 12 −0.030 −0.894 0.158 0.043 −0.078 −0.242 −0.776 −0.073 Poudel et al. Forest Ecosystems (2015) 2:1 Page 7 of 11 Table 4 Relative bias (percent) produced by different sampling methods and sample sizes based on 5,000 simulations Sampling strategies Sample size SRS SRS-RAT PPS SYS SYS-RAT STR STR-RAT STR-PPS 3 0.101 −2.437 −0.169 0.107 −6.086 −0.321 −2.107 −0.034 6 −0.001 −1.115 0.024 0.061 −1.061 0.197 −0.900 −0.012 9 0.063 −0.600 −0.027 0.038 0.033 0.148 −0.543 −0.069 12 −0.011 −0.523 0.100 0.037 0.032 −0.035 −0.439 −0.040 1. Bias: For each tree the bias (kg) was calculated as amount of crown biomass sampled. Therefore the the mean difference between observed and predicted amount of crown biomass sampled was also used as total crown biomass for that tree as follows: a criterion for the evaluation of sampling strategies. The amount of crown biomass sampled (sampling intensity) is calculated as follows: B ¼ ðÞ τ −τ^ i is is s¼1 XX BS ¼ y ijs where τ and τ^ are the observed and predicted is is th th s¼1 j∈S total crown biomasses for i tree in s iteration, th respectively. y is the observed total crown biomasses for i tree, ijs th th j sample branch in s iteration. 2. Relative bias: Relative bias percentage is the ratio of bias to the total observed crown biomass for that 6. Relative biomass sampled (RBS%) indicates the tree and computed as follows: proportion of crown biomass sampled with respect to the total crown biomass measured and is 1 ðÞ τ −τ^ is is RB ¼ calculated as follows: 5000 τ is s¼1 XX ijs where all the variables are same as defined RBS ¼ ij 5000 τ ijs s¼1 j∈S previously. 3. Root mean square error (RMSE): Results and discussions vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Except for the ratio estimators, the estimators of popula- u X tion totals were unbiased, with biases close to zero for RMSE ¼ ðÞ τ −τ^ i is is s¼1 all sample sizes (Tables 3 and 4). The squared bias for these methods ranged from zero to 0.435 kg. Ratio esti- 4. Relative RMSE: mators resulted in greater bias than the other methods. vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi The absolute bias of the ratio estimators decreased with 5000 2 u X ^ increasing sample size as expected. 1 τ −τ is is R−RMSE ¼ As expected, the RMSE (and relative RMSE) decreased 5000 τ is s¼1 with increasing sample size (Tables 5 and 6) for all sam- pling strategies. Based on the RMSE values obtained 5. Biomass sampled (BS): Amount of cost for crown from 5,000 simulations, the stratified sampling with biomass estimation is directly proportional to the PPS estimation was the superior method compared to Table 5 Average RMSE produced by different sampling methods and sample sizes based on 5,000 simulations Sampling strategies Sample size SRS SRS-RAT PPS SYS SYS-RAT STR STR-RAT STR-PPS 3 88.57 42.56 38.04 113.17 48.54 85.05 42.08 34.95 6 60.49 30.01 29.23 57.94 29.98 58.54 29.56 27.99 9 48.60 23.92 25.19 37.88 22.12 46.48 23.55 24.46 12 40.77 20.18 22.78 30.77 17.91 38.89 19.75 22.33 Poudel et al. Forest Ecosystems (2015) 2:1 Page 8 of 11 Table 6 Relative RMSE percent produced by different sampling methods and sample sizes based on 5,000 simulations Sampling strategies Sample size SRS SRS-RAT PPS SYS SYS-RAT STR STR-RAT STR-PPS 3 55.70 25.72 23.46 72.02 28.80 53.41 25.61 21.57 6 38.07 17.93 18.23 35.23 17.53 36.63 17.78 17.59 9 30.38 14.19 15.83 23.58 13.29 29.03 14.07 15.55 12 25.42 11.92 14.40 18.37 11.11 24.27 11.76 14.22 all other methods when sample size is 3 or 6 branches is obtained by sampling just a little more amount of per tree. However, while using PPS, stratification of the biomass(1.03 timeson average). crown into sections did not reduce the RMSE and relative Use of allometric equations is inevitable in above- RMSE significantly. On the other hand, when at least nine ground biomass estimation because weighing the trees branches per tree were sampled, the SYS-RAT was the and their components for direct biomass determination best and the SRS-RAT was the second best method. is destructive and prohibitively expensive. Choice of Number of branches required to achieve desired preci- biomass sampling strategy determines the quality of data sion is another important aspect of estimating crown available for fitting such equations. Use of auxiliary biomass. On average, the RMSE decreased by 34.3% information in design and/or estimation phase (ratio when the sample size increased from three branches per estimation and PPS) produced better results in terms of tree to six branches per tree. The RMSE further decreased RMSE compared to the methods that do not make use by 22.1% and 15.4% when the sample size increased from of such information in this study. Previous researches 6 to 9 and 9 to 12 respectively. (e.g. Temesgen et al. 2011) have also shown the benefits The amount of biomass sampled determines the cost from using auxiliary information in the design and/or that would be incurred in estimating crown biomass. estimation concerning tree biomass. Biomass sampled and relative biomass sampled in differ- The model used in estimating branch biomass which ent sampling strategies are presented in Tables 7 and 8. is later used as a dependent variable in the test popula- The Strategy-Cost-Accuracy graph (Figure 2) shows the tion, was a logarithmic model (Equation 2). There is efficiency trade-off across the strategies compared in the an inherent negative bias in this method because the study. The SRS and SYS methods resulted in the lowest dependent variable is transformed prior to estimation amount of biomass sampled. On average, the amount of (Snowdon 1991). The ratio estimation strategies, SRS- biomass sampled using the PPS method was 1.6, 1.5, 1.4, RAT, SYS-RAT, and STR-RAT in this study, were nega- and 1.4 times higher than the amount of biomass sampled tively biased. However, in terms of RMSE, these strategies in stratified random sampling when 3, 6, 9, and 12 were clearly superior methods compared to the SRS branches per tree were selected respectively. approach. As noted in Temesgen et al. (2011), however, On average, selecting 12 instead of 9 branches per tree the efficiency of sampling strategies with ratio estimation increased the amount of biomass sampled by 29.2%. may be affected by the amount of work and difficulty in Therefore, nine branches in each tree were selected in implementing these techniques in the field. evaluating the performance of unequal stratified sam- The amount of biomass sampled determines the cost pling strategy. Results from unequal branch selection are that would be incurred in estimating crown biomass. presented in Table 9. This strategy reduced the relative Choice of a sampling strategy determines the amount of RMSE by 0.6%, 4.5% and 3.5% compared to selecting biomass and relative biomass sampled. This ultimately 9 branches using stratified random sampling, stratified determines the amount of time and cost required for a biomass estimation project. The SRS and SYS methods sampling with ratio estimation, and stratified sampling with PPS respectively. This reduction in relative RMSE resulted in the lowest amount of biomass sampled. Our Table 7 Amount of biomass sampled (kg) by different Table 8 Relative amount of biomass sampled (%) by sampling strategies and sample sizes different sampling strategies and sample sizes Sampling strategies Sampling strategies Sample size Sample size SRS PPS SYS STR STR-PPS SRS PPS SYS STR STR-PPS 3 7.74 12.58 7.73 7.68 12.40 3 5.36 8.67 5.35 5.33 8.45 6 15.49 23.79 15.46 15.50 23.29 6 10.71 16.37 10.71 10.72 15.87 9 23.17 33.77 23.18 23.19 33.05 9 16.08 23.16 16.06 16.07 22.45 12 30.91 42.83 30.92 30.86 41.79 12 21.42 29.27 21.43 21.40 28.33 Poudel et al. Forest Ecosystems (2015) 2:1 Page 9 of 11 Figure 2 Relative RMSE (%) produced Vs. relative biomass sampled (percent of total crown mass) in different sampling strategies and sample sizes. results in terms of RMSE values reported and the the SYS-RAT was the best and the SRS-RAT was the amount of biomass sampled by each strategy are consistent second best method when at least nine branches per tree with the findings of Temesgen et al. (2011) in estimating were sampled. It should also be noted that the lower RMSE foliar biomass of Douglas-fir (Pseudotsuga menziesii var. values in the PPS estimation techniques are obtained menziesii)and ponderosapine(Pinus ponderosa). with an increased amount of biomass sampled in each tree. On the other hand, if the auxiliary information on Conclusions branch size is not used, the systematic sampling pro- Crown biomass estimation is a complex process that re- vided better results than the SRS or STR method when quires intensive manual field work involving destructive at least 6 branches per trees were selected. Thus the sampling. The amount of fieldwork required and the ac- selection of a specific sampling strategy is dependent curacy of biomass estimation is dependent on the sam- on the availability of the time and cost for the given pling strategy used. Furthermore, the accuracy of the biomass sampling project. Based on our finding we estimation can be improved by adopting appropriate would recommend sampling 9 branches per tree to techniques in both the design and estimation phases, obtain reasonable efficiency and amount of work in- beginning with the selection of sample plots and sample volved in the field. trees through model development. In this study, we The logic for selecting unequal numbers of branches evaluated 11 different sampling strategies that belonged per stratum within a tree is justified by the fact that the to three main categories: simple random sampling, biomass distribution within a tree is not uniform. Select- systematic sampling and stratified sampling. The SRS, ing equal branches per stratum produced approximately PPS, and ratio estimation techniques were used to similar results to unequal sampling when the SRS esti- obtain the total crown biomass in each tree. mation technique was used. However, making use of Based on the RMSE values obtained from 5,000 simu- auxiliary information on branch size in the design and lations, the stratified sampling with PPS estimation pro- estimation phases further decreased the relative RMSE. duced better results as compared to all other methods Once again, the decreased RMSE by use of auxiliary in- when 3 or 6 branches per tree were sampled. However, formation is attained by having to sample slightly higher Table 9 Evaluation statistics produced when selecting 4, 3, and 2 branches from lower, middle, and upper stratum Method Bias Relative bias RMSE Relative RMSE Biomass sampled Relative biomass sampled Un-STR 0.100 0.061 46.16 28.87 24.25 16.87 Un-STRRAT −0.731 −0.491 22.58 13.44 Un-PPS 0.140 0.063 23.67 15.00 33.85 23.04 Poudel et al. Forest Ecosystems (2015) 2:1 Page 10 of 11 amount of biomass. Findings of this study should prove Hansen M (2002) Volume and biomass estimation in FIA: national consistency vs. regional accuracy. In: McRoberts RE, Reams GA, Van Deusen PC, Moser beneficial for the stakeholders working in the field of JW (eds) Proceedings of the third annual Forest Inventory and Analysis aboveground biomass and carbon estimation. Additional symposium. General Technical Report NC-230. U.S. Department of work using the data from different species and location Agriculture, Forest Service, North Central Research Station, St. Paul, MN, pp 109–120 should be done to further validate the findings in this Harrison RB, Terry TA, Licata CW, Flaming BL, Meade R, Guerrini IA, Strahm BD, study. Xue D, Lolley MR, Sidell AR, Wagoner GL, Briggs D, Turnblom EC (2009) Biomass and stand characteristics of a highly productive mixed Douglas-Fir Competing interests and Western Hemlock plantation in Coastal Washington. West J Appl For The authors declare that they have no competing interests. 24(4):180–186 He Q, Chen E, An R, Li Y (2013) Above-ground biomass and biomass components Authors’ contributions estimation using LiDAR data in a coniferous forests. Forests 4:984–1002 KP designed the sampling experiments, performed the sampling Henry M, Picard N, Trotta C, Manlay RJ, Valentini R, Bernoux M, Saint-André L experiments, analyzed the data, and wrote the paper. TH conceived the (2011) Estimating tree biomass of sub-Saharan African forests: a review of sampling experiments, critically reviewed the manuscript, contributed to available allometric equations. Silva Fenn 45(3B):477–569 coding and data analysis, and edited the manuscript. AG critically reviewed Hepp TE, Brister GH (1982) Estimating crown biomass in loblolly pine plantations the manuscript, edited the manuscript and contributed ideas at all phases of in the Carolina Flatwoods. For Sci 28(1):115–127 the project. All authors read and approved the final manuscript. Horvitz DG, Thompson DJ (1952) A generalization of sampling without replacement from a finite universe. J Am Stat Assoc 47:663–685 Acknowledgements IPCC (2007) Climate change 2007: synthesis report. In: Core Writing Team, We thank Professors Lisa Madsen and Glen Murphy (both at Oregon State Pachauri RK, Reisinger A (eds) Contribution of working groups I, II and III to University) for their insights and comments on an earlier draft, and the the fourth assessment report of the intergovernmental panel on climate Forest Inventory Analysis Unit for funding the data collection and analysis change. IPCC, Geneva, Switzerland, p 104 phases of this project. Ishii H, McDowell N (2001) Age-related development of crown structure in coastal Douglas-fir trees. For Ecol Manag 169:257–270 Author details Ishii H, Wilson ME (2001) Crown structure of old-growth Douglas-fir in the western Department of Forest Engineering, Resources, and Management, College of Cascade Range, Washington. Can J For Res 31:1250–1261 Forestry, Oregon State University, 280 Peavy Hall, Corvallis, OR 97331, USA. 2 Jenkins CJ, Chojnacky DC, Heath LS, Birdsey RA (2003) National-scale biomass USDA Forest Service, PNW Research Station, 3200 SW Jefferson Way, estimators for United States tree species. For Sci 49(1):12–35 Corvallis, OR 97331, USA. Jessen RJ (1955) Determining the fruit count on a tree by randomized branch sampling. Biometrics 11(1):99–109 Received: 15 August 2014 Accepted: 17 December 2014 Kershaw JA, Maguire DA (1995) Crown structure in Western hemlock, Douglas-fir, and grand fir in western Washington: trends in branch-level mass and leaf area. Can J For Res 25:1897–1912 References Kuyaha S, Dietz J, Muthuri C, Noordwijk MV, Neufeldt H (2013) Allometry and Barney RJ, Vancleve K, Schlenter R (1978) Biomass distribution and crown partitioning of above- and below-ground biomass in farmed eucalyptus characteristics in two Alaskan Picea mariana ecosystems. 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Aust J Ecol 17:121–131 28:1116–1124 Chiric G, Puletti N, Salvati R, Arbi F, Zolli C, Corona P (2014) Is randomized branch Paladinic E, Vuletic D, Martinic I, Marjanovic H, Indir K, Benko M, Novotny V sampling suitable to assess wood volume of temperate broadleaved old- (2009) Forest biomass and sequestered carbon estimation according growth forests? For Ecol Manag 312:225–230 to main tree components on the forest stand scale. Period Biol R Core Team (2014) R: A language and environment for statistical computing. R 111(4):459–466 Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org/ Pooreter H, NIklas KJ, Reich PB, Oleksyn J, Poot P, Mommer L (2012) Biomass de-Miguel S, Mehtatlo L, Durkaya A (2014a) Developing generalized, calibratable, allocation to leaves, stems and roots: meta-analyses of interspecific variation mixed-effects meta models for large-scale biomass prediction. Can J For Res and environmental control. New Phytol 193:30–50 44:648–656, a or b Ritchie MW, Zhang J, Hamilton TA (2013) Aboveground tree biomass for Pinus de-Miguel S, Pukkala T, Assaf N, Shater Z (2014b) Intra-specific difference in ponderosa in northeastern California. Forests 4:179–196 allometric equations for aboveground biomass of eastern Mediterranean Saatchi S, Halligan K, Despain DG, Crabtree RL (2007) Estimation of forest fuel load Pinus brutia. Ann For Sci 71:101–112, a or b from radar remote sensing. IEEE Trans Geosci Remote Sens 45:1726–1740 Devine WD, Footen PW, Harrison RB, Terry TA, Harrington CA, Holub SM, Gould Sedjo R, Sohngen B (2012) Carbon sequestration in forests and soils. Annu Rev PJ (2013) Estimating Tree Biomass, Carbon, and Nitrogen in two Vegetation Resour Econ 4:127–144 Control Treatments in an 11-Year-old Douglas-fir Plantation on a Highly Snowdon P (1986) Sampling strategies and methods of estimating the biomass Productive Site. Res. Pap. PNW-RP-591. U.S. Department of Agriculture, Forest of crown components in individual trees of Pinus radiata D Don. Aust For Service, Pacific Northwest Research Station, Portland, OR, p 29 Res 16(1):63–72 Flewelling JW, Pienaar LV (1981) Multiplicative regression with lognormal errors. Snowdon P (1991) A ratio estimator for bias correction in logarithmic regressions. For Sci 27(2):281–289 Can J For Res 21:720–724 Good NM, Paterson M, Brack C, Mengersen K (2001) Estimating tree component Swank WT, Schreuder HT (1974) Comparison of three methods of estimating biomass using variable probability sampling methods. J Agric Biol Environ surface area and biomass for a forest of young eastern white pine. For Sci Stat 6(2):258–267 20:91–100 Goodman RC, Phillips OL, Baker TR (2013) The importance of crown dimensions Temesgen H (2003) Evaluation of sampling alternatives to quantify tree leaf area. to improve tropical tree biomass estimates. Ecol Appl. http://dx.doi.org/ Can J For Res 33:82–95 10.1890/13-0070.1 Gregoire TG, Valentine HT, Furnival GM (1995) Sampling methods to estimate Temesgen H, Monleon V, Weiskittel A, Wilson D (2011) Sampling strategies for foliage and other characteristics of individual trees. Ecology 76(4):1181–1194 efficient estimation of tree foliage biomass. For Sci 57(2):153–163 Poudel et al. Forest Ecosystems (2015) 2:1 Page 11 of 11 Tumwebaze SB, Bevilacqua E, Briggs R, Volk T (2013) Allometric biomass equations for tree species used in agroforestry systems in Uganda. Agroforest Syst 87:781–795 Valentine HT, Hilton SJ (1977) Sampling oak foliage by the randomized-branch method. Can J For Res 7:295–298 Zhou X, Hemstrom MA (2009) Estimating aboveground tree biomass on forest land in the Pacific Northwest: a comparison of approaches. Res. Pap. PNW-RP-584. 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Evaluation of sampling strategies to estimate crown biomass

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Abstract

Background: Depending on tree and site characteristics crown biomass accounts for a significant portion of the total aboveground biomass in the tree. Crown biomass estimation is useful for different purposes including evaluating the economic feasibility of crown utilization for energy production or forest products, fuel load assessments and fire management strategies, and wildfire modeling. However, crown biomass is difficult to predict because of the variability within and among species and sites. Thus the allometric equations used for predicting crown biomass should be based on data collected with precise and unbiased sampling strategies. In this study, we evaluate the performance different sampling strategies to estimate crown biomass and to evaluate the effect of sample size in estimating crown biomass. Methods: Using data collected from 20 destructively sampled trees, we evaluated 11 different sampling strategies using six evaluation statistics: bias, relative bias, root mean square error (RMSE), relative RMSE, amount of biomass sampled, and relative biomass sampled. We also evaluated the performance of the selected sampling strategies when different numbers of branches (3, 6, 9, and 12) are selected from each tree. Tree specific log linear model with branch diameter and branch length as covariates was used to obtain individual branch biomass. Results: Compared to all other methods stratified sampling with probability proportional to size estimation technique produced better results when three or six branches per tree were sampled. However, the systematic sampling with ratio estimation technique was the best when at least nine branches per tree were sampled. Under the stratified sampling strategy, selecting unequal number of branches per stratum produced approximately similar results to simple random sampling, but it further decreased RMSE when information on branch diameter is used in the design and estimation phases. Conclusions: Use of auxiliary information in design or estimation phase reduces the RMSE produced by a sampling strategy. However, this is attained by having to sample larger amount of biomass. Based on our finding we would recommend sampling nine branches per tree to be reasonably efficient and limit the amount of fieldwork. Keywords: Aboveground biomass; Crown; Sampling strategies; Pacific Northwest * Correspondence: Hailemariam.Temesgen@oregonstate.edu Department of Forest Engineering, Resources, and Management, College of Forestry, Oregon State University, 280 Peavy Hall, Corvallis, OR 97331, USA Full list of author information is available at the end of the article © 2015 Poudel et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. Poudel et al. Forest Ecosystems (2015) 2:1 Page 2 of 11 Background The common understanding among researchers and The global issue of climate change and an increasing practitioners is that an accurate carbon stock estimate interest in the reduction of fossil fuel carbon dioxide requires improved and consistent methods for tree and emissions by using forest biomass for energy produc- component biomass estimation (Hansen 2002; Zhou and tion has increased the importance of forest biomass Hemstrom 2009). quantification in recent years. Different national and Crown biomass is the oven dry weight of the entire international reports have presented the amount of crown, including the leading shoot above the last- carbon sequestered by forest ecosystems. For example, formed whorl, excluding the main bole (Hepp and the Intergovernmental Panel on Climate Change reports Brister 1982). The components of crown biomass are that forests contain about 80% of aboveground and 40% wood, bark, and foliage weights. Crown biomass of belowground carbon stock (IPCC 2007). Addition- accounts for a significant portion of total tree biomass ally, it is reported that the amount of carbon stored in but the amount and its distribution vary by tree and dry wood is approximately 50% by weight (Brown 1986; site characteristics. Using the data from two Alaskan Paladinic et al. 2009; Sedjo and Sohngen 2012). Picea mariana ecosystems, Barney et al. (1978) re- Biomass, in general, includes both above and below ported that foliage comprised 17% to 37% of the total ground living and dead mass of trees, shrubs, vines, and tree mass for the lowland stands and 17% to 50% of the roots. However, most of the researches on biomass total tree mass in the upland stands. Total bole mass estimation have focused on aboveground biomass ranged from 11% to 58% in lowland stands and 21% because of the difficulty in collecting belowground data to 61% in the upland stands. In a study to determine (Lu 2006). The amount of biomass in a forest is influ- the patterns of biomass allocation in dominant and enced by various site factors such as stand density and suppressed loblolly pine (Pinus taeda), Naidu et al. site productivity; soil characteristics such as texture (1998) found that the dominant trees allocated 24.5% and moisture content; and tree characteristics such of biomass to the crown (13.2% in branch and 11.3% in as species and age. On the other hand, distribution needle) and the suppressed trees allocated 12.3% (6.7% of crown biomass affects the carbon cycle, soil nutrient in branch and 5.6% in needle). Kuyaha et al. (2013) allocation, fuel accumulation, and wildlife habitat found that crown biomass formed up to 26% (22% in environments in terrestrial ecosystems and it governs branch and 4% in needle) of aboveground biomass in the potential of carbon emission due to deforestation farmed eucalyptus species. In assessing the importance (Lu 2005). The major components of aboveground tree of crown dimensions to improve tropical tree biomass biomass are merchantable stem biomass (bole including estimate, Goodman et al. (2013) found the trees in bark and wood), stump biomass, foliage biomass, and their study to have nearly half of the total aboveground branches/top biomass (Zhou and Hemstrom 2009). tree biomass in branches (44% ± 2%). The common biomass estimation approach selects Estimates of crown biomass for each stand condition some trees, which are representative of the populations is necessary to understand nutrient depletion and for of interest, for destructive sampling and weighs their evaluating the economic feasibility of crown utilization components. Regression models are then fit to relate for energy production or forest products (Hepp and some easily measurable attributes, such as diameter at Brister 1982). Furthermore, estimates of crown biomass breast height and total tree height, with tree (or compo- aid in fuel load assessments and fire management strat- nent) biomass. The amount of biomass distributed in egies (He et al. 2013) because it is one of the important different components is dependent on species and their input variables in most wildfire models (Saatchi et al. geographic location (Pooreter et al. 2012), management 2007). Much of the focus in estimating crown biomass practices (Tumwebaze et al. 2013) and tree size and has been in the form of regression models and in the selection of predictor variables rather than in the stand density (Jenkins et al. 2003). Ritchie et al. (2013) found that for the given DBH and crown ratio, thinned methods of sample selection. In addition, comparisons stands had more foliage biomass but slightly less branch of sampling strategies have been carried out mainly for foliar biomass sampling rather than the total crown biomass than unthinned stands. Similarly, the contribu- tion of component biomass to the total aboveground (branch wood, bark, and foliage) biomass. Thus, the biomass varies by tree size (de-Miguel et al. 2014b). evaluation of different sampling designs and sample size in estimating crown biomass is an important Henry et al. (2011) found differences in biomass due to floristic composition, tree species and growth strategies aspect of aboveground biomass estimation. for the tree species within a given climatic zone. Thus, Common sampling strategies used in aboveground the component biomass estimations, for example branch biomass estimation include simple random sampling, or crown biomass, bole biomass, and bark biomass, are systematic sampling, stratified random sampling, and important to account for the variability within the tree. randomized branch sampling. The suitability of a technique Poudel et al. Forest Ecosystems (2015) 2:1 Page 3 of 11 is determined by the availability of funds, required accuracy, with ratio estimation as the most efficient estimate of structure and composition of vegetation, and desired individual tree foliage biomass. de-Miguel et al. (2014a) specificity of estimation (Catchpole and Wheeler 1992). developed generalized, calibratable, mixed-effects meta- Additionally, the amount of time a particular technique models for large-scale biomass prediction. One of their takes to implement in the field is also important. The objectives was to investigate and demonstrate how the simple random sampling is generally used as the basis biomass prediction differed when calibration trees were to evaluate the performance of other sampling designs selected using different sampling strategies. They found (e.g. Snowdon 1986; Temesgen 2003). that a stratified sampling was better compared to the Gregoire et al. (1995) have proposed a number of sam- simple random sampling. Thus there is no strong rationale pling procedures (randomized branch sampling, import- to support one method as being superior to another. ance sampling, control-variate sampling, two-stage and Crown biomass is difficult to predict because of the vari- three-stage sampling) that can be used to estimate foliage ability within and among species and various sites. A good and other characteristics of individual trees. The random- allometric equation for predicting aboveground biomass ized branch sampling (RBS) was originally introduced by should be based on data collected with an appropriate Jessen (1955) to determine the fruit count on orchard (precise and unbiased) sampling method. In this context, trees. Valentine and Hilton (1977) used this method to the objective of this study was to evaluate different obtain estimates of leaf counts, foliar area, and foliar mass sampling strategies to estimate crown biomass. We also of mature Quercus species. Good et al. (2001) have evaluated how the performance of different methods was employed RBS with importance sampling for estimating affected when different number of branches (3, 6, 9, and tree component biomass. Since the sample is accumulated 12) per tree was sampled in estimating crown biomass. sequentially along the path, RBS does not require locating and counting the total number of branches beforehand. Methods However, Chiric et al. (2014) posed some doubts on the ef- Study area fectiveness of RBS in sampling big trees or trees with ir- This study was conducted in the McDonald-Dunn regular forms. According to Valentine and Hilton (1977), Forest, an approximately 4,550 ha property, managed by the the accuracy of RBS is largely dependent on the probabil- Oregon StateUniversityin the westernofthe edge of ity assignment and the time required to take RBS samples the Willamette Valley in Oregon and on the eastern depends on the size of the trees and experience of those foothills of the Coast Range (123°15' W, 44°35' N, 120 m taking the samples. elevation). The forest consists predominantly of the Swank and Schreuder (1974) compared stratified two- Douglas-fir (Pseudotsuga menziesii (Mirbel) Franco) and a phase sampling, two-phase sampling with a regression small Grand fir (Abies grandis (Dougl. ex D. Don) Lindl.) estimator, and two-phase sampling with a ratio-of-means and has a wide range of overstory age-class distribution estimator. They found the stratified two-phase sampling with majority of the stands less than 80 years old and as the most precise and appropriate method for estimat- some stands that are 80 to 120 years old. The forest ing surface area and biomass for a young eastern white receives approximately 110 cm of annual rainfall and aver- pine forest. Temesgen (2003) found that stratified age annual temperature ranges from 6°C to 17°C. random sampling produced the lowest mean squared error value in comparing five sampling designs to quan- Data tify tree leaf area. Stratification in branch biomass Twenty sample trees (11 Douglas-fir and 9 Grand fir) sampling can be done in many different ways. Snowdon were subjectively selected from stands of different ages (1986) showed improved accuracy of estimates by strati- for destructive sampling avoiding the trees with obvious fication based on crown position compared to those defects and trees close to stand edges. The field work obtained by simple random sampling, especially at low was carried out between the first week of July and third sampling intensities. Their findings suggest that stratifi- week of September 2012. Trees that were forked below cation by whorl was slightly but not significantly inferior breast height and with damaged tops were not included to stratification based on crown position or branch in sampling. Tree level attributes including total height, diameter. Another approach used in selecting branches height to the base of first live branch, crown width, and for estimating crown biomass is to divide the bole into main stem diameter at 0.15, 0.76, 1.37, and 2.40 m above sections and pile up the branches from each section into ground, and every 1.22 m afterwards were recorded. The different size classes and randomly select a number of branches were divided into four diameter classes (1.3 cm branches proportional to the total number of branches in class = 0–2.5 cm, 3.8 cm class = 2.6–5.1 cm, 6.4 cm class = each size class (e.g. Harrison et al. 2009, Devine et al. 5.2–7.6 cm, 8.9 cm class = 7.7–10.2 cm). For all first order 2013). In an evaluation of ten different sampling strategies, branches, height to- and diameter- at branch base were Temesgen et al. (2011) found that systematic sampling measured. Poudel et al. Forest Ecosystems (2015) 2:1 Page 4 of 11 For the first and every third branch, when proceeding the best fit (Adj-R = 0.93), therefore was used to predict from the base, in each diameter class, length and weight individual branch biomass within each tree. of both live and dead branches were recorded. From those selected branches, four branches per diameter ln y ¼ β þ β ln BD þ β ln BL þ ε ð2Þ ij ij ij ij 0i 1i 2i class were weighed with and without foliage. The nee- dles were removed in the field to obtain the green where y , BD and BL are oven dry weight (kg) of branch ij ij ij weight of foliage and branch wood with bark. Two of (wood, bark, and foliage combined), branch diameter th th these four branches were taken to the lab, keeping (cm), and branch length (m) of the j branch on i tree branch and foliage in separate paper bags, for drying. respectively; β ‘s are regression parameters to be esti- ij The branches were chipped in to small pieces to exped- mated; ln(·) is the natural logarithm; and ε ‘s are the ran- ij ite the drying process and placed in a kiln for drying at dom error. The full model included other variables such 105°C. The oven dry weight was recorded by tracking as height to the base of the branch, crown width and the weight lost by each sample until no further weight crown length, but were dropped because they were not was lost. Table 1 presents the tree and branch level sum- statistically significant (p-value > 0.05). Lengths for the rd mary of the felled-tree data used in this study. 2/3 branches (not measured in the field) were obtained by fitting the following log linear model (Adj-R =0.74): Individual branch biomass ln BL ¼ β þ β ln BD þ β ln RBD þ ε ð3Þ ij ij ij ij Kershaw and Maguire (1995) developed a tree specific 0i 1i 2i log linear model (Equation 1) using branch diameter where BD , BL , and ε are same as defined in Equation 2 ij ij ij (BD) and depth into the crown (DINC: the distance and RBD is the relative branch depth (relative position of ij from tip to the base of the branch) as covariates to esti- th th the subject branch from the crown base) of j branch in i mate branch foliage biomass. Temesgen et al. (2011) tree and is computed as follows (Ishii and Wilson 2001): successfully used this model in comparing sampling strategies for tree foliage biomass estimation. total tree height−height to the base of subject branch RBD ¼ total tree height−height to the base of lowest live branch The RBD is 1.0 for the first live branch. The logarith- ln y ¼ β þ β ln BD þ β ln DINC ij ij ij 0i 1i 2i mic regressions are reported to result in a negative bias þ ε ð1Þ ij when data are back transformed to arithmetic scale. The commonly used remedy to this is to multiply the back MSE transformed results by a correction factor exp , This model was modified by replacing DINC with branch length (Equation 2). The modified model provided where MSE is the mean squared error obtained by the Table 1 Summary of felled-tree and branch-level attributes used in this study Variable n Mean SD Minimum Maximum Tree data DBH (cm) 62.8 27.0 23.9 114.0 Height (m) 34.6 10.3 18.3 46.5 Crown base height (m) 10.2 6.3 0.8 23.7 Crown length (m) 24.4 6.2 12.2 34.4 Crown width (m) 8.6 2.4 5.2 13.4 Branch data Diameter (cm) 3464 3.7 2.1 0.8 10.4 Length (m) 1178 2.8 1.6 0.1 10.2 Total green weight (kg) 1102 4.14 5.61 0.05 46.99 Green weight of branch wood (kg) 326 3.98 5.61 0.05 38.01 Green foliage weight (kg) 264 1.80 1.84 0.05 9.71 Total dry weight (kg) 128 3.44 4.08 0.12 18.40 Dry weight of branch wood (kg) 128 2.68 3.49 0.07 15.37 Dry foliage weight (kg) 128 0.76 0.79 0.04 4.58 Poudel et al. Forest Ecosystems (2015) 2:1 Page 5 of 11 least-squares regression. However, there are conflicting selection, first a random starting point between 1 and total remarks about the correction factor itself. For example number of branches was randomly chosen, the interval Beauchamp and Olson (1973) and Flewelling and then is added obtaining exactly n (sample size) branches. Pienaar (1981) suggested that this correction factor was Then the numbers are divided by the sample size and still biased because the sample variance is consistent rounded to the nearest whole number to get the selected but it is biased for finite sample sizes. We did not use samples. the correction factor in our study. The trend in the Methods 6–11 belonged to different stratified sampling relationship between crown biomass and branch diameter strategies. The stratified sampling method divides the popu- and length was similar but the variability in biomass lation into subpopulations of size n ,where n is the h h increased with increasing branch length (Figure 1). All number of elements in stratum h. The total crown length statistical procedures were performed using statistical was divided into three sections having equal number of software R (R Core Team 2014). branches as three strata. In methods 6 (STR) and 7 (STR- RAT), n/3 branches were randomly selected with equal Methods for crown biomass sampling probability, where n is the sample size. Again, the difference We evaluated 11 sampling methods to select branches for between these two methods lies in the estimation of total estimating crown biomass. The 11 sampling strategies crown biomass. STR method uses the SRS estimation tech- belonged to three main categories: simple random nique while STR-RAT method uses the ratio estimation sampling, systematic sampling, and stratified sampling. technique to obtain the total crown biomass. Method 8 Methods 1 and 2 are based on simple random sampling (STR-PPS), stratified sampling with PPS, selected branches (SRS) strategy. In each of these methods, each branch was in each stratum with probability proportional to the square chosen randomly such that each individual branch has of branch diameter. Total crown biomass in this method equal probability of selection at any stage of selection. The was obtained by summing the stratum total crown biomass difference in these methods is in the estimation of total calculated using Horvitz-Thompson unequal probability tree biomass: method 1 uses SRS estimator while method estimator (Horvitz and Thompson 1952). 2 (SRS-RAT) uses the ratio estimator with squared branch Methods 9–11 (stratified, unequal) are based on the idea diameter as auxiliary information. Method 1 is also the that the distribution of crown biomass in different strata basis for comparing the performance of other methods. depends on the relative position of the branches in the tree. Method 3, probability proportional to size (PPS), uses Ishii and McDowell (2001) found that mean branch branch size as auxiliary information in sample selection. volume increased from upper- to lower-crown. For a given Total crown biomass in this method was calculated using density, biomass (oven dry weight) is the function of Horvitz-Thompson estimator (Horvitz and Thompson volume. Therefore, the stratified sampling method was 1952). Methods 4 (SYS) and 5 (SYS-RAT) are systematic modified to incorporate the variability of biomass distribu- sampling with similar design phase but different estima- tion within a tree. Trees were first divided into three sec- tion phase. Method 4 uses the SRS estimator while tions having equal number of branches. Then, 4, 3, and 2 method 5 uses the ratio estimator. The fractional inter- branches from the lower, middle, and upper section of the val systematic sample selection procedure was used in trees were selected respectively. This corresponds that the the systematic selection of the branches because it number of branches selected in each section is propor- ensures the equal probability of selection for all the tional to the observed biomass in that section of the tree. branches (Temesgen et al. 2011). The interval was Because stratification based on crown length resulted in determined based on the total number of branches the biased estimation of crown biomass, the balanced in each tree. In fractional interval systematic sample stratification method was applied. The total number of Figure 1 Scatterplot of dry biomass (kg) against branch diameter (a) and branch length (b) by species (DF = Douglas-fir, GF = Grand fir). Poudel et al. Forest Ecosystems (2015) 2:1 Page 6 of 11 Table 2 Summary of methods used for crown biomass estimation in this study Methods Equations for total crown biomass Selection probability Inclusion probability Simple random sampling 1 1 n SRS ^ τ ¼ NB y i i ij n NB NB i i j¼1 NB y X ij j¼1 2 1 n ^ X SRS-RAT τ ¼ BD i n ij NB NB i i BD ij j¼1 j¼1 X 2 y BD ij ij PPS PPS ^ τ ¼ π ¼ X π ¼ 1− 1−π i PPS ij ij NB ij ij BD j∈S ij j¼1 Systematic sampling 1 n n SYS τ ¼ NB y i i n ij NB NB i i j¼1 NB y X ij j¼1 2 n n ^ X SYS-RAT τ ¼ BD i n ij NB NB i i BD ij j¼1 j¼1 Stratified sampling H n XX 2 BD N ij n ih h STR τ ¼ y X n ijh NB N h ih BD h¼1 j¼1 ij j¼1 X X H n ih y 2 n ijh h BD h¼1 j¼1 ij n STR-RAT τ ¼ X X X H n NB N h ih ih 2 2 BD BD n ijh ij h¼1 j¼1 h j¼1 XX 2 y BD ijh ijh STR−PPS STR-PPS ^ τ ¼ X π ¼ 1− 1−π ij iSðÞ TR−PPS ðÞ STR−PPS NB ij ih ijh BD h¼1 j∈S h ijh j¼1 th th th th Notation: ^ τ is the estimated total crown biomass for i tree; y is the oven dry weight of j branch on i tree; NB is the number of branches on i tree; n is ij i th th th number of branches sampled; N is the number of branches in h stratum on i tree; and n is the number of branches sampled in h stratum. ih h branches selected in each tree (nine) was determined based sampling with equal number of branches per stratum. on the amount of biomass sampled. Total crown biomass Methods 9–11 were based on selecting nine branches in in each stratum was computed using the SRS estimation each tree. Table 2 summarizes the inclusion probability, technique in method 9 (Un-STR), PPS in method 10 (Un- selection probability, and the estimator of the total crown PPS), and ratio estimation in method 11 (Un-STRRAT). biomass in each of the sampling strategies evaluated in Total crown biomass in each tree was computed by sum- this study. ming the crown biomass in each stratum. The unequal branch selection strategy was also evaluated using similar Evaluation of sampling strategies evaluation statistics used for the other eight methods. We evaluated the performance of 11 sampling strategies to Performances of first eight methods were evaluated by estimate crown biomass using the following six statistics selecting four different sample sizes (3, 6, 9, and 12) in estimated from 5,000 iterations. These measures were suc- each tree. These sample sizes were chosen for the ease of cessfully used to evaluate the performance of sampling strat- distributing samples into three different strata in stratified egies to estimate foliage biomass in Temesgen et al. (2011). Table 3 Average bias (kg) produced by different sampling methods and sample sizes based on 5,000 simulations Sampling strategies Sample size SRS SRS-RAT PPS SYS SYS-RAT STR STR-RAT STR-PPS 3 0.237 −4.091 −0.158 0.433 −9.320 −0.659 −3.554 −0.104 6 0.215 −1.711 0.010 0.139 −1.922 0.399 −1.387 −0.101 9 −0.081 −0.937 −0.068 0.133 0.166 0.191 −0.857 −0.094 12 −0.030 −0.894 0.158 0.043 −0.078 −0.242 −0.776 −0.073 Poudel et al. Forest Ecosystems (2015) 2:1 Page 7 of 11 Table 4 Relative bias (percent) produced by different sampling methods and sample sizes based on 5,000 simulations Sampling strategies Sample size SRS SRS-RAT PPS SYS SYS-RAT STR STR-RAT STR-PPS 3 0.101 −2.437 −0.169 0.107 −6.086 −0.321 −2.107 −0.034 6 −0.001 −1.115 0.024 0.061 −1.061 0.197 −0.900 −0.012 9 0.063 −0.600 −0.027 0.038 0.033 0.148 −0.543 −0.069 12 −0.011 −0.523 0.100 0.037 0.032 −0.035 −0.439 −0.040 1. Bias: For each tree the bias (kg) was calculated as amount of crown biomass sampled. Therefore the the mean difference between observed and predicted amount of crown biomass sampled was also used as total crown biomass for that tree as follows: a criterion for the evaluation of sampling strategies. The amount of crown biomass sampled (sampling intensity) is calculated as follows: B ¼ ðÞ τ −τ^ i is is s¼1 XX BS ¼ y ijs where τ and τ^ are the observed and predicted is is th th s¼1 j∈S total crown biomasses for i tree in s iteration, th respectively. y is the observed total crown biomasses for i tree, ijs th th j sample branch in s iteration. 2. Relative bias: Relative bias percentage is the ratio of bias to the total observed crown biomass for that 6. Relative biomass sampled (RBS%) indicates the tree and computed as follows: proportion of crown biomass sampled with respect to the total crown biomass measured and is 1 ðÞ τ −τ^ is is RB ¼ calculated as follows: 5000 τ is s¼1 XX ijs where all the variables are same as defined RBS ¼ ij 5000 τ ijs s¼1 j∈S previously. 3. Root mean square error (RMSE): Results and discussions vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Except for the ratio estimators, the estimators of popula- u X tion totals were unbiased, with biases close to zero for RMSE ¼ ðÞ τ −τ^ i is is s¼1 all sample sizes (Tables 3 and 4). The squared bias for these methods ranged from zero to 0.435 kg. Ratio esti- 4. Relative RMSE: mators resulted in greater bias than the other methods. vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi The absolute bias of the ratio estimators decreased with 5000 2 u X ^ increasing sample size as expected. 1 τ −τ is is R−RMSE ¼ As expected, the RMSE (and relative RMSE) decreased 5000 τ is s¼1 with increasing sample size (Tables 5 and 6) for all sam- pling strategies. Based on the RMSE values obtained 5. Biomass sampled (BS): Amount of cost for crown from 5,000 simulations, the stratified sampling with biomass estimation is directly proportional to the PPS estimation was the superior method compared to Table 5 Average RMSE produced by different sampling methods and sample sizes based on 5,000 simulations Sampling strategies Sample size SRS SRS-RAT PPS SYS SYS-RAT STR STR-RAT STR-PPS 3 88.57 42.56 38.04 113.17 48.54 85.05 42.08 34.95 6 60.49 30.01 29.23 57.94 29.98 58.54 29.56 27.99 9 48.60 23.92 25.19 37.88 22.12 46.48 23.55 24.46 12 40.77 20.18 22.78 30.77 17.91 38.89 19.75 22.33 Poudel et al. Forest Ecosystems (2015) 2:1 Page 8 of 11 Table 6 Relative RMSE percent produced by different sampling methods and sample sizes based on 5,000 simulations Sampling strategies Sample size SRS SRS-RAT PPS SYS SYS-RAT STR STR-RAT STR-PPS 3 55.70 25.72 23.46 72.02 28.80 53.41 25.61 21.57 6 38.07 17.93 18.23 35.23 17.53 36.63 17.78 17.59 9 30.38 14.19 15.83 23.58 13.29 29.03 14.07 15.55 12 25.42 11.92 14.40 18.37 11.11 24.27 11.76 14.22 all other methods when sample size is 3 or 6 branches is obtained by sampling just a little more amount of per tree. However, while using PPS, stratification of the biomass(1.03 timeson average). crown into sections did not reduce the RMSE and relative Use of allometric equations is inevitable in above- RMSE significantly. On the other hand, when at least nine ground biomass estimation because weighing the trees branches per tree were sampled, the SYS-RAT was the and their components for direct biomass determination best and the SRS-RAT was the second best method. is destructive and prohibitively expensive. Choice of Number of branches required to achieve desired preci- biomass sampling strategy determines the quality of data sion is another important aspect of estimating crown available for fitting such equations. Use of auxiliary biomass. On average, the RMSE decreased by 34.3% information in design and/or estimation phase (ratio when the sample size increased from three branches per estimation and PPS) produced better results in terms of tree to six branches per tree. The RMSE further decreased RMSE compared to the methods that do not make use by 22.1% and 15.4% when the sample size increased from of such information in this study. Previous researches 6 to 9 and 9 to 12 respectively. (e.g. Temesgen et al. 2011) have also shown the benefits The amount of biomass sampled determines the cost from using auxiliary information in the design and/or that would be incurred in estimating crown biomass. estimation concerning tree biomass. Biomass sampled and relative biomass sampled in differ- The model used in estimating branch biomass which ent sampling strategies are presented in Tables 7 and 8. is later used as a dependent variable in the test popula- The Strategy-Cost-Accuracy graph (Figure 2) shows the tion, was a logarithmic model (Equation 2). There is efficiency trade-off across the strategies compared in the an inherent negative bias in this method because the study. The SRS and SYS methods resulted in the lowest dependent variable is transformed prior to estimation amount of biomass sampled. On average, the amount of (Snowdon 1991). The ratio estimation strategies, SRS- biomass sampled using the PPS method was 1.6, 1.5, 1.4, RAT, SYS-RAT, and STR-RAT in this study, were nega- and 1.4 times higher than the amount of biomass sampled tively biased. However, in terms of RMSE, these strategies in stratified random sampling when 3, 6, 9, and 12 were clearly superior methods compared to the SRS branches per tree were selected respectively. approach. As noted in Temesgen et al. (2011), however, On average, selecting 12 instead of 9 branches per tree the efficiency of sampling strategies with ratio estimation increased the amount of biomass sampled by 29.2%. may be affected by the amount of work and difficulty in Therefore, nine branches in each tree were selected in implementing these techniques in the field. evaluating the performance of unequal stratified sam- The amount of biomass sampled determines the cost pling strategy. Results from unequal branch selection are that would be incurred in estimating crown biomass. presented in Table 9. This strategy reduced the relative Choice of a sampling strategy determines the amount of RMSE by 0.6%, 4.5% and 3.5% compared to selecting biomass and relative biomass sampled. This ultimately 9 branches using stratified random sampling, stratified determines the amount of time and cost required for a biomass estimation project. The SRS and SYS methods sampling with ratio estimation, and stratified sampling with PPS respectively. This reduction in relative RMSE resulted in the lowest amount of biomass sampled. Our Table 7 Amount of biomass sampled (kg) by different Table 8 Relative amount of biomass sampled (%) by sampling strategies and sample sizes different sampling strategies and sample sizes Sampling strategies Sampling strategies Sample size Sample size SRS PPS SYS STR STR-PPS SRS PPS SYS STR STR-PPS 3 7.74 12.58 7.73 7.68 12.40 3 5.36 8.67 5.35 5.33 8.45 6 15.49 23.79 15.46 15.50 23.29 6 10.71 16.37 10.71 10.72 15.87 9 23.17 33.77 23.18 23.19 33.05 9 16.08 23.16 16.06 16.07 22.45 12 30.91 42.83 30.92 30.86 41.79 12 21.42 29.27 21.43 21.40 28.33 Poudel et al. Forest Ecosystems (2015) 2:1 Page 9 of 11 Figure 2 Relative RMSE (%) produced Vs. relative biomass sampled (percent of total crown mass) in different sampling strategies and sample sizes. results in terms of RMSE values reported and the the SYS-RAT was the best and the SRS-RAT was the amount of biomass sampled by each strategy are consistent second best method when at least nine branches per tree with the findings of Temesgen et al. (2011) in estimating were sampled. It should also be noted that the lower RMSE foliar biomass of Douglas-fir (Pseudotsuga menziesii var. values in the PPS estimation techniques are obtained menziesii)and ponderosapine(Pinus ponderosa). with an increased amount of biomass sampled in each tree. On the other hand, if the auxiliary information on Conclusions branch size is not used, the systematic sampling pro- Crown biomass estimation is a complex process that re- vided better results than the SRS or STR method when quires intensive manual field work involving destructive at least 6 branches per trees were selected. Thus the sampling. The amount of fieldwork required and the ac- selection of a specific sampling strategy is dependent curacy of biomass estimation is dependent on the sam- on the availability of the time and cost for the given pling strategy used. Furthermore, the accuracy of the biomass sampling project. Based on our finding we estimation can be improved by adopting appropriate would recommend sampling 9 branches per tree to techniques in both the design and estimation phases, obtain reasonable efficiency and amount of work in- beginning with the selection of sample plots and sample volved in the field. trees through model development. In this study, we The logic for selecting unequal numbers of branches evaluated 11 different sampling strategies that belonged per stratum within a tree is justified by the fact that the to three main categories: simple random sampling, biomass distribution within a tree is not uniform. Select- systematic sampling and stratified sampling. The SRS, ing equal branches per stratum produced approximately PPS, and ratio estimation techniques were used to similar results to unequal sampling when the SRS esti- obtain the total crown biomass in each tree. mation technique was used. However, making use of Based on the RMSE values obtained from 5,000 simu- auxiliary information on branch size in the design and lations, the stratified sampling with PPS estimation pro- estimation phases further decreased the relative RMSE. duced better results as compared to all other methods Once again, the decreased RMSE by use of auxiliary in- when 3 or 6 branches per tree were sampled. However, formation is attained by having to sample slightly higher Table 9 Evaluation statistics produced when selecting 4, 3, and 2 branches from lower, middle, and upper stratum Method Bias Relative bias RMSE Relative RMSE Biomass sampled Relative biomass sampled Un-STR 0.100 0.061 46.16 28.87 24.25 16.87 Un-STRRAT −0.731 −0.491 22.58 13.44 Un-PPS 0.140 0.063 23.67 15.00 33.85 23.04 Poudel et al. Forest Ecosystems (2015) 2:1 Page 10 of 11 amount of biomass. Findings of this study should prove Hansen M (2002) Volume and biomass estimation in FIA: national consistency vs. regional accuracy. In: McRoberts RE, Reams GA, Van Deusen PC, Moser beneficial for the stakeholders working in the field of JW (eds) Proceedings of the third annual Forest Inventory and Analysis aboveground biomass and carbon estimation. Additional symposium. General Technical Report NC-230. U.S. Department of work using the data from different species and location Agriculture, Forest Service, North Central Research Station, St. Paul, MN, pp 109–120 should be done to further validate the findings in this Harrison RB, Terry TA, Licata CW, Flaming BL, Meade R, Guerrini IA, Strahm BD, study. Xue D, Lolley MR, Sidell AR, Wagoner GL, Briggs D, Turnblom EC (2009) Biomass and stand characteristics of a highly productive mixed Douglas-Fir Competing interests and Western Hemlock plantation in Coastal Washington. West J Appl For The authors declare that they have no competing interests. 24(4):180–186 He Q, Chen E, An R, Li Y (2013) Above-ground biomass and biomass components Authors’ contributions estimation using LiDAR data in a coniferous forests. Forests 4:984–1002 KP designed the sampling experiments, performed the sampling Henry M, Picard N, Trotta C, Manlay RJ, Valentini R, Bernoux M, Saint-André L experiments, analyzed the data, and wrote the paper. TH conceived the (2011) Estimating tree biomass of sub-Saharan African forests: a review of sampling experiments, critically reviewed the manuscript, contributed to available allometric equations. Silva Fenn 45(3B):477–569 coding and data analysis, and edited the manuscript. AG critically reviewed Hepp TE, Brister GH (1982) Estimating crown biomass in loblolly pine plantations the manuscript, edited the manuscript and contributed ideas at all phases of in the Carolina Flatwoods. For Sci 28(1):115–127 the project. All authors read and approved the final manuscript. Horvitz DG, Thompson DJ (1952) A generalization of sampling without replacement from a finite universe. J Am Stat Assoc 47:663–685 Acknowledgements IPCC (2007) Climate change 2007: synthesis report. In: Core Writing Team, We thank Professors Lisa Madsen and Glen Murphy (both at Oregon State Pachauri RK, Reisinger A (eds) Contribution of working groups I, II and III to University) for their insights and comments on an earlier draft, and the the fourth assessment report of the intergovernmental panel on climate Forest Inventory Analysis Unit for funding the data collection and analysis change. IPCC, Geneva, Switzerland, p 104 phases of this project. Ishii H, McDowell N (2001) Age-related development of crown structure in coastal Douglas-fir trees. For Ecol Manag 169:257–270 Author details Ishii H, Wilson ME (2001) Crown structure of old-growth Douglas-fir in the western Department of Forest Engineering, Resources, and Management, College of Cascade Range, Washington. 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U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station, Portland, OR, p 18 Submit your manuscript to a journal and benefi t from: 7 Convenient online submission 7 Rigorous peer review 7 Immediate publication on acceptance 7 Open access: articles freely available online 7 High visibility within the fi eld 7 Retaining the copyright to your article Submit your next manuscript at 7 springeropen.com

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"Forest Ecosystems" – Springer Journals

Published: Dec 1, 2015

Keywords: Ecology; Ecosystems; Forestry

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