Forestry An International Journal of Forest Research

Forestry 2017; 90, 359–366, doi:10.1093/forestry/cpw044 Advance Access publication 9 September 2016

Form factor functions for nine commercial tree species in Bhutan

Jigme Tenzin1,2*, Tenzin Wangchuk3 and Hubert Hasenauer1

1Institute of Silviculture, University of Natural Resources & Life Sciences, Peter-Jordan-Str. 82, A-1190 Vienna, Austria 2Watershed Management Division, Department of Forests & Park Services (DoFPS), Ministry of Agriculture & Forests (MoAF), 11002 Downloaded from https://academic.oup.com/forestry/article-abstract/90/3/359/2605859 by guest on 09 March 2020 Thimphu, Bhutan 3Royal Manas National Park, DoFPS, MoAF, 31101 Gelephu, Bhutan

*Corresponding author. Tel: +43 147654 4073; Fax: +43 147654 4092; E-mail: [email protected]

Received 19 May 2016

Standing timber volume in combination with the expected volume increment rates derived from volume func- tions are essential for developing sustainable forest management plans. Tree volume cannot be measured dir- ectly. It is derived from the diameter at breast height, tree height and a so-called form factor, which reduces the volume of a cylinder to the actual tree form. In this paper, we test four different types of form factor func- tions (Pollanchütz, Short Swedish, Meyer and F. Evert) for estimating total merchantable timber volume of nine commercial tree species in Bhutan: Abies densa, Picea spinulosa, Pinus wallichiana, Tsuga dumosa, Pinus roxburghii, Castanopsis tribuloides, Quercus glauca, Quercus lanata and Quercus lamellosa. The data for fitting the form factor functions come from 395 felled trees. The resulting functions are evaluated using independent validation data. Fitted statistics for evaluation include: root mean square error and mean absolute deviation. Although all form factor functions performed similarly, we suggest that the Pollanschütz function because of its consistency in the estimated form factors for all tree species. The evaluation of the calibrated form factor functions by species exhibited consistent and unbiased predictions.

Introduction characterizes the shape of the tree (Burkhart and Tomé, 2012), whereas the stem taper is the relative rate of change in stem Forests provide services that are important for sustaining rural diameter with increasing height (Larson, 1963; West, 2009; livelihoods and national development, including timber produc- Burkhart and Tomé, 2012). tion (Führer, 2000). With the increasing demand for timber, the According to Philip (1994), there are three different form fac- correct and accurate assessment of forest growing stock (stem tor definitions: (1) the absolute form factor (based on cross- volume) in combination with volume increment predictions sectional area at the ground level), (2) the normal or Pressler’s derived from growth models are essential to ensure sustainable form factor (based on cross-sectional area at 0.9 of the total forest management (Martin, 1981; Tarp-Johansen et al., 1997; height measured from the tip) and (3) the artificial form factor Brooks et al., 2008; Hasenauer et al., 2012). The development of (based on cross-sectional area at breast height) which is consid- the United Nations Framework Convention on Climate Change’s ered the most useful one. Different methods, such as form fac- Reducing Emissions from Deforestation and Forest Degradation tor, form quotient, form point, taper tables, taper equation, (REDD+) also requires accurate volume predictions for deriving taper curve and formula, exist to express the stem form to cor- carbon stocks from our forests (United Nations Framework rectly determine the volume (Husch et al., 2002). If the form of Convention on Climate Change, 2014). a tree can be accurately determined, then the volume can also The volume of trees is commonly derived from the diameter at be correctly estimated (West, 2009). The standing volume can breast height (d.b.h.), height (h) and a form factor (f); which may be calculated within a 0.2 per cent error range if calculated with be seen as a reduction factor of a cylinder (with d.b.h. and h)to a form factor (Eastaugh, 2014) while an overestimation is evi- the actual form of the tree (Husch et al., 2002; Akindele and dent if only the d.b.h. and h are used in a volume LeMay, 2006; Adekunle, 2007). Stem form is an important com- equation (Hoyer, 1985; Socha and Kulej, 2007). ponent for volume estimation (Pollanschütz, 1965; Colgan et al., In an effort to increase mitigation options against climate 2014) as trees differ in shape due to different forest manage- change and to meet the increasing demand for sustainable for- ment practices (Larson, 1963; Ikonen et al., 2006), climatic/gen- est resources, Bhutan plans to bring large forest areas under etic factors (Socha and Kulej, 2005; Socha and Kulej, 2007), sustainable forest management. This will require accurate esti- species, age and d.b.h. (Avery and Burkhart, 2002) or by species mation methods for assessing forest resources, such as stand- composition and size (Adekunle et al., 2013). Stem form ing timber volume and volume growth (Forest Resources

© Institute of Chartered Foresters, 2016. All rights reserved. For Permissions, please e-mail: [email protected].

359 Forestry

Management Division, 2013). In Bhutan, the demand for timber The purpose of this study is to develop form factor functions has increased due to the rapid urbanization and construction for improving the volume predictions for five coniferous species, activities (Forest Resources Management Division, 2013; i.e. A. densa (fir), Picea spinulosa (spruce), Pinus wallichiana Department of Forests & Park Services, 2014). Approximately 9 (bluepine), T. dumosa (hemlock), P. roxburghii (chirpine) and four per cent of the 2.71 million hectares of total forested area are broadleaved species, i.e. C. tribuloides, Quercus glauca, Quercus under sustainable management (Department of Forests & Park lanata and Quercus lamellosa, the primary commercial tree spe- Services, 2014). cies in Bhutan. We (1) compare the performances of different Currently, tree volume is estimated with a general volume form factor functions and (2) select the most suitable one for equation using only d.b.h. and h. The results by species are avail- estimating stem volume.

able as so-called local volume tables. The general volume Downloaded from https://academic.oup.com/forestry/article-abstract/90/3/359/2605859 by guest on 09 March 2020 equations were developed during the forest inventory carried out in 1976 (Laumans, 1994) and the local volume tables were Material and methods developed by the Forest Resources Development Division, Department of Forests (Forest Resources Development Division, Data 2005). The local volume tables are currently being used in other The research material consisted of five conifers and four broadleaved areas of the country. However, it is speculated that the existing species along different elevation gradients from different regions of volume equations may overestimate/underestimate the vol- Bhutan. Data from 395 trees were used for model calibration. The ume, which suggests that the need for a systematic review of data were collected through destructive sampling that was carried the results and the equations that derived them (Rosset, 1999; out in timber harvesting areas as well as outside when the required Whitfield, 2001; Forest Resources Development Division, 2004). species were not available on the harvesting sites. For each sample For instance, the existing general volume equations for tree, the d.b.h. at 1.37 m and the total tree height after felling was Castanopsis tribuloides and Pinus roxburghii estimate a negative recorded. Diameter measurements were recorded at 1, 3, 5 and 7m volume for the smaller trees; the Tsuga dumosa and Larix grif- and then at intervals of 6 m along the rest of the stem until a 5 cm fithiana are two different species which share the same volume diameter was reached at the top. For the hardwoods, the main ter- equation; there is also only one volume equation for all minal leader was chosen for the diameter measurements along the Castanopsis and Quercus species; in the local volume table, stem. The measurements were recorded up until 5 cm top diameter to Castanopsis is grouped under the category of other broadleaves. address the fact that in Bhutan, small round wood is also harvested. Additional information, such as slope, topography and aspect were As an alternative to the existing volume equations, Schieler recorded for each tree. (1991) calculated the volume of Abies densa in Central Bhutan We obtained separate datasets for the four tree species (A. densa, by including the form factor in a volume equation in addition to P. spinulosa, P. wallichiana and T. dumosa) from the biomass fi d.b.h. and h. Whit eld (2001) suggested that adopting the equation development project of the Department of Forests & Park approach by Schieler (1991) to all tree species in Bhutan Services, Ministry of Agriculture & Forests. This additional dataset because volume calculations derived from form factors enhance (Table 1) was used for validation so that based on these validation the accuracy of the volume predictions (Adekunle et al., 2013). results, the best form factor function can be selected.

Table 1 Summary of the data used in the study showing the sample size and the mean, range and standard deviation of d.b.h., height, elevation and slope for all species

Species n d.b.h. (cm) h (m) Elevation (m.a.s.l) Slope (°)

Mean Range SD Mean Range SD Mean Range SD Mean Range SD

Data for calibration Abies densa 30 32.8 5.0–60.3 16.15 21.7 5.8–33.3 8.52 3597 3555–3600 11.42 29.0 20–30 2.42 Picea spinulosa 32 32.9 5.6–75.3 18.83 23.5 6.1–39.7 10.23 3604 3600–3670 17.22 30.6 30–37 1.90 Pinus wallichiana 34 37.0 4.6–95.8 25.15 24.0 6.2–51.5 11.93 –– – –– – Tsuga dumosa 46 34.6 6.4–107.4 22.05 20.9 5.8–43.3 9.10 3154 2760–3429 195.86 21.9 2–48 13.68 Pinus roxburghii 31 43.4 8.5–77.8 21.29 26.7 5.6–41.9 10.34 –– – –– – Castanopsis tribuloides 31 42.3 6.0–89.0 23.78 20.4 5.6–34.4 8.37 2268 1970–2590 202.45 37.0 5–60 15.59 Quercus glauca 31 39.1 4.2–77.2 22.95 18.9 5.9–36.0 7.63 2279 1950–2694 242.45 35.7 15–65 13.52 Quercus lanata 31 42.4 6.6–77.5 21.84 16.0 7.2–27.9 5.18 2091 1790–2506 142.81 32.0 0–60 12.91 Quercus lamellosa 20 46.0 24.3–72.5 13.07 20.9 15–29.0 3.60 1909 1895–1935 9.51 18.5 15–44 6.64 Data for validation A. densa 15 28.6 7.2–64.0 18.65 19.1 6.5–37.6 10.85 3231 2780–3430 156.69 29.6 14–47 14.86 P. spinulosa 26 44.9 7.1–95.0 29.72 27.7 6.8–46.0 14.02 3154 2920–3340 146.19 23.8 3–46 12.1 T. dumosa 43 42.7 8.3–86.5 21.28 26.8 7.9–46.4 9.42 2954 2820–3141 84.68 38.3 5–72 19.35 P. wallichiana 25 32.6 5.1–79.1 23.28 23.2 6.1–45.3 13.40 3013 2770–3860 255.74 15.6 3–22 3.72 n = number of trees; d.b.h. = diameter at breast height in centimetres; h = tree height in metres; – = information not available; SD, standard deviation.

360 Form factor functions

Form factor functions Analysis Standing tree volume (V) can be derived from the d.b.h., h and form Calculation of form factor factor f: We started our analysis by calculating the volume of the log ⎛ ⎞ ’ d. b .h.2 . π sections Vi by tree using Huber s formula: =()⎜ ⎟ Vhf⎝ ..⎠ 1 4 n ⎛ ⎞ D 2. π VV==⎜ 1 .6L ⎟ () Tree ∑ ii⎝ ⎠ where d.b.h. and h are in metres. i=1 4 The form factor refers to the characteristic shape of the tree and is the reduction factor of the cylinder volume to the actual tree volume. where Vi is the volume of the section i, Di is the mid-diameter of Downloaded from https://academic.oup.com/forestry/article-abstract/90/3/359/2605859 by guest on 09 March 2020 Different form factor functions are available for predicting the form fac- the section in metres and Li is the length of the section in tor based on d.b.h. and h. For our study, we consider the form factor metres. The sum of volume of the sections provided the true functions of Pollanschütz, Short Swedish, Meyer (equations 2–4) volume of an individual tree (equation 6). ’ (Pollanschütz, 1965) and F. Evert s Australian Function (equation 5) Next we calculated for this tree the volume of a cylinder (Evert, 1969): (VCylinder) with its d.b.h. in metres and h of the tree in metres:

⎛ 1 1 1 ⎛ 2 ⎞ fab=+⎜ .ln2 ( dbhb . . . )++ . b . +b . d. b. h. . π ⎝ 1 23 42 VhCylinder =()⎜ .7⎟ h dbh... dbh... ⎝ 4 ⎠ ⎞ 1 1 ⎟ ++b56. b . ()2 dbh.... h dbh....2 h⎠ Thus, for each tree in our dataset, we have the total ‘true’ tree volume from equation (6) and the volume of the cylinder ⎛ ⎞ from equation (7). The corresponding ratio provides the required ⎜ 1 h h ⎟ fab=+12. +b . +b 3. ()3 reduction or form factor by tree: ⎝ h d. b. h. d. b .h.2 ⎠ ⎛ ⎞ ⎜ VTree ⎟ fObserved =()8 1 1 1 ⎝ VCylinder ⎠ fa=+ b1. +b23. +b . d. b. h.2 . h d. b. h. . h d. b. h. 1 1 ++b45. b . ()4 h d. b. h.2 Selection of the form factor function ⎛ ⎞ We used the calibration dataset (Table 1) of the four species ⎜⎟1 1 1 fab=+1. +b23. +b . ()5 ⎝ d. b. h.2 . h h d. b. h.2 ⎠ (A. densa, P. spinulosa, P. wallichiana and T. dumosa) to start the process of model calibration for the four selected form factor where f is the form factor; in equation (2), d.b.h. and h are in decimetres functions (see equations 2–5). Parameters were estimated using and in equations (3–5) d.b.h. is in centimetres and h is in decimetres. the non-linear (nls) function of the R statistical software package

Table 2 Model fitting results for the validation data (only for the four species with validation data) for choosing the best form factor function

Species Obs. f Form factor function RMSE Rank MAD Rank Sum (rank)

A. densa 0.5590 Pollanschütz’s function 0.1147 3 0.0903 3 6 (3) Short Swedish’s function 0.1112 2 0.0861 2 4 (2) Meyer’s function 0.1225 4 0.0982 4 8 (4) F. Evert’s function 0.0958 1 0.0828 1 2 (1) P. spinulosa 0.5054 Pollanschütz’s function 0.0591 3 0.0405 2 5 (2) Short Swedish’s function 0.0521 1 0.0390 1 2 (1) Meyer’s function 0.0566 2 0.0416 3 5 (2) F. Evert’s function 0.0566 2 0.0416 3 5 (2) P. wallichiana 0.4986 Pollanschütz’s function 0.0499 1 0.0392 1 2 (1) Short Swedish’s function 0.0506 2 0.0402 2 4 (2) Meyer’s function 0.0522 3 0.0428 3 6 (3) F. Evert’s function 0.0548 4 0.0450 4 8 (4) T. dumosa 0.4820 Pollanschütz’s function 0.0487 1 0.0382 1 2 (1) Short Swedish’s function 0.0490 2 0.0385 2 4 (2) Meyer’s function 0.0516 3 0.0412 3 6 (3) F. Evert’s function 0.0541 4 0.0439 4 8 (4)

Obs. f = mean of observed form factor for the validation data; MAD = mean absolute deviation. Values in parentheses indicate average ranking of the models for each species.

361 Forestry

(R Core Team, 2015), requiring the parameters to have a signifi- Results and discussion cance level of α = 0.05 to be included in the final species model. Next, we obtained the parameter estimates by species and Model selection and validation form factor function and predicted the form factors for the The results of the two fit statistics criteria (1) RMSE and (2) MAD independent validation data to evaluate the performances suggest that the Pollanschütz function ranked highest for the according to the form factor functions. As a selection criteria, species P. wallichiana and T. dumosa, the Swedish function for we employed (1) root mean square error (RMSE) and (2) mean P. spinulosa and Evert’s function for A. densa (Table 2). However, fi absolute deviation (MAD) (Weiskittel et al., 2011)de ned as the results also indicate that the Pollanschütz function provides consistent and unbiased form factor predictions for all four spe- n 2

ˆ Downloaded from https://academic.oup.com/forestry/article-abstract/90/3/359/2605859 by guest on 09 March 2020 ∑(−YYi ) cies. Thus, we decided to select the Pollanschütz function (equa- RMSE= i=1 () 9 n tion 2) for our further analysis. We employed (1) MB, (2) SDR and (3) Student’s t test for fur- n ˆ ther assessment of the selected Pollanschütz function (Table 3). ∑−YYi MAD= i=1 () 10 The MB (equation 11) for A. densa, P. spinulosa, P. wallichiana n and T. dumosa ranged between 0.0207, 0.0159, 0.0126 and ˆ −0.0077, respectively (Table 3). The SDR between predicted vs where Yi is the observed form factor, Y is the predicted form fac- tor and n is the number of observations. observed form factors exhibited a value of 0.0568 or 11 per Model validation examines the usefulness or behaviour of the cent of the observed form factor for P. spinulosa, 0.1168 or 21 model by comparing predicted vs observed values using the per cent for A. densa, 0.0493 or 10 per cent for P. wallichiana ’ independent dataset (Rykiel, 1996; Hasenauer, 2006). Mean bias and 0.0487 or 10 per cent for T. dumosa. The paired Student s t 2 fi (MB), standard deviation of residuals (SDR), R values (correl- test shows P-values greater than 0.05, indicating no signi cant ation coefficient) (equations 11–13) and Student’s t test were differences between predicted and observed form factor values fi used for further assessment and evaluation of the selected (Table 3). The MB and SDR values are small with no signi cant function. Table 3 Validation results for the Pollanschütz function for predicting n ˆ the form factors with Student’s t test for the four species with separate ∑(−YYi ) MB= i=1 () 11 calibration and validation dataset n Species Statistical indices Student’s t test 2 ∑(−n YYˆ)− ∑n ( YYn − ˆ)/ i==11()i ()i i SDR = ()12 Obs. f Bias SDR t-Stat P-value n − 1 A. densa 0.5590 0.0207 0.1168 (21%) 0.6882 0.5026 ⎛ ⎞ ∑(−n ˆ)2 P. spinulosa 0.5054 0.0159 0.0568 (11%) 1.4363 0.1633 2 ⎜ i=1 YYi ⎟ R =−113⎜ ⎟ ()P. wallichiana 0.4986 0.0126 0.0493 (10%) 1.2728 0.2153 ⎝ n 2 ⎠ ∑(−)i=1 YYi T. dumosa 0.4820 −0.0077 0.0487 (10%) −1.0402 0.3042 ˆ where Yi is the observed form factor, Y is the predicted form fac- Notes: results displayed only for those species where separate model tor, Y is the mean of the observed form factor and n is the num- calibration and validation data were available. The t-stat and P-values ber of observations. for Student’s t test were generated using the R statistical package. Graphical analysis by plotting the residuals vs d.b.h. and h Values in parentheses are per cent of the observed value. Obs. f = mean and the Anderson–Darling test for assessing the normal distri- observed form factor for the validation dataset for the four species; bution of the residuals (R Core Team, 2015) were carried out. Bias = mean of difference between observed and predicted values.

Table 4 Final parameter estimates for the Pollanschütz function for all species based on all sample data

Species n Coefficient for the parameters Statistical indices

2 ab1 b2 b3 b4 b5 b6 R SDR

A. densa 45 0.5367 −0.0161 ns ns −0.0966 14.752 ns 0.45 0.0676 (12%) P. spinulosa 58 0.4505 ns −16.412 0.2808 −0.1530 14.270 ns 0.57 0.0385 (8%) P. wallichiana 59 0.6384 −0.0237 −39.308 ns −0.0861 43.190 −7.639 0.43 0.0446 (9%) T. dumosa 89 0.5425 −0.0194 −5.847 ns ns 4.994 ns 0.32 0.0427 (9%) P. roxburghii 31 0.5677 −0.0350 ns −0.1749 0.1534 ns −2.559 0.73 0.0398 (8%) C. tribuloides 31 0.3899 ns −4.394 0.2967 ns −7.239 ns 0.60 0.0449 (10%) Q. glauca 31 0.3397 ns −5.563 ns 0.1422 12.466 −11.026 0.57 0.0571 (16%) Q. lanata 31 0.5112 −0.0340 −21.385 ns ns 14.032 −1.515 0.84 0.0302 (9%) Q. lamellosa 20 0.2883 ns ns ns 0.7755 199.370 −434.582 0.32 0.0447 (10%) n = number of trees; ns = non-significant parameters; values in parentheses are in per cent of the observed values.

362 Form factor functions Downloaded from https://academic.oup.com/forestry/article-abstract/90/3/359/2605859 by guest on 09 March 2020

Figure 1 Trend analysis of residuals vs d.b.h. (cm) and h (m) for all the species to examine the model fitting of Pollanschütz function. differences between predicted and observed form factors. This Final model calibration and evaluation confirms the selection of the Pollanschütz function for predicting Based on the results of Tables 2 and 3,werefitted the selected the form factors. Pollanschütz function by obtaining all the available data

363 Forestry Downloaded from https://academic.oup.com/forestry/article-abstract/90/3/359/2605859 by guest on 09 March 2020

Figure 2 Evaluation of the selected Pollanschütz function by plotting the observed and predicted form factor against tree parameters of (1) d.b.h. (cm) and (2) h (m) for all the species.

(calibration and validation) for P. spinulosa, A. densa, P. wallichiana lamellosa) to estimate the final parameters. We combine both and T. dumosa as well as the data available of the remaining five datasets to ensure that we cover the full range of possible varia- species (P. roxburghii, C. tribuloides, Q. glauca, Q. lanata and Q. tions. The results for our nine commercial tree species analysed

364 Form factor functions

in this study are presented in Table 4. R2 and SDR (see Table 4) are provided to assess the final form factor functions for each Acknowledgements species (Zhang, 1997; Brooks et al., 2008). The BC-CAP project was executed by the Department of Forests & Park The SDR ranged between 0.0302 and 0.0676 and the R² Services (DoFPS), Ministry of Agriculture & Forests, Royal Government of explained ~32 per cent to 84 per cent of the variation, Bhutan (RGoB) and the University of Natural Resources and Life depending on the tree species (Table 4). The lowest SDR and Sciences, Austria. We thank Georg Gratzer, Lobzang Dorji, Pema Wangda, highest R2 confirm the precision and accuracy of the Purna B. Chettri and Andras Darabant for the managerial support and Pollanschütz function in predicting form factors (Teshome, Mr Yograj Chhetri for coordinating and arranging of the validation data. 2005; Brooks et al., 2008; Weiskittel et al., 2011)(Table4). SDR Gratitude to Yograj Chhetri, Kezang Yangden, Madan Lama and Harka Bdr for their support during the field work. We thank Younten Phuntsho, is a common measure for predictive values of a non-linear Downloaded from https://academic.oup.com/forestry/article-abstract/90/3/359/2605859 by guest on 09 March 2020 Kinley Dem and Saran Pradhan for providing information on forest regression where low values indicate better fit(Akindele and management, and Adam Moreno for English editing. We also thank the LeMay, 2006). editor and the anonymous reviewers for their helpful suggestions. Graphical presentation of the residuals exhibited no system- atic trend or bias in the resulting form factor estimates (Figure 1). The Anderson–Darling test revealed P-values of more than 0.05, confirming normal distribution of the residuals. Conflict of interest statement None declared.

Form factor predictions The predicted form factors gradually decrease with increasing d. Funding ‘ b.h. and h and remain constant at a d.b.h. > 60 cm (Figure 2). This work was supported by the project Climate change adaptation These trends are a typical behaviour and were also observed in potentials of forests in Bhutan-building human capacities and knowledge base (BC-CAP)’ with funding from the Austrian Government through the previous studies as given by Pollanschütz (1965) using more Austrian Federal Ministry of Agriculture, Forestry, Environment and Water than 10 000 trees to provide form factors for all main tree Management (BMLFUW-UW.1.3.2/0124-V/4/2013). Calibration data (Pinus species in Austria or by Sendi et al. (2014) for form factors of roxburghii, Quercus glaucaandQuercus lanata) and validation data (Picea Tilia begonifolia as well as by Gezahgn (2015) for form factors spinulosa, Abies densa, Pinus wallichiana and Tsuga dumosa) were of 20 broadleaved tree species in Ethiopia. The predicted obtained from the Biomass equation development project of Department mean form factor values derived from the Pollanschütz func- of Forests & Park Services, Ministry of Agriculture & Forests, Royal tion and the species-specific parameter estimates in Table 4 Government of Bhutan (RGoB), the part which was funded by the Bhutan are 0.490 (P. spinulosa), 0.493 (A. densa), 0.548 (P. wallichiana), Trust Fund for Environmental Conservation and RGoB. 0.491 (T. dumosa), 0.479 (P. roxburghii), 0.458 (C. tribuloides), 0.436 (Q. lamellosa), 0.354 (Q. glauca) and 0.336 for Q. lanata (Figure 2). For none of these tree species, form factor estimates are References available for comparison. The only exception is a study by Adekunle, V. 2007 Non-linear regression models for timber volume esti- Schieler (1991) for A. densa in Central Bhutan. In this study, mation in natural forest ecosystem, Southwest Nigeria. Res. J. For. 1, Schieler (1991) used a different dataset for this species and 40–54. 2 calibrated a form factor function with an R of 0.25 and a Adekunle, V., Nair, K., Srivastava, A. and Singh, N. 2013 Models and form mean form factor of 0.591, while our study revealed an R2 factors for stand volume estimation in natural forest ecosystems: a case valueof0.45andanestimatedmeanformfactorof0.548for study of Katarniaghat Wildlife Sanctuary (KGWS), Bahraich District, A. densa. Our form factor predictions using the Pollanschütz India. J. For. Res. 24, 217–226. approach ranged from 0.479 to 0.548 for the conifer species Akindele, S. and LeMay, V. 2006 Development of tree volume and from 0.348 to 0.458 for the broadleaved species and thus equations for common timber species in the tropical rain forest area of is within the range of 0.25 and 0.50 according to West Nigeria. For. Ecol. Manage 226,41–48. (2009). Avery, T.E. and Burkhart, H.E. 2002 Forest Measurements. McGraw Hill Higher Education. Brooks, J.R., Jiang, L. and Ozçelik, R. 2008 Compatible stem volume and taper equations for Brutian pine, Cedar of Lebanon, and Cilicica firin Conclusions Turkey. For. Ecol. Manage 256, 147–151. We developed form factor functions for nine commercial tree Burkhart, H.E. and Tomé, M. 2012 Modeling Forest Trees and Stands. species in Bhutan to allow accurate and consistent volume and Springer Science & Business Media. volume increment predictions, key information needs within Colgan, M.S., Swemmer, T. and Asner, G.P. 2014 Structural relationships sustainable forest management. The form factor functions for between form factor, wood density, and biomass in African savanna the nine tree species presented in this study are the first in the woodlands. Trees 28,91–102. region and allow for a species-specific volume assessment. The Department of Forests & Park Services 2014 Forestry Statistics 2014. selected Pollanschütz form factor approach provides unbiased Ministry of Agriculture & Forests, Royal Government of Bhutan. and consistent estimates and can be easily recalibrated and/or Eastaugh, C.S. 2014 Relationships between the mean trees by basal area extended to any other tree species if new calibration data are and by volume: reconciling form factors in the classic Bavarian yield and available. volume tables for Norway spruce. Eur. J. For. Res 133, 871–877.

365 Forestry

Evert, F. 1969 Estimating stand volume by measuring form class without the International Union of Forest Research Organizations, Section 25, measuring diameters. For. Sci. 15, 145–148. Stockholm, pp. 7–17. Forest Resources Development Division 2004 Forest Management Code R Core Team 2015 R: A Language and Environment for Statistical of Bhutan. Department of Forests, Ministry of Agriculture, Royal Computing. R Foundation for Statistical Computing. Government of Bhutan. Rosset, J. 1999 Temperate conifer forests of Bhutan: a review of forestry Forest Resources Development Division 2005 Volume Table of Bhutan. research sctivities until June, 1998. In RNR-RC Jakar. Special Publication Department of Forests, Ministry of Agriculture, Royal Government of No. 3, 1999. Research Extension and Irrigation Division, Ministry of Bhutan. Agriculture, Royal Government of Bhutan, 95 pp. Forest Resources Management Division 2013 Forest Resources Potential Rykiel, E.J. 1996 Testing ecological models: the meaning of validation. – Assessment of Bhutan 2013. Department of Forest & Park Services, Ecol. Model 90, 229 244. Downloaded from https://academic.oup.com/forestry/article-abstract/90/3/359/2605859 by guest on 09 March 2020 Ministry of Agriculture & Forests, Royal Government of Bhutan. Schieler, K. 1991 Local Forest Inventory, Bumthang, Wangtha-La Führer, E. 2000 Forest functions, ecosystem stability and management. Thrumshing-La Volume 1, Integrated Forest Management Project. Ministry For. Ecol. Manage 132,29–38. of Agriculture, Royal Government of Bhutan. Gezahgn, T.T. 2015 Development of Form Factor and Height-Diameter Sendi, M.R.N., Navroodi, I.H., Poorbabaei, H., Milan, M.S. and Bakhshandeh, Functions for Selected Tree Species in the Amhara Region, Ethiopia. B. 2014 Determination of lime tree (Tilia begonifolia Stev.) stems form University of Natural Resources and Life Sciences. based on quantitative parameters (Study area: Shafaroud forests of Guilan – Hasenauer, H. 2006 Sustainable Forest Management: Growth Models for province, Iran). Folia Forestalia Polonica, series A 56 (4), 165 170. Europe. Springer. Socha, J. and Kulej, M. 2005 Provenance-dependent variability of Abies ą Hasenauer, H., Petritsch, R., Zhao, M., Boisvenue, C. and Running, S.W. grandis stem form under mountain conditions of Beskid S decki (south- – 2012 Reconciling satellite with ground data to estimate forest productiv- ern Poland). Can. J. For. Res. 35, 2539 2552. ity at national scales. For. Ecol. Manage 276, 196–208. Socha, J. and Kulej, M. 2007 Variation of the tree form factor and taper in Hoyer, G.E. 1985 Tree Form Quotients as Variables in Volume Estimation. European larch of Polish provenances tested under conditions of the ą – U.S. Department of Agriculture, Forest Service, Pacific Northwest Forest Beskid S decki mountain range (southern Poland). J. For. Sci. 53,538 547. and Range Experiment Station, 16 pp. Tarp-Johansen, M., Skovsgaard, J., Madsen, S., Johannsen, V. and Husch, B., Beers, T.W. and Kershaw, J.A.Jr. 2002 Forest Mensuration.Wiley. Skovgaard, I. 1997 Compatible stem taper and stem volume functions for oak (Quercus robur L and Q petraea (Matt) Liebl) in Denmark. Ann. Ikonen, V.-P., Kellomäki, S., Väisänen, H. and Peltola, H. 2006 Modelling Sci. For. 54, 577–595. the distribution of diameter growth along the stem in Scots pine. Trees 20, 391–402. Teshome, T. 2005 A ratio method for predicting stem merchantable vol- ume and associated taper equations for Cupressus lusitanica, Ethiopia. Larson, P.R. 1963 Stem form development of forest trees. For. Sci. Monogr. For. Ecol. Manage 204, 171–179. Society of American Foresters. United Nations Framework Convention on Climate Change 2014 Key Laumans, P. 1994 Height-diameter functions from PIS for country level Decisions Relevant for Reducing Emissions from Deforestation and Forest site classification and local volume table selection. Working Document Degradation in Developing Countries (REDD+). United Nations Framework No.11 (FO: DP/BHU/911002). Thimphu (Bhutan): UNDP/FAO Forest Convention on Climate Change. Resources Management and Institutional Development Project, Department of Forestry, Ministry of Agriculture, Royal Government of Weiskittel, A.R., Hann, D.W., Kershaw, J.A.Jr and Vanclay, J.K. 2011 Forest Bhutan. Growth and Yield Modeling. John Wiley & Sons, Oxford. Martin, A.J. 1981 Taper and Volume Equations for Selected Appalachian West, P.W. 2009 Tree and Forest Measurement. Springer, Australia. Hardwood Species. US Department of Agriculture, Forest Service, West Whitfield, P. 2001 Planning and Implementation for Sustainable FMU Virginia. Management. Wang Watershed Management Project ALA/97/50. Philip, M.S. 1994 Measuring Trees and Forests. CAB international. Ministry of Agriculture, Royal Government of Bhutan. Pollanschütz, J. 1965 A new method of determining stem form factor of Zhang, L. 1997 Cross-validation of non-linear growth functions for mod- – – standing trees. Presented at the Advisory Group of Forest Statisticians of elling tree height diameter relationships. Ann. Bot. 79, 251 257.

366