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