Prediction models for above-ground wood of some fast growing trees of Nepal's eastern Terai H. B. Thapa1 Biomass study of Acacia auriculiformis, Acacia catechu, Dalbergia sissoo, Eucalyptus camaldulensis and Eucalyptus tereticornis was conducted on a five and half years old 'Fuelwood Species Trial under Short Rotation' through destructive sampling at Tarahara, Sunsari District of Nepal. The lowest Furnival Index (FI) was the main criteria for selecting a model. Among the six models tested, the transformed model Ln W= a + b Ln DBH from a power equation W = a DBHb (W = weights of stem or branch or above- ground wood in kg, DBH= Diameter at breast height in cm) was selected. Selected prediction models of tree components and above-ground wood (green as well as oven dry), and their coefficient of determination (R2) values, regression constant and coefficient, correction factor, precision and bias percent of five species are presented. With the exclusion of branchwood models, R2 is higher in a range of 88.7% for oven dry stemwood of Acacia catechu to 99.3% for above-ground wood model of Dalbergia sissoo. However, R2 is less than 80% in branchwood (green and oven dry) of Acacia auriculiformis, Eucalyptus camaldulensis, and Eucalyptus tereticornis showing moderate relationship between branchwood and DBH. In the case of E. tereticornis, precision is more than 49% which leads to low reliability in biomass estimation resulting in true biomass deviation in a range of about 49.51% to 56.74%, so biomass model's could not be used for estimation of tree components and above-ground wood. Despite it, generally, precision percent of the selected models has been found less than 15%. Bias percent was found quite large for allometric branchwood model comparatively to stemwood and above-ground wood models. D. sissoo had less than 10 % bias. Bias percent was the highest (23.11%) for green branchwood of Acacia auriculiformis. Others had in a range of 0.5% for green aboveground wood model of D. sissoo to 18.4% for green and oven dry branchwood models of E. tereticornis. Keywords: Prediction models, wood biomass, fast growing trees, Terai, Nepal E stimation of biomass yield is an important tool in the management of forests both for the large scale plantations and the small village woodlot. The established plantations always require appropriate estimates of growth and production so that forest managers and plantations owners can make decisions for further planning and management. Growth models and development of biomass (stem, branch, above-ground wood, leaf, root) tables based on these may help quantify and compare firewood production of various fast growing tree species of a particular locality. Moreover, keeping in view of increasing number of Forest User Groups (FUGs) in the Terai, there is an acute need to develop an above-ground wood (stem and brance) model for established community plantations to quantify the wood biomass for distribution and sale. This will ensure the productivity of the site for further management. The exiting situation of plantations based on short rotations in the Terai region is still in infancy (Hawkins 1987). Although, the Forestry Research and Sagarnath Forestry Development Projects have identified some promising fast growing firewood species for plantations and smaller community woodlots under short rotations (White 1986) in the Central Terai/Bhabar region of Nepal. However, the results of this region may not be applicable without verification for the eastern Terai where no biomass models for the fast growing tree species have been developed yet. And, to achieve it A Fuelwood Species Trial under Short Rotation' was set up in July 1985 at Tarahara in the eastern Terai With the five fast growing fuelwood tree species Acacia auriculiformis, Acacia catechu, Dalbergia sissoo, Eucalyptus camaldulensis and Eucalyptus tereticornis. It is expected that the result of the present study will fill the gap, in quantifying established plantations. 1 Research Officer, Department of Forest Research and Survey, Kathmandu Banko Janakari, Vol. 9, No. 2 Thapa Methods The reliability of green weight regressions is higher when trees are harvested during the winter months. The data (DBH, height, green weights of stem and branch) were collected in January 1991 from five and half years old trees planted at a spacing of 2.5 m x 2.5 m at Tarahara (for description of the study site see Thapa,1998). Twenty trees each of Acacia auriculi formis and Dalbergia sissoo, twenty two trees of Acacia catechu, twenty one trees of Eucalyptus camaldulensis and seventeen trees of Eucalyptus tereticornis were cut down for this purpose from the four replicates. Percentage dry matter values of the samples were used to convert fresh to oven dry weights for the general data for the development of oven dry wood models. Green weights of tree components were kept outside for about one month to find out the conversion factor to change green weight to air dry weight figures. Regression analysis of variance was performed on six models using MINITAB for green and oven dry weights of tree components and above-ground wood of five species to find out the values of regression constant a and coefficient b, coefficient of determination (R2), F- value, residual mean squares. The regressor variables used were diameter at breast height (DBH), square of DBH, square of DBH and height (D2H), Ln DBH, Ln DBH and Ln height; DBH and height independently to find out the best model. The relation was determined to select the best fitted prediction equation for green and oven- dry weights of tree components and above-ground wood. This method was based on the assumption that the two variables are connected by a straight line relationship (Mountford and Bunce 1973). The following six models (linear and allometric) were chosen on the use of these for biomass study by many researchers: Model I W=a+bX (i) Model II W=a+bXj + cX2 (ii) Model III W=a+bX2 (iii) Model IV W = a+bX (iv) Model V W=a+Xb After logarithmic transformation, LnW = a'+bLnX (v) Model VI Ln W = a' + b Ln X, + c Ln X2.... (vi) Where: W= Estimated green or oven dry weight of tree components (stem and branch) and above-ground wood (stem plus branch) in kg. X = Diameter at breast height in cm (overbark) X] = Diameter at breast height in cm (overbark) X2= Total height (m) to the tip of tree a' = Ln a In model IV X = square of diameter at breast height (cm2) times height (m) i. e. D2 H The standard deviation and coefficient of determination are not suitable to compare weighted and transformed models having different dependent variables (Unnikrishnan and singh 1984). So comparisons of the above six models were made by an index developed by Furnival (1961). Since the logarithmic transformation changes the distribution of residuals causing a slight underestimation in biomass prediction (Meyer 1941; Baskerville 1972; Mountford and Bunce (1973), Pukkala et al. (1990), and Sprugel (1983), a correction factor was added to the equation as follows: 0= exp (S2/2) i. e. eS S/2 Where S2 = residual mean square of the regression equation 0 = Correction factor Bias (%) was calculated using the formula given by Brown (1976) Uncorrected biomass (green and oven dry tree components and above-ground wood) was calculated using the model exp^a + b Ln DBH^ whereas corrected biomass was calculated using the model exp (a + b Ln DBH + c. f.) wjiere c> £ stands for correction factor (Annex 2). Results Close relationship were determined between the green and oven dry wood biomass of branches (including twigs without leaves), stemwood including bark and total above-ground wood respectively and the breast height diameter (logarithmic transformed) for all the five species. £ ■O W- Figure 1: Regression of Ln above-ground wood (green) 5 5 versus Ln DBH of Acacia auriculiformis 5 4.5 4 ; *•* 3 2.5 2 1 5 Actual Ln aboveground wood Regression line 1.5 2.5 Ln DBH (cm) 29 Thapa Banko Janakari, Vol. 9, No. 2 The transformed logarithmic model V, Ln W = a + b Ln DBH with DBH as independent variable was selected for biomass estimation of above-ground wood and tree components, since it has the lowest FI in most cases (Annex 1). The regression lines with observed values of green above-ground wood of Acacia auriculiformis, A. catechu, D. sissoo and E. camaldulensis are shown in figure 1 to 4. The actual green above-ground wood (AGW) weights of A. auriculiformis were found to be less than the predicted values in lower diameters (up to about 7.5 cm) indicating a slight bias. Actual green AGW weights of A. catechu were found more than the estimated values (13 out of 22 data i. e. 59% of the total sample data) in lower and higher diameters (Figure 2). Coefficient of determination (R2) is higher in a range of 88.7% for oven dry stemwood of A. catechu to 99.3% for AGW of D. sissoo in selected regression equations. However, R2 is less than 80% in branchwood (green and oven dry) of A. auriculiformis, E. camaldulensis, and E. tereticornis showing moderate relationship between branchwood and DBH (Annex 2). Figure 2: Regression of Ln aboveground wood (green) 2 o) U) 6 5.5 5 4.5 4 3.5 3 2.5 2 versus Loge DBH-Acac/a catechu Actual Ln Above-ground wood _ Regression line 1.5 2.5 Ln DBH (cm) 3.5 figure 3: Regression of Ln above-ground wood (green) versus Ln DBH of Dalbergia sissoo < 5 1 1 .5 ; LnDBI I 2 H (cm) .5 : With the exclusion of E. tereticornis, precision percent ranged 11.28 for green stemwood of Acacia catechu to 16.24 for oven dry stemwood of D. sissoo, 14.20 for oven dry branchwood of E. camaldulensis to 19.62 for green The inclusion of height as an additional variable did not improve the precision as well as R^ and residual mean squares significantly, and similar case for exclusion of outliers. Bias percent was quite large for allometric branchwood model in comparison to stemwood and AGW models. D. sissoo had less than 10 % bias. Bias percent was the highest (23.11%) for green branchwood of A. auriculiformis. Others had in a range of 0.5% for green AGW model of D. sissoo to 18.4 for green and oven dry branchwood models of E. tereticornis (Annex 2). branchwood of D. sissoo, 12.84 for green AGW of A. catechu to 16.81 for oven dry AGW of D. sissoo. Precision percent of branch wood models was found quite lower than the models of stemwood and AGW. Precision percent of selected models used for branch, stem wood and AGW (green and oven dry) of E. tereticornis was found more than 49 percent (Annex 2) resulting in an unreliable estimates of tree components and AGW. Discussions Hawkins (1987) useing both DBH and height as predictor variables for biomass estimation of some species in the Central/Bhabar Terai of Nepal, he found that measurement of total height was time consuming and also created large errors. There was only a small increase in the precision of regressions with the inclusion of height, while the time increased three times due to height measurement in the field inventory. DBH is the preferred predictor variable of biomass per unit area for practical reasons and simplicity of measurement in the field (Applegate et al. 1988). An additional variable height is not necessary as a predictor variable from the cost point of view, if equally efficient prediction models are available with DBH alone (Tondon et al. 1988). Obviously, various researchers findings clarify the benefit of using predictor variable DBH alone. So far the biomass equation (Ln W = a + b Ln DBH) could be used elsewhere for these species with conditions similar to Tarahara, but may not be appropriate to a wide geographical area. However, these equations need to be tested for validation by destructive sampling for each of these species but prediction error should be under 15 % (Hawkins 1987) of actual weights. If the prediction error is within 15 % of the actual weights, the models can be used safely in that place. Oven dry and green wood biomass models are produced for single tree species 30 Banko Janakari, Vol. 9, No. 2 Thapa separately but not for mixed stands. No such mixed plantations in large scale have yet been established at the district level, however, such models may have importance in future. On the one hand, wood biomass models developed using the single predictor variable, DBH, which could be measured easily with less error than height, may increase the utility of these models to develop weight tables to the forestry sector as well as to the community and interested individuals. On the other hand, single tree biomass tables developed using DBH as the only variable have been found to be reliable for undamaged trees of a number of species in Nepal (Raeside 1986 quoted in Thompson 1990; Hawkins 1987). However, the benefit of DBH use lies in the fact that if the relationship (weight and DBH) is valid for a sufficiently large plantation area and if it does not change over a period of time, then the model can be used in subsequent inventories. Again this relationship breaks down if the tree has been lopped or pruned, in such situations, a new set of models for the development of biomass tables are essential for the pruning operation (Thompson 1990). The above equetion is necessary to change the nonlinear power equation (W = a DBH11) to a linear form. Moreover, in the above power equation, the relation between W and DBH is non-linear, the transformed variables Ln W and Ln DBH are connected by the straight line relationship (Mountford and Bunce 1973). For weighted and transformed models with different dependent variables, the standard deviation and coefficient of determination are not suitable to compare these models (Unnikrishnan et al. 1984). In such case, Furnival Index can be used for comparing and selecting the models with the lowest FI. It has the concept of maximum likelihood and reflects both the size of residuals and possible departures from linearity, normality and homoscadasticity (Mohd 1988). The precision is lower in the equation of branchwood of A. catechu and D. sissoo except E. tereticornis as compared to the stemwood and AGW equation. It is subjected to large variation in the sample data from the mean (i.e. standard error of the mean being large). In the case of E. tereticornis, it is more than 49% which accounts for low reliability in biomass estimation resulting in true biomass deviation in a range of about 49.51% to 56.74% (Annex 2). The sample data of this species did not represent the 10-15 cm diameter class. Due to a big gap in the sample data and low precision of the selected models, biomass tables need to be developed only after validation. Biomass estimation in other species is reasonably accurate, since precisions are mostly under 15 % i.e. actual yields are within 15 % of the estimated wood biomass. Before using the air dry weight conversion factors for stem and branchwood of these five species, they may need to be verified for confirmation, if the duration of drying for green stem and branchwood of these species is less than or more than one month, or samples are dried, or are in large quantity, etc. Most of the equations of tree components and AGW consists of a coefficient of determination greater than 90% indicating a strong relationship between tree DBH and component weights and AGW. However, R^ in branchwood equation of A. auriculiformis, E. camaldulensis and E. tereticornis was found to be quite low, which indicates a reasonable relationship between branch weight and DBH. Furthermore, it indicates more variability in the form of trees. The general assumption of increasing branchwood with the increase in size of trees is not true here. The predictive biomass equations developed in this paper are an early attempt to estimate the tree components of these species in the eastern Terai of Nepal. As suggested by Hawkins (1987) the models need to be revised and improved in due course when more data and new establishment methods and management techniques will be developed. However, these models have importance in providing reliable estimates of existing plantations of these species at present. Conclusions and recommendations Selected model Ln W = a + b Ln DBH (green as well as oven dry) would be valuable for forest managers, Forest User Groups and private growers to quantify the yield in their plantations managed on short rotations in the eastern Terai to make informed decisions for further management, distribution, and sale of products. But, it is necessary to validate these models before using them elsewhere. If the prediction error is within 15 % of the actual weights, the models can be used safely in that place. Due to low precision of the regression models of tree components and AGW (oven dry and green) of £. tereticornis, caution should be taken in the apply these models elsewhere. The models need to be tested and improved in due course time when new management methods and management techniques will be developed. References Applegate, B., Gilmour D. A. and Mohns Bernhard 1988. Biomass and productivity estimations from community forest management: a case study from the hills of Nepal-I. Biomass 31 Thapa Banko Janakari, Vol. 9, No. 2 and productivity of chir pine [Pinus roxburghii Sargent) plantations. Biomass 17: 115-136. Baskerville, G. L. 1972. Use of logarithmic regression in the estimation of plant biomass. Canadian Journal of Forestry Research 2 (1): 49-53. Beauchamp, John J. and Olson, Jerry S. 1973. Corrections for bias in regression estimates after logarithmic transformation. Ecology 54 (6): 1403-1407. Autumn 1973. Brown, K. 1976. Estimating shrub biomass from basal stem diameters. Canadian Journal of Forestry Research 6 (2): 153-158. Chippandale, G. M. and Wolf, L. 1981. The natural distribution of Eucalyptus in Australia. Australian National Parks and Wildlife Service, Canberra. Furnival, M. 1961. An index for comparing equations used in constructing volume tables. Forest Science 7 (4): 337-341. Hawkins, T. 1987. Biomass and volume tables for Eucalyptus camaldulensis, Dalbergia sissoo, Acacia auriculiformis and Cassia siamea in the Central/Bhabar Terai of Nepal. Oxford Forestry Institute, Department of Plant Sciences, University of Oxford. OFI Occasional paper No. 33. Kojak, A. 1970. Methods of ensuring additivity of biomass components by regression analysis. Forestry Chronicle 46, 402-404. Meyer, H. A. 1941. A correction for a systematic error occurring in the application of the logarithmic volume equation. Pa. State Forest School Research. Paper 7, 3 p. Mohd, W. R. 1988. Modelling the tree growth in mixed tropical forests I. Use of diameter and basal area increment. Journal of Tropical Forest Science 2:114-121. Mohns, B., Applegate, G. B. and Gilmour, D. A. 1988. Biomass and productivity estimates for community forest management: A case study from the hills of Nepal-II. Dry matter production in mixed young stands of chir pine [Pinus roxburghii) and broad-leaved species. Biomass 17: 165-184. Mountford, M. D. and Bunce, R. G. H. 1973. Regression sampling with allometrically related variables with particular reference to production studies. Forestry 46 (2): 203-212. Pukkala, T.; Sharma, E. R. and Rajbhandari, M. D. 1990. A guide to biomass modelling for forest inventory in Nepal. Publication No. 51, Forest Survey and Statistics Division, Ministry of Forests and Environment, Kathmandu. Sprugel, D. G. 1983. Correcting for bias in log transformed allometric equations. Ecology 64 (1): 209-210. Thompson, I. S. 1990. Biomass tables and inventory. Banko Janakari (A Journal of Forestry Information in Nepal) 2(4): 356-362. Forest Research Division, Babar Mahal, Kathmandu, Nepal. Tondon, V. N, Pande, M. C. and Singh, R. 1988. Biomass estimation and distribution of nutrients in five different aged Eucalyptus grandis plantation ecosystem in Kerala State. Indian Forester 114 (4): 184-199. Unnikrishnan, K. P. and Singh, R. 1984. Construction of volume tables: A generalised approach. Indian Forester 110: 561- 576. White, K. 1986. Tree farming practices in the Bhabar Terai of Central Nepal. Manual No. 2. Sagarnath Forest Development Project. Ministry of Forests and Soil Conservation. 32 Thapa Banko Janakari, Vol. 9, No. 2 Annex 1: Furnival indices for six models of oven dry weights of four species Models are as follows: Model I: W = a + b D Model II: W = a+ bD + cH Model III: W = a + b D2 Model IV : W = a + b D2H Model V: Ln W = a + b Ln DBH Model VI: Ln W = a + b Ln DBH + c Ln H Where: W = tree component weights; DBH = diameter at breast height (cm); H = intercept; b = slope total height (m); a = Species Models I II III IV V VI Acacia auriculiformis Stem wood 6.02 5.79 6.28 4.25 3.34 2.18 Branch wood 5.61 ___ 15.90 19.26 2.08 2.13 Above-ground wood 5.30 3.99 4.13 3.41 2.46 Acacia catechu Stem wood 5.96 6.11 4.47 4.20 4.15 4.49 , Branch wood 6.52 5.83 4.45 5.26 1.74 1.75 Above-ground wood 10.77 10.49 5.74 7.00 5.41 5.44 Dalbergia sissoo Stem wood 3.59 3.69 1.82 1.45 1.44 0.73 Branch wood 2.33 2.01 1.62 1.90 1.00 1.00 Above-ground wood 5.12 5.13 1.73 1.97 1.37 0.93 Eucalyptus camaldulensis Stem wood 6.78 6.89 5.10 5.10 4.90 4.85 Branch wood 1.40 1.31 1.31 1.45 0.79 0.89 Above-ground wood 6.85 6.83 4.79 5.20 4.60 4.70 Furnival indices for six models of green weights of five species I II III IV V VI Acacia auriculiformis Stem wood 14.10 13.60 14.70 10.00 7.80 14.70 Branch wood 13..08 12.05 11.71 4.85 4.92 Above-ground wood 12.41 12.73 9.33 9.64 8.00 5.66 Acacia catechu Stem wood 12.92 13.27 9.70 9.73 9.65 9.50 Branch wood 14.93 13.35 10.20 12.04 3.94 3.92 Above-ground wood 24.12 23.39 12.81 15.72 6.55 6.56 Dalbergia sissoo Stem wood 11.70 11.70 4.00 4.47 3.13 2.12 Branch wood 5.34 4.60 121 4.32 2.41 2.41 Above-ground wood 8.16 8.40 4.13 2.75 2.60 1.58 Eucalyptus Stem wood 16.24 16.43 12.23 12.23 5.50 13.75 camaldulensis Branch wood 16.46 16.33 11.39 12.47 10.60 14.32 Above-ground wood 3.60 3.38 3.40 3.73 2.06 2.09 Eucalyptus tereticornis Stem wood 15.78 14.73 6.00 2.00 1.92 1.08 Branch wood 5.43 4.73 3.05 1.97 1.05 0.06 Above-ground wood 21.07 19.36 8.77 2.83 1.94 1.53 Single underline indicates the lowest Furnival Index followed by the second lowest by double underline. 33 Banko Janakari, Vol. 9, No. 2 Thapa Annex 2: Intercept, slope, R , precision (%), correction factor, bias (%) and conversion factor from green weight to air dry and oven dry weight Regression model for green and oven dry weight for all species: Ln W = a + b Ln DBH, where: DBH = Diameter at breast height (cm) W = Weights of tree components and above-ground wood Species Green weight Oven dry weight Acacia auriculiformis Stem Branch Stem + Branch Stem Branch Stem + Branch Intercept -1.64 -3.97 -1.63 -2.49 -4.85 -2.48 Slope 2.28 2.75 2.40 2.28 2.76 2.41 R2 (%) 92.5 77.7 95.9 92.4 77.6 95.9 Precision (%) 13.02 16.46 13.85 13.04 16.6 13.95 Correction 0.041 0.211 0.024 0.041 0.213 0.024 Factor (s.e.2/2) Bias (%) 4.0 23.1 2.4 4.1 19.2 2.4 Conversion factor for green to oven dry weight Conversion factor for green to air dry weight Stem Branch Stem Branch 0.426 0.429 0.74 0.57 Species Green weight Oven dry weight Acacia catechu Stem Branch Stem + Stem Branch Stem + Branch Branch Intercept -4.300 -6.02 -1.517 -2.15 -6.91 -2.51 Slope 0.434 3.56 2.33 2.17 3.58 2.43 R2 (%) 95.3 87.9 92.0 88.7 87.6 92.7 Precision (%) 12.3 19.51 14.50 11.35 19.55 15.10 Correction 0.0405 0.118 0.0318 0.0405 0.1225 0.0314 Factor (s.e.2/2) Bias (%) 4.0 11.1 11.1 4.0 11.2 11.2 Conversion factor for green to oven dry weight Conversion factor for green to air dry weight Stem Branch Stem Branch 0.460 0.437 0.52 0.67 Species Green weight Oven dry weight Dalbergia sissoo Stem Branch Stem + Stem Branch Stem + Branch Branch Intercept -2.30 -5.12 -2.28 -3.15 -5.88 -3.13 Slope 2.58 3.25 2.69 2.59 3.22 2.70 R2 (%) 98.7 93.0 99.3 98.7 93.7 99.3 Precision (%) 16.16 19.62 16.73 16.24 19.23 16.81 Correction 0.0055 > 0.0895 0.0055 0.010 0.078 0.0055 Factor (s.e.2/2) Bias (%) 0.6 8.9 0.5 0.9 7.5 0.6 Conversion factor for green to oven dry weight Conversion factor for green to air dry weight Stem Branch Stem Branch 0.438 NA 0.79 0.68 34 Thapa Banko Janakari, Vol. 9, No. 2 Species Green weight Oven dry weight Eucalyptus Stem Branch Stem + Branch Stem Branch Stem + camaldulensis Branch Intercept -1.9353 -3.57 -1.739 -2.8094 -4.52 -2.6204 Slope 2.5799 2.25 2.539 2.5806 2.24 2.5397 R2 (%) 91.1 79.5 92.0 91.1 79.5 92.1 Precision (%) 14.65 15.80 14.50 14.89 15.75 14.40 Correction 0.0694 0.138 0.0595 0.0690 0.138 0.0588 Factor (s.e.2/2) Bias (%) 6.7 12.9 5.8 6.7 12.6 5.7 Conversion factor for green to oven dry Conversion factor for green to air dry weight weight Stem Branch Stem Branch 0.418 0.387 0.62 0.55 Species Green weight Oven dry weight Eucalyptus Stem Branch Stem + Stem Branch Stem + Branch tereticornis Branch Intercept -2.03 -4.53 -1.91 -3.02 -5.53 -2.90 Slope 2.47 2.75 2.49 2.47 2.75 2.49 R2 (%) 98.2 80.5 98.7 98.2 80.5 98.7 Precision (%) 50.79 56.74 51.24 49.51 56.09 50.60 Correction I 0.012 5 0.2035 0.0095 0.0125 0.2035 0.0095 Factor (s.e.2/2) Bias (%) 1.3 18.4 0.9 1.2 18.4 0.9 Conversion factor for green to oven dry Conversion factor for green to air dry weight weight Stem Branch Stem Branch 0.37 NA 0.61 0.58 NA - Not available 35