Nigerian Journal of Agriculture, Food and Environment. 8(2):12-17 INDIVIDUAL TREE VOLUME EQUATION FOR A PLANTATION OF TECTONA GRANDIS IN THE CROSS RIVER UNIVERSITY OF TECHNOLOGY (CRUTECH), OBUBRA, CROSS RIVER STATE, NIGERIA ABSTRACT Ajayi, S. and Odey, P. O. Department of Forestry and Wildlife Resources Management, Cross River University of Technology, P.M.B 102,Obubra, Cross River State, Nigeria. Phone +234 (0)8038368014; +234 (0)8059456270 Individual Tree Volume Equation was developed for Tectona grandis in the Cross River University of Technology (CRUTECH) forest plantation using total height and diameter at breast height (dbh) over bark as predictor variables. Volume estimates were made based on data collected from 68 trees in the 20 years old Teak (T. grandis) plantation in CRUTECH. Four sample plots were selected randomly in the plantation and the trees in each plot were measured for dbh and total height using diameter tape and Sunnto altimeter respectively. Each plot size was 0.04 m and plots 1, 2, 3 and 4 had 20, 18, 14 and 16 trees respectively. The mean dbh of plots 1, 2, 3 and 4 were 22.05 cm, 17.16cm, 20.21cm and 18.75cm respectively. The mean height ranged from 14.77m 16.76m, mean volume from 0.28 m 3-0.52 m 3 while the standard deviation of volume ranged from 0.1 m 3 0.27 m 3. The initial stocking at 2.5m x 2.5m amounted to 1600 plants per hectare while the current stock of the plantation is 425 plants per hectare amounting to 26.56%. Individual tree volume was calculated using cylindrical volume and Normal form factor. Multiple regression analyses on SPSS were used to relate the dependent and independent variables. The selected equation involved an untransformed double entry volume model. Paired t statistics (0.78 at p < 0.05) and an estimated bias of 2.04% indicate that the selected model can be adequately used for predicting tree volume in CRUTECH teak plantation. Keywords : Individual tree, diameter at breast height, volume equation, teak, Cross River INTRODUCTION Food and Agricultural Organization (FAO, 1981) estimated that between eight million and twenty million hectares of tropical forest are depleted annually. To meet the challenge of providing high quality wood for the increasing population and rapid industrialization at sustained production level while preserving our natural environment for future generation, studies were carried out and extensive plantation of indigenous species such as Terminalia, Triplochiton and Nauclea have been established. The pace of the studies was however, comparatively slow and what was produced was limited compared to what was needed and time was running out (Ajayi et al., 2004). On the other hand, exotic tree species were introduced to Nigeria and other developing countries. Some of these species such as Pinus caribea, Pinus oocarpa, Tectona grandis and Gmelina arborea proved very successful in several tropical countries. Within the last four decades, the Federal and State governments in Nigeria in conjunction with the World Bank have heavily invested in plantation establishment of those exotic species in some parts of the country (predominantly Gmelina and Teak) to provide raw materials and products in the form of poles, timber, veneer, wood particles, pit props, pulp, fuelwood and for research. Teak (Tectona grandis) is one of the species widely used for plantation forestry by the government, private and individuals in virtually all parts of Nigeria and more in Cross River State (Akande, 2002). According to International Tropical Timber Organization (ITTO) (2001), these plantations had addressed a few global problems. They have reduced deforestation, restored degraded land, ameliorated climate change, improved local livelihood, returned good profits, created employment and bolstered national economies. However, despite the fact that one of these species, teak, attains prices of several thousand US $ per m 3 on the world market (Teak Net, 1997), not all the plantations are in good shape. The proper management of CRUTECH Tectona grandis plantation requires a reliable volume estimate of the tree species. For this purpose and its goal to be achieved, volume equation based on the established relationship between some measurable tree parameters and tree volume is very paramount. Tree parameters include basal area, breast height diameter (Anon, 1980), basal area and merchantable height (Ogbeibu, 1980). At the moment, no individual tree volume equation had been developed for Tectona grandis plantation of CRUTECH. Volume of standing trees cannot be measured directly but can be predicted using measured tree attributes such as diameter at breast height (dbh) and height. Since volume measurement is indirect, time is wasted and the calculation cumbersome for the non-mathematically inclined (Akindele, 1985). The objective of this study therefore is to develop a regression equation for predicting individual tree volume of Tectona grandis in CRUTECH plantation using diameter at breast height (dbh) and total height as predictor variables. For sustainable management to be effective, its volume prediction must be guaranteed. Hence, a volume equation for the plantation remains imperative because selling timber without measuring the products is like NJAFE VOL. 8 No. 2, 2012 12
selling livestock without weighing the animals (Akindele, 2008). Therefore knowing what you have to sell and securing several bids can mean much additional income from your timber sales. Therefore, there is the need for volume equation of CRUTECH Tectona grandis plantation. MATERIALS AND METHODS Study area The research was conducted in a fifteen-year-old teaching and research plantation of CRUTECH, in Obubra Local Government Area of Cross River State. Obubra lies between latitude 6 05 and 8 20 N and longitude 6 08 and 8 33 E (Stock and Redmond, 2009). The wet season starts from April to October, while the dry season spans from November to March. Temperature is fairly uniform with a mean monthly average of 27 0 C (Ekwaozor, 1982). The annual rainfall is between 2000mm and 2250mm, while the relative humidity varies from 60% -70% in January and 70% - 80% in July (Bulk Trade and Investment Company, 1989). Sampling techniques Reconnaissance survey was carried out in the area and a map of the teak plantation produced. Grids equivalent to 20m x 20m on the ground was made on the map and this formed the sampling frame of 38 plots (20m x 20m each). Simple random sampling was used to select four plots from the frame. In each plot, tree numbering was done with the help of red marker on a plastic tags nailed to each tree. Data collection Diameter of the sampled trees was determined with the use of diameter tape on winding the tape around the tree at point of measurement (1.3m or 4.5ft) above the ground on the uphill side of the tree.) Sunnto altimeter was used to measure total height of each tree in each sample plot; measurements of Diameter at Breast Height over bark were made on all trees with dbh equal to or greater than 10cm (Ajayi, et al., 2006). Measurements were made on a total of 68 trees. Volume estimation: Individual tree volume was estimated using cylindrical formula and breast height form factor of 0.759 (Novendra, 2008). V = πd 2 x Ht x FF.eq. (1) 4 Where, V= volume (m 3 ) π= 22/7 D= diameter at breast height (cm) Ht= Height (m) FF= form factor of teak. Model formulation The forms of the dependent variable employed for initial screenings were untransformed and the logarithmic transformation (common and natural) of tree volume. The transformed and untransformed dependent variables were regressed against diameter at breast height (DBH) and total height (H). Data analysis The multiple regression analysis was used to develop equation relationship between height, dbh and volume. The linear and semi-log (common and natural) form of the equation was used to select the best equation. The regression (stepwise) was performed using the enhanced version of SPSS (17.0) on a computer. The multiple regression models advanced for further screening were patterned after the one presented by Ajayi et al., (2006). (i) V= b 0 +b 1 D +b 2 h.eq. (2) (ii) Log V= b 0 +b 1 D +b 2 h..eq. (3) (iii) In V= b 0 +b 1 D +b 2 h eq. (4) where, b 0 = intercept b 1, b2= Regression co-efficient D= dbh H= height In= natural logarithm Log= logarithm NJAFE VOL. 8 No. 2, 2012 13
Criteria for model selection The selection of the best volume equation was based on significant of variance ratio (F) at 5% level of probability, a goodness of fit with high coefficient of determination (R) 2, and least residual mean square error. Validation Once a model has been constructed, the question of validity must be answered before the model or the result could be used in practical forest management. Ajayi et al., (2006) stated that Validation is the process of building an acceptable level of confidence that an inference about a simulated process is a valid inference about the actual process. A critical reason forwarded by Montgomery et al, (1991) for validating a model is that, frequently, the user of the model is a different individual from the developer and often has little or no control over the model. Paired t-test and test of bias were carried out on the error associated with the final prediction. Ten (10) trees were randomly selected from the four (4) compartments (independent of those used for developing the model) for the purpose of validation. Null (H o ) = paired observations are not different. Alternative (H 1 ) = paired observations are different. The formula is given as t = D.eq.(5) Sd / Where, t =t-test statistics D = mean of the difference between pairs (cm) Sd = standard deviation of the difference between pairs (cm) n= number of paired observations Degree of freedom is n-1 The null hypothesis was accepted if the value of t was greater than that at 5% probability. When the average of error differs significantly from zero, a check of bias was considered. In practice, a bias of less than 2% is rarely worth correcting whereas one of 5% may be (Philip, 1994). Bias = Residuals x 100. Eq. (6) Actual observation RESULTS AND DISCUSSION Summary of trees in established temporary sample plots Data were collected from trees which were originally measured for dbh and total height, the numbers of plots established in the plantation were four (4) and 68 trees were measured for dbh in the four plots and the dbh ranged from 15cm 35cm. Each Plot size is 0.04 m, Plot 1, 2, 3 and 4 has 20, 18, 14 and 16 trees respectively (Table 1). Table 1: Stand summary of teak (Tectona grandis) in CRUTECH plantation (spacing - 2.5m x 2.5m) S/N Summary Plot 1 Plot 2 Plot 3 Plot 4 Total Mean (plantation) 1 Plot size (ha) 0.04 0.04 0.04 0.04 0.16 0.04 2 Number of stem/plot 20 18 14 16 68 17.00 3 Mean DBH (cm) 22.05 17.16 20.21 18.75 78.57 19.64 4 Standard deviation of dbh 5.39 2.64 3.24 3.84 15.11 3.78 5 Mean of height (m) 16.76 14.77 16.73 15.34 63.60 15.90 6 Standard deviation of height (m) 1.25 1.32 0.65 1.07 4.29 1.07 7 Mean of volume (M 3 ) 0.52 0.28 0.42 0.34 1.56 0.39 8 Standard deviation of volume (m 3 ) 0.27 0.1 0.14 0.17 0.68 0.17 The mean dbh of plot 1, 2, 3 and 4 was 22.05 cm, 17.16cm, 20.21cm and 18.75cm respectively. The mean height ranged from 14.77m 16.76m. The current range of mean dbh and height for the fifteen years implies that the trees are predominantly of pole size. Intensive plantation management is necessary to meet the objective of producing trees of varying products (fuelwood, poles and timber) valued for teaching and research in Forestry. The mean volume ranged from 0.28 m 3-0.52 m 3 while the standard deviation of volume ranged from 0.1 m 3 0.27 m 3. The initial stocking at 2.5m x 2.5m amounted to 1600 plants per hectare while the current or actual stocking of the plantation is 425 plants per hectare or 26.56% survival. This is indication of high mortality in the NJAFE VOL. 8 No. 2, 2012 14
plantation can be attributed to regular fire outbreak, illegal felling by residents of host communities for fuelwood and poor management. Replanting in the entire plantation is of paramount importance. Regression equation for individual tree in CRUTECH teak plantation The three developed models presented in Table 2 were judged suitable for predicting individual tree volume in teak (T. grandis) plantation of CRUTECH. They had high R 2 values, significant F-ratio and relatively low Root Mean Square Error (RMSE) values. However, model one (1) is selected because it has the lowest RMSE of 0.001; this indicates that the model is adequate for predicting tree volume in CRUTECH plantation. Table 2: Individual tree volume equation and related statistics for teak plantation in CRUTECH Model Dependent variables Regression constant Regression coefficients R 2 (%) RMSE F-Ratio Remarks 1 V -.759.045dbh+.017 h 97.3 0.001 1167.969 Selected 2 Log. V -4.012 0.092dbh+0.072 h 98.5 0.003 2094.145 Suitable 3 Ln V -4.012 0.092dbh+0.072 h 98.5 0.003 2094.145 Suitable V = - 0.759 + 0.045 dbh + 0.017 h Where, V = volume (m 3 ) Log V = logarithm of volume Ln v = Natural logarithm of volume. dbh = diameter at breast height (cm) h = total height (m) Validation of selected model Changes in tree volume are of prime concern in predicting future stand composition and for selecting the ideal crops in a pure stands. Volume is imperative for estimating individual tree increase and the derived model is also a useful tool for evaluating the innate productive capacity of the plantation site at CRUTECH for the purpose of recommending species and number of rotation (Ajayi et al., 2006). Table 3 shows residual analysis for ten trees independently sampled from the plantation. The volume residuals follows a random pattern, the paired t-test conducted on the residuals indicate no significant difference between the actual and the predicted tree volume (0.78 at p < 0.05) in T. grandis plantation at CRUTECH without any corrections on the predicted values with estimated bias of 2.04% which indicate that the selected model can be adequately used for predicting tree volume in CRUTECH teak plantation (Philip, 1994). Table 3: Independent data for validating individual tree volume equation in CRUTECH plantation S/N DBH (cm) Height (m) Actual volume y Predicted volume Ŷ Residual Y- Ŷ (D) 1 28 17.0.7948 0.7900 0.0048 2 35 17.5 1.2778 1.1135 0.1643 3 27 16.5.7176 0.7365-0.0189 4 24 17.2.5914 0.6134-0.0220 5 25 17.3.6447 0.6601-0.0154 6 21 17.4.4583 0.4818-0.0235 7 16 17.3.2639 0.2551 0.0088 8 27 17.6.7655 0.7552 0.0103 9 16 17.1.2609 0.2517 0.0092 10 29 17.0.8529 0.8350 0.0179 Total 248 1719 6.6278 6.4923 0.1355 Pair T- Test t = Ď Sd/ where, Ď = mean of the deference between pairs Sd = standard deviation of the deference NJAFE VOL. 8 No. 2, 2012 15
n = number of paired observation Hypothesis H o = There is no deference between the actual volume and the predicted volume. H 1 = There is deference between the actual volume and the predicted volume. t = Ď Sd/ D = 0.1355 D 2 = 0. 0292 ( D) 2 = 0. 0184 n = 10 Sd = 0.055 = 3.162 Ď = 0.01355 Therefore; t = 0.01355/0.01739 t = 0.78 The t - calculated was 0.78 The t - tabulated was 1.83 at 5% Bias = Total residual volume / Total actual volume x 100 i.e. Bias = Y-Ŷ x 100 eq. (7) y Bias = 0.135 / 6.6278 x 100 Bias = 0.0204 x 100 Bias = 2.04% Where: Y-Ŷ (D) = Total residual volume y = Total actual volume CONCLUSION AND RECOMMENDATIONS The measurement of individual volume is an important mensurational issue in forest management. The current trend towards production of multiple products from a single tree has created an increased interest in the development of tree function. The prediction of individual volume equation in CRUTECH plantation did not require the transformation of dependent and independent variables. For all practical purpose therefore, total height and diameter at breast height (dbh) were adequate for predicting tree volume. Further research and replanting should be carried out in the plantation. REFERENCES Ajayi. S., Ogar, N. E., Anyaorah C. N. 2004. A Mathematical Programming Approach to Sustainable Management of Gmelina arborea (Roxb) Plantations in a Nigerian rain forest. International Journal of Education, 2(1&2):146 157. Development Universal Consortia, Ikot Ekpene, Nigeria. Ajayi, S. Olajide, O., Uzowulu, G.I.; Ebu, V.T., 2006. Predicting Individual Tree Heights in Gmelina arborea Plantation of Ukpon River Forest reserve, Cross River State, Nigeria. Journal of Agriculture, Forestry and the Social Sciences.. 4(2): 107-118 Akande, J. A. 2002. Wood Biomass Form In: Abu J. E., Oni P. I. and Popoola L. (Ed). Forestry and challenges of sustainable livelihood, Proceedings of 28 th Annual Conference of the Forest Association of Nigeria held in Akure, Ondo. Akindele, S. O. 1985. The Development of Various Linear Equations for Teak in Gambari Forest Reserve, Green canopy Consultants, Choba, Port Harcourt, Nigeria. Akindele, S. O. 2008. The Place of Biometrics in Forestry Research, In Research for development in forestry, forest products and natural resources management (Eds. Onyekwelu, J. C., Adekunle, V. A. J and Oke, D. O) Proceedings of the 1 st National Conference of the Forest and forest product society, Federal University of Technology, Akure, Nigeria 16 th - 18 th April, 2008 pp 100-256. Anon, 1980. Annual Report, Forest Research Institute of Nigeria, Ibadan, Nigeria. Bulk Trade and Investment Company Ltd, 1989. Soil and land use survey of Cross River State. May Report, Ministry of Agriculture and Natural Resources, Nigeria. Pp. 44. NJAFE VOL. 8 No. 2, 2012 16
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