İlker Ercanlı 1, Ferhat Bolat 2, and Aydın Kahriman 3. Abstract:

Transcription

1 ORAL PRESENTATION Comparing Parameter Recovery Methods for Diameter Distribution Models of Oriental Spruce (Picea orientalis (L.) Link.) and Scotch Pine (Pinus sylvestris L.) Mixed Stands Located Trabzon and Giresun Forest Regional Directorate İlker Ercanlı, Ferhat Bolat 2, and Aydın Kahriman 3 Asst. Prof., Cankiri Karatekin University, Cankiri, Turkey; 2 Res. Asst., Cankiri Karatekin University, Cankiri, Turkey; 3 Asst. Prof., Artvin Coruh University, Artvin, Turkey. ilkerercanli@karatekin.edu.tr Abstract: Diameter distributions are important stand characteristic for describing forest stand structure and stand dynamic. The knowledge about diameter distribution has been required to forecast the range of products, which might be expected from a stand in forest management. There are several methods for predicting the diameter distribution of a stand, varying from methods which utilize theoretical distribution functions to non-parametric methods. In these methods, the studies characterizing diameter distributions with probability density functions (pdf) have provided the most successful and predictive results to model diameter distributions. In fitting the probability density functions, percentiles and moments values of diameter distributions have been used successfully to characterize distributions. The parameter recovery methods for calculating the parameters of probability density functions include the different percentiles values for distribution, e.g. 67, 3, 25, 50 or 95% values of the diameter distribution. In this study, 6 sample plots were used to compare some parameter recovery methods using different percentiles and moment values for distribution for fitting 3-paramaters Weibull in Oriental spruce and Scotch pine mixed stands located in Trabzon and Giresun Forest Regional Directorate. The parameter recovery methods were compared by based on Rennolds et al. (988) s error index values calculated by difference between observed and predicted diameter distributions. The comparative results have shown that the parameter recovery method using 25%, 50% and 63% values with mean rank has the more successful results for describe different diameter distributions than other recovery methods. Keywords: Diameter distribution, Parameter recovery Methods, Weibull, Probability density functions Introduction: The prediction of diameter distributions is not only important for estimating the type of products to be obtained for forest areas, but also useful in forest planning for resource management (Nanang 998). The diameter distribution is an indicator of structure of growing stock, stand structure, biological diversity, carbon sequestration (Fonseca et al. 2009). In this regard, efficient forest management planning requires the detailed information about diameter distribution under different management schedules (Palahí et al. 2007). To describe diameter distributions of forest stands, many continuous probability density functions, such as log-normal, gamma, beta, Weibull, and Johnson s SB, have been used for decision-making process in forest planning (Poudel and Cao 202). As pioneer studies for modeling diameter distributions, Clutter and Bennett (965) used the beta distribution with four parameters to define diameter distribution of slash-pine plantations. Bailey and Dell (973) introduced the use of the Weibull function for modeling diameter distribution (Cao 2004). The Weibull with three parameters has been widely used in forestry applications to describe the diameter distributions more than other distribution functions because the function have been shown to be more flexible for fitting various diameter distributions without the need for numerical integration (Nanang 998; Cao 2004). In predicting the parameters of diameter distribution functions, four different methods have been used: () nonlinear regression, (2) maximum likelihood estimation, (3) momentsbased method and (4) percentile-based method. The percentile-based prediction method has been widely used to model diameter distribution because the percentilebased method can give more compatible 9 I n t e r n a t i o n a l C a u c a s i a n F o r e s t r y S y m p o s i u m

2 Comparing Parameter Recovery Methods for Diameter Distribution Models of Oriental Spruce (Picea orientalis (L.) Link.) and Scotch Pine (Pinus sylvestris L.) Mixed Stands Located Trabzon and Giresun Forest Regional Directorate results to estimate future diameter distributions than other prediction methods. Especially, the percentile values of distribution are important indicator to diameter distribution and also, these values have robust relations with stand age and other stand variables. Lohrey and Bailey (977) used the some percentiles including 24 th and 93 rd to calculate the shape and scale parameters of the Weibull distribution. Bailey et al. (989) used the Weibull parameters from the predicted minimum diameter, quadratic mean diameter, 25 th, 50 th, and 95 th percentiles (Poudel 2007). Many studies have been used successfully the different percentiles values to calculate the parameters of distribution functions, e. g. Knowe 992; Bailey et al. 989; Knoew et al. 997; Liu et al. 2004; Cao 2004; Poudel 20; Poudel and Cao 203). In this study, some parameter recovery methods with different percentile values for 3-paramaters Weibull probability density functions were compared to describe diameter distributions in Oriental spruce (Picea orientalis L.) and Scotch pine (Pinus sylvestris L.) mixed stands located in Trabzon and Giresun Forest Regional Directorate. Material and Methods: In this study, 6 sample plots obtained by Ercanlı (200) were used to calculate the parameters of the 3-paramaters Weibull probability density function. These sample plots were randomly selected to represent the range of site qualities and ages variability throughout Oriental spruce and Scotch pine mixed stands located in Trabzon and Giresun Forest Regional Directorate. These sampled mixed stands were naturally regenerated and uniformly stocked stands (60-90% tree layer cover), without any evidence of historical damage such as fire or storms. The plot size ranged from 0.06 to 0.2 ha, depending on stand density in order to achieve a minimum of trees per species in sample plots. In these sample plots, diameter at breast height (dbh) were measured to the nearest 0. cm with calipers for every living tree with dbh>8.0 cm. Total tree heights (h) were measured on a subset of trees selected by using the rule of two tree per each 4 cm diameter class with Blume-Leiss Altimeter with the 0. m precision. The 3-paramaters Weibull probability density function were used to describe diameter distributions in studied mixed stands. These functions are given as follows: 3-paramaters Weibull F(x, α, β, γ) = α β (x γ β )α exp ( ( x γ β )α ) () Where x: diameter at breast height, α, β, γ: location, scale and shape parameter of weibull function. In fitting the parameters of these functions, some parameter recovery methods with different percentile values were used to describe diameter distributions. These parameter recovery methods including different formulas based on percentiles values were shown in Table. Reynolds et al. s (988) error index values were computed to evaluate the methods with different percentile values. The formulae of error index value is as follows: m e = N predicted N observed i= Where m: diameter class, N predicted ; the predicted number of trees in diameter class with different parameter recovery methods, N observed ; observed number of trees in diameter class. The predicted and observed numbers of trees in diameter classes were compared by the Reynolds et al. s (988) error index values. Especially, ranking procedure based on the error index values was applied to each sample plots. The most successful methods with the lowest error values were codded as and others with higher error values have the ascending code. As a result, the parameter recovery method with the lowest mean rank was selected as the successful method to describe diameter distribution 20 I n t e r n a t i o n a l C a u c a s i a n F o r e s t r y S y m p o s i u m

3 İlker Ercanlı, Ferhat Bolat, and Aydın Kahriman Table. The parameter recovery formulas of 3-parameter Weibull function including different percentile values Method Formulas 3% and 63% values α = 0.5 d min γ = 50% and 95% values α = 0.5 d min γ = 25%, 50% and 63% values 3%, 50% and 63% values minimum and quadratic mean diameter, 25%, 50% and 95% values β = α = 0.5 d min γ = β = α = 0.5 d min γ = β = α = n d min d %50 n β = α Γ Γ 2 Ln( Ln( 0.63) Ln( 0,3) ) Ln(d %63 α) Ln(d %3 α) β = Ln( Ln( 0.95) Ln( 0,50) ) Ln(d %95 α) Ln(d %50 α) d %50 α ( Ln( 0.50)) γ Ln( Ln( 0.95) Ln( 0,25) ) Ln(d %95 α) Ln(d %25 α) d %50 α ( Ln( 0.50)) γ Ln( Ln( 0.63) Ln( 0,3) ) Ln(d %63 α) Ln(d %3 α) d %50 α ( Ln( 0.50)) γ γ = Ln(d %95 α) Ln(d %25 α) + ( α ) (Γ 2 Γ Γ ) + ( d 2 g ) 2 Γ 2 d %63 α ( Ln( 0.63)) γ n; number of trees in sample plots, d min ; minimum diameter in plot, d max ; maximum diameter, d %25, d %3, d %50 d %63, d %95 ; percentile values, Z 95 ; standardized values based on d 95,d g ; quadratic mean diameter ve Γ; gamma distribution, Γ = Γ ( + γ ) ve Γ 2 = Γ ( + 2 γ ). Results: The comparative results for the recovery methods including different percentile values were presented by using error index and rank codes for each sample plots in Table 2. In these results, method based on 3% and 63% values were scored as st at 42 times, 2 nd at 38 times, 3 rd at 39 times, 4 th at 35 times and 5 th at 7 times, and also mean score of this method is The method 2 based on 50% and 95% values were scored as st at 32 times, 2 nd at 3 times, 3 rd at 4 times, 4 th at 6 times and 5 th at 23 times, and also mean score of this method is The method 3 based on 25%, 50% and 63% values were scored as st at 48 times, 2 nd at 40 times, 3 rd at 46 times, 4 th at 24 times and 5 th at 3 times, and also mean score of this method is The method 4 based on 3%, 50% and 63% values were scored as st at 27 times, 2 nd at 46 times, 3 rd at 49 times, 4 th at 32 times and 5 th at 7 times, and also mean score of this method is The method 5 based on 3%, 50% and 63% values were scored as st at 2 times, 2 nd at 6 times, 3 rd at 3 times, 4 th at 9 times and 5 th at 2 times, and also mean score of this method is Thus, the parameter recovery method using 25%, 50% and 63% values with mean rank has the more successful results for describe different diameter distributions than other recovery methods. Fig.. has presented the graphical comparisons between the observed and predicted number of trees in some sample plots. 2 I n t e r n a t i o n a l C a u c a s i a n F o r e s t r y S y m p o s i u m

4 Frequency Frequency Comparing Parameter Recovery Methods for Diameter Distribution Models of Oriental Spruce (Picea orientalis (L.) Link.) and Scotch Pine (Pinus sylvestris L.) Mixed Stands Located Trabzon and Giresun Forest Regional Directorate Diameter classes (cm) Diameter classes (cm) Fig.. Graphical comparisons between the observed and predicted number of trees for two sample plots, No.. and No. 4. Discussion: In this study, some parameter recovery methods for 3-paramaters Weibull probability density functions were used to describe diameter distributions in Oriental spruce and Scotch pine mixed stands located in Trabzon and Giresun Forest Regional Directorate. Five parameter recovery methods have included some percentile values: 3% and 63% values (Method ), 50% and 95% values (Method 2), 25%, 50% and 63% values (Method 3), 3%, 50% and 63% values (Method 4) and minimum and quadratic mean diameter, 25%, 50% and 95% values (Method 5). The comparisons based on Reynolds et al. s (988) error index values for these methods were shown that the parameter recovery Method 3 using 25%, 50% and 63% values presented the most successful results for describing diameter distributions, because of the ability of these percentile values, 25%, 50% and 63%, to represent different diameter distributions of the studied mixed stands model stand. Moreover, other some studies have shown that diverse percentile values were successful to model diameter distributions. Bullock and Burkhart (2005) used the 25 th and 97 th percentiles to characterize the juvenile diameter distributions of loblolly pine by the Weibull function. Lohrey and Bailey (977) and Bailey et al. (989) used the some percentiles including 24 th and 93 rd, minimum diameter, quadratic mean diameter, 25 th, 50 th, and 95 th percentiles to define diameter distributions. The characteristics of diameter distributions differ in forest stand structure and forest site attributes, thus the achievement of different percentile values to model diameter distribution depend on these features of forest areas. 22 I n t e r n a t i o n a l C a u c a s i a n F o r e s t r y S y m p o s i u m

5 İlker Ercanlı, Ferhat Bolat, and Aydın Kahriman The knowledge about forest structure including the detailed product predictions is important in sustainable and planned forestry, and so many diameter distribution models have been developed for different forest management activities. In this regard, for main our tree species and forest sites, these diameter distribution models have required in forest resource management. Table 2. The comparative results including Reynolds et al. s (988) error index values for the recovery methods with different percentile values Sample No. Method Method 2 Method 3 Method 4 Method Continuing Table I n t e r n a t i o n a l C a u c a s i a n F o r e s t r y S y m p o s i u m

6 Comparing Parameter Recovery Methods for Diameter Distribution Models of Oriental Spruce (Picea orientalis (L.) Link.) and Scotch Pine (Pinus sylvestris L.) Mixed Stands Located Trabzon and Giresun Forest Regional Directorate Continuing Table I n t e r n a t i o n a l C a u c a s i a n F o r e s t r y S y m p o s i u m

7 İlker Ercanlı, Ferhat Bolat, and Aydın Kahriman I n t e r n a t i o n a l C a u c a s i a n F o r e s t r y S y m p o s i u m

8 Comparing Parameter Recovery Methods for Diameter Distribution Models of Oriental Spruce (Picea orientalis (L.) Link.) and Scotch Pine (Pinus sylvestris L.) Mixed Stands Located Trabzon and Giresun Forest Regional Directorate References Bailey, R.L., and Dell, T. R Quantifying diameter distributions with the weibull function. Forest Science (9); Bullock, B., and Burkhart, H., Juvenile diameter distributions of loblolly pine characterized by two-parameter Weibull function. New Forests 29, Cao, Q. V Predicting parameters of a weibull function for modelling diameter distribution. Forest Science (50); Clutter, J. L., and Bennet, F. A Diameter distributions in old-field slash pine plantation. Georgia Forest Research Council Report No: 3. Ercanlı, İ Trabzon ve Giresun Orman Bölge Müdürlükleri sınırları içeresinde yer alan Doğu ladini (Picea orientalis (L.) Link)- Sarıçam (Pinus sylvestris L.) karışık meşcerelerine ilişkin büyüme modelleri. Doktora Tezi, 337 s., KTÜ, Trabzon. Fonseca, T. F., Marques, C. P., and Parresol, B. R Describing Maritime pine diameter distributions with Johnson s S B distribution using a new all-parameter recovery approach. Forest Science 55(4): Knowe, S. A Basal area and diameter distribution models for loblolly pine plantations with hardwood competition in the piedmont and upper coastal plain. Southern Journal of Applied Forestry (6); Knowe, S. A., Ahrens, G. A., and DeBell, D. S Comparison of diameter-distribution prediction, stand table projection and individual-tree growth modeling approaches for young red alder plantations. For. Ecol. Manage. 96: Liu, C., Zhang, S.Y., Lei, Y., Newton, P.F., and Zhang, L Evaluation of tree methods for predicting diameter distributions of black spruce (Picea mariana) plantations in central Canada. Canadian Journal of Forest Research (34); Lohrey, B. E., and Bailey, R. L Yield tables and stand structure for untinned long leaf pine plantations in Louisiana and Texas. USDA For. Ser. Res. Pap. SO s. Nanag, D. M Suitability of the normal, log-normal and weibull distributions for fitting diameter distributions of neem plantations in Northern Ghana. Forest Ecology and Management (03); -7. Palahí, M., Pukkala, T., and Trasobares, A Modelling the diameter distribution of Pinus sylvestris, Pinus nigra, and Pinus halepensis forest stands in Catalonia using the truncated Weibull function. Forestry 79, 5, Poudell, K. P. 20. Evaluation of methods to predict Weibull parameters for characterizing dimater distributions. Msc. Graduate Faculty of the Louisiana State University and Agricultural and Mechanical Collage, 60 s. Poudel, K.P., and Cao, Q.V Evaluation of methods to predict weibull parameters for characterizing diameter distributions. Forest Science. Poudell, K. P., and Cao Q. V., 203. Evaluation of methods to predict Weibull parameters for characterizing diameter distributions. Forest Science 59(2), Rennolls, K., Geary, D. N., and Rollinson, T. J. D Characterizing diameter distributions by the use of the weibull distributions Forestry (58); I n t e r n a t i o n a l C a u c a s i a n F o r e s t r y S y m p o s i u m