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An empirical model for predicting dbh growth with age for Eucalyptus grandis
By Admin | January 7, 2009
Eucalyptus grandis Hill ex Maiden (rose gum) is commonly grown as even-aged monocultures in colder climates in the hilly region of Sri Lanka. Trees harvested from those plantations are used for sawn timber, railway sleepers and fuel. In order to manage those plantations, estimation of diameter growth is essential with age and therefore that was the objective of this study.
Data were collected from 26 plantations for the model construction covering the entire region, which is favourable for rose gum growth. According to the above objective, age was selected as the primary explanatory variable. A Site index was selected as a second explanatory variable where there were growth differences apparent due to different site qualities. After developing the theoretical model structures, the modelling process was divided into three stages. Variables were also transformed to different forms to obtain the best models. R2 values and standard residual distributions were used as preliminary evaluations.
At stage one, it was tried to build a simple (linear or exponential) model to predict the dbh growth using age as the only explanatory variable. However, this was not successful due to low R2 values and non-constant variances.
Data were partitioned due to site differences at stage two using a site index, i.e., top height/age. It was possible to identify three site types with mean index values of 2.4, 1.6 and 1.1. After that similar model structures were separately fitted to each site class to estimate different parameters. The selected linear models over-estimated the dbh values for the lower ages. The parameter associated with age for the exponential models always indicated an indefinite increase of dbh with age. In addition to the above two, logistic functions were also fitted at this stage. However, for the poor sites, it had large outliers. Therefore stage two was also not successful.
Finally it was decided to use stage three with pooled data. Exponential and logistic functions were modified at this stage with a site index as a second explanatory variable in addition to the age. However, other than top height/age index, a partially qualitative site classification (site class) was also used. Initial parameters required for the iterations in SPSS were decided by simply fitting exponential and logistic functions without the second explanatory variable. For the second variable it was assumed as 1. Models with partially qualitative site classes had to be removed due to having parallel distributions between three site types. Finally it was possible to select 7 best models based on R2 and residual distribution. All those models indicated a high modelling efficiency and minimum bias when tested. Then the estimated dbh values were fitted against an age series of 5 to 50 to identify the distribution and compatibility with biological reality. After all those evaluations, the model shown below was identified as the best model to predict the dbh growth for rose gum in Sri Lanka for all site types. When tested with the data reserved at the beginning of the study, this model proved its suitability for field use.
Subasinghe, S.M.C.U.P.
Department of Forestry and Environmental Science
University of Sri Jayewardenepura
Nugegoda, Sri Lanka
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