Error Structure Of Individual Tree Volume For Larix Gmelinii And Pinus Sylvestris Var.Mongolica In Daxing’Anling

Individual tree volume model is widely used in forestry work.It’s establishmentt is not only of great significance in the study of forest resources,but also can provide good suggestions for improving the commercial value of timber.In this study,three individual tree volume models were developed for Larix gmelinii and Pinus sylvestris var.mongolica in Daxing’anling.Error structure was studied and error functions were added in each model to reduce heteroscedasticity..Ballantyne(2013)provides the method how to test the error structure by likelihood analysis.For comparison,nonlinear model was fitted using GNLS in S-Plus.Variance functions(fixed variance,exponential function,power function and constant plus power function)were incorporated into general nonlinear model to reduce heteroscedasticity.Coefficient determination(R2),root mean square error(RMSE),mean absolute bias(Bias),and mean relative error(MRE),were employed to evaluate the precision of different individual volume models.The results show that through likelihood analysis,error structure of each individual tree volume model is multiplicative.In order to describe the variance phenomenon in the process of individual tree volume model,variance functions(fixed variance,exponential function,power function and constant plus power function)were incorporated into volume model,and all variance functions could reduce heteroscedasticity.Base on data of Larix gmelinii,power function and constant plus power function were best for mode(1)and model(2),model(3)respectively.But base on data of Pinus sylvestris var.mongolica,constant plus power function and power function were best for model(1)and model(2),model(3)respectively.Model fitting and validation indicated that the results were pretty similar for both error structures of Larix gmelinii,however,volume model(1)with additive error structure was slightly better than multiplicative error structure,volume model(2)and volume mode(3)with additive error structure were slightly worse than multiplicative error structure.On the contrary,the results were pretty similar for both error structures of Pinus sylvestris var.mongolica,nevertheless,volume model(1)with additive error structure was slightly better than multiplicative error structure,volume model(2)with additive error structure was slightly worse than multiplicative error structure,however,volume model(3)with additive error structure was slightly worse than multiplicative error structure in fitting results,volume model(3)with additive error structure was slightly better than multiplicative error structure in validation results.The results of large-diameter class trees were more important than those of medium-diameter class tress and small-diameter trees,even it directly affected the overall results.This study did not give an absolute and consistent conclusion from comparison.If model prediction is the first,error structure should be selected based on prediction precision.