A single-tree additive biomass model of Quercus variabilis Blume forests in North China
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To make the sum of estimated values from biomass models of various components of a tree equal to estimated tree total biomass for Quercus variabilis Blume (cork oak) forests in North China, single-tree additive biomass models were developed. 100 trees from 100 plots in North China were felled to obtain biomass of aboveground components, and roots of 19 of those trees were extracted for measurement of root biomass. After Box–Cox transformations of variables, two sets of independent component biomass models with a dummy variable to define stand origin were separately built using linear mixed effects analyses (one set of models with site as a random factor; the other set without any random factor). Then three methods were compared to force additivity of those models: sums of linear mixed effects models, sums of linear models, and simultaneous equation fits based on linear models. Model parameters were estimated by ordinary least squares (OLS) or seemingly unrelated regression procedures (SUR). Coefficients of determination (R 2), root mean square error (RMSE), confidence interval of predictions (CI), residuals plots and histograms of residuals indicated that models fitted with sums of linear mixed effects models were the least biased and most precise at estimating total aboveground biomass. Further testing for the linear mixed effects models with jackknife validation and prediction sum of squares (PRESS) statistics indicated that the additive biomass models can be used to predict biomass or carbon stocks of cork oak forests in North China within specific tree diameter at breast height and height ranges