Construction And Accuracy Analysis Of Individual Tree Biomass Model Of Larix Olgensis Considering Random Effects

Accurate assessment of forest biomass in China is of great significance for studying the carbon cycle and carbon storage control mechanisms of global terrestrial ecosystems.Based on the biomass data of 376 species of Larix olgensis in Heilongjiang Province,this study used simple random sampling,equal proportion stratified sampling,and equal number stratified sampling to obtain biomass models with different cost sizes and fitting error structures of multiplicity and additivity to determine the error structure of the biomass model.A seemingly unrelated regression(SUR)method was used to construct a unary biomass SUR model(SUR1)with diameter at breast height as the independent variable,and a binary biomass SUR model(SUR2)with the combination of diameter at breast height and tree height as the independent variable.On the basis of the SUR model,random effects at the sample level were considered,and then a mixed effect model of unary and binary seemingly unrelated effects(SURM1,SURM2)was constructed.According to the characteristic that the calculation of random effects in the SURM model does not require the measured values of all dependent variables,the bias of the following four types of SURM models in predicting biomass is analyzed and compared in detail:1)SURM1-a,SURM2-a,and the random effects are calculated based on the measured values of stem,branch,and foliage biomass;2)SURM1-b,the random effect is calculated based on the measured value of tree height;3)SURM1-c,SURM2-c,the random effect is calculated based on the measured crown length;4)SURM1-d,the random effect is calculated based on the measured values of tree height and crown length.The results showed that sample size and sampling method had a small impact on the judgment of biomass models.When the sample size is greater than 40,the logarithmically transformed linear model is more suitable for fitting the biomass model regardless of the sampling method.The SURM model has a better fitting effect than the SUR model.The adjusted determination coefficient Ram~2 of the SURM model is always greater than the corresponding SUR model,and the root mean square error RMSE is always smaller than the corresponding SUR model.After considering the random effect at the sample plot level,the fitting effect of the branch and foliage biomass models improved significantly,with Ra~2 increasing by more than 14%,while the fitting effect of the stem and root biomass models improved slightly,with Ra~2 increasing by 1.4%and 4.5%,respectively.When using five randomly selected trees to calculate random effects at the sample site level,the prediction performance of the SURM model is better than that of the SURM model and the SURM model that only considers fixed effects,especially the SURM1-a model(the average absolute error percentages of stem,branch,foliage,and root are 10.4%,29.7%,32.1%,and 19.5%,respectively)and the SURM2-a model(the average absolute error percentages of stem,branch,foliage,and root are 7.3%,29.9%,33.8%,and 20.5%,respectively).In addition to the SURM1-a and SURM2-a models,the deviation of using the SURM1-d model to predict the biomass of branches,foliages,and roots is less than the SURM1-b,SURM1-c models,and SURM2-c.In actual prediction,although the prediction accuracy of the SURM model using measured aboveground biomass values to correct random parameters is the highest,it needs to measure the aboveground biomass of several trees,and the use cost is relatively high.Therefore,this study recommends using the SURM1-d model with measured tree height and crown length to predict the standing biomass of Larix olgensis.