Study On Dynamic Models For Caragana Korshinskii Biomass Based On Nonlinear Simultaneous Equation System

Biomass,as one of the important indicators to measure stand productivity and carbon sequestration capacity,plays an important role in natural resource management decision-making in the arid desert areas.To accurate estimatese biomass dynamic variations of Caragana korshinskii,a typical shrub found in the arid desert area.In this study,C.korshinskii in Yanchi County of Ningxia was taken as the research object.Based on the measured biomass data of 38 plots and the analytic data of 87 shrubs,five theoretical growth equations(Logistic、Richards、Gompertz、Mitscherlich、Korf)with ground diameter or shrub height changing with age were constructed,and the allometric growth equations of biomass(total,aboveground,stem,foliage and root)of each component with diameter or shrub height were constructed.The absolute mean residual(AMR),root mean system error(RMSE),and adjusted determination coefficient(adj-R2)were used to evaluate the performance of the equations,the optimal theory and allometric growth equation are selected by using these three evaluation indexes.Then,the optimal equations are combined by four nonlinear simultaneous(NLS)equations,the four nonlinear simultaneous equations include nonlinear ordinary least square(NOLS),nonlinear seemingly uncorrelated regression(NSUR),two-stage least squares(2SLS),three-stage least squares(3SLS).The dynamic model system of growth and biomass of C.korshinskii was established.Results showed that:(1)The data of diameter growth,height growth and biomass(total biomass,above-ground biomass,stem biomass and foliage biomass)did not accord with the normal distribution,so the generalized nonlinear model(GNL)was established.Among the five theoretical growth equations of ground diameter growth and height growth,Gompertz equation has the highest fitting accuracy,and Gompertz equation is the best theoretical growth equation.(2)The residual plots of basal diameter growth,height growth and biomass models of C.korshinskii showed trumpet shape,that is the data had heteroscedasticity.When the heteroscedasticity of diameter growth,height growth and biomass model of each component is eliminated by using power function,exponential function and constant plus power function,using power function as variance function is the best method to eliminate heteroscedasticity of the model.(3)In allometric growth model of Caragana Korshinskii,when the total diameter squared multiplied by height((nBDm)2Hm)was used as independent variable,the precision of the model was higher,the allometric growth equation with(nBDm)2Hm as independent variable is the optimal allometric growth equation.(4)The nonlinear seemingly uncorrelated regression(NSUR)method of nonlinear simultaneous methods has better performance than other methods or the independent equations of diameter growth,height growth and biomass of each component.