| Classical statistics is a statistical inference method based on population and sample information,which is widely used in the individual tree model.Bayesian statistics adds a prior information on the basis of population and sample information.Its application in forestry modeling is much less than the classical method,but in recent years,it has also became a research trend.The data of this study contains two parts:the first part is the ground survey data of 1515strains of Larix principis-rupprechtii Mayr.from Guandi Mountain in Shanxi Province,and the second part is the airborne lidar and ground survey data of 402 Picea Crassifolia Kom.from Xishui Forest Farm in Gansu Province.In this study,the first dataset was used to establish the crown width model and tree height curve of Larix principis-rupprechtii Mayr.based on ground survey data,and the second dataset was used to establish the above-ground biomass inversion model of Picea Crassifolia Kom based on ground and lidar data.In this study,in order to consider the practicality of the model,only the diameter at breast height(D)was selected as the independent variable in the crown width model.The parameter estimation methods used in crown width model are least squares regression,mixed effects model,Bayesian method,and hierarchical Bayesian model.In the modeling process,the model fitting effects and parameter estimation stability of these four methods are compared and analyzed.In addition to D,the independent variables some stand variables(HDOM and BA)were included in the tree height curve.Lidar diameter(D),Lidar tree height(LH)and Lidar crown projection area(CPA)were also added as independent variables in the above-ground biomass inversion model.In the individual tree height curve and above-ground biomass inversion model,we mainly compared the fitting effect of the mixed effect model and the hierarchical Bayesian model.Through random sampling,samples of different sizes were drawn from the population.The fitting performance of the mixed effect model and the hierarchical Bayesian model with different sample sizes has been studied.The results of this study are summarized as follows:(1)By analyzing the parameter estimation results of the three individual tree models developed in this study,when predicting the crown width and tree height of Larix principis-rupprechtii Mayr.and the individual tree aboveground biomass of Picea Crassifolia Kom.,it is concluded that the parameter estimation results of the Bayesian method are more stable than the classical method,the standard deviation and its fluctuation of Bayesian methods is smaller.(2)After adding the plot level random effect into the best crown width model,the fitting effect of the model is significantly improved.The R~2 of the model fitted by the least squares regression and the Bayesian method are both 0.349,and the R~2 of the mixed effect model and the hierarchical Bayesian model are both 0.673.(3)The fitting results of the crown width model in this study show that there is no significant difference between the classical method and the Bayesian method in the full dataset.According to the model test index,the fitting effect of the least square regression is basically the same as the Bayesian method;and the fitting effect of the mixed effect model is also basically the same as the hierarchical Bayesian model.(4)The addition of stand variables stand dominant height(HDOM)and stand basal area(BA)improved the prediction accuracy of the tree height curves,and the effect of HDOM on height-diameter relationship is larger than BA.When using only one independent variable(D)to predict tree height,the model’s R~2 is 0.673,and when the HDOM,BA and D are added together to the tree height curves,the R~2 of the model is increased to 0.785.(5)The hierarchical Bayesian model and the mixed effect model were used to fit the tree height curves and the aboveground biomass model under different sample sizes,and it was concluded that the fitting effect of the hierarchical Bayesian model is better than the mixed effect model when the sample size is small.The smaller the sample size,the greater the difference between the fitting effects of the two methods.In the tree height curves,at the full dataset(1515),the R~2 of the mixed effect model and the hierarchical Bayesian model are 0.812 and 0.814,which are basically the same.When the sample size is 5%(105)of the population,the R~2 of the mixed effect model and the hierarchical Bayesian model are 0.855 and 0.862,respectively,the difference become relatively larger;the results are similar in the aboveground biomass model.(6)According to the parameter estimation results of the tree height curves,the parameter estimation stability of the mixed effect model fluctuates greatly with the change of the sample size,and the parameter estimation stability of the hierarchical Bayes model fluctuates little with the change of the sample size. |
