关键词: 贝叶斯统计, 全局敏感性, 树高生长, 不确定性量化, 油松, 幼树

Abstract:

Objective: This study aimed to propose a theoretical basis for the uncertainty analysis in modeling young tree growth. A height increment model for young Pinus tabulaeformis was built using research inventory data of pine-oak forests in the Qinling Mountains. The effect of uncertainty sources on model predictions was then analyzed by disaggregating the predictive uncertainty into contributions from every single parameter. Method: The height increment model of young P. tabulaeformis was constructed using 132 sampled young trees. The Markov Chain Monte Carlo (MCMC) method was used to obtain the joint posterior distribution of parameters,and to quantify the uncertainty of model outputs,in terms of the uncertainty of prediction error,measurement errors of the inputs and the parametric uncertainty. A combination of Bayesian statistics and global sensitivity analysis (GSA) was used to quantify the uncertainty propagation. The contributions of different parameters to the predictive uncertainty were represented by the variable coefficient (CV,%) and 95% Bayesian credible intervals (B). Result: 1) The largest uncertainty source of model predictions was the random error,accounting for 51% of the total uncertainty. The least uncertainty source was parametric uncertainty,accounting for 43% of total uncertainty. The minimum uncertainty source was the measurement errors of model input,i.e. light interception (LI) and crown competition factor (CCF),accounting for only 6% of total uncertainty. The 95% credible interval of model prediction included 97% of observations,and sufficiently covered the ranges of random errors of observed data. 2) The parameter relating to CCF resulted in the largest contribution to the uncertainty of the predictions,and the propagated uncertainty attributed 64.87% of total parametric uncertainty. Parameters of LI and slope (SL) propagated 15.88% and 10.02% of total parametric uncertainty,respectively. The parameter of height accounted for only 1.78%,and the uncertainty contributed from other parameters was less than 1%. The uncertainty propagated from parametric interaction was less than 1%,except for the parameters relating to CCF and SL. 3) The Bayesian MAP (maximum a posteriori probability estimate) showed that the effects of CCF,LI and SL on the 5-year height increment of young P. tabulaeformis were negative,but positive on tree height. The results revealed that the higher parametric uncertainty,the less effects of corresponding variables on predictions. Conclusion: The uncertainty sources in the predictions of height increment for young P. tabulaeformis were complicated. Bayesian statistics and global sensitivity analysis (GSA) were combined to quantify and explain the uncertainty of young P. tabulaeformis growth by disaggregating the uncertainty into multiple sources. The contribution of each parameter to predictive uncertainty was quantified by sampling from the joint posterior distribution of parameters. Such a Bayesian approach might be capable for the quantification and disaggregation of uncertainty analysis in simulating of forest ecosystem dynamics.

Key words: Bayesian statistics, global sensitivity analysis, height growth, uncertainty quantification, Pinus tabulaeformis, young trees