Forest Growth Simulation And Management Optimization Using Process-based Models

A scientific approach to decision-making requires an optimal design of strategies and programs in forest management planning,which relies on an integration of stand growth dynamics and forest management measures into a complete simulation-optimization system.The realization of forest management relies on two key tools:the forest growth model and the management optimization model.An accurate description of the forest ecosystem from a stand growth model enables managers to obtain more detailed varying characteristics of stand dynamics,while the optimization algorithm guarantees the reliability of the optimal management scheme.Simulating forest growth mechanism has been advantageous in forest management research under the background of global climate change.The construction of a process-based model is based on the theoretical relationship between plants and the external environment.The structure of a process-based model is complex,with a large number of parameters.Those parameters should be measured from physiological control experiments.Compared to fitting an empirical model,the parameterization of a process-based model is more complicated.Meanwhile,as the simulators evolve from simple empirical models to complex process-based models,forest management is requiring more advanced optimization algorithms.Given the above issues,this study applied an inverse modeling method,i.e.the optimization technique in the operational research,to parameterize the process-based model CROBAS and 3-PG.Furthermore,the prospect of applying process-based models and optimization algorithms in forest management planning was discussed by testing the PipeQual model（Extended CROBAS）and population-based algorithms.The main contents and results are as follows:（1）An application of three global sensitivity analysis techniques to a process-based model CROBAS was demonstrated.This study focused on ten parameters related to the hypothesis about the tree structure of Pinus armandii.Using Nash-Sutcliffe efficiency（NSE）of tree height and organ biomasses,three global sensitivity analysis techniques were compared,including the Morris screening methods,the variance-based Sobol indices,and the Extended Fourier Amplitude Sensitivity Test（EFAST）.The results showed that the order of parametric sensitivity slightly changed with the chosen methods,while greatly changed with objective functions.Both Morris and EFAST methods outperformed the Sobol method in terms of convergence efficiency.All outputs were sensitive to the maximum rate of canopy photosynthesis per unit area,the specific leaf area,and the extinction coefficient.The light interception of tree canopy played a key role in the simulation of tree growth with CROBAS.Moreover,the validation of foliage biomass module was crucial when applying this carbon balance theory to biomass simulations.（2）Based on the literature of tree physiology and empirical models,an inverse modeling method based on optimization techniques was used to parameterize the process-based model CROBAS and 3-PG.Deviations between outputs from process-based models and empirical models were used as the objective function.Considering the dependences on plant traits,parameters were partially selected as decision variables in the optimization model.CROBAS-PA and 3-PG-PT were parameterized by using differential evolution algorithm（DE）and particle swarm optimization algorithm（PSO）,respectively.The results showed that the height predictions from CROBAS-PA were lower than those from the empirical model QUASSI 1.0,and the maximum of the deviations was only 1.0 m.The deviations of DBH predictions between CROBAS-PA and QUASSI 1.0 varied with site classes,while the maximum value was only 1.2 cm.The 3-PG-PT underestimated most stand variables,and the maximum relative error was 8.65%.The maximum deviation of volume between 3-PG-PT and QUASSI 1.0 was 6.83%.Although the parameterizations of process-based models assimilated information from empirical models,a certain deviation of predictions between those two types of models still existed.This distinction demonstrated that process-based models are strictly constrained with complex structures,which means a lower risk of overfitting.（3）The study of 3-PG-PT model analyzed the sensitivity of key physiological parameters affecting the growth of Pinus tabulaeformis.Soil effective moistureshowed a strong effect on volume and foliage weight,while only a slight effect on root weight.Specific leaf area at stand initial age₀,specific leaf area for mature leaves₁,and the agewhen specific leaf area reaches（₀+₁）/2,performed large effects on predictions of stand volume and foliage weight.Thus,the parameters affecting photosynthesis were influential in model predictions.（4）Thinning and rotation were optimized by linking the process-based growth model PipeQual with four population-based algorithms that include differential evolution（DE）,particle swarm optimization（PSO）,evolution strategy（ES）and Nelder-Mead（NM）algorithms.For all experimental stands,optimal rotations varied with algorithms.The optimal rotation was flexible considering that the difference among optimal rotations could change from one to fifteen years in some stands.The number of thinnings was consistent,i.e.three or four times.The denser the stand was,the earlier the first thinning,and the more times of thinning occurred.The type of thinning significantly changed in selecting different tree size classes to be removed from early pre-commercial thinnings to later commercial thinnings.For early thinnings,most small and medium size trees were remained,and only some large size trees were thinned.For later thinnings,large and medium size trees were mostly removed,and some of the small size trees were selectively thinned.（5）This study evaluated the performance of four different population-based algorithms in solving high-dimensional forest management optimization problems.Compared with the optimal value of Direct and Random Search（DRS）,algorithm PSO and DE were more accurate,and NM performed the worst among the four algorithms.For the globally optimal values calculated from algorithm NM,the deviation increased with the increasing number of decision variables.The computational time of PSO was the longest,while that of NM was the shortest.The computational time of PSO was twice the time of NM.The speed of convergence of NM was the fastest,followed by ES and PSO,and DE was the slowest.The robustness of DE was the best,followed by PSO and NM,and ES was the worst.The reason for the different performance of each algorithm is complex,which is mainly caused by the parameters of the algorithm,the operation mode and the model used.