Intelligent optimization algorithms to VDA of models with on/off parameterizations

Some variational data assimilation (VDA) problems of time- and space-discrete models with on/off parameterizations can be regarded as non-smooth optimization problems. Same as the sub-gradient type method, intelligent optimization algorithms, which are widely used in engineering optimization, can also be adopted in VDA in virtue of their no requirement of cost functions gradient (or sub-gradient) and their capability of global convergence. Two typical intelligent optimization algorithms, genetic algorithm (GA) and particle swarm optimization (PSO), are introduced to VDA of modified Lorenz equations with on-off parameterizations, then two VDA schemes are proposed, that is, GA based VDA (GA-VDA) and PSO based VDA (PSO-VDA). After revealing the advantage of GA and PSO over conventional adjoint methods in the ability of global searching at the existence of cost functions discontinuity induced by on-off switches, sensitivities of GA-VDA and PSO-VDA to population size, observational noise, model error and observational density are detailedly analyzed. Its shown that, in the context of modified Lorenz equations, with proper population size, GA-VDA and PSO-VDA can effectively estimate the global optimal solution, while PSO-VDA consumes much less computational time than GA-VDA with the same population size, and requires a much lower population size with nearly the same results, both methods are not very sensitive to observation noise and model error, while PSO-VDA shows a better performance with observational noise than GA-VDA. It is encouraging that both methods are not sensitive to observational density, especially PSO-VDA, using which almost the same perfect assimilation results can be obtained with comparatively sparse observations.     

THE EFFECTIVENESS OF GENETIC ALGORITHM IN CAPTURING CONDITIONAL NONLINEAR OPTIMAL PERTURBATION WITH PARAMETERIZATION "ON-OFF" SWITCHES INCLUDED BY A MODEL

In the typhoon adaptive observation based on conditional nonlinear optimal perturbation (CNOP), the ‘on-off’ switch caused by moist physical parameterization in prediction models prevents the conventional adjoint method from providing correct gradient during the optimization process. To address this problem, the capture of CNOP, when the on-off switches are included in models, is treated as non-smooth optimization in this study, and the genetic algorithm (GA) is introduced. After detailed algorithm procedur...     

模式含有开关时遗传算法求解条件非线性最优扰动的有效性研究

在基于条件非线性最优扰动(CNOP)的台风适应性观测研究中,针对预报模式的湿物理参数化产生的“on-off”开关导致传统伴随方法不能为最优化过程提供正确梯度这一现象,将模式含有“on-off”开关时求解CNOP的问题视为非光滑最优化问题,引入遗传算法,在给出详细的算法流程后,以一个在强迫项中含“on-off”开关的理想模式,分析了“on-off”开关对求解CNOP的影响,三个数值试验检验了模式含有“on-off”开关时遗传算法求解CNOP的有效性,并分析了不同初始种群对最优化结果的影响。结果显示,所采用的含有“on-off”开关的理想模式下,遗传算法能有效求解CNOP,最后对遗传算法求解CNOP的优缺点进行了详细讨论。     

THE EFFECTIVENESS OF GENETIC ALGORITHM IN CAPTURING CONDITIONAL NONLINEAR OPTIMAL PERTURBATION WITH PARAMETERIZATION “ON-OFF” SWITCHES INCLUDED BY A MODEL

In the typhoon adaptive observation based on conditional nonlinear optimal perturbation (CNOP), the ‘on-off’ switch caused by moist physical parameterization in prediction models prevents the conventional adjoint method from providing correct gradient during the optimization process. To address this problem, the capture of CNOP, when the “on-off” switches are included in models, is treated as non-smooth optimization in this study, and the genetic algorithm (GA) is introduced. After detailed algorithm procedures are formulated using an idealized model with parameterization “on-off” switches in the forcing term, the impacts of “on-off” switches on the capture of CNOP are analyzed, and three numerical experiments are conducted to check the effectiveness of GA in capturing CNOP and to analyze the impacts of different initial populations on the optimization result. The result shows that GA is competent for the capture of CNOP in the context of the idealized model with parameterization ‘on-off’ switches in this study. Finally, the advantages and disadvantages of GA in capturing CNOP are analyzed in detail.