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 function’s 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 function’s 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. It’s 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.
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