中文摘要：

利用条件非线性最优扰动（conditional nonlinear optimal perturbation,CNOP）可以实现最大预报误差的上界估计。CNOP通常由基于梯度信息的约束优化算法进行求解,且其中的梯度信息由伴随模式提供。然而当非线性模式中含不连续＂开关＂时,传统伴随方法不能为优化过程提供正确的梯度方向,从而导致优化失败。为此,采用自适应变异和混合交叉的遗传算法,联赛选择机制和小生境技术的约束处理方法来求解最大预报误差上界。为检验新方法的有效性,以修改的Lorenz模型作为预报模式,对3个初始态分别用新方法和传统伴随方法进行比较,数值试验结果显示新方法求解出的最大预报误差的上界更加精确。

英文摘要：

Estimating the upper bound of maximum prediction errors can be achieved by using the conditional nonlinear optimal perturbation（CNOP） .Generally,CNOP is obtained by the constrained optimization algorithm based on gradient information provided by the associated adjoint model.However,when the nonlinear model contains discontinuous ＂on-off＂ switches,the conventional adjoint method cannot provide the correct gradient direction,and eventually induces the optimization to fail.Hence,genetic algorithm（GA） with self-adaptive mutation and blend crossover operators,tournament selection mechanism and niche strategy are adopted to solve the upper bound of maximum prediction errors in this paper.In order to test the effectiveness of the new method,we take the modified Lorenz model as the prediction model,and make comparison between the new method and the conventional adjoint method respectively aiming to three different initial reference states.The numerical experiment results show that the new method is more effective for solving the upper bound of maximum prediction errors.