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一种有效求解含有不连续“开关”过程的变分资料同化的遗传算法

, PP. 458-470

Keywords: 变分资料同化,“开关”,遗传算法

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Abstract:

?随着大气或海洋模式的不断完善,越来越多的物理过程以参数化形式并入到模式中,这一方面使得模式能更加准确的描述大气或海洋的运动,但另一方面也在模式中引入了“开关”形式的非光滑过程,提高了模式的非线性性,最终导致基于传统伴随方法(ADJ)的变分资料同化(VDA)不能有效发挥作用.本文利用遗传算法(GA)的非光滑寻优能力,采用自适应的选择和变异算子以及混合交叉算子,并结合精英保留策略,提出了一种能有效求解含不连续“开关”过程的变分资料同化问题的GA(称为GANEW).为检验GANEW的有效性和可行性,一个描述实际数值天气预报模式中单格线上比湿随时间发展的偏微分方程被用作同化试验中的控制方程,并对基于GANEW的同化结果与基于ADJ的同化结果进行了比较,结果显示:尽管控制方程中的“开关”过程导致代价函数出现严重的跳跃不连续以及多极值点,但由于GANEW的遗传算子的适当配置,加之其不需要代价函数的梯度信息且在最优化搜索过程中可以充分考虑模式初值的物理约束,基于GANEW的变分同化方案在同化效果上明显优于传统伴随方法.此外,研究结果也显示基于GA的同化效果与遗传算子(选择、交叉、变异)选取有直接关系,采用合适的遗传算子可以获得更优的同化结果.最后,本文利用相似度对GANEW相应于观测误差、模式误差及观测密度的敏感性进行了分析,并与传统伴随方法进行了比较,结果显示GANEW在含有不连续的“开关”过程的变分资料同化中对观测误差,模式误差及稀疏观测具有更强的鲁棒性.

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