基于切线伴随技术计算GRAPES-Meso模式的奇异向量
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摘要: 集合数值天气预报的关键问题就是如何生成有效的初始扰动。奇异向量反映了初始扰动在大气系统相空间中演变发展的最不稳定方向,基于奇异向量产生的集合样本是模拟概率密度函数的最合理方法。以非静力、半隐式半拉格朗日GRAPES-Meso中尺度数值预报模式为基础,采用Lanczos迭代算法,利用GRAPES-Meso的切线伴随模式计算GRAPES奇异向量。为了检验求得的奇异向量的正确性,提出了两种检验奇异向量正确性的方法:一是比较计算的奇异值的一致性;二是依据特征向量在矩阵变换中的方向不变性意义,验证GRAPES奇异向量空间结构的正确性。最后研究了不同的时间间隔对GRAPES奇异向量的影响,结果表明GRAPES奇异向量在36小时的最优时间间隔误差增长速度最快,这表明在非静力、半隐式半拉格朗日格点模式中利用切线伴随技术计算奇异向量是可行的。
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