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基于奇异值分解的计算条件非线性最优扰动的集合投影算法

, PP. 366-376

Keywords: 奇异值分解,集合投影算法,ENSO,条件非线性最优扰动

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Abstract:

?条件非线性最优扰动(CNOP)是线性奇异向量(LSV)在非线性领域的拓展,它代表了在一定物理约束条件下且在预报时刻导致最大预报误差的一类初始误差.CNOP类型的初始误差在天气和气候的可预报性研究中具有重要作用.在求解复杂数值模式的CNOP中,一般通过数值计算目标函数关于初始扰动的梯度,并沿着梯度下降方向在相空间搜索极值点而得到CNOP.计算梯度常用的一个方法是利用伴随模式得到梯度,然而发展一个复杂模式的伴随模式是困难且非常繁琐的,大大限制了CNOP方法在复杂数值模式中的广泛应用.本文在前人工作的基础上,提出了一种基于奇异值分解(SVD)的集合投影算法.该算法避免了集合投影算法中采用的局地化步骤,从而克服了局地化半径的经验性选择带来的不确定性.将该算法应用于中等复杂程度的ENSO预报模式中计算CNOP.结果表明,用新集合投影算法得到的CNOP能够有效地逼近用伴随算法得到的CNOP,抓住了CNOP的主要空间特征.因此,本文提出的基于SVD的集合投影算法是计算CNOP的一种有效近似算法.

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