On the approximation of the inverse error covariances of high‐resolution satellite altimetry data
On the approximation of the inverse error covariances of high‐resolution satellite altimetry data
复制标题
高分辨率卫星测高数据反误差协方差的近似
DOI：
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发表时间：
2018
影响因子：
8.9
通讯作者：
G. Jacobs
中科院分区：
文献类型：
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作者：
M. Yaremchuk;J. D’Addezio;G. Panteleev;G. Jacobs
计划在不久的将来监测海洋表面的高分辨率（条带）高度计任务具有观测误差协方差（OEC）和缓慢衰减的非对角线元素。这一特性对大多数数据同化算法提出了挑战，这些算法是在对角线 OEC 很容易反转的假设下设计的。在本文中，我们提出了一种通过空间非齐次微分算子多项式表示的稀疏矩阵来近似稠密 OEC 的逆的方法，其系数通过最小化二次成本函数来优化以拟合目标 OEC。导出了成本函数梯度和 Hessian 矩阵的显式表达式。该方法使用 SWOT 模拟器生成的 OEC 模型进行测试。
High‐resolution (swath) altimeter missions scheduled to monitor the ocean surface in the near future have observation‐error covariances (OECs) with slowly decaying off‐diagonal elements. This property presents a challenge for the majority of the data assimilation algorithms which were designed under the assumption of the diagonal OECs being easily inverted. In this note, we present a method of approximating the inverse of a dense OEC by a sparse matrix represented by the polynomial of spatially inhomogeneous differential operators, whose coefficients are optimized to fit the target OEC by minimizing a quadratic cost function. Explicit expressions for the cost function gradient and the Hessian are derived. The method is tested with an OEC model generated by the SWOT simulator.