单多普勒天气雷达反演降水粒子垂直速度Ⅰ：算法分析

The precipitation particles’ vertical velocity retrieval with single Doppler weather radar. PartⅠ： Retrieval method’s analysis

中文关键词:  单多普勒天气雷达  改进的VVP方法  病态矩阵  垂直速度  敏感性分析

英文关键词:Single Doppler weather radar  Modified VVP method  Ill-conditioned matrix  Vertical velocity  Sensitivity analysis

中文摘要:

      针对多普勒雷达风场反演的体积速度处理（Volume Velocity Processing， VVP）方法中系数矩阵的病态问题，从数学上进行了分析和论证，对反演的误差进行了敏感性分析，并对垂直速度的求解方程作了改进。系数矩阵的条件数将随着待反演参量的不同而差别很大，通常的处理方法是舍弃量级较小的参量，通过对误差范数的分析，证明这种处理尽管存在模型误差，但能够降低求解难度和结果误差。对系数矩阵病态原因的分析发现，系数矩阵矢量的线性相关造成了矩阵奇异，当合并或舍弃线性相关项时，待反演参量会受模型误差的影响，并且这种模型误差的大小并不仅与待反演参量的量级有关，而且随着位置的不同而改变，但是部分待参量仍然可以保持准确值。在对VVP算法误差分析的基础上，分析并验证了舍弃部分参量时的反演误差，改进的算法为准确反演降水粒子的垂直速度提供了理论基础。

英文摘要:

      The ill-conditioned coefficient matrix and error sensitivities of the Volume Velocity Processing (VVP) wind retrieval method with Doppler radar are analyzed in mathematics, and the equations for resolving vertical velocity are modified especially. Given the condition number varies largely when the different fitted parameters chosen, the partial parameters with small magnitude are always neglected in retrieval. The analysis of error's norm verified that model errors might be introduced, but simplified wind model can decrease the difficulty in solving and stabilize the retrieval results. In the VVP retrieval algorithm, the linear correlation among the coefficient matrix vectors caused the matrix singularity. It is demonstrated that the accuracy of the fitted parameters could be affected when combining or abandoning linear correlation items in the coefficient matrix, and the model bias varied along with the position of analyzed points, not with the magnitude of parameters only, but the partial fitted parameters could remain accuracy. Based on the error analysis of VVP retrieval method, the errors when abandoning some parameters are analyzed and examined. The demonstrations of solving equations' modification further provide a fundamental understanding for the accurate retrieval of the vertical velocity.