中文摘要：

气象观测数据不可避免地带有观测误差,而对带有误差的离散数据求导是一个不适定的反问题.为了解决这一长期困扰气象工作者的问题,利用吉洪诺夫正则化思想,提出了矩形区域内观测数据的二维一阶偏导数重构算法.通过系列模拟观测数据试验检验了该算法的性能,表明该算法有效且计算精度高.另外,应用该算法对气象观测资料进行客观分析,结果表明：该算法作为一种新的客观分析方法是可行的,并且还能提高小尺度天气系统的识别能力.

英文摘要：

Meteorological observation data have observational errors inevitably. It is an ill-posed inverse problem to perform the derivation of discrete data with observation errors. In order to solve the perplexing problem,this paper puts forward the new algorithm which reconstructs the first-order partial derivatives of the two-dimensional observation data in the rectangular region,which is based on the idea of Tikhonov regularization . We test the performance of the algorithm with a series of simulating observation data,the results show that the algorithm is effective and has higher accuracy. It is feasible to analyze meteorological observation data with the algorithm and can enhance the recognizing ability for the smallscale weather systems.