﻿ 基于变分法的客观分析算法及应用
 气象学报  2013, Vol. 71 Issue (6): 1172-1182 PDF
http://dx.doi.org/10.11676/qxxb2013.091

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#### 文章信息

LIU Couhua, CAO Yong, FU Jiaolan. 2013.

An objective analysis algorithm based on the variational method

Acta Meteorologica Sinica, 71(6): 1172-1182.
http://dx.doi.org/10.11676/qxxb2013.091

### 文章历史

An objective analysis algorithm based on the variational method
LIU Couhua, CAO Yong, FU Jiaolan
National Meteorological Centre, Beijing 100081, China
Abstract:In meteorological operations, station data are often needed to be transformed to the regular grid with requirements of the gridded field being both accurate and smooth. Due to the contradiction between accuracy and smoothness, the existing objective analysis methods are very difficult to achieve the above requirements. In this paper, based on the variational method, by introducing accuracy and smoothness into a cost function of the gridded field, the optimal objective analysis results can be obtained by solving the minimum value of the cost function. The objective analysis of precipitation examples show that both accurate and smooth requirements can be met by using the variational objective analysis methods.
Key words: Variational method     Objective analysis     Smoothing
1 引 言

 图 1 一次试验中的一维变分法客观分析的解析解和数值解(细实线：真实函数，圆圈：观测值序列，粗实线：变分法客观分析的解析解，×线：变分法客观分析的数值解，带点实线：两种解之差) Fig. 1 Analytical solution and numerical solution from the variational objective analysis in a test(thin line is true function，circles are observations，thick line is the analytical solution from the variational objective analysis，×-line is the numerical solution from the variational objective analysis and line with dot is their difference)
4 敏感性试验

 图 2 失真度函数中的反插算法采用线性插值(实线)和三次多项式插值(×线)时分别对应的客观分析结果以及两者之差(带点实线)，圆圈为观测 Fig. 2 Corresponding objective analysis results of different distortion degrees with linear and cubic as reverse interpolation(solid line and ×-line，respectively) and their difference(line with dot)，circles are observations

 图 3 格距d=1(实线)和d=2(×线)分别对应的客观分析结果以及两者之差(带点实线)，圆圈为观测 Fig. 3 Corresponding objective analysis results to the grid distances setting as d=1(solid line) and d=2(×-line)，and their difference(line with dot)，circles are observations

 图 4 平滑系数β=10(实线)和β=0.1(×线)分别对应的客观分析结果以及两者之差(带点实线)，圆圈为观测 Fig. 4 Corresponding objective analysis results to the smooth coefficients setting as 10 and 0.1(solid line and ×-line)，and their difference(line with dot)，circles are observations
 图 5 失真度和粗糙度对平滑系数的响应 Fig. 5 Response of the distortion degree and the coarseness to the smooth coefficient

 图 6 2012年9月2日08时24 h累积降水量的地面观测(数字)和客观分析的降水量分布(阴影区)(a. 变分法； b. Cressman方法) Fig. 6 Observation of 24 h cumulative rainfall(figure)at 08:00 BT 2 Sep 2012 and its objective analysis distribution(shaded)(a. Variational method，b. Cressman method)

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