水平相关模型的性质及其在GRAPES三维变分系统中的应用

在变分资料同化中背景误差水平相关模型不仅决定着观测信息传播到格点空间的远近，而且影响着频谱空间中不同尺度上的分析增量信息的多少。本文比较高斯（Gauss）、二阶自回归（Soar）以及尺度叠加高斯模型（Supergauss）在时空域随着空间距离和在频谱域随着不同尺度分布的特点，阐述三种相关模型在区域GRAPES三维变分分析（GRAPES-3DVar）中的实施方案，同时通过单点观测试验研究不同相关模型对分析的影响。研究表明Gauss相关模型造成分析中小尺度信息的不足，同时当流函数和非平衡的势函数作为分析变量时，依据动力场变量之间的相关关系，会造成风场观测不合理的较大负相关信息。Soar相关模型能增加分析的中小尺度信息，但在三维变分分析实施中只能采用一阶递归滤波方案，由于计算精度不够会造成风场分析增量异常。当采用Supergauss相关模型时，不仅缓解单一高斯模型造成的不恰当风场观测负相关信息，并可增加分析增量的中小尺度信息，同时在递归滤波实施中可获得合理的分析增量。因而Supergauss相关模型在三种模型中最适合描述背景误差水平相关，对高分辨率3DVar系统的中小尺度分析有益。

Properties of Horizontal Correlation Models and Its Application in GRAPES 3DVar System

The background error correlation function in data assimilation systems is important because it determines the spread distance of observed data in the grid space and the analyzed increments on different scales in the spectral space. Herein, the features in the time-space domain and the spectral space domain are compared among Gaussian function (Gauss), second-order auto-regressive function (Soar), and superposition of Gaussian components (Supergauss). The three correlation functions are then applied in the Global/Regional Assimilation and Prediction System, three-dimensional variational data assimilation (GRAPES-3DVar), and their impacts on the analysis increments are analyzed through a single observation test. Research has demonstrated that the Gaussian correlation function contributes to the insufficiency of meso- and small-scale analysis increments. This leads to a larger negative correlation, which is the inverse of the wind field observation according to the correlation among the dynamic field variables when the stream function and unbalanced velocity potential function are used as the control variables. The Soar correlation function can increase the meso- and small-scale analysis increments. However, the less accuracy of a one-order recursive filtering scheme in the 3DVar system causes an abnormal analysis increment of the wind field. Application of the Supergauss correlation function can not only mitigate the inappropriate negative analysis increments of wind observation but also increase the meso- and small-scale power spectrum in analysis increments. Moreover, the analysis increment structure of isotropy with the Supergauss correlation function can be obtained through recursive filter implementation. Thus, the Supergauss correlation function is the most suitable one to describe the background error correlation among the three functions, which is beneficial for the meso- and small-scale analysis in the high-resolution 3DVAR system.