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.