An Optimization Of The Background Error Covariance In The GRAPES Variational Assimilation System

In variational data assimilation, the background error covariance is defined implicitly by the physical variable transform operator and the spatial transform operator. The physical variable transform operator defines the error cross-correlations between analysis variables by extracting the dynamic balance constraints of them. These cross-correlations are very important to variational assimilation, because they control the observation information spreading between the variables and can suppress noise caused by gravity waves.The existing GRAPES three-dimensional variational data assimilation system, which defined on sigma coordinates, uses linear balance equation to ensure that mass and wind analysis increments to be geostrophically coupled. In this formulation, to deal with the difficulties in solving the balance equation at sigma levels, analysis variables need to be interpolated to a series of auxiliary isobaric surface to calculate balanced components, In addition to the repeated interpolation problem, another disadvantage of the formulation is that the linear balance equation is not appropriate in some spatial regions.To solve the problems in the existing program and optimize the structure of the background error covariance, a new physical variable transform formulation has been developed in the GRAPES variation assimilation system. In the new scheme, dynamic balance operator (N) obtained by statistical methods between stream function and dimensionless pressure (Exner function) is used to describe the balance relationship between rotational wind and mass field. In addition, the balance relationship between rotational wind and divergent wind is similarly described by dynamic balance operator (M) between stream function and velocity potential which is also obtained by statistical methods. In the calculation of the operator N, single-layer-related model and multilayer-related model were compared, and ultimately chose the former into the new formulation. Single-layer-related model was also chose to calculate operator M. Compared to the original scheme, the new formulation can avoid repeated interpolations along the vertical direction.Statistical results show that, the explained variance of dimensionless pressure is primarily in the extratropics with the variance best explained below100hPa in this new formulation. And the explained velocity potential ratio has a maximum in the middle-and high-latitude near the surface. Results of randomization and single-observation experiments indicate that, in regions where geostrophic balance is appropriate, the new formulation behaves similarly to the old scheme. However, in regions where geostrophic balance is not appropriate, the new formulation could allow for a smooth decoupling of stream function and dimensionless pressure, while the old scheme cannot. Moreover, by adding the balance relationship between rotational wind and divergent wind, the new formulation could derive a more reasonable wind field in boundary layer. The results of analysis forecast cycle experiment show that, the new formulation could help improve the quality of the analysis fields of both the northern and southern hemispheres and could help improve short-term forecasting results of the East Asian region.