Statistical Estimation of Dynamic Balance Constraints in GRAPES Variational Data Assimilation System

Dynamic balance constraints that govern the atmospheric circulation play very important roles in the analysis of atmospheric state. These constraints indicate how it might be possible to determine one variable from another. As a result, they could help to avoid noise caused by gravity waves, and enable maximum information to be extracted from the observations.The existing GRAPES three-dimensional variational data assimilation system, which is 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 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. A new formulation of estimating dynamic balance constraints is developed in the variation assimilation system. In the new scheme, regression coefficients between stream function and dimensionless pressure (Exner function), instead of the geostrophic balance equation in the original scheme, 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 regression coefficients between stream function and velocity potential. Compared to the old scheme, the new formulation avoids repeated interpolations along the vertical direction, which would make the estimation simpler and more accurate.In the new formulation, the balanced coefficients are computed using NMC method, which is found to produce a useful approximation to the true balance constraints in atmosphere. Based on 24 h, 48 h GRAPES forecast differences, linear regression is carried out for each level and for each latitude. By doing this an implied latitude-dependent structure in the dimensionless pressure is directly included in the analysis. Statistical results show that the explained variance of dimensionless pressure is primarily in the extratropics with the variance best explained below 100 hPa in this new formulation. And the explained velocity potential ratio has a maximum in the middle and high latitudes 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 original 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 original scheme can not. Such properties of the new formulation could help variational data assimilation system get more reasonable analysis results in tropics and tropopause. 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.