Developments of the Three-Dimensional Variational Data Assimilation System for the Nonhydrostatic GRAPES

Based on the original GRAPES（Global/Regional Assimilation and PrEdiction System）3DVAR（p3DAR）, which is defined on isobaric surface,a new three-dimensional variational data assimilation system（m3DVAR） is constructed and used exclusively with the nonhydrostatic GRAPES model in order to reduce the errors caused by spatial interpolation and variable transformation,and to improve the quality of the initial value for operational weather forecasts.Analytical variables of the m3DVAR are fully consistent with predictands of the GRADES model in terms of spatial staggering and physical definition.A different vertical coordinate and the nonhydrostatic condition are taken into account,and a new scheme for solving the dynamical constraint equations is designed for the m3DVAR.To deal with the diffculties in solving the nonlinear balance equation atσlevels,dynamical balance constraints between mass and wind fields are reformulated,and an effective mathematical scheme is implemented under the terrain-following coordinate.Meanwhile,new observation operators are developed for routine observational data,and the background error covariance is also obtained.Currently,the m3DVAR system can assimilate all routine observational data. Multi-variable idealized experiments with single point observations are performed to validate the m3DVAR system.The results show that the system can describe correctly the multi-variable analysis and the relationship of the physical constraints.The difference of innovation and the analysis residual forπalso show that the analysis error of the m3DVAR is smaller than that of the p3DVAR.The T s scores of precipitation forecasts in August 2006 indicate that the m3DVAR system provides reduced errors in the model initial value than the p3DVAR system.Therefore,the m3DVAR system can improve the analysis quality and initial value for numerical weather predictions.