New Developments of a 3dvar System for a Nonhydrostatic Nwp Model

An important advantage of variational data assimilation methods is that observations that differ from the analysis variables can be directly analyzed as long as they can be expressed in terms of the model state variables. Examples include radar radial velocity and reflectivity, the GPS precipitable water, and satellite radiances. A variational method produces an analysis that minimizes a cost function that measures the fit of this function to the observations while subjecting to the background and other dynamical constraints. Three dimensional variational (3DVAR) analysis systems, thanks to their relatively low cost compared to 4DVAR, have been developed and used operationally for large-scale NWP at a number of operational centers in recent years (e.g., Parrish and Derber 1992; Courtier 1998) and progress is also being made in developing systems for mesoscale mo dels (e.g., Wu et al, 2001). In the 14 NWP conference, we reported an incremental 3DVAR data assimilation system developed for the ARPS model (Gao et al. 2001;Xue et al. 2000, 2001). The system is developed based on the existing infrastructure of the ARPS Data Analysis System (ADAS, Brewster 1996). The 3DVA R system is preconditioned by the background error covariance matrix (Courtier 1997) and uses recursive filter (Hayden and Purser 1995) to model the background covariances. Numerical experiments show that a reasonable reduction in the cost function is achieved in the minimization process and the quality of the analysis is good. The method is flexible and computationally efficient. In this paper, we report further development of this system, in particular, the addition of two dynamic constraints based on the ARPS equations and the inclusion of the anelastic mass continuity equation as the third constraint. We consider such features very important for the assimilation of data at the convective scales. The inclusion of these equation constraints couple together the analysis variables and make the analysis of variables not directly observed (e.g., temperature and pressure by radar) possible.