Developing a 3D constrained variational analysis method to obtain accurate gridded atmospheric vertical velocity and horizontal advections

Based on the constrained variational analysis (CVA) algorithm developed by Zhang and Lin (1997), a 3-dimensional (3D) version of CVA is developed. The new algorithm used gridded surface and TOA observations as constraints to adjust atmospheric state variables in each grid point to satisfy column-integrated mass, moisture and static energy conservation. From the process of adjustment a set of high-quality 3D large-scale forcing data (vertical velocity and horizontal advections) can be derived to drive Single-Column models (SCM), Cloud-Resolving Models (CRM) and Large-Eddy Simulations (LES) to evaluate and improve parameterizations. Since the 3D CVA can adjust gridded state variables from any data source with observed precipitation, radiation and surface fluxes, it also gives a potential possibility to use this algorithm in data assimilation system to assimilate precipitation and radiation data.