Rainfall forecasting using variational assimilation of radar data in numerical cloud models

In this paper, a variational data assimilation procedure for initialization of a cloud model using radar re ̄ectivity and radial velocity observations and its impact on short term rainfall forecasting are investigated in a simulation framework. The procedure is based on the formulation of an objective function, which consists of a linear combination of the squared di€erences between model forecasts and actual observations. The model's initialization requires the gradient-based minimization of the objective function. Three sources of errors in assimilation and forecasting are considered. These include observational errors, mathematically ill-posed structure (the observations are incomplete and do not uniquely determine the cloud model's initial conditions) and optimization related issues (the observations are complete, but the optimization procedure involved in the initialization fails to ®nd the best solution). It is found that the re ̄ectivity observation errors have signi®cant impact on forecasts and that the mathematical structure and optimization caused errors are related. Conclusions and recommendations for future work are formulated. Ó 2000 Elsevier Science Ltd. All rights reserved.