Covariance propagation and updating in the context of real-time radar data assimilation by quantitative precipitation forecast models

The objective of the research work documented herein is the development of a methodology for the assimilation of weather radar data of vertically integrated liquid water content and surface rainfall into spatially distributed models for precipitation forecasting. State estimators may be used for this purpose, as they are superior to conventional assimilation methods because they account for both model error uncertainty and observation error uncertainty, and they provide uncertainty measures for real-time model forecasts. The primary deterrent for using such methodologies in real-time precipitation forecasting with spatially distributed models is the heavy computational requirements that state estimators impose for propagation (prediction) and updating of the state covariance matrix in real time. The present work formulates propagation and updating equations only for the non-zero elements of the covariance matrix, under mild assumptions on precipitation model numerical form, and under the assumption of spatially uncorrelated observation errors at the scale of discretization of the precipitation model equations. The algorithm is provided in a recursive form. Study of a simple example of application for a two grid-column domain suggests that the formulated estimator may have a strong competitor in the formulation that treats each grid-column of the model domain independently for propagation and updating of the local model state variance. Inter-comparison studies with actual data should be undertaken to clarify this point for particular field situations.