Covariance propagation and updating in the context of real-time radar dataassimilation 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 inte grated liquid water content and surface rainfall into spatially distributed models for precipitation forecasting. State estimators may be used for thi s purpose, as they are superior to conventional assimilation methods becaus e they account for both model error uncertainty and observation error uncer tainty, and they provide uncertainty measures for real-time model forecasts . The primary deterrent for using such methodologies in real-time precipita tion forecasting with spatially distributed models is the heavy computation al requirements that state estimators impose for propagation (prediction) a nd updating of the state covariance matrix in real Lime. The present work f ormulates propagation and updating equations only for the non-zero elements of the covariance matrix, under mild assumptions on precipitation model nu merical form, and under the assumption of spatially uncorrelated observatio n errors at the scale of discretization of the precipitation model equation s. 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 e stimator may have a strong competitor in the formulation that treats each g rid-column of the model domain independently for propagation and updating o f the local model state variance. Inter-comparison studies with actual data should be undertaken to clarify this point for particular field situations . (C) 2000 Elsevier Science B.V. All rights reserved.