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Zhiyong Meng and Fuqing Zhang

1. Introduction The accuracy of numerical weather prediction (NWP) depends critically on the qualities of the initial conditions and the forecast model. The initial conditions of an NWP model usually come from data assimilation, a procedure that aims to estimate the state and uncertainty of the atmosphere as accurately as possible by combining all available information (including both model forecasts and observations, and their respective uncertainties). In the data assimilation community, the

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Loïk Berre and Gérald Desroziers

1. Introduction Usual data assimilation systems for numerical weather prediction (NWP), using Kalman filter or variational techniques, are based on a statistical combination of observations and a background, which is usually a short-term forecast. This statistical estimation requires the specification of spatial covariances of errors in these two kinds of information. As presented in Hollingsworth (1987) and Daley (1991 , p. 125), the role of background error covariances is to spatially

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