A General Weak Constraint Applicable to Operational 4DVAR Data Assimilation Systems

Abstract

A technique to apply the forecast model as a general weak constraint in a complex variational algorithm, such as NCEP’s regional 4DVAR data assimilation system, is presented. The proposed definition of the model error has a flexible time resolution for the random error term. It has a potential for operational application, because the coarse time resolution of the random error term and a diagonal in time random error covariance matrix, as used in this study, require less computational space. The results presented in this study strongly indicate the need for a weak constraint (as opposed to a strong constraint formulation) in order to get the full benefit of a 4DVAR method. The inclusion of the model error term, even only the systematic error part, gives a main contribution to the capability of the 4DVAR method to outperform the optimal interpolation method.