Four-dimensional variational data assimilation with digital filter initialization

A four-dimensional variational (4DVAR) data assimilation problem may be con strained so that the solution closely fits the observations but is balanced . In this way, the processes of data analysis and initialization are combin ed. The method of initialization considered here, digital filtering, is wid ely used in weather forecasting centers. The digital filter was found to co ntrol high-frequency noise when implemented as a strong or as a weak constr aint in the context of a global shallow water model. Implementation of a st rong constraint did not result in a recovery of small scales although some recovery of intermediate scales did occur. Implementation of a weak constra int as a penalty method with a single fixed value of the penalty parameter resulted in analyses that were smooth, but depended upon the choice of the parameter. With a parameter value that was too large, the divergent kinetic energy spectrum of the analysis was excessively damped in the large scales . The rotational kinetic energy spectrum was also affected by the choice of penalty parameter. Both types of constraint were found to adequately contr ol gravity wave noise although caution is advised in choosing the penalty p arameter for the simple penalty term method.