Coastal ocean data assimilation using a multi-scale three-dimensional variational scheme

A multi-scale three-dimensional variational scheme (MS-3DVAR) is implemented to improve the effectiveness of the assimilation of both very sparse and high-resolution observations into models with resolutions down to 1 km. The improvements are realized through the use of background error covariances of multi-decorrelation length scales and by reducing the inherent observational representativeness errors. MS-3DVAR is applied to coastal ocean data assimilation to handle the wide range of spatial scales that exist in both the dynamics and observations. In the implementation presented here, the cost function consists of two components for large and small scales, and MS-3DVAR is implemented sequentially from large to small scales. A set of observing system simulation experiments (OSSEs) are performed to illustrate the advantages of MS-3DVAR over conventional 3DVAR in assimilating two of the most common types of observations-sparse vertical profiles and high-resolution surface measurements-simultaneously. One month of results from an operational implementation show that both the analysis error and bias are reduced more effectively when using MS-3DVAR.