Three- and Four-Dimensional Variational Assimilation with a General Circulation Model of the Tropical Pacific Ocean. Part I: Formulation, Internal Diagnostics, and Consistency Checks

Abstract

Abstract Three- and four-dimensional variational assimilation (3DVAR and 4DVAR) systems have been developed for the Ocean Parallelise (OPA) ocean general circulation model (OGCM) of the Laboratoire d'Oceanographie Dynamique et de Climatologie. An iterative incremental approach is used to minimize a cost function that measures the statistically weighted squared differences between the observational information and their model equivalent. The control variable of the minimization problem is an increment to the background estimate of the model initial conditions at the beginning of each assimilation window. In 3DVAR, the increment is transported between observation times within the window using a persistence model, while in 4DVAR a dynamical model derived from the tangent linear (TL) of the OGCM is used. Both the persistence and TL models are shown to provide reasonably good descriptions of the evolution of typical errors over the 10- and 30-day widths of the assimilation windows used in the authors' 3DVAR an...