Weak and Strong Constraints Variational Data Assimilation with the NCOM-4DVAR in the Agulhas Region Using the Representer Method

Abstract

he difference between the strong and weak constraints four-dimensional variational (4DVAR) analyses is examined using the representer method formulation, which expresses the analysis as the sum of a first guess and a finite linear combination of representer functions. The latter are computed analytically for a single observation under both strong and weak constraints assumptions. Even though the strong constraints representer coefficients are different from their weak constraints counterparts, that difference is unable to help the strong constraints compensate for the loss of information that the weak constraints includes. Numerical experiments carried out in the Agulhas retroflection for single and multiobservation assimilations clearly show that the weak constraint 4DVAR produces analyses that fit the observations with significantly higher accuracy than the strong constraints.