A comparison of the performance of 4D-Var in an explicit and implicit version of a nonlinear barotropic ocean model

Abstract. A comparison is made of the performance of the four-dimensional variational data assimilation (4D-Var) method in an explicit and implicit version of a barotropic quasi-geostrophic model of the wind-driven double-gyre ocean circulation. As is well known, implicit methods have the advantage that relatively large time steps can be taken with respect to explicit methods, but the computational costs of each time step is larger. We focus here on two issues: (i) the computational efficiency in the range of time steps where the chosen explicit method is still numerically stable and (ii) the performance of 4D-Var in the implicit model for time steps out of reach for the explicit model. For the same time step Δt and the same number of points n per assimilation interval, the analyses in the implicit model is always more accurate than that in the explicit model. Due to this property the use of 4D-Var combined with the implicit model can be computationally more efficient than its use in the explicit model.