A new approach is presented for the modeling of the quasi-stationary circulation through the sequential application of a variational algorithm and a nonlinear diagnostic model. The model loop begins with data assimilation of temperature, salinity, surface elevation, and velocity data in a simplified geostrophic model in which transport and continuity equations are treated as weak constraints. The temperature/salinity fields and balanced open boundary conditions points are then used as input to a nonlinear primitive equation model, which employs a turbulent closure scheme. The nonlinear model is then run to produce a diagnostic flow field. A radiation open boundary condition is applied at the outflow points of the open boundaries. These two steps are organized into an iteration cycle by using output from the nonlinear model as input to the variational model. The proposed approach combines the advantages of variational data assimilation in simplified models with a complicated fully nonlinear primitive equation model. We apply the approach to Western Bank on the Scotian Shelf. Comparisons with observed current from Western Bank, in September and October 1998, show that the sequential application of the variational approach and the fully nonlinear model allow determination of the quasi-stationary circulation whose agreement with the observations is ≈10--30% better than circulation determined from the variational or the nonlinear model alone. Our calculations of the cross-shelf transport across Western Bank show that it varies from 0.20 Sv to 0.35 Sv over a 2-week period. The combined models also allow us to determine the character of the circulation over the Bank, the role of wind forcing and the implications for resident biological populations.