Imperfections of the thermohaline circulation: Multiple equilibria and flux correction

Within one of the simplest models that represents thermohaline transport in the ocean, a two-dimensional Boussinesq model under mixed boundary conditi ons, the relationship between multiple equilibria in a flux-corrected model and an uncorrected model is considered. Flux-correction procedures are use d in some climate models to maintain a climate state close to observed, com pensating for model errors by introducing artificial fluxes between model c omponents. A correction procedure used in many ocean or ocean-atmosphere mo dels of the thermohaline circulation involves calculating the freshwater nu x required to maintain observed surface salinity and then specifying this f lux. In the prototype system here, one model solution is chosen as the "tru e" solution and flux correction is applied to model versions with different parameters. When the flux correction is not too large, it is qualitatively successful, particularly in reproducing the equilibrium state for which th e correction is designed. However, other equilibria are more strongly affec ted, and the connections between equilibria are changed. Furthermore, areas in parameter space exist with multiple equilibria in the flux-corrected ca se that have a unique state in the uncorrected case. Care should thus be us ed in drawing conclusions on the existence of multiple equilibria and the s tability of the thermohaline circulation when a flux-correction procedure i s used. Guidelines are provided to help distinguish spurious equilibria in a flux-corrected model. The computation of an uncorrected equilibrium is us eful, even if it does not resemble observations.