Imperfections of the thermohaline circulation: Multiple equilibria and flux correction

Abstract

Within one of the simplest models that represents thermohaline transport in the ocean, a two-dimensional Boussinesq model under mixed boundary conditions, the relationship between multiple equilibria in a flux-corrected model and an uncorrected model is considered. Flux-correction procedures are used in some climate models to maintain a climate state close to observed, compensating for model errors by introducing artificial fluxes between model components. A correction procedure used in many ocean or ocean-atmosphere models of the thermohaline circulation involves calculating the freshwater flux required to maintain observed surface salinity and then specifying this flux. In the prototype system here, one model solution is chosen as the "true" 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 the correction is designed. However, other equilibria are more strongly affected, and the connections between equilibria are changed. Furthermore, areas in parameter space exist with multiple equilibria in the flux-corrected case that have a unique state in the uncorrected case. Care should thus be used in drawing conclusions on the existence of multiple equilibria and the stability of the thermohaline circulation when a flux-correction procedure is used. Guidelines are provided to help distinguish spurious equilibria in a flux-corrected model. The computation of an uncorrected equilibrium is useful, even if it does not resemble observations.