A two-dimensional Boussinesq model of the thermohaline convection in a rectangular domain is forced at the top by a prescribed temperature and a prescribed salinity flux. The two forcings have opposite effects on the density field, which leads to the formation of fronts and multiple equilibria. Numerical results are interpreted through a comparison with the solutions of an asymptotic equation, derived in the limit of a shallow basin by Cessi & Young (1992). In order to explain the discrepancies between the numerical and the asymptotic solutions, we extend this asymptotic approach through a geometrical representation and a topological classification of the surface forcings. By comparing three forcings, we propose a global picture which gives clues to interpret the numerical solutions.