Accurate computation of surface fluxes is vital for the coupling of surface and atmosphere components in earth system models such as the Energy Exascale Earth System Model (E3SM). Past work has demonstrated the sensitivity of earth system models to surface flux calculations and algorithm choice. In this presentation, we discuss rather fundamental issues of model sensitivities to the well-posedness of surface flux formulations. Namely, we demonstrate that under certain conditions, the underlying equations associated with some ocean-atmosphere surface flux algorithms have no solution or have more than one solution. In this scenario, we present various techniques, such as regularization, to ensure existence and uniqueness of the computed surface fluxes and discuss overall model impacts.