A pressing problem for the climate community is the inability of global warming research to reduce the range of uncertainties in the equilibrium sensitivity of climate and in future climate projections. Despite successful large-scale simulations, climate models still exhibit high sensitivity in regional climatology features, with challenges including high-dimensionality, computationally-expensive simulations, and ambiguity in the choice of objective function. Here we examine the parameter sensitivity in the International Center for Theoretical Physics atmospheric general circulation model forced by observed sea surface temperature or coupled to a mixed-layer ocean. We find that many climatic variables yield smooth parameter dependence for leading climate fields with root-mean-square error objective functions. This occurs despite nonlinearity strong enough to reverse the curvature of the objective function in some parameters, and implies limitations on multi-model ensemble means as an estimator of climate changes. Optima often occur at the limit of the feasible parameter range, identifying key parameterization aspects warranting attention-here the interaction of convection with free tropospheric water vapor. Analytic results help to visualize trade-offs at a regional level, e.g., how mismatches between sensitivity and error spatial fields yield regional error under minimization of global objective functions. The approach we propose is sufficiently simple to guide parameter choices and to aid intercomparison of sensitivity properties among climate models.