Results of detailed numerical models yielding the amplitudes of the atmospheric variations of solar radius, luminosity, and temperature that arise from rapid perturbations to properties of the convective envelope are presented. The numerical models, predict significantly different surface responses for perturbations of the temperature gradient at the convective envelope base, variations of convective efficiency, and the effects of magnetic flux tubes, than was previously found based on simple hydromagnetic arguments. A detailed critique of previous and current efforts for modeling solar variability based on mixing length theories of convection and simple physical arguments is given, and alternative modeling efforts are suggested.