Thermal convection in a horizontal water layer being cooled from above and absorbing solar radiation is simulated numerically at the Prandtl number Pr = 7. Three different regimes arising are investigated here. The first is characterized by intermittent convection, the second by steady-state convection, and the third is convection free. The transitions occur at different values of J0/Q, the ratio of downward solar-radiation flux just below the surface to heat flux through the interface (assumed to be constant), but at almost the same Rayleigh number. The generalized heat-conduction law is found to be valid.