On the Choice of Average Solar Zenith Angle

Abstract:

Studies with idealized climate models often make simplifying decisions to average solar radiation over space and time. But clear-sky and cloud albedo are increasing functions of the solar zenith angle, so the choice of average solar zenith angle is important and can lead to significant climate biases. Here, I use radiative transfer calculations for a pure scattering atmosphere and with a more detailed radiative transfer model to argue that one should in general choose the insolation-weighted zenith angle, rather than the simpler daytime-average zenith angle. The insolation-weighted zenith angle is especially superior if clouds are responsible for much of the shortwave reflection. Use of the daytime-average zenith angle may lead to a high bias in planetary albedo of ~3%, equivalent to a deficit in shortwave absorption of 10 W m^-2 in the global energy budget (comparable to the radiative forcing of a roughly sixfold change in CO₂ concentration). Other studies that have used general circulation models with spatially constant insolation have underestimated the global-mean zenith angle, with a consequent low bias in planetary albedo of ~2-6%, or a surplus in shortwave absorption of ~7-20 W m^-2 in the global energy budget. I also discuss how a simple time-varying solar zenith angle could be used to minimize zenith angle-related biases in albedo for models of global climate that choose to spatially homogenize insolation.