On the Choice of Average Solar Zenith Angle

Idealized climate modeling studies often choose to neglect spatiotemporal variations in solar radiation, but doing so comes with an important decision about how to average solar radiation in space and time. Since both clear-sky and cloud albedo are increasing functions of the solar zenith angle, one can choose an absorption-weighted zenith angle that reproduces the spatial- or time-mean absorbed solar radiation. Calculations are performed for a pure scattering atmosphere and with a more detailed radiative transfer model and show that the absorption-weighted zenith angle is usually between the daytime-weighted and insolation-weighted zenith angles but much closer to the insolation-weighted zenith angle in most cases, especially if clouds are responsible for much of the shortwave reflection. Use of daytime-average zenith angle may lead to a high bias in planetary albedo of approximately 3%, equivalent to a deficit in shortwave absorption of approximately low 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 approximately 2%-6% or a surplus in shortwave absorption of approximately 7-20 W m(-2) in the global energy budget.