“…where −R TOA (t, i) is the local incoming extraterrestrial solar flux at TOA in time step t and region i, which is a function of latitude, K T (t, i) is the fraction of local −R TOA that reaches the surface in time step t ("all-sky clearness index") and region i, which may be considered the downwelling transmittance coefficient for the single atmospheric layer, α s (t, i) is the local change in surface albedo in time step t and region i, and T a is a constant denoting the globally averaged annual fraction of upwelling shortwave radiation exiting a clear sky, which is around 80-85 % (Lenton and Vaughan, 2009;Kiehl and Trenberth, 1997). A value of 0.854 (Lenton and Vaughan, 2009) for T a was applied in Cherubini et al (2012) and the forcing results using this simple parameterization aligned well with those calculated using a more sophisticated radiative transfer model (Fu-Liou, 2005;Liou, 1992, 1993) that required detailed prescriptions of cloud and aerosol optical properties.…”