Long-term solar irradiance modelled using monthly-average aerosol optical depth (AOD) is biased compared to what is obtained using daily AOD values. This is due to a modification of the AOD frequency distribution that results from the coarsening of the time scale, combined with the nonlinear sensitivity of irradiance to AOD. The resulting alteration of the mean and standard deviation of AOD has been evaluated worldwide in this study's Part 1. Here, the focus is to evaluate how the progressive coarsening (in 1-day steps) of the temporal representation of AOD affects the calculated long-term values of both global and direct irradiances. It is shown that, on average, their long-term values can be underestimated by as much as approximate to 6 W m(-2) (approximate to 1.2%) and approximate to 40 W m(-2) (approximate to 8%) respectively, over regions of North Africa and Asia, with respect to the reference case for which daily AODs are used. This irradiance underestimation can be parameterized as a function of the AOD time scale by means of four sitedependent parameters. The proposed parameterization provides a simple way to correct the long-term irradiance datasets that are commonly obtained using monthly-average AOD data. (C) 2016 Elsevier Ltd. All rights reserved.