Near the Equator, some cloud types can boost the terrestrial solar irradiance to above 1.8 kW/m(2). Even at high latitude close to 60 degrees N, we have measured bursts up to 1.6 kW/m(2), almost at sea level. For comparison, the extraterrestrial irradiance peaks at about 1.4kW/m(2) in early January. The global upper limit for extreme overirradiance is still unknown. The enhancement is strongest within about 3 degrees from the unobstructed solar disk. We use the NASA's I3RC Monte Carlo model to simulate the radiative transfer of solar photons in a cloudy atmosphere. The geometry includes an overhead sun and an infinite plane parallel water cloud with a 'circular' gap of the same angular diameter as that of the solar disk (approximate to 0.53 degrees). We vary the effective droplet radius, cloud's thickness, and liquid water mass density. At a non-absorbing lambda = 0.67 mu m, we obtain a maximum enhancement factor of about 1.80 times with respect to the clear-sky downwelling flux, at an optimal cloud optical thickness of about 3.1. Although these values are very similar to those obtained by Wen et al. (2001) with the DISORT model, the simulated extent of the strong narrow forward scattering (within 1.5 degrees around the sun) differs significantly from our experimental observation (about 8 degrees). We conclude that a revision of the Mie scattering phase functions programmed in the I3RC code may be necessary, and that the obtained enhancement threshold at sea level is not entirely physical, as perhaps was the result in Wen et al. (2001). Interestingly, there are typographical errors in some equations in the original German paper by Mie (1908) which survived the English translations from 1976 and 1978. The typos were corrected only recently in the Spanish translation from 2007. (C) 2015 Elsevier Ltd. All rights reserved.