The new direction of the photon after reflection was determined with respect to the normal to the surface at the point of intersection. selleck screening library A detailed description of the mathematical solution of this problem is given in Mayer et al. (2010). A technique called ‘Russian roulette’ was applied to a photon of weight < 0.5 to speed up computations (Iwabuchi 2006). The photon disappeared when its weight was less than a random number, otherwise its weight was set to 1. The radiance measured by a satellite instrument was simulated using the ‘local estimation’ technique (Marchuk et al., 1980 and Iwabuchi, 2006). The radiance

measured by a satellite is represented by the normalized radiance and given by the sum of all scattering events

i of photon j in the atmospheric column (k, l) within the domain, divided by the number of photons incident at the top of this column NTOA, and multiplied by π (adopted from Spada et al. 2006): equation(2) I=πNTOA∑j=1NTOA∑i=1NscajIi,j. The relative slope-parallel irradiance at the Earth’s surface Esrel was computed according to the following equation: equation(3) Esrel=EsETOA=ApAsNTOA∑j=1Nwj, where click here Es is the slope-parallel irradiance at the Earth’s surface in a pixel/column (k, l), ETOA is the solar irradiance at the TOA, NTOA is the number of photons incident at the top of the atmospheric column (k, l), As is the area of the Earth’s surface within Thiamet G the pixel/column (k, l), Ap is the area of the pixel (k, l), N is the number of photons reaching the Earth’s surface within the pixel/column (k, l), and wj is the weight of the j-th photon reaching the Earth’s surface within the pixel/column (k, l). For a horizontal surface, like a fjord, the open ocean or flat land surfaces, the slope-parallel

irradiance Es is the downward irradiance Ed and the relative slope-parallel irradiance is the atmospheric transmittance of the downward irradiance TE. The relative slope-parallel net-irradiance Enetrel was computed analogously to the relative slope-parallel irradiance except that only photons absorbed by the surface were counted, so N in equation (3) would mean the number of photons absorbed by the Earth’s surface within the pixel/column (k, l), and wj would be the weight of the j-th photon absorbed by the Earth’s surface within the pixel/column (k, l). Random numbers were generated with a KISS number generator (Marsaglia and Zaman, 1993 and Marsaglia, 1999; http://www.fortran.com/kiss.f90). We did the computations for selected MODIS channels: 3 (459–479 nm), 2 (841–876 nm), 5 (1230–1250 nm) and 6 (1628–1652 nm). In most cases the cloud layer was assumed to be 1000 m above sea level, which is higher than most mountains. The elevation of the highest peak in the area, Hornsundtind, is 1431 m. The cloud optical thickness in the simulations was typically set to 12.