Although a number of fully spherical models were available from various research groups, those that we tested were found to be numerically unstable, dependent partly on the specific computing platform, e.g., machine precision and compiler differences, and therefore not suitable for our purposes. The comparisons showed that pseudo-spherical models tend to overestimate the brightness of scattered radiation originating near the horizon, as shown in Figure 1. The errors are present even for high sun, which to our knowledge had not been previously recognized. For calculations of J values and surface visible and UV radiation, the accuracy of the pseudo-spherical method is sufficient for most practical applications at any solar zenith angle. We caution, however, that for studies in which horizon radiation is important, fully spherical radiative transfer calculations are required even for high sun.
Errors are largest at wavelengths where the atmosphere is non-absorbing.
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