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6 Calculated for "typical" summer conditions of a solar zenith angle of 20° and a surface albedo of 5% with an incident light beam that is collimated.

' Calculated for "typical" winter conditions of a solar zenith angle of 70° and a surface reflectivity of 80% for a collimated incident light beam.

6 Calculated for "typical" summer conditions of a solar zenith angle of 20° and a surface albedo of 5% with an incident light beam that is collimated.

' Calculated for "typical" winter conditions of a solar zenith angle of 70° and a surface reflectivity of 80% for a collimated incident light beam.

a solar zenith angle of 20° for the case of a 5% surface albedo and second, for typical winter conditions with a solar zenith angle of 70° and a surface albedo of 80%, which would be characteristic of snow, for example.

The cloudless case shown first for a small solar zenith angle and typical summertime conditions shows an enhancement due to reflections from the surface. The cloud with an optical depth of 8 corresponds to a total of 67% transmission of the light through the cloud, but essentially all of it is diffused by the cloud and is therefore not directly transmitted light. The cloud with an optical depth of 128 only transmits a total of 9% of the light, essentially all of which is again diffuse.

Under the typical summertime conditions, the thinner cloud shows an increase of 65% in the actinic flux above the cloud whereas the thicker cloud shows an increase of almost a factor of three, the maximum theoretically possible. This is due to scattering of diffuse light from the top of the cloud, as well as from the ground. As expected, below the thicker cloud, the total actinic flux is reduced, in this calculation, to 19% of the clear-sky value. However, for the thinner cloud of optical density 8, the actinic flux below the cloud is actually calculated to be greater than for the cloudless case. This occurs in the case of a small solar zenith angle and direct (rather than diffuse) incident light because the direct incident light is diffused as it traverses the cloud; as discussed earlier for the case of the actinic flux above a Lambertian surface, conversion of a direct to diffuse source leads to an enhancement in the actinic flux.

Similar trends are predicted for the winter case chosen, except that the unexpected below-cloud enhancement discussed is not seen.

Interestingly, in the air inside the cloud itself, particularly near the top of the cloud, there can be significant enhancements of the actinic flux due to this scattering phenomenon. The enhancements expected depend on a variety of factors, including the solar zenith angle, the amount of direct vs diffuse incident light, surface albedo, cloud optical depth, etc. Madronich (1987) suggests for a "typical" summer average that the enhancement factors vary linearly from 1.7 near the top of the cloud, to 1.0 (i.e., no enhancement) in the middle of the cloud, to 0.4 (i.e., a reduction in actinic flux) at the bottom of the cloud.

This behavior has been borne out experimentally. Figure 3.26, for example, shows some vertical measurements of the actinic flux below, in, and above a cloud (Vila-Guerau de Arellano et al., 1994). The dotted line shows the calculated actinic flux in the absence of clouds for these particular conditions. At the cloud

(a) Continental, average RH (b) Continental, high RH