Effect of cloud inhomogeneities on the solar zenith angle dependence of nadir reflectance

A significant discrepancy has been noted between satellite measurements of shortwave reflectance at nadir and the results of plane-parallel model calculations: For moderate to large solar zenith angles, observed nadir reflectances increase with solar zenith angle, whereas plane-parallel values decrease. Consequently, cloud optical depths retrieved using one-dimensional (1-D) theory have a bias which increases systematically with solar zenith angle. Using Monte Carlo model simulations of photon transport through stochastic, isotropic, scale-invariant cloud fields with variable cloud top heights and volume extinction coefficients, we show that nadir reflectances from three-dimensional cloud fields increase with solar zenith angle, consistent with the observations. The difference from the 1-D case is shown to be explainable by cloudside illumination as well as by the presence of structured (i.e., non-flat) cloud tops. Cloud sides enhance the amount of incident solar radiation intercepted by cloud, allowing more radiation to be scattered upward in the nadir direction. Structured cloud tops change the slope of illuminated cloud top surfaces, such that nadir reflectance at low solar elevations increases with the slope of the illuminated surface. For simple cloud geometries the two effects make equivalent contributions to the increase in nadir reflectance with solar zenith angle. While this increase is most pronounced for vertically extensive broken cloud fields, it also affects reflectances from overcast cloud fields with inhomogeneous (bumpy) cloud tops. Thus the observed solar zenith angle bias in cloud optical depth for the general cloud scene likely also occurs for extensive overcast cloud fields. Internal inhomogeneities due to small scale liquid water content variations within clouds are shown to cause no changes at low Sun and only slight decreases in nadir reflectance for high solar elevations.