Reflectance of broken cloud fields - Simulation and parameterization

The transfer of solar irradiance in plane parallel and broken cloud fields is simulated using a Monte Carlo method. The angular distribution pattern of radiances exiting the cloud layer is studied with varying cloud geometries, optical thicknesses, cloudiness, and solar zenith angles. A rather large anisotropy of the reflected flux is found, usually increasing with solar zenith angle and with patterns that strongly depend on cloud geometry. The main features are (1) a local maximum of reflected intensity in the forward direction for all cases, (2) a limb darkening for the plane parallel case, and (3) a limb brightening and a local maximum of reflected intensity in the backward direction for broken clouds. A parameterization for the azimuth-average reflectance function is developed. It reproduces the Monte Carlo simulation with a reasonable accuracy and illustrates that, when azimuthally averaged, the reflectance function is dominated by side viewing and intercloud shadowing effects.