Theory for microwave thermal emission from a layer of cloud or rain

Microwave thermal emission from a layer of cloud or rain consisting of spherical particles has been investigated. Scattering effects are studied in great detail with both numerical and analytical approaches. In the absence of ground emission, it is found that scattering induces brightening for optically thin layers and vice versa for optically thick layers. As a function of observation angle, brightening occurs near nadir, while darkening occurs at large angles in the case of small optical thickness. For large optical thickness, darkening occurs at all angles because of backscattering effects. When the layer of cloud or rain is above an air layer and an ocean surface at a higher temperature, it is found that the darkening effect at large optical thickness is much more pronounced. The darkening effect is also larger for vertical polarizations because the ocean emits more vertically polarized components. The effect of thermal emission and molecular absorption by atmospheric gases is also taken into account. Results obtained from analytical formulas under single-scattering assumptions are compared and illustrated.