Polarized microwave radiation transfer in precipitating cloudy atmospheres: Applications to window frequencies

A microwave radiation transfer model taking into account Mie scattering polarization effects is developed for a plane-parallel precipitating cloudy atmosphere. In the model the azimuthally averaged Mie scattering phase matrix elements are expressed in terms of double Legendre polynomial expansion and the cloud temperature is approximated by a linear function of the optical depth. The complete solution of the fundamental transfer equation is derived utilizing the discrete-ordinates method for horizontal and vertical polarization components. Using this model, the brightness temperature and degree of polarization for three microwave window frequencies of 19.35, 37.0, and 85.5 GHz are calculated for a number of rainfall rates over both land and ocean surfaces. We show that the brightness temperature computed for 85.5 GHz using a simple Rayleigh scattering approximation is underestimated by about 7°K for a layer thickness of 4.7 km and a rainfall rate of 5 mm/hr. Effects of the Mie scattering function and nonisothermal cloud structure must both be included for brightness temperature calculations of 37 and 85.5 GHz when thick precipitating clouds are involved. Moreover, we also find that there is a significant degree of polarization for emergent radiation of 19.35 GHz at a zenith angle of 50° under a light rainfall condition over ocean surfaces. Over land surfaces, polarization produced by precipitating clouds is rather small for the three window frequencies. Finally, we show that the existence of ice particles in the upper part of a precipitating cloud largely reduces the upward radiances of the 85.5 GHz frequency.