Conversion issues between microwave radiance and brightness temperature

Microwave radiances are usually converted into brightness temperatures for data assimilation and retrievals. The Rayleigh-Jeans approximation has been believed to be a good approximation for the conversion at low frequencies, but inaccurate at high frequencies. However, the simplified radiative transfer models under the Rayleigh-Jeans approximation (hereafter referred as BT-RTE) have been successfully applied in radiance simulations for frequencies below 183 GHz, which has somewhat puzzled the radiative transfer community. This paper clarifies the confusion. In addition, the conversion formula for the third and the fourth Stokes components are derived. Simulations for a polarized sensor, the Special Sensor Microwave Imager and Sounder, show that the BT-RTE is generally accurate. Results for a polarimetric sensor, WINDSAT, show that the third and the fourth Stokes radiances should be converted using the exact conversion formula given in this study rather than using a direct Planck function conversion