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The atmospheric transmittance model for the Advanced Microwave Sounding Unit-A (AMSU-A) and the Humidity Sounder for Brazil (HSB) channels on the Aqua spacecraft uses a polynomial approximation to the temperature dependence of oxygen-band opacity within atmospheric layers. It uses lookup tables to calculate local water-vapor line intensity and pressure-broadening parameters as well as contributions to absorption from the water-vapor continuum, distant lines, and cloud liquid water. The algorithm includes water-line self-broadening and the magnetic-field effect on AMSU-A channel 14. The microwave surface emission model is based on a preliminary classification of the surface type, with subsequent adjustments to the emissivity spectrum that are obtained from the retrieval algorithm. A simple approximate correction for surface nonspecularity is included. The algorithm has been tested by comparisons to a line-by-line calculation and to measurements made by the NOAA-15 AMSU-A.