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The microwave emission from a half-space medium characterized by coordinate dependent scattering and absorbing centers has been calculated by numerically solving the radiative transfer equation by the method of invariant imbedding. A Mie scattering phase function and surface polarization have been included in the calculation. Also included are the physical temperature profile and the temperature variation of the index of refraction for ice. Using published values of grain-size anddoi:10.1017/s0022143000010303 fatcat:vwwtvxwrznaapeuxru542kobp4