Inversion of tropospheric profiles from ground-based microwavemeasurements requires a simple and accurate model for calculating the brightness temperatures as received by the radiometer. In the first part, an analytic solution of the radiative transfer equation is derived for an exponentially decaying absorption coefficient and a linear temperature gradient. Based on the obtained analytic expressions, a discretized radiative transfer scheme is developed in the second part. The new scheme incorporates the generic behavior of the atmosphere with the effect that brightness temperatures can be modeled more accurately and with fewer grid points compared to commonly used radiative transfer schemes. The brightness temperature modeling accuracy was improved by a factor of six. The results suggest that the model could be employed for the retrieval of temperature and humidity profiles.