A computationally efficient and accurate model is derived for the calculation of the atmospheric transmittance along inhomogeneous paths and within spectral bands dominated by molecular line absorption. It is a Stieltjes integration of transmission weighted by the frequency of occurrence of absorption coefficient within the band. Path inhomogeneitites are accounted for by assuming that the rank of absorption coefficient at any wavenumber is independent of temperature and pressure. The technique is then applied to the ground based radiometric determination of precipitable water. It is found that the technique predicts the behavior of the ρστ water vapor absorption band very well. An RMS disagreement of 11% is found when the model predictions are compared to radiosonde determinations of precipitable water. The model is also applied to the determination of vertical water vapor distributions in the stratosphere given measured effective optical depths as a function of tangent height from a limb scanning satellite. A new iterative reduction technique is introduced which incorporates the transmission model and it is shown to be both numerically stable and rapidly convergent. A comparison of the results with an independent reduction technique shows good overall agreement with a small systematic difference above 20 km. The uncertainty in the measurements, which yields solution uncertainties on the order of 30%, renders this systematic difference unimportant.