We present the algorithm and results for a new fast forward modeling technique applied to the retrieval of atmospheric water vapor from satellite measurements using a weak ro-vibrational overtone band in the visible. The algorithm uses an Optical Absorption Coefficient Spectroscopy (OACS) method which is well suited to situations where line widths in the absorption spectrum are much narrower than the instrumental resolution and where efficient numerical solutions of the equation of radiative transfer are needed. We present examples of OACS forward modeled reflectivity which include the differential contribution of singly scattered photons and compare them with spectral measurements of the Global Ozone Monitoring Experiment (GOME). In particular, we apply OACS to the retrieval of water vapor column (WVC) densities from GOME spectral data between 585 and 600 nm. Method precisions are better than 0.7% for high and better than 3.4% for low WVC. The total accuracy of the retrieval method appears to be better than 0.8 and 4% for high and low WVC, respectively. The retrieval results are compared to WVC values given by European Centre for Medium-Range Weather Forecasts and Special Sensor Microwave Imager and allow us to conclude that the OACS retrieval method is reliable except in cloud-rich situations. In cloud-free cases, an upper limit of 18% error on the retrieved WVC due to the impact of multiple and aerosol scattering as well as aerosol extinction is estimated. In addition, the accuracy of the retrieval is sufficient to permit the detection of systematic differential fit mismatches between modeled and real GOME spectra. The magnitude of such mismatches places an upper limit on the accuracy of HITRAN'96 water vapor line strength values of about 10--20%.