Radar reflectivity (Z) and visibility (Vis) can be linked theoretically since they are related to the 6th and the 2nd moments of an assumed gamma shaped DSD. The model can be tested on measurements and used in an inverse mode to predict Vis from Z. However, in reality the fog DSD is almost never gamma shaped, leading to errors in the Vis estimation in the actual datasets. A further development of the model includes the attenuation factor (La), which is related to the 3rd moment and proportional to the liquid water content. This improves the estimated accuracy of visibility, in the theoretical moments-based model. Finally we were able to arrive at a higher accuracy by introducing an empirical exponential model, estimating Vis from Z and La. Various modeling approaches have been investigated by us and will be reported upon in this paper. A test based on DSD datasets for various fog types in literature, showed robust performance of the Vis-Z-La model for large variations in DSD. The Vis-Z-La model is also validated with the fog datasets that were collected by the synergy of in-situ and remote sensing instruments at Cabauw. The results indicate that the Vis-Z-La model is a well-performing model to estimate visibility from radar measurements.