The authors developed an approach for deriving a statistical model of range-dependent error (RDE) in radar-rainfall estimates by parameterizing the structure of the non-uniform vertical profile of radar reflectivity (VPR). The proposed parameterization of the mean VPR and its expected variations are characterized by several climatological parameters that describe dominant atmospheric conditions related to vertical reflectivity variation. We have used four years of radar volume scan data from the Tulsa weather radar WSR-88D (Oklahoma) to illustrate this approach and have estimated the model parameters by minimizing the sum of the squared differences between the modeled and observed VPR influences that were computed using radar data. We evaluated the mean and standard deviation of the modeled RDE against rain gauge data from the Oklahoma Mesonet network. No rain gauge data were used in the model development. The authors used the three lowest antenna elevation angles to demonstrate the model performance for cold (November-April) and warm (May-October) seasons. The RDE derived from the parameterized models shows very good agreement with the observed differences between radar and rain gauge estimates of rainfall. For the third elevation angle and cold season, there are 82% and 42% improvements for the RDE and its standard deviation with respect to the no-VPR case. The results of this study indicate that VPR is a key factor in the characterization of the radar range-dependent bias, and the proposed models can be used to represent the radar RDE in the absence of rain gauge data. © 2011 Elsevier B.V.