Physically-based models of groundwater flow are powerful tools for water resources assessment under varying hydrologic, climate and human development conditions. One of the most important topics of investigation is how these conditions will affect the discharge of groundwater to rivers and streams (i.e. baseflow). Groundwater flow models are based upon discretized solution of mass balance equations, and contain important hydrogeological parameters that vary in space and cannot be measured. Common practice is to use least squares regression to estimate parameters and to infer prediction and associated uncertainty. Nevertheless, the unavoidable uncertainty associated with physically-based groundwater models often results in both aleatoric and epistemic model calibration errors, thus violating a key assumption for regression-based parameter estimation and uncertainty quantification. We present a complementary data-driven modeling and uncertainty quantification (DDM-UQ) framework to improve predictive accuracy of physically-based groundwater models and to provide more robust prediction intervals. First, we develop data-driven models (DDMs) based on statistical learning techniques to correct the bias of the calibrated groundwater model. Second, we characterize the aleatoric component of groundwater model residual using both parametric and non-parametric distribution estimation methods. We test the complementary data-driven framework on a real-world case study of the Republican River Basin, where a regional groundwater flow model was developed to assess the impact of groundwater pumping for irrigation. Compared to using only the flow model, DDM-UQ provides more accurate monthly baseflow predictions. In addition, DDM-UQ yields prediction intervals with coverage probability consistent with validation data. The DDM-UQ framework is computationally efficient and is expected to be applicable to many geoscience models for which model structural error is not negligible. (C) 2015 Elsevier Ltd. All rights reserved.