This book explores how to minimize the inevitable mismatch between physically-based models and the actual processes as described. The author uses principles based on information theory to detect the presence and nature of residual information in model errors that might help to develop a data-driven model of the residuals by treating the gap between the process and its model as a separate process. The complementary modeling approach is applied to various hydrodynamic and hydrological models to forecast the expected errors and accuracy, using neural network and fuzzy rule-based models. The possibility that information may be obtained which will help to improve the physically-based model is also demonstrated.