The complementary nature of physically-based and data-driven models in their demand for physical insight and historical data, leads to the notion that the predictions of a physically-based model can be improved and the associated uncertainty can be systematically reduced through the conjunctive use of a data-driven model of the residuals. The objective of this thesis is to minimise the inevitable mismatch between physically-based models and the actual processes as described by the mismatch between predictions and observations. The complementary modelling approach is applied to various hydrodynamic and hydrological models.