Uncertainty, sensitivity analysis and the role of data based mechanistic modeling in hydrology

In this paper, we discuss a joint approach to calibration and uncertainty estimation for hydrologic systems that combines a top-down, data-based mechanistic (DBM) modelling methodology; and a bottom-up, reductionist modelling methodology. The combined approach is applied to the modelling of the River Hodder catchment in North-West England. The top-down DBM model provides a well identified, statistically sound yet physically meaningful description of the rainfall-flow data, revealing important characteristics of the catchment-scale response, such as the nature of the effective rainfall nonlinearity and the partitioning of the effective rainfall into different flow pathways. These characteristics are defined inductively from the data without prior assumptions about the model structure, other than it is within the generic class of nonlinear differential-delay equations. The bottom-up modelling is developed using the TOPMODEL, whose structure is assumed a priori and is evaluated by global sensitivity analysis (GSA) in order to specify the most sensitive and important parameters. The subsequent exercises in calibration and validation, performed with Generalized Likelihood Uncertainty Estimation (GLUE), are carried out in the light of the GSA and DBM analyses. This allows for the pre-calibration of the the priors used for GLUE, in order to eliminate dynamical features of the TOPMODEL that have little effect on the model output and would be rejected at the structure identification phase of the DBM modelling analysis. In this way, the elements of meaningful subjectivity in the GLUE approach, which allow the modeler to interact in the modelling process by constraining the model to have a specific form prior to calibration, are combined with other more objective, data-based benchmarks for the final uncertainty estimation. GSA plays a major role in building a bridge between the hypothetico-deductive (bottom-up) and inductive (top-down) approaches and helps to improve the calibration of mechanistic hydrological models, making their properties more transparent. It also helps to highlight possible mis-specification problems, if these are identified. The results of the exercise show that the two modelling methodologies have good synergy; combining well to produce a complete joint modelling approach that has the kinds of checks-and-balances required in practical data-based modelling of rainfall-flow systems. Such a combined approach also produces models that are suitable for different kinds of application. As such, the DBM model considered in the paper is developed specifically as a vehicle for flow and flood forecasting (although the generality of DBM modelling means that a simulation version of the model could be developed if required); while TOPMODEL, suitably calibrated (and perhaps modified) in the light of the DBM and GSA results, immediately provides a simulation model with a variety of potential applications, in areas such as catchment management and planning.