Resolving the Individual Contributors to Total Modeling Error in Conceptual Hydrology: Data, Structural and Numerical Errors

Hydrological modeling has traditionally suffered from a variety of errors - including input-output data errors, structural errors in the model conceptualization and, finally, numerical errors in the model implementation. These errors have distinctly different origins, behavior and require specialized treatment. Following a brief theoretical review, we present a number of case studies where these errors are identified and treated. First, we demonstrate the occurrence of numerical errors when the model equations are solved using unreliable techniques. Remarkably, the hydrological community has allowed such errors to arise and persist despite the weaknesses of these techniques being well known for decades in the applied mathematics literature, and despite far more robust techniques being widely available. Second, we demonstrate the use of statistical techniques to get useful insights into rainfall and runoff data errors. When exploited within a Bayesian inference, these data insights can be used to estimate structural errors. Third, we demonstrate a methodology for characterizing structural errors using stochastic parameters, and flexible model structures. The case studies move us another step closer towards the elusive goal of reliably understanding and treating the distinct sources of error afflicting hydrological models. Benefits for improved scientific hypothesis-testing and more reliable operational predictions are discussed.