Abstract
Abstract. In this paper the difficult problem of how to legitimise data-driven hydrological models is addressed using an example of a simple artificial neural network modelling problem. Many data-driven models in hydrology have been criticised for their black-box characteristics, which prohibit adequate understanding of their mechanistic behaviour and restrict their wider heuristic value. In response, presented here is a new generic data-driven mechanistic modelling framework. The framework is significant because it incorporates an evaluation of the legitimacy of a data-driven model's internal modelling mechanism as a core element in the modelling process. The framework's value is demonstrated by two simple artificial neural network river forecasting scenarios. We develop a novel adaptation of first-order partial derivative, relative sensitivity analysis to enable each model's mechanistic legitimacy to be evaluated within the framework. The results demonstrate the limitations of standard, goodness-of-fit validation procedures by highlighting how the internal mechanisms of complex models that produce the best fit scores can have lower mechanistic legitimacy than simpler counterparts whose scores are only slightly inferior. Thus, our study directly tackles one of the key debates in data-driven, hydrological modelling: is it acceptable for our ends (i.e. model fit) to justify our means (i.e. the numerical basis by which that fit is achieved)?
Highlights
In this paper a new, data-driven mechanistic modelling framework (DDMMF) is presented as a response to the complex, long-standing problem of how to determine the mechanistic legitimacy of a hydrological, data-driven model (DDM)
The DDMMF we have developed provides methodological direction that has been absent from many datadriven modelling studies in hydrology
This paper has argued that gaining an understanding of the internal mechanisms by which a hydrological model generates its forecasts is an important element of the model development process
Summary
In this paper a new, data-driven mechanistic modelling framework (DDMMF) is presented as a response to the complex, long-standing problem of how to determine the mechanistic legitimacy of a hydrological, data-driven model (DDM). The use of black-box models is most commonly limited to catchment-specific, operational prediction tasks where there is usually no expectation of model transferability In such applications the model’s validity can be adequately assessed via the goodness-of-fit of its outputs (Klemes, 1986; Refsgaard and Knusden, 1996), but there is no formal requirement to legitimise the modelling mechanism by which the fit is obtained. An important question remains about whether they can ever offer more than the optimisation of goodness-of-fit between inputs and outputs through the delivery of insights to hydrologists (Minns and Hall, 1996; Babovic, 2005; Abrahart et al, 2011) This question is pertinent for ANN-based models, which represent the most widely used type of a black-box DDM in hydrology. If such views are to be countered, researchers need to demonstrate much greater understanding about why and how such models deliver their results (c.f. Beven, 2002), and the minimum that must be delivered is a demonstration that DDMs possess two basic characteristics over and above their goodness-of-fit performance: 1. a logical and plausible structure (including input selection); 2. a legitimate mechanistic behaviour
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