Hypothetico‐inductive data‐based mechanistic modeling of hydrological systems

Abstract

[1] The paper introduces a logical extension to data-based mechanistic (DBM) modeling, which provides hypothetico-inductive (HI-DBM) bridge between conceptual models, derived in a hypothetico-deductive manner, and the DBM model identified inductively from the same time-series data. The approach is illustrated by a quite detailed example of HI-DBM analysis applied to the well-known Leaf River data set and the associated HyMOD conceptual model. The HI-DBM model significantly improves the explanation of the Leaf River data and enhances the performance of the original DBM model. However, on the basis of various diagnostic tests, including recursive time-variable and state-dependent parameter estimation, it is suggested that the model should be capable of further improvement, particularly as regards the conceptual effective rainfall mechanism, which is based on the probability distributed model hypothesis. In order to verify the efficacy of the HI-DBM analysis in a situation where the actual model generating the data is completely known, the analysis is also applied to a stochastic simulation model based on a modified HyMOD model.

A guide to good practice in modeling semantics for authors and referees

“…Such alternative descriptions are more acceptable and correct. Even simple transfer function models derived from observations can have a mechanistic interpretation in terms of meaningful time constants or gains [e.g., Young, 2003Young, , 2013, but there are (at least as yet) no models that are based on correct physical principles in hydrology. Models based on the Darcy-Richards equation and Manning equation might claim to have a physical foundation, but the empirical ''physics'' on which they are based is clearly not universally applicable [see, for example, Beven and Germann, 2013;Beven, 2013].…”

“…[5] Of course, the deductive-inductive dichotomy is rather unsatisfactory [Young, 2011[Young, , 2013, and these approaches are certainly not mutually exclusive. The best aspects of both approaches can be exploited to produce a systematic approach to hydrological model development.…”

“…The best aspects of both approaches can be exploited to produce a systematic approach to hydrological model development. For example, there are deductive models that are based on principles originally derived by induction (Darcy-Richards, Manning), and the calibration (estimation) of parameters will introduce an inductive element (and associated uncertainty) to even the most deductive model [Beven, 2012;Young, 2011Young, , 2013. Referees should ensure, however, that the deductive and inductive elements of a modeling study are clearly differentiated.…”

“…It is necessary to differentiate between ''ex-ante'' and ''ex-post'' forecasting. These are terms that are well known in the forecasting literature [Young, 2013]. Here ex-ante forecasts are real forecasts, only dependent on data up to the forecasting origin.…”

“…[10] Ex-post forecasting (actually more strictly ex-post hindcasting since measured inputs cannot be available into the actual future) should never be portrayed either as real forecasting or as real simulation, since this is highly misleading: indeed, it is difficult to justify ex-post forecasting in any realistic application [e.g., Beven, 2009;Young, 2013], unless it is made quite clear that it is being used only as a check on the stochastic simulation abilities of the model. Again we suggest that referees should act to ensure good practice by requiring revision to papers that use ''prediction'' without clarification of its purpose, and in particular where it is used to mean ex-post forecasting.…”