Hypothetico-Inductive Modelling

Sunday, 19 February 2012

The standard Data-Based Mechanistic (DBM) modeling procedures normally exploit the CAPTAIN identification and estimation routines to produce an efficiently parameterized (parsimonious) model that explains the data well and can be interpreted in reasonable, physically meaningful terms. But this physical interpretation is inferred directly from the data using statistical methods, under the assumption that the system is inherently stochastic. Consequently, the identified model may not always be fully acceptable or credible to an audience that has been educated to believe strongly in hypothetico-deductive modeling based on conceptual, often deterministic, simulation models. Moreover, the model obtained in this completely inductive manner may be restricted to some degree: for instance, previous DBM rainfall-flow models function very well within an adaptive flow forecasting context but they utilize the flow measurement as a surrogate measure of catchment storage (soil moisture) in the `effective rainfall' nonlinearity. Consequently, they cannot be used for stochastic simulation purposes as this would imply a physically meaningless feedback mechanism and could make the model unstable.

If, in any particular example, the DBM model is not considered acceptable for the above reasons, then it needs to be modified to correct any such perceived deficiencies. One obvious approach is to retain the statistically identified structure of the DBM model and base any modifications on conceptual ideas about the nature of those elements in the model that require further elucidation. For instance, various nonlinear conceptual models have been evolved to synthesize the effective rainfall and can provide possible replacements for the DBM effective rainfall nonlinearity; modifications that would allow it to be used for stochastic simulation. This is the stimulus for Hypothetico-Inductive DBM (HI-DBM) modelling.

A paper and a Report will be available soon that discuss a lengthy example of DBM and HI-DBM modelling based on rainfall, potential evapotranspiration and flow data from the humid Leaf River basin (1944 km2) located north of Collins, Mississippi, USA, over the forty water-years from Oct 1948 to Sept 1988. It shows that, although the DBM model of the data out-performs the well known HyMOD model (see e.g. Moradkhani et al, 2005), it is restricted to forecasting applications. However, the HI-DBM analysis shows that the input effective rainfall nonlinearity of the DBM model can be replaced by the Probability Distributed Model (PDM) conceptual model (see e.g. Moore, 2007) used in HyMOD without any significant degradation in the DBM model performance. Moreover, unlike the DBM model, the resulting HI-DBM model is more flexible and can be used for deterministic or stochastic simulation purposes, as well as forecasting. However, the analysis also suggests that there are probably some remaining deficiencies in the HI_DBM, PDM and HyMOD models that need to be investigated and resolved by further research and development. One interesting HI-DBM model that is identified in the analysis is a new version of the HyMOD model in which the 3rd order Nash Cascade of the original is replaced by a 10th order Cascade. This model performs very well and suggets that the HyMOD model should be replaced by this new version.

R. J. Moore. The PDM rainfall-runoff model. Hydrol. Earth Syst. Sci., pages 483–499, 2007.

H. Moradkhani, S. Sorooshian, H. V. Gupta, and P. R. Houser. Dual state-parameter estimation of hydrological models using ensemble Kalman filter. Advances in Water Resources, 28:135–147, 2005.