Identification of Dominant Hydrological Mechanisms Using Bayesian Inference, Multiple Statistical Hypothesis Testing, and Flexible Models

Abstract

In hydrological modeling, the identification of model mechanisms best suited for representing individual hydrological (physical) processes is of major scientific and operational interest. We present a statistical hypothesis-testing perspective on this model identification challenge and contribute a mechanism identification framework that combines: (i) Bayesian estimation of posterior probabilities of individual mechanisms from a given ensemble of model structures; (ii) a test statistic that defines a “dominant” mechanism as a mechanism more probable than all its alternatives given observed data; and (iii) a flexible modeling framework to generate model structures using combinations of available mechanisms. The uncertainty in the test statistic is approximated using bootstrap sampling from the model ensemble. Synthetic experiments (with varying error magnitude and multiple replicates) and real data experiments are conducted using the hydrological modeling system FUSE (7 processes and 2–4 mechanisms per process yielding 624 feasible model structures) and data from the Leizarán catchment in northern Spain. The mechanism identification method is reliable: it identifies the correct mechanism as dominant in all synthetic trials where an identification is made. As data/model errors increase, statistical power (identifiability) decreases, manifesting as trials where no mechanism is identified as dominant. The real data case study results are broadly consistent with the synthetic analysis, with dominant mechanisms identified for 4 of 7 processes. Insights on which processes are most/least identifiable are also reported. The mechanism identification method is expected to contribute to broader community efforts on improving model identification and process representation in hydrology.