Identification of dominant hydrological mechanisms using Bayesian inference, multiple statistical hypothesis testing and flexible models

Abstract

<p>In hydrological modelling, the identification of hydrological model mechanisms best suited for representing individual hydrological (physical) processes is a major research and operational challenge. We present a statistical hypothesis-testing perspective to identify dominant hydrological mechanism. The method 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; (iii) a flexible modelling framework to generate model structures using combinations of available mechanisms. The uncertainty in the test statistic is approximated via bootstrap from the ensemble of model structures. Synthetic and real data experiments are conducted using 624 model structures from the hydrological modelling system FUSE and data from the Leizarán catchment in northern Spain. The findings show that 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.</p>

An Exploration of Bayesian Identification of Dominant Hydrological Mechanisms in Ungauged Catchments

“…Finally, as discussed in Prieto et al. (2021), the degree of difference in the competing mechanisms is also of clear relevance. If two mechanisms are very similar, it is harder to distinguish them.…”

“…F id is broadly similar to the power metric P used in Prieto et al. (2021), except that F id can be calculated for any experiment while P can be calculated only when the “true” model is known.…”

“…The null hypothesis $${\text{H0}}_{k}^{\wp }$$ is then tested using the procedure in Prieto et al. (2021) as given in Appendix . These stages of the analysis are illustrated schematically in Figure 1 row g.…”

“…In this article, we consider 7 processes: (a) (water) storage in the unsaturated zone, defined by the architecture of the upper soil layer; (b) storage of water occurring in the unsaturated zone, defined by the architecture of the lower soil layer; (c) evaporation; (d) interflow for the lateral movement of the water into the soil; (e) percolation for the vertical movement of water from the unsaturated zone (upper soil layer) to the saturated zone (lower soil layer); (f) surface runoff generation; and (g) routing for the evolution (shape and time) of the surface runoff hydrograph as the water moves through the river. The number of mechanisms for each process ranges from 2 to 4, with a total of 19 mechanisms (Table 1 in Prieto et al., 2021). In this article, we use the implementation of FUSE in the R language (Vitolo et al., 2016).…”

“…The key definitions of the multiple hypothesis testing methods are as follows (Prieto et al., 2021): An individual comparison is an individual test of whether a mechanism $${m}_{k}^{\wp }$$ is “dominant”, that is, substantially more likely than alternative mechanisms available in $$\mathbf{G}$$ to represent $$\wp $$ The null hypothesis for an individual test $${\text{H0}}_{k}^{\wp }$$ is “mechanism $${m}_{k}^{\wp }$$ is not the dominant mechanism for process $$\wp $$” A family of comparisons for a process $$\wp $$ is the set of individual tests of each mechanism against all other mechanisms that represent that process The null hypothesis for a family of comparisons $${\text{H0}}^{\wp }$$ is “none of the proposed hydrological mechanism is dominant for process $$\wp $$” The family wise error rate (FWER) is the probability of making one or more type I errors in the family of multiple tests, that is, the probability of incorrectly identifying a mechanism as dominant for a given process. The (conservative) Bonferroni's correction is employed to keep the FWER below a prescribed significant level $$\alpha $$, by imposing a stricter $${\alpha }^{\ast }$$ in each individual test (Hochberg, 1988) A test statistic $$t$$ is required for each individual null hypothesis $${\text{H0}}_{k}^{\wp }$$.…”