Development of a formal likelihood function for improved Bayesian inference of ephemeral catchments

• Published in: Water resources research 2010-12, Vol.46 (12), p.n/a
• Main Authors: Smith, Tyler, Sharma, Ashish, Marshall, Lucy, Mehrotra, Raj, Sisson, Scott
• Format: Article
• Language: English
• Subjects: Bayesian inference; Binomial distribution; Calibration; Case studies; Catchments; ephemeral catchment; error model; Hydrology; likelihood; Markov chain Monte Carlo; rainfall-runoff model; Scientific apparatus & instruments; Stream flow; Uncertainty; Watersheds
• ISSN: 0043-1397; 1944-7973
• DOI: 10.1029/2010WR009514

The application of formal Bayesian inferential approaches in hydrologic modeling is often criticized for requiring explicit assumptions to be made about the distribution of the errors via the likelihood function. These assumptions can be adequate in some situations, but often little attention is paid to the selection of an appropriate likelihood function. This paper investigates the application of Bayesian methods in modeling ephemeral catchments. We consider two modeling case studies, including a synthetically generated data set and a real data set of an arid Australian catchment. The case studies investigate some typical forms of the likelihood function which have been applied widely by previous researchers, as well as introducing new implementations aimed at better addressing likelihood function assumptions in dry catchments. The results of the case studies indicate the importance of explicitly accounting for model residuals that are highly positively skewed due to the presence of many zeros (zero inflation) arising from the dry spells experienced by the catchment. Specifically, the form of the likelihood function was found to significantly impact the calibrated parameter posterior distributions, which in turn have the potential to greatly affect the uncertainty estimates. In each application, the likelihood function that explicitly accounted for the nonconstant variance of the errors and the zero inflation of the errors resulted in (1) equivalent or better fits to the observed discharge in both timing and volume, (2) superior estimation of the uncertainty as measured by the reliability and sharpness metrics, and (3) more linear quantile‐quantile plots indicating the errors were more closely matched to the assumptions of this form of the likelihood function.