On Constructing Limits-of-Acceptability in Watershed Hydrology using Decision Trees

Abstract

A hydrological model incurs three types of uncertainties: measurement, structural and parametric uncertainty. For instance, in rainfall-runoff models, measurement uncertainty exists due to errors in measurements of rainfall and streamflow data. Structural uncertainty exists due to errors in mathematical representation of hydrological processes. Parametric uncertainty is a consequence of our inability to measure effective model parameters, limited data available to calibrate model parameters, and measurement and structural uncertainties. Measurement and structural uncertainties are inseparable without additional information about measurement uncertainties. The existence of these predominantly epistemic uncertainties makes the model inference difficult. Limits-of-acceptability (LOA) framework has been proposed in the literature for model inference under a rejectionist framework. LOAs can be useful in model inference if they reflect the effect of errors in rainfall and streamflow measurements. In this study, the usefulness of quantile random forest (QRF) algorithm has been explored for constructing LOAs. LOAs obtained by QRF were compared to the uncertainty bounds obtained by rating-curve analysis and the LOAs obtained by runoff ratio method. Rating curve analysis yields uncertainty in streamflow measurements only and the runoff ratio method is expected to reflect uncertainty in rainfall and streamflow volume measurements. LOAs obtained by using QRF were found to envelop the uncertainty bounds due to streamflow measurement errors. The variation of width of LOAs was similar for QRF and runoff ratio methods. Further, QRF LOAs were scrutinized in terms of their ability to reflect the effect of rainfall uncertainty, both qualitatively and quantitatively. Results indicate that QRF LOAs reflect the effect of rainfall uncertainty: increase in standard deviation with increase in mean streamflow values and decrease in coefficient of variation with increase in mean streamflow values. A mathematical analysis of the LOAs obtained by the QRF method is presented to provide a theoretical foundation.