Benefits of Explicit Treatment of Zero Flows in Probabilistic Hydrological Modeling of Ephemeral Catchments

Abstract

Probabilistic modeling of streamflow in ephemeral catchments, where streamflow is frequently zero or negligible, is a major scientific and operational challenge. This paper evaluates the benefits of an explicit treatment of zero flows in the residual error models used for hydrological model calibration and prediction. In this approach, the lower bound of zero for streamflow is implemented using a censoring approach. The explicit approach is compared to a simpler pragmatic approach, which imposes the zero streamflow bound in prediction but not in calibration. Following a theoretical exposition, empirical comparisons are reported using a daily rainfall‐runoff model (GR4J), four residual error schemes (based on log, log‐sinh, and Box‐Cox [BC] transformations with λ = 0.2 and 0.5), 74 Australian catchments with diverse hydroclimatology, and five performance metrics (reliability, precision, bias, proportion of zero flow days, and Continuous Ranked Probability skill score). The key findings are as follows: (1) in mid‐ephemeral catchments (5–50% zero flows) the explicit approach improves predictive performance, especially reliability, through better characterization of residual errors; (2) BC0.2 and BC0.5 schemes are Pareto optimal in mid‐ephemeral catchments (when the explicit approach is used): BC0.2 achieves better reliability and is recommended for probabilistic prediction, whereas BC0.5 attains lower volumetric bias; (3) in low‐ephemeral catchments (<5% zero flows) the pragmatic approach is sufficient; (4) in high‐ephemeral catchments (>50% zero flows) theoretical limitations result in poor performance of these particular explicit and pragmatic approaches, and further development is needed. The findings provide guidance on improving probabilistic streamflow predictions in ephemeral catchments.

Multi‐temporal Hydrological Residual Error Modeling for Seamless Subseasonal Streamflow Forecasting

“…Future work on seamless streamflow forecasting will focus on the following aspects: Application and refinement of the MuTHRE model over a wider range of hydroclimatic conditions and hydrological models. Further development is required to improve forecasts in ephemeral catchments, including explicit treatment of zero flows (McInerney et al, 2019). Further work will also evaluate the robustness of our findings using hydrological models other than GR4J, in particular, using physically based distributed models which are becoming more common in operational systems (e.g., Gochis et al, 2018).…”

“…Both practical and statistical significance testing is implemented using the method of McInerney et al (2019). The pairwise Wilcoxon signed rank test (Bauer, 1972) is used to compare the distributions of a performance metric for the MuTHRE and baseline models over all catchments.…”

“…Statistical significance testing evaluates whether differences in the distribution of metric values (regardless of their magnitude) could be explained by sampling variability alone. Practical significance testing assesses whether the difference between metric values are large enough to provide tangible benefits in a practical (and necessarily subjective) sense (e.g., Jacobson et al, 1984;McInerney et al, 2019;Vaske, 2002). , where N cat is the total number of catchments and lower metric values represent better performance.…”

“…The wet season in these catchments spans June to October. Note that these catchments are selected to have fewer than 5% zero flow days, in order to avoid the limitations of not using an explicit treatment of zero flows (McInerney et al, 2019). Rainfall forecasts for the same period are obtained from the Australian Community Climate Earth-System Simulator-Seasonal (ACCESS-S), which is the Australian Bureau of Meteorology's seasonal climate forecasting system (Hudson et al, 2017).…”

“…The wet season in these catchments spans June to October. Note that these catchments are selected to have fewer than 5% zero flow days, in order to avoid the limitations of not using an explicit treatment of zero flows (McInerney et al, 2019).…”