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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 lambda = 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.