A Framework for Evaluating Uncertainty From Multiple Sources in Probable Maximum Precipitation Estimation by the Hershfield Method Using Imprecise Probability

Abstract Design flood corresponding to probable maximum precipitation (PMP) is often used in risk assessment of large hydraulic structures. PMP is widely estimated using the Hershfield method (HM) when reasonably long precipitation records are available, but other hydrometeorological data are unavailable/limited. Uncertainty in HM‐based PMP estimates can arise from multiple sources, but the literature lacks methodologies to identify significant contributors to the uncertainty and determine the overall uncertainty bounds. To address this research gap, a novel framework based on imprecise probability (IP) theory is proposed. It facilitates quantifying the overall uncertainty in PMP estimates arising from multiple sources and discerning contributions from individual sources and their combinations. Uncertainties analyzed include those due to (i) the sampling effect of precipitation observations, and (ii) 24 combinations of options for (a) defining a meaningful region/zone, (b) envelope curve space preparation, and (c) the curve construction. The effectiveness of the proposed framework in determining IP bounds of PMP estimates is illustrated through case studies on two major flood‐prone river basins (Mahanadi and Godavari) in India and the Brazos River basin in the United States. Results revealed that the highest contributor to the overall uncertainty in PMP estimates is the combined/interaction component of all four uncertainty sources for the Indian river basins and the statistical sampling effect for the United States basin. Whereas the least contribution to uncertainty is consistently from envelope curve construction. Options/guidelines are provided to reduce the uncertainty (interval between IP bounds) arising from different sources in PMP estimation with HM.