Quantifying Uncertainty of Probable Maximum Flood

Probable maximum flood (PMF) has been used in large hydraulic infrastructure design for decades. However, a complete framework for deriving PMF with uncertainty analysis is lacking. This study investigates procedures ranging from probable maximum precipitation(PMP) with uncertainty to probable maximum storm (PMS), rainfall–runoff (R-R) with uncertainty, and PMF with uncertainty. A case study of Hurricane Harvey in the lower Brazos River basin in Texas is used to calibrate the R-R model and compare it with PMF. The uncertainty of PMF stems from these three components. The updated storm records indicate that except for the area size that drives PMP, the within-storm depth-area relation can generate depths greater than that of PMP for smaller areas, which runs counter to findings of a widely cited report. The PMF peak flow derived by the average PMP value was $\mathrm{12,716}{\mathrm{m}}^3/\mathrm{s}$, which was around three times the peak flow from Hurricane Harvey ($\mathrm{3,764}{\mathrm{m}}^3/\mathrm{s}$). The 95% PMP confidence interval band was 54.5 mm and resulted in a $\mathrm{3,656}{\mathrm{m}}^3/\mathrm{s}$ difference between the corresponding PMF peak flows. The return periods of PMP and rainfall of Harvey at a gauge station in Houston were around 400 years and 100 years, respectively, obtained from fitting either a generalized Pareto (GP) or generalized extreme value (GEV) probability distribution. For peak flow uncertainty, the PMP uncertainty accounted for most (81%) of the parts, while the R-R model uncertainty accounted for less (19%). The framework of this study can be expanded to other areas of interest having sufficient data sets.