Basin-Scale Statistical Method for Probable Maximum Precipitation with Uncertainty Analysis

Abstract

Probable maximum precipitation (PMP) is used for computing probable maximum flood (PMF), which is then used to design large hydraulic structures. A basin-scale model, based on the Hershfield method, was developed for calculating PMP and PMP uncertainty in this study. It showed that PMP from the proposed method was more consistent with the values reported by the Texas Commission on Environmental Quality (TCEQ). PMP uncertainties were more reliable than those from the previous studies because of the improvement in assumptions and methodology. Utilizing basin-wide data, the proposed method developed equations for frequency factor (K) enveloping curves and calculated and mapped 1-h, 6-h, and 24-h duration PMPs for the Brazos River basin, Texas, United States. The PMP values computed by the basin-scale method were smaller than those computed by the Hershfield method but were more consistent with the values reported by TCEQ (TCEQ results were smallest among the three). The average improvements of the difference percentages for 1-h, 6-h, and 24-h duration PMP were 53.84%, 81.04%, and 72.60%, respectively. The longer-duration PMP map showed a declining trend from east coast to west (inland) and was consistent in spatial distribution with the TCEQ map. The PMP uncertainty was determined using the delta and bootstrap methods, which produced consistent results. The uncertainty differences between the delta values and bootstrap values were 10.05%, 10.35%, and 19.02%, and between the Salas values and bootstrap values for each duration were 25.59%, 20.06%, and 27.95%, respectively, which means the delta method results were more supported by the bootstrap method results. Comparison showed that the uncertainty by other studies was smaller because uncertainty caused by K and normality assumption was not considered. Using bootstrap resampling, the distribution of PMP was explored, and then PMPs with 95% confidence intervals were obtained.