Probable Maximum Precipitation Estimation Using Multifractals: Application in the Eastern United States

Abstract

Probable maximum precipitation (PMP) is the conceptual construct that defines the magnitude of extreme storms used in the design of dams and reservoirs. In this study, the value and utility of applying multifractal analysis techniques to systematically calculate physically meaningful estimates of maximum precipitation from observations in the eastern United States is assessed. The multifractal approach is advantageous because it provides a formal framework to infer the magnitude of extreme events independent of empirical adjustments, which is called the fractal maximum precipitation (FMP), as well as an objective estimate of the associated risk. Specifically, multifractal (multiscaling) behavior of maximum accumulated precipitation at daily (327 rain gauges) and monthly (1400 rain gauges) timescales, as well as maximum accumulated 6-hourly precipitable water fluxes for the period from 1950 to 1997 were characterized. Return periods for the 3-day FMP estimates in this study ranged from 5300 to 6200 yr. The multifractal parameters were used to infer the magnitude of extreme precipitation consistent with engineering design criterion (e.g., return periods of 106 yr), the design probable maximum precipitation (DPMP). The FMP and DPMP were compared against PMP estimates for small dams in Pennsylvania using the standard methodology in engineering practice (e.g., National Weather Service Hydrometeorological Reports 51 and 52). The FMP estimates were usually, but not always, found to be lower than the standard PMP (FMP/PMP ratios ranged from 0.5 to 1.0). Furthermore, a high degree of spatial variability in these ratios points to the importance of orographic effects locally, and the need for place-based FMP estimates. DMP/PMP ratios were usually greater than one (0.96 to 2.0), thus suggesting that DPMP estimates can provide a bound of known risk to the standard PMP.