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 10 6 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.

Multifractal analysis of the rainfall time distribution on the metropolitan area of Barcelona (Spain)

“…2). As reported by Douglas and Barros (2003), the most common range values of q D extend between a little less than 2 and slightly more than 3. Other studies have found values of q D between 1.7 and 5 (Fraedrich and Larnder 1993;Labat et al 2002).…”

Investigating the multifractality of point precipitation in the Madeira archipelago

“…Mandelbrot, 1977Mandelbrot, , 1982) deals with simple scaling, which means that such behaviour is determined by one parameter, called fractal dimension (e.g. Mandelbrot, 1977Mandelbrot, , 1982Feder, 1988;Falconer, 1990;Hastings and Sugihara, 1993). In defining (fractal) dimension the idea of measurement at scale δ is fundamental.…”

“…This parameter can be obtained by the box-counting method (see e.g. Feder, 1988;Falconer, 1990;Hastings and Sugihara, 1993). In practical applications of this method, the D-dimensional space of the observations is covered with gradually-decreasing (it is common that the size is decreased gradually by a factor of 2), non-overlapping boxes of side δ.…”

“…Very roughly, the dimension of a set tells how densely the set occupies the metric space in which it lies (e.g. Falconer, 1990).…”

Recent changes in extreme precipitation and drought over the Songhua River Basin, China, during 1960–2013

“…Extreme precipitation events have been increasing since the late 20th century in the mid-latitude and high-latitude land Atmospheric Research 157 (2015) 137-152 precipitation events have received worldwide attention due to their large-scale impacts (Alexander et al, 2006;Boccolari and Malmusi, 2013;Déqué, 2007;Douglas and Barros, 2003;Easterling et al, 2000;Fu et al, 2010;Fu et al, 2013;Goswami et al, 2006;Schmidli and Frei, 2005).…”