ARF : a multifractal analysis

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2005.Includes bibliographical references (leaves 110-115).The Areal Reduction Factor (ARF) [eta] is a key parameter in the design for hydrologic extremes. For a basin of area A, [eta](A, D, 7) is the ratio between the area-average rainfall intensity over a duration D with return period T and the point rainfall intensity for the same D and T. Besides depending on A, D and possibly T, the ARF is affected by the shape of the basin and by a number of seasonal, climatic and topographic characteristics. Another factor on which ARF depends is the advection velocity, Vad, of the rainfall features. Commonly used formulas and charts for the ARF have been derived by smoothing or curve-fitting empirical ARFs extracted from raingauge network records. Here we derive some properties of the ARF under the assumption that space-time rainfall is exactly or approximately multifractal. We do so for various shapes of the rainfall collecting region and for Vad = 0 and Vad [not equal to] 0. When Vad = 0, a key parameter in the analysis is the ratio Ures = Vres/Ve between the "response velocity" Vres = L/D, where L is the maximum linear dimension of the region, and the "evolution velocity" Ve, = Le/De, where Le and De are the characteristic linear dimension and characteristic duration of organized rainfall features. The effect of Vad [not equal to] 0 depends on the shape of the region. For highly elongated basins, both the direction and magnitude of advection are influential, whereas for regular shaped regions only the magnitude Vad matters. We review ways in which rainfall has been observed to deviate from exact multifractality and models that capture such deviations. We show how the ARF behaves when rainfall is a bounded cascade in space and time.(cont.) We also investigate the effect of estimating areal rainfall from raingauge network measurements. We find that bounded-cascade deviations from multifractality and sparse spatial sampling distort in similar ways the scaling properties of the ARF. Finally we show how one can reproduce various features of empirical ARF charts by using multifractal and bounded cascade models and considering the effects of sparse spatial sampling.by Andreas Langousis.S.M

Extreme rainfall intensities and long-term rainfall risk from tropical cyclones

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2009.Includes bibliographical references (leaves 78-85).We develop a methodology for the frequency of extreme rainfall intensities caused by tropical cyclones (TCs) in coastal areas. The mean rainfall field associated with a TC with maximum tangential wind speed Vmax, radius of maximum winds Rmax, and translation speed Vmax, is obtained using a physically-based model, whereas rainfall variability at both large scales (from storm to storm) and small scales (due to rainbands and local convection) is modeled statistically. The statistical component is estimated using precipitation radar (PR) data from the TRMM mission. Taylor's hypothesis is used to convert spatial rainfall intensity fluctuations to temporal fluctuations at a given location A. The combined physical-statistical model gives the distribution of the maximum rainfall intensity at A during a period of duration D for a TC with characteristics (Vmax, Rmax, Vt) that passes at a given distance from A. To illustrate the use of the model for long-term rainfall risk analysis, we formulate a recurrence model for tropical cyclones in the Gulf of Mexico that make landfall between longitudes 85°-95°W. We then use the rainfall and recurrence models to assess the rainfall risk for New Orleans. For return periods of 100 years or more and long averaging durations (D around 12-24 hours), tropical cyclones dominate over other rainfall event types, whereas the reverse is true for shorter return periods or shorter averaging durations.by Andreas Langousis.Ph.D