The Areal Reduction Factor (ARF) : a multifractal analysis

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Civil and Environmental Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2005

Author dc:creator

• Langousis, Andreas, 1981-

Advisor dc:contributor.advisor

• Daniele Veneziano.

• Civil and Environmental Engineering.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/30196

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/30196