Equivalent distributions with application to rainfall as an upper bound to flood distributions

Alexander, Gavin; Karoly, A.; Susts, A.B.

doi:10.1016/0022-1694(69)90025-0

Cited by 18 publications

(7 citation statements)

References 14 publications

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“…Early attempts to use rainfall data to extrapolate flood volume frequency distributions date back to the late 1960s [see Guillot and Duband, 1967;Alexander et al, 1969]. In particular, Gulllot and Duband [1967] described a method called GRA-DEX, which was developed in 1966 by the electrical company "Electricit6 de France."…”

Section: Su(xlt) = P{xi -< Xly• > U Re = T}mentioning

confidence: 99%

Estimating the upper tail of flood‐peak frequency distributions using hydrometeorological information

Naghettini¹,

Potter²,

Illangasekare³

1996

Water Resources Research

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In its 1988 report, the National Research Council Committee on Estimating the Probabilities of Extreme Floods identified principles for improving the estimation of floods with annual exceedance probabilities of the order of 10−3 or smaller. This paper presents a methodology for estimating the probability of extreme floods which makes use of these principles. Its core is the “peak‐to‐volume” method [Bradley and Potter, 1992], which is based on separately estimating the probability distributions of flood volumes and flood peaks conditioned on volumes. In its original form it relies on extrapolating a conventionally estimated probability distribution, the distribution of flood volumes. To strengthen this step, we propose use of the gradient of extreme values (GRADEX) method [Guillot and Duband, 1967], in which the upper tail of the flood volume distribution is deduced from that Of precipitation. We enhance the GRADEX method by exploiting the work of Smith [1989], who developed a regional model for estimating the upper tail of a frequency distribution based on extreme order statistics. An example illustrates the proposed method.

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Section: Su(xlt) = P{xi -< Xly• > U Re = T}mentioning

confidence: 99%

Estimating the upper tail of flood‐peak frequency distributions using hydrometeorological information

Naghettini¹,

Potter²,

Illangasekare³

1996

Water Resources Research

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“…The AM approach has been very popular, as demonstrated by the large number of works in which it is used (e.g. Chow, 1964;Alexander et al, 1969;Kirkby, 1969;Yevjevich, 1972;Potter, 1987;Bobeé and Ashkar, 1991;García-Ruiz et al, 2000).…”

Section: Introductionmentioning

confidence: 98%

Uncertainties in partial duration series modelling of extremes related to the choice of the threshold value

Beguería

2005

Journal of Hydrology

171

105

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Partial duration series modelling is a robust tool with which to model hydrologic extremes, but because of several technical problems it remains underused. The most important obstacle is the choice of the threshold value, a matter that is currently under investigation by several authors.The truncation value affects the basic assumptions of the model, including arrival times and exceedance magnitudes. This paper considers changes in parameter and quantile estimates as a function of the threshold value (sampling variability). Simulated and real data were used to test the consistency of the model, and a new modelling procedure based on increasing threshold censoring is proposed to overcome these problems. Poisson arrivals and Generalized Pareto exceedances were assumed, and the suitability of this model at different threshold values has been also addressed.

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“…Alexander, Karoly, and Susto (1969) showed that there was a tendency for extreme-value probability distributions used to predict extreme floods to converge in their long tails. They stated that "once it is recognized that rare floods can be analyzed using statistical procedures, given sufficient incentive, we should ultimately be able to dispense with subjective methods such as the estimation of floods using the so-called 'probable maximum precipitation' (p. 354).…”

Section: )mentioning

confidence: 99%

Thunderstorm Runoff in Southeastern Arizona

Osborn

Laursen

1973

J. Hydr. Div.

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Rainfall Rainfall-Runoff Relationships Rainfall Extremes 12 Maximum Expected Peak Discharge 15 Uncertainty and Error 3 DESCRIPTION OF EXPERIMENTAL WATERSHED 23 vii viii LIST OF ILLUSTRATIONS-Continued Figure Page 4.1 Descriptive hydrographs for a semiarid rangeland watershed of approximately square miles 47 4.2 Maximum 30-minute storm rainfalls versus peak discharges, Walnut Gulch 1, 1955-1969 52 4.3 Maximum 30-minute storm rainfalls versus peak discharges, Walnut Gulch 5, 1955-1969 52 4.4 Maximum 30-minute storm rainfalls versus peak discharges, Walnut Gulch 3, 1955-1969 53 4.5 Maximum 30-minute storm rainfalls versus peak discharges, Walnut Gulch 4, 1955-1969 53 4.6 Predicted (Equation 2) versus actual peak discharges, Walnut Gulch 1, 1955-1969 64. 4.7 Predicted (Equation 5) versus actual peak discharges, Walnut Gulch 5, 1955-1969 65 4.8 Predicted (Equation 7) versus actual peak discharges, Walnut Gulch 1, 1955-1969 68 4.9 Predicted (Equation 12) versus actual peak discharges, Walnut Gulch 1, 1955-1969 69 4.10 Predicted (Equation 14) versus actual peak discharges) Walnut Gulch 5, 1955-1969 71 4.11 Predicted (Equation 15) versus actual peak discharges, Walnut Gulch 3, 1955-1969 74 4.12 Predicted (Equation 16) versus actual peak discharges, Walnut Gulch 3, 1955-1969 74 4.13 Predicted (Equation 17) versus actual peak discharges, Walnut Gulch 4, 1955-1969 75 4.14 Predicted (Equation 23) versus actual peak discharges, Walialt Gulch 1, 1955-1969 79 i x LIST OF ILLUSTRATIONS-Contirued Figure Page 4.15 Predicted (Equation 24) versus actual peak discharges, Walnut Gulch 1, 1955-1969 80 4.16 Predicted (Equation 25) versus actual peak discharges, Walnut Gulch 1, 1955-1969 81 4.17 Predicted (Equation 26) versus actual peak discharges, Walnut Gulch 5, 1955-1969 83 5.1 Comparison of Woolhiser-Schwalen and Fogel-Duckstein models for a 2-inch storm 88 5.2 Schematic representation of 4 extreme rainstorms based on distance from storm center to given isohyets, Walnut Gulch, 1961-1968 91 5.3 Schematic representation of the maximum rainstorm and 3 averaged events based on distance from storm center to given isohyets, Walnut Gulch, 1961-1968 93 5.4 Schematic representation of the maximum rainstorm and 3 averaged events based on distance from storm center to given isohyets, Walnut Gulch, 1961-1968 94 5.5

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Equivalent distributions with application to rainfall as an upper bound to flood distributions

Cited by 18 publications

References 14 publications

Estimating the upper tail of flood‐peak frequency distributions using hydrometeorological information

Estimating the upper tail of flood‐peak frequency distributions using hydrometeorological information

Uncertainties in partial duration series modelling of extremes related to the choice of the threshold value

Thunderstorm Runoff in Southeastern Arizona

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