Scaling and muitiscaling models of depth-duration-frequency curves for storm precipitation

Burlando, Paolo; Rosso, Renzo

doi:10.1016/s0022-1694(96)03086-7

Cited by 268 publications

(239 citation statements)

References 14 publications

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“…A natural process fulfills the simple scaling property if the underlying probability distribution of some physical measurements at one scale is identical to the distribution at another scale. The basic theoretical development of scaling has been investigated by many authors and considerable amount of studies were devoted to extreme rainfall and its scaling properties, including Waymire and Gupta (1981) ;Waymire, et al(1984); ; Marien and Vandewiele (1986); Sivapalan and Wood (1987); Gupta and Waymire(1990); Rosso and Burlando (1990); Smith (1992); Koutsoyiannis and Foulfoula-Georgiu (1993); Burlando and Rosso (1996); Veneziano et al (1996), Bendjoudi et al (1997) Ghanmi (2014). In this work the simple scaling hypothesis is adopted to test the scaling behavior of rainfall in northern of Benin, following the methods described in Menabde et al (1999); Yu et al (2004); Kuzuha et al (2002); Nhat et al (2007); Bara et al (2009) and Ghanmi (2014) and are briefly outlined in the ensuing sections.…”

Section: Methodsmentioning

confidence: 99%

“…Bendjoudi, et al (1997) used a multifractal point of view on rainfall IDF curves. Rosso and Burlando (1990) and later Burlando and Rosso (1996) used this concept to study traditional forms of depth-durationfrequency relationships. De Michele et al (2002) developed IDF curves design for storms in Milan (Italia); Yu, et al (2004) developed regional IDF formulas for non-recording sites in Taiwan, Molnar and Burlando (2005) examined the variability of scaling exponents in Alpine mountainous region of Switzerland; Nhat, et al (2007) developed regional relationship for ungauged locations based on the scaling theory in Japan.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of IDF Curves of Extreme Rainfall by Simple Scaling in Northern Oueme Valley, Benin Republic (West Africa)

Agbazo¹,

N’Gobi²,

Kounouhéwa³

et al. 2016

Earth sci. res. j.

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Rainfall intensity-duration-frequency (IDF) curves are of particular importance in water resources management, for example, in urban hydrology, for the design of hydraulic structures and the estimation of the flash flood risk in small catchments. IDF curves describe rainfall intensity as a function of duration and return period, and they are significant for water resources planning, as well as for the design of hydraulic constructions and structures. In this study, scaling properties of extreme rainfall are examined to establish the scaling behavior of statistical non-central moment over different durations. IDF curves and equations are set up for all stations by using the parameter obtained from scaling behavior, the location and scale parameters μ24 and σ24 of the Gumbel distribution (EVI) sample of annual maximum 1440 min rainfall data. In another hand, we have established the IDF curves for ten selected rain gauge stations in the Northern (Oueme Valley) parts of Benin Republic, West Africa by using the simple scaling approach. Analysis of rainfall intensities (5 min and 1440 min rainfall data) from the ten rainfall stations shows that rainfall in north-Benin displays scales invariance property from 5 min to 1440 min. For time scaling, the statistical properties of rainfall follow the hypothesis of simple scaling. Therefore, the simple scaling model applies to the rainfall in (Oueme Valley). Hence, the simple scaling model is thought to be a viable approach to estimate IDF curves of hourly and sub-hourly rainfall form rainfall projections. The obtained scaling exponents are less than 1 and range from 0.23 to 0.59. The empirical model shows that the scaling procedure is a good estimator as it is more efficient and gives more accurate estimates compared with the observed rainfall than the traditional method which only consists the Gumbel model in all stations for lower return periods (T<5 years) but not for higher return periods.Las curvas de precipitación Intensidad-Duración-Frecuencia (IDF) son de particular importancia en el manejo de los recursos hídricos, como es el caso de la hidrología urbana o para el diseño de estructuras hidráulicas y la estimación del riesgo de crecidas en pequeñas captaciones. Las curvas IDF describen la intensidad de las precipitaciones como una función con períodos de duración y recurrencia, lo que las hace significativas en la planeación de recursos hídricos así como en el diseño de construcciones y estructuras hidráulicas. Este estudio examina las propiedades de escala en precipitaciones extremas para establecer un comportamiento en momentos estadísticos marginales en diferentes períodos de duración. Se establecieron las curvas IDF y las ecuaciones para todas las estaciones a partir del parámetro obtenido del comportamiento de escala, la ubicación y los parámetros de escala μ24 and σ24 de la muestra de información de precipitación máxima anual de 1440 minutos de la distribución de Gumbel (EVI). Por otro lado, se establecieron las curvas IDF para 10 estaciones pluviométricas sele...

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Estimation of IDF Curves of Extreme Rainfall by Simple Scaling in Northern Oueme Valley, Benin Republic (West Africa)

Agbazo¹,

N’Gobi²,

Kounouhéwa³

et al. 2016

Earth sci. res. j.

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“…In contrast to the above treatments, which depend on curvefitting techniques, a natural source for theories regarding the rescaling of rainfall statistics is to be found in the scaling hypotheses popularized by Mandelbrot [1982] and Lovejoy and Schertzer [1985]. Burlando and Rosso [1996] in a pioneering paper sought to apply the scaling hypotheses to annual maximum series of rainfall depth. In their work the scaling and multiscaling properties of the statistical moments of rainfall depth of different duration were analyzed and a lognormal probability distribution was used to model its statistical properties.…”

Section: Introductionmentioning

confidence: 99%

A simple scaling model for extreme rainfall

Menabde¹,

Seed²,

Pegram³

1999

Water Resources Research

160

177

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Abstract. The simple scaling hypothesis is applied to the intensity-duration-frequency (IDF) description of rainfall. It is shown that the cumulative distribution function for the annual maximum series of mean rainfall intensity has a simple scaling property over the range 30 min to 24 hours and in some instances to 48 hours. This behavior is demonstrated through an examination of the scaling properties of the moments and the scaling of the parameters of an extreme value distribution fitted to the data. A simple analytical formula for the IDF relationship is proposed, which embodies the scaling behavior. Once the scaling parameter has been obtained for a gauge or set of gauges in a region, this formula enables the calculation of rainfall amounts, of a chosen return period and duration shorter than a day, directly from the information obtained from the analysis of daily data. IntroductionThe relationship between rainfall intensity, duration, and frequency has been of considerable interest to practicing engineers and hydrologists for over a century. Sherman [1905] where 0 and ,/ are phenomenological parameters to be estimated.Daily rainfall is by far the most accessible form of rainfall data, and long sequences of rainfall data at higher time resolution are still relatively rare despite the fact that the technology to record such data has been available since the 1880s. There is much to be gained therefore in developing a methodology that is able to use daily rainfall statistics to infer the IDF characteristics for short duration rainfall. One such attempt was made by Adamson [1981], who compiled the statistics for 2500 rain gauges in South Africa. For each of the stations, he listed (inter alia) the estimates of the 1-, 2-, 3-, and 7-day total rainfall occurring with return periods of 2-200 years. To make these useful for intervals of less than a day, he compiled a table of disaggregation coefficients for the coastal and inland regions of South Africa, based on digitized data, fitting a model of the type [Bell, 1969] referred to above and purporting to be independent of return periods. In contrast to the above treatments, which depend on curvefitting techniques, a natural source for theories regarding the rescaling of rainfall statistics is to be found in the scaling hypotheses popularized by Mandelbrot [1982] and Lovejoy and Schertzer [1985]. Burlando and Rosso [1996] in a pioneering paper sought to apply the scaling hypotheses to annual maximum series of rainfall depth. In their work the scaling and multiscaling properties of the statistical moments of rainfall depth of different duration were analyzed and a lognormal probability distribution was used to model its statistical properties.In the present paper it will be shown that based on the empirically observed scaling properties of rainfall and some general assumptions about the cumulative distribution function (CDF) for the annual maximum of the mean rainfall 335

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“…Burlando & Rosso (1996), having summarized the relevant previous works, verified that the conventional moments of ERS of different durations were dependent on rainfall duration (tr), and they called this dependence "simple scaling" if the relationship of any such moment against tr plotted as a straight line on doublelogarithmic graph paper, or "multiple scaling" if the plot deviated from a straight line. Later, Willems (2000) studied scaling properties of precipitation using a seasonal (summer and winter) precipitation and partial duration series approach.…”

Section: Log-pearson-3 Distributionmentioning

confidence: 88%

Divergence criteria in extreme rainfall series frequency analyses

Haktanır

2003

Hydrological Sciences Journal

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Extreme rainfall series (ERS) are treated as successive-duration events of from 5 min to 24 h in most parts of the world. In Turkey, as in European countries, the ERS of standard durations of 5, 10, 15, 30, 60 min, and 2, 3, 4, 5, 6, 8, 12, 18, 24 h are recorded, and these sample series are analysed to ultimately determine the depthduration-frequency (DDF) relationships. If a probability distribution function (pdf) is used for these ERS, the frequency curves in the form of graphical quantile functions may intersect each other at high return periods, due to possible data recording errors, and an extreme rainfall magnitude of a longer duration may turn out to be smaller than that of a shorter duration beyond some high return period. In this study: (a) the criteria of divergence of the quantile functions of various pdfs used in frequency analyses of ERS are depicted; (b) necessary and sufficient conditions for divergence of the quantile functions and ultimately of the DDF curves are analytically deduced; (c) scaling relationships between conventional statistics and rainstorm durations, and between probability-weighted moments and rainstorm durations, are investigated; (d) necessary adjustments to the parameters of four commonly-used pdfs are shown; and (e) a comprehensive example using rainfall data recorded at the Florya gauging station (Istanbul, Turkey) is presented.Key words extreme precipitation; frequency analysis of extreme rainfalls; depth-durationfrequency curves; divergence of quantile functions Critère de divergence dans des analyses fréquentielles de séries de pluies extrêmesRésumé Généralement, dans le monde, les séries de pluies extrêmes sont traitées comme des événements de durées successives allant de 5 min à 24 h. En Turquie, comme dans certains pays européens, les séries de pluies extrêmes sont enregistrées pour les durées standard de 5, 10, 15, 30 et 60 min, et 2, 3, 4, 5, 6, 8, 12 et 24 h; et ces séries d'échantillonnage sont analysées pour finalement déterminer les relations hauteur-durée-féquence (HDF). Si une fonction densité de probabilité (fdp) est utilisée pour ces séries de pluies extrêmes, les courbes de fréquences mises sous la forme graphique de fonctions de quantiles peuvent se couper pour les grandes périodes de retour, à cause d'éventuelles erreurs d'acquisition. Cela signifie que, au delà d'une certaine période de retour, la hauteur de pluie extrême pendant une longue durée peut apparaître plus faible que la hauteur correspondante pendant une durée plus courte. Dans cette étude: (a) le critère de divergence des fonctions de quantiles de diverses fdp utilisées en analyse fréquentielle de séries de pluies extrêmes est décrit; (b) les conditions nécessaires et suffisantes pour la divergence des fonctions de quantiles et donc des courbes HDF sont déduites analytiquement; (c) les relations d'échelles sont étudiées, entre les statistiques conventionnelles et les durées de pluie, et entre les moments de probabilité pondérée et les durées de pluie; (d) les nécessaires ajustements...

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Scaling and muitiscaling models of depth-duration-frequency curves for storm precipitation

Cited by 268 publications

References 14 publications

Estimation of IDF Curves of Extreme Rainfall by Simple Scaling in Northern Oueme Valley, Benin Republic (West Africa)

Estimation of IDF Curves of Extreme Rainfall by Simple Scaling in Northern Oueme Valley, Benin Republic (West Africa)

A simple scaling model for extreme rainfall

Divergence criteria in extreme rainfall series frequency analyses

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