Multifractality of rainfall and scaling of intensity‐duration‐frequency curves

Veneziano, Daniele; Furcolo, Pierluigi

doi:10.1029/2001wr000372

Cited by 123 publications

(99 citation statements)

References 31 publications

(62 reference statements)

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“…Whereas some have found statistical measures of rainfall extremes to exhibit linear (sometimes termed simple) scaling (Menabde et al, 1999;Garcia-Bartual and Schneider, 2001;De Michele et al, 2001) under at least some conditions (Burlando and Rosso, 1996;Veneziano and Furcolo, 2002;Yu et al, 2004), most authors describe them by means of nonlinear (often called multiscaling) models (Burlando and Rosso, 1996;Veneziano and Furcolo, 2002;Castro et al, 2004;Langousis and Veneziano, 2007;Mohymont and Demarée, 2006). Statistical measures of peak stream flows were considered by Javelle et al (1999), Menabde and Sivapalan (2001) and Rigon et al (2011) to scale linearly.…”

Section: Published By Copernicus Publications On Behalf Of the Europementioning

confidence: 99%

Scalable statistics of correlated random variables and extremes applied to deep borehole porosities

Guadagnini

Neuman

Nan

et al. 2015

Hydrol. Earth Syst. Sci.

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Abstract. We analyze scale-dependent statistics of correlated random hydrogeological variables and their extremes using neutron porosity data from six deep boreholes, in three diverse depositional environments, as example. We show that key statistics of porosity increments behave and scale in manners typical of many earth and environmental (as well as other) variables. These scaling behaviors include a tendency of increments to have symmetric, non-Gaussian frequency distributions characterized by heavy tails that decay with separation distance or lag; power-law scaling of sample structure functions (statistical moments of absolute increments) in midranges of lags; linear relationships between log structure functions of successive orders at all lags, known as extended self-similarity or ESS; and nonlinear scaling of structure function power-law exponents with function order, a phenomenon commonly attributed in the literature to multifractals. Elsewhere we proposed, explored and demonstrated a new method of geostatistical inference that captures all of these phenomena within a unified theoretical framework. The framework views data as samples from random fields constituting scale mixtures of truncated (monofractal) fractional Brownian motion (tfBm) or fractional Gaussian noise (tfGn). Important questions not addressed in previous studies concern the distribution and statistical scaling of extreme incremental values. Of special interest in hydrology (and many other areas) are statistics of absolute increments exceeding given thresholds, known as peaks over threshold or POTs. In this paper we explore the statistical scaling of data and, for the first time, corresponding POTs associated with samples from scale mixtures of tfBm or tfGn. We demonstrate that porosity data we analyze possess properties of such samples and thus follow the theory we proposed. The porosity data are of additional value in revealing a remarkable cross-over from one scaling regime to another at certain lags. The phenomena we uncover are of key importance for the analysis of fluid flow and solute as well as particulate transport in complex hydrogeologic environments.

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Section: Published By Copernicus Publications On Behalf Of the Europementioning

confidence: 99%

Scalable statistics of correlated random variables and extremes applied to deep borehole porosities

Guadagnini

Neuman

Nan

et al. 2015

Hydrol. Earth Syst. Sci.

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“…A complete overview is not presented; only the main principles are outlined. For detailed information on the theoretical background on the multifractal behavior of rainfall, the reader is referred to Veneziano, Furcolo (2002), andLovejoy, Schertzer (1985); more practice-oriented results can be found, e.g., in Gupta, Waymire (1990), Menabde et al (1999), Yu et al (2004 and Molnar, Burlando (2008).…”

Section: Simple Scaling Of Rainfallmentioning

confidence: 99%

On the use of the simple scaling of heavy rainfall in a regional estimation of IDF curves in Slovakia

Bara¹,

Gaál²,

Kohnová³

et al. 2010

Journal of Hydrology and Hydromechanics

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The aim of this study was to test the applicability of a simple scaling methodology for a regional estimation of intensity-duration-frequency (IDF) curves in Slovakia. The analysis is based on the regionalization process of Gaál (2006), which focused on the delineation of homogeneous regions for a regional frequency analysis of precipitation maxima. In order to examine the regionally estimated IDF curves, a region covering the western parts of Slovakia was chosen. The selected region, which encompasses 19 raingauging stations, may be characterized by the dominant influence of Atlantic circulation patterns. Three of the 19 stations belonging to the target region were set aside and flagged as verification stations.The regional dimensionless growth curve of 1-day precipitation maxima in the warm season was derived for the region, and the local T-year quantiles were estimated by the index value method for the stations. At the same time, a regionally averaged scaling exponent was derived using all the stations except for the three verification ones. The local IDF curves at the verification stations were estimated by downscaling the Tyear quantiles of the 1-day precipitation maxima using the regionally averaged scaling exponent. Finally, the IDF curves for these stations were compared with those defined by Šamaj, Valovič (1973). This study is the first step in assessing the applicability of a simple scaling theory for the regional estimation of IDF curves in Slovakia. Cieľom tejto práce bolo otestovať možnosť použitia metódy jednoduchého škálovania zrážok pri regionálnom odhade návrhových hodnôt zrážkových intenzít na Slovensku. Pre analýzu bolo vybraných 19 zrážkomerných staníc vo vopred vyčlenenom regióne na území západného Slovenska, pričom tri stanice boli separované ako verifikačné stanice. Pre vybraný región sme odvodili bezrozmernú regionálnu čiaru prekročenia jednodenných maximálnych úhrnov zrážok v teplom polroku a následne sme pre verifikačné stanice metódou indexovej hodnoty odhadli lokálne návrhové hodnoty pre rôzne významné doby opakovania T (tzv. T-ročné kvantily). Vo vyčlenenom regióne sme určili priemerný regionálny škálovací koeficient. Návrhové zrážkové intenzity pre tri verifikačné stanice sa stanovili zoškálovaním T-ročných kvantilov jednodenných maximálnych zrážok pomocou regionálneho škálovacieho koeficientu. Určené návrhové hodnoty sme porovnali s výsledkami Šamaja, Valoviča (1973). Štúdia potvrdila možnosť využitia metódy jednoduchého škálovania na regionálny odhad návrhových hodnôt zrážkových intenzít na Slovensku.KĽÚČOVÉ SLOVÁ: regionalizácia, intenzita zrážok, jednoduché škálovanie, návrhové hodnoty, teplý polrok, jednodenné maximálne úhrny zrážok.

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“…Carbonnel, 1989, 1991;Olsson et al, 1992) and evolved towards the use of multifractal theory (see e.g. Schertzer, 1990, 1995;Ladoy et al, 1991Hubert, 1992Hubert, , 1995Tessier et al, 1992Tessier et al, , 1993Tessier et al, , 1996Hubert et al, 1993;Olsson and Niemczynowicz, 1994;de Lima and Bogardi, 1995;Olsson, 1995Burlando and Rosso, 1996;Harris et al, 1996;Svensson et al, 1996;Bendjoudi et al, 1997;de Lima, 1998de Lima, , 1999de Lima and Grasman, 1999;Kiely and Ivanova, 1999;Deidda, 2000;Sivakumar, 2001;de Lima et al, 2002;Veneziano and Furcolo, 2002;Nykanen and Harris, 2003;Veneziano and Langousis, 2005;Kantelhardt et al, 2006;Veneziano et al, 2006;Venugopal et al, 2006;Langousis and Veneziano, 2007;García-Marín et al, 2007;Royer et al, 2008).…”

Section: Some Aspects Of Scaling Theoriesmentioning

confidence: 99%

Investigating the multifractality of point precipitation in the Madeira archipelago

Lima

2009

Nonlin. Processes Geophys.

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Abstract. The purpose of this work is to contribute to a better understanding of the variability of precipitation in the Madeira archipelago. This archipelago is located in the Atlantic subtropical belt under the direct influence of the Azores high pressure system. It is formed by Madeira Island (728 km 2 ) and Porto Santo Island (42 km 2 ) and by two other groups of very small inhabited islands. The complex topography of the islands in the Madeira archipelago and their small size play a crucial role in the local precipitation regime, which is marked by high spatial variability.This paper explores the invariance of properties manifested across scales and determines the fractal and multifractal behaviour observed in the temporal structure of precipitation using daily and 10-min time series from several locations scattered over the main islands. The period covered by the precipitation records is 34 years for the daily data and almost 4 months for the 10-min data. The results show that the temporal structure of precipitation in the Madeira Archipelago exhibits scale-invariant and multifractal properties. The empirical exponent functions describing the scaling statistical properties of the precipitation intensity were characterized using multifractal parameters; these parameters are increasing our awareness of the dynamics of this process in these islands.

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Multifractality of rainfall and scaling of intensity‐duration‐frequency curves

Cited by 123 publications

References 31 publications

Scalable statistics of correlated random variables and extremes applied to deep borehole porosities

Scalable statistics of correlated random variables and extremes applied to deep borehole porosities

On the use of the simple scaling of heavy rainfall in a regional estimation of IDF curves in Slovakia

Investigating the multifractality of point precipitation in the Madeira archipelago

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