Multifractal rainfall extremes: Theoretical analysis and practical estimation

Langousis, Andreas; Veneziano, Daniele; Furcolo, Pierluigi; Lepore, Chiara

doi:10.1016/j.chaos.2007.06.004

Cited by 70 publications

(72 citation statements)

References 20 publications

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“…These models range from those based on the fractal and multifractal theories (Lovejoy and Schertzer, 1985;Veneziano et al, 1996;Deidda, 2000;Langousis et al, 2009), to algorithms assuming parametric distributions of storm occurrence and structure (i.e., number, intensity and duration of individual cells) (Rodriguez-Iturbe et al, 1987;Onof and Wheater, 1993;Robinson and Sivapalan, 1997).…”

Section: Introductionmentioning

confidence: 99%

On the nature of rainfall intermittency as revealed by different metrics and sampling approaches

Mascaro

Deidda

Hellies

2013

Hydrol. Earth Syst. Sci.

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Abstract. A general consensus on the concept of rainfall intermittencyhas not yet been reached, and intermittency is often attributed to different aspects of rainfall variability, including the fragmentation of the rainfall support (i.e., the alternation of wet and dry intervals) and the strength of intensity fluctuations and bursts. To explore these different aspects, a systematic analysis of rainfall intermittency properties in the time domain is presented using high-resolution (1-min) data recorded by a network of 201 tipping-bucket gauges covering the entire island of Sardinia (Italy). Four techniques, including spectral and scale invariance analysis, and computation of clustering and intermittency exponents, are applied to quantify the contribution of the alternation of dry and wet intervals (i.e., the rainfall support fragmentation), and the fluctuations of intensity amplitudes, to the overall intermittency of the rainfall process. The presence of three ranges of scaling regimes between 1 min to ∼ 45 days is first demonstrated. In accordance with past studies, these regimes can be associated with a range dominated by single storms, a regime typical of frontal systems, and a transition zone. The positions of the breaking points separating these regimes change with the applied technique, suggesting that different tools explain different aspects of rainfall variability. Results indicate that the intermittency properties of rainfall support are fairly similar across the island, while metrics related to rainfall intensity fluctuations are characterized by significant spatial variability, implying that the local climate has a significant effect on the amplitude of rainfall fluctuations and minimal influence on the process of rainfall occurrence. In addition, for each analysis tool, evidence is shown of spatial patterns of the scaling exponents computed in the range of frontal systems. These patterns resemble the main pluviometric regimes observed on the island and, thus, can be associated with the corresponding synoptic circulation patterns. Last but not least, we demonstrate how the methodology adopted to sample the rainfall signal from the records of the tipping instants can significantly affect the intermittency analysis, especially at smaller scales. The multifractal scale invariance analysis is the only tool that is insensitive to the sampling approach. Results of this work may be useful to improve the calibration of stochastic algorithms used to downscale coarse rainfall predictions of climate and weather forecasting models, as well as the parameterization of intensity-duration-frequency curves, adopted for land planning and design of civil infrastructures.

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Section: Introductionmentioning

confidence: 99%

On the nature of rainfall intermittency as revealed by different metrics and sampling approaches

Mascaro

Deidda

Hellies

2013

Hydrol. Earth Syst. Sci.

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“…Lovejoy (1987, 2006), Gupta and Waymire (1993), Tessier et al (1993) and developed a universal model (multi-fractal), as well as different methods of identification of its parameters. In addition, the fractal and/or multi-fractal characterization of rain intensity has been adopted for the elaboration of intensity-duration-frequency (IDF) curves (Bendjoudi et al 1997, Menabde et al 1999, De Michele et al 2002, Castro et al 2004, Langousis and Veneziano 2006, Bara et al 2009, Langousis et al 2009.…”

Section: Introductionmentioning

confidence: 99%

Investigation of the fractal dimension of rainfall occurrence in a semi-arid Mediterranean climate

Ghanmi¹,

Bargaoui²,

Mallet³

2013

Hydrological Sciences Journal

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The scale invariance of rainfall series in the Tunis area, Tunisia (semi-arid Mediterranean climate) is studied in a mono-fractal framework by applying the box counting method to four series of observations, each about 2.5 years in length, based on a time resolution of 5 min. In addition, a single series of daily rainfall records for the period 1873-2009 was analysed. Three self-similar structures were identified: micro-scale (5 min to 2 d) with fractal dimension 0.44, meso-scale (2 d to one week) and synoptic-scale (one week to eight months) with fractal dimension 0.9. Interpretation of these findings suggests that only the micro-scale and transition to saturation are consistent, while the high fractal dimension relating to the synoptic scale might be affected by the tendency to saturation. A sensitivity analysis of the estimated fractal dimension was performed using daily rainfall data by varying the series length, as well as the intensity threshold for the detection of rain.Key words semi-arid Mediterranean climate; fractal dimension; rainfall time series; scale-invariance; on-off intermittency; mono-fractal; box counting Etude de la dimension fractale d'occurrence de pluie dans un climat méditerranéen semi-aride Résumé La loi d'invariance d'échelle de l'occurrence de pluie dans un climat semi-aride a été étudiée dans le cadre d'une analyse fractale. La dimension fractale du support est estimée en appliquant la méthode de comptage de boîtes. Des séries d'observations, issues de quatre stations de la région de Tunis (Tunisie), de résolution 5 min pendant la période 2007-2010, ainsi qu'une série de résolution journalière de plus de 100 ans (1873-2009) ont été analysées. Ainsi, trois structures auto-similaires ont été identifiés: les micro-échelles (5 min à 2 j) ayant une dimension fractale de 0,44, les méso-échelles (2 j à une semaine) et l'échelle synoptique (une semaine à huit mois) ayant une dimension fractale de 0,9. L'interprétation de ces résultats suggère que seules les micro-échelles et la transition vers la saturation sont significatives, tandis que la dimension fractale assez élevée relative à l'échelle synoptique pourrait être affectée par la tendance à la saturation. Une étude de sensibilité de la dimension fractale de l'occurrence de pluie utilisant la série de précipitations journalières a été effectuée en faisant varier la longueur de la série ainsi que le seuil de détection de la pluie.

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“…The rainfall values reported in TP-40 cover the whole range of averaging durations D from 0.5 to 24 h, whereas Babak et al [1991] and Singh and Zhang [2007] give rainfall values only for D = 6, 12 and 24 h. It is clear from Figure 9b that for T > 100 years also the dependence of the rainfall intensity on T is of the power law type, say T g T with g T % 0.32. This exponent is higher than the values around 0.20 -0.25 that are typical of ordinary rainfall [Langousis et al, 2007;Veneziano et al, 2006b]. The higher exponent in tropical cyclones is related to the large dispersion of the amplification factor b l,max (see example plots in Figure 8).…”

Section: Idf Curves For Tc Rainfall and Comparison With Other Stormsmentioning

confidence: 77%

“…This exponent is slightly smaller than the values around 0.6 -0.7 that are typical of extratropical rainfall (because the rainfall intensities associated with long durations in TCs tend to be high relative to extratropical events) [see, e.g., Langousis et al, 2007]. For longer averaging durations, the exponent g D rapidly increases and is effectively 1 for D > 24 h; see dashed lines in Figure 9a.…”

Section: Idf Curves For Tc Rainfall and Comparison With Other Stormsmentioning

confidence: 91%

Long‐term rainfall risk from tropical cyclones in coastal areas

Langousis

Veneziano

2009

Water Resources Research

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[1] We develop a methodology for the frequency of extreme rainfall intensities caused by tropical cyclones (TCs) in coastal areas. The model does not account for landfall effects. This makes the developed framework best suited for open water sites and coastal areas with flat topography. The mean rainfall field associated with a TC with maximum tangential wind speed V max , radius of maximum winds R max , and translation speed V t 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 data from the Tropical Rainfall Measuring 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 an averaging period D for a TC with characteristics (V max , R max , V t ) 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°and 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 h), tropical cyclones dominate over other rainfall event types, whereas the reverse is true for shorter return periods or shorter averaging durations.

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Multifractal rainfall extremes: Theoretical analysis and practical estimation

Cited by 70 publications

References 20 publications

On the nature of rainfall intermittency as revealed by different metrics and sampling approaches

On the nature of rainfall intermittency as revealed by different metrics and sampling approaches

Investigation of the fractal dimension of rainfall occurrence in a semi-arid Mediterranean climate

Long‐term rainfall risk from tropical cyclones in coastal areas

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