Multiscaling pulse representation of temporal rainfall

Veneziano, Daniele; Iacobellis, Vito

doi:10.1029/2001wr000522

Cited by 62 publications

(69 citation statements)

References 34 publications

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“…Due to the occurrence of a 4-month dry period in Mediterranean semi-arid areas, it is not surprising to observe a particular behaviour concerning the length of the saturation period. We obtained a beginning for the saturation period after 113 d. Considering Table 1, Olsson (1993) used rainfall data collected at Lund (Sweden), Hubert and Carbonnel (1989) data obtained in Ouagadougou (Burkina Faso), Lavergnat and Golé (1998) data from Palaiseau (France), Schmitt et al (1998) (Belgium) and Veneziano and Iacobellis (2002) data collected at Florence (Italy), and in each case the scale break for saturation is observed to be a few days, respectively 7, 21, 7, 3.5 and 3.5 d, which attests to the importance of the length of the saturation regime as well as the relative homogeneity of the rain support throughout the year. In other words, the length of the saturation period is very particular to the area considered.…”

Section: With the Sensor Detection Thresholdmentioning

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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Section: With the Sensor Detection Thresholdmentioning

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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“…Cascade weights have been found to be dependent on scale (Veneziano et al, 1996;Menabde et al, 1997;Menabde and Sivapalan, 2000;Molnar and Burlando, 2005;Paulson and Baxter, 2007), on covariates such as large-scale rainfall intensity (Over andGupta, 1994, 1996;Deidda, 2000;Molnar and Burlando, 2005), and on the interval class, i.e. intervals at the beginning, middle, or end of a rainfall event (Olsson, 1998;Olsson and Berndtsson, 1998;Güntner et al, 2001;Veneziano and Iacobellis, 2002). Veneziano et al (2006) have explored the dependence of the cascade weights on rainfall intensity and cascade level, assuming the so-called discrete canonical logstable model, which accounts for zero rainfall (hereinafter, also denoted as lacunarity) thanks to a thresholding procedure, and the beta-logstable (BLS) model (described in Sect.…”

Section: Introductionmentioning

confidence: 99%

Multifractality, imperfect scaling and hydrological properties of rainfall time series simulated by continuous universal multifractal and discrete random cascade models

Serinaldi

2010

Nonlin. Processes Geophys.

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Abstract. Discrete multiplicative random cascade (MRC) models were extensively studied and applied to disaggregate rainfall data, thanks to their formal simplicity and the small number of involved parameters. Focusing on temporal disaggregation, the rationale of these models is based on multiplying the value assumed by a physical attribute (e.g., rainfall intensity) at a given time scale L, by a suitable number b of random weights, to obtain b attribute values corresponding to statistically plausible observations at a smaller L/b time resolution. In the original formulation of the MRC models, the random weights were assumed to be independent and identically distributed. However, for several studies this hypothesis did not appear to be realistic for the observed rainfall series as the distribution of the weights was shown to depend on the space-time scale and rainfall intensity. Since these findings contrast with the scale invariance assumption behind the MRC models and impact on the applicability of these models, it is worth studying their nature. This study explores the possible presence of dependence of the parameters of two discrete MRC models on rainfall intensity and time scale, by analyzing point rainfall series with 5-min time resolution. Taking into account a discrete microcanonical (MC) model based on beta distribution and a discrete canonical beta-logstable (BLS), the analysis points out that the relations between the parameters and rainfall intensity across the time scales are detectable and can be modeled by a set of simple functions accounting for the parameterrainfall intensity relationship, and another set describing the link between the parameters and the time scale. Therefore, MC and BLS models were modified to explicitly account for these relationships and compared with the continuous in Correspondence to: F. Serinaldi (f.serinaldi@unitus.it) scale universal multifractal (CUM) model, which is used as a physically based benchmark model. Monte Carlo simulations point out that the dependence of MC and BLS parameters on rainfall intensity and cascade scales can be recognized also in CUM series, meaning that these relations cannot be considered as a definitive sign of departure from multifractality. Even though the modified MC model is not properly a scaling model (parameters depend on rainfall intensity and scale), it reproduces the empirical traces of the moments and moment exponent function as effective as the CUM model. Moreover, the MC model is able to reproduce some rainfall properties of hydrological interest, such as the distribution of event rainfall amount, wet/dry spell length, and the autocorrelation function, better than its competitors owing to its strong, albeit unrealistic, conservative nature. Therefore, even though the CUM model represents the most parsimonious and the only physically/theoretically consistent model, results provided by MC model motivate, to some extent, the interest recognized in the literature for this type of discrete models.

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“…combine a stochastic rainfall forcing with a reliable representation of physical dynamics affecting basin response. In particular, Fiorentino et al (2007) used a distributed hydrological model (Manfreda et al, 2005) in cascade with a rainfall generator with multifractal properties (Veneziano and Iacobellis, 2002). They investigated the role of climate, soil and vegetation in runoff generation during extreme events and concluded that runoff source areas are mainly affected by pedologic features in arid basins, while a geomorphologic control prevails in humid basins.…”

Section: Introductionmentioning

confidence: 99%

Runoff thresholds in derived flood frequency distributions

Gioia

Iacobellis

Manfreda

et al. 2008

Hydrol. Earth Syst. Sci.

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Abstract.In general, different mechanisms may be identified as responsible of runoff generation during ordinary events or extraordinary events at the basin scale. In a simplified scheme these mechanisms may be represented by different runoff thresholds. In this context, the derived flood frequency model, based on the effect of partial contributing areas on peak flow, proposed by Iacobellis and Fiorentino (2000), was generalized by providing a new formulation of the derived distribution where two runoff components are explicitly considered. The model was tested on a group of basins in Southern Italy characterized by annual maximum flood distributions highly skewed. The application of the proposed model provided good results in terms of descriptive ability. Model parameters were also found to be well correlated with geomorphological basin descriptors. Two different threshold mechanisms, associated respectively to ordinary and extraordinary events, were identified. In fact, we found that ordinary floods are mostly due to rainfall events exceeding a threshold infiltration rate in a small source area, while the so-called outlier events, responsible of the high skewness of flood distributions, are triggered when severe rainfalls exceed a threshold storage in a large portion of the basin.

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Multiscaling pulse representation of temporal rainfall

Cited by 62 publications

References 34 publications

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

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

Multifractality, imperfect scaling and hydrological properties of rainfall time series simulated by continuous universal multifractal and discrete random cascade models

Runoff thresholds in derived flood frequency distributions

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