A Stochastic Raindrop Time Distribution Model

Lavergnat, J.; Golé, P.

doi:10.1175/1520-0450(1998)037<0805:asrtdm>2.0.co;2

Cited by 76 publications

(62 citation statements)

References 16 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: 57%

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: 57%

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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“…Cheng et al (1995) observe = 1.6 in the waiting time between earthquakes, and a similar value for waiting time between`starquakes' in neutron stars. Lavergnat and Golé (1998) measured power law waiting times with = 0.68 between large raindrops. Smethurst and Williams (2001) find = 1.4 in the waiting times for a doctor appointment.…”

Section: Introductionmentioning

confidence: 99%

Extremal limit theorems for observations separated by random power law waiting times

Meerschaert

Stoev

2009

Journal of Statistical Planning and Inference

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This paper develops extreme value theory for random observations separated by random waiting times whose exceedence probability falls off like a power law. In the case where the waiting times between observations have an infinite mean, a limit theorem is established, where the limit is comprised of an extremal process whose time index is randomized according to the non-Markovian hitting time process for a stable subordinator. The resulting limit distributions are shown to be solutions of fractional differential equations, where the order of the fractional time derivative coincides with the power law index of the waiting time. The probability that the limit process remains below a threshold is also computed. For waiting times with finite mean but infinite variance, a two-scale argument yields a fundamentally different limit process. The resulting limit is an extremal process whose time index is randomized according to the first passage time of a positively skewed stable Lévy motion with positive drift. This two-scale limit provides a second-order correction to the usual limit behavior.

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“…The observations of Olsson et al (from Sweden) were later corroborated by Lavergnat and Golé [3] in an experiment performed near Paris. The latter study generated data on raindrop arrival times and sizes over a 14-month period, and confirmed the scaling r ∼ τ −0.82 over six orders of magnitude (from 0.01 to 10 4 minutes).…”

Section: Fractal Rain Distributionsmentioning

confidence: 59%

Fractal rain distributions and chaotic advection

Dickman¹

2004

Braz. J. Phys.

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Localized rain events have been found to follow power-law distributions over several decades, suggesting parallels between precipitation and seismic activity [O. Peters et al., PRL 88, 018701 (2002)]. Similar power laws can be generated by treating raindrops as passive tracers advected by the velocity field of a two-dimensional system of point vortices [R. Dickman, PRL 90, 108701 (2003)]. Here I review observational and theoretical aspects of fractal rain distributions and chaotic advection, and present new results on tracer distributions in the vortex model.

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A Stochastic Raindrop Time Distribution Model

Cited by 76 publications

References 16 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

Extremal limit theorems for observations separated by random power law waiting times

Fractal rain distributions and chaotic advection

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