A stochastic model of raindrop release: Application to the simulation of point rain observations

Lavergnat, J.; Golé, P.

doi:10.1016/j.jhydrol.2005.11.044

Cited by 18 publications

(24 citation statements)

References 8 publications

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“…Thus, this scaling regime is a dynamical property of the quiescent phases only. This is also confirmed by the results with a time resolution D 5 1 ms reported by Lavergnat andGolé (1998, 2006). There is no scaling regime for inter-drop time intervals #5 min, which occurs during active phases.…”

Section: <supporting

confidence: 85%

“…A closer examination of the sequence of drop diameters also reveals that the standard deviation cannot be considered constant. Support for this thesis also comes from the results of Lavergnat and Golé (2006). They report a slow decay for the autocorrelation function of the sequence of drop diameters (the autocorrelation function reaches zero at lag ' 1250) followed by a long negative tail (lag * 1250).…”

Section: <mentioning

confidence: 71%

“…(14) together with Eqs. (11) and (12) connect the probability P D (lD) with the probability density function c(t) of having an inter-drop time interval of duration t. The observations reported by Lavergnat andGolé (1998, 2006) with a time resolution D 5 l ms suggest that the probability density function c(t) is a well-behaved (continuous and derivable), slow, decaying function. Therefore, it is reasonable to expect that if t ) D 0 c(t 1 D) 5 c(t) (0th order Taylor approximation).…”

Section: A Inter-drop Time Intervals Versus Drought Durationsmentioning

confidence: 95%

“…Double stochastic Poisson processes have been used to describe the variability in the drop counts per unit interval (e.g., Smith 1993). Only recently extensive studies (Smith and De Veaux 1994;Lavergnat andGolé 1998, 2006) have been done about the properties of the sequences of interdrop time intervals and drop diameters as measured on the ground by disdrometers. Because of its importance for many aspects of earth's life, the rainfall phenomenon has been widely investigated.…”

Section: Introductionmentioning

confidence: 99%

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The Droplike Nature of Rain and Its Invariant Statistical Properties

Ignaccolo

Michele

Bianco

2009

Journal of Hydrometeorology

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This study looks for statistically invariant properties of the sequences of inter-drop time intervals and drop diameters. The authors provide evidence that these invariant properties have the following characteristics: 1) large inter-drop time intervals (*10 s) separate drops of small diameter (&0.6 mm); 2) the rainfall phenomenon has two phases: a quiescent phase, whose contribution to the total cumulated flux is virtually null, and an active, nonquiescent, phase that is responsible for the bulk of the precipitated volume; 3) the probability density function of inter-drop time intervals has a power-law-scaling regime in the range of ;1 min and ;3 h); and 4) once the moving average and moving standard deviation are removed from the sequence of drop diameters, an invariant shape emerges for the probability density function of drop diameters during active phases.

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Section: <supporting

confidence: 85%

Section: <mentioning

confidence: 71%

Section: A Inter-drop Time Intervals Versus Drought Durationsmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Droplike Nature of Rain and Its Invariant Statistical Properties

Ignaccolo

Michele

Bianco

2009

Journal of Hydrometeorology

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“…This method can more efficiently use experimental data and characterize the physical correlations of time scales. Meanwhile, previous studies show that the recurrence of extreme events is not necessary to follow a pure memoryless Poisson distribution [15,16].…”

Section: Introductionmentioning

confidence: 99%

An Investigation of Stretched Exponential Function in Quantifying Long‐Term Memory of Extreme Events Based on Artificial Data following Lévy Stable Distribution

et al. 2018

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Extreme events, which are usually characterized by generalized extreme value (GEV) models, can exhibit long-term memory, whose impact needs to be quantified. It was known that extreme recurrence intervals can better characterize the significant influence of long-term memory than using the GEV model. Our statistical analyses based on time series datasets following the Lévy stable distribution confirm that the stretched exponential distribution can describe a wide spectrum of memory behavior transition from exponentially distributed intervals (without memory) to power-law distributed ones (with strong memory or fractal scaling property), extending the previous evaluation of the stretched exponential function using Gaussian/exponential distributed random data. Further deviation and discussion of a historical paradox (i.e., the residual waiting time tends to increase with an increasing elapsed time under long-term memory) are also provided, based on the theoretical analysis of the Bayesian law and the stretched exponential distribution.

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Simulation of yearly rainfall time series at microscale resolution with actual properties: Intermittency, scale invariance, and rainfall distribution

et al. 2015

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Rainfall is a physical phenomenon resulting from the combination of numerous physical processes involving a wide range of scales, from microphysical processes to the general circulation of the atmosphere. Moreover, unlike other geophysical variables such as water vapor concentration, rainfall is characterized by a relaxation behavior that leads to an alternation of wet and dry periods. It follows that rainfall is a complex process which is highly variable both in time and space. Precipitation is thus characterized by the following features: rain/no-rain intermittency, multiple scaling regimes, and extreme events. All these properties are difficult to model simultaneously, especially when a large time and/or space scale domain is required. The aim of this paper is to develop a simulator capable of generating high-resolution rain-rate time series (15 s), the main statistical properties of which are close to an observed rain-rate time series. We also attempt to develop a model having consistent properties even when the fine-resolutionsimulated time series are aggregated to a coarser resolution. In order to break the simulation problem down into subcomponents, the authors have focused their attention on several key properties of rainfall. The simulator is based on a sequential approach in which, first, the simulation of rain/no-rain durations permits the retrieval of fractal properties of the rain support. Then, the generation of rain rates through the use of a multifractal, Fractionally Integrated Flux (FIF), model enables the restitution of the rainfall's multifractal properties. This second step includes a denormalization process that was added in order to generate realistic rain-rate distributions.

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A stochastic model of raindrop release: Application to the simulation of point rain observations

Cited by 18 publications

References 8 publications

The Droplike Nature of Rain and Its Invariant Statistical Properties

The Droplike Nature of Rain and Its Invariant Statistical Properties

An Investigation of Stretched Exponential Function in Quantifying Long‐Term Memory of Extreme Events Based on Artificial Data following Lévy Stable Distribution

Simulation of yearly rainfall time series at microscale resolution with actual properties: Intermittency, scale invariance, and rainfall distribution

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