Application of Superstatistics to Atmospheric Turbulence

Rizzo, Salvo; Rapisarda, Andrea

doi:10.1142/9789812701558_0029

Cited by 18 publications

(25 citation statements)

References 9 publications

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“…This type of behavior is different from e.g. fully developed hydrodynamic turbulence, which is better described by lognormal superstatistics [2], or wind velocity fluctuations, described by inverse χ 2 superstatistics [19,23]. In future work one might aim to develop a generalized statistical mechanics for the complex behavior of these types of observables in complex environmental systems.…”

Section: Discussionmentioning

confidence: 96%

“…the local relaxation time of the system must be much shorter than the typical time scale on which the parameter β changes. Many interesting applications of the superstatistics concept have been worked out for a variety of complex systems, for example the analysis of train delay statistics [13], hydrodynamic turbulence [14], cancer survival statistics [15] and much more [16][17][18][19][20][21]. Typical distributions of the superstatistical parameter β that occur in many of these applications are the χ 2 , inverse χ 2 or lognormal distribution [2].…”

Section: Introductionmentioning

confidence: 99%

“…Of particular interest are superstatistical techniques to analyse and model the complexity inherent in environmental time series, such as rainfall, wind, surface temperature, and related quantities. Rapisarda et al [19] and Kantz et al [23] investigated superstatistical aspects of wind velocity fluctuations. Yalcin et al [24] did a data analysis of relevant surface temperature distributions on the earth, which is important if one wants to understand the effective statistical mechanics for thermodynamic devices (or local ecosystems) that are kept in the open air outside a constanttemperature environment.…”

Section: Introductionmentioning

confidence: 99%

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Superstatistical analysis of sea-level fluctuations

Rabassa

Beck

2015

Physica A: Statistical Mechanics and its Applications

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We perform a statistical analysis of measured time series of sea levels at various coastal locations in the UK, measured at time differences of 15 minutes over the past 20 years. When the astronomical tide and other deterministic components are removed from the record, a stochastic signal corresponding to the meteorological component remains, and this is well-described by a superstatistical model. We do various tests on the measured time series, and compare the data at 5 different UK locations. Overall the χ 2 -superstatistics is best suitable to describe the data, in particular when one looks at the dynamics of sea-level differences on short time scales.

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Section: Discussionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Superstatistical analysis of sea-level fluctuations

Rabassa

Beck

2015

Physica A: Statistical Mechanics and its Applications

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“…It is also worth remarking that several turbulent systems have been analyzed recently using the superstatistics framework. These include velocity differences in Taylor-Couette flow [29], intermittency of the wind [30] or solar wind [31].…”

Section: (B) Previous Measurementsmentioning

confidence: 99%

Intensity Thresholds and the Statistics of the Temporal Occurrence of Solar Flares

2006

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Introducing thresholds to analyze time series of emission from the Sun enables a new and simple definition of solar flare events, and their interoccurrence times. Rescaling time by the rate of events, the waiting and quiet time distributions both conform to scaling functions that are independent of the intensity threshold over a wide range. The scaling functions are well described by a two parameter function, with parameters that depend on the phase of the solar cycle. For flares identified according to the current, standard definition, similar behavior is found.PACS numbers: 96.60. Rd, 05.45.Tp, 05.65.+b The solar corona is a very high Reynolds number turbulent plasma producing intermittent bursts of radiation. Plasma forces twist the coronal magnetic fields until stresses are suddenly released, an avalanching process governed by magnetic reconnection [1]. The released magnetic energy induces radiative emission that can be detected as a flare. Flares exhibit scale invariant statistics. For instance, the probability distribution of flare energies is a power law spanning more than eight orders of magnitude [2,3], similar to the Gutenberg-Richter law for earthquakes. The distribution of magnetic concentration sizes on the photosphere is also scale invariant, and the coronal magnetic network embodies a scale-free network [4,5]. In fact, a model of self-organized criticality (SOC) with avalanches of reconnecting flux tubes reproduces the observed scale-free network structure [4,6].As part of the debate on the characterization of magnetohydrodynamic turbulence in this regime [1,4,5,6,7,8,9], interest has focused on comparing interoccurrence times between flares with those in models of SOC. Analyses of flare catalogs have indicated scale invariance of the waiting times, but the behavior was found to vary with the phase of the solar cycle [10] and with the methods used to analyze the catalogs. (See e.g. Ref. [10,11].) The prior belief that avalanches occur with Poissonian waiting times in the well-known BTW sandpile model [12] (giving an exponential distribution of waiting times) argued against the SOC hypothesis [8]. However, including a finite detection threshold leads to a power law distribution of quiet times even for the BTW model [13], when durations and quiet times are measured with the same clock. Since the turnover time scale for flux to be regenerated in the corona is of the order of ten hours [14], while the correlated waiting time intervals between flares can extend up to years, the physical mechanism(s) responsible for these correlations resides in the turbulent convective region beneath the photosphere that generates magnetic flux and drives it into the corona. Systematic studies of the temporal pattern of flares can give insight into the dynamics of magnetic flux in the convective region, or the solar dynamo, which is difficult to observe directly.Here we show that the interoccurrence times between flares has a hierarchical scaling structure when flares are defined as intervals during which the emissi...

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“…Recent applications of the superstatistics concept include a variety of physical systems. Examples are Lagrangian [24,25,26,27] and Eulerian turbulence [28,29,30], defect turbulence [31], atmospheric turbulence [32,33], cosmic ray statistics [34], solar flares [35], solar wind statistics [36], networks [37,38], random matrix theory [39], and mathematical finance [40,41,42].…”

Section: Introductionmentioning

confidence: 99%

Stretched exponentials from superstatistics

Beck

2006

Physica A: Statistical Mechanics and its Applications

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Distributions exhibiting fat tails occur frequently in many different areas of science. A dynamical reason for fat tails can be a socalled superstatistics, where one has a superposition of local Gaussians whose variance fluctuates on a rather large spatio-temporal scale. After briefly reviewing this concept, we explore in more detail a class of superstatistics that hasn't been subject of many investigations so far, namely superstatistics for which a suitable power β η of the local inverse temperature β is χ 2 -distributed. We show that η > 0 leads to power law distributions, while η < 0 leads to stretched exponentials. The special case η = 1 corresponds to Tsallis statistics and the special case η = −1 to exponential statistics of the square root of energy. Possible applications for granular media and hydrodynamic turbulence are discussed.

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Application of Superstatistics to Atmospheric Turbulence

Abstract: We successfully apply the recent developed superstatistics theory to a temporal series of turbulent wind measurements recorded by the anemometers of Florence airport. Within this approach we can reproduce very well the fluctuations and the pdfs of wind velocity returns and differences.

Cited by 18 publications

References 9 publications

Superstatistical analysis of sea-level fluctuations

Superstatistical analysis of sea-level fluctuations

Intensity Thresholds and the Statistics of the Temporal Occurrence of Solar Flares

Stretched exponentials from superstatistics

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