Quasi-geostrophic turbulence and generalized scale invariance, a theoretical reply

Schertzer, D.; Tchiguirinskaia, Ioulia; Lovejoy, S.; Tuck, A. F.

doi:10.5194/acp-12-327-2012

Cited by 26 publications

(25 citation statements)

References 49 publications

(44 reference statements)

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“…Exploring the existence of power law frequency statistical behaviour and fractal properties in time series of natural system has shown to be a successful approach to characterise their complexity (Mandelbrot, 1983;Schertzer, 2012). This section introduces the methods used in the present work to examine the scaling properties of rainfall and Saharan dust events in the studied area.…”

Section: Methodsmentioning

confidence: 99%

Scaling properties of rainfall and desert dust in the Canary Islands

Peñate

Martín-González

Rodrı́guez

et al. 2013

Nonlin. Processes Geophys.

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Abstract. Precipitation and desert dust event occurrence time series measured in the Canary Islands region are examined with the primary intention of exploring their scaling characteristics as well as their spatial variability in terms of the island's topography and geographical orientation. In particular, the desert dust intrusion regime in the islands is studied in terms of its relationship with visibility. Analysis of dust and rainfall events over the archipelago exhibits distributions in time that obey power laws. Results show that the rain process presents a high clustering and irregular pattern on short timescales and a more scattered structure for long ones. In contrast, dustiness presents a more uniform and dense structure and, consequently, a more persistent behaviour on short timescales. It was observed that the fractal dimension of rainfall events shows an important spatial variability, which increases with altitude, as well as towards northern latitudes and western longitudes.

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Section: Methodsmentioning

confidence: 99%

Scaling properties of rainfall and desert dust in the Canary Islands

Peñate

Martín-González

Rodrı́guez

et al. 2013

Nonlin. Processes Geophys.

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“…Thanks both to modern empirical evidence (e.g. the review Schertzer 2010, 2013) and a recent massive aircraft study (Pinel et al 2012), but also to theoretical arguments showing that the governing equations are symmetric with respect to anisotropic scaling symmetries , the question increasingly has been settled in favor of anisotropic scaling (see the recent debate Lovejoy et al 2009Lindborg et al 2010a, b;Schertzer et al 2011Schertzer et al , 2012Yano 2009). The implications of this anisotropic spatial scaling for the temporal statistics are discussed in Radkevitch et al (2008), and Pinel et al (2014).…”

Section: Scaling In the Weather Macroweather And Climate Regimesmentioning

confidence: 99%

A voyage through scales, a missing quadrillion and why the climate is not what you expect

Lovejoy

2014

Clim Dyn

Self Cite

116

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with the help of the new, pedagogical "H model". Both deterministic General Circulation Models (GCM's) with fixed forcings ("control runs") and stochastic turbulencebased models reproduce weather and macroweather, but not the climate; for this we require "climate forcings" and/ or new slow climate processes. Averaging macroweather over periods increasing to ≈30-50 yrs yields apparently converging values: macroweather is "what you expect". Macroweather averages over ≈30-50 yrs have the lowest variability, they yield well defined climate states and justify the otherwise ad hoc "climate normal" period. However, moving to longer periods, these states increasingly fluctuate: just as with the weather, the climate changes in an apparently unstable manner; the climate is not what you expect. Moving to time scales beyond 100 kyrs, to the macroclimate regime, we find that averaging the varying climate increasingly converges, but ultimately-at scales beyond ≈0.5 Myr in the megaclimate, we discover that the apparent point of convergence itself starts to "wander", presumably representing shifts from one climate to another.

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“…It is easy to check that I 2 = −J 2 = −K 2 = −1, where 1 denotes the identity, as well as J = IK = −KI and IJK = −1 and therefore equation (40). (Schertzer & Lovejoy, 1983, 1985a, 1985bSchertzer et al, 2012). The corresponding anisotropic metric ||.|| is illustrated by Figure 4 that displays balls B defined by it:…”

Section: Generalized Scale Transform and Metricsmentioning

confidence: 99%

A Century of Turbulent Cascades and the Emergence of Multifractal Operators

Schertzer

Tchiguirinskaia

2020

Earth and Space Science

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A century of cascades and three decades of multifractals have built up a truly interdisciplinary framework that has enabled a new approach and understanding of nonlinear phenomena, in particular, in geophysics. Nevertheless, there seems to be a profound gap between the potentials of multifractals and their actual use. For instance, it seems ironic that multifractals have been mostly restricted to scalar‐valued fields, whereas cascades were first invoked for the wind velocity. We argue that this requires to proceed to new developments of the multifractal formalism and to the emergence of multifractal operators. This paper therefore aims to first simplify the introduction to the most recent developments based on the analysis and generation of multifractal fields with the help of the group property of the responses of a nonlinear system to a scale change. The generators of the multifractal operators are introduced with the help of symmetries as simple and basic as orthogonal rotations and mirror symmetries. This leads in a rather straightforward manner to the large class of Gauss–Clifford and Lévy–Clifford generators that combine a number of seductive properties, including universal statistical and robust algebraic properties. At the same time, we obtain new results on the entanglement of spherical and hyperbolic geometries, as well as on the existence of finite statistics of these cascades.

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Quasi-geostrophic turbulence and generalized scale invariance, a theoretical reply

Cited by 26 publications

References 49 publications

Scaling properties of rainfall and desert dust in the Canary Islands

Scaling properties of rainfall and desert dust in the Canary Islands

A voyage through scales, a missing quadrillion and why the climate is not what you expect

A Century of Turbulent Cascades and the Emergence of Multifractal Operators

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