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Many physical systems that have interacting structures that span wide ranges in size involve substantial scale invariant (or scaling) subranges. In these regimes, the large and small scales are related by an operation that involves only the scale ratio. The system has no intrinsic characteristic size. In the atmosphere gravity causes differential… (More)

- DANIEL SCHERTZER, IOULIA TCHIGUIRINSKAIA, SHAUN LOVEJOY, PIERRE HUBERT, HOCINE BENDJOUDI, MICHELE LARCHEVÊQUE
- 2002

In the 1980s, there were numerous claims, based on estimates of the correlation dimension, that the variability of various geophysical processes, in particular rainfall, is generated by a low-dimensional deterministic chaos. Due to a recent attempt (Sivakumar et ai, 2001) to revive the same approach and with claims of an analogous result for the… (More)

- S. Lovejoy, D. Schertzer
- 2012

[1] Climate sensitivity (l) is usually defined as a deter-ministic quantity relating climate forcings and responses. While this may be appropriate for evaluating the outputs of (deterministic) GCM's it is problematic for estimating sensitivities from empirical data. We introduce a stochastic definition where it is only a statistical link between the forcing… (More)

- S Lovejoy, D Schertzer, D Varon
- 2012

This discussion paper is/has been under review for the journal Earth System Dynamics (ESD). Please refer to the corresponding final paper in ESD if available. Abstract We are used to the weather – climate dichotomy, yet the great majority of the spectral variance of atmospheric fields is in the continuous " background " and this defines instead a trichotomy… (More)

- D. Schertzer
- 1998

- D. Schertzer
- 2008

The Fokker-Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian noises. In this paper, we derive a Fractional Fokker–Planck equation for the probability distribution of particles whose motion is governed by a nonlinear Langevin-type equation, which is driven by a non-Gaussian Levy-stable… (More)

We demonstrate that the Fokker-Planck equation can be generalized into a 'Fractional Fokker-Planck' equation, i.e. an equation which includes fractional space differentiations, in order to encompass the wide class of anomalous diffusions due to a Lévy stable stochastic forcing. A precise determination of this equation is obtained by substituting a Lévy… (More)

- D. Schertzer
- 1999

After having closely reexamined the notion of a Lévy's stable vector, it is shown that the notion of a stable multivariate distribution is more general than previously defined. Indeed, a more intrinsic vector definition is obtained with the help of non isotropic dilations and a related notion of generalized scale. In this framework, the components of a… (More)

Ahtruct-Multifrequency, multipolarization imaging radar scattering coefficient data sets, acquired by synthetic aperture radar (SAR) over sea-ice, were studied in order to reveal their scale-invariant properties. Two distinct scenes were acquired at C-band (5.6 cm) and L-band (25 cm) wavelengths for three different linear polarizations (HH, VV, and HV).… (More)