Daniel Schertzer

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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)
The Fokker–Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian noises. However, there are both theoretical and empirical reasons to consider similar equations driven by strongly non-Gaussian noises. In particular, they yield strongly non-Gaussian anomalous diffusion which seems to be(More)
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)
In buoyancy-driven flows, another dimensional quantity appears in addition to the energy flux. Classically, this leads to the prediction that at large scales, isotropic Bolgiano-Obukhov (BO) scaling can dominate isotropic Kolmogorov scaling. We investigate this in the atmosphere by using state-of-the-art high-powered lidar data. We examine simultaneous(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)
The complexity of geophysics has been extremely stimulating for developing concepts and techniques to analyze, understand and simulate it. This is particularly true for multifractals and Generalized Scale Invariance. We review the fundamentals, introduced with the help of pedagogical examples, then their abstract generalization is considered. This includes(More)
We use 909 satellite images spanning the scale range 1-5000 km at both visible and infrared wavelengths to show that the variability at all observed scales and at all levels of intensity is very close to that predicted for a direct multiplicative scale invariant cascade starting at planetary scales. To within 1.6%/octave in scale, the observed type of(More)
AhtructMultifrequency, 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)