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- S Lovejoy, D Schertzer, A A Tsonis
- Science
- 1987

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)

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)

- Daniel Schertzer, Shaun Lovejoy
- Fractals in the Natural and Applied Sciences
- 1993

- 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)

- S Lovejoy, D Schertzer, J D Stanway
- Physical review letters
- 2001

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)

- Marc Lilley, Shaun Lovejoy, Kevin Strawbridge, Daniel Schertzer
- Physical review. E, Statistical, nonlinear, and…
- 2004

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)