Following Mandelbrot's theory of fractals, the area-perimeter relation is used to investigate the geometry of satellite- and radar-determined cloud and rain areas between 1 and 1.2 x 10(6) square kilometers. The data are well fit by a formula in which the perimeter is given approximately by the square root of the area raised to the power D [See equation in the PDF], where D is interpreted as the fractal dimension of the perimeter. It is concluded that rain and cloud perimeters are fractals-they have no characteristic horizontal length scale between 1 and 1000 kilometers.

The Fokker-Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian 1 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 relevant in different domains of Physics. We therefore derive in this paper 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 Levy-stable noise rather than a Gaussian. We obtain in fact a general result for a Markovian forcing. We also discuss the existence and uniqueness of the solution of the Fractional Fokker-Planck equation.

Advances in remote sensing and in situ measurement techniques have revealed the full continuum of atmospheric motions and have underlined the importance of mesoscale processes. This paper examines the implications of three observed characteristics of mesoscale circulations: 1) the energy spectrum of the horizontal wind in the horizontal is of the form k"ft with fa ~ 5/3, (k is a wavenumber); 2) the corresponding spectrum in the vertical direction is of the same scaling form, but with a very different slope (fa ~ 11/5); and 3) the variability is extreme. Some recent work in turbulence, physics, and meteorology, that is relevant to systems with extreme variability over a wide range of scales is reviewed. The concepts of scaling, intermittency, and fractals, are briefly introduced to show how they can be used to understand the physics of both homogeneous and intermittent energy cascades in isotropic atmospheres. These concepts may be generalizable (with a formalism called generalized scale invariance), to account for atmospheric intermittency and especially for anisotropy. Finally, it is shown how to construct fractal models. These models are useful because they produce realizations of random fields that are broadly of the same sort as those that may be allowed by the equations, while at the same time depending on empirically determined parameters. This enables them to retain close links with both the data and the physics. Finally, possible applications in mesoscale modeling, sampling problems, remote sensing, nowcasting, hydrology, and numerical weather prediction (NWP) systems are briefly discussed.

Abstract. In this paper, we present evidence that intermittency of Eulerian and Lagrangian turbulence of ocean temperature and plankton fields is multifractal and furthermore can be analysed with the help of universal multifractals. We analyse time series of temperature and in vivo fluorescence taken from a drifter in the mixed coastal waters of the eastern English Channel. Two analysis techniques are used to compute the fundamental universal multifiractal parameters, which describe all the statistics of the turbulent fluctuations: the analysis of the scale invariant structure function exponent ζ(q) and the Double Trace Moment technique. At small scales, we do not detect any significant difference between the universal multifiractal behavior of temperature and fluorescence in an Eulerian framework. This supports the hypothesis that the latter is passively advected with the flow as the former. On the one hand, we show that large scale measurements are Lagrangian and indeed we obtain for temperature fluctuations a ω2 power spectrum corresponding to the theoretical scaling of a Lagrangian passive scalar. Furthermore, we show that Lagrangian temperature fluctuations are multiscaling and intermittent. On the other hand, the flatter slope at large scales of the fluorescence power spectrum points out that the plankton is at these scales a "biologically active" scalar.

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