Modélisation de la variabilité spatiale et temporelle des précipitations à la sub-mésoéchelle par une approche multifractale

Sébastien Verrier 1
1 SPACE - LATMOS
LATMOS - Laboratoire Atmosphères, Milieux, Observations Spatiales
Abstract : Rainfall is characterized by an extreme variability over a wide range of space- and timescales. Underlying nonlinear phenomena produce strong and localized extremes that are poorly represented in current meteorological models. There is a need of stochastic representations that could reproduce rainfall statistics whatever the scale. Multifractal cascades, initially introduced in statistical physics of turbulence, are possible candidates. In this work, the "Universal Multifractal" model (Schertzer & Lovejoy, 1987) is considered. This model enables multiscale statistical characterization of a field by the means of three fundamental ("universal") parameters. Multifractal analysis tools have been applied to rainfall datasets representative of submesoscale variability, especially to weather radar measurements and to high-resolution disrometer time series. "Scaling ranges", i.e. ranges of scales dominated by multifractal symmetries are identified and associated with specific estimated universal parameters. It is shown that analysis algorithms applied conditionnally in the interior of the rain events provide results that differ significantly from those reported in scientific literature. By the means of theoretical calculations and of simulations, it is demonstrated that classical multifractal analysis algorithms are very sensitive to the proportion of zeros, which is obviously problematic in the case of rainfall. A new methodology of analysis has been proposed, based on the computation of weighted statistics that overweight nonzero values. Consistent parameters that are not affected by zeros are estimated and the obtained values suggest that rainfall and passive scalars share some statistical scaling symmetries at scales sufficiently large so that turbulent advection dominates inertial effects. Finally, it is shown how the existence of multifractal properties may impact applications. In particular, a universal multifractal downscaling algorithm has been defined. This algorithm exploits scaling symmetries associated with universal parameters in order to simulate a statistically consistent and realistic variability at scales inaccessible to observation or simulation. For instance, this algorithm could be used to build hourly rainfall time series from daily ones, or even to increase the resolution of observed precipitation maps, leading to possible hydrological applications.
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  • HAL Id : tel-00734327, version 1

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Sébastien Verrier. Modélisation de la variabilité spatiale et temporelle des précipitations à la sub-mésoéchelle par une approche multifractale. Météorologie. Université de Versailles-Saint Quentin en Yvelines, 2011. Français. ⟨NNT : 2011VERS0039⟩. ⟨tel-00734327⟩

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