HR: 08:15h
AN: NG41A-02    [PDF]
TI: Multifractals and Chaos, Predictability and Prediction Skills in Geophysics
AU: * Schertzer, D J
EM: schertze@cereve.enpc.fr
AF: CEREVE Ecole Nationale des Ponts et Chausses, 6-8, avenue Blaise Pascal Cit‚ Descartes, Marne-la Vall‚e, 77455 Cede France
AU: * Schertzer, D J
EM: schertze@cereve.enpc.fr
AF: Meteo-France, 1 quai Branly, Paris, 75007 France
AU: Lovejoy, S
EM: lovejoy@physics.mcgill.ca
AF: Dept. Physics McGill U., 3600 University St., Montreal, PQ H3A 2T8 Canada
AB: The question of prediction - from short to very long term - and its intrinsic limits is a fundamental question in Geophysics; it cross-cuts traditional discipline boundaries. The chaos revolution emphasized the fact that nonlinearity is at the core of this question. This was widely popularized as the 'butterfly effect' with the help of the celebrated Lorenz model, which was introduced as a highly simplliefied mathematical model of convection and has the lowest possible dimensionality, i.e. three, for chaotic differential systems. Unfortunately, this success may have lead to an awkward tendency to reduce complex systems to their low dimensional caricatures including the corresponding predictibility limits. This tendency may have been reinforced by the apparent success of the rather straightforward correlation dimension algorithm to estimate the dimensionality for various complex systems. As a consequence - in spite of observed discrepancies - the existence of characteristic predictability time and a corresponding exponential fall-off of predictability were considered as the universal long-time asymptotic laws. However, for rather well known reasons, the low dimension estimates of geophysical systems turn out to be spurious. It is now rather clear that the chaos of these spatially extended systems, requires approaches dealing with very large number of degrees of freedom and that certain asymptotic behaviors correspond instead to the infinite limit. The modelling of this high number of degreees of freedom liimit can be obtained by an original blending of stochastics and scaling dynamics, e.g. multiplicative cascade processes, more generally with the help of multifractal processes. The latter do not yield characteristic times of predictability: a limited uncertainty on initial and/or boundary conditions on a given range of time and space scales rapidly grows across the scales and yields scaling (i.e. power-law) decays of the predictability, therefore we should be able to predict on the average much better and longer than previously thought. However, intermittency plays a crucial role, as it will be illustrated with the help of multifractal simulations. Decay of predictability is not homogeneous, but occurs by bursts. Some non trivial questions about multifractal prediction are related to it: it is not sufficient, although an improvement in respect to usual methods, to forecast a field with a lower and lower resolution for larger and larger time lag. Indeed, one need to take into account the interactions between the rather predictable large scales with the hihgly impredictible smaller scales. This is particularly indispensable to forecast the extreme events.
UR: http://www.multifractal.jussieu.fr
DE: 3200 MATHEMATICAL GEOPHYSICS (New field)
DE: 3220 Nonlinear dynamics
DE: 3240 Chaos
DE: 3250 Fractals and multifractals
DE: 3300 METEOROLOGY AND ATMOSPHERIC DYNAMICS
SC: Nonlinear Geophysics [NG]
MN: 2003 Fall Meeting