HR: 17:35h
AN: NG44A-06 INVITED     [Abstracts]
TI: Mutltifractal Predictability, Predictions and Forecasts
AU: * Schertzer, D J
EM: Daniel.Schertzer@enpc.fr
AF: CEREVE, Ecole Nationale des Ponts et Chaussees , 6-8, avenue Blaise Pascal Cite Descartes , MARNE-LA-VALLEE, 77455 Cx2, France
AU: * Schertzer, D J
EM: Daniel.Schertzer@enpc.fr
AF: CNRM, Meteo-France , 1 Quai Branly, PARIS, 75007, France
AU: Macor, J L
EM: Jose.Macor@cereve.enpc.fr
AF: CEREVE, Ecole Nationale des Ponts et Chaussees , 6-8, avenue Blaise Pascal Cite Descartes , MARNE-LA-VALLEE, 77455 Cx2, France
AU: Macor, J L
EM: Jose.Macor@cereve.enpc.fr
AF: FICH, Universidad Nacional del Litoral, CiudadUniversitaria, SANTA FE, 3000, Argentina
AU: Tchiguirinskaia, I
EM: Ioulia.Tchiguirinskaia@cereve.enpc.fr
AF: CEREVE, Ecole Nationale des Ponts et Chaussees , 6-8, avenue Blaise Pascal Cite Descartes , MARNE-LA-VALLEE, 77455 Cx2, France
AU: Lovejoy, S
AF: Physics dept., McGill University, 3600 University st., MONTREAL, QUE H3A 2T8, Canada
AB: Multifractals are widely recognized as powerful tools to analyze spatial heterogeneities or temporal variability of complex fields. They are in fact extremely powerful to analyze together space and time fluctuations, in particular their scaling anisotropy. Furthermore, we argue that multifractals are not limited to analyze: their capacity to predict and forecast has to be better investigated and exploited. It was first necessary to clarify the intrinsic predictability limits of space time scaling systems, e.g. dynamics of the atmosphere coupled with various fields such as the water content. They are quite different from those of systems that are only complex in time. Indeed, space time scaling systems 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 power-law decays of the predictability, not exponential decays. Furthermore, the predictability decay is highly intermittent: the loss of information occurs by intermittent puffs. The predictability itself is multifractal: an infinite hierarchy of power-law exponents is required to characterize the predictability decay from average to extreme events. In particular, we will discuss the multifractal behaviour of the error flux. The second step was the recognition that multifractals can lead to statistical predictions, e.g. that the extremes of a field can be predicted from its rather average behavior. More recently, we have been interested to predict its maxima at different scales. The third step is to proceed to multifractal forecasts in a dynamical manner. We were first interested by stochastic forecasts, i.e. simulating a given number of possible future realizations and comparing their relative dispersion to their multifractal predictability. More recently we have been developing probability forecasts.
UR: http:www.enpc.fr/multifractal/
DE: 3238 Prediction (3245, 4263)
DE: 3245 Probabilistic forecasting (3238)
DE: 3275 Uncertainty quantification (1873)
DE: 4430 Complex systems
DE: 4440 Fractals and multifractals
SC: Nonlinear Geophysics [NG]
MN: 2007 Joint Assembly