Mutltifractal Predictability and Mutltifractal Forecasts
Abstract
Multifractals have been more and more recognized as powerful tools to analyze spatial heterogeneities and/or temporal variability of complex fields. They are indeed extremely powerful to analyze together space and time fluctuations, in particular their scaling anisotropy. We argue that multifractals are not limited to analyze: we show that they can be further exploited to first study the predictability of complex space-time fields and secondly to obtain optimal forecasts. The intrinsic predictability limits of space time scaling systems, e.g. dynamics coupled with various fields such as the water content, 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 instead of 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 behavior of the decorrelation and correlation fluxes, as well as their required extension. Secondly, this framework allows to proceed to multifractal forecasts in a dynamical manner This can be achieved with the help of ensemble stochastic forecasts, i.e. simulating a given number of possible future realizations and comparing their relative dispersion. We also discuss the possibility to directly achieve multifractal probabilistic forecasts. In both cases, these forecasts are optimal in the sense that they only limited by the intrinsic predictability limits discussed above.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2007
- Bibcode:
- 2007AGUFM.U43B1134S
- Keywords:
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- 3238 Prediction (3245;
- 4263);
- 3245 Probabilistic forecasting (3238);
- 4415 Cascades;
- 4440 Fractals and multifractals;
- 4475 Scaling: spatial and temporal (1872;
- 3270;
- 4277)