The stochastic multiplicative cascade structure of deterministic numerical models of the atmosphere
Résumé
By direct statistical analysis we show that over almost all their range of scales and to within typically better than +/- 1%, atmospheric fields obtained from analyses and numerical integrations of atmospheric models have the multifractal structure predicted by multiplicative cascade models. We quantify this for the horizontal wind, temperature, and humidity fields at 5 different pressure levels for the ERA40 reanalysis, the Canadian Meteorological Centre Global Environmental Multiscale (CMC, GEM) model, as well as the National Oceanographic and Atmospheric Administration Global Forecasting System (NOAA, GFS). We investigate the additional prediction that the cascade belongs to a universal multifractal basin of attraction. By demonstrating a 'Levy collapse' of the statistical moments to within +/- 2 to +/- 5% over most of the range of scales, we conclude that there is good evidence for this. Finally, we discuss how this stochastic multiplicative cascade structure can be exploited in improving ensemble forecasts.