The temporal cascade structure of reanalyses and global circulation models



The spatial stochastic structure of deterministic models of the atmosphere has been shown recently to be well modelled by multiplicative cascade processes; in this paper we extend this to the time domain. Using data from the European Centre for Medium Range Weather Forecasting's (ECMWF) reanalyses (ERA40) and two meteorological models (Global Forecast System and Global Environmental Multiscale), we investigate the temporal cascade structures of the temperature, humidity and zonal wind at various altitudes, latitudes and forecast times. First, we estimate turbulent fluxes from the absolute second-order time differences, showing that the fluxes are generally very close to those estimated in space at the model dissipation scale; thus validating the flux estimates. We then show that temporal cascades with outer scales typically in the range 5–20 days can accurately account for the statistical properties over the range from 6 h up to 3–5 days. We quantify the (typically small) differences in the cascades from model to model, as functions of latitude, altitude and forecast time. By normalizing the moments by the theoretical predictions for universal multifractals, we investigate the ‘Levy collapse’ of the statistics somewhat beyond the outer cascade limit into the low-frequency weather regime. Although due to finite size effects and the small outer temporal scale, the temporal scaling range is narrow (12–24 h up to 2–10 days), we compare the spatial and temporal statistics by constructing space-time (Stommel) diagrams, finding space-time transformation velocities of 450–1000 km day−1, comparable to those predicted based on the solar energy flux driving the system. This transition time-scale corresponding to planetary size structures objectively defines the transition from usual weather to a low-frequency weather regime with much lower variability. Finally, we discuss the implications for ensemble forecasting systems, stochastic parametrization and stochastic forecasting. Copyright © 2012 Royal Meteorological Society