Space-time cascades and the scaling of ECMWF reanalyses: Fluxes and fields



[1] We consider the space-time scaling properties of the European Centre for Medium-Range Weather Forecasts (ECMWF) interim reanalysis products for the wind (u, v, w), humidity (hs), temperature (T), and geopotentials (z) and their corresponding turbulent fluxes using the daily 700 mbar products for the year 2006. Following previous studies on T, hs, and u, we show that that the basic predictions of multiplicative cascade models are well respected over space-time scales below ∼5000 km, shorter than ∼5–10 days providing precise scale by scale determination of the reanalysis statistical properties (needed for example for stochastic parameterizations in ensemble forecasting systems). We innovate by including the meridional and vertical wind components (v, w) and geopotential (z), and by considering their horizontal anisotropies, their latitudinal variations and, perhaps most importantly, by directly analyzing the fields (not just fluxes). Whereas the fluxes have nearly isotropic exponents in space-time with little latitudinal variation (displaying only scale independent “trivial” anisotropy), the fields have significant scaling horizontal anisotropies. These complicate the interpretation of standard isotropic spectra and are likely to be artifacts. Many of the new (nonconservation) exponents (H) are nonstandard and currently have no adequate theoretical explanation although the key horizontal wind and temperature H exponents may be consequences of horizontal Kolmogorov scaling, combined with sloping isobaric surfaces. In time the scaling is broken at around 5–10 days, i.e., roughly the lifetime of planetary structures; lower frequencies are spectrally flatter: the “spectral plateau,” weather-low-frequency weather regime.