The horizontal space–time scaling and cascade structure of the atmosphere and satellite radiances

•Atmospheric spectra are power laws of a quadratic form in horizontal space–time.•The anisotropic scaling model reproduces the observed space–time spectral density.•Atmospheric radiance fluxes statistics can be described by a cascade model.•Atmospheric radiance fluxes statistics can help to define weather and climate.

Classically, turbulence has been modeled by a hierarchy of different isotropic scaling regimes. However, gravity acts at all scales and theory and modern observations point towards an atmosphere described by a single anisotropic scaling regime with different scaling laws in the horizontal and vertical directions: the 23/9D model. However, the implications of this anisotropic spatial scaling for the temporal statistics (i.e. the full space–time scaling) have not been worked out and are the subject of this paper. Small structures are advected by larger turbulent structures, by considering averages over the latter we obtain estimates for the structure functions and spectra.To test these predictions, we analyze geostationary satellite MTSAT Infra red radiances over wide scale ranges in both horizontal space and in time (5 km to ~ 10 000 km, 1 h to 2 months). We find that our model accurately reproduces the full 3D (kx, ky, ω) spectral density up to 5000 km in space and 100 h in time. For example, to within constant factors, the 1D spectral exponents were the same in both horizontal directions and in time with spectral exponent β ~ 1.55 ± 0.01. We also considered the various 2-D subspaces ((kx, ky), (kx, ω), (ky, ω)) and showed how these could be used to determine both mean advection vectors (useful for atmospheric motion vectors) but also the turbulent winds.Going beyond these second order statistics we tested the predictions of multiplicative cascade models by estimating turbulent fluxes from both MTSAT but also the polar orbiting TRMM satellite at infrared and passive microwave bands over scale ranges 100 km to 20 000 km, 1 day to 1 year. These accurately obeyed the predictions of multiplicative cascade models over large ranges of spatial scales with typically slight deviations at smallest and largest scales. Analogous temporal analyses showed similar agreement at small scales, but with significant deviations at scales larger than a few days, marking two regimes, associated with weather and macroweather. This allows us to determine Eulerian frame space–time diagrams relating the sizes and lifetimes of structures.