Atmospheric complexity or scale by scale simplicity?

Abstract

Is the numerical integration of nonlinear partial differential equations the only way to tackle atmospheric complexity? Or do cascade dynamics repeating scale after scale lead to simplicity? Using 1000 orbits of TRMM satellite radiances from 11 bands in the short wave (visible, infra red) long wave (passive microwave) and radar regions and 8.8 to 20,000 km in scale, we find that the radiance gradients follow the predictions of cascade theories to within about ±0.5%, ±1.25%, ±5.9% for the short waves, long waves and reflectivities respectively and with outer scales varying between ≈5,000 to ≈32,000 km. Since the radiances and dynamics are strongly coupled, we conclude that weather can be accurately modeled as a cascade process.

The stochastic multiplicative cascade structure of deterministic numerical models of the atmosphere

“…This accuracy is very close to those of the same moments of the visible and IR radiances over the range 10-5000 km (≈±0.5%, Lovejoy et al, 2009a).…”

“…It is worth noting that the outer scales for these fields (∼8000-27 000 km) are approximately the same as the outer scales of the radiances (∼5000-32 000 km in Lovejoy et al, 2009a). We also mention that the C 1 's are not too different from the C 1 's for passive scalars (∼0.1) (Lilley et al, 2004).…”

“…In comparison, the atmospheric boundary conditions are quite different. In particular both the topography (Gagnon et al, 2006) and the critical energy-containing short and long wavelengths radiances responsible for the forcing (Lovejoy et al, 2001(Lovejoy et al, , 2009a have been found to have wide scale range cascade structures so that the boundary conditions and flux sources and sinks apparently do not introduce characteristic scales and so need not destroy the cascades.…”

“…These studies show empirically that to within ≈±1%, the energy containing short and long wave atmospheric radiances respect the predictions of multiplicative cascades from planetary scales down to at least several kilometres (Lovejoy et al, 2001(Lovejoy et al, , 2009a so that the relevant sources and sinks of fluxes are likely to be scaling. Similarly, Lovejoy et al (2009c, d) showed that the vertical structure of horizontal wind, passive scalars, temperature, pressure, humidity, potential temperature, etc.…”

From molecules to meteorology via turbulent scale invariance

“…There have been attempts to examine the scaling of model fields, both on a case-study basis as described above and more generally. Lovejoy et al (2009c) and Stolle et al (2009) concluded that weather could be modelled as a cascade process, pointing out that whereas horizontal scaling could be investigated for models with regularly spaced grids, the general absence of such regularity with altitude in atmospheric models used for assimilation and forecasting hampered analysis of their vertical scaling. In this case, the cascades refer to the meaning whereby the same processes are at work scale by scale across the whole scaling range…”