Towards a new synthesis for atmospheric dynamics: Space–time cascades

In spite of the unprecedented quantity and quality of meteorological data and numerical models, there is still no consensus about the atmosphere's elementary statistical properties as functions of scale in either time or in space. This review paper proposes a new synthesis based on a) advances in the last 25 years in nonlinear dynamics, b) a critical re-analysis of empirical aircraft and vertical sonde data, c) the systematic scale by scale, space–time exploitation of high resolution remotely sensed data and d) the systematic re-analysis of the outputs of numerical models of the atmosphere including reanalyses, e) a new turbulent model for the emergence of the climate from “weather” and climate variability. We conclude that Richardson's old idea of scale by scale simplicity — today embodied in multiplicative cascades — can accurately explain the statistical properties of the atmosphere and its models over most of the meteorologically significant range of scales, as well as at least some of the climate range. The resulting space–time cascade model combines these nonlinear developments with modern statistical analyses, it is based on strongly anisotropic and intermittent generalizations of the classical turbulence laws of Kolmogorov, Corrsin, Obukhov, and Bolgiano.