Cascade processes, emergent turbulent laws and multiscale dynamics in the atmosphere

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Since the 1980's there have been several breakthroughs in nonlinear dynamics and turbulence. Of particular importance to this proposal are: a) the development of scale invariance as a general and powerful nonclassical symmetry; b) the discovery of multifractals and their relation to turbulent cascade processes. During the next five years I propose to build on this in several ways: a) Stochastic Parametrisations: Numerical weather models are deterministic, yet the aim of modern meteorology is to predict future atmospheric states and their relative probability of occurrence, i.e. the objective is stochastic (probabilistic). The fact that the stochastic structure turns our to be almost exactly as predicted by multiplicative cascade models opens the door for rapid advances including finally placing "stochastic parametrization" procedures on a sound theoretical basis while opening the way to qualitatively new parametrization schemes. This work will be done in collaboration with NOAA's Climate Diagnostic Centre. b) The weather - Climate transition and stochastic climate prediction: The difference between the weather and climate is currently based on subjectively chosen space-time averaging scales. The new synthesis provides an objective quantitative basis for this distinction treating the weather - climate change as a kind of "dimensional transition". It further accurately predicts the statistical properties of a weather-climate spectral plateau that extends to decadal periods and beyond. This is the basis for stochastic forecasting, analogous to the Stochastic Linear Forcing approach which operational forecasts climate variables such as El-Nino and Sea Surface Temperatures up to scales of 6 -9 months. c) Radiative transfer and the scale by scale relation between cloud and radiation fields: Global climate models treat clouds as homogeneous slabs of material; yet down to small turbulent dissipation scales, cloud liquid water and the corresponding radiation fields are highly variable; implying systematic biases in the models. These biases undermine the credibility of the model predictions including global warming scenarios. The simplest heterogeneity assumption is that the it is the consequence of cascades. Here we will investigate the detailed scale by scale statistical relations between clouds and radiation and use this to improve parametrizations.