Review article: Scaling, dynamical regimes, and stratification. How long does weather last? How big is a cloud?

Abstract

Until the 1980s, scaling notions were restricted to self-similar homogeneous special cases. I review developments over the last decades, especially in multifractals and generalized scale invariance (GSI). The former is necessary for characterizing and modelling strongly intermittent scaling processes, while the GSI formalism extends scaling to strongly anisotropic (especially stratified) systems. Both of these generalizations are necessary for atmospheric applications. The theory and some of the now burgeoning empirical evidence in its favour are reviewed. Scaling can now be understood as a very general symmetry principle. It is needed to clarify and quantify the notion of dynamical regimes. In addition to the weather and climate, there is an intermediate “macroweather regime”, and at timescales beyond the climate regime (up to Milankovitch scales), there is a macroclimate and megaclimate regime. By objectively distinguishing weather from macroweather, it answers the question “how long does weather last?”. Dealing with anisotropic scaling systems – notably atmospheric stratification – requires new (non-Euclidean) definitions of the notion of scale itself. These are needed to answer the question “how big is a cloud?”. In anisotropic scaling systems, morphologies of structures change systematically with scale even though there is no characteristic size. GSI shows that it is unwarranted to infer dynamical processes or mechanisms from morphology. Two “sticking points” preventing more widespread acceptance of the scaling paradigm are also discussed. The first is an often implicit phenomenological “scalebounded” thinking that postulates a priori the existence of new mechanisms, processes every factor of 2 or so in scale. The second obstacle is the reluctance to abandon isotropic theories of turbulence and accept that the atmosphere's scaling is anisotropic. Indeed, there currently appears to be no empirical evidence that the turbulence in any atmospheric field is isotropic. Most atmospheric scientists rely on general circulation models, and these are scaling – they inherited the symmetry from the (scaling) primitive equations upon which they are built. Therefore, the real consequence of ignoring wide-range scaling is that it blinds us to alternative scaling approaches to macroweather and climate – especially to new models for long-range forecasts and to new scaling approaches to climate projections. Such stochastic alternatives are increasingly needed, notably to reduce uncertainties in climate projections to the year 2100.