09 Feb 2023
 | 09 Feb 2023
Status: a revised version of this preprint was accepted for the journal NPG.

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

Shaun Lovejoy

Abstract. Until the 1980’s, 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 is 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 time scales 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 the 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 two 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 is 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.

Shaun Lovejoy

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on npg-2023-5', Anonymous Referee #1, 22 Feb 2023
    • AC1: 'Reply on RC1', Shaun Lovejoy, 10 May 2023
  • RC2: 'Comment on npg-2023-5', Anonymous Referee #2, 26 Feb 2023
    • AC2: 'Reply on RC2', Shaun Lovejoy, 10 May 2023

Shaun Lovejoy

Shaun Lovejoy


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Short summary
“How big is a cloud?” and “How long does the weather last?” require scaling to answer. We review the advances in scaling that have occurred over the last four decades: a) intermittency (multifractality), b) stratified and rotating scaling notions (Generalized Scale Invariance). Although scaling theory and the data are now voluminous, atmospheric phenomena are too often viewed through an outdated scalebound lens, and turbulence remains confined to isotropic theories of little relevance.