Scaling Up: Molecular to Meteorological via Symmetry Breaking and Statistical Multifractality

Abstract

The path from molecular to meteorological scales is traced and reviewed, beginning with the persistence of molecular velocity after collision induces symmetry breaking, from continuous translational to scale invariant, associated with the emergence of hydrodynamic behaviour in a Maxwellian (randomised) population undergoing an anisotropic flux. An empirically based formulation of entropy and Gibbs free energy is proposed and tested with observations of temperature, wind speed and ozone. These theoretical behaviours are then succeeded upscale by key results of statistical multifractal analysis of airborne observations on horizontal scales from 40 m to an Earth radius, and on vertical scales from the surface to 13 km. Radiative, photochemical and dynamical processes are then examined, with the intermittency of temperature implying significant consequences. Implications for vertical scaling of the horizontal wind are examined via the thermal wind and barometric equations. Experimental and observational tests are suggested for free running general circulation models, with the possibility of addressing the cold bias they still exhibit. The causal sequence underlying atmospheric turbulence is proposed.