Nonlinear Physics
(S. Lovejoy)

The weather and climate as problems in physics

Since the 1980's, the nonlinear physics and atmospheric physics group has worked on a series of new geophysical paradigms. A particularly exciting one is the idea that atmospheric dynamics repeat scale after scale from large to small scales in a cascade-like way. The key is recognizing that as the scales get smaller, the horizontal gets “squashed” much more than the vertical so that the stratification which starts out being extreme (structures very flat at planetary scales) become rounder and rounder at small scales. This allows the scaling (and the stratified cascades) to occur over huge ranges of scale. The cascade mechanism implies that the variability builds up scale by scale; the resulting “intermittency” is huge and is a consequence of the large range of scales. It has nonclassical statistical features, the result is a multifractal process. The physical implications are that atmospheric fluxes of energy, moisture etc. are far from uniform, they are concentrated in storms, and even in the centre of storms.

In the last five years, with the help of massive amounts of in situ, aircraft, satellite data, and reanalysis data, these emergent laws have been extensively verified up to planetary scales. An overall in depth review (for atmospheric scientists) has recently been published: “The weather and climate: emergent laws and multifractal cascades” Lovejoy and Schertzer 2013; a powerpoint presentation is available here. It was also found that over almost all of their ranges, numerical models of the atmosphere (and reanalyses) also have cascade structures, so that cascades do indeed provide stochastic models of deterministic Global Circulation Models (GCM's) and can be used to understand and improve the latter (for example by “stochastic” subgrid paramertrisations).

Solid earth Geophysics

In the area of solid earth studies, we have shown that the surface topography is a universal multifractal, showing that - contrary to prevailing wisdom - scaling surfaces cannot generally be regarded as self-affine fractals (Gagnon et al 2006). Similarly, the variability of the earth's surface magnetic field can be explained by a similar scaling stratification of the rock susceptibility (Lovejoy et al 2001). Interestingly, the lithospheric stratification is opposite to that of the atmosphere becoming stronger at smaller rather than larger scales. Analogous results apply to the rock density and geogravity fields (Lovejoy et al 2008), see Lovejoy and Schertzer 2007 for a review.

Other applications

Other applications include the analysis and simulation of scaling properties of ocean and ice surfaces, chemical pollution, low frequency human speech, hadron jets and the large scale structure of the universe. As disparate as some of these applications may seem, they are linked by the common theme of (nonlinear, dynamical) scale invariance, a symmetry principle whose generality and significance is great.

Nonlinear Geophysics

This work is part of a family of approaches to geophysics collectively termed “nonlinear geophysics”. For more information on this and on its place in the American Geophysical Union and the European Geosciences Union, see “Nonlinear geophysics: why we need it ”.