Global Space-Time Cascades and Multifractals in Precipitation: Basic Issues and Empirical Status
Shaun Lovejoy1, Julien Pinel1, Daniel Schertzer2
1Physics, McGill, Montreal, QC, Canada; 2ENPC/CEREVE, U. de Paris Est, Cité Descartes, Marne-la-Vallee, France

Precipitation is the key input field into hydrological systems and models; it displays extreme variability with complex structures embedded within structures, from drop to planetary scales in space and from milliseconds to millennia in time. The only hope for taming such variability is the existence of some scale by scale regularity, the existence of scale invariant regimes. Scale invariance is a symmetry principle of great generality; a system can be scale invariant even when it is highly anisotropic. It is also known that multiplicative cascades are the generic multifractal process and are typically associated with nonlinear scale invariant dynamics.

Since the 1980's, this merging of turbulence and precipitation science has stimulated several important developments in cascade processes in atmospheric science and in hydrology. This has raised numerous fundamental issues including: a) the relation of the rain rate field to the cascading precipitation “flux” field: what is the value of the nonconservation exponent H; is it zero or nonzero? b) the nature of the scale by scale cascade conservation: is it microcanonical or canonical? c) the question of universality: is it weak (Log Poisson) or strong (Log Levy) … or none at all? d) the nature of the low and zero rain rates: is the rain process on a fractal support or is there a low threshold below which the values are effectively truncated to zero? e) what is the nature of the extremes: are they classical (thin or long tailed) or are they power laws? (is the critical probability exponent qD infinite or finite?).

We examine these issues in the light of observations of precipitation over wide ranges of scales including the extreme small drop scales (using stereophotography) and the extreme large planetary scales (using satellite borne radar) as well as gauge networks and meteorological reanalyses.

Keywords: Cascades; Multifractals; Precipitation; Scale invariance

Biography: Shaun Lovejoy received a BA and MA in theoretical physics at Trinity College Cambridge (1976, 1981) and a phD in atmospheric physics from McGill University, 1981 (thesis: “The Remote Sensing of Rain”). He has been on faculty in the McGill Physics department since 1985 and has published over 200 papers on cascades, multifractals and their applications to precipitation and other geosystems. Since 2008, he has been the president of the Nonlinear Geophysics focus group at the American Geophysical Union and is author of the book “Multifractal cascades and the emergence of atmospheric dynamics”.