Chaos, ergodicity and multifractal singularities

Overview

GRIP Greenland Ice Core

Low dimensional chaos?

Low dimensional chaos (2)?

High dimensional chaos ?

High dimensional chaos(2)?

Richardsonís Poem (*)

Richardson Diffusion law

Scaling Experiment in Geophysics

Dimension of atmospheric motions?

Van der Hoven
wind spectrum (1957)

2D and 3D :
atmospheric motions?

Space-Time
("Stommel") diagram

Stommel diagram for atmosphere and oceans

Wind: the GASP Experiment

Landes experiment

Wind: results from MOZAIC

What is the outer scale of atmospheric turbulence?

Cascades

Cascades (2)

Multifractal Fields

Multifractal Fields (2)

C(g) curve

K(q) curve

Outer scale estimate from a climatological ensemble

Atmospheric Cascades from cloud imagery

Strong anisotropy

Scaling anisotropic cascades

The scale changing operator

Generalized Scale functions

A 23/9-D Model of atmospheric dynamics

Slide 33

Nonlinear GSI

Linear GSI: analysis and simulation of clouds

3-D anisotropic multifractal cloud simulations

Radiative transfer on multifractal clouds

Cascade factorization and singular statistics

Divergence of Moments

Hydrometeorological long time series

Hydrometeorological long time series (2)

Multifractal Phase Transitions

Ice Core Multifractal Analysis(1)

Ice Core Multifractal Analysis(2)

Temperature simulations

a nonlinear toy

...and a hierarchical model of toys

Conclusion