On the Distinctively Skewed and Heavy Tailed Character of Atmospheric and Oceanic Probability Distributions

Abstract:

The probability distributions of large-scale atmospheric and oceanic variables are generally

skewed and heavy-tailed. We argue that their distinctive departures from Gaussianity arise fundamentally

from the fact that in a quadratically nonlinear system with a quadratic invariant, the coupling

coefficients between system components are not constant but depend linearly on the system

state in a distinctive way. In particular, the skewness arises from a tendency of the system trajectory

to linger near states of weak coupling. We show that the salient features of the observed non-

Gaussianity can be captured in the simplest such nonlinear 2-component system. If the system is

stochastically forced and linearly damped, with one component damped much more strongly than

the other, then the strongly damped fast component becomes effectively decoupled from the

weakly damped slow component, and its impact on the slow component can be approximated as a

stochastic noise forcing plus an augmented nonlinear damping. In the limit of large time-scale

separation, the nonlinear augmentation of the damping becomes small, and the noise forcing can

be approximated as an additive noise plus a correlated additive and multiplicative noise

(CAM noise) forcing. Much of the diversity of observed large-scale atmospheric and oceanic

probability distributions can be interpreted in this minimal framework.