The Origin of Nonlinear Signatures of Planetary Wave Dynamics: Mean Phase Space Tendencies and Their Information

Mean phase space tendencies are investigated to systematically identify the origin of nonlinear signatures and the dynamical significance of small deviations from Gaussianity of planetary low-frequency waves. A general framework for the information content of mean phase space tendencies in complex geophysical systems is derived. In the special case of purely Gaussian statistics, this theory predicts that the interactions amongst the planetary waves themselves are the source of the nonlinear signatures in phase space, whereas the unresolved waves contribute only a constant forcing, and cannot contribute to any nonlinear signature. The predictions of the general framework are confirmed by investigating a simple stochastic climate model which represents key features of low-frequency planetary waves. This toy model has a strong nonlinear signature in the form of a double swirl in its mean phase space tendencies of its low-frequency variables. Such double swirl structures have been recently identified as signatures of nonlinear planetary wave dynamics in prototype and comprehensive atmospheric General Circulation Models (GCM). The analysis of the dynamics of planetary waves in the prototype atmospheric GCM shows a complex interplay between resolved and unresolved waves. It is found that the unresolved waves play a crucial role in the planetary wave dynamics. The interactions amongst the planetary waves themselves do not produce the nonlinear signature, it is the interaction with the unresolved waves which is responsible for the nonlinear dynamics. Interpreting this within the general framework suggests that this impact of the unresolved waves is due to their small deviations from Gaussianity and has significant contributions from both additive and multiplicative triad interactions between resolved and unresolved modes.