Master equations for climatic parameter sets

Abstract

A data set comprising the equatorial components of global atmospheric momentum and the related mountain and friction torques is used to demonstrate the usefulness of a novel analysis technique in climate research. The technique consists in deriving a Master equation in the phase plane of a pair of climate variables on the basis of time series of this pair. The Master equation predicts changes of the pair's probability distribution in this phase plane. A mean velocity and a diffusion coefficient can be derived from the coefficients of this equation. An analysis of the dynamics of the parameter pair is based on the Master equation. The circulation of the angular momenta in the phase plane is anticyclonic with an attraction towards the origin. The diffusion is strongest close to the center of the probability density distribution of the equatorial momenta. The anticyclonic motion reflects the westward propagation of those Rossby waves which contribute to the mass term. It is found that the mountain and orographic torques induce only a small fraction of the observed changes of the angular momenta. It is essentially the impact of both the Earth's deviation from sphericity and its rotation, which induces the variability of the angular momenta. The mass and wind terms are barely related to each other in contrast to the predictions of normal mode theory. Surprisingly, however, the mountain torque and the wind terms are closely linked.