Climate: The Elements

Abstract

The authors present an analytical climate model, which has the features that (i) the atmosphere is a simple oscillator for all periods ≤1 year, (ii) the ocean stores heat, (iii) the ocean exchanges momentum with the atmosphere, and (iv) random forcing exists due to atmospheric thermodynamics and oceanic dynamics. The piecewise analytical integration of coupled linear equations for sea temperature, air-sea temperature difference, and air-sea velocity difference generates experimental climates. The exchange parameters of the algorithm, except for the exchange coefficient for heat with the deep ocean, am calibrated to the observed climate using the annual cycle, and random forcing is applied over intervals of one year. The atmospheric random forcing leads to bounded random walks, the extent of which increases as the exchange coefficient with the deep ocean decreases, and the oceanic random forcing generates a stationary response. It is found that the observed statistics of the global temperature series can be reproduced by either a relatively large heat exchange coefficient with the deep ocean and little oceanic variability or a smaller exchange coefficient with a larger oceanic variability. Plausible exchange coefficient values imply random walk lengths of at least a century-long timescale.