Climate Variability

The global climate system is composed of a number of subsystems F atmosphere, biosphere, cryosphere, hydrosphere, and lithosphere F each of which has a distinct characteristic time, from days and weeks to centuries and millennia. Each subsystem, moreover, has its own internal variability, all other things being constant, over a fairly broad range of time scales. These ranges overlap between one subsystem and another. The interactions between the subsystems thus give rise to climate variability on all time scales. We outline here the rudiments of the way in which dynamical systems theory is starting to provide an understanding of this vast range of variability. Such an understanding proceeds through the study of successively more complex flow patterns. These spatiotemporal patterns are studied within narrower ranges of time scales, such as intraseasonal, interannual, interdecadal and multimillennial; each of these frequency bands is covered in a separate article of this Encyclopedia. The main results of dynamical systems theory that are important for the study of climate involve essentially bifurcation theory and the ergodic theory of dynamical systems. In the next section, we describe the climate system’s dominant balance between incoming solar radiation and outgoing terrestrial radiation. This balance is consistent with the existence of multiple equilibria of surface temperatures. Such multiple equilibria are also present for other balances of climatic actions and reactions. Thus, on the intraseasonal time scale, the thermal driving of the mid-latitude westerly winds is countered by surface friction and mountain drag. Multiple equilibria typically arise from saddle-node bifurcations of the governing equations. Transitions from one equilibrium to another may result from small and random pushes, a typical case of minute causes having large effects in the long term. In the following section, we sketch the ocean’s overturning circulation between cold regions, where water is heavier and sinks, and warm regions, where it is lighter and rises. The effect of temperature on the density and, hence the motion, of the water masses is in competition with the effect of salinity: increases in density, through evaporation and brine formation, compete further with decreases in salinity and, hence, in density through precipitation and river runoff. These competing effects can also give rise to two distinct equilibria. In the present-day oceans, a thermohaline circulation prevails, in which the temperature effects dominate. In the remote past, about 50 My ago, a halothermal circulation may have obtained, with salinity effects dominating. In a simplified mathematical setting, these two equilibria arise by a pitchfork bifurcation that breaks the problem’s mirror symmetry. On shorter time scales, of decades to millennia, oscillations of intensity and spatial pattern in the thermohaline circulation seem to be the dominant mode of variability. We show how interdecadal oscillations in the ocean’s circulation arise by Hopf bifurcation.