A gallery of simple models from climate physics

Abstract

The climate system of the earth is one of the most complex systems presently investigated by scientists. The physical compartments – atmosphere, hydrosphere and cryosphere – can be described by mathematical equations which result from fundamental physical laws. The other ’nonphysical’ parts of the climate system, as e.g. the vegetation on land, the living beings in the sea and the abundance of chemical substances relevant to climate, are repre- sented by mathematical evolution equations as well. Comprehensive climate models spanning this broad range of coupled compartments are so complex that they are mostly beyond a deep reaching mathematical treatment, in par- ticular when asking for general analytical solutions. Solutions are obtained by numerical methods for specific boundary and initial conditions. Simpler models have helped to construct these comprehensive models, they are also valuable to train the physical intuition of the behavior of the system and guide the interpretation of the results of numerical models. Simple models may be stand-alone models of subsystems, such stand-alone general circulation mod- els of the ocean or the atmosphere or coupled models, with reduced degrees of freedom and a reduced content of the physical processes. They exist in a wide range of structural complexity but even the simplest model may still be mathematically highly complicated due to nonlinearities of the evolution equations. This article presents a selection of such models from ocean and atmosphere physics. The emphasis is placed on a brief explanation of the physical ingredients and a condensed outline of the mathematical form.