Current computer simulations of climate and weather prediction models can only take into account a limited number of the relevant degrees of freedom of the climate system. Therefore the physical dynamical equations need to be reduced to a smaller subset of variables.
The reduction of the number of degrees of freedom (also known as parametrization in the modeling community) is a central task in statistical mechanics and it is therefore not surprising that many techniques used in this field are also used in the derivation of stochastic parametrizations.
In this talk I will discuss some of these techniques and how they have been applied to climate modeling. I will then discuss how we have used the Mori-Zwanzig formalism and response theory to derive parametrizations for weakly coupled dynamical systems.