Having consulted Tim Palmer’s Lorenzian Meteorological Office
‘Prediction of weather and climate are necessarily uncertain: our observations of weather and climate are uncertain, the models into which we assimilate this data and predict the future are uncertain, and external effects such as volcanoes and anthropogenic greenhouse emissions are also uncertain. Fundamentally, therefore, therefore we should think of weather and climate predictions in terms of equations whose basic prognostic variables are probability densities ρ(X,t) where X denotes some climatic variable and t denoted time. In this way, ρ(X,t)dV represents the probability that, at time t, the true value of X lies in some small volume dV of state space. Prognostic equations for ρ, the Liouville and Fokker-Plank equation are described by Ehrendorfer (this volume). In practice these equations are solved by ensemble techniques, as described in Buizza.’ (Predicting Weather and Climate – Palmer and Hagedorn eds – 2006)
Don’t ask me for the details – I mistook an ordinary differential equation for a form of lyric verse.