Climate Theory versus a Theory for Climate

While famous theoretical work has been done historically on climate, no precise testable physical theory for climate has ever emerged. That is because, among other reasons, the definition of the objective is imprecise. The most common definition of climate as averaged weather, is more cliche than definition. Average over what? Average in what way? Is there a function relating resulting averages to each other, or do the averages satisfy differential equations? There is not one but many divergent approaches to defining climate in terms of averages, which seem to coexist without mutual competition. The three primary approaches employ time averages, field averages, and model solution ensemble averages, respectively. Each is problematic in its own way. While it is easy to produce an average, finding equations that can stand on their own in terms of averaged quantities only is not straightforward. But such equations are the ultimate aim of a search for a theory of climate, examining the questions of what averaging rule over what physical quantities help point to what an actual theory for climate ought to be like. This paper discusses averaging and closure in other fields, such as kinetic theory and turbulence, and how they are relevant to a theory of climate. It suggests how we might learn from them, while identifying how these issues need more exploration in terms of the climate problem.