Climate: a dynamical system with mismatched space and time domains

Climate is a special spatiotemporal dynamical system. Its time scale can be extended indefinitely, but its space scale can never exceed that of the size of the system. We call this a “mismatching” in space and time domains. With the help of a simplified system of primitive equations, this exploratory paper shows that these scale characteristics may have a significant impact on the mathematical and physical structure of the system. The results show that the mismatching of space–time scales will lead to a decrease of the system’s dimension, degenerating the system from an infinite dimensional to a finite one. Also they show that “mismatched” domains can lead to a greater consistency of the system’s structure in space, as they form a system of uniform structures which are described as “patches”. This may lead to an alternative way of representing climate and its variability as a pattern system defined by the collective behavior of interacting patches or subsystems.