As a formal definition, I am partial to the idea that weather is the
trajectory of the system instance through state space and that climate is
the manifold on which that trajectory moves.
The trouble with this definition is that it essentially assumes a stationary
ergodic system and thus makes the notion of "climate change" a bit fuzzy.
Is there an extension to a nonstationary system? Here it is necessary to
distinguish between the real world and its models. It is possible to have a
rigorous definition of climate change in a model; we simply have to presume
an infinite ensemble of instantiations under identical forcing. The climate,
then, is the distribution of states across the ensemble at a given moment.
Whether this has a meaningful interpretation in the real world is not
obvious to me; in the real world it is not possible to perfectly define the
system and the idea of an ensemble is pretty clearly excluded. We only get
one world. That's the problem.
It should be noted that this is not the only definition of climate. Some
groups use heuristics and/or ocean dynamics to make long term predictions of
the types of weather to be expected a few months out. They call these
"climate predictions". I think in practice these estimates, are of very
limited skill and utility, and the heuristic ones lack intellectual
interest, and that far too much has been made of them, but that being as it
may the skill involved is somewhat greater than chance.
In this definition of climate, any prediction of general seasonal anomalies
made outside the window of weather predictability would be considered
climate predictions. This is an intermediate definition, where neither the
exact trajectory of the system (weather) nor its general statistics
(climate) are of interest. Rather, there is some guess made as to some
properties of the trajectory of the state through state space in a period
outside the predictability of the fast atmospheric components but within the
limits of the next fastest component, the upper ocean.
mt
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