Michael Tobis wrote:
> 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.
IMO this can be adequately dealt with by being precise about what is the
"system" under consideration, certainly when working in model-world. Eg
it may be the Lorenz model with a specific parameter set, or an AOGCM
with specified boundary conditions. The change in climate is then easily
defined as the shift in the manifold when the boundary conditions are
altered.
Of course the real world is messier...although splitting off the
atmosphere-ocean system and considering it as a stand-alone system
forced by GHG concentrations (and sun and land surface conditions...) is
a useful approximation. I think a pedantic Bayesian would not in any
case be directly interested in abstract concepts as "sensitivity" or
"climate" for the real world, but instead would prefer to focus on
(potential) observations. OTOH the observations (of future change) are
strongly dependent on things like "sensitivity" for all our models that
we may use to make predictions, so it's clearly a useful concept.
> 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.
But integrating over time serves much the same purpose as integrating
over an ensemble (as long as the climate change is slow enough). Hence
30y normals...I agree it's not formally identical in a nonstationary
system, but the issue is how much error is introduced by the
approximation. I think it is rarely the case that the next year of
weather would be distinguishable from the distribution over the previous 30.
James
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