How is it that we go about building climate models? One thing is, that we would like to build our model to represent everything that we know happens. If we could actually do so -- mainly meaning if the computers were fast enough -- life would be simple. As usual, life is not simple.
I'll take one feature as a poster child. We know the laws of motion pretty well. I could write them down pretty easily and with only a moderate amount more effort write a computer program to solve them. These are the Navier-Stokes equations. On one hand, they're surprisingly complex (from them comes dynamical chaos), but on the other, they're no problem -- we know how to write the computer programs to do conservation of momentum. Ok entire books have been written on even a single portion of the problem. Still, the books have already been written.
The problem is, if you want to run your climate model using what we know is a representation sufficient to capture everything we need to do, in order to represent everything we know is going on, you need to have your grid points only 1 millimeter apart. That's ok, but it means something like 10^30 times as much computing power as the world's most powerful computer today. (A million trillion trillion times as much computing power.)
What do we do in the mean time?
What we do in the mean time is realize that there are simpler ways to represent almost exactly, or at least fairly well in an average sense, what is going on -- even though we don't have computers emormously more powerful than currently exist. This is where we encounter 'parameterizations'.
A parameterization is where we try to represent all those tiny features that we don't (currently) have the computing power to represent directly. In an ideal world (which includes infinite computer speed), we wouldn't need any parameterizations.
Since we live in the real, and imperfect, world, we deal with the fact that we don't have infinitely fast computers. But we do have amazingly fast computers which are able to deal with problems that we never used to be able to consider. Still, not infinitely fast, or even as fast as we already know enough science make use of.
Now, one of the things which leads to dynamical chaos is that momentum advects (fast winds here shove themselves over there) as well as dissipates (tiny blobs, the 1 mm I mentioned, whirl about fast enough that the energy gets turned in to heat, and the air comes to a stop). We know this. And give us a computer that can cover everything down to the 'dissipation scale' (the 1 mm or so), we can do a fair job of running a model that predicts what you see. (Some interesting exceptions exist, but that's for a different note.) The problem, for climate modeling, is that the volume we can manage this way is the size of a fish tank. And not necessarily that large a fish tank (about 1000 L, 250 gallons).
On the other hand, we do have simplified representations of what happens at that smaller scale. And they do a moderately good job (bulk aerodynamics) to pretty good job (Monin-Obukhov similarity theory). And, of course, there are more elaborate methods, with correspondingly better behavior. So, again, what do we do in the mean time?
One thing is, we take our parameterization and see how closely it lets us match what we observe about the world. For turbulence parameterizations (which is what I've taken at the moment) this means observing how the wind changes with distance above the surface, and how it changes as you move across a new surface. That means, for instance, taking a field with known characteristics (freshly plowed, let's say) and putting wind measuring devices (anemometers) on towers along the prevailing wind direction. Then look at how the wind speed changes as you move down the wind path, and as you move up from the surface. If your parameterization has some tunable numbers, you tune them to get the best representation of these observed winds.
What we don't do is tune (change) those numbers until we get some particular climate change sensitivity. On the one hand, it's probably impossible computationally (the globe is tremendously larger than the field you plowed). On the other hand, it is also dishonest and undesirable. Undesirable because it means that your turbulence parameterization wouldn't be representing turbulence nearly as well as it could. (I'll take it as given that the dishonest aspects are obvious.)
This makes for one aspect of building a climate model -- you can't represent everything that you know exists, so you simplify some of it. But you do your best to represent that aspect (turbulence for now) as well as you can -- in its own terms. Turbulence parameterizations try to represent how heat, moisture, momentum, get transported near the earth's surface (among other places), so you check them by how well they do that job.
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