The limits of climate models

There are two main lines of argument that are used to show that CO₂ induced global warming is a likely proposition, (a) historical records, and geological proxies of temperature, and (b) predictions of Global Climate Models (GCMs). The instrumental temperature record indicates that the climate has warmed over the last 150 years, but the geological proxy record does not indicate that we are seeing anything particularly extraordinary especially when the problems associated with the urban heat island effect are taken into account.

The Holocene Climatic Optimum (HCO) and the Medieval warm periods (MWP) are evidence of warmer climates than today. The ice-core data also indicates considerable fluctuations in climate on all times scales from decades to millennia. However even if the temperature is not outside the bounds of normal fluctuations, one cannot be sure that the present warming is not at least in part caused by CO₂ . In the end the worries about Global Warming rest upon the GCMs. How good are these models and to what extent can they be trusted?

GCMs are essentially the same models that are used for weather prediction. They solve Newton's equations of motion combined with thermodynamics, radiative transfer processes and other physical processes. The world is broken into a grid of cells of perhaps 10-100 km in size. The vertical profile of the atmosphere and ocean is taken into account by a dozen or so vertical layers with details varying significantly between different GCMs. The conditions of the atmosphere are then calculated at some time step into the future.

Basic physics can be used to make some phenomenal predictions. Newton's laws of motion and gravitation can be used to predict the position of the planets into the distant future with remarkable accuracy. When NASA sends a space probe to Pluto, we know where Pluto will move to in the few years that it takes the probe to travel the distance. These remarkable predictions can be made because we have a very good understanding of the physics, and an equally good understanding of the uncertainties. In the case of gravity, which determines the movement of the planets, the product of the Gravitational Constant (G) and the suns mass (M) is a crucial number and is

GM = 398600.4418 ± 0.0008 km³/s²

Note the number of significant figures. It has an accuracy of better than 1 part in a hundred million.

GCMs also use Newton’s laws of motion, but they also rely upon other far less well understood areas of physics such as the formation of clouds which are crucial to the predictions.

In many cases physical processes are "parameterized" by very crude approximations which are only vaguely based upon what might be described as deep and fundamentally understood physics. Whereas space flight relies upon the gravitational constant given above, sometimes with a correction by Einstein’s relativity, GCMs rely upon dozens or even hundreds of very poorly constrained constants . Many of these are not known to an accuracy of better than 1 part in 100, and in some cases, it is very difficult to make any meaningful uncertainty estimate of the constant.

So the problem boils down to the fact that climate is a horribly complicated and many aspects of simulations are poorly rooted in well-understood basic physics. But this by itself is not a reason to ignore the GCMs. One might be surprised to learn that many areas of science and engineering rely upon models where very crude parameterisations are necessary. These models are tested against data and a measure of their accuracy can be gauged. Parameters are "tuned" to give better accuracy. In the end, if the models make a good prediction, who cares how pure they are?

The GCMs can give a very good prediction of the weather up to a week in advance. The various parameters can be tuned to improve accuracy, and this process of tuning can continue as more data becomes available with time. This is a process which our own Bureau of Meteorology uses with its weather prediction models.

Provided we work within the bounds of conditions for which the models have been tuned, we can make reasonable predictions, and most importantly, make an estimate in the uncertainly of the prediction. But this is a big problem when we use the models for CO₂ variations; we are using them to make predictions for conditions outside the range of conditions for which they have been tuned.

We presently have little data on the affect of changes in CO₂ on the weather (or climate) so we don’t know if the parameterizations are applicable to this new scenario. We have insufficient data to be sure that we can rely on the models to extrapolate to a new climate regime. This would not be a problem if we had a good understanding of the physics such as with the space shot to Pluto.