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.

One unfair criticism of the GCMs goes like this; "if the models can’t predict the weather 2 weeks in advance how can they hope to predict the weather 100 years in advance"?However we are not interested in predicting the weather on perhaps December 25^th 2110. What we want to know is what will be the average weather (i.e climate) in a few decades around 2110.

A more realistic expectation should be that the model will predict a weekly average one week in advance, a monthly average a month in advance and a ten year average ten years in advance etc.

The table below gives an indication of the usefulness of GCMs/weather models for different forecast periods. Over a few days they give predictions which are nothing short of brilliant and a real triumph of modern physics. They are certainly useful for periods of up to a couple of months for predicting phenomenon such as El Niño and La Nina events. However my own experience with forecasting El Niño events is that the GCMs are no better than trivially simple models (Halide and Ridd, 2008) so it is doubtful that the impressive complexity of the GCMs contributes a great deal to accuracy.

At periods greater than a few months, the GCMs fail. They do not simulate the cooling of the '40s to '70s (decadal scale), the Holocene Climatic Optimum (millennial scale) or the large scale events associated with glaciations (10000 year time scale). In the light of such comprehensive failure of the models over periods from 1 to 10000 years, why would one believe that GCMs would be accurate over the 100 year time scales which are of greatest concern to us?

A close examination of the GCMs indicate that despite the horrific complexity of the models, a few processes completely dominate the predictions.

The most important is the well-documented water vapour positive feedback . C0₂ doubling by itself would create a temperature rise of around 1^o, i.e. easily tolerable. However such a warming will allow the atmosphere to increase in absolute humidity, and because water is a very powerful greenhouse gas, this humidity increase will increase the temperature further.

It is this water vapour feedback that is necessary for the nightmare scenarios of a few degrees warming. So in the final analysis, if we can have some faith that the GCMs can handle the water vapour problem properly, albeit with a significant uncertainly, then they are useful.

So how do GCMs deal with humidity, clouds and the water cycle? The water vapour remaining in the atmosphere is the result of two processes working in opposite directions viz evaporation and rainfall. Over long periods, and averaged over the earth, these processes are in exact balance, but if C0₂ is added this balance is slightly perturbed – very slightly.

Evaporation is relatively easy to predict with a tolerable uncertainty but rainfall is a different matter. It is no coincidence that of all the parameters that the Weather Bureau predicts, rainfall is the least reliable. It is difficult to predict even whether it will rain tomorrow let alone how much. The Bureau uses qualitative terms such as "scattered or isolated showers". If they predict "rain", expect anything from bone-dry to a deluge.

Rain is formed by a very complex and poorly understood set of processes. Vertical motion of air often by unstable (and difficult to predict) convection is frequently necessary to adiabatically cool the air until a cloud forms.

The formation of cloud is very complicated and depends upon the presence of small particles upon which the drops can form. But most clouds don’t rain, and rain is necessary to remove the moisture from the atmosphere. A cloud will start to rain when the drops coalesce to form bigger drops. But even when the drops have become large enough to fall out of the cloud, it is hard to quantitatively predict how much water will be lost from the atmosphere in as rain.

It may well be a fairly hopeless ambition to model these processes in any way but the crudest manner.

In reality the parameters in the model controlling rainfall, (and there are many of them) can be tweaked to give roughly the right humidity around the world and about the right rainfall (although this is sometimes disputed). This is fine provided one is not then going to operate outside the range of conditions that the models have been tuned against. Unfortunately this is what we are forced to do in the case of C0_2. Because of the parameterisation schemes, the models inevitable create more water vapour due to an initial C0₂ warming. They hardwire positive feedback of a significant magnitude. The question is whether they get the magnitude correct.

From basic physical reasons it is plausible that the water vapour feedback is real and possibly powerful. But is assumes that no other powerful negative feedback mechanisms exist in the water cycle. For example, will all the extra water vapour produce more cloud which could have the effect of reflecting more incoming solar radiation? And will the extra cloud be at high level (where it would likely heat the earth) or at low level and cool the earth. I have no idea and it is a hotly debated topic (see hereand here).If we understood these processes better, we could have more faith.

In the end we are relying upon models which are based upon poorly understood physics and operating for conditions outside the range for which they have been tuned. They have been demonstrated to be not useful in making predictions on any timescale longer than a couple of months. Although the GCMs are of considerable scientific value in pushing ahead our understanding of climate physics, it is difficult to tell if they have any value in making predictions.