General Circulation Models or Global Climate Models – aka GCMs – often have a bad reputation outside of the climate science community. Some of it isn’t deserved. We could say that models are misunderstood.
Before we look at models on the catwalk, let’s just consider a few basics
In an earlier series, CO2 – An Insignificant Trace Gas we delved into simpler numerical models. These were 1d models. They were needed to solve the radiative transfer equations through a vertical column in the atmosphere. There was no other way to solve the equations – and that’s the case with most practical engineering and physics problems.
Here’s a model from another world:
Here’s a visualization of “finite element analysis” of stresses in an impeller. See the “wire frame” look, as if the impeller has been created from lots of tiny pieces?
In this totally different application, the problem of calculating the mechanical stresses in the unit is that the “boundary conditions” – the strange shape – make solving the equations by the usual methods of re-arranging and substitution impossible. Instead what happens is the strange shape is turned into lots of little cubes. Now the equations for the stresses in each little cube are easy to calculate. So you end up with 1000’s of “simultaneous” equations. Each cube is next to another cube and so the stress on each common boundary is the same. The computer program uses some clever maths and lots of iterations to eventually find the solution to the 1000’s of equations that satisfy the “boundary conditions”.
Finite element analysis is used successfully in lots of areas of practical problem solving, many orders simpler of course, than GCMs.
Uses of Models
One use of models is to predict, no project, future climate scenarios. That’s the one that most people are familiar with. And to supply the explanation for recent temperature increases.
But models have more practical uses. They are the only way to provide quantitative analysis of certain situations we want to consider. And they are the only way to test our understanding of the causes of past climate change.
On this blog one commenter asked about how much equivalent radiative forcing would be present if all the Arctic sea ice was gone. That is, with no sea ice, there is less reflection of solar radiation. So more absorption of energy – how do we calculate the amount?
You can start with a very basic idea and just look at the total area of Arctic sea ice as a proportion of the globe, and look at the local change in albedo from around 0.5-0.8 down to 0.03-0.09, multiply by the current percentage area in sea ice to find a number in terms of the change in total albedo of the earth. You can turn that into the change in radiation.
But then you think a little bit deeper and want to take into account the fact that solar radiation is at a much lower angle in the Arctic so the first number you got probably overstated the effect. So now, even without any kind of GCM, you can simply use the equation for the reduction in solar insolation due to the effective angle between the sun and the earth:
I = S cos θ – but because this angle, θ, changes with time of day and time of year for any given latitude you have to plug a straightforward equation into a maths program and do a numerical integration. Or write something up in Visual Basic or whatever your programming language of choice is. Even Excel might be able to handle it.
This approach also gives the opportunity to introduce the dependence of the ocean’s albedo on the angle of sunlight (the albedo of ocean with the sun directly overhead is 0.03 and with the sun almost on the horizon is 0.09).
This will give you a better result. But now you start thinking about the fact that the sun’s rays are travelling in a longer path through the atmosphere because of the low angle in the sky.. how to incorporate that? Is it insignificant or highly significant? Perhaps including or not including this effect would change the “radiative forcing” by a factor of two? (I have no idea).
So if you wanted to quantify the positive feedback effect of melting ice your “model” starts requiring a lot more specifics. Atmospheric absorption by O2 and O3 depending on the angle of the sun. And the model should include the spatial profile of O3 in the stratosphere (i.e., is there less at the poles, or more).
It’s only by doing these calculations that the effect of sea ice albedo can be reliably quantified. So your GCM is suddenly very useful – essential in fact.
Without it, you would simply be doing the same calculations very laboriously, slowly and less accurately on pieces of paper. A bit like how an accounts department used to work before modern PCs and spreadsheets. Now one person in finance can do the job of 10 or 20 people from a few decades ago. Without an accountant someone can just change an exchange rate, or an input cost on a well-created spreadsheet and find out the change in cash-flow, P&L and so on. Armies of people would have been needed before to work out the answers.
And of course, the beauty of the GCM is that you can play around with other factors and find out what effect they have. The albedo of the ocean also changes with waves. So you can try some limits between albedo with no waves and all waves and see the change. If it’s significant then you need a parameter that tells you how calm or stormy the ocean is throughout the year. And if you don’t have that data, you have some idea of the “error”.
Everyone wants their own GCM now..
Of course, in that thought experiment about sea ice albedo we haven’t calculated a “final” answer. Other effects will come into play (clouds).. But as you can see with this little example, different phenomena can be progressively investigated and reasonably quantified.
Do we understand the causes of past climate change or not? Do the Milankovitch cycles actually explain the end of the last ice age, or the start of it?
This is another area where models are invaluable. Without a GCM, you are just guessing. Perhaps with a GCM you are guessing as well, but just don’t know it.. A topic for another day.
The idea floats around that models have “positive feedback” plugged into them. Positive feedback for those few who don’t understand it.. increases in temperature from CO2 will induce more changes (like melting Arctic sea ice) that increase temperature further.
Unless it’s done very secretly, this isn’t the case. The positive feedbacks are the result of the model’s output.
The models have a mixed bag of:
- fundamental equations – like conservation of energy, conservation of momentum
- parameterizations – for equations that are only empirically known, or can’t be easily solved in the “grid” that makes up the 3d “mesh” of the GCM
More on these important points in the next post.
“Necessary but Not Sufficient”
A last comment before we see them on the catwalk – the catwalk “retrospective” – is that models matching the past is a necessary but not sufficient condition for them to match the future. However, it is – or it would be – depending on what we find.. a great starting point.
Models On the Catwalk
Most people have seen this graph. It comes from the IPCC AR4 (2007).
The IPCC comment:
Models can also simulate many observed aspects of climate change over the instrumental record. One example is that the global temperature trend over the past century (shown in Figure 1) can be modeled with high skill when both human and natural factors that influence climate are included.
In summary, confidence in models comes from their physical basis, and their skill in representing observed climate and past climate changes. Models have proven to be extremely important tools for simulating and understanding climate, and there is considerable confidence that they are able to provide credible quantitative estimates of future climate change, particularly at larger scales. Models continue to have significant limitations, such as in their representation of clouds, which lead to uncertainties in the magnitude and timing, as well as regional details, of predicted climate change. Nevertheless, over several decades of model development, they have consistently provided a robust and unambiguous picture of significant climate warming in response to increasing greenhouse gases.
Now of course, this is a hindcast. Looking backwards. One way to think about a hindcast is that it’s easy to tweak the results to match the past. That’s partly true and, of course, that’s how the model gets improved- until it can match the past.
The other way to think about the hindcast is that it’s a good way to test the model and find out how accurate it is.
The model gets to “past predict” many different scenarios. So if someone could tweak a model so that it accurately ran temperature patterns, rainfall patterns, ocean currents, etc – if it can be tweaked so that everything in the past is accurate – how can that be a bad thing? Also the model “tweaker” can change a parameter but it doesn’t give the flexibility that many would think. Let’s suppose you want to run the model to calculate average temperatures from 1980-1999 (see below) so you put your start conditions into the model, which are values for 1980 for temperature and all other “process variables” and crank up the model.
It’s not like being able to fix up a painting with a spot of paint in the right place – it’s more like tuning an engine and hoping you win the Dhaka rally. After you blew the engine halfway through you get to do a rebuild and guess what to change next. Well, analogies – just illustrations..
Obviously, these results would need to be achieved by equations and parameterizations that matched the real world. If “tweaking” requires non-physical laws then that would create questions. Well, more on this also in later posts.
More model shots.. The top graphic is the one of interest. This is actual temperature (average 1980-1999) in contours with the shading denoting the model error (actual minus model values). Light blue and light orange (or is it white?) are good..
The model error is not so bad. Not perfect though. (Note that for some reason, not explained, the land temperature average is over a different time period than sea surface temperatures).
The standard deviation in temperature gives a measure of the range of temperatures experienced. The colors on the globe indicate the difference between the observed and simulated standard deviation of temperatures.
Simplifying, the light blue and light orange areas are where the models are best at working out the monthly temperature range. The darker colors are where the models are worse. Looks pretty good.
This one is awesome. Remember that rainfall is calculated by physical processes. Temperature, available water sources, clouds, temperature changes, winds, convection..
Ocean potential temperature, what’s that? Think of it as the real temperature with unstable up and down movements factored out, or read about potential temperature.. Note that the contours are the measurements (averaged over 34 years) and the shaded colors are the deviations of actual – model. So once again the light blue and light orange are very close to reality, the darker colors are further away from reality.
This one you would expect to be easier to get right than rainfall, but still, looking good.
It’s just the start of the journey into models. There will be more, next we will look at Models Off the Catwalk. So if you have comments it’s perhaps not necessary to write your complete thoughts on past climate, chaos.. Interesting, constructive and thoughtful comments are welcome and encouraged, of course. As are questions.
Hopefully, we can avoid the usual bunfight over whether the last ten years actual match the model’s predictions. Other places are so much better for those “discussions”..
Update – Part Two now published.