Climate Modelling

Physicist Joanna D. Haigh on how climate modelling can help in weather forecasting, the role of fundamental physic equations, and various factors that influence climate change

videos | May 18, 2018

In studying the climate we can do it in many different ways. We need observations to tell us about the structure of the atmosphere and oceans, and how they change. Then we need the physics to understand that, and then we now increasingly use climate models. By that I don’t mean a physical model constructed out of string or straws, or plastic, or whatever. I mean a computer model, which is based on the fundamental physics and mathematics that we understand and put into a way that the computer can interpret and integrate.

So, climate models are, as I say, built very basic physics understanding. If I can just go through some equations that you may be familiar with. The first one is Newton’s second law of motion. You will know forces mass times acceleration or acceleration is force per unit mass. Now we’re talking about the forces acting on a parcel of air or indeed in the oceans. I’m going to focus on the atmosphere. The forces acting on a parcel of air are: number one – gravity – will be putting it towards the Earth, number two pressure gradients. So, you have seen weather maps with high pressure regions and low pressure regions everything else being equal, the air would try to go from the high pressure to a low pressure. It doesn’t because of the next sort of force (it’s not really a force, but it’s how it appears to be a force). It’s called the Coriolis force and that’s due to the fact that the Earth is rotating. The fourth force we need to consider is if frictional drag or viscosity.

We can write down fources mass times acceleration with those forces and that’s the first equation or actually three equations, because it’s a vector. We’ve got to go up down left right and forward and back, so there are three equations there as a starting point.

The next equation that we use is conservation of energy. That’s telling us if we have a parcel of air and we add heat to it, either it will get hot or it will expand. That’s very easy to understand equation. The third equation is conservation of mass. That’s saying that if we have a volume of air and we have motion through it, if the air accumulates, the density will go up or it’ll go out the other side. That’s just the conservation of mass. The final equation is just the equation of state. You would have heard of the ideal gas law, for example.

Physicist Joanna D. Haigh on greenhouse gases, the impact of aerosols on climate change, and how clouds reflect radiation
Now we’ve had six equations: three for the momentum, one for the mass, one for the heating and one for the equation of state. Six equations and we’ve got six unknowns: we’ve got pressure, temperature, density, and three components of wind. So, we have simultaneous equations and we can solve them.

I described the fundamental physics that goes into the equations that are used in the climate models, but of course the problem comes in the implementation. In the thermodynamic equation I mentioned, how we needed to know the heating sources and they will come from, for example, solar radiation heating the atmosphere, heat radiation leaving the atmosphere, they come from latent heat release, when water is evaporated or condensed. All those need to be included in this heating term. Then I described how we need to know about the frictional forces. Here, of course, we need to have some sort of representation of air flowing over rough surfaces (forests or mountains). And again this is very difficult to describe accurately.

Another factor that we need to include in the models is the topography: we can either have a very smooth surface or we can try and put in the mountains and cover properly. In the climate models they will have topographic variations: mountains and valleys prescribed at the resolution of the model to try and make it more accurate. That brings us on to the whole issue of resolution.

When we write down these equations, we can do them in a variety of ways. The most common way is to write each on grid, which is covering the globe, perhaps, latitude and longitude, and then different levels in height. So, you’ve got a three-dimensional grid and you solve the equations at each of these points on the grid. You iterate in time and you solve them all again, and that is what is running the computer model.

Another complication that I haven’t mentioned yet is how we create clouds and indeed rainfall and snow. We understand the physics of clouds to a fairly good extent. It’s been studied over many years, many centuries indeed. When you have air rising, it cools and the water vapor tend to condense out and form clouds. So, while the fundamental equations are very easy to write down and very easy to understand, actually the implicit implementation becomes more complicated and yet the actual physics of the problem needs to be specified very carefully. Then we integrate in time and we can understand actually the same equations are used for forecasting the weather as for integrating it into the climate in the future. So, we step forward in time and we see what happens.

When you set down these equations on a grid and you’re going to solve them numerically, you have to start from somewhere. If you are doing a weather forecast, you have all the data that’s coming in today, and you start today, and you do it tomorrow and then you correct it from the data and you do it again, and you correct it, and you do it again. Each time you’re essentially initializing the whole data set, you are making store that is starting in a correct place.

What we find with climate modeling, very long distance into the future, if we start from a very slightly different initial data set, the evolution of the climate will go in different ways. You can start it from a slightly different point and it will wiggle into the future in different sort of ways. You can run this hundreds of times and you’ll get different wiggles overlying each other into the future. We can’t say particularly what wiggle is on: the Earth will be on one wiggle, but we can’t say precisely which wiggle. We do know that overall of the wiggles will give us an envelope of possibilities into the future. When we forecast climate change, we can see how we get an envelope of variability, which tracks into the future in one way or another depending on what we assume particularly with regard to the concentrations of greenhouse gases.

When we use climate models, we need to think in advance what question it is we’re trying to answer or what it is that we’re actually trying to use them for. We have this big climate model and we can ask different questions of it. We can say: “What would happen, if the cloud physics is slightly different to what we had originally assumed?” That means, for example, if the air temperature went a little bit colder and would the ice crystals get a little bit bigger, how much would that affect the temperature? How much the temperature would affect that and how much that would affect the climate in general? That’s one particular question.

Another question is how we represent air-sea interactions. I’ve talked about heating of the atmosphere. There’s also heating of the oceans and there’s transfer of heat between the atmosphere and oceans, and, of course, of water vapor. How we represent those processes and how they depend on the wind speed and on the humidity is crucial to how the model behaves and how we understand the behavior.

Professor of Biosphere and Climate Impacts Iain Colin Prentice on global warming, the science of ecology, and climate models with a long time perspective
If we want to look into the future, looking ahead to what is going to happen with climate change, of course, we have to make some assumptions about how the composition of the atmosphere will change. That’s a big question that climate scientists can’t answer. That’s really for the economist’s to tell us how much coal or whatever is going to be burnt in the future, what will the CO2 concentration of the atmosphere be. Then we can use those as input data to the model and see how they respond.

We can also look at the coupling between things like climate change and temperature, and air quality. You’ll be aware that when you use coal-fired power stations, they not only emit CO2, they also emit an awful lot of particulates. Basically, it’s sulfate particles. So, those sulfate particles will affect people’s health, but that’s not what I’m going to talk about now. It’ll also affect the radiation balance. It reflects sunshine back to space. There is an interesting byplay between the greenhouse gas heating the atmosphere and these particulates reflecting sunshine to space, which tends to cool the atmosphere, and how these two things interact together and that depends very much on the physical properties of those aerosol particles. So again, we need to prescribe these in the model to try and see if we can get a better simulation.

There’s a number of developments in climate modelling, all of which are very interesting and very exciting ones. One, of course, is the use of more and more high-powered computers, which is going to enable us to have much better high-resolution simulation, higher spatial resolution, and also a better representation of individual processes.

We’re never going to be able to simulate in detail all the parts of the climate system. You’d need to get down to tiny little scales of molecules. You can’t do that. If we can get down to 10 meters and we can really see the shape of clouds, for example, which we can’t do at the moment. There is also better understanding going on of the physical processes, these processes between the particulate in the atmosphere. We’ve got industrial pollution, we’ve also got natural particulates, say sea salt, we’ve got dust coming from the blown up, from the deserts and all these things hanging around in the air. What they do to the radiation budget in the climate, we will be able to understand that in more detail in the future. Tying all these things together, I hope and I predict that we will have a much stronger ability to constrain how climate is evolving and our understanding of it in the future.

Professor, Faculty of Natural Sciences, The Grantham Institute for Climate Change, Imperial College London; Co-Director,Grantham Institute forClimate Change&Environment
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