Hello and welcome to this introduction to climate modeling. How likely is it that the area where you live will be affected by rising sea level within your lifetime? Or perhaps affected by extreme weather events like droughts or floods? What's the likely range of possibilities for future global temperatures, given the range of possible future pathways we might choose? Or how is Earth's climate system as a whole likely to respond to future changes in energy flows?
Climate models can help us understand how Earth's climate system works, and they are our only tools for peering into the future to help us estimate the likely ranges of possibility down the road. We can't actually run more than one experiment on the real planet Earth, so climate models allow us to try out all sorts of what-if scenarios. We can turn things on and off, and we can see what happens.
If you've ever folded a piece of paper into the shape of an airplane and thrown it, You have made a model. If you speak or write or gesture in some language, you're using a model. Language is a representation of your thoughts, but can never really quite be what you're thinking. Though in our language, we do aim to get as close as possible to communicating what it is that we're thinking.
We use physical models in architecture to show what something might look like if we were to build it. We use models in engineering to test designs before putting the time, effort, and energy into building the real thing. We even model our own futures ourselves, and our models help us plan ahead because we have expectations of the future. We expect, for example, that next winter will be colder than the following summer. We might not know exactly how cold or how warm the seasons next year will be, but we have a pretty good idea what clothes would be useful to have handy and whether it would be useful to buy a snow shovel.
How is it that we're able to model these things? We have experience and we have observations from the world around us. We certainly have varying levels of confidence in our experience and our observations, depending on how extensive they are, how many times they might have been repeated, and whether we're pretty sure we've considered most of the things that are relevant or if we're leaving something out.
Essentially, our models of the future fit within what we think is the likely range of possibility, and we revise and refine them all the time. as we gain new insights. Climate modeling is conceptually similar to the future modeling you and I do all the time for ourselves. Climate models are based on physical principles of how the world works.
Things like conservation of mass and energy, gravity, laws of motion, how chemical reactions work, and what we know about how biology works. These models don't exist in a vacuum, nor do they arise out of thin air. They are our attempts to represent Earth's climate system with the purpose to help us learn more about it, since, again, we can't run a global-scale, real-life experiment here more than once.
This is a drawing of the major components of Earth's climate system, with arrows representing the flows of mass and energy among the different parts. This essentially represents a static model of what Earth's climate system looks like, which helps us get started thinking about it. The next step...
is to try to represent how the mass and energy flow through the system, turning this into something dynamic that can change over time. We'd use what we know about physics, chemistry, and biology to give the model information about how different processes work and how fast and under what conditions. So we're giving the model information about how to deal with stocks and flows. Typically, this is done using a bunch of equations, which represent stocks, flows, and feedbacks.
including time scales on which different processes operate, and then the equations are solved by a computer. Once we've built a model, and it seems to operate with reasonable stability, then we could add, for example, some kind of perturbation. Then, if our model does a decent job of linking the different parts together, we could see how that perturbation ripples through the system and affects other parts. We could see whether and how fast the system approaches some equilibrium again, and what processes were largely responsible. We could actually turn different processes on or off to try to isolate their influence on the system.
Again, something we can't do on the real planet. We also test our climate models output against observations of the real world, and we might find out that the model aligns well with those observations, or we might find out that we need to revise the model, or maybe... that we need to go out and make some more real-world observations to get a better handle on how things really work.
Here's an example of a real-world constraint on climate models that has to do with the relative proportions of liquid water and water vapor. At warmer temperatures, more of the water present will be in vapor form, and at colder temperatures, less of the water present will be in vapor form, and more will be as liquid water or even solid ice, which isn't shown here. If a model is trying to represent what happens to water cycling through the climate system, it would have to take into account how the proportion of vapor to liquid changes if the temperature changes. If some air warms up in the model, then the model should also make some of the water in that air change phase from liquid to vapor within some range that makes physical sense.
If some air cools, as is common, and as air rises through the atmosphere, then in the model, some of the water vapor present in the air should condense. Using a relationship like this, which is based on observations in the real world, a modeler can tell the model what to do with water as temperature changes. This is just one example.
of how observations help inform what goes into climate models. There are many more, like the rate at which CO2 exchanges with the ocean, or the heat capacity of water, or the average growth of trees each year, or the temperature profile of the atmosphere. Ideally, climate models align with physical reality. So, observations inform climate models, but climate models also can inform observations.
For example, we've talked about how some of the excess CO2 emitted from human activities gets taken up by plants on land and some gets taken up by the oceans. With models and observations together, we can learn in more detail, more specifically, about where that carbon goes. Observations of atmospheric carbon dioxide in different parts of the world can be incorporated into models of atmospheric circulation, which tell us how the air moves around. And the output from those air circulation models can indicate which parts of the world are likely responsible for the uptake of CO2 from the atmosphere.
Is it tropical forests? Is it certain areas of the ocean? The model output can actually help people decide in what regions of Earth would it be useful to conduct further observational work.
Okay, to illustrate a climate model using information we've encountered earlier, we're going to construct a simple energy balance model. This model uses essentially one physical relationship, and we've seen it before. It's the Stefan-Boltzmann equation, which relates energy output to the temperature of an object.
You'll recall from earlier that warmer objects emit more energy, and that energy goes up as a function of the object's temperature raised to the fourth power. So it goes up exponentially as things heat up. We'll use that equation, plus some addition and subtraction of energy flows, to make this model.
First, we'll start with something completely unrealistic. Imagine turning off the sun so there's no solar energy coming in. We'll let the Earth's surface keep its tiny amount of geothermal energy coming from the planet's interior, about 0.06 watts per meter squared. With this little energy flow, Earth's surface has to emit 0.06 watts per meter squared to be in thermal equilibrium, and it can do that at a temperature of about 32 Kelvin. or about minus 241 degrees Celsius.
Now we'll turn on the sun to its current energy output, which means Earth gets about 341 watts per meter squared. This is an example of an observation that's used in climate models. If we want to model the Earth, we need to use a realistic number for the incoming solar radiation.
We'd use a different number if we were modeling Mars, for example. Okay, we're going to assume for now that Earth absorbs all the radiation it gets from the Sun. Nothing is reflected and there are no greenhouse gases.
When the Sun first turns on, Earth is emitting just 0.06 watts per meter squared, but now it's getting 341 watts per meter squared. So we have an imbalance. Over time, Earth warms up until it reaches the right temperature to emit the same amount of energy as it absorbs.
That temperature, according to Stefan Boltzmann, where energy Inflow equals energy outflow is about 278 Kelvin, or about 5 degrees Celsius. So that's a very simple model, and it doesn't quite capture what's really going on. So let's add another important process, reflection.
First, a question for you. What's going to happen to the temperature of our modeled Earth after we add reflection? Will temperature go up, go down, stay the same?
What's going to happen? Today, Earth reflects about 30% of the incoming energy from the Sun. So let's make our model do that. Now Earth's surface only absorbs 70% of what's coming in. So it only has to re-emit 239 watts per meter squared.
And so it cools down to a new equilibrium, where energy inflow equals energy outflow, now at minus 18 degrees Celsius. So that's a little closer to representing the real Earth. And minus 18 Celsius is about the temperature of the upper atmosphere. And the temperature Earth's surface would be if we had 30% reflection and no greenhouse gases.
Next step, add greenhouse gases. For our purpose here, we're going to make a simplifying assumption that the greenhouse gases absorb all the radiation coming from our surface, and they re-emit half of it upward and half of it downward. just to make things conceptually more straightforward. We know that for the planet to be in energy balance, the upward emission from greenhouse gases will have to equal the solar inflow minus reflection. So that's 239 watts per meter squared.
We've assumed in this model that the downward emission from greenhouse gases equals the upward emission. So that's also 239 watts per meter squared. So now, Earth's surface is absorbing 239 from the Sun, plus 239 from greenhouse gases, so it has to re-emit two times 239 watts per meter squared back upward, in order for inflow to equal outflow. And so it warms up to 303 Kelvin, or 30 degrees Celsius.
If we take a look at what happens to our energy balance model over time, it looks something like this. From the left, we start... just when we conceptually turn the sun back on, and suddenly inflow far exceeds outflow.
The red line is way above the green line. Temperature is the blue line, and you can see the Earth starts off very cold, and it takes some time for it to warm up to its new equilibrium temperature with its new inflow of energy from the sun. When it does warm up enough, so that inflow equals outflow, our model Earth's temperature stabilizes at about 5 degrees Celsius.
But then we added reflection. So 30% of the incoming solar energy gets reflected away immediately, and our model Earth cools down to minus 18 Celsius. Then we added greenhouse gases to the model, and it warmed up again, and it stabilized at about 30 degrees Celsius once outflow caught up with inflow again. So one thing to notice is that there are transition periods in the model.
When we change something, Earth doesn't respond immediately. There's some lag time before it reaches a new equilibrium state. Okay, so there's an example of an energy balance model with some assumptions and some simplifications.
And this model produces a temperature for Earth's surface that we can compare to observations again and see how it does. Well, Earth's average surface temperature is about 15 degrees Celsius, not 30. So how could our model get closer to approximating reality? Well, we could divide the atmosphere into layers and could more realistically represent the flows of energy due to greenhouse gases in the atmosphere, which aren't simply half up and half down.
We could also take into account the fact that some energy emitted from Earth's surface proceeds directly to space. It doesn't all get absorbed by greenhouse gases. Or we could include that some energy leaves Earth's surface through latent heat transfer and thermals, not only via radiation. We could get specific about what's on Earth's surface. Is it water?
Is it rock? We could make our energy balance model more closely approximate the real Earth by dividing our model planet into different latitude bands, not just treat the whole thing as one big average. The purpose of going through this model is to illustrate how we can use a few equations and construct a model that actually does approximate some of the processes happening on Earth. You could build this model yourself in a spreadsheet.
With more sophistication, you could include more processes, giving them magnitudes based on observations in the real world, and bring your model closer to resembling reality. To summarize, with climate models, we're attempting to represent Earth's climate system. So it's important to ground the model in how physics, chemistry, and biology work in the real world. We use real-world observations to help define what's realistic in a model.
And sometimes modeling can help us decide what new observations would be helpful. Ultimately, people build models to help better understand Earth's climate system. It's an ongoing effort.