Q&A: How do climate models work? - What is a climate model?

Carbon Brief | Robert McSweeney and Zeke Hausfather | 15 January 2018

A global climate model typically contains enough computer code to fill 18,000 pages of printed text; it will have taken hundreds of scientists many years to build and improve; and it can require a supercomputer the size of a tennis court to run.

The models themselves come in different forms – from those that just cover one particular region of the world or part of the climate system, to those that simulate the atmosphere, oceans, ice and land for the whole planet.

The output from these models drives forward climate science, helping scientists understand how human activity is affecting the Earth’s climate. These advances have underpinned climate policy decisions on national and international scales for the past five decades.

In many ways, climate modelling is just an extension of weather forecasting, but focusing on changes over decades rather than hours. In fact, the UK’s Met Office Hadley Centre uses the same “Unified Model” as the basis for both tasks.

The vast computing power required for simulating the weather and climate means today’s models are run using massive supercomputers.

The Met Office Hadley Centre’s three new Cray XC40 supercomputers, for example, are together capable of 14,000 trillion calculations a second. The timelapse video below shows the third of these supercomputers being installed in 2017.

Fundamental physical principles

So, what exactly goes into a climate model? At their most basic level, climate models use equations to represent the processes and interactions that drive the Earth’s climate. These cover the atmosphere, oceans, land and ice-covered regions of the planet.

The models are based on the same laws and equations that underpin scientists’ understanding of the physical, chemical and biological mechanisms going on in the Earth system.

For example, scientists want climate models to abide by fundamental physical principles, such as the first law of thermodynamics (also known as the law of conservation of energy), which states that in a closed system, energy cannot be lost or created, only changed from one form to another.

Another is the Stefan-Boltzmann Law, from which scientists have shown that the natural greenhouse effect keeps the Earth’s surface around 33C warmer than it would be without one.

Then there are the equations that describe the dynamics of what goes on in the climate system, such as the Clausius-Clapeyron equation, which characterises the relationship between the temperature of the air and its maximum water vapour pressure.

The most important of these are the Navier-Stokes equations of fluid motion, which capture the speed, pressure, temperature and density of the gases in the atmosphere and the water in the ocean.

However, this set of partial differential equations is so complex that there is no known exact solution to them (except in a few simple cases). It remains one of the great mathematical challenges (and there is a one million dollar prize awaiting whoever manages to prove a solution always exists). Instead, these equations are solved “numerically” in the model, which means they are approximated.

Scientists translate each of these physical principles into equations that make up line after line of computer code – often running to more than a million lines for a global climate model.

The code in global climate models is typically written in the programming language Fortran. Developed by IBM in the 1950s, Fortran was the first “high-level” programming language. This means that rather than being written in a machine language – typically a stream of numbers – the code is written much like a human language.

You can see this in the example below, which shows a small section of code from one of the Met Office Hadley Centre models. The code contains commands such as “IF”, “THEN” and “DO”. When the model is run, it is first translated (automatically) into machine code that the computer understands.

There are now many other programming languages available to climate scientists, such as C, Python, R, Matlab and IDL. However, the last four of these are applications that are themselves written in a more fundamental language (such as Fortran) and, therefore, are relatively slow to run. Fortran and C are generally used today for running a global model quickly on a supercomputer.

Spatial resolution

Throughout the code in a climate model are equations that govern the underlying physics of the climate system, from how sea ice forms and melts on Arctic waters to the exchange of gases and moisture between the land surface and the air above it.

The figure below shows how more and more climate processes have been incorporated into global models over the decades, from the mid-1970s through to the fourth assessment report (“AR4”) of the Intergovernmental Panel of Climate Change (IPCC), published in 2007.

So, how does a model go about calculating all these equations?

Because of the complexity of the climate system and limitation of computing power, a model cannot possibly calculate all of these processes for every cubic metre of the climate system. Instead, a climate model divides up the Earth into a series of boxes or “grid cells”. A global model can have dozens of layers across the height and depth of the atmosphere and oceans.

The image below shows a 3D representation of what this looks like. The model then calculates the state of the climate system in each cell – factoring in temperature, air pressure, humidity and wind speed.

For processes that happen on scales that are smaller than the grid cell, such as convection, the model uses “parameterisations” to fill in these gaps. These are essentially approximations that simplify each process and allow them to be included in the model. (Parameterisation is covered in the question on model tuning below.)

The size of the grid cells in a model is known as its “spatial resolution”. A relatively-coarse global climate model typically has grid cells that are around 100km in longitude and latitude in the mid-latitudes. Because the Earth is a sphere, the cells for a grid based on longitude and latitude are larger at the equator and smaller at the poles. However, it is increasingly common for scientists to use alternative gridding techniques – such as cubed-sphere and icosahedral – which don’t have this problem.

A high-resolution model will have more, smaller boxes. The higher the resolution, the more specific climate information a model can produce for a particular region – but this comes at a cost of taking longer to run because the model has more calculations to make.

The figure below shows how the spatial resolution of models improved between the first and fourth IPCC assessment reports. You can see how the detail in the topography of the land surface emerges as the resolution is improved.

In general, increasing the spatial resolution of a model by a factor of two will require around 10 times the computing power to run in the same amount of time.

Time step

A similar compromise has to be made for the “time step” of how often a model calculates the state of the climate system. In the real world, time is continuous, yet a model needs to chop time up into bite-sized chunks to make the calculations manageable.

Each climate model does this in some way, but the most common approach is the “leapfrogging method”, explains Prof Paul Williams, professor of atmospheric science at the University of Reading, in a book chapter on this very topic:

“The role of the leapfrog in models is to march the weather forward in time, to allow predictions about the future to be made. In the same way that a child in the playground leapfrogs over another child to get from behind to in front, the model leapfrogs over the present to get from the past to the future.”

In other words, the model takes the climate information it has from the previous and present time steps to extrapolate forwards to the next one, and so on through time.

As with the size of grid cells, a smaller time step means the model can produce more detailed climate information. But it also means the model has more calculations to do in every run.

For example, calculating the state of the climate system for every minute of an entire century would require over 50m calculations for every grid cell – whereas only calculating it for each day would take 36,500. That’s quite a range – so how do scientists decide what time step to use?

The answer comes down to finding a balance, Williams tells Carbon Brief:

“Mathematically speaking, the correct approach would be to keep decreasing the time step until the simulations are converged and the results stop changing. However, we normally lack the computational resources to run the models with a time step this small. Therefore, we are forced to tolerate a larger time step than we would ideally like.”

For the atmosphere component of climate models, a time step of around 30 minutes “seems to be a reasonable compromise” between accuracy and computer processing time, says Williams:

“Any smaller and the improved accuracy would not be sufficient to justify the extra computational burden. Any larger and the model would run very quickly, but the simulation quality would be poor.”

Bringing all these pieces together, a climate model can produce a representation of the whole climate system at 30-minute intervals over many decades or even centuries.

As Dr Gavin Schmidt, director of the NASA Goddard Institute for Space Studies, describes in his TED talk in 2014, the interactions of small-scale processes in a model mean it creates a simulation of our climate – everything from the evaporation of moisture from the Earth’s surface and formation of clouds, to where the wind carries them and where the rain eventually falls.

Schmidt calls these “emergent properties” in his talk – features of the climate that aren’t specifically coded in the model, but are simulated by the model as a result of all the individual processes that are built in.

It is akin to the manager of a football team. He or she picks the team, chooses the formation and settles on the tactics, but once the team is out on the pitch, the manager cannot dictate if and when the team scores or concedes a goal. In a climate model, scientists set the ground rules based on the physics of the Earth system, but it is the model itself that creates the storms, droughts and sea ice.

So to summarise: scientists put the fundamental physical equations of the Earth’s climate into a computer model, which is then able to reproduce – among many other things – the circulation of the oceans, the annual cycle of the seasons, and the flows of carbon between the land surface and the atmosphere.

You can watch the whole of Schmidt’s talk below.

While the above broadly explains what a climate model is, there are many different types. Read on to the question below to explore these in more detail.