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Modelling the climate

This page attempts to give you a brief overview of how climate models work, and some details about the models used in the experiment. The page is divided into the following sections:

  1. The Unified Model
  2. Horizontal resolution - Grids
  3. Vertical resolution - Levels
  4. Time steps
  5. Parameterizations
  6. Ocean Models and their interaction with the atmosphere
  7. Chaos, Ensembles and Probabilities
  8. Map Projections, Latitude and Longitude

Introduction to Climate Models

What is a climate model? Climate models are numerical representations of various parts of the Earth's climate system. There are two ways of looking at this. In some respects, scientists are trying to reduce the complex behaviour of the climate down to a set of mathematical equations, in the hope that they can then begin to understand the processes that are going on. This is true especially of fairly simple models. In the case of state of the art General Circulation Models/ Global Climate Models (GCMs) such as the one used in the experiment, it is more a case of trying to represent everything, even if things then get so complicated that we can't always understand what's going on. The equations are tweaked, within reasonable boundaries, so that the model does as well as possible at producing past and current climates (compared to archived observations). It can then be used to try to predict what the climate is going to do in the future.

GCMs try to simulate as much as possible about the climate system: the incoming and outgoing radiation, the way the air moves, the way clouds form and precipitation falls, the way the ice sheets grow or shrink, etc. They are frequently (as in the model we use) coupled to a representation of the ocean. They may take into account how the vegetation on the Earth's surface changes. Critically, they try to calculate how all these different parts of the climate system interact, and how the feedback processes work.

This is why the "best" estimates of future climate come from general circulation models, rather than simplified models.

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The Unified Model

The atmospheric part of the model used by is the UK Met Office's state-of-the-art Unified Model; the same model that is used to produce every weather forecast you see on British terrestrial television. There are of course some differences between the way the model is run to produce a commercial weather forecast and how we are running it. The most obvious difference is the resolution. Figure 1 shows the difference in resolution over the British Isles; the resolution we are using would obviously be of no use at all for telling people how much it was going to rain in Manchester (for example).

The finer the grid box, the better the model is at getting small scale features of the
				climate, such as rainfall, right.

Figure 1. This figure shows the difference in the number of grid boxes covering the British Isles in the version of the model (left), and a regional version (right). This image shows that a regional model gives a better simulation of British rainfall than the coarser climate prediction model does. [Figure courtesy of the Hadley Centre].

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Horizontal resolution -- Grids

GCMs work by calculating what the climate is doing (in terms of wind, temperature, humidity, etc.) at a number of discrete points on the Earth's surface and in the atmosphere/ ocean. These points are laid out as a grid covering the surface of the Earth, dividing it up into a lot of little boxes (see Figure 2). The more boxes there are, the finer the resolution of the model and the smaller-scale climate features it can represent. From this point of view, the best climate model would be the one with the finest resolution. Unfortunately this has disadvantages; the more points, the more calculations need to be made, and so the more computer time the model takes to run. In general, we have to make a compromise between resolution and run time. For a weather forecast, which is only interested in what is going to happen in the next 5 days or so, the resolution can be much finer than a climate forecast that is concerned with the next few hundred years! Paleoclimate modellers, who are interested in what the climate was doing thousands of years ago, have to use even coarser resolution models.

This is why, in the model, there are only 4 grid boxes over the British Isles. This is obviously not going to do very well at representing the climate in, for example, the Lake District, which is a mountainous region which covers an area much smaller than one grid box. It should however be good enough to get an accurate picture of the large scale climate of, for example, the British Isles. The resolution is 2.5° in latitude by 3.75° in longitude.

A coarse grid of boxes covers the Earth's surface

Figure 2. A typical display from the model, showing the temperature of the surface of the Earth in each of the model grid boxes.

Regional Climate Models use a finer resolution for a limited area of the globe.

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Vertical resolutions -- Levels

In a similar way to the horizontal grid, the vertical profile of the atmosphere is divided into a number of different levels. The model used in has 19 vertical levels in the atmosphere (and 20 in the ocean), and Figure 3 shows how they are distributed in height. Unlike the horizontal grid the vertical grid is not evenly spaced. They're not even equally spaced in pressure, which could make sense as, for example, the 950 hPa (near the surface) and 900 (a bit further up) hPa levels have the same mass of air between them as the 100hPa and 50hPa levels, even though the physical distance between them is much less. This is because the density of air decreases exponentially with distance from the Earth's surface: the difference in pressure between the top of Everest (about 10km up) and about 9km up is much smaller than the difference in pressure between sea level and 1km up.

The levels are in fact unevenly spaced even in terms of pressure. This is so that they can be concentrated in the areas, i.e. near the surface, where we are more interested in knowing what is going on than at other levels. The model levels take into account what the surface is doing; so a level doesn't suddenly vanish as it intersects a mountain! The top level is at about 30km; in the middle of the stratosphere.

There are more model levels at the bottom of the atmosphere than further up

Figure 3. The 19 model levels in the version of the Unified Model, the model used by The levels are not equally spaced in altitude (right scale) or pressure (left scale).

As a result of both the horizontal and vertical gridding of the atmosphere, it is effectively divided up into three dimensional boxes; figure 4 shows how.

The whole atmosphere is divided up into 3 Dimensional boxes

Figure 4. The vertical and horizontal grid over Britain

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Time Steps

As well as dividing the atmosphere up into boxes, time also progresses in finite intervals. In the model, the basic time step is half an hour. The model starts from a set of initial conditions for the atmosphere and ocean and then calculates what they will have evolved to after half an hour, 1 hour etc. Choosing the time step is not easy. If you want to run a model through 50 years as quickly as possible, you want to use as large a time step as possible. Unfortunately, this isn't possible because, with a time step over some critical level, the model becomes unstable and stops working. In very simplified terms, you can think of this as happening when the time step is so large, that air (or, more accurately, energy) can travel further than one grid box in one time step, and it becomes impossible to accurately determine how the fields develop. However, some things in the atmosphere change more rapidly than others, and so need to be calculated more frequently. So, for example, the dynamics (essentially the movement of the air) needs to be calculated every half hour, but the radiation (the balance of incoming and outgoing energy) can be calculated less frequently. This is why, if you watch the model running, it seems to complete some time steps much more quickly than others. In the ocean, the ratio of the horizontal grid size to the length of a timestep must not exceed the largest flow speed of water in the ocean.

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The problem with dividing the atmosphere into lots of little cubes is that there are many processes that are smaller than the cubes. So, for example, individual clouds may well be smaller than a grid box. They do still play an important role in the climate system, especially collectively, so somehow the processes that form them and the consequences of them existing must be represented. So, for example, based on knowledge of the temperature and humidity in a box, we must estimate how much cloud and how much rain there is in the box. We also need to know how much dust (i.e. ‘aerosol’) is in the box, as raindrops require a very small solid particle in the air to form on. This process is called parameterizing. There are many parameterization schemes in the model, such as the scheme which calculates how much cloud there is. Some of these schemes are well-constrained by observations and are believed to be quite reliable, but others are far less well understood and we're not very sure about them.

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Ocean Models and their Interaction with the Atmosphere

The ocean, like the atmosphere, is a fluid component of the climate system and must be represented in climate models. Heat and water are passed between the ocean and atmosphere, and these processes must be represented as accurately as possible. Also, the wind speed at the surface affects the way that the top of the ocean is mixed and so how rapidly it responds to changing atmospheric temperatures.

Ocean "weather systems" or eddies, which play an important role in the climate system, tend to be much smaller (up to about 100km) than atmospheric weather systems, so the ocean components of climate models tend to have a finer resolution than the atmosphere components. Oceans take much longer to react to changes in the balance between incoming and outgoing radiation than the atmosphere. This means that ocean models need to run for many decades if they are to be included in climate predictions. These factors mean that they require significantly more computing power than atmosphere models. This is sometimes avoided by using a simplified model called a "slab ocean", which effectively just represents the top 50m of the ocean, with none of the deep sea currents which can transport a huge amount of heat, albeit very very slowly. The effects of the currents therefore need to be parameterized.

Both a slab ocean model and a 'complete' ocean model will be 'coupled' to the atmosphere model in the experiment. The complete ocean model used by the experiment 2 in fact has the same horizontal resolution (2.5° in latitude by 3.75° in longitude) as the atmosphere, and 20 vertical levels, with finer vertical resolution near the surface.

The coupled model runs asynchronously, which means that the atmosphere model runs first for some time then the ocean model runs for some time, taking turns. In the case of the model used in the experiment, the individual components run for one day at a time.

Fluxes of heat, wind, and freshwater are passed between the ocean model and the atmosphere model at the ocean-atmosphere interface.

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Chaos, Ensembles and Probabilities

Why is the weather so unpredictable? It's not random; this would mean there was no possible way of knowing what it was going to do next, but chaotic; the weather does obey the laws of physics, every effect has a cause. The problem is, there are so many possible causes, that we can't possibly know about all of them. The frequently quoted example (which originated with Ed Lorenz in the 1960s) of this is that a butterfly flapping its wings in the Amazon rainforest might, through a long line of unlikely, but possible, consequences, cause a storm over Texas.

For another example, imagine letting go of a stick on the upstream side of a bridge over a shallow stream. Just how you let go of the stick, which way round it is, etc. will affect exactly where and how it lands on the water. Under the bridge there are rocks and vegetation, which cause patterns in the stream's flow. A tiny push to the stick as you drop it could make the difference between it going one side or other of the first rock it reaches, and this might make the difference between it getting stuck in some vegetation or staying in the fastest flowing water. If you run over to the other side of the bridge to watch for the stick, it is virtually impossible to predict when and where it will appear, because you don't know what has happened to it under the bridge. Even if you know exactly what the stream bed looks like, the fact that there is uncertainty in the way you dropped the stick means that there are lots of possible ways it might pass under the bridge.

So does this mean that making an accurate weather forecast, or climate prediction, is a hopeless cause? The answer is no! We need to get an idea of all the possible ways the atmosphere could develop, and what the likelihood, or probability, of each possible way is. The way we do this is by running ensembles of GCM runs. An ensemble is a collection of runs of the same GCM, which differ very slightly in their initial conditions (so for example, there might be a 1% difference in wind speed over Oxford), or their parameterizations. Ensemble sizes vary hugely. The European Centre for Medium-Range Weather Forecasts (ECMWF) currently uses an ensemble of 50 to make the weather forecast. In, we're hoping for ensembles with millions of members! It will then be possible to build up statistics for how many ensemble members produced each possible outcome. For example, Figure 5 shows (made up!) London temperatures from an ensemble with 500 members. You can see that there are a very wide range of possible temperatures. There are some outliers; those predicting temperatures below 10°C or over 21°C. However, most of the runs have predicted temperatures between 13-18°C, and there is a clear peak at 15.5°C.

The height of the bars show how many models predicted each temperature

Figure 5. London temperature as predicted by 500 (imaginary) runs of a GCM for a 5 day forecast

Our best guess at what the temperature is actually going to do is the one that most runs predicted, i.e. the one with the largest probability. We call graphs like this Probability Density Functions or pdfs.

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Map Projections, Latitudes and Longitudes

Latitude: A measure of distance from the Equator. The equator is 0° latitude, and the North and South Poles are at +90° and -90° latitude respectively. Lines of latitude are lines joining up all the places with the same latitude, so they run around the globe; in Figure 6, they are the horizontal ones. If you walk in a straight line north between 0° latitude and 1° N, you'll cover exactly the same distance as if you walk between 89° N and 90° N. However, if you imagine walking around the Earth along a line of latitude, you'll have to walk a lot further to get round at the Equator than, for example, at 50°S.

Longitude: A measure of how far East or West you are. The Greenwich Meridian, passing through East London, is 0°longitude, and the date line, going down the centre of the Pacific, is 180°. Lines of longitude are lines joining up all the places with the same longitude, so they run from Pole to Pole; in Figure 6, they are the vertical curvy ones. If you walk around the Equator, the distance between 80°E and 90°E is the same as between 130°E and 140°E. However, at the Poles, the lines of longitude are much closer together than at the Equator, so the distance between 80°E and 90° E is smaller than it was at the Equator.

Lines of equal latitude are horizontal and lines of equal longitude are vertical

Figure 6. A projection of the world with latitudes and longitudes marked in 10° intervals.

A map projection is an attempt to draw the surface of the 3 Dimensional, spherical Earth on a flat, 2-dimensional (2-D) piece of paper/ computer screen. To do this, compromises have to be made. It is not possible to keep everything completely accurate. For example, the angle from one place to another might become distorted, or the relative size of one country with respect to another one might be wrong. In many projections such as cylindrical projections, the land has to be spread out at the poles to neatly fill a rectangular box. This means that countries closer to the Poles (such as the U.K.) appear much bigger relative to countries nearer the Equator (such as countries in Africa) than they really are.

Different projections can make the Earth appear very different

Figure 7. Some examples of projections: The Miller Cylindrical, Cylindrical Equidistant and Mercator projections are all examples of cylindrical projections, that is, a projection of the surface of the Earth on to a piece of paper wound like a cylinder around it, with the equator being in contact with the sheet of paper. The cylindrical equidistant projection is the simplest, and all the latitudes and longitudes keep the same spacing wherever you are and are always parallel/ perpendicular to each other. This means that the shapes of countries get very distorted. In the Miller cylindrical projection, the lines of latitude get further from each other the closer you get to the Poles. This is a simple method of reducing the amount of distortion, but it doesn't completely solve the problem; neither the areas of countries nor the angles of, for example, their coastlines, are correct. In the Mercator projection shapes are, at least locally, correct. The stereographic projection is not a cylindrical projection, and the sizes of countries get very distorted as you go towards the edge of the plot, however all the angles are correct.

The graphics use the simplest, Cylindrical Equidistant, projection.

The projection used by is very simple

Figure 8. Example of the cylindrical equidistant projection used by graphics

Examples of Latitudes and Longitudes

  • Tropic of Cancer 23.5 °N
  • Tropic of Capricorn 23.5 °S
  • Arctic Circle 66.5 °N
  • Antarctic Circle 66.5 °S

  • London (UK) 0 °W, 51.5 °N
  • Denver, Colorado (US) 105 °W 39 °N
  • Milton Keynes (UK) 1 °W 52 °N
  • Alice Springs (Australia) 134 °E 23 °S
  • Hawaii (US) 155 °W 20 °N
  • Moscow (Russia) 38 °E 56 °N
  • Cape Town (South Africa) 18 °E 33 °S
  • Rio de Janeiro (Brasil) 43 °W 23 °S

For more detailed, technical information about the Unified Model, visit the UGAMP web site

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