These models solve complex mathematical equations that are based on well established physical laws that define the behaviour of the weather and climate.

However, it is not possible to represent all the detail in the real world in a computer model, so approximations have to be made. The models are tried and tested in a number of ways:

• They are used to reproduce the climate of the recent past, both in terms of the average and variations in space and time.

• They are used to reproduce what we know about ancient climates (which are more limited).

• The Met Office Hadley Centre model is unique among climate models in that it is used with more regional detail to produce the weather forecasts every day.

Two critical factors have helped us to improve these models over the years. First, our knowledge of the real world has improved, which allows us to improve the models.

Second, the speed and power of computers has increased dramatically, allowing us to represent more detail in the models.

Improvements in the science

The climate system is highly complex, with many potential interactions and feedbacks. Over the years, more of this complexity has been included in models.

In the 1970s, models included a simple representation of the atmosphere. Rain was included but not clouds; carbon dioxide (CO₂) concentrations were considered and the radiation (heating) that determines the effect of CO₂ on temperature was also included.

Now, current state-of-the-art climate models include fully interactive clouds, oceans, land surfaces and aerosols, etc. The latest models include detailed chemistry and the carbon cycle.

The climate system is highly complex, with many potential interactions and feedbacks. It is worth thinking a little about why these processes are important, and a few examples are highlighted here:

1. Clouds affect the heating and cooling of the atmosphere
For example, on a cloudy day, less radiation (heating) from the sun reaches the Earth's surface and we feel cool.

On the other hand, on a cloudy night the heat generated during the day is trapped and the temperature near the surface remains relatively warm.

However, it is not just the amount of cloud that is important, but also the detailed properties of the cloud. Thin cirrus cloud high up in the atmosphere has a different effect on climate to thick cloud nearer the Earth's surface.

2. The oceans take much longer to warm up than the land
They also move heat around the globe; for example, the Gulf Stream in the north Atlantic Ocean brings warm water from the tropical Atlantic up to northern Europe, and has a strong effect on the temperatures that the UK experiences.

3. The land surface influences how much radiation is absorbed at the surface
An area that is covered in trees will be dark and will heat up more by absorbing more radiation. Areas covered in ice, or at the opposite extreme desert, will both reflect more radiation and absorb less heat.

4. Aerosols
These are atmospheric particles, such as sulphate and black carbon that are produced naturally from volcanoes and forest fires, as well as by humans from fossil fuel power stations and other industrial activities.

They generally have a cooling effect on climate, by reducing the amount of sunlight reaching the surface (the so-called global dimming effect) and by changing the properties of clouds. The presence of man-made aerosols offsets some of the warming in the short term.

5. The chemistry and carbon cycle determine how much carbon dioxide remains in the atmosphere
Currently the biosphere (plants, soils, phytoplankton) absorbs half of the carbon dioxide that man produces.

The latest climate model predictions suggest that this will not continue indefinitely and that some parts of the biosphere (in particular soils) could start to release carbon if temperatures increase too much.

Improvements in computer power

Climate modelling has always made use of the best computers, but has been limited by the available computer power.

Our model has begun to include some of the complexities of the Earth system In the 1970s, as well as including only limited science, the models included very little detail and could only be run for very short periods.

A typical model divided the world up in to boxes 600km across with five levels to represent all the vertical structure. They were used to predict changes on timescales of months up to a year or so.

They were mainly used to understand climate processes rather than to predict the future.

The latest Hadley Centre model, HadGEM2-ES (which is at the forefront of state-of-the-art Earth system models), uses 135km boxes with 38 levels in the vertical. Critically though, it is one of the first models to include those complexities the Earth system already mentioned above.

The massive increases in computer power since the 1970s are used in the following ways in the Met Office Hadley Centre:

• Much higher resolution is used to give more regional detail. The changes between the 1970s and the present day outlined above required 256 times more computer power.

• Representations of all the key processes identified as important for climate change are included in the latest version of the model.

• Much longer predictions are run, typically reproducing the last 150 years and predicting the next 100 to 1,000 years.

• Far more experiments are run with different versions of the models so that we can quantify the uncertainty in our predictions.

The results 

The latest climate models predict similar possible global average temperature changes to models used 10 to 15 years ago, ranging from 1.6-4.3C (2.9-7.7F) in the current best estimates using a mid-range emissions scenario.

However, we are much more confident about these ranges. Using Met Office models we have even been able to start to assign probabilities to more dangerous high temperature changes at the upper end of this range that could arise if climate turns out to be very sensitive to increased greenhouse gases.