Similar numerical models to those used to produce weather forecasts are run for seasonal forecasting. These are global models which include a representation of the atmosphere and ocean processes (and their interactions) to simulate the Earth’s climate.
However, there are a few differences between forecasting the weather a few days ahead and trying to do it for the coming season. A fundamental one is that the models are run forward in time for a longer period. The main reason that seasonal forecasts are possible is that there are some slow varying components of the Earth’s climate. Particularly important is the evolution of the surface temperature of the global oceans which can influence the weather patterns (e.g. El Nino / La Nina). These influences are not easily noticed in day-to-day weather forecasting but become evident in long-term weather averages. Other slow varying components of the Earth’s climate are the sea-ice, the land surface moisture content and the chemical composition of the atmosphere.
Because the link between weather and these slow varying processes is best detected in long-term averages, seasonal forecasts are usually presented as average conditions over three-month periods (e.g. December-January-February for winter time) and compared to normal or average climate conditions. For example: "Is the mean UK temperature this winter likely to be above or below the long-term average?”.
Another important factor is that models are run many times, with slight variations to represent uncertainties in the forecast process, in what is known as an ensemble. Probabilities can be extracted from a large number of runs and the forecast presented accordingly. For example: “There is a 20% probability that the mean UK temperature for this winter will be colder than average, 30% that it will be average and 50% that it will be warmer than average”.
For more information on seasonal prediction see ENSEMBLES newsletter Issue 2