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# Forecasting by computer

### The weather is governed by physical laws

The behaviour of the atmosphere is governed by a set of physical laws which can be expressed as mathematical equations. These represent how atmospheric quantities or fields (such as temperature, wind speed and direction or humidity, for example) will change from their initial current values (at the present time). If we can solve these equations, we will have a description of the future state, a forecast, of the atmosphere, derived from a current state (initial values), which we can interpret in terms of "weather" - rain, temperature, sunshine and wind.

### Computers can be used to calculate changes to the atmosphere

However, these equations are complex (they are 'non-linear partial differential equations'). There is no exact solution that can give us the future values. Instead, numerical modelling techniques are employed to provide approximate solutions. In these numerical models the fields are represented by a finite set of numbers. By using approximate forms of the equations, we can calculate the future values of the numbers with a computer. Representing fields with approximate numerical values is called 'discretization', which emphasises the limits of the numerical approach. The smaller the set of numbers, the coarser the discretization and the less detail we will have about the future state of the atmosphere. On the other hand, the finer the discretization, the larger the amount of numbers we have to deal with and the more expensive in terms of computer time the solution becomes.

### Modelling for a limited area for short-range forecasting by Member States

The task can be made more manageable if we forecast not the whole atmosphere but only for a local area, for example part of Europe. We have then a Limited Area Model. These models can produce a very detailed forecast, but they are useful only in the range from several hours to about two days into the future - what is happening outside the treated area, influences the weather inside it, and the longer the forecast, the further the influence.

### Medium-range forecasting

ECMWF predicts the behaviour of the atmosphere in the medium-range up to ten days ahead. In this time the future state of the atmosphere at any point can be influenced by phenomena at very distant geographical locations. Many applications of medium-range forecasting, for example ship routeing, or pollution dispersion, are not confined to limited areas of the globe. Therefore the whole atmosphere must be included in the model - a model for medium-range forecasting must be global and must describe the atmosphere from the earth's surface to a height of 65km. The discretization we can afford depends on the power of the computer we have available and how efficiently we use this power.

### Small-scale effects have to be taken into account

Some important factors influencing the evolution of the atmosphere occur on a very small scale. These include the heating of the soil by the sun, the turbulence of the air near the ground and at high levels in the atmosphere, for example when air flows over mountains, and cumulus cloud systems. These cannot be represented properly by the discretization we can afford in even the most powerful computers available. We must represent their effects by taking into account their influence on the behaviour of the parameters of the large scales. This "parametrization" is one of the areas where much effort has to be concentrated in order to improve our forecasts.

### More powerful computers allow us to use finer grids

ECMWF's High Performance Computing Facility (HPCF) comprises two identical but independent IBM Cluster 1600 supercomputer systems. Read more...

The resolution of the discretization of the Centre's current high resolution model is equivalent to having gridpoints separated by about 16 km around the globe. The points are evenly distributed geographically. This network of points is then repeated at 91 levels in the vertical. The model forecasts the wind, the temperature and the humidity at 194,804,064 points throughout the atmosphere. Read more about resolution (and other operational changes) in our forecast models.

With this resolution it is possible, for example, to distinguish clearly between the French Massif Central and the Alps, and the Po valley in northern Italy is identifiable. With this detail the Centre's model can produce a realistic forecast of the near surface weather parameters, such as local winds, and the temperature at the level of the measurement stations.

### Making the forecast

In order to start the computer model, initial or starting conditions are required. Observations are used to calculate the weather (wind etc.) at each point throughout the model atmosphere. The forecast is made in short steps, of about 15 minutes ahead, with each forecast providing initial conditions for the next forecast step.

The preparation of initial conditions is a delicate and demanding task, which in the ECMWF forecasting system requires almost as much computer resources as a ten day forecast.

Initial conditions for the ECMWF global model are prepared by making the appropriate synthesis of observed values of atmospheric fields taken over a 24 hour period, and short-range forecasts provided by the global model itself. This synthesis is a process of assimilating observed values into a model. The use of both observations and model forecasts in the construction of initial values is required. High quality data are sparsely and irregularly distributed over the globe. Short-range model forecasts carry forward knowledge of earlier observations and also provide a crucial background for extracting useful information from expensive satellite observations.

 22.01.2013