## Modelling the weather

An English mathematician, Lewis Fry Richardson, set up the first numerical model of the weather. During his spare moments while working for the Friends' Ambulance Unit (he was a Quaker) in France during the First World War he carried out the first numerical weather forecast. With much painstaking calculation with his slide rule, he solved the appropriate equations and produced a six-hour forecast. It took him six months - and then it was not a very good result. But his basic methods, described in a book published in 1922,1 were correct. To apply his methods to real forecasts, Richardson imagined the possibility of a very large concert hall filled with people, each person carrying out part of the calculation, so that the integration of the numerical model could keep up with the weather. But he was many years before his time! It was not until some forty years later that, essentially using Richardson's methods, the first operational weather forecast was produced on an electronic computer. Computers more than one trillion times faster than the one used for that first forecast (Figure 5.1) now run the numerical models that are the basis of all weather forecasts.

Numerical models of the weather and the climate are based on the fundamental mathematical equations that describe the physics and dynamics of the movements and processes taking place in the atmosphere, the ocean, the ice and on the land. Although they include empirical information, they are not based to any large degree on empirical relationships - unlike numerical models of many other systems, for instance in the social sciences.

Setting up a model of the atmosphere for a weather forecast (see Figure 5.2) requires a mathematical description of the way in which energy from the Sun enters the atmosphere from above, some being reflected by the surface or by clouds and some being absorbed at the surface or in the atmosphere (see Figure 2.7). The exchange of energy and water vapour between the atmosphere and the surface must also be described.

Lewis Fry Richardson (11 October 1881-30 September 1953).

Year of first use

Figure 5.1 The growth of computer power available at major forecasting centres. The computers are those used by the UK Met Office for numerical weather prediction research, since 1965 for operational weather forecasting and most recently for research into climate prediction. Richardson's dream computer of a large 'human' computer mentioned at the beginning of the chapter would possess a performance of perhaps 500 FLOPS (floating point operations per second). The largest computer on which meteorological or climate models are run in 2007 is the Earth Simulator in Japan. The straight line illustrates a rate of increase in performance of a factor of 10 every five years.

### Year of first use

Figure 5.1 The growth of computer power available at major forecasting centres. The computers are those used by the UK Met Office for numerical weather prediction research, since 1965 for operational weather forecasting and most recently for research into climate prediction. Richardson's dream computer of a large 'human' computer mentioned at the beginning of the chapter would possess a performance of perhaps 500 FLOPS (floating point operations per second). The largest computer on which meteorological or climate models are run in 2007 is the Earth Simulator in Japan. The straight line illustrates a rate of increase in performance of a factor of 10 every five years.

Figure 5.2 Schematic illustrating the parameters and physical processes involved in atmospheric models.

Top of atmosphere

Atmosphere

Surface

Top of atmosphere

Density depends on temperature and pressure

Motion horizontal and vertical

Composition water vapour, carbon dioxide, clouds, etc.

Surface exchange of heat, momentum (friction) and water vapour

Figure 5.3 Illustration of the horizontal model grid over Europe as in a typical global climate model (a) in 1990 employed for the IPCC 1st Assessment Report and (b) in 2007 as employed for the IPCC 4th Assessment Report. Note the large improvement from the coarse grid of 1990.

Water vapour is important because of its associated latent heat (in other words, it gives out heat when it condenses) and also because the condensation of water vapour results in cloud formation, which modifies substantially the interaction of the atmosphere with the incoming energy from the Sun. Variations in both these energy inputs modify the atmospheric temperature structure, causing changes in atmospheric density (since warmed gases expand and are therefore less dense). It is these density changes that drive atmospheric motions such as winds and air currents, which in their turn alter and feed back on atmospheric density and composition. More details of the model formulation are given in the box below.

To forecast the weather for several days ahead a model covering the whole globe is required; for example, the southern hemisphere circulation today will affect northern hemisphere weather within a few days and vice versa. In a global forecasting model, the parameters (i.e. pressure, temperature, humidity, wind velocity and so on) that are needed to describe the dynamics and physics (listed in the box below) are specified at a grid of points (Figure 5.3) covering the globe. A typical spacing between points in the horizontal would be 100 km and about 1 km in the vertical; typically there would be 20 or 30 levels in the model in the vertical. The fineness of the spacing is limited by the power of the computers available.

Having set up the model, to generate a forecast from the present, it is started off from the atmosphere's current state and then the equations are integrated forward in time (see box below) to provide new descriptions of the atmospheric circulation and structure up to six or more days ahead. For a description of the atmosphere's current state, data from a wide variety of sources (see box below) have to be brought together and fed into the model.

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