Weather forecasting has been an important application area over the past 100 years. The complex numerical calculations and modeling structures that have been developed, require a fairly sophisticated level of technological development. Prior to the advent of digital computers it was practically impossible to forecast the weather. As technology progressed, so did the theoretical models, leading to increases in detail and accuracy levels of weather forecasting.
             The first steps in scientific weather forecasting
             The numerical models had been developed by Lewis Fry Richardson, who used basic equations of motion and state to model atmospheric dynamics. The data sets in the model included that barometric pressure and wind speed for a particular region. In 1922 he published "Weather Prediction by Arithmetic Finite Differences" which demonstrated the correlation of mathematics and the weather. Essentially the model would simulate the evolution of weather patterns. The computational power needed to carry out the calculations involved some 64000 people armed with slide rules and mechanical calculators. Each member would carry out parts of the calculation; telegraph and flashing coloured lights would transmit results. Despite the huge efforts exerted, weather could only be calculated only as fast at it was happening and results were incorrect. This stemmed from lack of computational power and the lack of meteorological data.
             Richardson's equations worked by separating regions into areas of a specific size. The calculations performed in each area would be combined to form the weather forecast. In order to obtain more accurate readings, the separated regions have to be reduced in size. However this meant that more data and computational power would be needed (the ability to obtain both of were lacking at the time). In figure 1 we see Locations of meteorological stations from which Richardson obtained upper-air observations...