First numerical weather forecast

The first weather forecast to be produced solely using mathematical models was published by British mathematician Lewis Fry Richardson in 1922. The forecast was a retrospective six-hour outlook for 20 May 1910, based on a static picture of weather station and balloon data gathered from across Europe that day. He began work on this forecast in 1913, and continued his calculations throughout World War I (during which time he served as an ambulance driver on the Western Front). He published his forecast in his 1922 book Weather Prediction by Numerical Process, which explained his methods (which were broadly sound) and the resulting forecast (which was wildly wrong).

In a 1992 analysis of Richardson's data, meteorologist and mathematician Peter Lynch concluded that the errors in Richardson's forecast were caused by a failure to apply smoothing algorithms to his initial data set, as well as an overly ambitious time-step (looking forward six hours wasn't really feasible with the data he had). Richardson was trying to make projections based on data that included snapshots of atmospheric phenomena that rapidly fluctuate, and whose behaviour during a brief period of observation we now know can't be extrapolated into a longer-term trend. If the fluctuations in these initial readings are smoothed out or assumed to be static, and Richardson's calculations repeated (something that can be done in moments with modern computers), his forecasting technique turns out to have been fairly accurate.