1/ As it’s the 75th anniversary of ENIAC today, I thought I would share an extract from my forthcoming book, Computing the Climate. Because ENIAC played a crucial role in the birth of weather and climate models.

2/ ENIAC was the world’s first truly general purpose programmable electronic computer⁠, designed by John Mauchly and J. Presper Eckert at UPenn in 1946, with funding from the US army, who wanted a computer to produce ballistics tables for heavy artillery weapons.

3/ ENIAC was a thousand times faster than the best electro-mechanical calculators at the time. But it’s 17,000 vacuum tubes were so unreliable one would fail almost every day.

4/ Even with this handicap, ENIAC was a huge advance over existing calculators, and was used continuously by the US Army Ordinance Corps until 1955.

5/ During the development of ENIAC, most experts were skeptical that it could ever work. One of the few people who understood its potential was the mathematician John von Neumann, who, at the time, was seconded to Los Alamos to consult on the development of the atomic bomb.

6/ von Neumann was an expert on complex mathematical problems, such as the movements of fluids. These problems could readily be described using a set of equations, but were almost impossible to solve by hand.

7/ von Neumann heard about ENIAC almost by accident, when an army captain⁠ who was working on the ENIAC project recognized him at a railway station and struck up a conversation.

8/ He immediately arranged to visit the ENIAC team in Philadelphia, and within a few weeks he had signed on as a consultant to the project.

9/ His involvement had an immediate and unexpected impact: that first program 75 years ago on ENIAC wasn’t, as the Army had intended, a ballistics calculation at all.

10/ In December 1945, von Neumann arranged for the physicists at Los Alamos to use ENIAC for a thermodynamics calculation they needed for the design of a hydrogen bomb.

11/ They encoded the program, along with the data it needed, onto half a million punched cards, which were shipped from Los Alamos to Philadelphia. The program took six weeks to run, but completed successfully. The era of computational science had begun.

12/ One of the major legacies of the ENIAC project is a report⁠ von Neumann wrote in early 1946, to help guide the development of a successor to ENIAC. His design established von Neumann as “the father of the modern computer”.

13/ However, he was never really interested in design problems per se; his real interest was the computational science that computers would enable. There are several classes of mathematical problem that, up until the 1940s, were considered to be unsolvable.

14/ Among these were the equations for the flow of fluids and heat: hydrodynamics and thermodynamics. Oil companies needed to solve such problem when considering what flow rates to expect if they drill into an oil field at a particular location.

15/ Nuclear scientists needed to solve them to calculate the dispersion of heat and nuclear fallout during an explosion.

16/ And meteorologists needed them to attain the holy grail of weather forecasting: the ability to calculate how a particular weather pattern would evolve over days or weeks.

17/ This last problem particularly captured von Neumann’s imagination. Numerical weather forecasting would be an excellent demonstration of the value of electronic computers for science, and would build on his work on numerical solutions to partial differential equations.

18/ After the war, von Neumann returned to the Institute of Advanced Study at Princeton, where he recruited a team of experts in meteorology led by Jule Charney⁠.

19/ Charney is sometimes known as the father of numerical weather forecasting, but he’s also well-known as the lead author of the first scientific assessment of the risk of climate change, commissioned by President Jimmy Carter in 1979.

20/ Charney began with the set of primitive equations first worked out by Lewis Fry Richardson during the first world war. He simplified these equations by ignoring temperature and water vapour, and focussing instead just on air pressure.

21/ This gave him what he called a barotropic model (“baro-” for pressure, and “-tropic” for varying uniformly). In the real atmosphere, heating and cooling complicates things, but Charney was curious to find out how much this would matter.

22/ The resulting model had a single variable, representing, in each grid cell, the height in the atmosphere at which the air pressure is 500millibars. As the average air pressure at sea level is about 1000mb,

23/ so 500mb can be thought of as “halfway up”. Half the mass of the atmosphere is above this point. Imagine the bottom half of the atmosphere is made of something other than air. The 500millibar point would represent the ‘surface’ of this substance.

24/ Areas of low pressure would appear as dents or troughs in this surface, and areas of high pressure would appear as peaks or ridges. The jet stream would appear as a meandering ridge that circles the planet.

25/ The key idea in Charney’s barotropic model is that many large scale weather effects are a result of the shape of this surface, or changes in its shape.

26/ Wind speed and direction can be calculated by assuming that as air flows from high pressure areas to neighbouring low pressure areas, it is deflected by the Coriolis effect.

27/ Hence, the wind can be assumed to flow along the contour lines of this 500millibar surface, at a speed proportional to the steepness of the slope. If a trough is approaching you, it means a mass of low pressure air is coming your way, bringing colder, unsettled weather.

28/ If a ridge of high pressure holds still over a region, it’s called a blocking pattern, and tends to cause an extended period of hotter weather. So if a model could calculate the movement of this surface over time, it ought to be able to predict the weather.

29/ The theory made sense, but would it work? Two questions remained: were the equations good enough to capture how the 500millibar surface behaves, and could the calculations be done fast enough to give useful weather forecasts?

30/ Before running it on ENAIC, they tried an even simpler test by hand.

31/ They reduced the two dimensional barotropic model to a single dimension, by selecting a single latitude band - the 45th parallel, which stretches for 28,000km around the planet, roughly halfway between the equator and the North Pole.

32/ The idea was to analyze the progression of Rossby waves around the planet at a single latitude, without considering what was happening to the north and south of it.

33/ To initialize the model, they converted the air pressure readings into an estimated height for the 500mb surface at each 10 degrees of longitude, giving them 36 data points spaced out about 800km apart.

34/ The barotropic equation would calculate new values for these points, 24 hours later, and the result could be compared with the actual readings for the next day, to determine whether the “forecast” was any good.

35/ The actual calculations for this were handled by a team of three women, led by Margaret Smagorinsky, who was, at the time, a meteorological statistician⁠ with the US Weather Bureau.

36/ The three women hand-calculated over a hundred 24-hour forecasts for this one dimensional model, using data from the Weather Bureau to initialize the forecasts.

37/ So credit for performing the first successful numerical weather forecast doesn’t belong to ENIAC at all: it belongs to three “human computers”: Margaret Smagorinsky, Norma Gilbarg, and Ellen-Kristine Eliasson⁠.

38/ They found many of the the 24 hour forecasts to be surprisingly realistic⁠, although longer forecasts (e.g. over five days) were essentially useless.

39/ The model performed better where the initial data was the most reliable: over Europe, the Atlantic and North America, and it worked better for some 24 hour periods than others.

40/ But perhaps most surprising of all was that any of the the forecasts looked realistic, given the simplicity of the model and the lack of good data.

41/ Charney and von Neumann declared the experiment a success and vN pulled strings with the army to allow them to try a test run on ENIAC, which was by now installed in an army facility doing the ordinance calculations it was originally intended for.

42/ By March 1950 the programs were ready, and the team took over and operated ENIAC around the clock for 33 days with a series of tests of their model. The tests were somewhat disappointing.

43/ A number of programming errors had to be caught and corrected before a successful run could be completed, and as a result, the team only managed to complete a few of the hindcast runs they had prepared.

44/ Eventually, they successfully ran two 12-hour hindcasts and four 24-hour hindcasts using real weather data. The results themselves were rather mixed. Only one of the runs gave anything close to an accurate result.

45/ The machine was also much slower than they expected: ENIAC took 36 hours to compute 24 hours worth of weather, which made it rather useless for real weather forecasting. Despite these disappointments, von Neumann and Charney were enthused.

46/ Most of the time taken to complete the runs was spent on manual support - taking the stacks of punched cards output during one step in the calculation, and re-ordering them ready to provide input for the next step.

47/ Machines with more internal memory and faster processors were already under development, so it was easy to foresee that within a few years, the computer would be able to run a weather simulation faster than real-time, making real weather forecasting possible.

48/ And the model was one of the simplest the team had developed—a better model would surely produce better forecasts.

49/ Most importantly, they had overturned a widely held belief among meteorologists at the time that calculating the weather directly from a set of numerical equations was probably impossible.

50/50: And the rest, as they say is history. Within 5 years, the National Weather Bureau was using a model like Charney's for operational weather forecasting, and within 10 years, Charney's model had been adapted for the first global climate models. But that's another story.