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The Emergence of Numerical Weather Prediction: from Richardson to the ENIAC

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The Emergence of Numerical Weather Prediction: from Richardson to the ENIAC The Emergence of Numerical Weather Prediction: from Richardson to the ENIAC Peter Lynch School of Mathematical Sciences University College Dublin BIRS Summer School, Banff, 10–15 July, 2011 Prehistory 1890–1920 ENIAC Recreation PHONIAC Prehistory 1890–1920 ENIAC Recreation PHONIAC Outline Prehistory 1890–1920 ENIAC Recreating the ENIAC Forecast PHONIAC Prehistory 1890–1920 ENIAC Recreation PHONIAC Outline Prehistory 1890–1920 ENIAC Recreating the ENIAC Forecast PHONIAC Prehistory 1890–1920 ENIAC Recreation PHONIAC Aristotle’s Meteorologia Aristotle wrote the first book on Meteo- rology, the Mτωρoλoγια (µτωρoν: Something in the air). This work studied the causes of various weather phenomena. Aristotle was a masterly speculator: for example, he believed that the lightning followed the thunder! Aristotle (384-322 BC) Prehistory 1890–1920 ENIAC Recreation PHONIAC Money makes the world go round Prehistory 1890–1920 ENIAC Recreation PHONIAC Thus began quantitative meteorology. Galileo Galilei (1564–1642) Galileo formulated the basic law of falling bodies, which he verified by careful measurements. He constructed a telescope, with which he studied lunar craters, and discovered four moons revolving around Jupiter. Galileo is credited with the invention of the Thermometer. Prehistory 1890–1920 ENIAC Recreation PHONIAC Galileo Galilei (1564–1642) Galileo formulated the basic law of falling bodies, which he verified by careful measurements. He constructed a telescope, with which he studied lunar craters, and discovered four moons revolving around Jupiter. Galileo is credited with the invention of the Thermometer. Thus began quantitative meteorology. Prehistory 1890–1920 ENIAC Recreation PHONIAC Galileo’s Thermometer The Galileo Thermometer is a popular modern collectable and an attractive decoration. As temperature rises, the fluid expands and its density de- creases. The reduced buoyancy causes the glass baubles to sink, indi- cating temperature changes. Prehistory 1890–1920 ENIAC Recreation PHONIAC Galileo’s Ace Post-Doc. Evangelista Torricelli (1608–1647), a student of Galileo, devised the first accurate barometer. Torricelli inventing the barometer Prehistory 1890–1920 ENIAC Recreation PHONIAC Barometric Pressure The relationship between the height of the mercury column and the character of the weather was soon noticed. Prehistory 1890–1920 ENIAC Recreation PHONIAC Newton’s Law of Motion The rate of change of momentum of a body is equal to the sum of the forces acting on the body: Force = Mass × Acceleration Prehistory 1890–1920 ENIAC Recreation PHONIAC Edmund Halley (1656–1742) Edmund Halley was a contemporary and friend of Isaac Newton; this was quite an achievement: Newton didn’t have too many friends! Halley was largely responsible for persuading Newton to publish his Principia Mathematica. Prehistory 1890–1920 ENIAC Recreation PHONIAC Halley and his Comet Halley’s analysis of a comet was an excellent example of the scientific method in action. Prehistory 1890–1920 ENIAC Recreation PHONIAC Hypothesis: These events were due to the reappearance of one object on an orbit which brought it close to the Sun every 76 years. Prediction: In 1705, Halley forecast that the comet would return again in late 1758. Halley died in 1742. Verification: The comet was sighted, on schedule, on Christmas Day 1758 and has since borne Halley’s name. Further Confirmation: Appearances of the comet have since been found in the historic record as far back as 2000 years. Observation: The comets of 1456, 1531, 1607, and 1682 followed similar orbital paths around the Sun. Each appearance was separated from the previous one by about 76 years. Prehistory 1890–1920 ENIAC Recreation PHONIAC Prediction: In 1705, Halley forecast that the comet would return again in late 1758. Halley died in 1742. Verification: The comet was sighted, on schedule, on Christmas Day 1758 and has since borne Halley’s name. Further Confirmation: Appearances of the comet have since been found in the historic record as far back as 2000 years. Observation: The comets of 1456, 1531, 1607, and 1682 followed similar orbital paths around the Sun. Each appearance was separated from the previous one by about 76 years. Hypothesis: These events were due to the reappearance of one object on an orbit which brought it close to the Sun every 76 years. Prehistory 1890–1920 ENIAC Recreation PHONIAC Verification: The comet was sighted, on schedule, on Christmas Day 1758 and has since borne Halley’s name. Further Confirmation: Appearances of the comet have since been found in the historic record as far back as 2000 years. Observation: The comets of 1456, 1531, 1607, and 1682 followed similar orbital paths around the Sun. Each appearance was separated from the previous one by about 76 years. Hypothesis: These events were due to the reappearance of one object on an orbit which brought it close to the Sun every 76 years. Prediction: In 1705, Halley forecast that the comet would return again in late 1758. Halley died in 1742. Prehistory 1890–1920 ENIAC Recreation PHONIAC Further Confirmation: Appearances of the comet have since been found in the historic record as far back as 2000 years. Observation: The comets of 1456, 1531, 1607, and 1682 followed similar orbital paths around the Sun. Each appearance was separated from the previous one by about 76 years. Hypothesis: These events were due to the reappearance of one object on an orbit which brought it close to the Sun every 76 years. Prediction: In 1705, Halley forecast that the comet would return again in late 1758. Halley died in 1742. Verification: The comet was sighted, on schedule, on Christmas Day 1758 and has since borne Halley’s name. Prehistory 1890–1920 ENIAC Recreation PHONIAC Observation: The comets of 1456, 1531, 1607, and 1682 followed similar orbital paths around the Sun. Each appearance was separated from the previous one by about 76 years. Hypothesis: These events were due to the reappearance of one object on an orbit which brought it close to the Sun every 76 years. Prediction: In 1705, Halley forecast that the comet would return again in late 1758. Halley died in 1742. Verification: The comet was sighted, on schedule, on Christmas Day 1758 and has since borne Halley’s name. Further Confirmation: Appearances of the comet have since been found in the historic record as far back as 2000 years. Prehistory 1890–1920 ENIAC Recreation PHONIAC ... why can’t the Meteorologists do the same? A Tricky Question If the Astronomers can make accurate 76-year forecasts ... Prehistory 1890–1920 ENIAC Recreation PHONIAC A Tricky Question If the Astronomers can make accurate 76-year forecasts ... ... why can’t the Meteorologists do the same? Prehistory 1890–1920 ENIAC Recreation PHONIAC I Order versus Chaos The equations of the solar system are quasi-integrable and the motion is regular. The equations of the atmosphere are essentially nonlinear and the motion is chaotic. I Size of the Problem Cometary motion is a relatively simple problem, with few degrees of freedom; Dynamics is enough. The atmosphere is a continuum with infinitely many variables; Thermodynamics is essential. Prehistory 1890–1920 ENIAC Recreation PHONIAC I Size of the Problem Cometary motion is a relatively simple problem, with few degrees of freedom; Dynamics is enough. The atmosphere is a continuum with infinitely many variables; Thermodynamics is essential. I Order versus Chaos The equations of the solar system are quasi-integrable and the motion is regular. The equations of the atmosphere are essentially nonlinear and the motion is chaotic. Prehistory 1890–1920 ENIAC Recreation PHONIAC Leonhard Euler (1707–1783) I Born in Basel in 1707. I Died 1783 in St Petersburg. I Formulated the equations for incompressible, inviscid fluid flow: @V 1 + V · rV + rp = g : @t ρ r · V = 0 Prehistory 1890–1920 ENIAC Recreation PHONIAC Jean Le Rond d’Alembert The Euler equations are partial differential equations. D’Alembert introduced partial derivatives in studying the flow of wind in two dimensions. Prehistory 1890–1920 ENIAC Recreation PHONIAC George G Stokes, 1819–1903 George Gabriel Stokes, founder of modern hydrodynamics. Prehistory 1890–1920 ENIAC Recreation PHONIAC This leads on to Bjerknes’ Circulation Theorem: dC ZZ 1 I dp = − r × rp·da = − ; dt Σ ρ Γ ρ which generalized Kelvin’s Circulation Theorem to baroclinic fluids (ρ varying independently of p), and ushered in the study of Geophysical Fluid Dynamics. ASIDE: Stokes’ Theorem I ZZ Good for V·dl = r × V · n da T-shirts Γ Σ Stokes’ Theorem was actually discovered by Kelvin in 1854. It is of central importance in fluid dynamics. Prehistory 1890–1920 ENIAC Recreation PHONIAC ASIDE: Stokes’ Theorem I ZZ Good for V·dl = r × V · n da T-shirts Γ Σ Stokes’ Theorem was actually discovered by Kelvin in 1854. It is of central importance in fluid dynamics. This leads on to Bjerknes’ Circulation Theorem: dC ZZ 1 I dp = − r × rp·da = − ; dt Σ ρ Γ ρ which generalized Kelvin’s Circulation Theorem to baroclinic fluids (ρ varying independently of p), and ushered in the study of Geophysical Fluid Dynamics. Prehistory 1890–1920 ENIAC Recreation PHONIAC The minutest amount of viscosity has a profound qualitative impact on the character of the solution. The Navier-Stokes equations include effect of viscosity. Resolution of d’Alembert’s Paradox D’A, 1752: A body moving at constant speed through a gas or a fluid does not experience any resistance. Prehistory 1890–1920 ENIAC Recreation PHONIAC The minutest amount of viscosity has a profound qualitative impact on the character of the solution. The Navier-Stokes equations include effect of viscosity. Resolution of d’Alembert’s Paradox D’A, 1752: A body moving at constant speed through a gas or a fluid does not experience any resistance. Prehistory 1890–1920 ENIAC Recreation PHONIAC Resolution of d’Alembert’s Paradox D’A, 1752: A body moving at constant speed through a gas or a fluid does not experience any resistance.
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