History – an introductory overview The emergence of numerical weather prediction: fulfilment of a dream and realisation of a fantasy

Professor Peter Lynch, University College Dublin, Ireland


Peter Lynch is an Irish meteorologist, mathematician, blogger and book author. His interests include numerical weather prediction, dynamic meteorology, Hamiltonian mechanics, the history of meteorology, and the popularisation of mathematics.

He was born in Dublin, and educated at University College Dublin, where he obtained his BSc (1968) and MSc (1969) in mathematical science. He enlisted in the Irish meteorological service (now known as Met Éireann) in 1971, and worked there until 2004, rising to the rank of Head of the Research and Training Division and later Deputy Director. In 1982, he was awarded a PhD by Trinity College Dublin for his thesis Planetary-scale Hydrodynamic Instability in the Atmosphere written under the supervision of Ray Bates.

In 2004, he moved to academia, becoming Met Éireann Professor of Meteorology at the School of Mathematical Sciences. He has supervised several doctoral theses there. He is now an Emeritus Professor at the School of Mathematical Sciences.

Shortly after formally retiring from UCD in 2011, he started writing a weekly mathematical blog called “That’s Maths”, about half of the columns also appearing in The Irish Times newspaper (on the first and third Thursdays of each month).


The development of computer models for weather forecasting and climate prediction is one of the great scientific triumphs of the twentieth century. Today, numerical weather prediction plays a central and essential role in operational weather forecasting. Forecasts now have accuracy at ranges beyond a week. The improvement in forecasting skill over the past century has been something of a quiet revolution. There have been major advances on several fronts: enhancements in model resolution, better numerical algorithms, more realistic representation of physical processes, new observational data from satellites and more sophisticated methods of determining the initial conditions. In Prof. Lynch reviewed developments, from the pre-history of computer forecasting around 1900, through the first computer forecast in 1950 to the establishment of the European Centre for Medium-Range Weather Forecasts. As a bonus, he discussed an artist’s impression of Lewis Fry Richardson’s marvellous ‘fantasy’ of a Forecast Factory, uncovered from obscurity in Trinity College Dublin some years ago.

My notes from the talk (if they don’t make sense then it is entirely my fault)

Over time there has been a steady accumulation of technical advances. Among the greatest impacts on physical science was the use of computers.



Cleveland Abbe was born on December 3, 1838, in New York City. Growing up in the city, he became enthralled with weather by reading articles by Merriam, Espy, and Joseph Henry (among others) in the daily newspapers. In the summer of 1857, he read William Ferrel’s classic article on the theories of storms and winds in the Mathematical Monthly, which guided him into the study of meteorology. That year, he graduated from the Free Academy (now the College of the City of New York) and proceeded to conduct graduate studies in astronomy under F. Brunow at Ann Arbor, Michigan, until 1860, and then under B.A. Gould at Cambridge, Massachusetts, until 1864.

He was among the first to recognize the interdependency of the three dimensions of meteorology–forecasting, climatology, and physical theory and he was one of the pioneers of theoretical dynamic meteorology and hydrodynamics.

Vilhelm Friman Koren Bjerknes ForMemRS (14 March 1862 – 9 April 1951) was a Norwegian physicist and meteorologist who did much to found the modern practice of weather forecasting. He formulated the primitive equations that are still in use to this day in numerical weather prediction and climate modelling, and developed the so-called Bergen School of Meteorology, which was wildly successful in advancing weather prediction and meteorology in the early 20th century.


In 1897 he discovered the circulation theorems that led him to a synthesis of hydrodynamics and thermodynamics applicable to large-scale motions in the atmosphere and the ocean. This work ultimately resulted in the theory of air masses, which is essential to modern weather forecasting. In 1904 he presented a farsighted program for physical weather prediction.

In 1917 he accepted a position with a museum in Bergen, Norway, and there founded the Bergen Geophysical Institute. His most productive years were spent at Bergen; there he wrote On the Dynamics of the Circular Vortex with Applications to the Atmosphere and to Atmospheric Vortex and Wave Motion (1921). Now a classic, this work clearly details the most important aspects of his research. In 1926 he obtained a position with the university in Oslo, where he continued his studies until his retirement in 1932.

Bjerknes and his associates at Bergen succeeded in devising equations relating the measurable components of weather, but their complexity precluded the rapid solutions needed for forecasting. Out of their efforts, however, came the polar front theory for the origin of cyclones and the now-familiar names of cold front, warm front, and stationary front for the leading edges of air masses.

The process of forecasting that he set up included diagnostics, analysis, programming and integration.


Lewis Fry Richardson, FRS (11 October 1881 – 30 September 1953) was an English mathematician, physicist, meteorologist, psychologist and pacifist who pioneered modern mathematical techniques of weather forecasting, and the application of similar techniques to studying the causes of wars and how to prevent them. He is also noted for his pioneering work concerning fractals and a method for solving a system of linear equations known as modified Richardson iteration.

He produced direct solution of the equations of motion involved. Richardson’s interest in meteorology led him to propose a scheme for weather forecasting by solution of differential equations, the method used nowadays, though when he published Weather Prediction by Numerical Process in 1922, suitable fast computing was unavailable. Today’s weather forecasts are prepared using his methods.

Richardson’s Quaker beliefs entailed an ardent pacifism that exempted him from military service during World War I as a conscientious objector, though this subsequently disqualified him from having any academic post. Richardson worked from 1916 to 1919 for the Friends’ Ambulance Unit attached to the 16th French Infantry Division. After the war, he rejoined the Meteorological Office but was compelled to resign on grounds of conscience when it was amalgamated into the Air Ministry in 1920. He subsequently pursued a career on the fringes of the academic world before retiring in 1940 to research his own ideas. His pacifism had direct consequences on his research interests. According to Thomas Körner, the discovery that his meteorological work was of value to chemical weapons designers caused him to abandon all his efforts in this field, and destroy findings that he had yet to publish.

It took him two years to produce the first-ever numerical weather forecast by hand calculating changes in pressure and winds in two points in central Europe over a six-hour period. It wasn’t very successful due to the way the equations behaved. He realised that the sheer volume of calculations was a major challenge. “perhaps some day in the future it will be possible to advance the computations faster than the weather advances”. Describing the effect of atmospheric turbulence, he wrote “Big whirls have little whirls; That feed on their velocity; And little whirls have lesser whirls; And so on, to viscosity …”

Richardson lived to see the first-ever weather forecast generated by computer and, thanks to modern supercomputers, his dream of using mathematics to create weather forecasts is now an everyday reality.


Richardson’s Computing Form PXIII

The figure in the bottom right corner is the forecast change in surface pressure: 145 mb in six hours!

A modern value would be -0.9mb in six hours.

Dynamical core

In physics, the Navier–Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of viscous fluid substances.

These balance equations arise from applying Isaac Newton’s second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term—hence describing viscous flow. The main difference between them and the simpler Euler equations for inviscid flow is that Navier–Stokes equations also factor in the Froude limit (no external field) and are not conservation equations, but rather a dissipative system, in the sense that they cannot be put into the quasilinear homogeneous form.

They may be used to model the weather and ocean currents.

Claude-Louis Navier (10 February 1785 – 21 August 1836), was a French mechanical engineer, affiliated with the French government, and a physicist whose work was specialized in continuum mechanics.,_1st_Baronet


Sir George Gabriel Stokes, 1st Baronet, PRS (13 August 1819 – 1 February 1903) was an Anglo-Irish physicist and mathematician. Born in County Sligo, Ireland, Stokes spent all of his career at the University of Cambridge, where he was the Lucasian Professor of Mathematics from 1849 until his death in 1903. As a physicist, Stokes made seminal contributions to fluid mechanics, including the Navier–Stokes equations, and to physical optics, with notable works on polarization and fluorescence.

His work underlies all atmospheric and ocean flows.

ENIAC equations

Critical advances in weather forecasting between 1920 and 1950:

Dynamic Meteorology; Numerical Analysis; Atmopsheric Observations; Electronic Computing (ENIAC)


The ENIAC was the first multi-purpose programmable electronic digital computer.

It had: 18,000 vacuum tubes; 70,000 resistors; 10,000 capacitors; 6,000 switches; Power: 140 kWatts

Charney, Fjørtoft, von Neumann


Charney, J.G., R. Fjørtoft and J. von Neumann, 1950: Numerical integration of the barotropic vorticity equation. Tellus, 2, 237–254.

Jule Gregory Charney (January 1, 1917 – June 16, 1981) was an American meteorologist who played an important role in developing numerical weather prediction and increasing understanding of the general circulation of the atmosphere by devising a series of increasingly sophisticated mathematical models of the atmosphere. His work was the driving force behind many national and international weather initiatives and programs.

Considered the father of modern dynamical meteorology, Charney is credited with having “guided the postwar evolution of modern meteorology more than any other living figure.” Charney’s work also influenced that of his close colleague Edward Lorenz, who explored the limitations of predictability and was a pioneer of the field of chaos theory.

Ragnar Fjørtoft (1 August 1913 – 28 May 1998) was an internationally recognized Norwegian meteorologist. He was part of a Princeton, New Jersey team that in 1950 performed the first successful numerical weather prediction using the ENIAC electronic computer. He was also a professor of meteorology at the University of Copenhagen and director of the Norwegian Meteorological Institute.

John von Neumann (December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, and polymath. Von Neumann was generally regarded as the foremost mathematician of his time and said to be “the last representative of the great mathematicians”; who integrated both pure and applied sciences.


A method is given for the numerical solution of the barotropic vorticity equation over a limited area of the earth’s surface. The lack of a natural boundary calls for an investigation of the appropriate boundary conditions. These are determined by a heuristic argument and are shown to be sufficient in a special case. Approximate conditions necessary to ensure the mathematical stability of the difference equation are derived. The results of a series of four z4-hour forecasts computed from actual data at the 500 mb level are presented, together with an interpretation and analysis. An attempt is made to determine the causes of the forecast errors. These are ascribed partly to the use of too large a space increment and partly to the effects of baroclinicity. The role of the latter is investigated in some detail by means of a simple baroclinic model.”

The atmosphere is treated as a single layer. Flow is nondivergent with absolute vorticity.



Forecast of CFvN from 5 Jan 1949. (a) Analysis of 500-hPa geopotential height (thick lines) and absolute vorticity (thin lines) for 0300 UTC 5 Jan. (b) Analysis for 0300 UTC 6 Jan. (c) Observed change (solid) and forecast change (dashed), (d) Forecast height and vorticity valid at 0300 UTC 6 Jan (from CFvN). Height units are hundreds of feet, contour interval is 200 ft. Vorticity units and contour interval (I0~5 s~’).

Numerical Weather Prediction

The Joint Numerical Weather Prediction Unit (JNWPU), a financial, administrative, and personnel collaboration of the U.S. Weather Bureau, Navy, and Air Force, opened its doors on 1 July 1954.

The Joint Numerical Weather Prediction Unit was established on July 1, 1954 by 3 agencies: Air Weather Service of US Air Force; The US Weather Bureau; The Naval Weather Service.

The operational unit was the culmination of research by the Meteorology Project at the Institute for Advanced Study in Princeton, New Jersey; the Numerical Prediction Project at the Air Force Cambridge Research Laboratory’s Geophysical Research Directorate; and the International Meteorological Institute in Stockholm, Sweden.

The JNWPU issued its first operational forecast on 6 May 1955—the day of its dedication with a three-level quasi-geostrophic model.


ECMWF was established in 1975. Its purpose – then as now – was to pool Europe’s meteorological resources to produce accurate climate data and medium-range forecasts.

The project was created by COST (European Cooperation in Science and Technology), which supported co-operation between scientists and technicians in Europe. The UK won a bid to host the Centre, thanks to the proximity of its proposed site to the UK Met Office and the University of Reading.

The first real-time medium-range forecasts were made in June 1979, and ECMWF has been producing operational medium-range weather forecasts since 1 August 1979. At first, forecasts were made five days a week. From 1 August 1980, they were made seven days a week.

The first ensemble predictions, produced as part of the operational forecasting system, were achieved on 24 November 1992.

ECMWF is based in Reading, UK.

On 30th October 2012 hurricane Sandy made landfall on the U.S east coast with a devastating impact. In this report we evaluate the forecast performance from the ECMWF HRES and ENS forecasts together with ensemble forecasts from other NWP centres, available from the TIGGE archive. The results show that the ECMWF forecasts predicted the landfall 7-8 days in advance.

Researchers interested in studying the dynamics, forecasting and predictability aspects of Sandy are invited to explore the forecast data from ECMWF, NCEP and other centres available through the TIGGE archive at:

Operational configurations of the ECMWF Integrated Forecasting System (IFS) resolution halves about every 8 years.

There has been a growth in forecast skill.

NWP today and tomorrow

It will get faster, better, greater enhancements, new observations, more comprehensive understanding of physical processes in the atmosphere. There will be a paradigm shift.

The equations of the atmosphere

The motion in the atmosphere is governed by a set of equations, known as the Navier-Stokes equations. These equations, solved numerically by computers, are used to produce our weather forecasts. While there are details about these equations which are uncertain (for example, how we parameterize processes smaller than the grid size of the models), the equations for the most part are accepted as fact.

Scientific forecasting in a nutshell

Weather forecasting is the application of current technology and science to predict the state of the atmosphere for a future time and a given location.

Weather forecasts are made by collecting as much data as possible about the current state of the atmosphere (particularly the temperature, humidity and wind) and using understanding of atmospheric processes (through meteorology) to determine how the atmosphere evolves in the future.

The atmosphere is a physical system.


The equations are complicated. There is an inherent limit in predictability.

Future progress

New observations and faster computers

Richardson’s Fantastic Forecast Factory


“Weather Forecasting Factory” by Stephen Conlin, 1986. Based on the description in Weather Prediction by Numerical Process, by L.F. Richardson, Cambridge University Press, 1922, and on advice from Prof. John Byrne, Trinity College Dublin. Image: ink and water colour, c. 50 x 38.5 cm. © Stephen Conlin 1986. All Rights Reserved ´. (Courtesy: Hendrik Hoffmann, School of Mathematics & Statistics, University College Dublin)


Table 1: list of individuals in the figure

A Lewis F. Richardson (1881-1953) in the pulpit, directing operations.

B John Napier (1550–1617) inventor of logarithms, which had a profound influence on the course of astronomy, and of science in general.

C Charles Babbage (1791-1871), mathematician, inventor and mechanical engineer, originated the concept of a programmable computer and designed highly advanced mechanical calculating machinery.

D Blaise Pascal (1623–1662) French mathematician, inventor, writer and philosopher. When only 18 years old, he constructed a mechanical calculator capable of addition and subtraction, called the Pascaline.

E Georg von Peurbach (1423–1461), Austrian astronomer and instrument maker who arranged for the first printed set of sines to be computed. He also computed a set of eclipse tables, the Tabulae Eclipsium, which remained highly influential for many years.

F Edmund Gunter (1581-1626), English clergyman and mathematician, inventor of the logarithmic ruler.

G William Oughtred (1574-1660), English mathematician and Anglican minister, inventor of the slide rule.

Walter Lilly (c. 1900), Lecturer in Mechanical Engineering, Trinity College Dublin, with his circular rule.

H Gottfried Wilhelm von Leibniz (1646-1716), mathematician and philosopher, who invented the first mass-produced mechanical calculator. His ‘Stepped Reckoner’, which performed addition, subtraction, multiplication and division, is illustrated on the table behind him, between Leibniz and George Fuller (one-time Professor of Engineering at Queen’s College, Belfast) with his spiral rule.

I Per Georg Scheutz (1785-1873), Swedish lawyer, translator, inventor and builder of the first practical difference engine. Scheutz’s calculator was used for generating tables of logarithms.

J Sir G. I. Taylor (1886-1975), distinguished hydrodynamicist, grandson of George Boole.

K The Arithmetic Research Room. Left to right:

Lord Kelvin (1824-1907) and his brother James Thomson (with a ball and disk integrator);

Percy Ludgate (1883-1922), Irish inventor of an Analytical Engine;

Ada Lovelace (1815-1852), daughter of Lord Byron and friend of Babbage;

George Boole (1815-1864), inventor of Boolean algebra.

L Tube Room, or “quiet room”, in which weather information is communicated within the forecast factory by pneumatic tube and to and from the outside world by wireless telegraphy.

M Hollerith machines in the research department.

N Scheutz Difference Engine in the research department.

P Radio masts for reception of observations and transmission of forecasts.

Q Public viewing gallery.

R A rosy light – shone on computers who are forward in their computations.

S A blue light – shone on computers who are behind in their computations.

T Recreation area, since “those who compute the weather should breathe of it freely”.


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