Lewis Fry Richardson's Forecast Factory for Real

Lewis Fry Richardson’s forecast factory – for real

Andrew Charlton-Perez horizontal momentum, pressure, humidity 1. Forecasts are made by solving math- and stratospheric temperature over central ematical equations which represent and Helen Dacre Europe, using initial conditions from an the physical laws governing the University of Reading analysis by Bjerknes for 20 May 1910. This atmosphere. forecast was manually computed by 2. Forecasts are often made on a grid of The idea that supercomputers are an impor- Richardson between 1916 and 1918, when, points which represent different geo- tant part of making forecasts of the weather as a Quaker (and therefore a pacifist), he graphical locations. and climate is well known amongst the gen- served as an ambulance driver in Cham- eral population. However, the details of their pagne, France. Famously, his forecast pro- use are somewhat mysterious. A concept duced very large tendencies in most of its A scaled-down forecast factory Weather – February 2011, Vol. 66, No. 2 66, No. Vol. 2011, – February Weather used to illustrate many undergraduate components – much larger than those In order to make the problem tractable for numerical weather prediction courses is the observed in the real atmosphere (Lynch, secondary-school-age children and to make idea of a giant ‘forecast factory’, conceived 2006, p.133, discusses the reasons for this). it possible to complete the activity in a rea- by Lewis Fry Richardson in 1922. In this Nonetheless, the principles of Richardson’s sonably short time (~30 minutes) it was article, a way of using the same idea to forecast, particularly the application of math- necessary to design a forecast factory which communicate key ideas in numerical ematical techniques to solving the primi- solved a much simpler problem than that weather prediction to the general public is tive equations on a grid representing the used by Richardson. Of course, the most dif- outlined and tested amongst children from atmosphere over the Earth’s surface, were ficult part of this scaling down was to retain local schools. sound and remain in use for many modern enough of his original idea so that we could numerical weather prediction methods. still communicate the key principles to par- The emergence of the forecast Richardson recognised that his underly- ticipants. To this end, instead of solving the ing idea for weather forecasting was indeed full primitive equations, we solved a simple factory robust, and in WPNP imagined the now two-dimensional advection equation on a An excellent and very readable review of famous ‘forecast factory’: single level (http://en.wikipedia.org/wiki/ the emergence of numerical weather pre- After so much hard reasoning, may one Advection). The velocity field is fixed and diction has been given by Lynch (2006). play with fantasy? Imagine a large hall like prescribed at the start of the experiment Here we provide a short review of the devel- a theatre, except that the circles and gal- (Figure 1(a)) and there is no feedback bet- opments leading to Lewis Fry Richardson’s leries go right round through the space ween our advected variable (which we call forecast factory idea in his Weather Prediction usually occupied by the stage. The walls of temperature for ease of communication) by Numerical Process (WPNP) (Richardson, this chamber are painted to form a map and the velocity field. 1922). of the globe. The ceiling represents the The equation is solved on a 4 x 4 grid using At the start of the century, weather fore- north polar regions, England is in the gal- a forward, upstream, finite- difference scheme. casting relied mainly on a combination of lery, the tropics in the upper circle, Australia By setting the velocity field to always blow analogue methods (comparing present con- on the dress circle and the Antarctic in the from the north and west it is possible to ditions with similar historical precedent) and pit. A myriad computers are at work upon ensure that the scheme is stable by effectively empirical, highly local, forecasting rules. the weather of the part of the map where making it an upwind scheme. The grid spac- This approach was challenged by, amongst each sits, but each computer attends only ing used is 100 kilometres, and four time steps others, Cleveland Abbe (1901), Vilhelm to one equation or part of an equation. of 3600 seconds each are taken. The initial Bjerknes (1904) and Felix Exner (1908) who and final fields for the advected variable are proposed that forecasting should be based This description of a ‘forecast factory’ is shown in Figures 1(b) and (c), respectively, and on the solution of mathematical equations both fabulously evocative and, as noted by are produced using an implementation of the that represent the physical processes that Lynch, remarkably prescient. Chapter 12 of scheme in Matlab. On a typical laptop com- govern the atmosphere. Richardson was Lynch’s book notes the various ways in puter it takes less than five seconds to run the amongst those who set out to develop prac- which the description matches modern code. As can be seen, the initial conditions tical methods to produce weather forecasts numerical weather prediction by massively and flow field are designed so that cold air on this basis. In WPNP, he sought to develop parallel processors. The aim of our project blows into the domain from the north and ways of solving the primitive equations on was to design a scaled-down version of the west and is advected towards the eastern a grid of points distributed over the globe forecast factory which could be worked on boundary. Although this bears little resem- and in several layers above the Earth’s sur- by children at secondary schools. We hoped blance to a real meteorological situation, it is face. Details of his numerical schemes and that, by encouraging them to take part in a useful schematic way of illustrating to the their equivalents in modern numerical an activity of this sort, we could communi- participants the way in which advection of models are examined by Lynch (2006). cate two key elements of modern numerical different air masses can have profound effects 52 Richardson then attempted to forecast the weather prediction: on local weather conditions. (a) Winds (b) Initial Temperature (c) Final Temperature they resulted in large temperature changes 30 at a grid point. Students could clearly observe

300 300 300 Richardson’s – for real factory forecast 25 the propagation of this erroneous tempera- C ° 20 ture through the field as they repeated cal- 200 200 200 culations for three more time steps. It was 15 possible for all four groups to complete four 100 100 100 10 time steps in each 45-minute session, with Temperature / North–South / km 5 the help and guidance of volunteers. 0 0 0 The experiment was repeated during the 0 0 100 200 300 0 100 200 300 0 100 200 300 NSEW event on 16 March 2010, again involv- East–West / km ing four groups of 14–16-year-old students. The same procedure was followed, but in Figure 1. (a) Fixed wind field; (b) initial temperature field and (c) final temperature field for fixed this instance time-evolving boundary con- boundary conditions. Colours show the temperature reading at each point in the 4 x 4 domain. ditions were used in order to make the calculations at the western boundary more Weather – February 2011, Vol. 66, No. 2 The choices we have made here are by no including flags, hats, and even a model interesting. A trial of a wireless data-input means the only way in which a forecast fac- sheep. system for the students had to be aban- tory for public communication could be To start the experiment, initial conditions doned because of faulty equipment, but designed. Indeed, with older students of for wind components and temperature this may be a useful future development. greater mathematical competence (say, to were passed to the students on coloured degree level) a more complex problem pieces of card. Each student used a comput- Reaction of students and might be solved (perhaps a simplified sys- ing form (Figure 2) to calculate a prediction teachers tem of the primitive equations with no phys- for the local temperature change over an ics). Recreating Richardson’s original forecast hour at their grid-point, using both the local We conducted a formal assessment of the using his original computing forms (Lynch, initial conditions and those at upstream reaction of pupils and teachers to the NSEW 2006, p129) would of course be a mammoth grid-points (to the north and west). open day activities, which also included a task given that it took Richardson over two Following each calculation, student data gravity-current experiment in the fluids years to complete his calculations. collectors were sent to each grid-point to laboratory and a radiosonde launch. Overall, retrieve predictions and these were then responses from the students and teachers quickly displayed on a computer screen. on both open days were very favourable Making it work with local The results were then compared with the (Figure 3). We also collected comments from school children exact calculations made using the computer the students on the day – some of the more interesting were: The first tests of the forecast factory exper- code described. iment were carried out on 19 March 2009 Remarkably, predictions from the human To predict and read the weather is more during a National Science and Engineering computers compared favourably with those difficult than I originally thought. Week (NSEW) open day at the University of of the computer code, although calculations It’s more interesting when you can actually Reading which was jointly hosted by the took about 30 million times as long (around see what happens and how it works. Department of Meteorology and the Walker 0.2x10–4 seconds per time step for the Matlab I learnt how much work goes into predict- Institute (Charlton-Perez et al., 2010). The code on a standard laptop and around 10 ing the weather into the future and how to experiment was carried out four times in a minutes per time step for the students). It do it manually. standard university classroom using differ- was also found to be an excellent educa- I learnt how to predict the weather with ent groups of 14–16-year-old school chil- tional opportunity to avoid correcting any equations. dren. Desks were arranged in a 4x4 grid: one calculation errors at each time step, even if Exciting and interesting. student sat at each desk and was joined by a volunteer member of staff from the Forecast factory worksheet University. Two students remained at the Constant values front of the classroom to act as data collec- Time-step (Δt) = 3600s tors throughout the experiment. This Grid-spacing (Δx) = 100 000m (100km) (in both x and y) T with no other qualifier means temperature at your location at the current time (use the initial condition in the first step) arrangement mirrors that of the sketch of the forecast factory which appears in Gandin Timestep 1 (1965). This sketch along with other depic- Δt tions of the forecast factory can be viewed T – ⎯ x u x T – T west + v x T north – T Δx on Peter Lynch’s website (http://maths.ucd. = T future ie/~plynch/Dream/ForecastFactory/FF.html). Timestep 2 Before starting the experiment, a short Δt – ⎯ – introduction to the forecast factory and T x u x T T west + v x T north – T Δx numerical weather prediction was given = T future to the students. No equations were shown, Timestep 3 Δt but a diagram indicating that temperature – ⎯ – – T x u x T T west + v x T north T at each grid-point would depend on the Δx = T future strength of the wind and the local temper- Timestep 4 ature gradient was shown to explain the Δt concept to the students. In order to com- – ⎯ – – T x u x T T west + v x T north T municate the idea that each student rep- Δx = T future resented a grid-point calculator at a different physical location in the UK, sev- Figure 2. Student worksheet used to make calculations – designed to mimic the structure of the eral props were distributed to the students equation solved as much as possible. 53 45 References 40 Abbe C. 1901. The physical basis of long-range weather forecasts. Mon. 35 Enjoyable Interesting Wea. Rev. 29: 551–561. 30 Ashford O. 1985. Prophet or Professor: The Life and Work of L.F. Richardson. 25 Bristol: Hilger. 20 Bjerknes V. 1904. Das Problem der Wettervorhersage, betracht vom 15 Standtpunkte der Mechanik und der Physik, Meteor. Zeit. 21: 1–7. Translation 10 by Y. Mintz: The problem of weather

Richardson’s forecast factory real – for Richardson’s 5 forecasting as a problem in mechanics and physics. Los Angeles 1954. Reprinted 0 in Shapiro and Grønås (1999). pp 1–4. Very Fairly Not very Not at all Don't know Charlton-Perez AJ, Dacre H, Maskell K, Reynolds R, South R, Wood C. Figure 3. Results of the evaluation by students and teachers of their enjoyment and interest in the 2010. Meteorology and climate inspire NSEW events in 2009 and 2010. secondary science students. School Science Review 92: 75–82. Charney JG, Fjörtoft R, von Neumann Next steps On a different scale, a mass participation J. 1950. Numerical integrations of the exercise, involving several hundred peo- barotropic vorticity equations. Tellus This or a similar activity could be used in a ple, along the lines of Richardson’s original 2: 237–254. number of ways to help communicate the daydream, might be a fantastic attention- Exner F. 1908. Über eine erste basis of numerical weather prediction to dif- grabbing communication opportunity for Annäherung zur Vorausberechnung syn- ferent groups. We have produced back- optischer Wetterkarten. Meteor. Zeit. 25: Weather – February 2011, Vol. 66, No. 2 66, No. Vol. 2011, – February Weather meteorological science. Perhaps the Royal ground material for teachers which could 57–67. Translated from German as: A first Albert Hall might be a potential venue! approach towards calculating synoptic be used for them to run the forecast factory The story of Richardson and WPNP is also forecast charts, with a biographical note experiment in schools with very limited an interesting lesson in science communica- on Exner by L. Shields and an introduction equipment (pencil, paper, and calculator: tion and the acceptance of novel ideas. Only by P. Lynch, Historical Note 1, Met Éireann. please contact the authors for details). At about 500 copies of WPNP were sold and Gandin L. 1965. Machines Forecast the Weather. Gidrometeoizdat: Leningrad. university level, a similar activity could be several reviewers suggested the book was Hunt JCR. 1998. Lewis Fry Richardson used as an introduction to numerical mod- difficult to understand (Ashford, 1985). elling or numerical weather prediction and his contributions to Mathematics, Although Charney et al. (1950) were able to courses. It would also be possible to make Meteorology and Models of Conflict. successfully apply numerical techniques to Ann. Rev. Fluid Mech. 30: xiii–xxxvi. the activity more complex by solving a true make a numerical forecast on the ENIAC Knox JA. 2000. L. F. Richardson’s ‘Forecast predictive equation similar to that used by computer, the results from numerical weather Factory’: A great idea for teaching Richardson. Knox (2000) described using a prediction only really began to dominate those weather forecasting. Journal of Geoscience similar forecast factory activity with college Education 48: 579–580. derived by the Bergen approach for 1- to 3-day students in the United States to introduce 2006. The Emergence of forecasts in the middle 1980s (Hunt, 1998). Lynch P. the different elements which are required Numerical Weather Prediction. Cambridge to make a weather forecast, including the University Press: Cambridge, MA. taking and processing of observations. It Acknowledgements Richardson LF. 1922. Weather Prediction The authors would like to thank their many by Numerical Process. Cambridge should be emphasised, however, that this University Press: Cambrdige, MA. activity is simply descriptive and does not colleagues in the departments of Mete- Reprinted 2006 by Cambridge University involve students making any calculations orology, Mathematics and the Environ- Press with a new introduction by themselves (although it would be very easy mental Systems Science Centre, who were Peter Lynch. to combine the activity described by Knox willing participants in the two trials of the with our own forecast factory). There are forecast factory experiment and essential to also many other simple cases that might be its success. We also thank Rachel South in Correspondence to: Andrew Charlton-Perez, used to illustrate particular meteorological the University of Reading widening-partici- Univeristy of Reading, phenomena. An interesting example is that pation office and the local schools and Earley Gate, PO Box 243, of the generation of a front from a north– teachers who took part. Finally, we would Whiteknights Reading, south temperature gradient distorted by a like to thank Peter Lynch for his encourage- RG6 6BB, UK constant vortex (Lynch, Pers. Comm., 2010). ment and a helpful and thorough review of [email protected] An example Matlab code for this case can our article. Helpful additional comments be found at http://mathsci.ucd.ie/met/msc/ were also received from an anonymous © Royal Meteorological Society, 2011 index.php?view=MatLab/main.txt reviewer. DOI: 10.1002/wea.670