he first weather forecasts executed on an auto- However, they were not verified objectively. In this matic computer were described in a landmark study, we recreate the four forecasts using data avail- Tpaper by Charney et al. (1950, hereafter CFvN). able through the National Centers for Environmental They used the Electronic Numerical Integrator and Prediction-National Center for Atmospheric Research Computer (ENIAC), which was the most powerful (NCEP-NCAR) 50-year reanalysis project. A com- computer available for the project, albeit primitive parison of the original and reconstructed forecasts by modern standards. The results were sufficiently shows them to be in good agreement. Quantitative encouraging that numerical weather prediction be- verification of the forecasts yields surprising results: came an operational reality within about five years. On the basis of root-mean-square errors, persistence CFvN subjectively compared the forecasts to analy- beats the forecast in three of the four cases. The mean ses and drew general conclusions about their quality. error, or bias, is smaller for persistence in all four cases. However, when SI scores (Teweles and Wobus 1954) are compared, all four forecasts show skill, and three FIG. I. Visitors and some participants in the 1950 ENIAC are substantially better than persistence. computations, (left to right) Harry Wexler, , M. H. Frankel, Jerome Namias, John Freeman, Ragnar PREPARING THE GROUND. John von Fjortoft, Francis Reichelderfer, and Jule Charney. (Provided by MIT Museum.) Neumann was one of the leading mathematicians of

AMERICAN METEOROLOGICAL SOCIETY JANUARY 2008 BAPIS" | 45

Unauthenticated | Downloaded 10/04/21 11:55 AM UTC the twentieth century. He made important contribu- impossibility of accurately calculating the divergence tions in several areas: mathematical logic, functional from the observations. The key paper, "On a physical analysis, abstract algebra, quantum , game basis for numerical prediction of large-scale motions theory, and the development and application of in the atmosphere" (Charney 1949), addresses some computers. In the mid-1930s von Neumann became crucially important issues. In this paper, Charney interested in turbulent fluid flows. He saw that prog- considered the means of dealing with high-frequency ress in hydrodynamics would be greatly accelerated if noise, proposing a hierarchy of filtered models. In his a means for solving complex equations numerically baroclinic instability study, Charney had derived a were available. It was clear that very fast automatic mathematically tractable equation for the unstable computing machinery was required. According to waves "by eliminating from consideration at the Thompson (1983), von Neumann regarded weather outset the meteorologically unimportant acoustic prediction by numerical means as "the most complex, and shearing-gravitational oscillations" (Charney interactive, and highly nonlinear problem that had 1947). He realized that a general filtering principle ever been conceived of—one that would challenge the was desirable. Such a system would have dramatic capabilities of the fastest computing devices for many consequences for numerical integration. The time years." Indeed, has remained a step dictated by the CFL criterion varies inversely grand challenge for computing ever since. with the speed of the fastest solution—fast gravity In May 1946, a proposal to establish the waves imply a very short time step, and the removal Project at the Institute for Advanced Study (IAS) in of these waves leads to a far less stringent limitation, Princeton, New Jersey, was successful in attracting funds allowing a much larger time step to be used. from the U.S. Navy's Office of Research and Inventions An account of the filtered system was published [the proposal is reprinted in Thompson (1983)]. A in the paper "On the scale of atmospheric motions" conference on meteorology was arranged at IAS the (Charney 1948); this paper was to have a profound following August, and many of the leaders of the field impact on the subsequent development of dynamic attended. At the time, Jule Charney was visiting Rossby, meteorology. Charney analyzed the primitive equa- who arranged for him to participate in the conference. tions using the technique of scale analysis. He was Perhaps the most significant consequence of this con- able to simplify the system in such a way that the ference was the opportunity for von Neumann to meet gravity wave solutions were completely eliminated. Charney. Von Neumann later persuaded Charney to The resulting equations are known as the quasi- lead the Meteorology Project, the primary goal of which geostrophic equations. The system boils down to a was to investigate weather prediction by numerical single prognostic equation for the quasigeostrophic means. The project ran from 1948 to 1956. potential vorticity. All that is required by way of The initial plan was to integrate the primitive initial data to solve this equation is a knowledge of equations of the atmosphere, but the existence of the three-dimensional pressure field (and appropriate high-speed gravity wave solutions meant that the boundary conditions). volume of computation would exceed the capabilities In the special case of horizontal flow with con- of the available computers. The limitation, known stant static stability, the vertical variation can be as the Courant-Friedrichs-Lewy (CFL) criterion, separated out and the quasigeostrophic potential restricts the maximum time step permitted for vorticity equation reduces to the nondivergent baro- stable numerical integrations (Courant et al. 1928). tropic vorticity equation [BVE; see appendix A, (Al)]. There was also a more fundamental difficulty: the This equation represents the conservation of absolute vorticity, the sum of the vorticity of the flow, and the vorticity resulting from the Earths spin. The baro- AFFILIATIONS: —University College Dublin, Dublin, Ireland LYNCH tropic equation had, of course, been used by Rossby CORRESPONDING AUTHOR: Peter Lynch, UCD Meteorology in his analytical study of atmospheric waves (Rossby & Climate Centre, School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland 1939), but the scientific view was that it was incapable E-mail: [email protected] of producing a quantitatively accurate prediction of atmospheric flow. We will describe the pioneering The abstract for this article can be found in this issue, following the achievement of the group that carried out the first table of contents. DOI: 10.1175/BAMS-89-I-45 numerical integration of this simple equation, and will present the results of repeating the forecasts In final form 4 July 2007 ©2008 American Meteorological Society using initial data derived from the NCEP-NCAR 50-year reanalysis.

46 I BAflS- JANUARY 2008

Unauthenticated | Downloaded 10/04/21 11:55 AM UTC INTO ACTION. The original integrations, which required to solve the BVE were investigated. It tran- were the first computer weather forecasts ever made, spires that, to determine the motion, it is necessary are described in the much-cited paper of CFvN. This and sufficient to specify the height on the whole paper gives a complete account of the computational boundary and the vorticity over that part where the algorithm and discusses four forecast cases, all from flow is inward. initial data in 1949. The paper caused quite a stir when Initial data for the forecasts were taken from the it appeared. A close study of it is recommended to manual 500-hPa analysis of the U.S. Weather Bureau, readers wishing to have a deeper understanding of this discretized to a grid of 19 x 16 points (Fig. 2). The pioneering work, because we must omit many details. grid interval was 736 km at the North Pole (494 km The authors outlined their reasons for starting at 20°N), corresponding to 8° longitude at 45°N. with the barotropic equation as follows: the large- Centered spatial finite differences and a leapfrog scale motions of the atmosphere are predominantly time scheme were used. The boundary heights were barotropic; the simple model could serve as a valuable held constant, at their initial values, throughout each pilot study for more complex integrations; and, if the 24-h integration. The BVE gives an expression for the results proved to be sufficiently accurate, barotropic rate of change of the Laplacian of geopotential height forecasts could be utilized in an operational context. in terms of the advection (the Jacobian term). Once In fact, few if any people anticipated the enormous this quantity is calculated, the tendency of the height practical value of this simple model and the leading field is obtained by solving a Poisson equation with role it was to play in operational prediction for many homogeneous boundary conditions. The height may years to come (Platzman 1979). then be advanced to the next time level. This cycle The ENIAC, which had been completed in 1945, may be repeated as often as required. was the first multipurpose electronic digital computer As the construction of von Neumann s computer ever built. It was installed at the U.S. Army's Ballistics at IAS was delayed, permission was obtained to use Research Laboratories at Aberdeen, Maryland. ENIAC. This was arranged through the offices of ENIAC was gigantic, weighing 30 tons, with 18,000 Francis Reichelderfer, Chief of the Weather Bureau. thermionic valves, massive banks of switches, and The story of the mission to Aberdeen was recounted large plug boards with tangled skeins of connecting by George Platzman (1979) in his Victor P. Starr wires, filling a large room and consuming some Memorial Lecture. The venture began on 5 March 140 kW of power. Program commands were specified 1950 when "an eager band of five meteorologists by setting the positions of a multi- tude of 10-pole rotary switches on large arrays called function tables, and input and output were generated by means of punch cards. The time between machine failures was typi- cally a-few hours, making the use of the computer a wearisome task for those operating it. McCartney (1999) provides an absorbing account of the origins, design, development, and destiny of ENIAC. Figure 1 shows some of the key personalities associated with the first computer forecasts. The derivation of the basic pre- diction equation and the numerical algorithm used to solve it are fully described in appendix A. The equa- tion chosen by CFvN was formulated using the geopotential height as the prognostic variable. The advection FIG. 2. Computation grid used for the ENIAC forecasts. One line is term was expressed as a Jacobian. omitted from the southern edge and two lines from the remaining The lateral boundary conditions edges (from CFvN).

AMERICAN METEOROLOGICAL SOCIETY JANUARY 2008 BANS' | 47

Unauthenticated | Downloaded 10/04/21 11:55 AM UTC arrived in Aberdeen, Maryland, to play their roles the month). Despite these difficulties, the expedition in a remarkable exploit." The five players were ended in triumph. Four 24-h forecasts were made, Jule Charney, Ragnar Fjortoft, John Freeman, and the results clearly indicated that the large-scale George Platzman, and Joseph Smagorinsky. The features of the midtropospheric flow could be fore- work continued for 33 days and nights, with only cast barotropically with a reasonable resemblance brief interruptions. The trials and tribulations of to reality. this intrepid troupe were described in Platzman's The forecast starting at 0300 UTC 5 January 1949 lecture. There were the usual blunders familiar to is shown in Fig. 3. Figure 3a is the analysis of 500-hPa programmers. The difficulties were exacerbated by geopotential and absolute vorticity, based on the U.S. the primitive machine language, the requirement to Weather Bureau manual analysis. Figure 3b is the cor- set numerous switches manually, the assignment of responding analysis 24 h later. The forecast height and scale factors necessitated by the fixed-point nature vorticity are shown in Fig. 3d. This prediction was, of ENIAC, and the tedious and intricate card-deck according to CFvN, "uniformly poor." The feature of operations (about 100,000 cards were punched during primary interest was an intense depression over the

FIG. 3. 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 fore- cast 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~').

48 I BAflS- JANUARY 2008

Unauthenticated | Downloaded 10/04/21 11:55 AM UTC United States. This deepened and moved northeast reanalysis Web site, converted from Gridded Binary to the 90°W meridian in 24 h. The forecast displace- (GRIB) to American Standard Code for Information ment was too slow and the shape of the depression Interchange (ASCII), and interpolated to the ENIAC was distorted. Also, the low center over the Gulf of grid. California in the verifying analysis is absent in the forecast (but, as we will see, it is also absent in the RECREATING THE FORECASTS. At the time reanalysis). of the ENIAC experiment, computer programming CFvN considered the causes of the errors in their was at an embryonic stage of development. Given the forecasts, and attempted to distinguish between the limitations of the hardware, with just a dozen or so following various factors: spatial truncation, limita- internal registers for data storage, the solution of the tions of the model formulation, and the effects of equations had to be broken down into elementary, baroclinicity versus barotropy. We will not pursue discrete steps. The results of each computation this line; however, those interested may easily investi- were punched onto cards, and these punch cards gate the effects of truncation by rerunning the model provided the inputs for the following steps. The with a higher spatial resolution; both the model and programming was at the level of machine code; data are available (see appendix B). high-level languages such as FORTRAN were still in the future. In recreating the forecasts, we have THE NCEP-NCAR REANALYSIS. The initial the luxury of using powerful, user-friendly coding fields for the four ENIAC forecasts were valid for languages. The MATLAB system has been selected 5 January, 30-31 January, and 13 February 1949, because it is simple to learn, is widely available, and predating automated data assimilation and numerical has an embedded graphical system. (Free software prediction, so no objective analyses were produced in similar to MATLAB is available; www.gnu.org/ real time. Thus, when a reconstruction of the fore- software/octave/.) casts was first conceived, a laborious digitization of The CFvN paper provides a full description of the hand-drawn charts from the pre-NWP era appeared solution algorithm. The program eniac.m was con- necessary However, a retrospective global analysis structed following the original algorithm precisely, of the atmosphere, covering more than 50 years, has including the specification of the boundary condi- been undertaken by NCEP and NCAR. Because the tions and the Fourier transform solution method reanalysis extends back to 1948, it includes the period for the Poisson equation. Hence, given initial data chosen for the ENIAC integrations. The NCEP-NCAR identical to that used in CFvN, the recreated fore- 50-year reanalysis is described by Kistler et al. (2001); casts should be identical to those made in 1950. Of it is a development from an earlier 40-year reanalysis course, the reanalyzed fields are not identical to (Kalnay et al. 1996). The products are freely available those originally used, and the verification analyses from NCEP, NCAR, and the National Oceanic and are also different. Thus, the expectation of an exact Atmospheric Administration (NOAA). replication of the original forecasts is unrealistic. The reanalysis project used a three-dimensional Nevertheless, we will see that the original and new variational data assimilation (3DVAR) scheme called results are very similar. spectral statistical interpolation (Parrish and Derber Figure 4 is the reconstructed forecast for 0300 UTC 1992). The spectral representation had a triangular 6 January. The layout is as for Fig. 3. The main truncation of 62 waves, corresponding to a horizontal features of the analyses are in broad agreement with resolution of about 210 km. Prior to the International the originals. Also, the forecast shows the inad- Geophysical Year in 1957, upper-air observations equate speed of movement of the low center and its were generally made at 0300 and 1500 UTC, and distortion, as in the original forecast. Despite their occasionally at 0900 and 2100 UTC. For this reason, similarities, the original and reanalyzed fields have the reanalysis for the first decade (1948-57) was marked differences. Note, for example, the low center performed at 0300, 0900, 1500, and 2100 UTC. over the Gulf of California in the original verifying This is ideal, because the initial time for each of analysis (Fig. 3b), which is absent in the reanalysis. the four ENIAC forecasts was 0300 UTC. The data We may recall the dearth of upper-air observations are available on a 2.5° x 2.5° grid. While relatively in 1949, especially over the oceans, which resulted in coarse by modern standards, this is far above the significant uncertainties in the analysis. resolution used in the ENIAC runs, which had a grid Objective verification scores for the four recon- spacing of about 8° longitude (at 45°N). The 500-hPa structed forecasts are presented in Table 1. There is analyses were downloaded from the NCEP-NCAR a substantial bias error in all the forecasts; the mean

AMERICAN METEOROLOGICAL SOCIETY JANUARY 2008 BAPIS" | 49

Unauthenticated | Downloaded 10/04/21 11:55 AM UTC FIG. 4. Reconstructed forecast for 5 Jan 1949: (a) analysis of 500-hPa geopotential height (thick lines) for 0300 UTC 5 Jan, (b) analysis for 0300 UTC 6 Jan, (c) observed change (solid) and forecast change (dashed), and (d) forecast height valid at 0300 UTC 6 Jan. Height contour interval is 50 m.

errors greatly exceed those of a persistence forecast. putations (Nebeker 1995). Addressing the National The root-mean-square (RMS) error is greater than Academy of Sciences, Charney said, "It mattered persistence in case 1, less in case 2, and about equal little that the twenty-four-hour prediction was in the remaining cases. The SI score, introduced at twenty-four hours in the making. That was purely a an early stage of NWP (Teweles and Wobus 1954), technological problem. Two years later we were able measures skill in predicting gradients that are to make the same prediction on our own machine meteorologically significant. The SI score is about the [von Neumann's IAS computer] in five minutes" same as that of persistence for case 1 and significantly (Charney 1955). better for the other three cases. On the basis of this During his Starr Lecture, George Platzman score, all four forecasts have some skill. arranged with IBM to repeat one of the ENIAC In CFvN it is noted that the computation time for forecasts. The algorithm of CFvN was coded on an a 24-h forecast was about 24 h, that is, the team could IBM 5110, a desktop machine then called a portable just keep pace with the weather provided ENIAC computer or "PC" (having a tiny fraction of the did not fail. This time included offline operations: power of a modern PC). The program execution reading, punching, and interfiling punch cards. Von was completed within the hour or so of Platzman's Neumann estimated that it would have taken five lecture. This implies a 24-fold speedup over the best hand-computer years to duplicate the ENIAC com- rate achievable for ENIAC. The program eniac.m

50 I BAflS- JANUARY 2008

Unauthenticated | Downloaded 10/04/21 11:55 AM UTC was run on a Sony Vaio (model VGN-TX2XP) with TABLE 1. Mean error (bias), RMS error (m), and MATLAB version 6. The main loop of the 24-h fore- SI score for the four forecasts (Fcst) and for cast ran in about 30 ms. One may question the precise corresponding persistence forecasts (Pers). In each significance of the time ratio—about three million to case, bold type indicates whether the forecast or one—but it certainly indicates the dramatic increase persistence is better. in computing power over the past half-century. Mean error RMS error SI score Case Fcst Pers Fcst Pers Fcst Pers INTO OPERATIONS. In an interview with George Platzman, Charney said "I think we were 1 56 -9 113 95 61 62 all rather surprised that the predictions were as 2 31 6 99 115 46 63 good as they were" (Platzman 1990). Reviewing 3 -35 20 93 89 46 58 Charney's influence on meteorology some years 4 39 1 82 81 39 50 later, Norman Phillips wrote that the success of the ENIAC integrations was so clear that "the idea of numerical prediction began to be accepted November 1950. This storm became a popular case immediately by the meteorological community" study, because it brought unusually severe weather (Phillips 1990). The encouraging initial results of and had not been well predicted in real time.1 It was the Princeton team generated widespread interest believed that baroclinic processes, which are not rep- and raised expectations that operationally use- resented in the single-level model, were an essential ful computer forecasts would soon be a reality. factor in the rapid development of the storm. Phillips Within a few years research groups were active in found, using a two-level filtered model, that there several universities and national weather services. were large errors associated with the excess of the The striking success of the barotropic forecasts geostrophic wind over the true wind and that the had come as a surprise to most meteorologists. The streamfunction formulation resulted in a marked barotropic vorticity equation simply states that the improvement in the forecast. In that paper (Phillips absolute vorticity of a fluid parcel is constant along 1958), published in Festschrift for the 60th birthday its trajectory; the equation seemed too idealized to of Erik Palmen, Phillips remarked that operational have any potential for operational use. The richness experience with the streamfunction equation "has and power encapsulated in its nonlinear advection appreciably improved the forecasts." In a similar were greatly underestimated. Evidence that even vein, George Cressman, the first director of the Joint the rudimentary barotropic model was capable of Numerical Weather Prediction Unit, established in producing forecasts comparable in accuracy to those 1954, recalled that the spurious distortion of the produced by conventional manual means rapidly flow in low latitudes was partly resolved by using the accumulated. Indeed, baroclinic models used for streamfunction equation (Cressman 1996). Thus, it early NWP operations were found to perform poorly, is of interest to rerun the four ENIAC integrations and the single-level model was reintroduced. The using this equation and then compare them to the humble barotropic vorticity equation continued to original forecasts. provide useful guidance for almost a decade. The four forecasts were repeated using the streamfunction equation [appendix A, (A5)]; the A SIMPLE ENHANCEMENT. A commemora- initial streamfunction was obtained by dividing the tive symposium was held in Potsdam, Germany, in geopotential height by a constant mean-latitude value March 2000 to mark the 50th anniversary of NWP. of the Coriolis parameter. The verification scores are In his address at this gathering, Norman Phillips given in Table 2. The bias is more negative in all cases expressed the view that quasigeostrophic models and substantially smaller in all but case 3. The RMS might have been more productive if a streamfunction error is smaller in all cases. The SI score, averaged had been used in place of the geopotential (Phillips over all four cases, has improved by about a point. We 2000). Use of the streamfunction form avoids the conclude from this admittedly limited evidence that omission of a term involving the gradient of the the streamfunction form of the BVE is superior. Coriolis parameter (the beta term), yielding a more accurate equation (see appendix A). Phillips had good 1 The Thanksgiving storm has been successfully predicted reason for his claim: much earlier, he had rerun a using a modern NWP system and data from the NCEP- forecast of the famous Thanksgiving storm, a major NCAR 50-year reanalysis, yielding a remarkably accurate cyclonic development in the eastern United States in 4-day forecast (Kistler et al. 2001).

AMERICAN METEOROLOGICAL SOCIETY JANUARY 2008 BAPIS" | 51

Unauthenticated | Downloaded 10/04/21 11:55 AM UTC TABLE 2. Mean error (bias), RMS error (m), and SI score for the only an advance, but the beginning of four forecasts using the height equation (z EQN) and the stream- an onward march that is continuing function equation (y EQN). In each case, bold type indicates to this day. which forecast is better. Mean error RMS error SI score ACKNOWLEDGMENTS. The author acknowledges helpful correspon- Case z EQN y EQN z EQN y EQN z EQN y EQN dence with Kenneth Campana, Robert 44 107 61 61 1 56 113 Kistler, John Knox, Norman Phillips, 2 31 23 99 89 46 44 and George Platzman. The assistance 3 -35 -40 93 88 46 45 of Hendrik Hoffmann in preparing fig-

4 39 20 82 72 39 37 ures and Chi-Fan Shih in acquiring the 0300 UTC reanalysis data is gratefully acknowledged. The pioneers who performed the ENIAC integra- tions might have used this equation and obtained APPENDIX A. SOLUTION OF THE BARO- better results. But, the initial data were for heights, TROPIC VORTICITY EQUATION. The method and this must have seemed a more natural choice of chosen by CFvN to solve the barotropic vorticity variable. The determination of the initial streamfunc- equation, tion via the crude geostrophic relationship would not have appeared promising, and a more accurate + V-V(f+ /) = 0, (Al) relationship between the mass and wind fields, the dt dt nonlinear balance equation, would have been difficult to solve on ENIAC. Moreover, CFvN did not have the was based on using geopotential height as the prog- luxury of testing alternative formulations without nostic variable/1 If the wind is taken to be both considerable effort. geostrophic and nondivergent, we have

EPILOGUE: DOROTHY S VIEW. CFvN were V = (g/f) k x Vz; V = k x Vy. greatly inspired by the earlier attempt by Lewis Fry Richardson to predict atmospheric changes The vorticity is given by C = V2i//. These relationships (Richardson 1922). Richardson's experiment produced lead to the linear balance equation outlandish results, for reasons that are examined in depth by Lynch (2006). It is gratifying that Richardson C= V- (g/f) Vz = (g/f) V2z + pu/f. (A2) was made aware of the success in Princeton; Charney sent him copies of several reports, including the CFvN ignored the jS term, which can be shown by paper on the ENIAC integrations (Platzman 1968). scaling arguments to be small. They then expressed Richardson congratulated Charney and his collabora- the advection term as a Jacobian, tors "on the remarkable progress which has been made

in Princeton; and on the prospects for further improve- v.Va = -^ — — + ^ — — A3 ment which you indicate." He then described a "tiny fdydx f dx dy ( > psychological experiment" on the diagrams in the Tellus paper, which he had performed with the help of his wife Dorothy. For each of the four forecasts, he asked / her opinion as to whether a prediction of persistence Now, using (A2) and (A3) in (Al), they arrived at was better or worse than the numerical prediction. Dorothy's view, tabulated in detail in Platzman (1968), was that the numerical prediction was, on average, better, though only marginally. The case that Dorothy identified as definitely better was the forecast starting This was taken as their basic equation [Eq. (8) in from the 31 January analysis. This was also identified CFvN]. It is interesting to observe that, had they by Charney as "surprisingly good" (Platzman 1979). Richardson concluded that the ENIAC results were A1 All mathematical notation in this appendix is in accordance "an enormous scientific advance" on his own forecast, with standard meteorological usage and is consistent with which was completely unrealistic. Indeed, they were not CFvN.

52 I BAflS- JANUARY 2008

Unauthenticated | Downloaded 10/04/21 11:55 AM UTC chosen the streamfunction rather than the geopo- The Poisson equation [(A7)] was solved using tential as the dependent variable, they could have a direct method devised by von Neumann. This used the equation method was more suited to the ENIAC than itera- tive relaxation methods, such as that of Richardson. Each step required four one-dimensional Fourier —(vy)=/(vy+/.y). (as) ot transforms. For a grid of (K + 1) x (L + 1) points, the solution may be written as thereby avoiding the neglect of the /? term in (A2). The ikn jln kmn Inn boundary conditions required (dz\ f As2\K~l L~l K~l L~l sin -— sin —- sin sin K L K L to solve (A4) were investigated. I — J = - S S (A8) sjn 2 kn 2 In— dti It transpires that to determine \KLj iml H k9l M the motion it is necessary and 2K 2 L sufficient to specify z on the whole boundary and ( over that part where the flow (complete details may be found in CFvN). For the is inward. integration of (A5), the initial streamfunction was

The vorticity equation was transformed to a polar defined as xf/ = gz/fQ, where/0 is the Coriolis parameter stereographic projection; this introduces a map factor evaluated at 45°N. m = 2/(1 + sin

AMERICAN METEOROLOGICAL SOCIETY JANUARY 2008 BAPIS" | 53

Unauthenticated | Downloaded 10/04/21 11:55 AM UTC PrepICs.m to interpolate them FUNCTION ENIAC PUNCH-CARD PUNCH-CARD to a polar stereographic grid. TABLES OPERATIONS OUTPUT OPERATIONS Maps of the four original and m JUL recreated forecasts are also Coriolis parameter Time-step Map foctor New height and Prepare input deck extrapolation available, along with miscel- Scale factors new vorticity for Operation 4 m laneous supplementary ma- Jacobian terial relating to the ENIAC Scale foctors Vorticity (vorticity advection) tendency integrations. m x-smes First Fourier Ix-transform of I Prepare input deck Scole fodors transform (x) [vorticity tendency | for Operation 8 | REFERENCES m rsjoi Charney, J. G., 1947: The dy- y-sines Second Fourier yx - transform of Prepare input deck Scale factors tronsform (y) vorticity tendency for Operation II namics of long waves in a baroclinic westerly current. 1 12 1 y - sines Third Fourier fyyx-transform of Prepare input deck /. Meteor4, 135-162. Scale factors tronsform (y) 1 vorticity tendency [for Operation 13 | , 1948: On the scale of at- nr rwi mospheric motions. Geofys. x- sines 1 Height 1 Prepare input deck 1 Scale factors |tendency for Operation 15 Publ., 17, 3-17. , 1949: On a physical basis for LL. rw~] Interleave Height tendency Prepare input deck numerical prediction of large- height and vorticity and tendencies vorticity tendency for Operation 1 scale motions in the atmo- sphere. /. Meteor„ 6,371-385. FIG. Bl. Flowchart showing the 16 operations required for each time step , 1955: Numerical methods in of the ENIAC forecast (from Platzman 1979). dynamical meteorology. Proc. Nat. Acad. Sci41,798-802. 3) The initial and verifying analyses are read in and , R. Fjortoft, and J. von Neumann, 1950: Numeri- plotted. cal integration of the barotropic vorticity equation. 4) The main time loop begins. Tellus, 2, 237-254. a) Spatial derivatives are computed by finite Courant, R., K. O. Friedrichs, and H. Lewy, 1928: Uber differences. The vorticity and Jacobian are die partiellien Differenzengleichungen der math- determined. The tendency of the Laplacian ematischen Physik. Math. Ann., 100, 32-74. of height £ is given by the Jacobian. Cressman, G. P., 1996: The origin and rise of numerical b) Energy and enstrophy are calculated weather prediction. Historical Essays on Meteorol- (nonessential diagnostics). ogy 1919-1995, J. R. Fleming, Ed., Amer. Meteor. c) The updated values of t; at the lateral Soc., 21-39. boundaries are computed. Haltiner, G. J., and R. T. Williams, 1980: Numerical d) The values of £ and of z at the next time step Prediction and Dynamic Meteorology. John Wiley are calculated using the leapfrog method. and Sons, 477 pp. e) Intermediate forecast height fields may be Kalney, E., and Coauthors, 1996: The NCEP/NCAR plotted. 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., f) Housekeeping operations complete the time 77, 437-471. step. Kistler, R., and Coauthors, 2001: The NCEP-NCAR 50- 5) Energy and enstrophy are plotted (for diagnostic year reanalysis: Monthly means, CD-rom and docu- purposes). mentation. Bull. Amer. Meteor. Soc., 82, 247-268. 6) The forecast height field is plotted. Forecast and Lynch, P., 2006: The Emergence of Numerical Weather observed height changes are computed and plotted Prediction: Richardson's Dream. Cambridge in a format similar to that used in CFvN. University Press, 290 pp. 7) Verification scores are computed. McCartney, S., 1999: ENIAC: The Triumphs and Tragedies of the World's First Computer. Berkley The MATLAB code of eniac.m is available on the Books, 262 pp. authors Web site (http://mathsci.ucd.ie/~plynch/ Nebeker, F., 1995: Calculating the Weather: Meteo- eniac/). The relevant analyses, on a global 2.5° x 2.5° rology in the 20th Century. Academic Press, vii grid are also obtainable there, together with a program + 255 pp.

54 I BAflS- JANUARY 2008

Unauthenticated | Downloaded 10/04/21 11:55 AM UTC Parrish, D. F., and J. D. Derber, 1992: The National Meteorological Center spectral statistical inter- polation analysis system. Mon. Wea. Rev., 120, REQUEST FOR 1747-1763. Phillips, N. A., 1958: Geostrophic errors in predicting the PREPROPOSALS Appalachian storm of November 1950. Geophysica, 6, 389-405. FOR SCIENTIFIC RESEARCH AT , 1990: The emergence of quasi-geostrophic theory. THE U.S. DEPARTMENT OF ENERGY'S The Atmosphere—A Challenge. The Science of Jule Gregory Charney, R. S. Lindzen, E. N. Lorenz, ATMOSPHERIC RADIATION and G. W. Platzman, Eds., Amer. Meteor. Soc., MEASUREMENT (ARM) CLIMATE 177-206. RESEARCH FACILITY (ACRF) , 2000: The start of numerical weather prediction in the United States. 50th Anniversary of Numerical Atmospheric Radiation Measurement CLIMATE RESEARCH FACILITY Weather Prediction. Commemorative Symposium, A. U.S. Department of Energy Spekat, Ed., Deutsche Meteorologische Gesellschaft, 13-28. The U.S. Department of Energy welcomes Platzman, G. W., 1968: Richardson's weather prediction. preproposals for FY 2010 field campaigns Bull. Amer. Meteor. Soc., 49,496-500. requesting use of any of the ACRF sites/ facilities: the Southern Great Plains, Tropical , 1979: The ENIAC computations of 1950—Gateway Western Pacific, North Slope of Alaska, ARM to numerical weather prediction. Bull Amer. Meteor. Mobile Facility (AMF), or the ARM Aerial Soc., 60, 302-312. Vehicles Program (AVP). The due date for , 1990: Charney's recollections. The Atmosphere—A preproposals is February 1, 2008. Preproposals Challenge. The Science of Jule Gregory Charney, R. should be submitted online through the field S. Lindzen, E. N. Lorenz, and G. W. Platzman, Eds., campaign form at www.arm.gov/acrf. Requests for use of the AMF should include a deployment Amer. Meteor. Soc., 11-82. time of 6 to 10 months (any exceptions must Richardson, L. F., 1922: Weather Prediction by Numerical be approved by the DOE Program Director). Process. Cambridge University Press, 236 pp. Preference will be given to AMF deployments (Reprinted by Dover Publications, 1965, with a new in which the AMF is embedded in a larger field introduction by S. Chapman; 2d ed. by Cambridge campaign. It is recommended that proposals for University Press, 2007, with a new introduction by short-term ARM AVP campaigns (6 weeks or less) make use of the ARM fixed sites or the AMF. P. Lynch.) Flights over ground remote sensing facilities Rossby, C.-G., and Coauthors, 1939: Relations between (but not necessarily ARM's) are also desirable. A variations in the intensity of the zonal circulation of select number of full proposals will be invited, the atmosphere and the displacements of the semi- which will be due on May 15, 2008. For more permanent centers of action. /. Mar. Res., 2, 38-55. information on ACRF field campaigns, see Teweles, S., and H. Wobus, 1954: Verification of the planning document at http://www.arm. gov/acrf/iopdocs. To be invited to submit a prognostic charts. Bull. Amer. Meteor. Soc., 35, full proposal, the Principal Investigator (PI) 455-463. should demonstrate in the preproposal that Thompson, P. D., 1983: A history of numerical weather research funding for PI effort has already prediction in the United States. Bull. Amer. Meteor. been secured or that a proposal to a funding Soc., 64, 755-769. agency has already been submitted. ACRF supports facility use and logistical considerations, but does not support research effort, travel, or per diem. The ACRF has enormous potential to contribute to a wide range of interdisciplinary science in areas such as water cycle, carbon cycle, cloud physics, aerosols, and weather prediction. Proposals should focus on science issues that improve understanding of the interactions between clouds and atmospheric radiative fluxes and that have the potential to lead to improved climate models.

AMERICAN METEOROLOGICAL SOCIETY JANUARY 2008 BAPIS" | 55

Unauthenticated | Downloaded 10/04/21 11:55 AM UTC www.weatherwise.

56 | BAH* JANUARY 2008 Unauthenticated | Downloaded 10/04/21 11:55 AM UTC