The origins of computer weather prediction and climate modeling

Abstract

Numerical simulation of an ever-increasing range of geophysical phenomena is adding enormously to our understanding of complex processes in the Earth system. The consequences for mankind of ongoing climate change will be far-reaching. Earth System Models are capable of replicating climate regimes of past millennia and are the best means we have of predicting the future of our climate.

The basic ideas of numerical forecasting and climate modeling were developed about a century ago, long before the first electronic computer was constructed. There were several major practical obstacles to be overcome before numerical prediction could be put into practice. A fuller understanding of atmospheric dynamics allowed the development of simplified systems of equations; regular radiosonde observations of the free atmosphere and, later, satellite data, provided the initial conditions; stable finite difference schemes were developed; and powerful electronic computers provided a practical means of carrying out the prodigious calculations required to predict the changes in the weather.

Progress in weather forecasting and in climate modeling over the past 50 years has been dramatic. In this presentation, we will trace the history of computer forecasting through the ENIAC integrations to the present day. The useful range of deterministic prediction is increasing by about one day each decade, and our understanding of climate change is growing rapidly as Earth System Models of ever-increasing sophistication are developed.

Introduction

Among the most significant scientific advances of the past century is our ability to simulate complex physical systems using numerical models and therewith to predict their evolution. One outstanding example is the development of general circulation models (GCMs) of the atmosphere and ocean, which have brought two great advantages: We can now predict the weather for several days in advance with a high degree of confidence, and we are gaining great insight into the factors causing changes in our climate, and their likely timing and severity.

A century ago, weather forecasting was a haphazard process, very imprecise and unreliable. Observations were sparse and irregular, especially for the upper air and over the oceans. The principles of theoretical physics played little or no role in practical forecasting: the forecaster used crude techniques of extrapolation, knowledge of local climatology and guesswork based on intuition; forecasting was more an art than a science. The observations of pressure and other variables were plotted in symbolic form on a weather map and lines drawn through points with equal pressure revealed the pattern of weather systems – depressions, anticyclones, troughs and ridges. The forecaster used his experience, memory and a variety of empirical rules to produce a forecast map. The primary physical process attended to by the forecaster was advection, the transport of fluid characteristics and properties by the movement of the fluid itself. But the crucial quality of advection is that it is nonlinear; the human forecaster may extrapolate trends using an assumption of constant wind, but is quite incapable of intuiting the subtleties of complex advective processes.

The development of thermodynamics in the 19th century resulted in a completion of the set of fundamental physical principles governing the flow of the atmosphere. By about 1890, the great American meteorologist Cleveland Abbe (Fig. 1, left panel) had recognized that “meteorology is essentially the application of hydrodynamics and thermodynamics to the atmosphere” [28]. In his paper, The physical basis of long-range weather forecasting, Abbe [1] proposed a mathematical approach to forecasting. He expressed a hope that atmospheric scientists would “take up our problems in earnest and devise either graphical, analytical, or numerical methods” of solving the equations. A more explicit analysis of the weather prediction problem from a scientific viewpoint was undertaken shortly afterwards by the Norwegian scientist Vilhelm Bjerknes (Fig. 1, centre panel). Bjerknes set down a two-step plan for rational forecasting [3]: A diagnostic step, in which the initial state of the atmosphere is determined using observations; and a prognostic step, in which the laws of motion are used to calculate how this state changes over time.

There was a severe shortage of observations, particularly over the seas and for the upper air, but Bjerknes was optimistic: international observation programs were already under way, organized by the International Commission for Scientific Aeronautics, which might provide a reasonable diagnosis of the state of the atmosphere. The prognostic step was to be taken by assembling a set of equations, one for each dependent variable describing the atmosphere. Bjerknes listed seven basic variables: pressure, temperature, density, humidity and three components of velocity. He then identified seven independent equations: the three hydrodynamic equations of motion, the continuity equation, the equation of state and the equations expressing the first and second laws of thermodynamics (in fact, he should have specified a continuity equation for water rather than the second thermodynamic law).

Bjerknes developed a qualitative, graphical method for solving the equations, as he could not solve them numerically and an analytical solution was out of the question. His idea was to represent the initial state of the atmosphere by a number of charts giving the distribution of the variables at different levels. Graphical methods based on the fundamental equations could then be applied to construct a new set of charts describing the atmosphere some hours later. This process could be iterated until the desired forecast length was reached. Bjerknes contrasted the methods of meteorology with those of astronomy, for which predictions of great accuracy are possible, and he stated his goal: to make meteorology an exact science, a true physics of the atmosphere.

Bjerknes saw no possibility to put his ideas to practical use. The English Quaker scientist Lewis Fry Richardson was bolder, attempting a direct solution of the equations of motion. Richardson (Fig. 1, right panel) first heard of Bjerknes’ plan for rational forecasting when he took up employment with the Meteorological Office in 1913. In the Preface to his book Weather Prediction by Numerical Process [24] he writes

The extensive researches of V Bjerknes and his School are pervaded by the idea of using the differential equations for all that they are worth. I read his volumes on Statics and Kinematics soon after beginning the present study, and they have exercised a considerable influence throughout it.

Richardson’s book opens with a discussion of then-current practice in the Meteorological Office. He describes the use of an Index of Weather Maps, constructed by classifying old synoptic charts into categories. The Index [12] assisted the forecaster to find previous maps resembling the current one and therewith to deduce the likely development by studying the evolution of these earlier cases. But Richardson was not optimistic about this method. He wrote that “The forecast is based on the supposition that what the atmosphere did then, it will do again now. … The past history of the atmosphere is used, so to speak, as a full-scale working model of its present self” [24]. Bjerknes had contrasted the precision of astronomical prediction with the ‘radically inexact’ methods of weather forecasting. Richardson returned to this theme:

— the Nautical Almanac, that marvel of accurate forecasting, is not based on the principle that astronomical history repeats itself in the aggregate. It would be safe to say that a particular disposition of stars, planets and satellites never occurs twice. Why then should we expect a present weather map to be exactly represented in a catalogue of past weather?

Richardson’s forecasting scheme amounts to a precise and detailed implementation of the prognostic component of Bjerknes’ program. It is a highly intricate procedure: as Richardson observed, ‘the scheme is complicated because the atmosphere is complicated.’ It also involved a phenomenal volume of numerical computation and was quite impractical in the pre-computer era. But Richardson was undaunted:

Perhaps some day in the dim future it will be possible to advance the computations faster than the weather advances …. But that is a dream.

Today, forecasts are prepared routinely on powerful computers running algorithms that are remarkably similar to Richardson’s scheme – his dream has indeed come true.

Richardson began serious work on weather prediction in 1913 when he was appointed Superintendent of Eskdalemuir Observatory, in the Southern Uplands of Scotland. He had had little or no previous experience of meteorology when he took up this position ‘in the bleak and humid solitude of Eskdalemuir’. Perhaps it was his lack of formal training in the subject that enabled him to approach the problem of weather forecasting from such a breathtakingly original and unconventional angle. Richardson’s idea was to express the physical principles which govern the behavior of the atmosphere as a system of mathematical equations and to apply his finite difference method to solve this system. He had previously used both graphical and numerical methods for solving differential equations and had come to favor the latter. The basic equations had already been identified by Abbe and Bjerknes, but they had to be simplified using the hydrostatic assumption and transformed to render them amenable to approximate solution. The fundamental idea is that atmospheric pressures, velocities, etc., are tabulated at certain latitudes, longitudes and heights so as to give a general description of the state of the atmosphere an an instant. Then these numbers are processed by an arithmetical method which yields their values after an interval of time Δt. The process can be repeated so as to yield the state of the atmosphere after 2Δt, 3Δt, and so on.

Richardson was not concerned merely with theoretical rigor, but wished to include a fully worked example to demonstrate how his method could be put to use. Using the most complete set of observations available to him, he applied his numerical method and calculated the changes in the pressure and winds at two points in central Europe. The results were something of a calamity: Richardson calculated a change in surface pressure over a six-hour period of 145 hPa, a totally unrealistic value. The calculations themselves are presented in his book, on a set of 23 Computer Forms, rather like a modern Excel spread-sheet. These were completed manually, and the changes in the primary variables over a six hour period computed. Richardson explains the chief result thus:

The rate of rise of surface pressure … is found on Form ${\mathrm{P}}_{\mathrm{XIII}}$ as 145 millibars in 6 hours, whereas observations show that the barometer was nearly steady. This glaring error is examined in detail … and is traced to errors in the representation of the initial winds.

Richardson described his forecast as ‘a fairly correct deduction from a somewhat unnatural initial distribution’. He speculated that reasonable results would be obtained if the initial data were smoothed, and discussed several methods of doing this. In fact, the spurious tendencies are due to an imbalance between the pressure and wind fields resulting in large amplitude high frequency gravity wave oscillations. The ‘cure’ is to modify the analysis so as to restore balance; this process is called initialization. A numerical model has been constructed, keeping as close as possible to the method of Richardson, except for omission of minor physical processes, and using the same grid discretization and equations as used by him [18]. The results using the initial data which he used were virtually identical to those obtained by him; in particular, a pressure tendency of 145 hPa in 6 hours was obtained at the central point. The initial data were then initialized using a digital filter, and the forecast tendencies from the modified data were realistic.

In Table 1 we show the six-hour changes in pressure at each model level. The column marked LFR has the values obtained by Richardson. The column marked MOD has the values generated by the computer model. They are very close to Richardson’s values. The column marked DFI is for a forecast from data initialized using a Dolph–Chebyshev filter [18]. The initial tendency of surface pressure is reduced from the unrealistic 145 hPa/6 h to a reasonable value of less than 1 hPa/6 h (bottom row, Table 1). These results indicate clearly that Richardson’s unrealistic prediction was due to imbalance in the initial data used by him. Complete details of the forecast reconstruction may be found in Lynch [18].

The initial response to Weather Prediction by Numerical Process was unremarkable, and must have been disappointing to Richardson. It was widely reviewed, with generally favorable comments – Ashford [2] includes a good coverage of reactions – but the impracticality of the method and the apparently abysmal failure of the solitary example inevitably attracted adverse criticism. The true significance of Richardson’s work was not immediately evident; the computational complexity of the process and the disastrous results of the single trial forecast both tended to deter others from following the trail mapped out by him. Despite the understandably cautious initial reaction, Richardson’s brilliant and prescient ideas are now universally recognized among meteorologists and his work is the foundation upon which modern forecasting is built.