Chaos in the Atmosphere
Before they could understand how climates change, scientists would
have to understand the basic principles for how any complicated system
can change. Early studies, using highly simplified models, could see nothing
but simple and predictable behavior, either stable or cyclical. But in
the 1950s, work with slightly more complex physical and computer models
turned up hints that even quite simple systems could lurch in unexpected
ways. During the 1960s, computer experts working on weather prediction
realized that such surprises were common in systems with realistic feedbacks.
The climate system in particular might wobble all on its own without any
external push, in a "chaotic" fashion that by its very nature was unforeseeable.
By the mid 1970s, most experts found it plausible that at some indeterminate
point a small push (such as adding pollution to the atmosphere) could
trigger severe climate change. While the largest effects could be predicted,
important details might lie forever beyond calculation.
Few natural phenomena change so radically and unpredictably as the daily weather.
Meteorologists had long understood how the atmosphere in a given locality could be capricious
and unstable from hour to hour. As one authority explained in 1957, tiny disturbances in the air,
far below the limits of observation, could grow into large weather systems within a few days.
Nobody could predict these unstable processes, so "there is an effective time barrier beyond
which the detailed prediction of a weather system may well remain impossible." Beyond that
limit, which might be only a few days, one could only look to statistics, the probability of rain or
frost in a given month.(1)
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| Climate was expected to be steadier. Climate
was the statistics, defined as a long-term average. The daily fluctuations,
people assumed would cancel one another out over the long run, for
the atmospheric system was supposed to be self-stabilizing. True,
it was undeniable that even a large system could be unstable. Back
around the end of the 19th century, the great French mathematician
Henri Poincaré had noted that even the orbit of a planet could
depend on some tiny fluctuation, as difficult to predict as whether
a ball rolling down a knife-edge would fall to left or right. In the
1920s, quantum physicists showed that a lack of certainty was altogether
fundamental. This was Werner Heisenberg's Uncertainty Principle, made
vivid by Erwin Schrödinger's fable of a cat that might be alive
or dead depending on the strictly random decay of a single atom. These
ideas worked their way only gradually into common awareness. For decades,
scientists who studied complex systems mostly just ignored the ideas.
Few questioned that the automatic self-correction of the great natural
systems would always keep planets in their accustomed orbits, and
that over future decades the rains would fall pretty much as they
had in the past.
More discussion in
| Of course, anyone who lived through the harrowing Dust Bowl drought
of the 1930s, or heard grandfathers talk about the freezing winters
of the 1890s, knew that climate could be seriously different from
one decade to the next. Few wanted to explain this as mere random
drifting. Surely nature was not altogether capricious? Every change
must have its specific explanation. Perhaps, for example, rainfall
decreased when soils were dried up by overgrazing, and perhaps cold
spells followed an increase in smoke from volcanic eruptions. Even
more popular than this idea of particular causes for particular deviations
was an assumption that features of nature follow periodic patterns,
diverging only to return. Things from tides to rabbit populations
go through regular cycles, and it was easy to suppose that climate
too was cyclical. The idea fascinated many professional and amateur
meteorologists. If you could detect a regular cycle in climate, you
could develop a scientific explanation for climate change, and use
it to calculate predictions of economic value and perhaps make
a killing on the wheat futures exchange!
| From the
19th century forward, then, people who liked to play with data labored
to extract climate cycles from weather statistics. One or another
worker discovered a plausibly regular rise and decline of temperature
or of rainfall over months or decades in this region or that. Given
enough different bodies of data, people could also turn up correlations
between a weather cycle and some other natural ebb and flow, notably
the eleven-year cycle of sunspots. A 1941 U.S. Weather Bureau publication
noted that some 50 climate cycles had been reported, ranging from
days to centuries (not to mention the ice ages, which seemed to come
and go regularly over hundreds of thousands of years). "Each man who
has proposed one or more of these cycles," the Bureau remarked, "has
become convinced that he has found a particular
| Many meteorologists repudiated the whole enterprise, seeing nothing
but random fluctuations from the norm. There remained a good number
who believed that cycles were probably there, just at the edge of
what the data could prove. An indicator of middle-of-the-road opinion
was Helmut Landsberg's authoritative climatology textbook of 1941.
Among other cases, Landsberg described how "widespread attention"
had focused upon a cycle of around 33 years in the level of lakes
(which gave a good measure of average precipitation). Detected in
the 1890s, the cycle had been used to predict how much rain would
fall in the late 1920s but the prediction had failed ignominiously.
Nevertheless, Landsberg thought there was a real effect at work, perhaps
an irregular rhythm that varied between 30 and 40 years long. "Scientific
skepticism is well warranted in the research on climate cycles," he
admitted. "Nevertheless some of them seem to have much more than chance
characteristics..."(3) Meanwhile the stock of weather observations increased rapidly
and calculation techniques improved, so that it became increasingly
possible to offer solid proof of whether or not a given cycle was
valid. The answers were usually negative.
| By the middle of the 20th century, opinion
among meteorologists was divided about the same way as at the start
of the century. Some expected that a few cycles would eventually be
pinned down, while others believed that no cycles existed the
variations of climate were purely random. Progress was stymied unless
clues could be found in some new approach.
A big clue came in the 1950s, when a few scientists decided to
build actual physical models of climate. Perhaps if they studied how a fluid behaved in a rotating
pan, they would learn something general about the behavior of fluid systems like the rotating
planet's atmosphere. These "dishpan" studies turned out to be surprisingly effective in modeling
features of the atmosphere like weather fronts. What was most thought-provoking was the way
the circulation of a fluid in the laboratory could show different patterns even when the external
conditions remained the same. Stir the fluid in the rotating dishpan with a pencil, and you
couldn't predict which of two or three possible states the circulation would settle into. The choice
of pattern depended in some arbitrary, unpredictable way on the system's past history.(4)
| Of course, random behavior could be no surprise to anyone who watched
the tumbling of fluids. When water flows through a channel, if the
speed gradually increases, at some point the smooth, steady flow gives
way to a turbulent flow with vortexes swirling unpredictably. In 1921,
Vilhelm Bjerknes had suggested that a similar instability might be
at the root of major daily disturbances of the atmosphere. Beyond
some critical point, the symmetric flow of wind would become unstable
and spin off storms.(5) In
1956, Edward Lorenz proposed an explanation along those lines for
the dishpan experiments. As the dishpan experiments were refined,
however, they seemed to point to something much more unfamiliar.(6)
| A second essential clue came from another new field, digital computation.
As scientists applied computers to a variety of tasks, oddities kept
popping up. An important example came in 1953 when a group at Los
Alamos, led by the great physicist Enrico Fermi, used the pioneer
computer MANIAC to study how a complex mechanical system behaved.
They wrote equations that described a large number of "nonlinear"
oscillators (the mathematical equivalent of springs with flaws that
kept them from stretching smoothly), all coupled to one another. Physical
intuition insisted that the distribution of energy among the oscillators
in such a system should eventually settle down into a steady state,
as a shaken glass of water will gradually come to rest. That was indeed
what Fermi's group saw, after the computer had ground away at the
numbers for a while. Then one day, by accident, they left the computer
running long after the steady state had been reached. Fermi's group
was amazed to find that the system had only lingered for a while in
its steady state. Then it reassembled itself back into something resembling
the initial distribution of energy. Like the flow in the rotating
dishpan, the system had at least two states that it could flip between
for no obvious reason. Further computer experiments showed that the
system shifted unpredictably among several "quasi-states."(7) In retrospect, this was the first true computer experiment,
with an outcome that foreshadowed much that came later. The lesson,
scarcely recognized at the time, was that complex systems did not
necessarily settle down into a calm stable state, but could organize
themselves in surprising large-scale ways.
Fermi's group described these wholly unexpected results at a few meetings during the 1950s,
stirring curiosity among physicists and mathematicians. Meanwhile there were hints that such
behavior was not confined to abstract mathematical systems. For example, a pair of scientists
wrote a simple system of equations for the exchanges of carbon dioxide gas among the Earth's
atmosphere, oceans, and biosphere, and ran the equations through a computer. The computations
tended to run away into self-sustaining oscillations. In the real world that would mean climate
instability or even fluctuations with no regularities at all.(8) Nothing specific came of these and other peculiar results. It is not
uncommon for scientists to turn up mildly anomalous calculations. They stick them away in the
back of their minds until someone can explain what, if anything, it all has to do with the real
| The more people worked with computers, the
more examples they found of oddly unstable results. Start two computations
with exactly the same initial conditions, and they must always come
to precisely the same conclusion. But make the slightest change in
the fifth decimal place of some initial number, and as the machine
cycled through thousands of arithmetic operations the difference might
grow and grow, in the end giving a seriously different result. Of
course people had long understood that a pencil balanced on its point
could fall left or right depending on the tiniest difference in initial
conditions, to say nothing of the quantum uncertainties. Scientists
had always supposed that this kind of situation only arose under radically
simplified circumstances, far from the stable balance of real-world
systems like global climate. It was not until the 1950s, when people
got digital machines that could do many series of huge computations,
that a few began to wonder whether their surprising sensitivity pointed
to some fundamental difficulty.
|At first the problem
had seemed simply a matter of starting off with the right equations
and numbers. That caught attention as early as 1922, when Lewis Fry
Richardson published the results of a heroic attempt to compute by
hand how a weather pattern developed over eight hours. His starting
point was an observed pattern of winds and barometric pressure. Numerically
simulating a day of development, Richardson's numbers had veered off
into something utterly unlike real weather. He thought his calculation
would have worked out if only he could have begun with more accurate
wind data. But as the meteorologist Carl-Gustav Rossby pointed out
in 1956, people routinely made decent 24-hour predictions by looking
at weather maps drawn from very primitive data. "The reasons for the
failure of Richardson's prognosis," the puzzled Rossby concluded,
"must therefore be more fundamental."(9*)
| The question of unstable computations was addressed most persistently
by Philip Thompson, who had taken up weather prediction with the pioneering
ENIAC computer group. In 1956, Thompson estimated that because of
the way small irregularities got magnified as a computation went forward,
it would never be possible to compute an accurate prediction of weather
more than about two weeks ahead.(10)
Most scientists felt that all this resulted from the way computers
chopped up reality into a simplified grid (and in fact some clever
changes in the mathematics stabilized Phillips's model). As another
computer pioneer remarked, "meteorologists get so used to the idea
that something bad is going to go wrong with their forecast that you're
not surprised" if a calculation couldn't be made to work.(11) The real world itself was presumably
not so arbitrary.
| There had long been a few meteorologists, however,
who felt that the atmosphere was so "delicately balanced" that a relatively
minor perturbation could trigger not just a week's storm, but a large
and durable shift.(12) In the 1950s, the idea was developed
in speculative models of climate that showed abrupt variations, due
to self-sustaining feedbacks involving factors such as snow cover.
Support came from new data which suggested that climate conditions
in the past had sometimes in reality jumped quite rapidly into a different
state. The respected U.S. Weather Bureau leader, Harry Wexler, warned
that "the human race is poised precariously on a thin climatic knife-edge."
If the global warming trend that seemed to be underway continued,
it might trigger changes with "a crucial influence on the future of
the human race."(13)
The intellectual basis of the new viewpoint was well expressed in
1961 by R.C. Sutcliffe at an international climate conference. Using the popular new language of
cybernetics, he described climate as a complex nonlinear feedback system. Unceasing variation
might be "built-in," an intrinsic feature of the climate system. Thus it might be pointless to look
for external causes of climate change, such as solar variations or volcanic eruptions. Every
season the pattern of the general circulation of the atmosphere was newly created, perhaps in a
quite arbitrary way. The "sudden jumps" seen in the climate record, Sutcliffe concluded, are
"suggestive of a system controlling its own evolution."(14)
The father of cybernetics himself, mathematician Norbert Wiener, insisted that attempts to model
the weather by crunching physics equations with computers, as if meteorology were an
exact science like astronomy, were doomed to fail. Quoting the old nursery rhyme that told how a
kingdom was lost "for want of a nail" (which caused the loss of a horseshoe that kept a knight out
of a crucial battle), Wiener warned that "the self-amplification of small details" would foil any
attempt to predict weather. One pioneer in computer prediction recalled that Wiener went so far
as to say privately that leaders of the work were "misleading the public by pretending that the
atmosphere was predictable."(15)
| In 1961, an accident cast new light on the
question. Luck in science comes to those in the right place and time
with the right set of mind, and that was where Edward Lorenz stood.
He was at the Massachusetts Institute of Technology, where development
of computer models was in the air, and intellectually he was one of
a new breed of professionals who were combining meteorology with mathematics.
Lorenz had devised a simple computer model that produced impressive
simulacra of weather patterns. One day he decided to repeat a computation
in order to run it longer from a particular point. His computer worked
things out to six decimal places, but to get a compact printout he
had truncated the numbers, printing out only the first three digits.
Lorenz entered these digits back into his computer. After a simulated
month or so, the weather pattern diverged from the original result.
A difference in the fourth decimal place was amplified in the thousands
of arithmetic operations, spreading through the computation to bring
a totally new outcome. "It was possible to plug the uncertainty into
an actual equation," Lorenz later recalled, "and watch the things
grow, step by step."
| Lorenz was astonished. While the problem of sensitivity to initial
numbers was well known in abstract mathematics, and computer experts
were familiar with the dangers of truncating numbers, he had expected
his system to behave like real weather. The truncation errors in the
fourth decimal place were tiny compared with any of a hundred minor
factors that might nudge the temperature or wind speed from minute
to minute. Lorenz had assumed that such variations could lead only
to slightly different solutions for the equations, "recognizable as
the same solution a month or a year afterwards... and it turned out
to be quite different from this." Storms appeared or disappeared from
the weather forecasts as if by chance.(16)
| Lorenz did not shove this into the back of his mind, as scientists
too often do when some anomaly gets in the way of their work. For
one thing, the anomaly reminded him of the sudden transitions in rotating
dishpans, which he had worked on but never quite solved. He launched
himself into a deep and original analysis. In 1963 he published a
landmark investigation of the type of equations that might be used
to predict daily weather. "All the solutions are found to be unstable,"
he concluded. Therefore, "precise very-long-range forecasting would
seem to be non-existent."(17)
That did not necessarily apply to the climate system, which averaged over many states of
weather. So Lorenz next constructed a simulacrum of climate in a simple mathematical model
with some feedbacks, and ran it repeatedly through a computer with minor changes in the initial
conditions. His initial plan was simply to compile statistics for the various ways his model
climate diverged from its normal state. He wanted to check the validity of the procedures some
meteorologists were promoting for long-range "statistical forecasting," along the lines of the
traditional idea that climate was an average over temporary variations. But he could not find any
valid way to statistically combine the different computer results to predict a future state. It was
impossible to prove that a "climate" existed at all, in the traditional sense of a stable long-term
average. Like the fluid circulation in some of the dishpan experiments, it seemed that climate
could shift in a completely arbitrary way.(18)
| These ideas spread among climate
scientists, especially at a landmark conference on "Causes of Climate
Change" held in Boulder, Colorado in August 1965. Lorenz, invited
to give the opening address, explained that the slightest change of
initial conditions might randomly bring a huge change in the future
climate. "Climate may or may not be deterministic," he concluded.
"We shall probably never know for sure."(19)
Other meteorologists at the conference pored over new evidence that
almost trivial astronomical shifts of the Earths orbit might have
"triggered" past ice ages.. Summing up a consensus at the
end of the conference, leaders of the field agreed that minor and
transitory changes in the past "may have sufficed to 'flip' the atmospheric
circulation from one state to another."(20)
These concerns were timely. Around
the mid 1960s, many people were starting to worry about environmental change in general as
something that could come arbitrarily and even catastrophically. This was connected with a
growing recognition, in many fields of science and in the public mind as well, that the planet's
environment was a hugely complicated structure with points of vulnerability. Almost anything
might be acutely sensitive to changes in anything else. So it was hopeless to look for comfortably
regular weather cycles driven by single causes. The many forces that acted upon climate, all
interacting with one another, added up to a system with an intrinsic tendency to vary, hard to
distinguish from random fluctuation.
| A tentative endorsement of Lorenz's ideas came in a comprehensive
1971 review of climate change. While the authors did not feel Lorenz
had proved his case for certain, they found it "conceivable" that
sensitivity to initial conditions "could be a 'cause' of climate change."(21) A typical textbook of the time spoke
of the atmosphere as an overwhelmingly complex system of different
"types of circulation" with rapid transitions among them. "The restlessness
of the atmosphere sets a theoretical limit to its predictability,"
the author concluded. That not only ruined any hope of forecasting
weather beyond a week or so, but similarly hampered our ability to
foresee climate change. A high-level panel on climate change agreed
in 1974 that "we may very well discover that the behavior of the system
is not inherently predictable."(22)
In the early 1970s, concern about
arbitrary climate change was redoubled by news reports of devastation from droughts in Africa
and elsewhere. The most dramatic studies and warnings came from meteorologist Reid Bryson,
who pointed out that the African drought had "minuscule causes," which "suggests that our
climate pattern is fragile rather than robust."(23) Meanwhile speculative new models suggested that a slight variation
of external conditions could push the climate over an edge, plunging us from the current warmth
into an ice age.(24) Studies of dramatic
past climate events added plausibility to these models. It was a short step to imagining a system
so precariously balanced that it would go through self-sustaining fluctuations without any
external trigger at all. As an author of one of the simple models put it, the results raised "the
disturbing thought" that science could do no more than follow the history of climate as it
| Many meteorologists rejected this approach, what one prestigious
panel called "the pessimistic null hypothesis that nothing is predictable."
After all, the entire program of the postwar physics-based revolution
in meteorology aimed at prediction. Scientists holding to this ideal
expected that gross changes could in principle be predicted, although
perhaps not their timing and details.(26*) The task now was to determine where the limits of predictability
lay. Theorists worked out mathematical arguments that showed how changes
in climate could resemble a "random walk." Perhaps the atmosphere
was staggering like a drunkard among a multitude of possible states.
Enough steps this way and that could add up to a large excursion,
but in a random direction. If this picture was valid, then the places
the drunken climate reached would be halfway predictable but never
| The real world did follow a halfway predictable
path, according to one interpretation of new field studies. In 1976,
analysis of deep-sea cores revealed a prominent 100,000-year cycle
in the ebb and flow of ice ages. That corresponded to a predictable
astronomical cycle of variations in the Earth's orbit. However, the
cyclical changes of sunlight reaching the Earth seemed trivially small.
The group of scientists who published the evidence thought the cycle
of glacial periods must be almost self-sustaining, and the orbital
changes only nudged it into the shifts between states.(28) They called the variations in the Earth's orbit the "pacemaker
of the ice ages." In other words, the astronomical cycle triggered
the timing of the advance and retreat of ice sheets but was not itself
the driving force.(29) Without the timing set by this external stimulus, the ice
cycles might wander without any pattern at all. Or changes could be
set off arbitrarily with a nudge from any of various other forces
that were easily as strong as the slight deviations of sunlight. Indeed
the record showed, in addition to the main cycles, a great many fluctuations
that looked entirely random and unrelated to orbital variations. Meanwhile,
computer weather modelers were starting to admit they could find no
way to circumvent Lorenz’s randomness.
| The new viewpoint was captured in a fine review
by the leading meteorologist J. Murray Mitchell. He pointed out that
climate is variable on all timescales from days to millions of years.
There were naturally many theories trying to explain this multifarious
system, he said, and almost any given theory might partly explain
some aspect. "It is likely that no one process will be found
adequate to account for all the variability that is observed on any
given time scale of variation." Furthermore, the sheer randomness
of things set a limit on how accurately scientists could predict future
| Similar ideas were gradually becoming known
to the entire scientific community and beyond under a new name
"chaos theory."(31) The magnification of tiny initial variations,
and the unpredictable fluctuation among a few relatively stable states,
were found to matter in many fields besides meteorology. Most people
eventually heard some version of the question Lorenz asked at a 1979
meeting, "Does the flap of a butterfly's wings in Brazil set off a
tornado in Texas?" (Already in 1975 a science journalist had asked,
"can I start an ice age by waving my arm?") Lorenz's answer
perhaps yes became part of the common understanding of educated
To be sure, generations of historians had debated the "want of a nail" or "Cleopatra's nose"
question. How far could the course of human affairs be diverted by a chance event, such as the
beauty of one person, or even the weather, like the typhoon that sank Kublai Khan's attempted
invasion of Japan? Those who thought about the question more deeply recognized that you could
not pin a great consequence on one particular butterfly or horseshoe nail, but that in certain
circumstances the outcome might depend on the influence of a great many such factors, each
| Until the 1970s, scientists
had paid little attention to such ideas, concentrating their efforts
on systems where analyzing a few simple influences could indeed predict
the outcome. But once scientists started to look for less easily analyzed
systems, important examples turned up in fields from astronomy to
zoology. Could the configuration of a set of planets around a star
happen to be radically different from our own solar system? Did blind
chance determine the particular mix of species in an ecosystem? Lengthy
computer runs, backed up by field observations, gave answers that
mostly pointed toward unpredictability. During the 1980s, people began
to describe these developments as a major scientific revolution.(33)
The meteorological questions that had launched chaos theory
remained among the hardest to answer. Some scientists now insisted that the climate system's
intrinsic fluctuations would utterly defeat any attempt to calculate its changes. Thus the 1980
edition of one classic textbook said that predictions of greenhouse effect warming were dubious
because of chaotic "autovariations." Lorenz and others argued that the recently observed global
warming might be no evidence of a greenhouse effect or any other external influence, but only a
chance excursion in the drunkard's random walk.(34)
| Most scientists agreed that climate has features of a chaotic system,
but they did not think it was wholly unpredictable. To be sure, it
was impossible to predict well in advance, with any computer that
could ever be built in the actual universe, that a tornado would hit
a particular town in Texas on a particular day (not because of one
guilty butterfly, of course, but as the net result of countless tiny
initial influences). Yet tornado seasons came on schedule. That type
of consistency showed up in the supercomputer simulations constructed
in the 1980s and after. Start a variety of model runs with different
initial conditions, and they would show, like most calculations with
complex nonlinear feedbacks, random variations in the weather patterns
computed for one or another region and season. However, their predictions
for global average temperature usually remained within a fairly narrow
range under given conditions. Critics replied that the computer models
had been loaded with artificial assumptions in order to force them
to produce regular-looking results. But gradually the most arbitrary
assumptions were pared away. The models continued to reproduce, with
increasing precision, many kinds of past changes, all the way back
through the ice ages. As the computer work became more plausible,
it set limits on the amount of variation that might be ascribed to
| What if you just refused to believe computers?
The fact remained that climate over millions of years had responded
in a quite regular way to variations of sunlight (Milankovitch cycles).
And when gigantic volcanic outbursts had massively polluted the upper
atmosphere, weather patterns had reverted to normal within a few years.
This set strict limits on how far the climate system could drive its
own variations independent of outside forces.
Just about any decent computer model,
run repeatedly with just about any plausible initial conditions
plus a rise of greenhouse gases, predicted a global warming. As
the world's average temperatures climbed, it seemed less and less
likely that the match with the models was mere accident. However,
different models got different results for the future climate in
any particular region. And a given model for a given region might
come up with a surprising shift of the weather pattern in the middle
of a run. Some of these regional fluctuations might be fundamentally
chaotic. Occasionally a run of an entire global model would diverge
widely for a time, for example if an unusual combination of factors
perturbed the delicate balance of ocean circulation. But these divergences
were within limits set by the overall long-term average global warming.
In fact, it had become a test of a good model that it should show
fluctuations and variations, just as the real climate did. For predicting
future climates, it became common practice to run a supercomputer
model a few times (usually three to five), with slight variations
in the initial conditions. The details of the results would differ
modestly, and the modeller would publish an average of the
|Until the future actually came, there would be
no way to prove that the modelers understood all the essential forces.
If an unlucky combination sent the real climate temporarily into one
of the unusual states found in some model runs, that could confuse
people about what was happening. But it was not likely to change the
eventual outcome. What was no longer in doubt was the most important
insight produced by the half-century of computer experiments. Under
some circumstances a fairly small change in conditions, even something
that seemed so slight as an increase of greenhouse gases, could nudge
climate into a severely different state. The climate looked less like
a simple predictable system than like a confused beast, which a dozen
different forces were prodding in different directions. It responded
sluggishly, but once it began to move it would be hard to stop.
General Circulation Models of the Atmosphere
Simple Models of Climate
1. Mason (1957), p. 192.
2. Russell (1941), p. 91.
3. Landsberg (1941, rev. ed. 1947,
1960), pp. 261-268; he cites Brückner (1890).
4. Fultz et al. (1959).
5. Bjerknes (1921).
6. Lorenz (1967), p. 124.
7. Fermi et al. (1965), see
introduction by S. Ulam, pp. 977-78; Metropolis (1992), p.129;
note also Ulam (1976), pp. 226-28.
8. The authors called these "ergodic" fluctuations. Eriksson and Welander (1956), see p. 168.
9. Richardson (1922); Rossby (1959), p. 30 [this is a translation of Rossby (1956)]; recent analysis shows that Richardson's
primitive computation could have succeeded fairly well if he had started
with perfect data. But his process of computation with a large time-step
grossly magnified the wind data errors, which a human forecaster would
have intuitively adjusted in gazing at the map. Worse, the process failed
to filter out the random pressure oscillations ("gravity waves")
that show up in the complete solution of equations for a fluid. See discussion
by Lorenz (1967), p. 131; Norton and Suppe (2001), p. 93; for modern recalculation
by P. Lynch, see Hayes (2001).
10. Levenson (1989), p. 89.
11. Norman Phillips, interview by T. Hollingsworth, W.
Washington, J. Tribbia and A. Kasahara, Oct. 1989, p. 40, copies at National
Center for Atmospheric Research, Boulder, CO, and AIP.
12. C.E.P. Brooks quoted by Engel
(1953); Nebeker (1995), p. 189.
13. Wexler (1956), p. 480.
14. Sutcliffe (1963), pp.
278-79. Instead of "external" he speaks of "extraneous" causes.
15. "self-amplification": Wiener
(1956), p. 247, also warning that observations were "a very sketchy
sampling of the true data"; by "misleading" Wiener meant von Neumann and
Charney. Jule Charney and Walter Munk, "Early History of Computing in
Meteorology," unpublished, copy from Arakawa's papers kindly furnished
by Paul Edwards, p. 9. See also Cressman (1996),
p. 31. BACK
16. "Dialogue between Phil Thompson and Ed Lorenz," 31 July
1986, copies at National Center for Atmospheric Research, Boulder, CO; Gleick (1987) 1295, pp. 11-18.
17. Lorenz (1963), pp. 130, 141.
This paper, now considered a classic, was not noticed by mathematicians for nearly a decade; like
nearly all the stories in these essays, there is a lot more to this one, especially work by a number
of other mathematicians. For additional details, see Dalmedico
18. His term for arbitrary was "aperiodic." Lorenz (1964); Gleick (1987), pp.
19. Lorenz (1968), quote p. 3;
he described the randomness of a system of 26 equations (which was not very many for
meteorology), published in Lorenz (1965); see also Kraus and Lorenz (1966); Lorenz
20. Mitchell said his printed "Concluding Remarks" were based
on Roger Revelle's summary at the conference itself. Mitchell
(1968), pp. 157-58.
21. Wilson and Matthews
(1971), p. 109.
22. Stringer (1972), pp.
300, 307-08; Federal Council for Science and Technology
(1974); this is included as an appendix in United
States Congress (95:1) (1977), p. iii; another review accepting continual
and unpredictable change was Kutzbach (1976), p. 475. BACK
23. In sum, "numerically small changes in climatic variables
may produce significant environment changes," Bryson (1974),
pp. 753, 756, 759.
24. E.g., Newell (1974).
25. Lorenz (1970); as cited by
Sellers (1973), p. 253.
26. GARP (1975), pp. 32-33.
27. Hasselmann (1976).
28. Hays et al. (1976).
29. "orbital variations control the timing but not the amplitude."
Hays, Imbrie and Shackleton, reply to Evans and Freeland
(1977), p. 530.
30. "stochastic" or "probabilistic" variability Mitchell (1976), p. 481.
31. Lorenz (1993), p. 120.
32. "Predictability: Does the flap of a butterfly's wings..." was
the title of an address by Lorenz to the American Association for the Advancement of Science,
Washington, DC, Dec. 29, 1979. Waving arm: Calder (1975), p.
33. Gleick (1987).
34. Trewartha and Horn (1980)
(5th edition), pp. 392-95. Lorenz continued to press this view into the 1990s.
35. E.g., a computer run with a spontaneous North Atlantic
excursion: Hall and Stouffer (2001).
Such an excursion could make detection difficult: Randall
et al. (2007), p. 643BACK
© 2003-2009 Spencer Weart & American Institute of Physics