Weather, War, and Mathematics
From: Roger Bagula (tftn_at_earthlink.net)
Date: 10/17/04
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Date: Sun, 17 Oct 2004 14:56:57 GMT
Weather, War, and Mathematics
The Forgiving Air: Understanding Environmental Change
By Richard C.J. Somerville, University of California Press, Berkeley,
1996, 195 pages, $21.95
The Collected Papers of Lewis Fry Richardson Oliver M. Ashford et al.,
eds., Cambridge University Press, Cambridge, 1993, 2 volumes, 500 pages
each, $150.00 each
Prophet or Professor? The Life and Work of Lewis Fry Richardson By
Oliver M. Ashford, A. Hilger, Boston, 1985, 309 pages
We are all in the debt of any active researcher who takes time out to
explain to the public what his profession is about. In The Forgiving
Air, Richard Somerville, who is director of climate research at Scripps
Institution of Oceanography, describes the considerations that go into
scientific weather and climate prediction in a way that is accessible to
anyone interested in the subject in a general way, from the high school
level up. The book is a good read, and there is no mathematics in it
other than the powers of ten. Somerville looks at major meteorological
phenomena: The greenhouse effect, the ozone hole, acid rain,
reflectivity of ice caps are emphasized. A few selected feedback loops,
positive (bad) and negative (good), are discussed in some detail. More
carbon dioxide leads to more atmospheric water vapor, which leads to
higher temperatures. Clouds—how do they feed back? Do they heat or cool?
On average, they cool. But if CO2 levels were doubled, cloud formations
would change, leading to positive feedback; the decrease in ice levels
amplifies warming.
Somerville bases his assessments of meteorological trends on a variety
of mathematical models, but he recognizes the need for skepticism and
improvements. Example: The dire predictions of the effects of the fierce
oil well fires ignited in Kuwait during the gulf war turned out to be
over-pessimistic. Microweather, e.g., a hurricane or a tornado, has its
own difficulties. Although “there has been some success in predicting
year-to-year variations in hurricane climatology,” a hurricane can pass
through the grid of a model “like a small bug can pass through a small
window screen.”
Chaos theory informs us that there appear to be absolute limits to what
mathematics can accomplish with the best of models and the fastest
machines. The current time interval for reasonably good predictions is
three or four days for local weather. What is currently thought to be
the ultimate limit of predictability? Between four days and four months.
Probably a few weeks.
On prominent display in the book are a number of Somerville’s Heroes:
Lewis Fry Richardson (1881–1953), pioneer in numerical weather
prediction. Mario Molina, Sherwood Rowland, Paul Crutzen (1995
Nobelists), who predicted theoretically that chlorofluorocarbons destroy
ozone. Veerabhadran Ramana-than, who determined that these compounds
were greenhouse gases. Joseph Farman (and the British Antarctic Survey),
who discovered the ozone hole in Antarctica. Charles D. Keeling, who in
1958 began measuring the carbon dioxide concentration in the air.
He also has his Anti-Heroes: Thomas Midgely, Jr. (1889–1944), the
brilliant industrial chemist who in 1922 discovered the value of
tetraethyl lead as a gasoline additive and who in 1928 invented
chlorofluorocarbons as a refrigerant. (The side effects of neither were
known to him.) And, of course, all of us who drive cars, who use
electricity derived from nonrenewable sources, who would find it
extremely difficult to dig up our nice lawns and plant them over with
potatoes.
On page 125, Somerville tells a joke that’s no joke:
An alert frog dropped in a pot of boiling water, the frog will jump
out. It will be shocked and traumatized, but it will survive. But if
placed in lukewarm water, and gradually heated, the wretched animal
will adjust to the changing temperature without realizing it and end
its days as frog soup.
The Green message is strong in this book. All villages are global
villages. The air and the climate cannot be localized. Ultimately, then,
solutions must be global. The optimism expressed is guarded.
International conferences and agreements are necessary and encouraging,
but hardly sufficient.
Apparently, “there are limits to the compassion of the forgiving air.”
I’m particularly grateful to Somerville for the reminder that sent me
back to the works of Lewis Richardson.
Lewis Fry Richardson, applied mathematician, physical scientist,
inventor, and sociometrist, was born in Newcastle upon Tyne to a family
that for several centuries had been tanners and Quakers. In 1903 he took
a first-class degree at Kings College, Cambridge, where one of his
teachers was J.J. Thomson of electron fame. Richardson’s name does not
appear in the standard histories of mathematics, but it deserves to be
there. He was given a half column in the 1965 edition of the
Encyclopaedia Britannica—apparently Richardson is more important to the
world than to mathematics.
Once he left Cambridge, Richardson’s professional affiliations were with
government laboratories and with colleges not thought to be of the
Oxbridge class. Around 1910, on the strength of a major paper published
in the Philosophical Transactions of the Royal Society, he applied for a
fellowship at Kings. His work was sent over to Trinity College for the
opinion of their mathematicians. The response contains more than a
suggestion of prejudice against “approximate mathematics,” and
Richardson’s family heritage of trade and Quakerism probably didn’t help
him. He was passed over, and he never returned to academic Cambridge.
To numerical analysts, Richardson is known for his algorithms for the
numerical solution (in precomputer days) of ordinary and partial
differential equations. The terms “jury problem” for elliptic equations
and “marching problems” for hyperbolic equations come from him. The
Richardson “deferred approach to the limit,” i.e., a method for the
acceleration of convergence, is fundamental and widely employed.
In turbulence theory he has left a permanent mark in the “Richardson
number,” which characterizes the fraction of turbulent energy that comes
from temperature gradients, as opposed to wind velocity gradients.
He was one of the first to attempt the formulation and numerical
solution of a mathematical weather model. Well aware of the numerical
complexity in the solution of the partial differential equations, he
joked that one ought, really, to turn a concert hall into a “weather
forecast factory” by filling it with 64,000 computers (i.e., people)—one
person for each computational grid point, intercommunicating through a
conductor on the podium. This was his anticipation of parallel
supercomputers.
World War I began in Europe in August 1914. Two of his brothers-in-law
were killed in the war. In 1916, at the age of 35, Richardson joined the
Friends Ambulance Unit in France as a conscientious objector; he was
associated with the 16th French Infantry Division until 1919.
His deep convictions as a Quaker led him to study the statistics,
dynamics, and variety of reasons for the onset of war. In 1919, he
completed a small book, Mathematical Psychology of War, dedicated it to
his ambulance colleagues, and looked around for a commercial publisher.
Although it came recommended by the famous Bertrand Russell (then
another pacifist), no publisher would touch it and Richardson put it out
privately.
Beginning in 1926, he collected vast amounts of data on what he termed
“deadly quarrels,” which ranged in size from World War I to gang wars in
Chicago. He characterized the intensity of the “quarrels” by the
logarithm of the number of persons killed in them and found that
intensity was inversely proportional to frequency. Just as we classify
earthquakes on the Richter scale, it would be historically correct to
locate contemporary wars (e.g., Iraq–Iran, Yugoslavia, Chechnya) on the
Richardson scale. He found that the onset times of quarrels were random
and could be described by a Poisson law.
He became the father of war-gaming. The simple dynamic model he used to
discuss stability (derived actually from work of F.W. Lanchester) is now
in every elementary modeling textbook under the name predator–prey
equations. The study of this simple model led him to the pessimistic
conclusion that most confrontations between nations are unstable.
It is ironic that although Richardson undertook his studies in the hope
that a mathematical understanding of the causes and dynamics of war
would lead to an abatement of aggression, he came to the opposite
conclusion: War is a permanent feature of the human condition. He was
further vexed by the fact that his research on the flow of air was used
in the twenties and thirties by military technologists dealing with the
dispersal of poison gases.
Richardson was also a pioneer in the study of fractals. In classifying
and studying the variety of reasons for war, he had to define the length
of the boundary between two adjacent countries. Approximating a boundary
B empirically by inscribing piecewise linear segments of length h and
allowing h to approach 0, he found the total length determined in this
way to be proportional to 1/ha, a > 0. The quantity 1 + a is now known
as the fractal dimension of B. Richardson’s name is featured prominently
in Benoît Mandelbrot’s The Fractal Geometry of Nature, along with the
names of other fractal precursors.
Richardson was a man who walked independently, who openly admitted his
failures (unstable algorithms, inadequate models, inadequate data, far
too much computation), even publishing them. He was an unorthodox
scientist, never in the mainstream. He never played it safe. He threw
pieces of parsnip into Loch Long and measured their rate of separation
with a crude theodolite made of sticks (Journal of Meteorology, Vol. 5,
1948). The “inward light” saw him through the practical difficulties and
the questioning of his own ideals
. Richardson’s legacy is visible in many numerical strategies, in
“Prairie Warrior,” the annual $7 million exercise of war games at Fort
Leavenworth (Atlantic Monthly, September 1996), and in the activities of
any center of meteorology and oceanography.
------------------------------------------------------------------------
Philip J. Davis, professor emeritus of applied mathematics at Brown
University, is an independent writer, scholar, and lecturer. He lives in
Providence, Rhode Island, and can be reached at
AM188000@brownvm.brown.edu
<http://www.siam.org/siamnews/bookrevs/AM188000@brownvm.brown.edu>.
------------------------------------------------------------------------
© 1996 Society for Industrial and Applied Mathematics
SIAM News, Volume 29, Number 9, November 1996
http://www.siam.org/siamnews/bookrevs/weather.htm
Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
alternative email: rlbtftn@netscape.net
URL : http://home.earthlink.net/~tftn
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