Geography Reference
In-Depth Information
13.1
HISTORICAL BACKGROUND
The British scientist L. F. Richardson made the first attempt to predict the weather
numerically. His topic,
Weather Prediction by Numerical Process
, published in
1922, is the classic treatise in this field. In his work Richardson showed how the
differential equations governing atmospheric motions could be written approxi-
mately as a set of algebraic difference equations for values of the tendencies of
various field variables at a finite number of points in space. Given the observed
values of the field variables at these grid points, the tendencies could be calculated
numerically by solving the algebraic difference equations. By extrapolating the
computed tendencies ahead a small increment in time, an estimate of the fields at
a short time in the future could be obtained. The new values of the field variables
could then be used to recompute the tendencies, which could in turn be used to
extrapolate further ahead in time, and so on. Even for short-range forecasting over
a small area of the earth, this procedure requires an enormous number of arithmetic
operations. Richardson did not foresee the development of high-speed digital com-
puters. He estimated that a work force of 64,000 people would be required just to
keep up with the weather on a global basis!
Despite the tedious labor involved, Richardson worked out one example forecast
for surface pressure tendencies at two grid points. Unfortunately, the results were
very poor. Predicted pressure changes were an order of magnitude larger than
those observed. At the time this failure was thought to be due primarily to the poor
initial data available, especially the absence of upper-air soundings. However, it is
now known that there were other, even more serious, problems with Richardson's
scheme.
After Richardson's failure to obtain a reasonable forecast, numerical prediction
was not again attempted for many years. Finally, after World War II interest in
numerical prediction revived due partly to the vast expansion of the meteorolog-
ical observation network, which provided much improved initial data, but even
more importantly to the development of digital computers, which made the enor-
mous volume of arithmetic operations required in a numerical forecast feasible.
At the same time it was realized that Richardson's scheme was not the simplest
possible scheme for numerical prediction. His equations not only governed the
slow-moving meteorologically important motions, but also included high-speed
sound and gravity waves as solutions. Such waves are in nature usually very weak
in amplitude. However, for reasons that will be explained later, if Richardson had
carried his numerical calculation beyond the initial time step, these oscillations
would have amplified spuriously, thereby introducing so much “noise” in the solu-
tion that the meteorologically relevant disturbances would have been obscured.
The American meteorologist J. G. Charney showed in 1948 how the dynam-
ical equations could be simplified by systematic introduction of the geostrophic
and hydrostatic approximations so that the sound and gravity oscillations were
