Table Of ContentWeather Forecasting
for
Aeronautics
JOSEPH J. GEORGE
Eastern Air Lines
Atlanta, Georgia
With contributions from
R. J. SHAFER, P. W. FUNKE, W. R. BIGGERS,
H. B. VISSCHER, R. M. WHITING, R. E. BAILEY,
A. H. STAKELY
1960
®
ACADEMIC PRESS, New York and London
COPYRIGHT © 1960, BY ACADEMIC PRESS INC.
ALL RIGHTS RESERVED
NO PART OF THIS BOOK MAY BE REPRODUCED IN ANY FORM,
BY PHOTOSTAT, MICROFILM, OR ANY OTHER MEANS,
WITHOUT WRITTEN PERMISSION FROM THE PUBLISHERS.
ACADEMIC PRESS INC.
Ill FIFTH AVENUE
NEW YORK 3, N. Y.
United Kingdom Edition
Published by
ACADEMIC PRESS INC. (LONDON) LTD.
17 OLD QUEEN STREET, LONDON S.W. 1
Library of Congress Catalog Card Number 59-7680
PRINTED IN THE UNITED STATES OF AMERICA
DEDICATED
TO
THE MEN AND WOMEN
OF
EASTERN AIR LINES
WEATHER DEPARTMENT
FOREWORD
It is the purpose of this book to provide the practicing forecaster
and the pilot who desires to learn more about the art and science of
predicting weather with the necessary aids and methods for making
practical application of his knowledge of the fundamentals of the sci-
ence of meteorology. The treatment throughout is empirical in nature.
Weather is generated in such a complicated laboratory that, in general,
the best way to predict it is to analyze past situations to find suitable
predictions for the future.
Most of the available books on weather forecasting treat the subject
in the classical sense. That is, they discuss physical causes of weather
and develop where possible the basic equations which describe how the
atmosphere is regulated. Such treatments are essential to a good under-
standing of the physical processes of the atmosphere. However, those
who wish to apply these fundamentals successfully find that they need
a great deal more material of a different kind. This volume has been
planned to help overcome this deficiency.
Much of the material used herein has been prepared by Eastern
Air Lines meteorological staff under contract with the Air Force Cam-
bridge Research Center, Research and Development Command. Sub-
stantial portions also were prepared for the U. S. Navy Weather Re-
search Facility (formerly Project AROWA), and for the U. S. Weather
Bureau. All of these agencies have kindly given permission to use this
material. The approval or endorsement of any of these agencies how-
ever, is not implied.
The relationship between large-scale circulation patterns and short-
range forecast methods such as are stressed in this book is something
of which the aviation forecaster should always be aware. The broad
weather regime should be allowed to color his choice of tools and even,
at times, the resulting forecast itself.
Two excellent works which provide such a background are recom-
mended to the forecaster; (1) "Thirty Day Forecasting" by Jerome
Namias, published as a Meteorological Monograph of the American
Meteorological Society, and (2) "Physikalisch-Statistische Regeln als
Grundlagen für Wetter- und Witterungsvorhersagen" by Dr. Franz
Baur, published by Akademische Verlagsgesellschaft, Frankfurt am
Main (Volume 1, 1956; Volume 2, 1958). These latter two volumes not
only provide a broad background for medium and large-scale circulation
features, but give detailed tables of departures of various elements from
normal, and their relation with sun-spot cycles. A large number of fore-
vii
viii FOREWORD
casting rules are also given for shorter range work in Europe and some
applicable to North America.
In most of the individual forecasting problems treated in this book,
there are other solutions described in the literature than those given.
As a rule, such solutions are given by reference to the original paper
only.
In by far the great majority, the methods given in this book are
based on research and development performed in the Eastern Air Lines
meteorological laboratory, and all of them have been tested in day-to-
day forecasting practice. Those methods and practices which have with-
stood the critical appraisal of working forecasters, which have produced
consistently superior results, and above all, which are practical to use,
are the only ones which have been deemed suitable for inclusion in
these pages.
J. J. GEORGE
Atlanta, Georgia
January, 1960
CHAPTER ONE
THE FORECAST PROBLEM
I. APPLICATION OF WEATHER FORECASTS TO OPERATIONAL PROBLEMS
There are very few types of human endeavor that enter the daily
lives of man which are more widely misunderstood than that of weather
forecasting. The man in the street judges it solely by the public forecasts
which appear in newspapers, television, and radio. The pilot compares
the weather he encounters at a given time and place with that called for
by the forecast he carries. The theoretical meteorologist develops a
theory from the basic mathematical equations which for the atmosphere,
must always start with more or less broad assumptions, passes this to the
forecaster, and then cannot understand why it is not used by him
regularly.1 People who are responsible for decisions concerning opera-
tions dependent to some extent on weather usually insist that they re-
ceive a specific forecast, and are not concerned with the limitations of
the science, or whether there is a better way to arrive at the proper
decision.
Much of the blame (if it may be so called) for this situation lies at
the doors of the various forecasting organizations, both public and
private, which have made a practice, extending over many years, of
attempting to supply just such categorical forecasts.
It has been said that no future event which is noncyclical in nature
can be predicted with precision. Certainly that is true in the field of
economics, for instance, which is akin in this respect to meteorology.
Were it possible to do so on a mass basis, it would vastly improve
the usefulness of weather forecasts if the forecaster were treated as a
part of a team whose job it is to arrive at the most logical decision con-
cerning proposed actions by considering weather probabilities along with
all other operational factors.
Using weather in this fashion, a contractor wishing to pour concrete
during weather which would be above freezing with no precipitation
could ask the forecaster to pick for him, one day in advance, the period
of time in which he could be certain of these conditions. Such a choice
is relatively easy for a forecaster to make accurately, but there are many
situations in which the public forecast must express the balance of
probabilities, and in borderline cases this might represent only a 51%
chance (or even less, if 3 or more alternatives exist) in the mind of the
forecaster. There are many synoptic patterns when the forecaster may
know very well there is an appreciable chance of a cold front crossing
1 For a detailed discussion of this problem see Stephens et al. ( 1 ).
1
2 1. THE FORECAST PROBLEM
on the next day, producing both precipitation and below freezing tem-
peratures, but because he has to express only the greater probability in
his public forecast, he can do little in the way of conveying this possi-
bility to the users.
Consider the problem of dispatching an airline flight into a bad
weather area. The airline dispatcher and the captain of the flight each
have the authority to cancel but it takes the concurrence of both to
make the flight.
Practices differ considerably between the various airline companies,
but very few flights are actually canceled solely on the basis of a
terminal forecast which calls for weather conditions below operating
limits.
Nevertheless, the forecaster aids the operation of an airline in many
very real ways. Perhaps the most important thing he does (other than
improvement of general safety) is to prevent the cancellation of many
flights. During winter, when widespread bad weather causes flight inter-
ruptions, diversions, and delays, he is frequently the first one to perceive
coming improvement and, if he is alert to the operational problems,
can often influence the flight controller and crews to take advantage of
the improvement. On the other hand, it is on the basis of his advice
that fuel reserves, alternate landing fields, etc., are set up. These items
amount to a substantial operating expense and, properly chosen, they
not only enhance safety and increase efficiency, but perform real
economies.
On the practical side, there is usually a continual flow of informa-
tion between an airline dispatcher and a meteorologist, and many times
an operation is saved from unnecessary diversion or other misrouting
because the meteorologist is cognizant of the operational problem and
relates it to the weather situation which he is constantly following.
Thompson (2) has done a great deal of work illustrating the necessity
for relating the accuracy of the forecast, the cost of the operation, the
profit to be derived from it, and the cost of precautions taken to cir-
cumvent adverse meteorological effects. He points out that protective
measures for any eventuality should be taken if P > C/L when P is
the probability of that eventuality, C is the cost of taking preventive
measures, and L is the loss which would result on the same occasion if
these measures were not taken and the adverse eventuality materialized.
Also pointed out in Thompson's study is the following: "It will be
observed that for large values of C/L coupled with small values of P
c
(climatological expectancy) and vice versa, considerable accuracy is
required for categorical forecasts in order that the user of the forecast
may obtain as much benefit as from the climatological relative fre-
quency. In some cases, the required accuracy is greater than could
possibly be achieved with present meteorological knowledge and fore-
casting techniques. "
THE PROBABILITY FORECAST 3
In the matter of dispatching aircraft, the climatological expectancy
of below operating limits is on the order of 0.02 or 0.03—very low. Both
C and L are large and composed of so many intangibles that this ratio
is hard to calculate, but it seems certain that for some flights, at least,
this is so large that the present forecasts are not definitive enough to
provide the sole guide to the operation.
Gringorton (3) discusses the probability factor in dispatching air-
craft as follows:
"Suppose that a destination is presently closed, and that an airliner
is scheduled to depart for that airport in two hours. Let p be the
probability that the airport will be open by the scheduled time of arrival.
Let T be the net profit from a successful flight. Let I be the net cost
resulting from cancellation; this should be overhead, such as the cost
of rentals, maintenance of idle equipment, and salaries. Let L be the loss
resulting from an incorrect decision; in this case the decision would be
not to cancel, but to risk having the airliner return to the point of
departure when finding the destination closed upon arrival. [Author's
note: In actual practice L would much more likely be the cost of diver-
sion to an alternate airport nearer the destination.] The loss would be
due to overhead, the salaries of the crew, cost of gasoline, and loss of
prestige expressed in dollars and cents.
"For the critical frequency, p , it is immaterial which decision the
c
dispatcher makes, to cancel the flight or not; the average loss in similar
situations will be the same for either decision. Therefore, I = (l-p )L —
c
pT from which P = (L - I) (L + T)~\
€ c
"There is much logic summarized by this equation. If the loss L
following an incorrect decision is great, the likelihood p of ( operational )
weather must be great in order to justify the decision to maintain the
schedule. If the cost L is not much greater than the overhead, I, the dis-
patcher should find it worthwhile to base a positive decision on even a
small chance p of the airport opening. If the profit T is great, the dis-
patcher should try to maintain the schedule on the basis of a small
chance of the airport opening."
II. THE PROBABILITY FORECAST
In practical, day-by-day operations of an airline there are many
imponderables which must be taken into account in decisions of this
nature. The important point is that for any quantitative evaluation of
such an operation, the weather forecast must not be in categorical terms,
as most are at present, but in terms of probability.
From this discussion it is clear that categorical-type forecasts, such
as the conventional airways forecasts or newspaper forecasts, are very
restricted in their usefulness. There are two main reasons why this is so.
(1) Their absolute accuracy and precision are not high; and (2) they
convey to the user only a small part of what the forecaster knows.
4 1. THE FORECAST PROBLEM
Today, in those operational entities, such as the armed services or
the airlines, which maintain their own meteorological services, the prob-
ability factor is usually injected, consciously or unconsciously, into the
operational decision by subjective exchanges of opinions between dis-
patcher, flight controller, or commander, and meteorologists.
A corollary factor to probability in any forecast is the confidence
with which it is made. There are some situations in which the forecaster
can be reasonably sure of his forecast; in others, he knows he is issuing
something akin to a guess. If there is no way for the user to differentiate
between these two cases, then there is no way for him to make intel-
ligent use of a weather forecast. Furthermore, after several bad decisions
have been made on the "guess" type of forecast, the user will refuse to
believe the good ones when they come along, and again fail to make a
correct decision. In most forecasts, as issued currently, there is no ade-
quate way to judge the confidence of the maker. Even in private
meteorology, where relatively leisurely discussion of the problem may
take place, the man who makes the decision most often judges the
confidence of the maker either by his personal knowledge, or by the
salesmanship with which it is presented. Some more logical and objec-
tive method is needed, and a reasonably objective probability expression
would serve this purpose admirably.
That this problem of a suitable expression and evaluation for fore-
casts to the user is not a new one, is pointed up by the following passage
taken from an article by W. E. Cooke in the Monthly Weather Review
in 1906, as quoted from a paper by Brier (4). "Now this is the point I
wish to make clear. Those forecasts which were marked 'doubtful' were
the best I could frame under the circumstances. I could see no way of
improving them at the time, and they would not have been expressed
differently whether I weighted them or not. If I make no distinction
between these and others, I degrade the whole. But if, on the other
hand, I attach a figure which practically says Tm sorry but this is the
best I can do for you today—do not attach too much importance to it,'
I eliminate beforehand the adverse opinion which a great number of
incorrect forecasts must produce, and I raise the bulk of the predictions
to their true value. In particular, I create a series marked with the
maximum figure, which the public finds to be almost invariably correct
and this raises the value of this particular series enormously."
These writers are by no means the sole exponents of probability-type
forecasting. Jacobs (5) has been a longtime and outstanding advocate
of the use of this type of expression in climatology, especially when it is
coupled with a real understanding of the user's problem.
More recently, Malone (6) has covered this field in very thorough
fashion. He has this to say:
"The aspects of the problem we have been discussing in qualitative
terms are well known to meteorologists. There appears, however, to be
THE PROBABILITY FORECAST 5
a curious reluctance to accept their full significance with respect to the
prediction problem. Whenever uncertainty is admitted in a forecast it
is done in a loose, unsatisfactory way. Categorical predictions, which im-
ply by the positivism with which they are worded that weather predic-
tion is an exact science lending itself to a deterministic treatment, are
still the general rule. This practice places the forecaster in an untenable
position. Worse yet, with respect to the field of applied meteorology,
this point of view is contagious and frequently spreads to those who have
primary responsibility for making the operational decisions in which
weather enters as a factor. A vicious circle is often established in which
the more positive the forecaster tries to be, the more positive he is
expected to be and the more positive he tries to become. This process can
quickly reach ridiculous proportions. The occasional heady successes
sometimes achieved are often over-emphasized and in the long run may
well do more harm than good. The end result is often a failure to ex-
ploit fully the contribution that meteorological knowledge can make to
an operational problem.
"This unwillingness to take cognizance of the consequences of the
nature of the problem to be solved has roots far deeper than the
limitations enumerated above. . ..
"But does the lack of complete determination mean that there is no
coherent order in meteorological time series? By no means. There is
demonstrable skill evident in the forecasting techniques in use today.
This skill is sufficient to make weather predictions, even in their present
unsatisfactory state, of very considerable economic significance."
The next question which logically arises is, "Why are not all fore-
casts issued as probabilities? There are at least two reasons for the
slowness of meteorology to change to this type. The first is that, except
for isolated areas and special types of forecasts, no way has been devel-
oped to make a quantitative determination of probability in weather
forecasting. The second is the reluctance of many users to accept this
type of forecast.
With regard to the first reason, Malone has been in the forefront of
the effort to develop suitable techniques with which to make valid
quantitative probability forecasts. He has also apparently found public
acceptance of such forecasts. The U. S. Weather Bureau has also con-
ducted several experiments with somewhat mixed success.
The formulation of methods for the mathematical prediction of
weather probabilities is likely to be a slow process involving intricate
calculations, but fortunately it is not necessary to await this optimum
result before making a start on this highly necessary change. To begin
with, the forecaster can usually make a fairly skillful subjective estimate
as to his confidence for any particular forecast. In an experiment with
forecasters at Salt Lake City, Williams (7) found that the assignment
of confidence factors by the forecasters themselves demonstrated rather
