806 
larities. Once the singularities have been determined, 
individual five-day mean curves are extrapolated more 
or less parallel to the normal curves (but the ampli- 
tudes may be suppressed or exaggerated according to 
the seasonal behavior relative to the normal). This pro- 
cedure is followed for several points in Europe and the 
eastern Atlantic and results in the preparation of a five- 
day mean prognostic pressure-change chart which serves 
as an extended-range forecasting aid. 
The similarity of this method to the trend method 
lies in the fact that it, too, makes some use of persist- 
ence and the normal. Persistence is incorporated by 
drawing and keepimg the extrapolated five-day mean 
curves at the same general level (departure from 
normal) at which they have been operating. To the 
extent that singularities are real, the method also in- 
troduces the normal and its rate of change. It is difficult 
to compare trend and singularities methods as to ef- 
ficacy, especially since one of them (singularities) is to 
a considerable extent subjective. At least it can be said 
that the trend method, aside from its greater objec- 
tivity, arrives at a method for predicting an orderly 
evolution of an existing large-scale state with a mini- 
mum of questionable basic assumptions. 
Another statistical procedure—one concerning which 
considerable controversy has arisen—involves the con- 
cept of symmetry points. The strongest advocate of 
this method has been Weickmann who, along with his 
associates, has published many papers dealing with this 
subject (see, for example, [24, 25]). During World War 
II, investigations of the symmetry-pomt technique were 
made in Britain (e.g., Walker [23] and the following 
discussion by C. E. P. Brooks, N. Carruthers, and 
others) and in the United States by Haurwitz [6]. Both 
of these groups could find little in the way of prognostic 
significance in the symmetry-point method. Their meth- 
ods of testing undoubtedly involved the best available 
statistical procedures, and it would indeed be difficult 
to dispute the findings of these distinguished mvestiga- 
tors who, while admitting the existence of symmetry 
points in meteorological data, could find no method of 
detecting them in advance. Presumably, if the faith of 
the users of this method is still unshattered, it is to be 
concluded that its use mvolves certain subjective ele- 
ments which are as yet impossible to express quanti- 
tatively in a form suitable for testing. 
In order to pursue this interesting topic further, it 
will be helpful to describe briefly the practical proce- 
dure currently being used by Weickmann’s assistants 
working at Bad Kissingen. First, they work not with 
isolated points but with areas roughly 500-km square. 
The mean pressures of about ten stations in many such 
areas are plotted day-by-day im graphs. The graphs are 
then copied on transparent paper. By turning over the 
paper one obtains a mirror image and with the help of 
the original graphs tries to locate by inspection a point 
of symmetry. Cases of “inverted” symmetry, where the 
tissue must be folded along a horizontal line, are also 
sought. By working in this manner for several areas and 
then copying off portions of the observed curve as it 
would be reflected to produce the symmetry, an extra- 
WEATHER FORECASTING 
polation of the pressure distribution into the future 
may be made. 
Everyone must agree, along with Haurwitz, Brooks, 
and Carruthers, that symmetry points do exist in me- 
teorological data. However, Baur [2], in a statistical 
study, claimed the existence of such symmetry can be 
entirely accounted for by the serial correlation (per- 
sistence) present in day-to-day pressures. To what ex- 
tent symmetry pomts contain more information than a 
series of almost random data in which persistence oper- 
ates is indeed a formidable question for its proponents. 
On the other hand, no synoptic meteorologist who 
possesses the most fragmentary appreciation of art can 
deny that the flow patterns observed in mid-tropo- 
sphere evolve in a manner suggestive of a vast attempt 
on the part of the atmosphere to arrange itself into 
symmetrical patterns. The currently popular concepts 
of the conservation of the total absolute vorticity about 
the vertical may be looked upon as nature’s attempt to 
achieve symmetry. This attempt repeatedly shows up 
in the manner in which an upstream circulation subse- 
quently becomes reflected some distance downstream in 
a manner suggestive of folding the zonal flow pattern 
along a meridian. The frequent failure of the atmo- 
sphere to achieve this symmetry in space is due to 
ever-present forces which work to destroy and change 
one portion of the pattern before there has been time for 
it to be reflected downstream. 
The tendency toward symmetry described above ap- 
plies to symmetry in space, whereas Weickmann’s ideas 
are supposed to apply in time. Insofar as longitudinally 
symmetric patterns move steadily eastward or west- 
ward in an unchanging manner, they will produce 
symmetry of barograms. It may be that the method 
propounded by Weickmann is an attempt to capture 
the tendency toward spatial symmetry. If so, it would 
seem that it contains a germ of the truth, but this germ 
would be difficult to isolate in order to make diagnoses 
and prognoses. 
Weather Type and Analogue Methods. The concepts 
of weather types and analogues probably arose very 
early in the history of meteorology. As with all systems 
of classification, the type method is designed to sel up 
a certain partition of weather map sequences so that 
the differences between weather maps of one type are 
small compared to the differences between maps of 
different types. The work of Multanovsky [15] many 
years ago had indicated that the duration of a given 
type was not constant from year to year, and he re- 
ferred to the particular length of operation of one 
sequence as the ‘natural period.” But other typing 
systems have attempted to restrict the life history of a 
weather type to a certain number of days, it then 
being necessary for the type to change (or repeat) after 
this time interval. One such typing method is described 
at length elsewhere in this Compendium by one of the 
foremost exponents of the weather-type approach, R. 
D. Elliott.? 
2. Consult ‘‘Hxtended-Range Forecasting by Weather 
Types” by R. D. Elliott, pp. 834-840. 
