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range and daily forecasting routine as commonly prac- 
ticed today depends upon the effective synoptic presen- 
tation of current and past weather patterns, which serve 
as a basis of either synoptic or mathematical extrapola- 
tion, and of any physical forecasting techniques. These 
synoptic weather patterns usually present the two- 
dimensional distribution of the weather elements in 
selected planes. The primary patterns are those of the 
geographical distribution of the weather elements in 
horizontal or quasi-horizontal planes. A great variety of 
such weather charts may be plotted, starting usually 
with the sea-level or surface map. The upper-level charts 
may be plotted for selected heights, for selected iso- 
baric surfaces, for selected isentropic surfaces, or for the 
thickness between selected isobaric or isentropic sur- 
faces. Several upper-level charts are usually prepared, 
the highest one frequently being located near the top 
of the troposphere or the base of the stratosphere. 
The synoptic charts for the selected levels are fre- 
quently supplemented by vertical cross sections through 
the atmosphere, which follow a line of upper-level ob- 
servation stations, or at times by the use of individual 
point soundings through the troposphere. The essential 
purpose of the entire assemblage of synoptic charts, 
which, particularly at upper levels, may vary greatly as 
to number, form, elevation, weather data plotted, and 
geographical extent of the area covered, is to present as 
completely and effectively as practicable, in the area 
which is deemed necessary, the distribution of the 
weather elements in the form of two-dimensional pat- 
terns. It is the regular time sequence of a complete set 
of such synoptic charts, particularly the sequence of 
pressure and pressure-change patterns, to which are 
applied the various techniques of synoptic and mathe- 
matical extrapolation, and physical reasoning, by means 
of which the future, or prognostic, weather pattern is 
derived. 
It is possible to enumerate here only the more fre- 
quently applied synoptic techniques of extrapolation, 
and to comment briefly on their potential effectiveness. 
This type of forecasting has been practiced on surface 
weather maps since the beginning of synoptic weather 
forecasting nearly a century ago, while its application 
to upper-level charts is a development almost exclu- 
sively of the past quarter-century, except that upper- 
level wind observations have been used to some extent 
to supplement surface reports since the early 1900’s. 
The simplest extrapolation procedure consists of the 
linear extrapolation, or continued displacement at the 
same speed as that in the preceding period or periods, 
of the various features of the sea-level weather map, 
such as isobaric or isallobaric centers, isobaric trough or 
ridge lines, or frontal discontinuities with the attendant 
frontal phenomena and air-mass weather characteristics. 
The linear extrapolation technique is applied also to 
change or acceleration tendencies such as the deepening 
or filling of pressure centers and troughs or ridges, 
changes in the direction or speed of movement of pres- 
sure patterns, fronts and air masses, and frontogenesis 
or frontolysis. The approximate effect on the pressure 
field of even the second-order time derivatives of the 
WEATHER FORECASTING 
pressure may be anticipated by the deepening or filling 
of isallobaric centers, and by the proper use of 3-hr 
pressure tendencies corrected for the normal diurnal 
trend of pressure. 
Since the upper-level pressure patterns are uniquely 
related to the sea-level pattern and the temperature 
distribution, and since the upper-level charts present 
the large-scale dynamic state of the atmosphere more 
clearly than does the surface chart, there has been a 
strong tendency in recent years, with the increase of 
aerological data, to treat the 700- or 500-mb charts as 
the primary forecasting tools and the surface charts as 
secondary. The same type of extrapolation procedure 
as outlined above for the sea-level map can be applied 
effectively to the simpler upper-level pressure patterns 
to obtain prognostic upper-level charts, which then 
serve as a basis for the prognostic sea-level chart. 
Particularly useful for this type of upper-level synoptic 
extrapolation, although not as widely used in practice 
as they deserve to be, are certain kinematical principles 
formulated by Rossby [10] relating the deepening and 
filling, and the movement of upper-level troughs and 
ridges of the isobaric pattern, to the phase relation of the 
corresponding isothermal pattern. In addition to these 
synoptic techniques some of the more recent mathe- 
matical extrapolation techniques discussed below are 
properly applicable only to the upper-level flow pat- 
terns. 
Vertical cross sections through the atmosphere, no- 
tably meridional cross sections, also present synoptic 
information that should be most useful to physical 
diagnosis and prognosis of the weather, but up to the 
present time their incorporation into daily forecast 
practice has been limited primarily to the current and 
prognostic description of flight weather conditions along 
selected air routes. 
The synoptic extrapolation technique of forecasting 
has been placed on a relatively routine basis by the 
method of kinematical extrapolation which was de- 
veloped by Petterssen [7]. This method consists essen- 
tially of a quantitative determination of the in- 
stantaneous speed of displacement, in any selected 
direction, and the tendency toward deepening or filling, 
of characteristic features of the current horizontal pres- 
sure field which are being effected by the current pres- 
sure-tendency field. The calculated trend of movement, 
or of deepening, is assumed to continue unchanged. The 
method can be applied equally well to sea-level or to 
upper-level pressure patterns. In their complete form 
Petterssen’s formulas do melude acceleration terms 
which quantitatively evaluate the effect of the current 
change of trend of development. Unfortunately, how- 
ever, these complete formulas are both time consuming 
and difficult to apply because the synoptic data imevi- 
tably are inadequate for their objective evaluation; 
hence so much is left to the judgment of the individual 
forecaster that the method loses its principal advantage 
—that of being objectively and routinely applicable 
by the inexperienced forecaster. Consequently, Petter- 
ssen’s forecast method as it is usually applied is a 
quantitative method of routine extrapolation, which 
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