788 
this process may be continued until only one variable, 
W,, is left on the right-hand side of (5). 
The final variable W, thus derived is a function of all 
of the origmal X;. It has been obtained by a process 
which permits the distribution of the central tendency 
of the data to specify the form of the functional rela- 
tionship, thereby eliminating the major disadvantage of 
mathematical regression techniques, discriminant func- 
tions and the like, which require prior knowledge of, or 
assumptions regarding, the nature of the relationship 
between the independent variables and the dependent vari- 
ate. (Present mathematical regression techniques can 
treat only those relationships between variables of the 
memo 
< Ol e 
JOR oul MEAN =0.5 
If 0. OB Ga I 
| 0.3 Keon MEDIAN =0.5 
e 
I gOS O7I\ MODE =0.6 
tee Dalle 
Fie. 9.—Schematic analysis of the scatter diagram. The 
dashed inset square at the top is an example of a small area of 
the diagram containing, for the purposes of this illustration, 
eleven values of a weather element W, say, rainfall amounts. 
For these eleven values of W, some measure W; of their central 
tendency (e.g., the mean), represented in this instance by the 
quantity W; = b, is entered at X, the geometrical center of this 
small area. After such values of W; have been entered over the 
entire chart, W;-isograms of these quantities, a, b,...m, are 
drawn. 
form y = byt; + bow. + --- + b,2, or relations which 
can be transformed to that form. This permits the use 
of polynomial regression and sometimes exponential 
regression.) Practical application of the graphical inte- 
gration process will be illustrated in the subsection on 
precipitation. 
Temperature. The temperature ,7 at some point P 
on the ground can be predicted by starting from, say, 
the prognostic 700/1000-mb hypsography and by ap- 
plying the indirect aerological methods as presented 
by Godske and others [33]. Relabelled (according to 
Table 17-50-1 in [83]), the prognostic 700/1000-mb 
isohypses give directly the ground temperature ,7’, to 
which the predicted 700/1000-mb heights are reduced 
on the basis of the saturation-adiabatic lapse rate. 
Temperature corrections indicative of the effective 700/ 
1000-mb lapse rate are added to ,7’, by systematically 
considering at P the air-mass type (using Table 17-50-2 
WEATHER FORECASTING 
in [83]) and the pattern of the prognostic sea-level 
isobars (using Fig. 17-50-2 in [83]). Finally, additional 
corrections are applied to account for frontal surfaces, 
if any, predicted to be over P (using equation 17-50(1) 
in [83]) and anticipated ground inversions, if any, over 
P (using Fig. 17-50-1 in [33]). For predicting the rapid 
temperature changes occurring at frontal passages— 
one must take into account certain unrepresentative 
influences, such as the existence of cold-air films at the 
ground, pseudo fronts in advance of the real front, 
local wind systems such as the land and sea breezes and 
foehn winds,” evaporation cooling in falling precipita- 
tion, and the predictable cloud distribution in space 
and time. } 
The local, diurnal, temperature minimum can be 
predicted quantitatively by means of formulas and 
nomograms which relate empirically the sunset ob- 
servations of temperature, humidity, and wind at the 
place of prediction and at auxiliary stations some dis- 
tance upwind to the heat loss during the ensuing night 
for synoptic situations in which no new air masses are 
to be expected. Such numerical methods have been 
developed by Kammermann [45], Dufour [21], Kessler 
and Kaempfert [46], Brunt [13], and Jacobs [44]. Geiger 
[31] has presented many detailed considerations for 
forecasting the night frosts, a problem still remaining 
after the minimum temperature has been predicted. 
Speculating on the ways in which the total solar 
radiation received at the ground is dissipated, Gold 
[85], Neiburger [55], and Bundgaard [83] have pre- 
sented quantitative methods for predicting locally the 
daily temperature maximum. These methods are ap- 
plicable if, for at least the approximate half-day period 
from one hour after sunrise to the time of temperature 
maximum (normally 1300-1500 LMT), clear skies and 
no air-mass replacement are forecast locally. Under 
these conditions, then, the locality remains well within 
a homogeneous, extensive, and slowly moving air mass 
during this period, so that local advective changes are 
negligible. 
General Hydrometeors. Extrapolated frontal posi- 
tions at once indicate the future position of the areas of 
nimbostratus rain and altostratus cloud. The future 
location of drizzle and low stratiform cloud will extend 
through such parts of the extrapolated air masses 
where there will be cooling from below, showers and 
low cumuliform cloud where warming from below is 
anticipated. Using the predicted map changes of (1) 
surface temperature, (2) vertical motion, (3) upper-air 
humidity, and (4) upper-air stability, the regional fore- 
caster can issue general predictions about nonfrontal 
hydrometeors: stratiform cloud—with or without driz- 
zle, cumuliform cloud—with or without showers, thun- 
derstorm, and hail. The change (3) enables us to decide 
whether or not the processes leading to hydrometeors, 
once started by a thermal influence (1) or a kinematical 
impulse (2), will culminate in the condensation phe- 
9. Consult ‘“‘The Instability Line’? by J. R. Fulks, pp. 
647-652 in this Compendium. 
10. Consult ‘Local Winds” by F. Defant, pp. 655-672 in 
this Compendium. 
