430 
literature is provided by Abdullah who showed how the 
energies of motion and the rise in imversion height are 
transmitted to the leading edge of the cool air. 
TasBLE I. DisTaNcr or PRESSURE JUMP FROM FRONT 
Initial time of 12-h j T agp |) Beam || 2 Od- 
eae im) | CK) | CC) Hee se 
0400Z Jan. 19, 1947 1700 | 253 | 5.0 | 490 | 410 
1600Z Mar. 23, 1947 2000 | 259 | 3.5 | 670 | 550 
1600Z Mar. 4, 1947 1800 | 274 | 4.0 | 486 | 390 
Time-Dependent Flow as a Forecast Tool. The use- 
fulness of the method of characteristics in making fore- 
casts has been emphasized before [7, 21]. The success 
of Abdullah [1] in predicting the time of breaking and 
of Freeman [7] in predicting the height of the tropical 
inversion emphasizes this feature. Of course, the solu- 
tion of any equation with time as an independent vari- 
able gives a method of prediction. In most sciences the 
problem is to predict the behavior of a system with a 
given set of initial conditions which will be applied 
repeatedly. In weather forecasting the prediction is 
usually made from a set of initial conditions that is 
never repeated. The method of characteristics is par- 
ticularly suited for such a system because any set of 
initial conditions can be fitted to any accuracy desired, 
and regularity of the functions involved is not required. 
In any region in which the flow under an inversion 
can be considered one-dimensional and the effects of the 
Coriolis force are not important there are two pro- 
cedures for making forecasts that might be found use- 
ful. The most straightforward procedure is that of 
forecasting the weather along part of the z-axis from a 
given set of initial conditions on a larger part of that 
axis. The z-axis is a line in the 2, ¢ plane and the char- 
acteristics can be built up from it as in Fig. 12. Such a 
t 
Fie. 12.—Area for which a prediction can be made from 
initial data on the x-axis. 
method should be useful over large land areas in the 
tropics, such as Africa and South America, and prob- 
ably in island-studded oceans like the northern part of 
the South Pacific Ocean. This method could also be 
developed into a method of making forecasts from data 
gathered from aircraft flights, particularly those which 
make periodic observations of the inversion height. The 
most useful method between stations (in the tropics 
particularly) is outlined in Fig. 13. The procedure 
DYNAMICS OF THE ATMOSPHERE 
above, or a good estimate of the conditions between A 
and B, is used imitially and then new characteristics 
are found from information at A and B only. This pro- 
CHARACTERISTICS 
—_ 
x 
Fic. 13.—Area for which continuing predictions can be 
made from a series of weather observations (data along the 
t-axis) at two discrete points. 
cedure could be used to great advantage to predict 
conditions between two islands in the easterlies. Of 
course, to be used to best advantage, A and B should 
be a reasonable distance to the east and west of the 
region for which forecasts are desired. Forecasts for 
C and D can be made for appreciable periods. The 
usefulness of this method as a forecast tool for anything 
other than the qualitative aspects of flow under an 
inversion in the middle latitudes awaits the incorpora- 
tion of the effects of the Coriolis force into the method. 
High-speed computing machines will undoubtedly be 
needed to forecast two-dimensional time-dependent flow 
under an inversion. The extension to two dimensions 
will eliminate many of the restrictive assumptions in- 
volved in making a one-dimensional problem out of one 
that has such inherent two-dimensional aspects as the 
Coriolis force. 
Equations for Steady-State Flow under an Inversion. 
If we assume that there is steady-state flow under an 
inversion, that is, that there are no changes in the flow 
with time, then equations (11)—(18) become 
ou du p \ oh 
Ota. g, CU Ee 32 
De ae a(1 ae (2) 
ov dv p \ oh 
Sn ey (ils (| 33 
ee tO ay a( a ee 
oh oh ou , Ov 
E70) 34 
wih goths (4 2) (4) 
This is a system of equations similar to equations (1) 
and (2). It is complicated slightly by the presence of a 
third unknown h, but the same method of analysis is 
used on this set of equations. Three families of charac- 
teristics exist and the determinants used in equation 
(6) are of order six rather than four. In this case this 
third characteristic is a streamline and the vorticity 
a = “ is constant along it. If we assume the flow is 
wv y 
irrotational, this characteristic is not used. The flow 
