DYNAMIC FORECASTING 
For simplicity in computation, a rectangular area 
with sides « and y is chosen, and a rectangular lattice 
is defined by the coordinates 
& = (u/p)t, @ =0,1,--:, p), 
y = (»/Q)) GES Waly oo 5.05 
in which the boundary lines arez = 0,7 = p, andj = 0, 
jg = q. If G5, &5, nis, Jaz, (08/0t):;, (0E/dt).; 
denote the finite-difference approximations to 9, &, n, 
Jn, O/dt, d&/dt at the points (2,7), the procedure 
is as follows: From the initial values of @;; one de- 
termines first &;, then »:;, and finally J;;. The 
values of (0&/dt);; are then immediately found from 
(63): 
(0&/0t)is = Jis(miz , Bi3). 
To obtain (d&/dt);; one has to solve the finite-difference 
analogue of (64), that is, 
D*(a®/dt):; = (As) (0E/dt) 5 , (67) 
where D* is defined by (59) and As = p/p = v/q is 
the grid interval. On the assumption that © does not 
vary on the boundary (d®/d¢ = 0) the solution is found 
to be 
ot PQ = 1=1 m=1 r=1 s=1 
sin” “al + sin’ = (68) 
2, 9, 
- J7s Sin a sin” sin al sin 
qd Pp qd 
In the actual computation, the functions S, = 
sin (ru/p) and 7, = sin (zv/q) need only to be tabu- 
lated for integral values of uw from 0 to p/2 and for v 
from 0 to g/2, the functions for other values of the 
arguments being given by 
Ser = Siete = —S, 5 ins = Mote = —T, . 
This is a decided advantage in a machine with a 
limited storage capacity for numbers. Had an arbi- 
trary area rather than a rectangular one been selected, 
the solution would be given by the finite-difference 
form of (20). Instead of storing the (p + q)/2 sines, 
one would then have to store the p’q/2 independent 
values of a symmetric Green’s function. 
Having determined the quantities (d/dt);; , (@/dt);; 
the time extrapolation is performed by means of the 
formulas 
Eup = iy + 2A0(GE/at);; , 
Bit? = ei*' + 2at(ab/dt);;, 
and the entire process is repeated a required number 
of times. In the first step, uncentered time differences 
must, of course, be used. 
A number of 24-hr integrations have been carried 
out by this method on the Eniac” [5]. The space in- 
2. The Electronic Numerical Integrator and Computer of 
the Ballistic Research Laboratories, U. S. Army Proving 
Ground, Aberdeen, Maryland. 
479 
terval As was chosen to be eight degrees of longitude 
at 45° on the map and the time intervals 1, 2, and 3 hr 
were used on different occasions. The results indicated 
that the space interval was too large—about one-half 
its value seems to be recommended for future work— 
whereas even three hours was not too long for the time 
interval. 
Figure 3 shows the results of one such integration. 
A strip two grid intervals in width at the top and side 
borders and one grid interval in width at the lower 
border of each diagram has been excluded to eliminate 
spurious boundary influences from the forecast. The 
forecast is seen to be fairly good in regions where ade- 
quate data were available. The major discrepancy oc- 
curred south of Greenland. In order to ascertain 
whether the discrepancy was due to the effect of baro- 
clinicity, the 500-mb tendencies were calculated by 
means of the general advective equations (18) and 
(19), and to obtain a comparison with observation the 
computed tendency field was translated in the direction 
of the mean current for 24 hr with the speed of the 
trough to give a 24-hr change. The results are shown in 
Fig. 4. 
Objective Analysis 
After the mitial data were assembled and put on 
punch cards, the time required for the Eniac to pro- 
duce a 24-hr forecast using 2-hr time intervals was 
approximately 24 hr of contmuous operating time. 
However, this time is likely to be considerably reduced 
by machines with a greater memory capacity. It has 
been estimated that the time required for the electronic 
computer at The Institute for Advanced Study, with a 
memory capacity for 1024 forty-digit bmary numbers, 
will be about 14 hr. It is thus not entirely quixotic to 
contemplate the preparation of numerical forecasts for 
practical use in the near future. It then becomes obyi- 
ous that if the high speed and high capacity of the 
machines are to be used to greatest advantage, there 
must be an equally rapid method of preparing the data 
received by teletype, radio, and telegraph in a form 
accessible to the machine. Under present conditions 
the data must first be plotted and subjectively ana- 
lyzed, both of which operations are now painfully 
slow. J. von Neumann and H. A. Panofsky have there- 
fore suggested that weather reports be translated into 
initial data by purely objective methods. As Panofsky 
[11] has shown, the pressure field may be approximated 
by an mth order polynomial of the form 
pla, y) = >) assa"y! @+j<n 
uJ 
by the method of least squares, provided the number 
of coefficients a;; is less than the number of points at 
which p is known. The degree of the polynomial is 
determined by the amount of smoothing desired. For 
relatively small areas a third-degree polynomial is held 
to be adequate. 
One can easily envisage a process whereby the ma- 
chine is instructed in advance to take note of the data 
at a set of fixed observation points, to perform the 
