482 
it is more convenient to use pressure as an independent 
variable in place of height. The complete equations of 
motion in this variable are given by Eliassen [7]. Under 
the hydrostatic and adiabatic assumptions they become 
dv ov ov 
aa ap Wad om Oa 
= —V,6 — 20 sin ¢k X v, (67) 
8 Rs (68) 
dp p 
Bree = (69) 
p ap 7 
Ont + vv,ne+o 2B! 9, (70) 
where v is the horizontal velocity and » = dp/dt. 
The boundary conditions at the ground and at the 
upper limit of the atmosphere are, respectively, 
d®& Ob om 
ah ae ee Ba) (71) 
and 
dp 5 
di =o = 0 (72) 
In the process of numerical computation, the time 
increment in v is determined from (67) and w is 
found by integrating (69) and taking account of (72): 
‘Pp 
= i V>:V dp. 
0 
The time increment in In 6 is obtained from (70) and 
that of ®@ is obtained as follows: Combining (73) with 
(71), we find for the surface height tendency 
(73) 
Qo = 
‘PO 
eS) = — w:(Vpb)o — = || Vp:vdp, (74) 
dt Jo Po “0 
and from the relation 
dn@_ _—-.: oe 
at dp dt’ 
we derive by integration 
p 
ee iis =| + / (vvpmo+o2me)@. (75) 
dt Jo vi) Op p 
As (08/0dt)) is known from (74), d®@/dé is then immedi- 
ately determined. 
Since w is very nearly equal to w, one would begin 
by assuming dv/dt, Vp-v, and w to be 0 and then trust 
the compensation mechanism to yield a correct fore- 
cast. In six hours, the time interval used by Richard- 
son, twenty-four time extrapolations of fifteen minutes 
each will have been performed, during which time 
there would presumably be ample opportunity for this 
mechanism to operate. 
Nonadiabatic and Frictional Effects 
Nonadiabatic and frictional effects have been ignored 
in the body of the discussion only because it was 
thought that one should first seek to determine how 
much of the motion could be explained without them. 
Ultimately they will have to be taken into account, 
DYNAMICS OF THE ATMOSPHERE 
particularly if the forecast period is to be extended to 
three or more days. 
Condensation phenomena appear to be the simplest 
to introduce: one has only to add the equation of con- 
tinuity for water vapor and to replace the dry by the 
moist-adiabatic equation. Long-wave radiational ef- 
fects can also be provided for, since our knowledge of 
the absorptive properties of water vapor and carbon 
dioxide has progressed to a point where quantitative 
estimates of radiational cooling can be made, although 
the presence of clouds will complicate the problem 
considerably. 
The most difficult phenomena to incorporate have 
to do with the turbulent transfer of momentum and 
heat. A great deal of research remains to be done before 
enough is known about these effects to permit the 
assigning of even rough values to the eddy coefficients 
of viscosity and heat conduction. Owing to their sta- 
tistically indeterminate nature, the turbulent proper- 
ties of the atmosphere place an upper limit on the 
accuracy obtainable by dynamical methods of fore- 
casting, beyond which we shall have to rely upon 
statistical methods. But it seems certain that much 
progress can be made before these limits are reached. 
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