A PROCEDURE OF SHORT-RANGE WEATHER FORECASTING 
nonadvective changes in the relative height are due 
to (1) vertical motion, and (2) condensation or evapo- 
ration and radiative heating or cooling of the air. 
The Local Change in the Relative Height Asso- 
ciated with Transisobaric Motion. Also associated with 
the local changes in the relative height is another at- 
mospheric process known as the transisobaric displace- 
ment of the ar. This is a somewhat less important 
process than the isobaric advection and involves the 
conservation of entropy. Although in reality both ef- 
fects occur simultaneously with various degrees of rela- 
tive intensity, for the sake of convenience in the 
operations of prognosis they are considered separately. 
The greatest convective temperature changes are 
produced by the vertical advection of pressure, whereas 
only generally small convective changes in the tempera- 
ture are caused by the relative local pressure change 
and by the horizontal advective pressure change. For 
example, a modest and frequently observed value of 
the vertical motion is 1 km per 12 hr, corresponding 
to an individual pressure change of about 23 mb per 
3 hr for p = 700 mb and 7 = OC. This rate of pressure 
change in turn corresponds to a convective isobaric 
change in temperature of 1.3C per 3 hr. In extreme 
instances the isobaric temperature change resulting 
from transisobaric displacement may be as large as 4C. 
On the other hand, at 3 km the pressure tendency 
seldom exceeds 3 mb per 3 hr, corresponding to a 
temperature change of only 0.18C per 3 hr at 700 mb 
and OC. Extreme limits of cross-isobaric velocity com- 
ponent and pressure gradient are 5 m sec! (about 10 
knots) and 6 X 10 cb m~ (about 1 mb in 10 miles), 
respectively; such ageostrophic flow leads to a pres- 
sure change of 3 mb per 3 hr, corresponding to a 
temperature change of 0.18C per 3 hr at 700 mb and OC. 
The “convective” variation in the thickness of a 
mandatory layer is found by differentiating the statical 
equation with respect to time and ascribing the total 
convective changes in the temperature to the vertical 
advective pressure changes alone. In this differential 
equation, the pressure variable is eliminated by means 
of the statical equation, and the lapse rate of potential 
temperature is then introduced. Integrating this equa- 
tion by using appropriate mean values for the manda- 
tory layer, we obtain —®(@2 — 6,)/6, where 6 and 6, 
are values of the potential temperature at the lower 
and upper boundary surfaces, respectively, of the man- 
datory layer, and @ is the mean potential temperature 
of the layer. 
Since @ always increases upward in a deep layer, 
unsaturated adiabatic descent relative to a mandatory 
layer increases the partial relative height of the upper 
boundary surface. In a total layer of the lower tropo- 
pause, this motion is generally connected with sub- 
sidence which, after some time, makes the upward 
merease of 0 even larger and thereby tends to produce 
an especially large rate of local increase in the total 
relative height. (In Fig. 8a, for example, it is seen that 
there is a pronounced center of nonadvective increase 
m the 500/1000-mb height over the south-central 
United States, where the northwesterly flow is de- 
783 
scending from the Plateau Region.) However, the ini- 
tial descent is soon hindered more and more by the 
increasing upward ascendent of 0, which, as a second- 
order contribution, dampens and somewhat reduces 
this otherwise large rate of local mcrease in the total 
relative height. Over inactive fronts the subsidence 
produces an increase in the relative height. (In Fig. 
8a, for example, the cold front and occlusion in eastern 
United States are inactive, as evinced by the precipita- 
tion and altostratus-nimbostratus cloud system. It is 
seen that there is a ridge of nonadvective increase in 
the 500/1000-mb height to the rear of this front, the 
region traversed by this front during the past 24 hr.) 
At a cold front this effect partly reduces the generally 
larger relative-height decrease due to the advection of 
colder air, while at a warm front, it augments the 
relative-height increase due to the advection of warmer 
air. Consequently the spacing of the relative isohypses 
would be smaller for warm fronts than for mactive 
cold fronts. 
On the other hand, wnsaturated adiabatic ascent rela- 
tive to a mandatory layer is accompanied by a de- 
crease in its relative height. In a total mandatory 
layer of the lower troposphere, this motion is generally 
connected with vertical stretching, whereby the up- 
ward increase of @ through the mandatory layer is 
appreciably reduced, so that the associated rate of 
local decrease in the relative height will be smaller than 
the increase in the case of descent. (In Fig. 8a, for 
example, it is seen that there is a tongue of nonadvec- 
tive decrease in the 500/1000-mb hypsography along 
the western seaboard of British Columbia and Wash- 
ington where there is forced ascent of the westerly 
flow in crossing the Coast Mountains and the Cascade 
Range.) However, the initial ascent of air through a 
mandatory layer is abetted by the consequent reduc- 
tion in the upward increase of @ between the boundary 
surfaces of the layer, so that, as a second-order con- 
tribution, this decreasing vertical ascendent of @ partly 
increases the otherwise small rate of local decrease in 
the relative height. 
The lifting of saturated and conditionally stable air 
(or, more generally, of all saturated air below tts level 
of free convection), such as in most cases of warm air- 
mass or warm-front precipitation, also produces a de- 
crease in the relative height. (In Fig. 8a, for example, 
it is seen that there is a pattern of nonadvective de- 
crease in the 500/1000-mb hypsography along the east- 
ern seaboard of the United States and in southern 
Quebec, where a saturated and conditionally stable, 
warm air mass is being lifted in its poleward ascent 
over quasi-stationary warm-front surfaces. Over the 
corresponding (active) warm-front surface this rela- 
tive-height decrease partly compensates for the larger 
relative-height increase due to the advection of warmer 
air. On the other hand, above the level of free convec- 
tion, the relative-height increase due to the ascent of 
the conditionally unstable, saturated air over a cold- 
front surface would reduce the large relative-height 
decrease due to advection; above some warm-front 
surfaces the same effect would add to the height in- 
