May 1969 371
UDC 551.511.33:551.521.32:551.558.2
THECONTRIBUTION OF INFRAREDCOOLINGTOTHEVERTICALMOTION FIELD
AND ITS IMPLICATION IN ATMOSPHERICENERGETICS
BEN R. BULLOCK,' LYLE H. HORN, and DONALD R. JOHNSON
Deportment of Meteorology, University of Wisconsin, Madison, Wis.
ABSTRACT
The validity of the adiabatic assumption used in estimating vertical motion is examined by comparing the
relative contributions due to adiabatic processes with the diabatic process of infrared cooling. Radiometersonde data
are used to prepare vertical profiles of the adiabatic and infrared components of the vertical motion. These data are
first filtered to reduce the effect of random errors. Although the adiabatic component of the vertical motion is usually
much larger than the infrared component, the profiles indicate that the infrared component can be important in
determining the total vertical motion. A comparison of the contribution of the infrared component in cloudy versus
clear sky conditions shows that this component contributes more to downward vertical motion in clear air than in the
cloudy situations. The consequences of this systematic variation in estimating energy conversions is discussed. In
view of these results the effect of other diabatic processes is very briefly considered.
1. INTRODUCTION
In many studies the so-called adiabatic method, which
involves the first law of t,hermodynamics and the
adiabatic assumption, is used to obtain the field of vertical
motion. Despite the necessity of the adiabatic assumption,
this procedure for computing vertical motions (Haltiner
and Martin, 1957) is widely used in meteorology, primarily
because other techniques, such as the kinematic and
vorticity methods, require assumptions possibly as restric-
tive as the adiabatic assumption. I n a recent study,
Hansen and Thompson (1965) used TIROS cloud photo-
graphs and the vertical motion field obtained from both
the kinematic and adiabatic methods to examine smaller
scale vaxjiations in the vertical motion field. Although in
general they obtained their best results using the kinematic
method, they also concluded that when studying larger
scale motions where datal. imitations may e,xist, the
adiabatic velocities are of more value.
In several atmospheric energetics studies the adiabatic
method has beenused to estimate the conversion of
available potential energy to kinetic energy (White and
Nolan, 1960; Jensen, 1961)-a process that involves the
sinking of relatively cold air and the rising of warm air
(Lorenz, 1955). The importance of using accurate vertical
velocity estimates in these Gonversion computations
cannot be overemphasized, since the magnitude of kinetic
energy production determines the intensity of the general
circulation. Furthermore, an understanding of the mode
of the atmosphere's circulation requires a determination
Research Center at Melbourne, Australia.
oralogy, Pennsylvanja State University.
1 Research assignment for the academic year 1-69 with the Antarctic Meteorological
Visiting appointment for the academic year 1968-69 with the Department of Mete-
of the scales and mechanism by which this conversion
occurs. Wiin-Nielsen(1964) notes that use of adiabatic
vertical velocities to obtain the conversion of available
potential energy to kinetic energy can be misleading.
I n any study employing adiabatic vertical velocities,
the validity of the results depends critically upon the
adiabatic assumption. For certain cases high in t'he
atmosphere, this assumption is not unrealistic. However,
in other atmospheric regions, especially the lower and
midtroposphere, diabatic processes of absorption and
emission of radiant energy, release of latent heat, and
sensible heat addition at the earth's surface tend to make
estimates of the vertical motion field based on the adiabatic
method less reliable. While latent heat release and sensible
heat transfer are difficult to measure, radiational processes
can be measured by devices such as the Suomi-Kuhn
radiometersonde and satellites.
In view of the importance of an accurate determination
for both energy studies and the possibility of inferring the
large-scale vertical motion field from satellite data, the
significance of one diabatic component-infrared radia-
tion-upon adiabatic estimates of the field of vertical
motion is investigated in this paper. Soundings of infrared
cooling made a t Washington, D.C., Montgomery, Ala.,
Green Bay, Wis., International Falls, Minn., and Amarillo,
Tex., selected from the periods Dec. 20-28, 1960, and
Jan. 7-18,1961, are used to estimate the contribution of this
diabatic process to the field of vertical motion. Separate
vertical profiles of vertical motion associated with
adiabatic processes and with the infrared component of
the diabatic process are compared by using 1) a limited
sample of polynomial filtered profiles and 2) a larger but
unfiltered sample of profiles. Because of the importance
31 2 MONTHLY WEATHER REVIEW V O l . 97, No. 5
of vertical motion estimates in obtaining energycon-
versions, the effect of neglecting the diabatic processes is
discussed in some detail.
2. BASIC EQUATIONS
SYMBOLS
dh/dt=rate of heat addition per unit mass
c,=specific heat at constant pressure
CY = specific volume
Rd=gas constant for dry air
p = pressure
O=potential temperature
w=dp/dt=vertical velocity in pressure coordinates
Vh=horizontal wind velocity
g=acceleration of gravity
F,=net infrared radiation
f = Coriolis parameter
u=eastward component of the wind
w=northward component of the mind
Using the notation from the list of symbols, the first
law of thermodynamics may be expressed as
dh -&=c,~-CYw. dT
After expanding the total temperature derivative, the
solution for the vertical velocity is
aT 1 dh -+V*VpT-- -
c, dt
CY dT
at w=
Our discussion of vertical motion in this paper is based on
the definition for vertical velocity in constant pressure
coordinates and should not be confused with the vertical
velocity, w, for Cartesian coordinates.
Using the Poisson equation and the equation of state,
equation (2 ) becomes
w=
Equation (3) represents the true vertical motion, and all
adiabatic and diabatic processes must be known to obtain
its value. For purposes of discussion the vertical motion is
divided into two components, one associated with adi-
abatic processes and the other Cvith diabatic processes.
The adiabatic portion of the vertical motion obtained by
assumingdh/dt=O is
(4)
The diabatic component of the vertical motion obtained
by subtracting equation (4) from equation (3) is
1 dh "
Equation (4) is the usual expression for the adiabatic
component of the vertical motion field, and equation (5),
which represents the diabatic effect, will for convenience
be designated the diabatic component of the vertical
motion field. In this study, only nonadiabatic heating
due to the field of terrestrial radiation is considered. Under
steady-state conditions and horizontal isotropy for the
field of infrared irradiance, the heat addition per unit mass
due to infrared divergence is
Thus the diabatic component of vertical motion due to the
field of infrared irradiance is
The adiabatic estimate of the vertical motion fieldis
obtained using (4), and the infrared diabatic component
is estimated by (7) from radiometersonde data (Suomi-
Kuhn, 1958). The relative importance of infrared processes
isexamined by comparing profiles of this diabatic com-
ponent of the vertical motion field with profiles using the
adiabatic assumption.
3. COMPUTATIONALPROCEDURES
ADIABATIC ESTIMATES OF VERTICAL VELOCITIES
The calculation of adiabatic vertical velocities by equa-
tion (4) requires estimates of the local temperature tend-
ency, horizontal temperature advection, and the stability
measure. An inherent problem in using synoptic data is
that the local temperature tendency is a time-averaged
determination while the horizontal advection by the
geostrophic wind field is a spatially determined quantity
at a given time (Panofsky, 1951). The infrared component
is calculated from data taken at the same time as that
used in computing the advection term. In order to obtain
diabatic and adiabatic profiles that are representative
for the same time, the local temperature tendency has
been determined from observations taken 24-hr apart
while the advection term of the adiabatic equation and
infrared component computation were' made from data
taken at the midpoint of the 24-hr period. For compati-
bility we assume that the 24-hr temperature tendency is
representative and is the best estimate corresponding to
the radiometersonde data.
May 1969 Ben R. Bullock, Lyle H. Horn, and Donald R. Johnson 373
The above assumption seems reasonable because the
free-atmosphere temperature time series tends to be a
smooth function whose principal variation is associated
with large scales of motion with intervals of several days
between adjacent relative temperature maxima and
minima. For this scale of variation, a second order Taylors
series expansion about the midpoint time to should provide
a valid description of the temperature in the 24-hr interval
from to-12 hr to to+12 hr. If this condition is satisfied,
then the finite estimate of the 24-hr time-average temper-
ature tendency is a valid estimate for the local tendency
at to.
In this study, the horizontal temperature advection is
determined through the thermal wind relationship. This
allows the advection computation to be made solely from
the wind data for a single station and thus avoids the
problem of obtaining a geostrophic wind determination
from the large-scale pressure pattern. Under the assump-
tion that the acceleration and frictional force are constant
with height, the vertical shear of the horizontal wind i s
%= -%(k xv,T) . aP f P
A rearrangement and scalar multiplication by V h yields
the horizontal temperature advection
The accuracy of the temperature advection computed
with equation (8) depends upon the method used to eval-
uate u, v, aulap, and avjap. Since the u- and v-components
contain random errors plus small-scale wind variations,
serious errors in the estimation of these quantities result if a
method is not used to reduce the influence of random errors
and small-scale variations, both of which are essentially
noise superimposed upon the synoptic-scale variations.
One way of reducing the effect of noise is t o use least
squares approximating polynomials for filtering. Approx-
imating polynomials (Hildebrand, 1956) can be used when-
ever the basic observations are discrete measurements of
a smooth true function. The advantage of using least
squares approximating polynomials is that an exact fit to
the basic data is avoided. An exact fit requires the esti-
mated function to pass through each data point, thus
oscillating abaut the true function. On the other hand,
approximating polynomials supply a better estimate of
the smooth true function by suppressing the effects of
random errors and small scale wind variations.
In a portion of this study the u- and v-component pro-
files are filtered by fitting a second-degree polynomial to
five adjacent observations that are vertically spaced at
50-mb intervals. Pressure is used as the independent vari-
able for filtering. The resulting polynomials, of the form
&=u(p) and 6=v(p), are then differentiated, and a set of
filtered estimates &lap and d$/dp are obtained at the
midpoint of five observations. The next set of filtered
estimates is made bv adding a new observation adiacent
to the upper pressure level and deleting the observation
at the lower pressure level and then predicting the new
mid-observation. After obtaining values of 6, $, &/dp, and
&lap from 850 mb to 200 mb at 50-mb increments, filtered
estimates of the horizontal temperature advection are
computed.
Figure 1, which presents profiles of the raw and filtered
values of the u-component a t Washington, D.C., at 00 GMT
onDec. 22, 1960, clearly illustrates the filtering effect
of the least squares approximating polynomials. In figure
2 the estimates of duldp computed by a finite-difference
approximation given by
for two different pressure intervals (Ap=lOO mb and 200
mb) and those obtained by differentiating the second-
degree approximating polynomial estimate of the u-com-
ponent profile are compared. All finite differences were
computed using the basic observations. The 100-mb
finite-difference estimates include a random oscillation
that does not accurately characterize the behavior of the
large-scale wind profile. Both the 200-mb finite difference
and the polynomial technique provide smoother and bet-
ter behaved estimates at each level, with the polynomial
0 -
-
100
-
200
-
300 --
-
400 --
-
500 --

600 --
-
700 --
-
800 --
900
t
- FILTERED DATA
f + f RAW DATA
+
t
+
0 IO 20 30 40
u (meters/sec)
FIGURE 1.-Comparison of raw and filtered values of the eastward
comuonent of the windat Washington. D.C.. Dec. 22. 1960. OOGMT.
374 MONTHLY Vol. 97, No. 5
200 I I
400
6
II 5 0 0 1
v E
+ x+
0
LL
- P O L I N O l l l l L
800
I
+ + + 200.nD FINITE DlFFERENCE
0 0 D 100-mb F I N I T E D l F F E R E N C E
-12 -IO -8 -6 -4 -2 0 2 4 6 8
JP ?!i m s e d mb")
FIGURE 2.-Comparison of filtered and finite-difference estimates of
wind shear for the profile in figure 1.
giving the somewhat smoother profile. These two estimates
agree closely due to similar weighting in the computations.
The smoother appearanceof the polynomial estimate can prob-
ably be attributed to the fact that the random error vari-
ance of the polynomial estimate is 80 percent of the random
error variance of the finite difference. This can be verified
from an error analysis of the two methods. Furthermore,
by Gauss's theorem, differentiated polynomial estimates
are minimum variance estimates if polynomial estimates
are unbiased (Johnson, 1965).
Estimates of aulap and &lap were also made with a
finite-difference approximation with Ap=300 mb and also
with a polynomial fit to seven data points, but in some
cases this procedure tended to remove sigdicant features
of the wind profile. For this reason, the polynomial fit to
five adjacent observations to determine 2, ^v, a&//ap, and
&/dp was selected for computing horizontal temperature
advection. The nonfiltered advection estimates, which are
presented for comparison, were determined from observed
wind component values and a 200-mb finite evaluation.
The stability measure was also computed by differentiat-
ing the second-degree polynomial fit of potential tempera-
ture with respect. to pressure and, for comparison, by a
200-mbGnite-difference approximation. Values obtained
by these methods agree very well with few exceptions.
In this sample the improvement due to filtering the sta-
bility measure was not as striking as anticipated because
the static stability of the data for the middle-latitude
winter troposphere is large. In tropical regions and summer
conditions where the tropospheric lapse rate approaches
'the dry adiabatic, filtered estimates of stability would
provide a significant improvement. lncluded in figures 3,
4, 5, and 6 , which are discussed in section 4, are filtered
profiles of the stability measure. Because of the abrupt
change in the temperature and potential temperature
Stability measure "C/mb)
0 IO 20 30 40
200
300
400
- n E 500
$ 600
0- 2 700
v
#
#
000
10 -8 -6 -4 -2 0 2 4 6 8 IO
W mb/sec)
FIGURE 3."Clear sky profiles of adiabatic and infrared components
of vertical motion at Washington, D.C., on Dec. 20, 1960, 00
QMT.
profiles at the tropopause level, the stability measure
estimates should not be computed in the same way they
are at levels above and below the tropopause. If the
conventional fivepoint filtering or finite-difference tech-
nique with Ap=200 mb is used to evaluate stability at or
within 100 mb above or below the tropopause, the sudden
change in stability that actually occurs is partially re-
moved by smoothing. For this reason, values of static
stability determined from the highest complete 200-mb
interval in the upper troposphere should be used for those
levels below the tropopause that otherwise could not be
computed without using lower stratospheric data. A
similar procedure for determining stratospheric static
stability should be applied in the region just above the
tropopause. Since we have not incorporated this procedure
in our present study, care mus't be exercised in the com-
parison of magnitudes of the two biased estimates in the
vicinity of the tropopause.
INFRARED COMPONENT OF THEVERTICALVELOCITIES
The infrared cooling contribution to the field of vertical
motion was evaluated by applying equation (6) to data
obtained from radiometersonde flights made a t 00 GMT
a t Washington, D.C., Montgomery, Ala., Green Bay,
Wis., International Falls, Minn., and Amarillo, Tex.,
during the periods of Dec. 20-28,1960, and Jan. 7-18,
1961. Diabatic vertical velocity profiles were obtained by
differentiating the approximating polynomial description
of the profiles of net irradiance and potential temperature
in a manner similar to that used to obtain the filtered
wind estimate. However, for infrared component profiles
the independent variable for filtering is time rather than
Muy I 969 Ben R. Bullock, Lyle H. Horn, and Donald R. Johnson 375
S t a b i l i t y m e a s u r e "C/mb) Stability measure (IO-* "C/mb)
200
300
4 00
a 5 700
800
0 IO 20 30 40
h
n
v E
cn
a ?
-10 -8 -6 -4 -2 0 2 4 6 8 IO
W (io" mb/secl
FIGURE 4.-Clear sky profiles of adiabatic and infrared components
of vertical motion at Washington, D.C., on Dee. 26, 1960, 00
GYT.
pressure. This technique of polynomial filtering of radio-
metersonde data has been presented by Kuhn and
Johnson (1966).
4. DISCUSSION OF RESULTS
In this study the effect of neglecting infrared cooling
when computing adiabatic vertical motions is considered
by 1) comparing individual profiles of the adiabatic
component obtained from filtered data with the infrared
component for clear and cloudy regimes, 2) employing a
synoptic case study of the time variation of the adiabatic
and infrared profiles, and 3) comparing mean profiles of
the infrared with the adiabatic component obtained from
a relatively large sample of unfiltered data, also for clear
and cloudy conditions.
Before comparing the adiabatic and diabatic com-
ponents, the effect of finite-difference and filtering tech-
niques in estimating the adiabatic vertical velocities in a
clear atmosphere are presented in figure 3. Profiles of
adiabatic vertical velocity obtained by use of filtered
estimates of the horizontal temperature advection and
stability are shown by the continuous lines. The effect of
the pressure interval used in finite-difference evaluations
of the temperature advection and stability measure for
estimates of the adiabatic vertical velocities is shown for
twocases, Ap=lOO mb and Ap=200 mb. 'The 100-mb-
interval estimates portray a profile of adiabatic vertical
motion that is not characteristic of large-scale atmospheric
motions. The extreme oscillations very likely reflect the
presence of small-scale variations and random errors in
wind and temperature data. If a 50-mb interval is used,
338-8W 0 4 9 -3
0 10 20 30 40
LVV
300
400
500
600
700
800
-5 -4 -3 -2 -I 0 I 2 3 4 5
W mb/sec)
FIGURE 5.-Cloudy sky profiles of adiabatic and infrared compo-
nents of vertical motion at Green Bay, Wis., on Jan. 17, 1961, 00
GMT. Cloud cover was reported as 0.8 cirrostratus.
we would expect the resulting profiles to exhibit an even
more pronounced oscillatory behavior.
Comparison of the 200-mb, nodltered and filtered esti-
mates reveals good agreement; however, in this example,
the filtered profile is somewhat smoother than the non-
filtered one, and the region of maximum adiabatic vertical
motion is displaced upwards by about 50 mb.
INDIVIDUAL CLEAR ANDCLOUDY SKY PROFILESOF ADIA-
BATIC AND INFRARED COMPONENTS OF VERTICAL MOTION
In addition to adiabatic profiles of vertical motion,
figure 3 also presents the infrared component profile for
this clear sky case. In this instance, the 200-mb filtered
and nonfiltered estimates of the adiabatic vertical veloci-
ties agree well with our concept of vertical motion in a
clear atmosphere, with positive values of uA throughout
most of the troposphere. Likewise, the infrared component,
though small, is predominantly positive.
Unfortunately, not all vertical motion profiles from clear
sky cases are as consistent as that presented in figure 3.
For example, figure 4 sliows a reasonable infrared com-
ponent profile, but an adiabatic profile that displays
negative values of wA through a portion of the middle
troposphere. The fact that no cloud cover was observed
in this case could be attributed to a number of reasons.
Cloud formation is not instantaneous but requires some
finite time depending upon the initial degree of saturation.
In support of this reasoning is the observation by Hansen
and Thompson (1965) of a time lag between the initiation
of upward vertical motion determined kinematically and
cloud formation as observed by TIROS photographs. In
some situations, but not necessarily this particular clear
376 MONTHLYWEATHERREVIEW Vol. 97, No. 5 ,
Stability measure "C/mb)
0 IO 20 30 40
200
300
400
h
a
v E 500
600
a ?? 700
v)
v)
800
3
JANUARY I1 12 12 13 13 14 14 15 15 16
5 -
"
4
--
TIME(GMTH2 00 12 00 12 00 12 00 ' 12 00
.""_____ ,WrnD 500mb
FIGURE 7.-Time cross-section of the adiabatic component of verti-
cal motion a t four selected levels a t Washington, D.C., for the
1 period of Jan. 11-16, 1961.
900 I I I I
-5 -4 -3 -2 -I 0 I 2 3 4 5
W .. mb/sec)
FIGURE 6.-Cloudy sky profiles of adiabatic and infrared compo-
nents of vertical motion at Montgomery, Ala., on Jan. 12, 1961, 00
GMT. Cloud cover was a cirrostratus overcast.
case, the neglect of other diabatic effects leads to erroneous
estimates of vertical.motion. Finally, the possibility exists
that errors were present in the data.
The infrared component was largest, as expected, in the
presence of clouds..-Figure 5 shows the profiles for Green
Bay, Wis., on an evening with 0.8 cirrostratus overcast.
In this case, the adiabatic vertical velocity maximum 'near
350 mb corresponds closely to the cloud level while the
maximum infrared component occurred in- the vicinity of
the cloud top. The cloud top coincides very closely with
the tropopause and the sudden decrease in adiabatic
vertical velocities in the region above.
A secondexample of vertical velocity profiles for a
cirrostratus overcast condition is presented in figure 6. In
this case, the adiabatic contribution to the total vertical
motion is positive almost everywhere below 'the cloud,
which appears inconsistent with the maintenance of a
cloud.
CASESTUDY
To illustrate temporal variations that occurred in the
components of vertical motion with changes in the synoptic
weather pattern, the 4-day period of Jan. 12-15,. 1961, at
Washington, D.C., is considered. During the first 2 days,
skies at Washington were clear as high pressure dominated
the eastern United States. However, on January 13, a
low-pressure area that had formed off the Texas Gulf Coast
was just south of New Orleans and moving northeast at
about 15 kt. There was a cold-core Lorn aloft to 300 mb
over central Texas to the west of the surface depression.
By 06 GMT on January 14, the low-pressure center was
located just west of Tallahassee, Fla., with a cold front
along the western Florida coast and a warm front through
southern Georgia into the Atlantic. At 00 GMT on January
14 there was scattered cirrus, and at 06 GMT scattered
stratocumulus was present over Washington. On January
15 there was a nimbostratus overcast with continuous
rain as the low-pressure center moved southeast of Wash-
ington on a northeasterly course.
Figure 7 shows the time variation of the adiabatic
vertical velocities at four selected pressure levels. During
the first 2 days of. the period, the adiabatic method in-
dicated general subsidence at all levels except 500 mb.
The large negative value of wA on January 12 probably
results from an observational error. By 12 GMT on Janu-
ary 14 the adiabatic velocities indicated generally upward
motion, and by the end of the fourth day the strength of
the upward motion was decreasing at most levels.
Figure 8 presents the infrared component profiles at 00
GMT for each day of the period. The first 2 days show
profiles typical of clear skies, while. the third day shows
some effect of cirrus with bases located a t about 250 mb.
Examination of the profile for January 15 shows a more
pronounced effect with the top of the highest cloud layer
at about 300 mb. Apparently the effective emissivity of
the cirrus layer on January 15 was much greater than on
January 14. The lack of variation in the profile below 550
mb indicates nearly radiational equilibrium below this
level.
Adiabatic vertical-velocity estimates in this case study
showed generally good agreement with our concept of the
vertical motionfield for the synoptic pattern, a result
that was not true in all cases. Also, the diabatic com-
ponent correspondedwell with cloud conditions and
demonstrated its importance in the cloudy regions.
MEAN CLEAR AND CLOUDY PROFILES
Although filtered profiles of adiabatic velocities were
used for comparison with the infrared components in
individual cases, it was not possible, because of the limited
number of cases, to obtain mean profiles that were
significant. The limited number of filtered adiabatic
May 1969 Ben R. Bullock, Lyle H. Horn, and Donald R. Johnson 377
200
300
400
500
600
700
800
900
-2 -I . 0 I 2 3
W rnblsec)
JMUARY 12, 1961
JANUARY 14, 1961
\
200
300
400
500
600
700
800
900
JANUARY 13, 196 I
> ., I
I
-2 - -I 0 I 2 3
W (IO mb/sec)
2oo

JANUARY 15. 1961
t
-2 -I 0 I 2 3 -2 -I 0 I 2 3
W mb/sec) W mb/sec)
FIGURE &-Vertical profiles of the infrared component of vertical motion at 00 GMT for 4 days of the case study.
378
200
MONTHLYWEATHERREVIEW VOl. 97, No. 5
0
100
200
h
n
- 300 E
300'
400
500
600
700
800
900
2 400
L
v)
Q 500 E
600
700
-1.5 -1.0 -0.5 0 0.5 1.0 1.5 -1.5 -1.0 -0.5 0 0.5 1.0 1.5
W mb/sec) W (IO" mb/sec)
FIGURE 9.-Mean profiles of the adiabatic and infrared components FIGURE 10.-Mean profiles of the adiabatic and infrared components of vertical motion forclear sky conditions, compiled from 21 of vertical motion for cloudy sky conditions. Profiles arecon-
cases. structed with respect to the mean cloud position of the 10 cases
used.
profiles resulted from the fact that data at 50-mb incre-
ments, which were necessary for application of the filter-
ing technique, were available for only some cases.
Consequently, mean profiles of infrared and unfiltered
adiabatic velocities were prepared from a relatively
large sample of data obtained at standard levels.
Mean profiles of adiabatic vertical velocities and the
corresponding infrared components were obtained from
31 individual profiles computed from observations taken
during the data period described in the Introduction. As
in the case of filtered profiles, equations (4) and (7) were
used to compute the adiabatic and the infrared compo-
nents, respectively. The infrared data used to estimate
mean profiles were computed in the same way as in the
individual profiles. However, the unfiltered adiabatic
component used to obtain mean profiles differed from the
individual filtered profiles in that the time for which they
are valid differs by 6 hr from the time for which the
infrared profileswere calculated. This time difference
resulted from the fact that the local temperature tend-
ency was computed from observations taken 12 hr
rather than 24 hr apart.
Separate mean profileswere prepared for clear and
cloudy situations. To be classified as cloudy, at least 0.8
coverage of middle or high clouds was required; and to
be classified as clear, less than 0.1 cloud coverage was
necessary. Figure 9 presents mean profiles of adiabatic
and infrared components computed using 21 clear cases.
Both profiles correspond with the concept of subsidence
in the presence of clear skies. The mean adiabatic profile
shows positive values of uA throughout, averaging about
0.4X10-3 mb sec", with a maximum of 0.75X mb
sec-l at 500 mb. The infrared component averages about
0.25X10-3 mb sec". The small mean for the adiabatic
component indicates considerable heterogeneity in indi-
vidual profiles for clear conditions. In contrast, the
relatively large magnitude of the mean for the infrared
component indicates less heterogeneity for this class.
The slight negative value at 200 mb is associated with
convergence of infrared irradiance in the region of the
tropopause.
Figure 10 presents mean profiles obtained from 10
cloudy cases. In preparing this figure, a technique used
by Kuhn (1966) was employed to determine the pressures
at the base and top of the cloud layer for the individual
profiles of net irradiance. Once these pressures were
established for each case, infrared components were com-
puted at 50-mb intervals to a maximum of 200 mb above
the cloud top and 200 mb below the cloud base. These
values were then averaged to obtain the mean profile.
The adiabatic contribution at these levels was obtained
by interpolating between the values that had been
computed at standard levels for the individual cases and
then averaging those values. The dotted line within the
cloud connecting the infrared components a t t h e base
and top should not be considered as representing the
infrared component within the cloud, since most of the
cloud interior is in radiation equilibrium.
It should be noted that the relatively large negative
value of uz at the mean cloud base and large positive
value at the top are mainly due to a net absorption of
infrared radiation at the base and emission at the top and
are not representative of large-scale vertical motion.
However, these radiation processes are important in
enhancing small-scale turbulent motion in clouds. The
May 1969 Ben R. Bullock, Lyle H. Horn, and Donald R. Johnson 379
heating at the base and cooling at the top decreases the
static stability within the cloud and consequently may
lead to turbulent mixing and an increased upward heat
transfer. Moller (1951) estimated that, in a cloud 0.5 km
thick at an elevation of 2 k m , only 45 min would be
required to increase the lapse rate from isothermal to
0.5C/100 m, while in a cloud of the same thickness at an
elevation of 5 km only 20 min would be needed to produce
the same change. Moller assumed that no convective
transfer of heat occurred during the destabilization
process.
Although infrared processes are important in clouds, the
contribution of latent heat "t o vertical motions can be
more significant. Immediately beneath a precipitating
cloud layer the evaporating droplets cause cooling,
which may offset any infrared warming (and negative
values of wl), but at lower levels the evaporation may
reinforce any small positive values of or. In the cloud,
latent heat release due to condensation gives a negative
contribution to the total vertical motion. At the cloud
top there can be both condensation and evaporation of
moisture. The condensation is the result of ascending
motion, while evaporation results because of turbulent
mixing and subsequent entrainment of drier air from
above. Whether heating or cooling is occurring at the
cloud top depends upon which process is predominant.
Although the diabatic component of vertical motion in
the vicinity of cloud top and base must be neglected when
considering the large-scale vertical motion field, an.
examination of figures 9 and 10 shows an important
difference in the diabatic profiles that are representative of
large-scale atmospheric processes. Infrared cooling beneath
an extensive cloud layer is typically less than in clear
conditions. For example, the average value of the infrared
component of vertical motion in the mean cloudy profile
(fig. 10) between 450 and 600 mb is very close to zero,
while the average value of this component in the mean
clear profile(fig. 9) in the same pressure interval is
approximately 0.4 X mb/sec.
5. CONSEQUENCE IN ENERGYCONVERSION
ESTIMATES
Although the primary purpose of our study is to compare
the infrared with the adiabatic component of vertical
motion, it is also important to consider the significance of
these results in atmospheric energy studies. In this study
the contribution of infrared cooling to the total vertical
motion fieldwas usually positive, but much more so in
clear areas than in regions with middle or high clouds.
Since growing and organized weather disturbances are
now recognized as major sites of conversion of potential
to kinetic energy in middle latitudes (Starr, 1958), it is
important to consider the magnitude of the bias error
resulting from the use of adiabatic velocities (Wiin-
Nielsen, 1964) in estimating the production of kinetic
energy by the wcv integral. In troughs associated with
growing and organized disturbances, cloudy areas tend
to be associated with the warmer air to the east and clear
areas with the colder air in and below the midtropospheric
trough. Since the infrared component of vertical motion
tends to be in phase with the adiabatic component, the
actual conversion will tend to be underestimated if the
infrared component is neglected. Our results can be used
to estimate that portion of the bias error due to the
neglect of diabatic processes.
The general expression for the conversion of eddy
available potential energy to eddy kinetic energy is
C(P,K) = - f w'a 'dm (9)
where m is the mass, the primes denote deviations from a
latitudinal mean on a pressure surface, and the integra-
tion extends over the entire atmosphere. The true but
unknown eddy conversion, indicated by asterisks, is
C*(P,K) = -Jw'*a'*dm. (10)
Since the total vertical motion field is given by the sum
of adiabatic and diabatic portions, equation (10) may be
written as
c*(p,K)=-f (w'*A+g'*D)(Y'*dWL. (1 1)
If we assume that estimates of specific volume and
adiabatic vertical velocity are unbiased and their random
observational errors uncorrelated, the expected value of
conversion estimates using the adiabatic assumption is
E[C(P,K)]=-fw'*Aa'*dm=C*(P,K)-6 (12)
where
6=- f o'*,a'*dm. (13)
Equations (12) and (13) show that the bias error 6 is
given by the covariance of the diabatic component and
the specific volume. The diabatic component of the
vertical velocity is
OD=(J"S+wI+(JL+(JC+wF (14)
where the subscripts denote the following diabatic
components :
S= direc t solar absorption,
I=emission of infrared energy,
L=release of latent heat,
C=sensible heat addition by conduction a t the earth's
F=internal heat addition due to frictional dissipation
I n the developing and organized stages of the weather-
producing disturbance, the diabatic components of the
release of latent heat, infrared cooling, and solar absorp-
tion are in phase with the adiabatic vertical motion and
the specific volume fields. The component of sensible heat
addition at the earth's surface is opposite in phase to the
field of vertical motion, since the coldest air at the sur-
interface,
of kinetic energy.
380 MONTHLY Vol. 97, No. 5
face will be heated-more than the warm air. The frictional
component is unimportant, for there should be little
covariance between specific volume or w and the frictional
dissipation of the horizontal kinetic energy. Thus, the
systematic bias error due to the neglect of the four
heating components is
where the first three terms of the integral tend to be
positive, causing the adiabatic conversion estimates to
be low while the last term tends to be negative, causing
the adiabatic conversion estiniates t o be high.
Our results, although tentative, allow a quantitative
estimate for the infrared component. The results shown
in figures 9 and 10 indicate that the infrared diabatic
component may be expressed as
where the value of bI lies at least between 0.1 and 0.2 and
is possibly greater. For regions of the quasi-geostrophic
planetary waves (i.e., those without embedded, smaller
organized disturbances) for which the adiabatic assump-
tion is valid or for unorganized scales in which there is
probably no systematic relation between the diabatic
component of vertical motion and the adiabatic vertical
velocities, bI may be set to zero without inducing estima-
tion errors in the conversion integral. Under these approx-
imations the infrared bias error component in adiabatic
vertical velocities is
where the subscript one denotes values from atmospheric
regions possessing organized disturbances, and the sub-
script two denotes values associated with quasi-geostrophic
scales and unorganized circulations. If one assumes that
50 percent of the estimated conversion by the adiabatic
method occurs in organized disturbances of smaller
synoptic scales and 50 percent in the larger planetary
scale without an organized heating field in which bI, is
zero, the bias infrared error component related to the
expected value of adiabatic estimates is
0.1 S b I , 50.2. (18);
Thus, estimates of the conversion of potential energy are
underestimated, and the actual adiabatic estimates should
be adjusted upward by 5 to 10 percent to remove the in-
s frared component bias and to achieve better estimates
of the true conversion.
Undoubtedly there is a similar significant and more
striking bias error due to the neglect of the effects of
latent heat in the precipitating regions of the organized
disturbance. The results obtained by Danard (1964) for
wA and wL indicate that a possible range for b5 is from 1.0
to 1.5. Thus, it is possible that actual adiabatic estimates
should be adjusted upward by 50 to 75 percent t o remove
bias from the neglect of latent heat release.
With respect to the bias conversion error introduced by
the neglect of effects of sensible heat addition a t the earths
interface, the systematic bias error, 6,, should be negative.
Sensible heat addition at the earths interface will always
be larger in the colder air than in the warmer air. This is
particularly true in the winter when cold continental air
flows off the eastern portions of both the Asian and North
American Continents. The effect of neglecting the com-
ponent of the vertical motion associated with sensible heat-
ing and use of the adiabatic vertical component is to over-
estimate the magnitude of the downward vertical motion.
In the boundary layer, the magnitude of the true vertical
motion should be small; and in the presence of strong
sensible heating of the cold air, the adiabatic component,
which is a large positive value, may be nearly balanced by
a large negative diabatic component. Thus the sign of bo,
corresponding to the definition of bI, is probably negative,
and 6c is also negative. Although we are unable to estimate
the magnitude of this bias error, we speculate that it is
opposite in sign and larger in magnitude than the infrared
bias error but less than the latent heat bias error. When
adiabatic vertical velocities and the w integral are used
to estimate energy conversions, wewouldemphasize
Jensens (1961) statement . . . that the occurrence. of
very intense energy transformations within the boundary
region is questionable in view of certain nongeostrophic
and nonadiabatic effects.
Wiin-Nielsen (1964), using Jensens (1961) calculations
of the adiabatic conversion of available potential energy
to kinetic energy for individual layers, estimated that for
the Northern Hemisphere the conversion due to adiabatic
motions amounted to 4.24 watts m-2 during January 1958
and 2.71 watts m-2 during April 1958. Our crude estimates
of the vertical motion bias errors produced by diabatic
effects indicate that these energy conversion estimates
should be increased. With an increase, they would compare
more favorably with Eungs (1966) earlier estimate of
6.4 .watts m-2 and his later estimate (1967) of 4.12 watts
m-2 for frictional dissipation and Dutton and Johnsons
(1967) summary of the transformation rates involved in
the atmospheric energy cycle. Admittedly, our comments
concerning the bias errors due to neglect of diabatic
processes are quite speculative; however, our results for
infrared processes, Danards for latent heating, and the
questionable effects of sensible heating indicate that addi-
tional investigations of the energy conversion processes
should be undertaken. It is quite possible that the use of
adiabatic vertical motions in estimating the energy con-
versions on a hemispheric scale produce estimates which
may be significantly low.
May 1969
6. CONCLUSIONS
Although the adiabatic method iswidelyused to
estimate large-scale vertical motion and is probably as
effective as any of the other commonly used methods, the
results of this study indicate that its limitations are con-
siderable. If data from small intervals of pressure are used
(e.g., 50 mb) t o obtain profiles of adiabatic vertical veloci-
ties, it appears that some type of filtering technique such
as that used here should be employed to reduce the random
errors. In general, considerable variations exist between
individual adiabatic profiles,evenwhen the data are fil-
tered and classified according to the amount of cloudiness.
Although in individual cases the infrared contribution
to total vertical motion tends to be quite small, the
contribution is quite consistent from one case to another.
Thus when mean profiles of adiabatic and infrared
velocities are prepared, the contribution of infrared
processes appears quite significant, perhaps amounting to
30 percent of the adiabatic contribution. In regions of
clear skies the mean infrared contribution to the down-
ward motion is about 60 to 70 percent of the adiabatic
component. In cloudy regions the infrared contribution
is practically zero below the cloud, while above the clouds
it is just slightly positive. In the presence of a cloud layer
the infrared radiation process undoubtedly plays an
import.ant role by reducing the hydrostatic stability within
the cloud layer and thus increasing the vertical transfer of
heat.
The diabatic processes also reduce the reliability of
adiabatic estimates of conversion of available potential
energy to kinetic energy within the cyclone scale. Since,
within this scale, the diabatic components of infrared
radiation, the absorption of solar energy, and release of
latent heat are in phase while the component of sensible
heat addition is out of phase with the adiabatic component
of vertical motion, the net effect of these diabatic processes
should be considered. It appears that in a disturbance the
diabatic contribution to the vertical motion field may be
sufficient to result in a substantially larger energy con-
version than that obtained in studies based only on
adiabatic motions.
ACKNOWLEDGMENT
This research has been supported by the National Environ-
mental Satellite Center of the Environmental Science Services
Administration under grant WBG 52.
Ben R. Bullock, Lyle H. Horn, and Donald R. Johnson
[Received December 7, 1967; rewised September 23, 19681
381
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