JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL. 85, NO. AI3, PAGES 8219-8222, DECEMBER
30, 1980
Venus Lower AtmosphereHeat Balance
ANDREW
P. INGERSOLL
AND JUDITH
B. PECHMANN
Divisionof Geologicaland Planetary Sciences,California Institute of Technology,Pasadena,California 91125
PioneerVenusobservations
of temperaturesand radiativefluxesare examinedin an attemptto understandthe thermalbalanceof the lower atmosphere.If all observationsare correctand the probesitesare
typicalof the planet,the secondlaw of thermodynamics
requiresthat the bulk of the lower atmosphere
heatingmust comefrom a sourceother than direct sunlightor a thermally driven atmosphericcirculation. Neither the so-calledgreenhouse
modelsnor the mechanicalheatingmodelsare consistentwith this
interpretationof the observations.
One possibleinterpretationis that two out of the threeprobe sitesare
atypicalof the planet.Additionalloweratmosphere
heatsources
provideanotherpossibleinterpretation.
Theseincludea planetaryheat flux that is 250 timesthe earth's,a secularcoolingof the atmosphere,and
a chemicallyenergeticrain carryingsolar energyfrom the cloudsto the surface.Other data make these
interpretationsseemunlikely, so measurementerror remainsa seriouspossibility.
1.
INTRODUCTION
solid planet, and space.T is the temperatureof the masselement;
the temperatureof the sourceis irrelevantto this arguUnderstandingthe thermal balanceof Venus, particularly
the high surfacetemperatures,is one of the major objectives ment. For example, when sunlight is absorbed,the relevant
of the PioneerVenus mission[Schubertet al., 1977,this issue; temperatureis that at which a changeof atmosphericinternal
Tomaskoet al., 1977,this issue(a)]. Measurementsof temper- energy occurs.
If the atmosphereand solid planet are in a statistically
aturesand pressure[Sieff et al., 1979,this issue;Taylor, et al.,
1979,this issue],net solar flux [Tomaskoet al., 1979,this issue steady state, there can be no net work done and no net heat
(b)], and net infrared flux [Boeseet al., 1979,this issue;$uomi transferto the environment.(We are, for the present,neglectet al., 1979] were expected to satisfy this basic objective. ing tidal work and internal heatingin comparisonto absorbed
It is shown below that barring measurement error and as- sunlight.)Thus for a suitablylong time average,
sumingthe probe sitesare typical of the planet, the measuref Q dm = 0
(2)
mentscannotsatisfythe secondlaw of thermodynamicsunless
additional heat sourcesare present.
Equations(1) and (2) imply that the heat inputsto the atmoBefore Pioneer Venus the so-called greenhouse effect
sphere(Q > 0) must be at a highertemperature,on average,
seemedto be the processmost likely responsiblefor the high
than the heat outputs (Q < 0).
surfacetemperatures[Sagan, 1960]. Downward transport of
In adapting the above expressions
to PioneerVenus data it
mechanicalenergyhad alsobeen proposed[Goodyand Robinis convenientto divide by the area of the planet and use an
son, 1966; Schubertet al., 1977]. Since the ultimate energy
overbar to denote the areal average.We use pressureas a versource in both models is thermal, the sourcesmust be consistical coordinateand treat the surfacepressurePo as constant.
tent with the secondlaw. To satisfythis constraint,the atmo- Thus we define
spheremust emit infrared radiation at a lower averagetem-
peraturethan that at whichsunlightis absorbed.Our analysis
of the Pioneer Venus observations which takes into account
Q dm = - -- (Fs- Fi - Fc)dP dArea
the vertical and horizontal distribution of heat sourcesimplies
that the oppositeis true.
To avoid a contradiction, one must assumeeither that some
•s-- •i
at P-- 0
(3)
(4)
of the data are in error, that the probelocationsare atypicalof
the planet, that the lower atmosphereand/or the planet are
l•c'- l?•- l•i
at P= Po
(5)
losingnet heat, or that the solarenergyabsorbedat high altitudes somehowreachesthe surfaceas a chemicallyenergetic
rain. These possibilitiesare discussedin section 3. Section 2
showshow the data are used to test for thermodynamic con- Here F• is the net solarflux (powerper unit area) downward,
Fi is the net infrared flux upward, and Fc is the heat flux consistency.
ductedupward from the surfaceto the atmosphere.The latter
2.
METHOD
is assumedto fall rapidly to zeroabovethe surface.Equations
satisfy(2). Fcmay be eliminatedby the
Considerthe entire atmosphereas a thermodynamicsystem (3)-(5) automatically
with entropy S. In a statisticallysteady state the time rate of further assumption
change• mustbezero.Thusthesecond
lawof thermodynam-
Fc--F•--Fi--O at P--Po
ics requires
f Q dm/T _<$-- O.
(1)
(6)
whichis equivalentto havingenergyat the surfaceexchanged
immediatelywith the loweratmosphere.
Use of (6) makesour
Here Q dm is the rate of heat transferto an atmosphericmass estimateof f Q dm/T morenegative,sincesunlightreaching
at its warmelement dm from sourcesoutsidethe system,e.g., the sun, the the groundis then transferredto the atmosphere
est point.
PioneerVenus observations
suggestthat the largesthori-
Copyright¸ 1980 by the American GeophysicalUnion.
Paper number 80C0795.
0148-0227/807080C-0795501.00
8219
8220
INGERSOLL AND PECHMANN:
TABLE
Z, km
la.
VENUS
LOWER ATMOSPHERE
Profiles for the Standard Model
P, bar
•', K
AT, K
91.0
65.3
47.0
32.1
21.8
14.3
9.09
5.55
3.26
1.83
50
55
60
65
70
75
80
85
90
0.984
0.484
0.213
0.0908
0.0351
0.0129
0.0044
0.0014
0.00041
BALANCE
Above 65 kin, temperatureswere taken from the orbiter data
Ps, W m-2
[Tayloret al., 1979,thisissue].Our standardT(P) and AT(P)
profilesare listed in Table l a.
0
0
5
10
15
20
25
30
35
40
45
HEAT
The net flux Ps(P)is evaluatedfrom smoothed
profilesat
the boundingsurfaces
of the layers.Differences
of P, across
eachlayerdefineournumericalestimates
of dP,.Adoptedval-
732.8
693.9
655.2
614.9
574.1
532.4
490.5
449.9
412.7
381.8
-8.6
-7.0
-10.7
-2.5
0.8
2.1
0.8
0.6
3.5
7.0
15
15
15
16
20
24
27
30
32
33
344.2
295.4
256.8
245.0
233.8
220.9
205.4
192.6
182.2
9.7
14.4
47.5
0.0
-5.6
-11.7
-14.9
-12.5
-10.1
35
44
83
114
128
137
142
144
145
ues are listed in Table la. The solar net flux 'global average'
computedby the experimentersfrom sounderdata [ Tomasko
et al., this issue(b)] coversthe altitude range 0-65 km. The en-
try P, -- 0 at thelowestaltitudedoesnotcorrespond
to a measured flux but is included
in order to account for the 15 W
m-2 that is absorbedat the ground.The solarnet flux at altitudesgreater than 65 km was taken from a model by Tomasko
et al. [thisissue(a)]. The valueof 145W m-2 at the top of the
atmospherecorrespondsto an albedoof 0.78 for Venus [Taylor et al., this issue;Irvine et al., 1968].
The thermal net fluxes and the temperaturesused to evaluate the integralsin 13 are listed in Table lb. The temperatures below 15 km are experimenters'extrapolationsand
above 65 km are taken
from
orbiter
data.
Direct
measure-
ments[Suomiet al., 1979;Boeseet al., 1979]of Fi coverthe alzontal variationsof T are associatedwith equator-to-polediftitude range 15-60 km. Since the observednet flux at the day
ferences. Thus we assume
probe includes both solar and thermal contributions,these
data have beencorrectedby subtractingan estimatedsolarnet
r--/'(P) + ar(P)(cosßx + c,)
(7)
radiation profile basedon LSFR measurements
and scattering
where •, is latitude and AT is the equator-to-poletemperature models [Tomaskoet al., this issue(a)]. Below 12.5 km for the
difference.C! is a constantdependenton k suchthat the horinorth and day probesand below 27.5 km for the night probe,
zontal integral of the secondterm above is zero. Similarly, Fs we have assumeda linear variation of Fi with altitude due to
is assumed to be
lack of data in this region. Above 60 km, we have assumed
Fs = Fs(P)GcosnO 0 '• ql'/2
(8) that over a global averagethe atmosphereis in radiative equi-
where 8 is the solarzenith angle,and C2is a constantdepen-
librium.Thuswe takeFi -- P• for eachprobe.
denton n suchthat the horizontalintegralof (8) is/•(P). In
3. RESULTS
the above, F• is assumed to be zero for 8 > •r/2. Unfortu-
nately, we may not assumethat Fi is independentof horizontal position due to the unexpectedlylarge differencesshown
by the SNFR net flux data on the three Pioneer Venus small
probes[Suomiet al., 1979].Thus we evaluatethe infrared contribution to the integral in (1) separatelyfor eachprobe.In order to provide an estimateof the globally averagedvalue we
take the mean of the three probe integrals.Equation (1) may
Table 2 givesvaluesof the integralsI!, I2, I3 appearingin
(9). Case 1 is the standardmodeltabulatedin Tables la and
lb. The sumof the integralsIi + 12+ 13is positive,a physical
impossibilityunderthe assumptions
stated.The magnitudeof
the discrepancy
0.060 W K -! m-2, is equivalentto a heat
transfer of 23 W m -2 from T-- 740 K to T-- 250 K. The mean
solar heating term I! is large and positive.The horizontally
then be written
TABLE
Profiles for the Standard
T
øaL
Z, km
-- I! + 12+ 13
(9)
where a is a constantequal to 0.0634 for n -- k -- 1 and to
0.1333 for n -- k = 2. The sumj - 1, 3 is over the three probe
sites. Unless otherwise •dicated,
lb.
we shah use n -- k -- 1 in
what follows.
Theintegrals
I! and12in (9)areevaluated
bydividing
the
atmosphereinto layersboundedby surfacesof constantpressure.The midpointsof the layersare at altitudesof 0, 5, 10, --km at the sounderprobe location. The averagetemperature
•'(P) and the equatorto pole temperature
differenceAT(P)
werecomputedwith the aid of (7) from the observedtemperatures. Below 65 km, temperaturesfrom the sounderprobe at
4.4øN and the north probe at 59.3øN were used [Seiff et al.,
1979].The probe instrumentsdid not work below 15 km, and
the experimenters'
extrapolations
wereusedat loweraltitudes.
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
Day
731.0
692.4
652.9
614.4
574.3
532.8
490.7
450.0
413.4
383.3
346.3
298.4
266.8
245.0
233.7
218.2
203.6
191.6
181.6
Night
731.0
692.4
652.9
614.4
574.3
532.8
490.7
450.1
413.4
383.3
346.3
298.4
266.8
245.0
233.7
218.1
203.4
191.4
181.4
Model
F,
North
735.2
695.8
658.1
615.6
573.9
531.8
490.3
449.8
411.7
379.9
341.6
291.4
243.7
245.0
230.0
222.5
212.1
198.3
186.3
Day
Night
o
13
22
o
11
21
North
o
17
33
27
27
32
43
50
68
24
21
23
24
28
41
41
39
83
114
128
137
142
144
53
64
68
70
60
50
64
52
83
114
128
137
142
144
80
78
82
80
85
93
90
68
83
114
128
137
142
144
145
145
145
INGERSOLL AND PECHMANN: VENUS LOWER ATMOSPHERE HEAT BALANCE
varying solar heating term 12 is very small and negative, and
the infraredcoolingterm 13is alsonegative.The physicalimpossibility arises becausethe atmospherecannot spontaneously transfer energy from low temperatures,where it is ab-
TABLE 2. IntegralsContributingto J'Qdm/T
Case
I!
I
2
3
4
5
6
7
8
9
10
11
12
13
0.512
-0.0015
0.512
0.695
0.513
0.498
0.478
-0.0018
-0.0009
-0.0019
-0.0019
-0.0007
0.452
-0.0009
sorbed,to high temperatures,where it is emitted.
In case 1 above, 13 is the mean of the infrared integrals at
the three probe locations.In cases2, 3, and 4, 13is computed
from the day, night, and north flux profilesseparately.It is apparent from Table 2 that if the day probe net flux profile were
typical of the planet, the integral J'Qdm/T would be closeto
zero. However, if the night and north probeswere typical of
the planet,the integralwould be more positivethan in case1.
The variability of the net flux profilesmakesit difficult to generalize. Nevertheless, we shall use case 1 as a standard model
to studyhow J'Qdm/T is affectedby errorsof observation,assumptionsabout the profiles at altitudes where there are no
measurements,and physicalprocesses
that might be occurring
in the Venus atmosphere.
In order to assessthe sensitivityof these resultsto the assumedparametervalueswe presentcase5 with n -- k -- 2. The
horizontalvariation term 12is still very small, and the value of
$Q dm/T is still positive.In case6 the net flux at the top of the
atmosphere
hasbeenchangedto 184W m-2, corresponding
to
an albedo of 0.71 for Venus. This changewas achievedby increasingthe values of Fs and Fi above 65 km by 7, 14, 21, 28,
35, 39 W m-2 at successively
higherlevels.BothI, and
in-
creasesubstantially,but the total integral $Q dm/T staysthe
same.
Case 7 investigatesthe importance of horizontal temperature gradients.It seemssurprisingthat the poles should be
warmer than the equator at severallevelsin the atmosphere.
However, negative AT in the lower atmospherewere discovered before PioneerVenus by microwaveinterferometry[Sinclair et al.,. 1972; Pechmannet al., 1979], and the measurements agree with the interpretation of probe data given in
Table la. Negative AT in the upper atmospherewere discov-
8221
12
13
-0.451
-0.504
-0.449
-0.399
-0.633
-0.451
-0.439
-0.459
-0.514
-0.514
$Q dm/T
0.060
0.007
0.062
0.112
0.059
0.061
0.060
0.045
0.038
0.052
-0.003
-0.003
0.001
A blank entry indicatesthe case I value is appropriate.
heat source.We thereforechangethe three F• below 10 km to
18 W m-2 and add 18 W m-2 to the F• above70 km. The value
of $Q dm/T is nowslightlynegative.An imbalanceat the top
of the atmosphere
of 18W m-2 is almostruledout by orbiter
data [Taylor et al., this issue],however, and is 250 times the
earth'sinternal heat flux. In case 12 the atmosphereis assumedto be undergoinga secularcooling.To modelthis cool-
ing,13W m-2 is addedto theF•above70km.Thisvaluegives
I, + 12 + 13 close to zero. A net heat loss of 13 W m -2 would
cool the atmosphereby about 0.5 K yr-', and could arisebecause of fluctuationsin infrared opacity on decadal time
scales.Small changesof thismagnitudeprobablywouldhave
escapeddetectionduringthe periodof modemtelescopicobservations
of Venus.
Finally, in case 13 we assumeeither that the solar flux data
are too low or that solar energyreachesthe surfaceas chem-
ically energeticrain. This hypothesisis evaluatedby adding
23W m-2 to all •'• between
0 and60kmandadding10W m-2
to •'• at 62.5km.Thevalueof $Q dm/T isnowslightlynegative.
eredby PioneerVenusinfraredradiometry.To assess
the effect on the entropyintegrals,all negativeAT were setto zero
The chemicalrain hypothesis
was suggested
by Y. L. Yung
(personalcommunication,1979).At high altitudesthe chemisin case7. The value of I: decreasesslightly, but the integral try of the atmosphereis driven by absorptionof sunlight,
J'Q dm/T is still positive.
whereasin the lower atmosphere(below 20 km) thermodyIn case8 wehavereplacedall thePsabove65 km by 145W namic equilibriumchemistryshouldprevail, driving the sysm-2. This possibilityexistsowingto lack of probedata above tem towardsa stateof lower free energy.Hence exchangeof
that altitude.The changeraisesthe temperatureat which sun- air betweenthe upper and lower atmosphereresultsin a net
light is absorbed,but not nearly enough to make $Q dm/T
depositionof heat in the lower atmosphere.The downward
negative.It is difficultto lower the temperatureat which in- heat flux F is approximatelyq fAHM/•, whereq is the quanfrared radiation is emitted in the stratosphereand still have a tum yield,f is the massfractionof the absorbingconstituent,
net flux of 145W m-2, corresponding
to an effectivetemper- AH is the heat of formation,M is the massper unit area of the
ature of 225 K.
atmosphericcolumn,and • is the verticalmixingtime. Forf-In case 9 we increasethe solar net flux by the maximum
10-4, q -- 1,AH = 2 x 106J kg-', F-'- 23 W m-2, therequired
amount possibledue to systematicerrors[ Tomaskoet al., this
mixingtime is 100 days.Difficultieswith this hypothesisare
issue(b)].This increases
the solarflux by 2 W m-2 at the sur- that the atmospheremight not mix on this rapid time scale
face and by 25 W m-2 at 60-km altitude,with intermediate owing to the stablestratificationand that the quantumyield
values of the increase between these altitudes. There is no inmightbe smallowingto rapid recombination
in the upperat-
creaseabove 60 km. The value of I, decreasessignificantly.
Since,for consistency,
we mustcorrectthe day probe data by
usingthe higher solar flux profile, the contributionof the day
probe to 13decreases.
The contributionof the night and north
probesremainsthe same.The integralofQ dm/T is reducedby
one third, but it is still positive.
In case10 we have raisedthe altitudeof deepinfrared emission by replacingall Fi below 15-km altitude by 0 W m-2.
Again the effect is insignificant.
In case 11 we assume that Venus has a 18 W m -2 internal
mosphere.
Despite these difficulties,sulfur chemistry[Prinn, 1979;
Young,1979]providessomeinterestingpossibilities.The reactions [Rau et al., 1973]
H2S + 4H:O --• H2SO4 + 4H:
88"• 284"• 4S2
AH -- 2.3 X 106 J kg-'
AH -- 1.6 X 106J kg-'
are driven to the right by absorptionof sunlight.Recombination may be delayedif the photodissociation
productsprecipi-
8222
INGERSOLL AND PECHMANN:
VENUS
tate out as soon as they are formed. The vapor pressuresof S2
and S4are in fact lower than that of S8 [Young, 1979], and the
chemicalenergiesare greater than the energyof condensation.
Thus precipitation of S2and S4accompaniedby upward mixing of S8 vapor resultsin a net downward energy flux. The
magnitude of the flux is highly uncertain, however, and could
be muchlowerthan the 23 W m-: requiredto explainthe Pioneer Venus observations.
LOWER ATMOSPHERE
HEAT
BALANCE
Prinn, R. G., On the possibleroles of gaseoussulfur and sulfanesin
the atmosphereof Venus, Geophys.Res. Lett:, 6, 807, 1979.
Rau, H., T. R. N. Kutty, and J. R. F. Guedes de Carvalho, Ther-
modynamicsof sulfurvapour,J. Chem.Thermodyn.,
5, 833, 1973.
Sagan,C., The surfacetemperature
of Venus,Astron.J., 65,352, 1960.
Schubert,G., C. C. Counselman,J. Hansen, S.S. Limaye, G. Petten-
gill, A. Seiff, I. I. Shapiro,V. E. Suomi,F. Taylor, L. Travis, R.
Woo, and R. E. Young, Dynamics, winds, circulation, and turbulence in the atmosphereof Venus, SpaceSci. Rev., 20, 357, 1977.
Schubert, G., et al., Structure and circulation of the Venus atmo-
Mechanical transport of energy downward has not been
treated as a separatecasein Table 2. Sincethere is no external
sourceof mechanicalenergy,any work done by the upper atmosphereon the lower atmospheremust come from thermal
sources,and therefore must satisfy (1). But since we cannot
satisfy (1) without postulating additional heat sources(internal heat, secularcooling of the atmosphere,chemically energetic rain, etc.), we concludethat downward mechanical energy transportis quantativelyincapableof explainingthe net
flux data when the probe locationsare taken to be typical.
In summary, we cannot claim to understandthe high surface temperaturesof Venus on the basisof the Pioneer Venus
observations.If the variability of the observed infrared net
flux profilesis real and if the night and north profilesare not
anomalously high due to local conditions,then a transfer of
23 W m-2 fromthe upperto the loweratmosphere
is implied.
This transfer cannot be due to any steady state, thermally
driven processin the atmosphere. We conclude either that
some of the net flux data are in error or that they are from
anomalous regions or else that there is another sourceof energy for the deep atmosphere.Examplesinclude23 W m-: internal heat source,a secularcoolingof the atmosphere,or a
chemicallyenergeticrain carrying solar energydownward.
Acknowledgment. Contribution 3368 of the Division of Geological and Planetary Sciences,California Institute of Technology.
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