JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 85, NO. All,
PAGES 5871-5881, NOVEMBER 1, 1980
Saturn'sAtmosphericTemperatureStructureand Heat Budget
GLENN
$. ORTON
Earth and SpaceSciencesDivision,Jet PropulsionLaboratory, CaliforniaInstituteof Technology
Pasadena,California 91103
ANDREW
P. INGERSOLL
Divisionof Geologicaland Planetary Sciences,CaliforniaInstituteof Technology
Pasadena,California 91125
The effectivetemperatureof Saturn from 30øS to 10øN is 96.5 + 2.5 K. This value is 1.9 K higher than
our preliminary estimate(Ingersollet al., 1980).The atmosphericmole fractionof H2 relative to H2 + He
is 90 + 3%. This value is derived by comparinginfrared and radio occultationdata (Kliore et al., this
issue)for the samelatitude.The high valueof the effectivetemperaturesuggests
that Saturnhasan additional energysourcebesidescoolingand contraction.The high mole fraction of H2 suggests
that separation of heavierHe toward the coremay be supplyingthe additional energy.Atmospherictemperaturesin
the 60- to 600-mbar range are 2.5 K lower within 7ø of the equator than at higher latitudes. An almost
isothermallayer existsbetween60 and 160 mbar at all latitudes.
bration factors,which are also given, one can calculateall the
resultsthat follow. Then we describethe temperature-soundIn our preliminary report [Ingersollet aL, 1980] of the Pioing method. The results--temperature profiles, latitudinal
neer Saturn infrared radiometer (IRR) resultswe discussed
structure, whole disk infrared spectra, and net infrared heat
the data set and viewing geometry and presenteda prelimibudget--follow in succeedingsections.A final section disnary analysisbased on early postencountertrajectory inforcussesimplications for global energy budget and interior
mation. We now presenta more completeanalysis.This paper
models.
discusses
Saturn'sinfrared emissionsat 20- and 45-/•m wavelength, the atmosphericthermal structurefrom 30øS to 10øN
BASIC DATA
latitude and from 60- to 600-mbar pressure,the global energy
Observationsof the planet cover a range of emissionangle
budget of Saturn, and the atmosphericH2 to He ratio. Ancosine/• from 1.0 to 0.2. Unambiguousobservationsof emisother paper [Froidevaux and Ingersoll, this issue] discusses
sion at/• -- 0.2 were possiblebecauseof the relatively close
Saturn'srings and Titan.
trajectory of the spacecraftto the planet, in termsof planetary
Some of the numbershave changedsinceour preliminary
radius. For comparisonthe lowest value of/• used for Jupiter
report. The changesare all within the error limits quoted in
was 0.4.
the preliminary report, but they are neverthelessinteresting.
As in the Jupiter observations,no point on Saturn was obFirst, the estimatedeffectivetemperatureof Saturn is higher
servedmore than once.Therefore in order to acquire a useful
by 1.9 K, a change attributable to a different treatment of
setof intensitymeasurementsin each channelwhich would be
long-wave emissionbeyond the range of instrument sensitivuseful for atmosphericstructureretrieval, longitudinal homoity. This change,plus the likely possibilitythat Saturn scatters
geneityof the atmospherewas assumed.For the latitudesover
a higherproportionof incidentsunlightinto largephaseangles
which data were acquiredfrom both risingand settingsidesof
than Jupiter [Tomaskoet al., this issue],raisesthe estimate of
the central meridian (i.e., for latitudes where occultation by
Saturn's internal energy flux significantly.The other major
the ring systemdid not occur), no asymmetriesbetween the
change is that our results have now been thoroughly inintensitiesof the rising and settinglimbs were observedabove
tegratedwith thosefrom the Pioneerradio occultationexperithe variance of the data about the mean in either channel.
ment [Kliore et al., this issue],and a new estimateof the hyUnlike the Jupiter data, latitude binning of the data was not
drogen to helium ratio has been obtained. Our preliminary
done in preselectedregionsrepresentingmajor morphological
use of earth-basedspectrato infer the stratospherictemperfeatures,sincerelatively little was known about the properties
ature gradientled to a high value for the hydrogenabundance
of the planet as a function of latitude. Instead, adjacent bins
[Kliore et al., 1980]. Now, by using the radio occultation rewere used,with equal widths of 3o in latitude. This sizeallows
sults to constrain the stratospherictemperature profile the
a substantialnumber of data to be gatheredfor averagingover
mole fraction of hydrogenfrom the two experimentsis 90 +_
the widest possiblearea of the planet without unduly smooth3%. (The quotederror reflectsuncertaintiesin the IRR data
ing over the apparentextentof major bright and dark infrared
only.) These two changesare relevant to discussionsof Satregions, using the infrared map shown by Ingersoll et al.
urn's internal history, of whether separationof hydrogen and
[1980, Figure 1] as a guide. For each channel the set of latiINTRODUCTION
helium
isoccurring,
and
ofwhether
such
separation
iscon-•tude-binned
data
was
fitbyathree-term
polynomial
tributing to Saturn's internal energy output.
Thenextsection
givesthebasic20- and45-/andatafor Sat-
urn. From thesedata and a knowledgeof the filter and cali-
Copyright
¸ 1980by theAmerican
Geophysical
Union.
Paper number 80A0848.
0148-0227/80/080A-0848501.00
I•) -- IoPo•) + I•P•)
+ I2P•)
(1)
Thispolynomial
provided
a goodfittothetotaldatasetwithout imposingsuperfluousvariations in the limb structure.
5871
5872
ORTON AND INGERSOLL: SATURN'S TEMPERATURES AND HEAT BUDGET
SATURN 20-'Hm BRIGHTNESS
bration fall in the range +_4to _+8%.As with the Jupiter data,
the latter value will be used throughout this report.
i
6
5
--
94
--
92
TEMPERATURE-SOUNDING
METHOD
--90
The determination of the atmosphericstructureof Saturn
with IRR measurementsfollows essentiallythe same tech,
niquesas the analysisof Pioneer 10 and 11 IRR data on Jupi•=0.8
-- 92
5
ter [Orton, 1975; Orton and Ingersoll, 1976]. We assumethat
4
the collision-induceddipole of H2, under the influenceof both
88
'94
H2 and He collisions,providesmost of the atmosphericopac:• 6
tl =0.6
92
"'
ity. While the opacity of NH3 was also includedin the calcuz
5
lations,
as in the Jovian case,the inclusionof its opacity has a
<
4
negligible
effect on the atmospherictransmissionin the spec94
Z
#=0.4
6 _
tral regions covered by the two channels.This is due to the
5
low amount of NH3, whose abundanceis presumedto follow
4
saturationequilibrium, in this relatively cold region of the at88
94
mosphere.The weighting functionsare sensitiveto somewhat
6 -•=0.2
lower
pressuresthan are thosefor the Jovian atmosphereow- .
5
ing primarily to the greater value of the atmosphericscale
4
88
height for Saturn. This larger scaleheight is the result of the
lower gravitational accelerationof Saturn comparedwith that
30øS
20øS
10øS
0
10øN
LATITUDE
of Jupiter.
Fig. 1. Brightnessof Saturnat 20-/•mwavelength.Raw data numThe vertical range and resolutionfor temperaturesounding
bersare shownat left, and brightnesstemperaturescaleat right. Five
were evaluated from the weighting functionsshown in Figure
values of the emissionangle cosine/• are shown.
3, using Conrath's[1972] adaptation of Backus-Gilbert theory.
These estimateshave been found [Orton, 1977] to be consisHigher-order terms did not provide a better fit to the data.
tent with the temperature retrieval limitations of Chahine's
Figures I and 2 show the basicdata for the 20- and 45-/•m [1975] technique,which is the method usedin this work. The
channels,respectively.For each latitude bin centered at 0 ø, result is shown in Figure 4. It is apparent that meaningful re_+3ø, _+6ø, etc., the coefficientsIo, I,, and 12 were determined trieval of the temperaturecan be done only in the range 0.06
along with the 3 x 3 error matrix computedfrom the scatter _<p _<0.50 bar and that the vertical resolutionaveragesabout
of the data about (1). From this information, values of I½)
0.3 in units of 1oglop (bar), approximately0.7 pressurescale
and their uncertaintieswere computedat/• -- 0.2, 0.4, ---, 1.0. heights.We have thus attemptedto retrievethe temperature
Only values whose uncertainties are less than _+0.5DN are at four vertical levels (nodal points) where temperaturescan
plotted. (DN is the data number;the conversionto brightness be retrieved independently of one another, correspondingto
temperature is shown in the scaleat the right in the figures.) 1oglop (bar) -- -0.3, -0.6, -0.9, and -1.2 (p -- 0.501, 0.251,
Restrictingthe plotted curvesin this way eliminateslatitude-/• 0.126, and 0.063 bar, respectively).Between theselevels, temcombinations for which we have no data or for which a modperaturesare interpolatedlinearly in logp. We have restricted
est extrapolation in/• is not possible.For instance,we have the range of latitudeschosenfor temperaturesoundingso that
observationsat/• -- 1.0 only at one point on the planet near for each channel, observations at each latitude were available
6 øSlatitude,but a modestextrapolationfrom/• -- 0.98 enables for 0.7 _>/• _>0.3. For suchvaluesof/• the vertical resolution
us to plot the/• -- 1.0 curvesfrom 15øSto 3øN.
and range are virtually unchangedfrom thoseshownin FigCalibration procedureswere describedfollowing the Jupiter ure 4, which were computedfor 1.0 _>/• _>0.2.
encounters[Ingersollet al., 1976] and in the preliminary SatIn the deep atmosphere(1oglop -> -0.3 (p _>501 mbar)), we
urn report [Ingersollet al., 1980].The primary calibration was have assumedan adiabatic temperature lapserate. For 1oglop
done in the laboratory before launch. Part of the prelaunch
SATURN 45-#rn BRIGHTNESS
calibration involved measuring the responseto an internal
I
!
I
I
I
I
shutter at the known instrument temperature. After launch
106
55 -the instrument temperature and the responseto the shutter
104
were monitored.This responseis measuredwith respectto liq50 -uid nitrogenin the laboratoryand with respectto spaceduring
lO2
flight. The emissionfrom liquid nitrogenrequiresa 3% correclOO
45 -tion at 45/an and a 0.2% correctionat 20/•m. In accordwith
98
laboratory measurementsthe instrument responsein spaceis
40 -96
"'
representedby a linear relation. Values of interceptand slope
are derived from observationsof space and the shutter, re94 0
35 -spectively.These derivationswere repeated at least once per
92 "'"
year from 1973to 1980and during the encounterswith Jupiter
30 -and Saturn as planetary data were being taken. The difference
between the derived responseto a 100-K object and the labo40os
30øS
20øS
10øS
0
10øN
ratory value was no more than 3% for all these determina4
--
88
6
--'•-*'"'•
-- •u10--
tions. The instrument
seems to have been stable to +3% for 8
years. Our total estimatesof uncertainty in the absolutecali-
LATITUDE
Fig. 2.
Same as Figure I at 45-/•m wavelength.
ORTON AND INGERSOLL: SATURN'S TEMPERATURES AND HEAT BUDGET
PIONEERSATURNINFRAREDRADIOMETER
_<-1.2 (p _<63 mbar)we have,for the sakeof completeness,
RESOLUTION
(pressure
scaleheights)
assumedtwo alternative values for the inverted lapse rate.
One corresponds
to the meanlapserate in the lower portion
of the radio occultationprofile [Klioreet al., this issue],approximately21 K of increase
per decadeof pressure
decrease;
the othercorresponds
to the meanlapserate in the lowerpor-
5873
1.4
o
1,0
2.0
I
I
0.05
tion of the inversionin modelsbestmatchingearth-basedobservationsof thermal emissionfrom Saturn [Tokunaga and
Cess,1977],a steepergradientat approximately
36 K of increaseper decadeof pressure
decrease.
The profilesof both
0.1
Kliore et al. and Tokunagaand Cessare shownin Figure 12
and will be discussedlater in more detail. These lapse rates
are usedto extrapolatethe thermalstructuredownto 1og,o
p
(bar)-- 2.0 (100bars)andup to 1og,o
p (bar)= -3.2 (0.63
mbar),whereradiativetransfercalculations
werediscontinued,sincetemperature
changes
belowand abovethisleveldo
0.2 -•
-0,6 --
not affect radiation observedin either channel. In the numerical calculation of the radiative transfer integral the atmo-
sphere
wasdividedintofinitehomogeneous
layers,10perdecade of pressure
change.The temperature-sounding
iterations
_
-0,4
--
were continuedconservativelyfor 30 iterations,so that the
changes
in recovered
temperatures
at anygivenlevelbetween
the next to last and the last iteration were usually well below
0.1 K. Model test recoverieswith syntheticdata, to which the
observedlevel of noise was added, show that the uncertainty
in thetemperatures
recovered
at a givennodalpointfrom the
techniqueitself (as opposedto systematicerrorsor uncertaintiesin the opacitymodelsor in the calibration)is of the
0.5
_
-0,2
--
0.0
0,0
i
I
i
1.0
.0
0.5
RESOLUTION
(Iog10
P, bar)
Fig. 4. Spreadfunction,inverseof the verticalresolution,for temorder of 3 or 4 K, with a worst caseof 6 K in the neighborperaturesoundingwith the IRR experiment.This wascomputedachood of the temperatureminimum. The root mean squarere- cordingto the methodof Conrath[1972].
sidualsof a model fit to the data were computedby
0.025
i
I
I
TBmOde,
__TBdatal
2/
I
where i representsa (channel,/0 pair, Te is a brightnesstemperature,and the sum is taken over data in both channels.
Here the 'data' are intensitiesI(•) computedfrom (1).
0.05
COMPARISON
0,2
CHANNEL
1
0.100
(20•m)#= 1.0
=0.2
0.250
CHANNEL
2
WITH
RADIO
BULK
OCCULTATION
RESULTS:
COMPOSITION
The radio occultationexperiment [Kliore et al., this issue]
providesdata downto 125mbar,in the middleof the altitude
rangecoveredby the IRR. The exit data yield a profileof atmosphericrefractivityat a latitudeof 9.6øS.This latitudewas
also sampledby the IRR, althoughat differentlongitudes,at
times differingby at mosta few hours.The profile of temperature versuspressurethat one derivesfrom the radio occultation data dependson the assumedcomposition,represented
hereby all2,thenumberof H2molecules
relativeto H• + He.
(45.um)
.u= 1.0
Figure 12bof Kliore et al. [thisissue]givesa family of such
profilesfor variousassumptions
about the value of this parameter. The temperatureprofile that one derives from the
IRR dataalsodepends
on{XH2
, butin a different
way.Thusfor
anyvalueof aH•onecanusetheappropriate
radiooccultation
profileto get the temperatureabovethe 126-mbarlevel and
I
0.0
i
1o0
WEIGHTING
I
2.0
FUNCTION
allow the IRR data to determinetemperaturesat the two lowest nodal points at 1og,op (bar) -- -0.3 and -0.6 (0.501 and
0.251bar).The derivedvalueof all: is the onethat givesthe
lowest rms residual e, defined in (2).
Fig. 3. Effectiveweightingfunctionsfor the infraredradiometerat
Figure 5 displaysthe residualsfor eachtemperaturesoundSaturn. The mixing ratios of H2 and He are 0.90 and 0.10, respectively, in this model.The weightingfunctionis plottedin arbitrary ing as a functionof the H• mixing ratio assumed.They are
units.
minimizedfor aH•----0.90+_0.02(aHc----0.10+_0.02).The un-
5874
ORTON AND INGERSOLL:
SATURN: COMBINED
IRR AND
RADIO SCIENCE SOLUTION
SATURN'S
FOR
THEMIXINGRATIO
OFH2
TEMPERATURES
AND HEAT
BUDGET
/•mintensity
lea•lsto a 1-Koverestimate
of temperature
near
the 0.06-bar level, correspondingto a 0.01 underestimateof
aI4•.Errorsin opacitytendto havea smallereffect,because
3.00
•
the atmosphereat thesealtitudesis nearly isothermal,so that
the pressureat which the minimum temperatureoccursis irrelevant.
The addition
of the few levels of radio occultation
resultsfor p > 125 mbar makesan insignificantchangein the
results. The effect of clouds near the 500-mbar
2.00
level on out-
goingradiation,as will be discussed
below,has no effecton
1.oo-
O. 85
O. 90
O. 95
aH2
Fig. 5. Root mean squareresidualsto the fit betweenIRR data
and outgoingfluxescomputedfrom the radiooccultationmodelas a
functionof thehydrogenmixingratioa•,. The mixingratioof helium
these results,as the region of overlapping coverageis substantially higher in the atmosphere.Furthermore, an examination of Figure 13 of Kliore et al. [this issue]showsthat uncertainties in the retrieved radio occultation temperature
structuredue to the assumptionof an initial temperatureor to
bias selectionare negligiblein the regionof overlapwith IRR
results.The values of 90% H2 and 10% He by volume differ
from the initial resultsgiven by Kliore et al. [1980], because
their earlier comparisonwas made between IRR resultsderived by assuminga much steeperinverted lapse rate in the
stratospherethan is consistentwith the radio occultation results.
Temperaturedifferencesbetweenthe IRR range of longitudesand thosesampledby the radio signal are more difficult
to estimate.A 1-K differencein temperaturewould lead to a
isassumed
tobecomplementary.
Thesolldcurverepresents
theresid- 0.01changein a•. Nonequilibrium,
nonhydrostatic
effectsin
ualsto the unweightedfit to the data set;the dashedcurverepresents the atmosphereare alsodifficult to estimate,as are systematic
the residualsto the fit weightedas describedin the text.
effectsin the radio occultationexperimentbesidesthose dis-
certainty
quoted•sderived
fromtheequation
usedby Orton cussedabove.The temperatureerror in the overlapregiondue
and Ingersoll [1976], conservativelyassumingonly I degreeof to radio data alone is thought to be lessthan +_1K (A. J.
freedom, and it representsonly the uncertaintyof the fit. The Kliore, personalcommunication,1980).
Our final results,then, usingthis techniqueare
minimum residualvalue is 6.9 x 10-3, of the sameorder as residuals for this latitude from straightforward temperature
a• -- 0.90_ 0.03
sounding,discussedin the next section,for the full 0.501- to
aHe --• 0.10 _ 0.03
0.063-bar range. The resultingthermal structureis shown in
Figure 6.
1XlO
-3
i
As a test of the method we tried weighting the residualsin
eachpair of (channel,/0 setsaccordingto its degreeof overlap
with the radio occultationresults--stronglyfavoring the fit to
residualsto the 20-/an channel resultsnear the limb (small
'values
of/•). Theseweighted
residuals
wereminimized
for a.2
5X10
-3
= 0.90. Since there is only one significantobservation(in-
tensityat 20/•m for small/0 andonefreeparameter(a.), the
number of degreesof freedomis zero, and an uncertaintyestimate would be meaningless.Nevertheless,the result is consistent with that obtained by considerationof the full data set.
This comparisonbetweenradio occultationand IRR results
is valid only under the assumption that the longitudes
soundedby the radio occultationexperimentare representative of the average temperature structurein this latitude region over all longitudes.Further implicit assumptions
are required for either the radio occultationor the infrared remote
retrieval of temperatures(usingthe IRR data set) to be valid
in general: (1) the atmosphereis in thermodynamicequilibrium, (2) all constituentsbesidesH2 and He are negligibleat
the level of error in the fit, (3) the atmosphereis spheroidally
symmetric, with isobar surfacescompletely coincident with
geopotentialsurfaces,and an appropriatevalue for the planetary oblatehesshas been used,(4) the atmosphereis in hydrostatic equilibrium, (5) the infrared opacity is modeled correctly, (6) the thermal structure is longitudinally
homogeneous,and (7) the absolutecalibration of the radiancesmeasuredby the IRR experimentis accurate.
Violation of the above assumptionsleads to additional un-
certainties
in a•. For example,an 8%overestimate
of the 20-
•.1X10
-2
5X10-2
]X10
-1 __•--••_
____RADIO
OCCULTAT/ON.
!
INFRARED •
5X10
-1
1.00
80
I
I
•
100
I
120
•
140
TEMPERATURE
(K)
Fig. 6. Retrievedtemperaturestructurefor $.1ø-11.1øSlatitude,
centeredon the regionsoundedby the Pioneer11 egressradio occultation [Kliore et al., this issue].The radio occultationprofile is used
for p _< 126mbar. Residualsof the modelfit to IRR data are minimized by (1) temperaturesoundingthe regionwherep _> 126 mbar
and (2) adjustingthe mixingratiosof H2 and He as shownin Figure
5.
ORTON AND INGERSOLL:SATURN'STEMPERATURES
AND HEAT BUDGET
with no uncertaintiesin the values quoted other than those
correspondingto the internal fit and to the radiometer calibration. All other potential sourcesof systematicuncertaintyfollowing the assumptionslisted above cannot be estimatedin
quantitative terms. These values are assumedin all temperature-soundingcalculationsdiscussedbelow.
We note that the method usedby Orton and Ingersoll [1976]
to determinethe relative abundancesof H2 and He in Jupiter
took advantageof an overlap betweenthe 20- and the 45-/tm
channel vertical coverageof the atmosphere.This extra degreeof freedomalloweda testof a variety of valuesof the H2
and He mixing ratios to be made, sincethe collision-induced
opacityof H2 in the 45-pm channelversusthe 20-pm channel
is somewhat sensitiveto the relative number of H2 versus He
collisionswith the H2 molecule. As Figure 3 shows,however,
this degreeof freedomwas absentfor the Saturn atmosphere;
that is, there was no overlapin the vertical coverageof the atmospherebetweenthe two channelswithout making unrealistic assumptionsabout the integrity of the few 45-pm data col-
5875
SATURN TEMPERATURE STRUCTURE
-13.5 ø TO -16.5 ø LATITUDE
0.01
j
i
0.05
I
I
CASE 1
CASE 2
lectednearlow-latituderegionscharacterized
by valuesof p •
0.10.
The techniqueof correlatingradio occultationand infrared
resultshasbeen usedfor Jupiterin a comparisonof Voyager 1
radio sciencesystem(RSS) and infrared interferometerspectrometer(IRIS) data. The derivedvalue for the H2 mixing ra-
tio is a• 2 = 0.897+ 0.024[Gautieret al., 1980].Thisvalueis
remarkablycloseto the value derivedhere for Saturn. A comparisonof the Voyager I and 2 RSS and IRIS resultsshould
be made for Saturn also to determine the bulk composition,
following the respective spacecraft encounters with that
planet. Theseshouldproduceresultswhich do not require the
assumptionof longitudinal homogeneityof the atmospheric
structureto the sameextent as is required for IRR data analysis.
TEMPERATURE-SOUNDING
1.00
80
100
120
140
160
T(K)
Fig. 7. Retrieved temperaturestructurefor casesI and 2, de-
scribed
in thetextandin Table1,for datafroma latituderegionextendingfrom13.5øS
to 16.5øS,
oneof thewarmest
regions
examined.
Figures7 and 8 display the vertical temperaturestructures
retrieved from two latitude regions. They are (1) 13.5ø16.5øS, a region which is one of the warmest observed and
which is associatedwith a visually dark area in reflectedsunlight (propertiessimilar to a Jovian belt) and (2) 1.5øN to
1.5øS,a regionwhich is one of the coldestobservedand which
RESULTS
SATURN TEMPERATURE STRUCTURE
+1.5 ø TO -1.5 ø LATITUDE
Temperature soundingswere made at latitudes from 30øS
to 9øN in bins 3ø wide. The radio occultationprofile was not
usedto constrainthe data at p < 125mbar, as it wasin the last
section.Rather, the 20- and 45-pxndata were usedto solvefor
temperatureat the four nodal points 1og,op (bar) -- -0.3,
-0.6, -0.9, and -1.2 (p -- 0.501,0.251, 0.126, and 0.063 bar).
Severalassumptions
were made regarding(1) the value of the
invertedlapserate (temperatureincreasewith altitude) in the
1og,op < -1.2 region (p •_ 63 mbar) and (2) the pressureof
cloudsin the troposphere.The three major casesdiscussedbelow are summarizedin Table 1. Recall that an overlyinglapse
rate of 21 K per decadeof pressureis consistentwith the radio
occultationprofile at 9.6øS(casesI and 3). An overlyinglapse
rate of 36 K per decade of pressureis more consistentwith
earth-basedobservations(case2). Crude cloud models,where
invoked(case3), consistof a unit emissivitysurfacerepresenting a uniform, optically thick cloud top emitting at the ambient temperature.
0.01
•
I/•/ /'
I
/1/I;I
-,
/.//
0.05
.....
•
I
CASE
CASE
21
CASE
3
('
0.10
TABLE 1. Temperature-Sounding
Assumptions
Case
Overlaying
Lapse Rate,
K/log•o p
21
36
21
1.00
Cloud Presence
80
100
120
140
I
160
T(K)
no
no
whererequired
(seetext)
Fig. 8. Retrieved temperaturestructurefor cases1, 2, and 3 for
data from a latituderegionextendingfrom 1.5øNto 1.5øS,one of the
coolestregionsexamined.The locationof a cloudtop, modeledas a
unit emissivityblackbodysurface,is also marked.
5876
ORTON AND INGERSOLL:
SATURN'S
TEMPERATURES
PIONEER 11 SATURN DATA:
AND HEAT
BUDGET
-13.5 ø TO -16.5 ø LATITUDE
95
20• rnCHANNEL
20-•mCHANNEL
1,
0
0.8
0.6
0.4
0
1.0
0.8
0.6
0.4
0.2
#
105
•osj I
100
100
I
•
I
•
I
45-•m CHANNEL
i
,
DATA
DATA
CASE 1
CASE 1
CASE 2
CASE 2
WITH 110 K CLOUD TOP
85
1.0
0.8
0.6
0.4
0,2
lO
,U
Fig. 9.
0.8
0.6
0.4
,U
Fit of various retrieved modelsto data from the relatively warm 13.5ø-16.5øSlatitude region.
is associated
with a visuallybright area in reflectedsunlight shallowlapserate in the vicinityof the temperatureminimum.
(propertiessimilarto a Jovianzone),for Figures7 and 8, re- In fact, for case1 the equatorialcool regionis nearly isotherspectively.
Clear atmospheres,
free of the absorptionor scatteringeffectsof any aerosols,
wereassumedin cases1 and 2. Figures7
and 8 showthe vertical temperaturestructureassociatedwith
each of these casesfor the two latitude regionsdescribed
above.The lowerpart of theretrievedprofiles,betweenlog•oœ
-- -0.6 and -0.3 (501 _>œ _>251 mbar), is characterizedby
lapse rates which are slightly subadiabaticand therefore not
inconsistentwith the assumptionof adiabaticlapse rates at
deeper levels. We note, however, that we cannot rule out the
possibilityof a subadiabatic
lapserate at levelsdeeperthan
mal for more than an atmosphericscaleheight (Figure 8).
In case3 we pursuedthe possibilitythat the differencesin
the retrievedtemperaturesat 501 mbar betweencases1 and 2
result from changesin the propertiesof aerosolsnear that
level in the atmosphere.This correspondsto the alternative
model for temperaturesnear the 700-mbar level in Jovian
zones.For this 'cloudyzone' model we assumedthat the 501mbar level of the atmosphereis in convectiveequilibriumand
that latitudinal variations of temperature along isobars are
well below our observationalnoise. For the equatorial zones,
then, we introduced a uniform, fiat, and optically opaque
cloudtop with unit emissivity.Its altitudewasadjusteduntil
the retrievedtemperatureat 501 mbar wasnear 108K, an ap-
501 mbar, exceptby referenceto a variety of radiative-convective equilibrium models,all of which predict convective
equilibrium in this region (e.g., J. F. Appleby and J. Hogan,
unpublishedmanuscript, 1980). A comparisonbetweenthese
higher-latituderegionswhereaerosoleffectswerepresumedto
theoretical
be negligible.
models and the results derived here will be made
later.
The difference between the overlying lapse rates assumed
for cases1 and 2 appearsto affect only the temperaturesrecovered at the highest nodal point (63 mbar) to any substantial degree. In addition to the generally colder temperatures, comparedwith the Jovian temperaturestructure(e.g.,
500-mbar temperaturesnear 105 K instead of approximately
143 K for Jupiter), the next major differencebetween these
temperatureprofilesand thosederivedfor Jupiteris the rather
propriatemean of temperatures
retrievedat this depth in
The vertical structure and cloud location for this case are
shownin Figure8 for the equatorial'zone.'If the cloudis real
and, further,if it is similar to the Jovianammoniaice cloud,a
consistent
picturemay be found in which the NH3 cloud or
hazeis substantiallythicker(at leastat somelatitudes)than its
Jovian counterpart.The effectiveblackbodycloud top temperaturesfor Jovian zones are near 148 K [Orton, 1975; Orton and Ingersoll,1976],quite closeto the saturationtemperature for NH3. The Saturn cloud top temperaturesin the
ORTONAND INGERSOLL:
SATURN'S
TEMPERATURES
AND HEAT BUDGET
5877
PIONEER11 SATURNDATA: + 1,5 ø TO - 1.5 ø LATITUDE
20-/./.m CHANNEL
20-/jm CHANNEL
85
1.0
0,8
0.6
1,0
0.4
105
I
45-/.j.m
CHANNEL
0,6
0,4
0.2
105
•
100
•-
•'
0.8
45
-/./.m
CHANNEL
loo •
_
95
' DATA
CASE1
CASE 2
CASE 3
I . - CASE
2
85
1.0
0.8
0.6
0.4
0.2
1,0
0,8
0.6
0.4
0.2
Fig.10. Same
asFigure
9 butfortherelatively
cool1.5øNto 1.5øS
latitude
region.
We concludethat thesemodelsdo not representvaiablealternatives.
The differencebetweenthe optimummodelsfor
plained
solely
bysaturation
equilibrium
(which
wouldrequire
regionandthe45-/•mregions
isthatthereis
a substantialenrichmentof ammoniaabundancein the deep the8- to 14-/•m
10øNto 10øSlatituderegion(124K) are far toolow to be ex-
a substantial
wavelength
dependence
oftheoptical
atmosphere
of Saturnrelativeto that of Jupiter).However, probably
the ammoniasaturationlevel, if it is near temperaturesof 148
properties
ofaerosols
(presumably
NH3icecrystals).
In order
with boththe 10-/•mand the 45-/•mregions
K, is relativelydeepwithinthe convective
regionof Saturn. to be consistent
Thusit is plausible
to consider
thattheaerosols
maybe car- the cloudmustbe moreopaqueat 10/•m that at 45/•m. An
of Taylor's
[1973]calculation
oftheextinction
efriedaloftby convection
to regions
wheretheambienttemper- examination
ficiency
Qext
forNH3iceshows
thatcloudparticles
wouldbe
more
transparent
at
longer
wavelengths
if
the
particles
were
Caldwell's
[1977]analysis
of the8- to 14-/•mspectrum
of the
bymoderadiioftheorderof 1-10/•m.Whether
Saturndisk,observed
by GillettandForrest[1974],requires,
in characterized
aturesare well below thoseat the saturationlevel.
of Saturn
fact,an opticallyopaquecloudtop temperature
just below thisis the casefor ammoniaicein the atmosphere
must
be
determined
by
application
of
radiative
transfer
calcu110K. Wepursued
thatmodelbyassuming
thata 110-Koptilations
which
include
scattering
and
absorption
by
NH3
ice
callyopaque
cloudexists
in thetemperature
profileretrieval.
whichisoutside
thescope
of thisreport.
However,suchmodelsgivea consistently
worsefit to the data crystals,
A smoothed
plot of temperatures
between
60- and 500than the modelsin cases1, 2, and 3. The fitsof variousmodel
cases
to the dataareshownin Figures9 (13.5ø-16.5øS)
and 10 mbar altitudeand between30øSand 10øNlatitudeis shown
zoneisa prominent
coldregion
(1.5øNto 1.5øS).
It isclearthatcases
1,2,and3 provide
good in Figure11.Theequatorial
with Jupiterthereare refits to the data in each respectiveregion, with root mean at all altitudes.But in comparison
fewfeatures
atotherlatitudes.
Thesame
behavior
is
square
residuals
(equation
(2))oftheorderof 3.9x 10-3 and markably
2.5 x 10-3. For thesesameregions,modelswith an opaque seenin the raw data shownin Figures1 and 2. We have
for evidence
of ring shadowing
in thesedata.The
cloud
topat 110K yieldresiduals
of6.7x 10-3and7.5x 10-3 searched
latitude
of thesunwas2.83øS
at thetimeof
becauseof the inabilityof the modelsto providesufficient Saturnocentric
Northernspringequinoxoccurred51 days
limbdarkening
to matchthe45-/•mdata,asFigures9 and 10 the encounter.
later.The onlypossible
evidence
of ringshadowing
is the
show.
5878
ORTON AND INGERSOLL: SATURN'S TEMPERATURES AND HEAT BUDGET
0,02
the mixing ratio of ammonia in the deep atmosphereis parameterizedagainsta given temperaturestructure(essentially,
a given adiabat). These modelsthus provide no independent
verification of the temperaturesretrieved here. However, the
modelswe presenthere can be usedwith the microwavedata
to constrain the abundance of NH3 and H20 in the deep atmosphere,as is discussedby Klein et al. [1978].
I
1,6
T(K)
1,4
o. 05
•
88
•
1.2
87
88
0.1
SPECTRA
1,0
•
The models presentedin the preceding section have been
0.8
0,,2
%
o
•
o.6
0,4
0,,5
•
106
usedto generatelow-resolutionspectrain the 25- to 800-cm-•
region.Theseare summarizedin Figure 13. For convenience,
in comparisonwith many earth-basedobservationsthe hemispherically averaged brightness temperatures (equivalent
whole disk) have been plotted. This figure also showsa schematic plot of the spectralresponseof the 20- and 45-/tm filters.
The spectra are dominated by the collision-induceddipole
opacityof H2. Absorptionpeaksfor the S(0) and the S(1) rota-
tional lines are near 375 and 600 cm-•, respectively.These
spectral regions appear rather isothermal, becauseradiation
emerging
from them is originating to a large extent from the
I
I
I
1.0 - J
J 0.0
rather isothermal regionsof the atmospherenear 100 mbar.
10øN
40os
30øS
20øS
10øS
LATITUDE
At lower frequenciesthe translationalabsorptionband of H:
is apparent, and it becomesincreasinglytransparentat freFig. 11. Smoothcontours
of temperature
in a meridionalcrosssecquenciesbelow 100cm-•. The spectraof differentmodelcases
tion from 30øS to 10øN and from 0.50 to 0.06 bar.
are not very different from one another and are denoted by
slight northward displacementof the equatorial temperature the separationbetween the solid curvesrepresentingeach reminimum for p -- 0.2, 0.4, and 0.6 at 20 pm (Figure 1). Thus gion in Figure 13.
The generalagreementof earth-basedobservations
with the
temperaturesnear the 0.06-bar level might be • 1 K lower as a
result of the •50-day passageof the ring shadowfrom north spectracomputedfrom the modelsis good.The featurenear
830 cm-I in the Gillett and Forrest [1974] spectrumis due to
to south at latitudes from 2 ø to 5øN.
Figure 12 displaysthe vertical temperatureprofilesfor cases the •'9fundamentalband of ethane(C:H6), whoseopacitywas
0,2
1, 2, and 3 for both the 13.5o_16.5o$ and the 1.5ON to 1.5o$
regions.With thesewe comparethe radio occultationresults
of Kliore et al. [this issue], the semiempiricalequilibrium
model of Tokunaga and Cess[1977], and one of the equilibrium models of J. F. Appleby and J. Hogan (unpublished
manuscript, 1980). The structural details of the Kliore et al.
model are only crudely approximated by the constantlapse
rate adopted in casesI and 3. The agreementin the 125- to
60-mbar region between this result and the results derived
from the IRR data has been optimized by means of adjustment of the bulk composition.
.
Assumptionof a steeperoverlying inverted lapse rate, as is
consistentwith the model of Tokunaga and Cess,substantially
changesonly the 63-mbar nodal point in our retrieved temperatures and does not increasethe residualsof the model fit
to the data in any systematicway. It is thereforequite possible
to achieve a consistencybetween our derived thermal structure models and either of the equilibrium models. Appleby
and Hogan have shown,in fact, that it is possibleto change
the stratospherictemperaturestructuresubstantiallywith appropriate changesin the vertical distribution of absorbing
aerosols.Furthermore, as was mentioned earlier, the equilibrium models are consistentwith the assumptionin case 3
modelsthat the atmosphereis in convectiveequilibrium near
the 501-mbar
level.
Models fitting the microwavespectrumof Saturn have been
presentedby Klein et al. [1978].Unlike the casefor Jupiter, no
high-resolution data are available in the spectral region
around severalstronginversionlines of NH3. Their resultsare
accordinglyconstrainedonly to a family of models in which
not included in the calculation of the spectrashown. Between
400 and 600 cm -I most of the observations were made with
some degreeof spatial resolutionof the disk, and so a comparisonwith the hemisphericallyaveragedspectrummay not
be wholely appropriate. The Ericksonet al. [1978] spectrum,
shown somewhatschematicallyat a lower resolutionthan observed, includes flux from the entire disk and from the ring
system.The observationsby R. F. Loewensteinet al. (unpublished manuscript, 1980) and Hildebrand et al. [1980] are displayed also, as they were made during times when the ring
systemsubtendedan angle of 1o or lessas viewed from the
earth, so that their flux contribution relative to that of the
planetarydisk is consideredto be negligible.
The earth-basedobservationsare largely in agreementwith
our predictedspectra.A notable exceptionis the 40- to 100-
cm-• spectralregion,where broad-band-pass-filtered
radiometry displaysa substantialdrop in brightnesscomparedwith
that in our models. If we chooseto interpret this as a real feature, then absorptionby NH3 or H•O vapor is extremelyunlikely if we assumethat theseconstituentsare in saturation
equilibriumat the ambienttemperatures.Other possibleconstituents(e.g., PH3, CO) must also meet the constraintsimposed by their influenceon other spectralregions.Ice candidates such as NH3 [Taylor, 1973] or even H:O [Irvine and
Pollack, 1968] do not have strong absorption in this region
and are therefore unlikely to succeedin explaining the observeddrop in brightness.Alternatively,it is possiblethat this
feature is an artifact of the earth-basedcalibration, providing
that there is a correspondingspectral feature in the atmosphereof Mars (the primary calibrationsourcefor both Loe-
ORTON AND INGERSOLL:SATURN'STEMPERATURES
AND HEAT BUDGET
5879
SATURN TEMPERATURESTRUCTUREMODELS
1X10
-3
i
I
I
5X10-3
-
1X10-2--
/
!
/
/
/
/
I
/
I
5X10
-2
1X10
-1
5X10-1
-
1'0080
100
120
140
160
TEMPERATURE
(K)
Fig. 12. Comparison
of temperature
structures
herewithsomeothermodels.
Solidlinesrepresent
the temperature
structures
shown
in Figure
7 (cases
1and2) andFigure8 (cases
1,2, and3).At pressures
lessthan3 x 10-:bar,cases
1
and3 (three
lines)
lietotheleftofcase
2 (twolines).
Atpressures
between
10-• and5 x 10-• bartheprofiles
fromFigure7
(twolines)lietotherightofthose
fromFigure8 (threelines).Longdashes
represent
thetemperature
structure
derived
by
Klioreetal. [thisissue]
frominversion
of Pioneer
11radiooccultation
egress
data.Intermediate
dashes
represent
theglobal
model
of Tokunaga
andCess
[1977].
Short
dashes
represent
themodel
ofJ.F. Appleby
andJ.Hogan
(unpublished
manuscript,
1980)
in which15%oftheincident
sunlight
isabsorbed
uniformly
in thestratosphere.
greaterthan15øN) thanfor latitudebinsin the7.5øwensteinet al. and Hildebrandet al.). We suggest
that higher- latitudes
resolution
spectralobservations
of thisregionwouldat least 22.5øS region.
quotedby Ingersollet al. [1980]
verifythepresence
of thefeatureaswellasdetermine
whether The effectivetemperatures
distinctabsorption
featuresbelonging
to a gas(asopposed
to are some 1.5-2.0 K cooler than those shown in Figure 14 owtreatment
of theopacities
in the 100-cm
-•
the relativelybroaderfeaturesof an ice or liquid) are detect- ingto anincorrect
region,whichproducedan underestimate
of the flux. That
able.
TOTAL
INFRARED
BRIGHTNESS
treatment was, however, more consistentwith the spectrum
measurements
of R. F. Loewensteinet al. (unpublishedmanu-
script,1980)and may be closerto the truevalueof the total
measurements
are correct.However,
servedwas computedby usingmodelspectrasuchas those outputif the earth-based
shownin Figure13.The modelspectrum
wasintegratedfrom for the sake of consistencywe will use valueswhich are de0 to 750 cm-•, and the observeddisk spectrumof Gillettand rived from the theoreticalspectra,dependentmostlyon the H2
Forrest[1974]wasusedat higherfrequencies.
The resultsare dipoleopacityas shownin Figure13. If we makethe exassumptions
of symmetryaboutthe equashownin Figure14.We seeimmediatelythat a strongsymme- tremelysimplifying
try exists
abouttheequatorandrelatively
constant
valuesap- tor and a constantflux polewardof 7.5øS,thenthe valuesfor
The total infrared flux from eachof the latitude regionsob-
pearbetween
7.5øSand22.5øSlatitude.Poleward
of 22.5øS total thermalemissionshownin Figure 14,integratedoverthe
the data imply a total flux outputlessthan that in the 7.5o_ sphere,imply an effectiveplanetarytemperature
22.5øSregion. However,we note that the data are subTear= 96.5 + 2.5 K
stantially
fewerin numberfor theseregions
(asin thecasefor
(3)
5880
ORTON AND INGERSOLL: SATURN'S TEMPERATURES AND HEAT BUDGET
120
CHANNEL 2
CHANNEL 1
45 Hm
20 Hm
11o
lOO
0
100
200
300
400
500
600
700
800
FREQUENCY
(½m
-1)
Fig. 13. Comparisonof the spectraof modelsderivedin this paperwith earth-basedobservations.
'•.•:•eupperpair of
solid curvesrepresentboundsof all spectracomputedfor the warm 13.5ø-16.5øSlatitude region.The lov;er pair of solid
curvesare boundsfor the cool 1.5øSto 1.5øN latitude region.The effectiveresolutionelementof the calculatedspectrumis
25 cm-'. The opacityof NH3 vaporis included,calculatedby usingthe band modelparametersof Gille and Lee [1969].
The opacityof C2H6(at 825cm-') is not included.Curvesat the top arethe relativeresponses
of the two channels.
Long
dashesand short dashesare somewhatschematicrepresentationsof the spectraof Ericksonet al. [1978] and of Gillett and
Forrest[1974], respectively.Crossesrepresentthe spectraof Tokunagaet al. [1977] with representativeerror bars at the
high- and low-frequency
extentof the data.Filteredphotometricobservations
are represented
at appropriat/•effectivefrequenciesby solidcircles[Rieke, 1975],opendiamonds[Nolt et al., 1977],soliddiamonds[Nolt et al., 1978],open triangles
[Knacke et al., 1975], open square[Morrison,1974], solid triangles(R. F. Loewensteinet al., unpublishedmanuscript,
1980),and open circle [Hildebrandet al., 1980].An additionalopencirclelies off the scaleat 139 K, 12.5cm-•.
The uncertainty quoted largely reflectsthe calibration uncertainty. The uncertaintiesinvolved in the model extrapolation
to long wavelengthsand to latitudessouthof 31.5øSand north
of 10.5øN are not included in this value, as we do not know of
a cogentway to quantify them explicitly.
GLOBAL
ENERGY
BUDGET
AND
INTERIOR
MODELS
However, the new value of Saturn's internal heat flux is
probablytoo largeto be explainedby simplecoolingand contraction [Pollack et al., 1977; Stevenson,1980]. An additional
energysource,precipitationof .':.•elium
at the top of a metallic
hydrogenliquid interior, could supply someof the extra energy [Kieffer, 1967; Stevensonand Salpeter, 1977], but even
this energysupply is limited. Stevenson[1980] estimatesthat
Saturn'stotal emitted power per unit area is about 4.9 + 0.5 depletionfroman initial25%heliumby mass(a, 2= 0.86)to a
W m-2 accordingto (3). This valueis about0.4 W m-2 higher presentvalueof 15%(a,2 • 0.92)in theoutermolecularlayer
than that given in our preliminary report. In addition, there is
some evidence [Tomasko et al., this issue]that the phase integral of Saturn is about 1.50 insteadof 1.25, as observedfor
Jupiter. This raisesthe estimate of the Bond albedo •1 from
0.45 + 0.15 [Ericksonet al., 1978]to 0.54 + 0.15. The average
internal heat flux is then 3.2 + 1.0 W m -2, and the ratio of total emitted power to sunlightabsorbedis 2.8 + 0.9. The phase
integral and Bond albedo are still preliminary estimates,however, and the emitted flux was computedwith no information
poleward of about 40øS. Thus inferencesabout the internal
energysourceare still uncertainand subjectto change.
Nevertheless,it is clear from modelsof the coolinghistory
and interior [Pollack et al., 1977; Stevenson,1980] that 3.2 +
could accountfor a total internal heat flux at presentof 2.4 W
m-2, our preliminary published estimate [Ingersoll et al.,
5100
97.0
49oo
96.0 •'e
4700 -95.0
1.0W m-2 is a largeinternalheat flux for Saturn.For Jupiter
the Pioneer 10 and 11 IRR gave an effectivetemperatureof
125+_3 K [Ingersollet al., 1976].The photopolarimeter
gavea
phase integral of about 1.25 and a Bond albedo of 0.35 [Tomasko et al., 1978].When combined,theseimply an internal
heat flux of 5.6 W m-2, a valuethat agreeswith modelsof Jupiter's cooling history starting with gravitationalcollapse4.5
b.y. ago [Graboskeet al., 1975].
4.5OO
I
30øs
20øs
10øs
0ø
10øN
LATITUDE
Fig. 14. Total outgoing infrared flux (or local effective temperature) plotted as a function of latitude. Values are derived from integrationof the appropriatespectraalongwith considerationof earthbased observations[Gillett and Forrest, 1974] for frequenciesgreater
than 750 cm -l.
ORTON AND INGERSOLL: SATURN'S TEMPERATURES AND HEAT BUDGET
1980].Precipitationof additionalhelium doesnot resultin a
substantially
higherheat at present.Thuswe mightexpectdepletionof heliumin the atmosphere
of Saturn,thoughperhapsnot on Jupiter,to explainthe excessinternalheat flux.
Such a differencebetweenthe two planetsis consistentwith
interior models [Stevensonand Salpeter, 1977].
Direct estimatesof the atmospherichydrogento helium ra-
5881
of the infrared radiometerexperimenton Pioneers10 and 11, in Jupiter, edited by T. Gehrels, pp. 197-205, University of Arizona
Press, Tucson, 1976.
Ingersoll,A. P., G. S. Orton, G. Miinch, G. Neugebauer,and S.C.
Chase,PioneerSaturninfrared radiometer:Preliminary results,Science, 207, 439-443, 1980.
Irvine, W. M., and J. B. Pollack,Infraredopticalpropertieso•fwater
and ice spheres,Icarus, 8, 324-360, 1968.
Kieffer, H. H., Calculatedphysicalpropertiesof planetsin relation to
compositionand gravitationallayering,J. Geoœhys.
Res., 72, 3179-
tio are clearlyimportant.The atmosphere
is likely to reflect
the bulk compositionof the entire molecularenvelope,be3197, 1967.
causeconvectionprovidesrapid mixing.The hydrogento he- Klein, M. J., M. A. Janssen,S. Gulkis, and E. T. Olsen, Saturn's mi-
crowave spectrum:Implications for the atmosphereand the rings,
NASA Conf. Publ., 2068, 195-216, 1978.
Kliore, A. J., G. F. Lindal, I. R. Patel, D. N. Sweetnam, H. B. Hotz,
and T. R. McDonough,Vertical structureof the ionosphereand the
solar value is difficult to establish. But neither our estimate for
upper neutral atmosphereof Saturnfrom the Pioneerradio occultation, Science,207, 446-449, 1980.
Saturn'satmosphere,
a.2 = 0.90 +_0.03, nor Gautieret al.'s
[1980]estimate
for Jupiter'satmosphere,
a• = 0.897+_0.024, Kliore, A. J., I. R. Patel, G. F. Lindal, D. N. Sweetnam,H. B. Hotz, J.
H. Waite, Jr., and T. R. McDonough, Structure of the ionosphere
is significantlydifferentfrom the solarvalue,thoughboth are
and atmosphereof Saturn from Pioneer 11 Saturn radio occulthigh. It is possiblethat helium depletionhas taken placeon
ation, J. Geoœhys.
Res., this issue.
both planets,but the evidenceis inconclusive.
Thus it appears Knacke, R. F., T. Owen, and R. R. Joyce,Infrared observationsof the
surfaceand atmosphereof Titan, Icarus, 24, 460-464, 1975.
that our measurementsare not quite accurateenoughto resolve theseimportant questionsabout the historiesof the gi- Morrison, D., Infrared radiometry of the rings of Saturn, Icarus, 22,
liura ratio for the planet as a whole is likely to be no greater
thanthesolarcomposition
value,for whicha. 2= 0.88according to oneestimate[Cameron,1974].The uncertaintyin this
ant planets.
Acknowledgments.The Pioneerproject staffprovided reliable support during all phasesof the mission.J. D. Bennett,M. Schroeder,B.
Schupler,and J. C. Ingersolldevelopedcomputercodesfor analyzing
the data. G. Munch, G. Neugebauer,and S.C. Chasepresidedat the
creation of this simple but reliable instrument.R. A. Hanel provided
a helpful review of the manuscript.We thank them all.
The Editor thanks R. A. Hanel for his assistancein evaluating this
paper.
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revised June 2, 1980;
acceptedJune 3, 1980.)
Ingersoll,A. P., G. Miinch, G. Neugebauer,and G. S. Orton, Results
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