Structure of the Atmosphere of Mars in Summer at Midlatitudes

VOL. 82, NO. 28 JOURNALOF GEOPHYSICALRESEARCH SEPTEMBER30, 1977

Structureof the Atmosphereof Mars in Summerat Mid-Latitudes

ALVIN SEIFF AND DONN B. KIRK

AmesResearch Center, NASA, Moffett Field, California94035

The structureof Mars' atmospherewas measured in situby instrumentson boardthe two Viking landersfrom an altitudeof 120km to nearthe surface.The two entrieswere separated by 178ø in longitude,25 ø in latitude,45 dayselapsed time, and 6 hoursin Marslocal time. Atmosphere structure was verywell defined by themeasurements and was generally similar at thetwo sites.Viking 1 and2 surface pressuresand temperatures were 7.62 and 7.81 mbar and 238øK and 226øK, respectively, while pressures at theelevation of the referenceellipsoid were 6.74 and 6.30 mbar. Mean temperature decreased with a lapserate of about1.6øK/km, significantly subadiabatic, from above the boundary layer to about40 km, thenwas near isothermal but with a large-amplitudewave superimposed, attributed to thediurnal thermal tide. The meanprofile appears to be governedby radiativeequilibrium. Differences between the two temperatureprofiles are dueto diurnaleffects in the boundarylayer, a smallcooling of the Viking2 profileup to 40 km dueto latitudeand season, and effects bf timeof day,latitude, terrain, and season on thewave structure. The density data merge well with those of theupper-atmosphere mass spectrometer to definea continuousprofile to 200 km. The temperaturewave continues above 100 km, increasingin amplitudeand wavelength.

INTRODUCTION ing dataof comparablequality to that normallyobtained from Knowledgeof the structureof the neutralatmosphere of meteorologicalsounding techniques [Seiffet al., 1973].A de- Mars has advancedrapidly in the age of spaceastronomy. scriptionand discussionof the techniquesand instruments Remotesensing experiments from flyby and orbitingspace- whichhave been applied to the Vikingmission has been given craft have indicatedthe mean surfacepressure to be near 5 [Seiff, 1976]. mbar, muchlower than was previouslyaccepted (see, for ex- This paper reportsthe resultsof the atmospherestructure ample,Ktiore et at. [1972]),and in conjunctionwith ground- measurementsfrom Viking 1 and 2 as of May 1977. The basedspectroscopy have indicated that the atmosphereis pre- analysisof the data is not yet completein all respects,but we dominantlyCO•,. Remotesensing has also indicatedthat the expectthat the materialwe presentherein will be substantially temperaturestructure up to 45-km altitude is highly variable, unchangedby furtheranalysis. Two topicsnot yet readyfor dependenton latitude, season,and the dust content of the reportingare omittedmdataon thewinds encountered during atmosphere[Ktiore et at., 1972;Hanel et at., 1972]. entry and descent of the two landers and data on the terrain The temperature data have been limited to the lowest 35 km underthe entry trajectories.These will be the subjectof later (occultation)and 45 km (IR sounding)and have beensome- reports.Preliminary accounts of the atmosphericdata have whatpuzzling and hardto assessbecause of their diversity.It beengiven [Nier et at., 1976;Seiff and Kirk, 1976]. hasnot beenpossible to sayconclusively what accuracy, tem- peratureresolution, and altituderesolution should be assigned INSTRUMENT DESCRIPTION to these results. The overall definitionof the structureof Mars' atmosphere The USSR spacecraftMars 6 made some measurementsof to be describedherein was a result of synthesisof data from the atmospherestructure during its entryinto Mars in 1974 severalinstruments. In the upper regionsof the experiment, [Kerzhanot)ich,1977]. Very usefulinformation was obtained, altitudes from 120 to 26 kin, a set of three-axis accelerometers althoughit was limited by the lack of direct temperature measured the atmospheric density as a function of altitude sensing,an extensiveradio blackout, and accelerationsensing from the vehicledeceleration. To calibrate this measurement,a confinedto four points. It confirmedthe magnitudeof the thorough and extensiveground test programwas conductedto surfacepressure obtained from remote sensing, measuring 5.45 definethe drag coefficientas a function of velocity and Rey- + 0.3 mbar, and put boundson the temperaturestructure, nolds number in an atmosphereof CO2. Thesetests were made indicatinga lapse rate of 2.9øK/km up to 33 km and an with models of the Viking entry configurationin free flight isothermalmiddle atmosphere at 149ø + 8øKto 90 km in early through a ballistic range. springin the southernhemisphere (-24 ø latitude).There was During parachutedescent, which began nominally at 6 km, significantuncertainty in temperaturesbelow 30 km, with a pressure and temperature were directly measured. Also maximum of +18 ø at 29 km. throughout the high-speedentry the flow stagnationpressure The Viking missionprovided an opportunity for in situ was measured, and below about 25 km the flow recovery measurementsof the atmosphere,and experimentsto make temperature(a temperatureclosely related to stagnationtem- useof that opportunitywere describedby Nier et at. [1972]. perature) was directly sensed. The atmospherestructure measurement approach, initially The lander sytemsprovided three kinds of data which were proposedin 1962 [Seiff, 1963], was the subjectof intensive important to the determinationof atmospherestructure: (1) studyand development in theensuing 9 years,culminating in a altitudes, from a radar altimeter; (2) attitude changedata, testflight of the experimentin the earth'satmosphere in 1971. from gyroscopes,which were usedin the determinationof the Thisexperiment showed that thetechniques for measuringthe trajectoriesand for analysisof wind effects;and (3) velocity atmosphereduring high-velocity entry were capable of provid- data during parachute descent,from a three-axis Doppler radar. Copyright¸ 1977by the AmericanGeophysical Union. The nominal measurementaltitudes, telefnetry resolution,

Paper number 7S0499. 4364 SEIFF AND KIRK: STRUCTUREOF THE ATMOSPHEREOF MARS 4365

TABLE 1. Viking Atmosphere Structure Instruments

Measurement Telemetry Sample Altitude Sensors Altitudes, km Resolution Interval, s Resolution, km

Accelerometer 120-0 A V = 0.0127 m/s 0.1 0.006-0.1 Pressure Aeroshell* 90-6 0.16 and 0.74 mbar 0.2 0.01-0.5 Parachuter 4.5-1.5 0.085 mbar 0.5 0.03 Temperature Aeroshell 27-6 1.2øK 1.0 0.01-0.1 Parachute 3.8-1.5 1.2øK 0.5 0.03 Radar altimeter 132-0 5 m 0.2 0.01-0.2 Doppler radar (TDLR) 5-0 0.06 m/s 1.0 0.012 Gyros 250-0 0.0008ø 0.1 0.006-0.1

*The aeroshellphase of the experimentis from entry to nominally 6-km altitude. t The parachutephase is from 6 km to descentengine ignition at 1.5 km. sampling intervals, and altitude resolution of all these mea- obliquely upward. Thesesensors were retainedwith the lander surementsare shownin Table 1. These were generallymore through the landing and provided necessaryguidance data as than adequatefor atmosphericdefinition. The accuracyof well as scientificdata on the atmosphere. definitionof temperatureand pressuregradients with altitude The pressureinlet during high-speedentry was at the nomi- in the parachutedescent was constrainedby telemetryresolu- nal flow stagnation point on the heat shield at the entry atti- tion, as discussedbelow, but it was possibleto definethese tude. The aeroshell temperature sensor was deployed at a gradientsto the order of 1% or 2% on pressureand to within velocity of 1.1 km/s through the surface of the conical heat 0.1øK/km on temperature,or better. shieldto a position safelyoutside the aeroshellboundary layer, The locations of the sensors on the landers are shown in where it could sensethe atmosphericrecovery temperature, Figure 1. The accelerometersand gyros were located within without convectiveinfluence by the heat shield. the inertialreference unit, externalto the landerbody, along The pressureinlet during parachute descentwas mounted the z axis,which was in the nominallyvertical plane, pointing on an edge of the lander body, with a Kiel probe geometry facing into the theoretical flow direction at that location (Fig- ure lb). This insured that the stagnationpressure was sensed. (O) AEROSHELL PHASE The temperature sensor in this phase was mounted on the inboard edgeof the footpad on landing leg 2, whereit sampled LAA• .ACCELEROMETERS the temperature of oncoming stream tubes well away from thermal contact with the lander. This location also ensured a vigorousflow over the sensingelements at essentiallythe de- SENSOR• • .• scentvelocity. The location of the Doppler radar (terminal descentand landing radar (TDLR)) on the lander bottom is also indicated. Two altimeter antennaswere provided, one on the surfaceof the heat shield,used during high-speedentry, and the other on the lander bottom (LAA), usedduring parachute descent. _ The accelerationsensors were derivedfrom guidancequality ANTENNA'>?3"•TEMPERATURE accelerometersmanufactured by Bell Aerospace Company SENSOR (Bell model IX). They senseacceleration by electromagnetic- (b) PARACHUTE PHASE ally constraininga test mass to a precisenull position. The restoring force is provided by a current flowing in a coil • p SENSOR•=• mounted in the test mass, which reacts against the field of a • •_ LANDER •----•111 permanent magnet in the sensor.The nulling current is the measure of the acceleration. The scale factor accuracy achieved is believed to have been better than 0.02%, with bias uncertainties < 100 3tg. _ The temperature sensorswere multiple fine wire (0.0127-cm diameter) thermocouples,directly exposedto the atmospheric flow. They were designedto minimize errors due to spurious inputs (radiation, conduction, etc.) by maximizing thermal T SENS ' coupling to the atmosphere.Response times were typically •0.3 s in the aeroshellphase and 0.8 s in parachute descent. Referencejunction temperatureswere measuredwith platinum resistancethermometers, within the sensorhousing. "SAMPLED" The pressuresensors were thin stretchedstainless steel dia- phragms referenced to vacuum. Diaphragm displacementis Fig. 1. Location of atmospherestructure instruments on the Vik- ing landers.(a) The configurationof the spacecraftat atmosphere the measureof the appliedpressure. Unsupported diameters of entry. (b) The instruments on the landers after heat shields were the diaphragmswere --•2.5cm. Sensorcharacteristics are given jettisonedand parachuteswere deployedat a nominal altitude of 6 km. in Table 2. In a thorough preflight test evaluationthe sensors 4366 ENTRY SCIENCE

TABLE 2. Pressure Sensors

Displacement Mission Phase Range,mbar Repeatability Sensing

Aeroshell 0-150 +0.5% rdg capacitive 0-20 +0.5% rdg capacitive Parachute 0-18 +0.01 mbar inductive

were found to be stable through the flight environmentsin- beneaththe landers.In furtherdetail the atmosphericpressure cludingprelaunch sterilization and launchand entry vibration. providesa boundarycondition for the rocketjets, and thejets The sensortemperatures were nearly constant during entry block atmosphericflow from impingingon the landerbottom and descent.Data were correctedfor the effectsof temperature and hencesuppress dynamic effects on the pressuremeasure- on calibration where appropriate. ment. It is evident that pressuresmeasured then were within The design philosophy, development, and accuracy eval- 0.1 or 0.2 mbar of ambient.The effecton temperaturessensed uation programs for all these sensorshave been describedin was to raisethem abruptly,presumably a resultof mixingof detail elsewhere[Seiff, 1976]. Some remarks on the accuracies the rocket effluentwith the local atmosphere. achieved by the actual sensorsduring Mars entry will be incorporated into the discussionsof results below. PressureMeasurements and Landing Site Elevations ATMOSPHERIC MEASUREMENTS DURING PARACHUTE DESCENT Pressurewas sampledduring descentat 0.5-s intervals,cor- The two Viking landers deployedparachutes at altitudes of respondingto nominally30 m in altitude.The telemetryreso- 5.80 and 5.92 km abovethe terrain. Parachuteswere fully open lution was 0.085 mbar. Therewere typically 6-8 repetitionsof at 5.60 and 5.63 km, and the heat shieldswere jettisoned at the readingat every digital level, of which only the first are 5.03 and 4.96 km. This exposedthe parachutephase pressure plotted in Figure 2. Thesepoints have just surmounted,and sensors to the atmosphere, but there was some interference henceare very closeto, the readinglevel. It can be shownthat with both pressureand altitude data by the departing heat the effective resolution under these circumstances is the nomi- shield,down to an altitude of about 4.5 km. The temperature nal resolution/n,where n is the numberof readingrepetitions sensors,on the footpad of lander leg 2, were deployed at at the given level. Thus the effectiveresolution was about 0.014 altitudes near 3.9 km. From there until the terminal descent mbar. The curvesare put through the highestdata points, rocket engineswere ignited, at about 1.45 km, both landers sincewith pressurerising the resolutionerror is alwaysnega- transmittedgood-quality data on pressureand temperatureof tive. By this combinationof practicesthe uncertaintyin the the atmosphere(Figures 2 and 3). relative pressurelevels due to resolution was reducedto the Only a small fraction of the data points receivedare shown, order of 0.01 mbar. However,the uncertaintyin the absolute becausemany repetitionsoccurred at everydigital level. Cor- pressurelevel is up to 0.085 mbar becauseof resolutionuncer- rections made for dynamic pressureand temperatureeffects tainty in the zero reading. are indicated and will be discussed. These were of the order of The zero readingsof the sensorstaken just before atmo- 0.2 mbar and 1.5øK. sphereentry establishedthe zero readingsfor the measurement Below 1.45 km the descentrockets clearly affectedthe mea- period. For both landers the sensorsread a consistentzero surements,and no quantitative usewas made of the data. The level without deviationover a period of severalhundred sec- effect on measuredpressures was, surprisingly,to lower them onds prior to the actual pressurerise, and these readings to a level very near ambient. The jets aspirated the region differedby 0.10-mbarequivalent for Viking 1 and 0.027mbar 25OP / VlKIINGI 9 VIKING I _ / ½ DEPLOY [- • T SENSORS I08 f • , • • , 240• I"• meos. 7(•.•+..•. - i- .½*•+-•++.. / Pmeas DYNAMIC - T, p,mb / '• •'"'•./.• 'r•PREsSURE

220 • • • .... • • 1 t OTT,SO.t s,•,ss o, 1 .S,T s.•s,•sl

• DESCENTI JETTISON • _ - + , i , VIKING, 2 IOENGINES •Ni , H•ATSHIELBS • • 9- VIKING 2 _ + 250;+/ß• +• • - 8 - - 240- •Tmeos. - T, øK - } ,w2 4 - p.mb •. ' PRESSURE ) I 220-Tot = ß - ß 5 Pot _ 210 • • • • I 4 I I I I o I 2 3 4 5 6 0 2 5 4 5 6 z, km z, km Fig. 3. Atmospherictemperatures; direct sensingin the lowest 5 Fig. 2. Pressuresmeasured during parachutedescent. Dynamic kin. Dynamic correctionsare of the order of 2øK. The altitude of full correctionsare indicated.The equationsdefine the variation of atmo- deploymentof lander leg number 2, on which the sensorwas mounted, sphericpressure with altitude in the parachutephase. can be readily identified. SEIFF AND KIRK: STRUCTUREOF THE ATMOSPHEREOF MARS 4367

for Viking 2 from those obtained in calibration in uncertainty is 0.04 mbar in a large population of measure- July-November 1974.The repeatabilityof sensorscale factors, ments. from data taken over the course of 4 months during the Pressuresmeasured after landing on sol 1 at the sametime of preflight test program in which the sensorswere exposedto day by the same sensorwere reported by the Viking Mete- vibration, thermal cycling, etc., was better than 0.2% or 0.01 orology Team [Hesset al., 1976a]. These points are shown by mbar at 5 mbar. The Viking 2 sensorcalibrations were inde- circular symbolsat z = 0 in Figure 2. They are in satisfactory pendent of sensor temperature within the data scatter. For agreement, within the telemetry resolution, with those pro- Viking 1, scalefactor changedby 0.018%/øC, which, for 10ø jected downward from the parachute phase data. The scale uncertainty in sensor temperature during the measurement heightsat ground levelwere determinedfrom the pressuredata period, would lead to 0.01-mbar error at 5 mbar. Overall, we to be 11.70 km (Viking 1) and 11.36 km (Viking 2). Equations believe the errors due to calibration uncertainties to be within for p(z) suitablefor usein the lowest 30 km (Viking 1) and the 0.01-0.02 mbar. lowest 5 km (Viking 2) are given in Figure 2. The dynamic pressurecorrection «pV• proceedsiteratively The pressuredifference recorded betweenthe two landing with the density initially defined from the uncorrectedpres- sites is the combined result of differencesin elevation, season, sure. The correction accuracy is estimated to be 0.004 mbar. and time of day. The elevationswere best given by the radio Lander descentvelocities on the parachute were between 50 determinations of the landed radii 3389.38 q- 0.08 and 3381.88 and 90 m/s. Dynamic pressurecorrections were applied to the q- 0.22 km [Michael et at., 1976] in relation to the equipoten- individual data points, prior to the defining of the curve tial referenceellipsoid radii at the landing coordinates3390.87 Patrn(Z),and the correcteddata are shownby the heavy dotsin q- 0.23 and 3384.33 q- 0.23 km, respectively[Christensen, 1975]. Figure 2. These data indicate landing site elevationsrelative to the refer- For Viking 2 the plot of log p versusz was highly linear, enceellipsoid of- 1.49 + 0.24 km (Viking 1) and -2.45 q- 0.32 consistent with the isothermal character of the lowest 4 km of km (Viking 2). (The relative accuracyof thesetwo determina- the atmosphere.For Viking 1 a linear fairing also represented tions should be significantlybetter than the absolute accu- the pressuredata very well. For both setsof data, however, a racy.) Thus the secondlander came to rest 0.96 km lower than curve of the form the first, relative to the equipotentialsurface. Pressures at the equipotential surface at the times of landing are determined p/po = exp (-z/Ho - k•.z•') from Figure 2 to be 6.74 mbar (Viking 1) and 6.30 mbar was definedto representthe curvaturein the log p(z) plot and (Viking 2). The difference,0.44 mbar, reflectsprimarily the to merge smoothly with the lowest few pressuresobtained seasonalreduction in surface pressurebetween the landings. from the accelerometrynear 30-km altitude. The values of The seasonaldecrease reported (Viking Meteorology Team, surfacepressure p0 definedby simple logarithmic extensionof private communication,1977) was 0.56 mbar at the Viking 1 the data between1.5 and 4.0 km were 7.64 mbar for Viking 1 site. The effect of diurnal variations was significantat the and 7.81 mbar for Viking 2. The values defined by non- Viking 1 site, the pressureat the time of landing being 0.12 isothermal fits were 7.62 and 7.80 mbar, respectively.The mbar below the daily mean [Hess et at., 1976a].Subtracting recommendedvalues are 7.62 and 7.81 mbar, sinceViking 2 this from the seasonaleffect, 0.56 - 0.12, gives0.44 mbar. was indeed very closeto isothermal below 4 km. Hence the measurementsof pressureand of landingsite eleva- The fitted equationshad rms deviationsfrom the data points tion are consistent with the seasonal and diurnal variations of the order of 0.003-0.007 mbar, implying a high relative seenin the Viking meteorologyexperiment. accuracy in the measuredpressures. Since relative accuracy Temperature was important for definingthe slopesdp/dz usedin determining the mean molecularweight, pressuresare statedin Table 3 Selectedpoints from the temperaturedata from Viking 1 to the nearest 0.001 mbar. It must be understood that only and 2 are plotted in Figure 3. Sincethe sensorswere read every relative accuracyis implied, sinceabsolute accuracy is limited 0.5 s and readingswere repeatedat every digital level (7-15 by telemetry resolution of the zero reading. The maximum times on Viking 1), the effectiveresolution was •0. IøK, com- absolute uncertaintyis 0.085 mbar, and the expectedaverage paredto the telemetryresolution of 1.1øK. On Viking 2, which

TABLE 3. Lower AtmosphericState PropertiesFrom Direct Sensing

Viking 1 Viking 2

z, km p, mbar T, øK t>,* kg/m3 p, mbar T, øK p,* kg/m 3

0 7.620t 237.3t 0.01680t 7.820t 225.6t 0.01813t 0.5 7.301t 235.5t 0.01622t 7.48t 225.1t 0.01738t 1.0 6.994t 233.7t 0.01565t 7.16t 224.6t 0.01667t 1.5 6.707 231.8 0.01513 6.853 224.0 0.01600 2.0 6.427 230.1 0.01461 6.564 223.6 0.01536 2.5 6.150 228.3 0.01409 6.282 223.1 0.01473 3.0 5.885 226.5 0.01359 6.015 222.6 0.01413 3.5 5.635 224.7 0.01312 5.747 222.1 0.01353 4.0 5.39 222.8 0.01265 5.483 221.6 0.01294 4.5 5.16 222.1t' 0.01221 5.222 221.2t' 0.01235

For Viking 1, H0 = 11.697km, t• = 44.36 q- 0.41; for Viking 2, H0 = 11.363km, t• = 43.36 q- 0.35. *Calculated for t• = 43.49, R = 191.18J/kgøK. •'Extrapolated. 4368 ENTRY SCIENCE

encountereda nearly isothermalatmosphere below 4 km, the expression first 36 readingswere at a commondigital level,followed by 52 # = R•,T/gH (2) readingsat the next level, and one readingat a third level,just beforethe retro-rocketswere ignited. Every eighth one of these where R• is the universalgas constant,g is local acceleration data points is shownin Figure 3, but only the first at eachlevel due to gravity, and H is scaleheight. All planetaryproperties was usedto establishthe lapserate with an effectiveresolution on the right side of these expressionswere determinedby of 0.02 ø K. measurements.The accelerationdue to gravity determined The sensorreference junctions were at 265ø on Viking 1 and from the accelerometersafter landingwas extended upward as 263.7ø on Viking 2. The sensorswere automatically com- (R0 + z) -2. The accuracy-determiningfactor is dp/dz, which pensatedfor cold junction temperature by meansof a resist- couldbe definedonly to within about 1%in the presenceof the ance network employing a platinum resistanceelement, but a finite telemetry resolution. small residualcorrection was applied, as definedby the pre- The mean molecularweight from Viking 2 data was 43.34 + flight calibration data. The calibration data were repeatable 0.8%. This is the average of six values at 0.5-km altitude within +0.1øC, and interpolationerrors betweenthe widely incrementsfrom 1.5 to 4.0 km. The largestdeviations from the spacedcalibration points are estimatedto be lessthan 0.2øC. mean occurred at the end points, where dp/dz is less well The accuracyexpected from thesedata had beenextensively determined. Without the two end points the mean value is

analyzed in advanceof flight [Seiff, 1976] and was concluded 43.36-0.4%'+0.2% The derivativewas determined from the equations to be • 1øK, after consideration of errors due to the electron- fitted to the pressuredata, of the form p/po = exp (-k•z ics, responselag, conduction and radiation, calibration uncer- - k2z2),to accommodatepressures measured near 30 km (see tainties, and error in the dynamic temperature corrections. below). The fits were both within 0.007-mbar rms, well within The data presentedare still subjectto small refinements,of the the accuracyof determinationof pressure. order of IøK overall, by application of correctionsfor small Since the Viking 2 parachutephase data were essentially perturbationsdue to conductionand radiation. Lag and dy- isothermal,# was also calculatedfrom the isothermal relation- namic correction errors are presently •0.1 ø or less. ship to obtain 43.82 at z = 2.5 km, T = 223.1øK, and g = The dynamiccorrection is givenby r!,a/2c•,,where c•, is the 3.7252 m/s 2. This is slightly outside the scatter band of the specificheat at constantpressure of the atmosphere,V•/2c•, is more precise measurement. the temperatureincrement from conversionof kinetic energy The Viking 2 mean molecularweight agreeswell with that to thermal energyin the gas flow approachingthe sensor,and derivedfrom atmosphericcomposition data. The landedmass r, the recoveryfactor, is the fraction of this energyactually spectrometer has reported a mixture of CO2 with 0.027 + experiencedby sensorsin laboratory calibrations in 6-mbar 0.003 mol fraction of N2, 0.016 + 0.003 mol fraction of Ar, CO2 flows. The fraction r = 0.80 for the nominal wire diameter and 0.0015 + 0.0005 mol fraction of O2 [Owen and Biemann, Reynoldsnumber (8.4) and Mach number(0.23) duringpara- 1976], for which the mean molecularweight is 43.486 + 0.066. chute descent.The correctionsto the individual data points The presentmeasurement corresponds to a nitrogen fraction range from 1.3ø to 2.3 ø. of 0.035 for argon fractionsof 0.013-0.019. Straight lines put through thesedata points so as to pass Similar analysisof the Viking 1 data gave# = 44.36 + 1.0%, through the highestcorrected points and within the resolution and a simplescale height analysis gave 44.21, about 2% higher uncertainty of all lower points indicate lapse rates of than the Viking 2 and the massanalysis values. A considerable 3.7øK/km and 0.97øK/kin and are shown in Figure 3. The effort was made to understandthis discrepancy.It could be difference is a diurnal effect, as will be discussedbelow. Sur- due to accumulationof maximumpossible errors in pressure face temperaturesare indicated. and temperature.The measurementof T is accurateto •0.4%, The linear lapse rate definedby the lower two points from and while the molecular weight is insensitiveto scalefactor Viking 2 passesslightly above the third point. This indicates errors in pressure,since • • p-• dp/dz, it is sensitiveto bias that the initial reading at the 223.3øK level would have been errors in pressure,such as that due to the resolution uncer- observedto a somewhathigher altitude with earlierleg deploy- tainty in the zero reading, which could be as large as 1.5%. ment. Hence an accumulation of the maximum expectableerrors Ground level atmospheric temperatures obtained on the could add up to 1.9%.Two other possibleexplanations for the first day after landing, at the same Mars local time, from the discrepancyare (1) that the smalldynamic corrections require meteorologytemperature sensor are plotted as circular sym- further refinementfor the effectsof wind (a first-ordercorrec- bols on the T axis. Agreementis satisfactorybut suggestsa tion for wind is already incorporated)and (2) that the defini- region of slightly increasedlapse rate near the surface. tion of dp/dz has been affectedby terrain slopesunder the The steadinessof the temperaturereadings on both landers, lander. During the descentfrom 3.5 to 1.5 km the lander was evidencedby a complete lack of fluctuation in the data re- transportedabout 0.7 km horizontallyby winds, and if terrain turned, indicatesa thermally homogeneousatmosphere. Be- elevationchanged by 40 rn along this track, the mean molecu- cause the sensorresponse lag was 0.77 s (at 2.5 km), small lar weight would be close to that expected from the other fluctuations (• 1ø) of •20-m scalecould have occurredwith- measurements.The necessaryground slope is 3.27ø . It has out detection. been reported that the lander came to rest at an angle of 2.99o-3.6ø [Mutch et al., 1976], and the samesource reports, Mean Molecular Weight 'The topography(around Viking 1) is gently rolling .... The nominal horizon is 3 km away; however,nearby hills obscure Mean molecular weightswere determinedfrom data given our view of large segmentsof the far horizon.' We may have in Figures 2 and 3. The defining relationshipis detectedthis topographyin our molecularweight analysis. • = -(Ru r/pg) (dp/dz) (1) The molecular weight analysishas another significance.It shows the internal consistencyof the measurements.Even which is a generalizationto a nonisothermalatmosphere of the includingthe extraneouseffects of winds and terrain, the entire SEIFFAND KIRK: STRUCTUREOF THE ATMOSPHEREOF MARS 4369 set of measurements is consistent to within 1% or 2% in mean FREE MOLECULE FLOW molecular weight. 2.0 • , , , , AtmosphericDensities and Tabulated \xSLI•I P a= II .2 ø- '\ FLOWI _ State Properties CONTINUUM

The atmosphericdensities computed from the pressureand 4.63.4 1.6 4.6•2A - temperatureprofiles for • = 43.49 are plotted in Figure 4 and CD1.8 \\\\\\•' FLOW / - listedin Table 3, togetherwith the pressuresand temperatures I .4 4.6 4.6km/sec _ at 0.5-km intervals,scale heights, and meanmolecular weights determined from the experiment. 1.2 ATMOSPHERE RECONSTRUCTED FROM ACCELEROMETER DATA I02 I03 I04 I05 I06 I07 REYNOLDS NUMBER i i i i i i i i The determinationof the density,pressure, and temperature 115 I00 80 60 of the Martian atmospherefrom an altitude of about 120 km z, km to an altitude of about 26 km dependedprimarily on data from 1.7 [ [ [ ] / accelerometerscarried on board the entry vehicles.In its sim- a: l l.2ø-I plest sensethe densityof the atmosphere,p, is proportional to .71•5 12xio 5 ,..,• J CD the accelerationalong the flight path, -as, through the equa- 1.6•" '• 2•( IOt tion 0 I 2 3 4 5 p = -2mas/CoA Vr2 (3) V, km/sec Fig. 5. Drag coefficientsused to reconstructthe atmosphere.Test where m is the vehicle mass, Co the aerodynamic drag points are at velocity-Reynold number combinationswhich lie along coefficient, A the vehicle cross-sectionalarea, and Vr the ve- the nominalentry trajectory.The angleof attack is near the equilib- hicle velocity relative to the atmosphere.The massand refer- riumflight attitude. The jump in Cojust below Re = 105is due to l,aminar turbuleht transition in the vehicle wake and is also seen in the ence area are known cohstants,and the velocity can be contin- flight accelerometerrecords. ually tracked from the on-board deceleration measurements.

., The analytical approachused to definethe vehicletrajectory 9ariationsof Cowith Reynolds number arid velocity shown in from the measured accelerationsby use of the equations of Figure 5 for continuum flow. The accuracy with which the motion is describedin Appendix A. This analysisyields the dragcoefficient was measured was withig 1%(Appendix B). vehicle velocity and altitude as functionsof time and usesthe altimeterdata as an input.The measureddensities are coupled For altitudesabove 90 km the entry vehicleReynolds number drops below 1000, and continuum flow gives way to slip with the reconstructed altitudes, which differ somewhat from the measured altitudes because of variable terrain elevation flow. Near 115km, freemolecule flow begins.For thisregion we have not yet collectedcalibrating test data, although work and roughness,to definep(z), from whichp(z) is derivedunder is currentlyin progressto do so, and onepreliminary measure- the assumptionof hydrostaticequilibrium. From p, p, and • ment confirmsthe slip flow curveto within 5% at Re = 460. the temperature profile is obtained through the equation of state. We haveused literature values for thetransitional regime from continuumto free moleculedrag of si•heres[Masson et al., In (3) the drag coefficientmust be known precisely,since 1961] to model similarly the transitiori from laminar contin- fractional errors in Co are the negativeequivalent of fractional uumCo = 1.47to an assumedvalue of 2.0 in freemolecule errors in density.The drag coefficientwas measuredin a series of simulationfligh[ tests in the laboratory,by the useof a flow, with Knudsen number as the governingparameter. Ac- cordingly, the density results above 90 km are less accurate ballistic range with an atmosphereof CO2. Parameterssimu- than those below 90 km. lated were model velocity, Reynoldsnumber, gascomposition, and, of course, model geometry [Intrieri et al., 1977; P. F. Acceleration Data

Intrieri, personalcommunication, 1976]. These tests led to the The axial acceleration data from the two entries are shown in Figure 6. The accelerationswere integrated on board the .020

80 ,

.016 6O

.01 2 p, kg/m3 / / \ \ MORTAR .008

REFERENCE ELLIPSOID ELEVATIONS .004 - VIKINGI VIKING2 - II606..../ / •II760•,VlKING2 11860.... MORTAR IIl•O

t I I I I I I' I

0 2 3 4 5 i Z, km I 1500 I 1600 11700 II 800 Fig. 4. Ne•ir-surfaceatmospheric densities above the Viking land- TIME; sec ing sites. Density at the referenceellipsoid was 0.015 kg/m 3 at both Fig. 6. Axial decelerationdata. Time is measuredfrom the instant of landings. separationof the lander from the orbiter. 4370 ENTRY SCIENCE

2.0 125 15( I I

I00 12• 1.6

75 I0(

50 7• MORTAR FIRE 25 5(

2• 11660 TIME,ii 760sec, VIKING • II 500 II 600 II 700 118oo I I I TIME, sec II 500 I 1600 11700 I 1800 TIME, sec, VIKING 2 Fig. ?. Viking 2 z axis accelerationdata.

Fig. 9. Altitude data. Viking landers and transmitted to earth as velocity pulse counts. Each axial pulse representeda velocity change of over long integrationperiods just prior to atmosphereentry. It about 1.27cm?s, and eachlateral axisacceleration pulse about is apparent that significantatmospheric decelerations are de- 0.32 cm?s.Atmosphere-relative velocities at entry (arbitrarily fined to an altitude near 125 km. definedas an altitudeof 244 km abovethe referenceellipsoid) Altitude data from the altimeters on Viking 1 and 2 are were 4.418 and 4.477 km/s, respectively,for Viking 1 and 2, shown in Figure 9. Thesedata, at five samples/s,are also near and so the axial velocityresolution provided was about 3 ppm continuous.They are uncorrectedfor variableterrain eleva- of the entry velocity.At l0 samples?sthe plotteddata appear tion and local roughness.These terrain characteristicscan be almostcontinuous. The peak axial deceleration,about 73 m/s •' extractedby detailedcomparison of the altimeter data with the on Viking 2 and 71 m/s •'on Viking 1, occurredat altitudesjust altitudes determined from the equations of motion analysis. above 30 km. Both Viking entries, by virtue of their near glancing in- The z axisacceleration data, normal to x in the planeof the cidencerelative to the atmosphereand the use of aerodynamic aerodynamiclift, are shownfor Viking 2 in Figure 7. They lift, experiencedperiods of essentiallyhorizontal flight extend- essentiallyduplicate the shapeof the axial decelerationprofile ing over about 50 km at altitudes near 28 km. It was found to but at a much lower level, peaking at 1.74 m/½. The ratio be difficult to carry the atmospheredefinition from the acceler- a•/ax is a measureof the aerodynamiclift-to-drag ratio and of ation data through this region successfully,because of extreme the landerinstantaneous angle of attack.The third component sensitivityof the resultsto very small variations in the near- of acceleration,ay, remainedessentially zero. zero flight path angleand possiblyalso because of wind effects. From Figure 6 it can be seen that the axial acceleration We believe that we will be able to accomplishthis, but it has thresholdextends to at least 11490s (Viking 2, z = 83 km), but not been done at this writing. Hence the accelerometricdefini- at higherresolution it is seento extendto appreciablyhigher tion of the atmosphere presently terminates at the region altitude (Figure 8). At early times, less than one count?sis where horizontal flight begins. beingmeasured, and the numberalternates between adjoining levels,reflecting the fact that fractionalvalues are beinginter- A tmosœhericProfiles preted by a data systemdealing only in integers.An 11-point The densitydata for the atmosphereof Mars derived from runningaverage of thesedata, representingthe meandecelera- the accelerometerdata of Viking 1 and 2 are given in Figure tion over an l l-s interval and plotted at the central point, 10. Over the altitude range from about 28 to 120 km, the producesthe smoothedvariation shown by the dots, which density ranges from 10-3 to 10-8 kg/m 3 with a mean scale exhibit small scatter about the fitted line. The line, in turn, height of about 8 km but with significantcurvature or wavi- merges nicely with the values of instrument bias determined nesson the log p (z) plot, evidence of temperature variation

r- -- i - -f T i r - -w---- + TELEMETERED DATA 120 - __ . IIPOINT AVERAGE / -T--T-nr•r•7T TTT r T r•-----T ' ''1' ' '•1 _

_ _ USEDINANALYSIS ++••++ - 80 - E - -..*;+:_*_t _. ++ ++ + + - --• 60- •, -

-+ + + + ++ + -- 40 - SENSOR _ BIAS 20

o I I I I1 I I I[1 I I t t]• , I iI , I t[I [ • 125I 120I 115I I10i 105i I00I 9I5 ALTITUDE, km 10-8 10-7 10-6 10-5 10-4 i0-;• 10-2

1146•4 I 14'54 11462' ll470' II4 •78 p, kg/m3 TIME, sec Fig. 10. Density profiles of Mars atmosphere to 120 km. Data Fig. 8. Viking 2 axial velocity pulse counts near threshold.The shown by curved lines above 28 km are derived from accelerations. telemetereddata have been correctedfor the small-velocityincrements Pointsare from stagnationpressures (circles, Viking 1; squares,Viking due to firing of the attitude control jets (note the occasionaldeviations 2). Densities from measuredpressure and temperature during para- from integral numbersof counts). chute descent are shown in the lowest $ kin. SEIFFAND KIRK: STRUCTUREOF THE ATMOSPHEREOF MARS 4371

120 ] VIKING2 _ I ] "•[ VIKINGI _

I00 80 •VIKING I _ 8O

"'60 VIKING2/ _- • _ E 40 _ • 60 E_ VIKING2/ [ • q-•.RAD. EQ.

_ 20- 40 o ",,, "••Tgnd= 260OK 20 I ADIABATk •%• Tpor,

Fig. l l. Variation of pressurewith altitude in Mars atmosphere. o Above 28 kin, pressureis derived from the density data, hydrostatic 80 120 160 200 240 160 200 240 equilibrium being assumed;below 5 kin, pressureis derived from T,øK direct sensingduring parachutedescent. Fig. 12. Atmospheric temperature profiles below 120 km from Viking 1 and 2. The wave structure is the dominant characteristic, Comparisonsare shown with the radiative equilibrium prediction of with altitude. Accuracy analysis indicates that the absolute Gierasch and Goody and with an adiabaticprofile. The condensation accuracyof the densitiesshould be within • 1% for the region boundarylies well below the atmospherictemperatures. A curvewhich seeksto definethe meantemperature • about whichthe oscillations of continuum aerodynamics,z < 90 km. At higher altitudes, are centered is indicated. presentuncertainties in the drag coefficientin slip flow and free molecule flow could lead to errors of the order of 10%. The pressurestructure is plotted in Figure 11, and the temperature profiles in Figure 12. Since the data are essentially SupportingData From AeroshellPhase continuous,they are representedby lines rather than discrete Pressureand TemperatureSensing points.Table 4 is a listingof the atmosphericstate properties The stagnation pressure readings taken throughout the at 4-km intervals.The parachutephase direct-sensing data are high-speedentry are convertibleto measurementsof atmo- includedon thesefigures to show their relationshipto the state spheric density through the relation properties determined by accelerometry.and to define the atmosphereto ground level. In addition, the data obtained from Cp,,= (ps- Patm)/(•Pl/rs) (4) aeroshellphase pressure and temperature.sensingare included wherein Cps,the stagnationpressure coefficient, is a theoreti- as symbols. These are describedbelow. cally known function of velocity (and weakly of gas composi. The wave structurein the temperaturesprofileswas identified tion), Ps/Patm • 500 for z ? 35 km (so that Patm can b•. in early discussionsas evidencefor strongthermal tidal os- neglectedin firstapproximation), and l/r is availablefrom the cillationsin the atmosphereof Mars. Theimplicationsof these trajectory reconstruction.The atmosphericdensities derived wavesin relationto theorywill be discuSSedin a later section. from theseindependent data are plotted as symbolson Figure

TABLE 4. AtmosphereState Propertiesfrom AccelerometerData

Viking 1 Viking 2 Altitude, km p, kg/m 3 p, mbar T, øK p, kg/m 3 p. mbar T, øK

120 1.60(-8) 4.14(-6) 136.3 8.86(-9) 1.99(-6) 116.0 116 2.42(-8) 6.91(-6) 149.2 1.69(-8) 3.76(-6) 115.5 112 3.95(-8) 1.12(-5) 148.6 3.08(-8) 6.98(-6) 118.2 108 6.59(-8) 1.84(-5) 146.4 5.62(-8) 1.30(-5) 121.1 104 1.06(-7) 3.03(-5) 149.4 9.36(-8) 2.35(-5) 131.8 100 1.67(-7) 4.94(-5) 154.8 1.42(-7) 4.01(-5) 147.9 96 2.88(-7) 8.02(-5) 145.9 2.30(-7) 6.60(-5) 150.2 92 5.39(-7) 1.38(-4) 133.6 3.63(-7) 1.08(-4) 155.1 88 8.33(-7) 2.33(-4) 146.7 5.79(-7) 1.74(-4) 157.5 84 1.40(-6) 3.87(-4) 144.2 1.06(-6) 2.88(-4) 141.4 80 2.57(-6) 6.70(-4) 136.6 2.11(-6) 5.08(-4) 126.1 76 4.66(-6) 1.16(- 3) 130.5 3.83(-6) 9.22(-4) 125.9 72 7.70(-6) 2.05(-3) 139.1 6.71(-6) 1.68(-3) 130.9 68 1.17(-5) 3.43(-3) 152.9 1.07(-5) 2.91(-3) 143.0 64 1.88(-5) 5.55(-3) 154.6 1.82(-5) 4.94(-3) 142.3 60 3.19(-5) '9.11(-3) 149.5 3.26(-5) 8.54(-3) 137.3 56 5.96(-5) 1.56(-2) 136.8 5.27(-5) 1.47(-2) 146.4 52 9.56(-5) 2.67(-2) 146.3 8.23(-5) 2.46(-2) 156.5 48 1.57(-4) 4.45(-2) 148.6 1.20(-4) 3.92(-2) 170.7 44 2.65(-4) 7.46(-2) 147.5 1.94(-4) 6.19(-2) 166.8 40 4.10(-4) 1.23(-1) 157.4 3.14(-4) 9.87(-2) 164.5 36 6.25(-4) 1.98(- 1) 166.1 5.04(-4) 1.58(- 1) 164.4 32 9.32(-4) 3.12(-1) 175.1 7.92(-4) 2.54(-1) 167.6 28 1.38(- 3) 4.83(- 1) 183.8 1.22(- 3) 4.04(- 1) 173.2

Read 1.60(-8)as 1.60 X 10-8. 4372 ENTRY SCIENCE

10 and show very satisfactoryagreement with thosegiven by densitieswere convertedto massdensities through the relation the accelerometers. 0 = •'•.Nd•/N,•,where N• isthe number density of speciesi, #t Although intuitivelyone would like to obtain atmospheric isits molecular weight, and N,• i s Avogadro's number. (A. O. C. pressurefrom stagnationpressure data, (4) cannotbe directly Nier has pointed out that we have a definitionof Avogadro's solvedfor Patmwithout knowledge of p and henceof Tatm. numberimplicit in the data in regionsof overlapof the UAMS That is, in the absenceof independentlyobtained temperatures and accelerometers.)To extend the data to the highestalti- the equationcannot give directly more than a first apprOxima- tudes,it was necessaryto extrapolatenumber densities of some tion of the atmosphericpressure. It is evident, though, that of the minor species.Furthermore, an allowancewas made for Patmcan be obtainedfrom p throughintegration of (14) in the presenceof atomicoxygen, based on the observat!0nby AppendixA and that if p(z) from the stagnationpressure Hanson et al. [1977] that a number density of 5 X 108was measurementagrees with that from the accelerometers,atmo- indicatedfor an altitudeof 135km on Viking 1. This observa- sphericpressures and temperatures will likewiseagree. tion was extended upward by assumingthat the O was in The recoverytemperature data taken during the aeroshell hydrostaticequilibrium, at the sametemperature as the other phasebelow a velocityof 1.1 km/s were usedto definethe neutral constituents.The implied assumptionis that there are temperatureofthe atmosphere in the altitude gap between the no chemicalreactions acting as a majorsource or sinkfor O in accelerometerand the parachutephase measurements. Since this altitude range, which may not be the case. With this atmosphericspecific heat is not constantover a broadrange of assumption,atomic oxygenbecomes an important bulk con- temperatures,the solutionproceeds through the enthalpies. stituentabove about 150 km, risingto a mole fraction of 0.4 at The relation betweenrecovery and ambient enthalpiesis 170 km. Neglectingthe O fraction would not, however,change the essentialcharacter of the log0 (z) plot. The densitieswould harm= hr d- (Ere/2)[(1 -- ?')(Vl/Vr)2 - 1] (5) be shifted downward by about 15% at 170 km, a small shift wherehr is the gasenthalpy at the recoverytemperature, V• is on the logarithmicplot. (The smalleffect of O on massdensity the local gasvelocity incident on the sensorwithin the lander is due to its low molecular weight relative to those of other shocklayer, and r is the recoveryfactor definedearlier. The speciespresent.) temperaturesfrom this analysisare shownin Figure 12 as the The UAMS densitypoints, although more widely spaced, plusesbetween 3 and 25 km. The continuityof the data with exhibit a curvature with altitude on the semilogarithmicplot the parachutephase direct sensingis good, and the data sug- similar to that shown by the accelerometer-deriveddensities. gestthat the wave structureof the temperatureprofile begins (Becauseof the relativelywide point spacing,some of the fine in this low-lying region,at initially small amplitudes. structuremay be lost.) Furthermore,it is possibleto join data from the two instrumentswithout any discontinuitiesin den- MERGING OF THE ACCELEROMETER AND UPPER-ATMOSPHERE sity or its gradientif the curveis not forcedthrough the last MASS SPECTROMETER DATA data point from eachinstrument. There is excellentreason to Densitiesof the atmosphereabove 120 km also were mea- givethese last-obtained points low weight.For the accelerome- suredby the Viking Entry ScienceTeam, by useof the upper- try the reasonis that the measurementis near threshold,whei-e atmospheremass spectrometer (UAMS) [Nier et al., 1976; accuracyis diminishing,and is in free moleculeflow, whei'eCo Nier andMcElroy, 1976;Nier andMcElroy, 1977].The possi- is more uncertain. For the UAMS the reason is that the bility wasrecognized well in advanceof the Viking entriesof instrument is becomingsaturated by the high inlet flux, and joining thesedata with the accelerometerdata to definethe the calibration is less certain; also, if the transition to contin- structureof the atmospherefrom groundlevel to •200 kin, uum flow has begun, the ground test data obtained in the and it was with some eagernessthat we comparedthe data molecular beam cannot give the ratio betweenmeasured and to seethe degreeof compatibilitythat existed.This is shownin free stream densitiesreliably. It is evident that the joining of Figure 13. these two setsof data was very satisfactory,and in combina- To preparethis figure,the UAMS atmosphericnumber tion they define the density profile essentiallyfrom ground level to nearly 200 km. The densityprofiles were usedto derivepressures and tem-

180 peraturesas describedearlier, by meansof (14) and the equa- •00II _l I11I I II II 11•-[ •r3F1•T--T•T• T T•T T-II•1 I I I1• I I II II • I$1 / tion of state, with the results shown in Figures 14 and 15. 140• Valuesof thestate properties derived from the UAMS dataare I•0 • 200 [ T I I lI T TT TT • • Tl•-T •l•'l T r TrI [ T•l T q-TTT- T •TF-T I •I 1 I [ I_ 80 •8o• • •0 160

40 140 •0 E 120 IKINGI - o

10-12 I0-11 I0-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2

p, kg/m:• 40 Fig. 13. Densityprofiles from groundlevel to 200 km obtainedby merging the massspectrometer and accelerometerdensity data. The 20• • mergingaltitude is around 120 kin. Differencesbetween the ¾iking ! 10-9 10-8 10-7 10-6 10-5 10-4 I0-$ 10-2 I0-1 I 0 and ¾iking 2 soundingsare the combinedresult of differencesin latitude, season,and time of day. ¾iking 1 landed at 22.3øN at 4:13 p, mb P.M. MLT on July 20, 1976,¾iking 2 at 47.?øN at 9:49 A.M. MLT on Fig. 14. Pressurestructure of Mars atmosphereto 200 km derived September3, !976. from measureddensit• profilesof Figure 13. SEIFF AND KIRK: STRUCTURE OF THE ATMOSPHERE OF MARS 4373

It should be explained that the starting temperature at the - '••VIKING I - highestaltitude dependson the starting pressure,which in turn 180- •f 22.3ø N _ • 4:1;5 PM LMT dependson the column densityabove that altitude. Since this - ( % JULY20,1976- was not experimentally determined, the starting temperature 160-VIKING 2•k k / - was fixed by fitting a straight line to the uppermost 10 km of _47.6øN k, / _ the density curve to define the scale height and hence the 140 -SEPT. 5, I - temperature at that level, which was used with the measured _ densityand compositionto compute the starting pressure. 120 COMPARISON OF ATMOSPHERE STRUCTURE E FROM VIKING 1 AND 2 ENTRIES .100 The atmospheredensity data from Viking 1 and 2 are com- pared in Figure 13. The first-order conclusionis that they are 80- •% - closely similar. In the lower atmosphere,below 50 km, den- sitiesseen by Viking 2 were as much as 28% lower than those seen by Viking 1. The two profilescome together around 60 40 km and approach closely near 100 km before diverging strongly above 100 km. Near the surface, Figure 4 showed zo larger densities for Viking 2 than for Viking 1, but if the difference in landed elevation is taken into account, then at the o 2oo referenceellipsoid, p0v,(0.0150 kg/m s) is essentiallyequal to T, øK p0v,(0.0148 kg/m•). Fig. 1•. T•mp•rat.r• o•th• D•.tral atmosph•r• from syDth•siso• all It is natural to inquire whether thesedensity profiles satisfy available entry sciencedata. the observedsurface pressure differences through the equation of hydrostaticequilibrium. The answeris yes,since hydrostatic listed in Table 5. The mean molecular weight was allowed to equilibrium has been assumedin interpretingthe accelerome- vary with altitude in the fashion shown by the U AMS data. ter data, and it has been shown that for both sets of data an The wave structuredetermined below 120 km continuesup- equationof the form p/po = exp (-z/H) (representingisother- ward in a continuous fashion, increasingin both wavelength mal hydrostaticequilibrium) fits the near-surfacedata well. and amplitude with increasingaltitude. Between 5 and 30 km, temperature variations with altitude Our procedure for deriving the temperaturesdiffers from require only that the scaleheight vary slightlywith altitude. that usedby Nier and McElroy [1977] in severalrespects. First, Since95% of the pressureat any altitude is contributedby it is applied to the smootheddensity variation indicatedby the the mass of gas within 3 scale heights upward, one might total set of data, including the merging of the accelerometer expectto find differencesin pressurebetween Viking 1 and 2 densitieswith the UAMS densities,rather than being a linear, that are greater at higher altitudesthan those at the reference point-to-point type of calculation.(We make no assumptionof surface, where the difference is 6.7%. This proves to be the local linearity.) Second,it usesthe total atmosphericdensity as case,as shownin Figure 14. A pressuredifference of • 15% of a basisrather than the number density of CO2 alone. Never- the mean occurs,for example, at 35 km. At 58 km, however, theless,the temperaturesfrom the two analysesagree within pressuresfrom the two soundingswere within 4%. 10ø or 15ø below 160 km but diverge at higher altitudes, If these data were simultaneous, they would indicate a althoughour valuesare generallywithin the uncertaintybars strong driving potential for atmospherecirculation at some which they have indicated. altitudes. However, they are not simultaneous, and so a

TABLE 5. Mass Densities, Pressures,and Temperatures Derived from UAMS Data

Viking 1 Viking 2

Altitude, Altitude, km p, kg/m • p, mbar T, øK km p, kg/m s p, mbar T, øK

200 3.30(-12) 1.05(-9) 102 174 5.80(-12) 1.93(-9) 115 195 4.70(-12) 1.67(-9) 125 170 1.07(-11) 3.06(-9) 112 190 6.62(-12) 2.53(-9) 143 166 1.90(-11) 5.04(-9) 112 185 1.13(-11) 4.02(-9) 139 162 3.23(- 11) 8.46(-9) 116 180 1.80(-11) 6.48(-9) 148 160 4.15(-11) 1.10(-8) 119 175 2.77(-11) 1.03(-8) 158 156 6.82(- 11) 1.83(-8) 125 170 4.21(-11) 1.61(-8) 167 152 1.13(-10) 3.05(-8) 129 165 6.27(-11) 2.48(-8) 177 148 1.81(- 10) 5.04(-8) 135 160 9.35(-11) 3.78(-8) 186 144 2.75(-10) 8.15(-8) 145 155 1.48(-10) 5.80(-8) 185 140 4.90(-10) 1.33(-7) 135 150 2.41(-10) 9.05(-8) 182 136 8.65(-10) 2.24(-7) 130 145 4.10(-10) 1.45(-7) 175 132 1.43(-9) 3.81(-7) 136 140 7.25(- 10) 2.39(- 7 ) 166 128 2.31(-9) 6.36(-7) 141 135 1.59(-9) 4.21(-7) 136 130 3.80(-9) 8.77(-7) 120

Read 3.30(-12) as 3.30 X 10-• 4374 ENTRY SCIENCE primary differenceto be consideredis the effect of seasonal We will not attempt a quantitative comparison with this condensationof the atmosphere[Hess et al., 1976b].Approxi- theory, simply becausethe casescalculated and presenteddo mately 7.35% of the atmosphereof Mars condensedbetween not coincide closely with conditions of season,latitude, and the landings of Viking 1 and 2. Thus the pressuredifference ground temperatureactually encounteredby the Viking land- between the two soundingsoscillates about this mean reduc- ers. However, it is possibleto examine the theory relative to tion. the observations and to draw some conclusions. The first Very sizablepressure differences are indicated betweenthe concernsthe important role of radiative equilibrium. two entries at altitudes above 100 km, e.g., a factor >2 at 150 The radiation equilibrium temperature profile for a clear km and a factor >5 at 170 km. Pressure differences of this (dust free) atmosphere (interpolated from paper A for a magnitude are suggestiveof very strong circulations in the ground temperatureof 260ø) givesa first-order representation upper atmosphere of Mars. These differences are a con- of the mean profiles observed (Figure 12). The differences sequence of the lower temperatures, hence smaller scale between the calculated and observed (mean)profiles could heights, of the Viking 2 upper atmosphere, which lead to possibly be explained by the presenceof dust in the lower increasingdifferences in density with altitude. Thus the num- atmosphere,which would be expectedto warm the dust-carry- ber densitiesof CO2 at 170 km are 4.9 X 108(Viking 1) and ing levelswhile shieldingthe higher levels from ground radi- 1.04 X 108 (Viking 2) [Nier and McElroy, 1977]. Pressureis ation to some degree. They could also be explained by an then lowered because of both density and temperature, but underestimateof atmosphericradiative absorption. ultimately, the lower temperature is the cause. The major effect of a dust storm on the temperatureprofiles A comparisonof the temperatureprofiles is given in Figure was well displayed during the early stagesof the Mariner 9 15. The remarkable thing that emergesis the very closecorre- mission [Hanel et al., 1972; Kliore et al., 1972]. Gieraschand spondenceof the two profiles. We were fully expectingto find Goody [1971] showed that an absorption of 0.1 of the solar significanteffects of the changein seasonand latitude, both of heating by dust in the atmospherewould modify their results which should tend to lower Viking 2 temperaturesrelative to to agree with the Mariner 9 data during the height of the those of Viking 1. The data show that their combinedeffect is storm. During the entriesof the Viking landersthe atmosphere to lower temperaturesa few degreesat altitudes from 5 to 35 was quite transparent, but there was evidencefor a small dust km and to lower the mean temperature4ø-10 ø up to 120 km. fraction, seen in the scatteringof sunlight to produce a pink A larger effect on mean temperature is seen above 120 km, sky [Mutch et al., 1976]. where the mean appearsto be about 126ø for Viking 2, com- The Viking 1 entry at 4:15 P.M. was at the time of day for pared to 150ø for Viking 1. In the intermediate altitudes, which paper B predictsa sharply defined tropopauseat alti- 35-100 km, the major differencesappear to be due primarily to tudes near 15 km, with essentiallyadiabatic lapse below that. the phaseand modal makeup of the diurnal oscillationand not This type of structure,predicted for winter and summermid- to differences in the mean. latitudes and for the equatorial region at equinox, was not The upper-atmospherictemperature differenceappears to encounteredby the Viking landers. be a result of one large dynamic half-wave extendingfrom 135 Below about 5 km the radiative equilibrium temperature km to upward of 185 km. Thus the differencein mean temper- profiles are unstable,for Tgnd= 260øK, and shouldgive way ature may be a consequenceof more vigorous dynamic os- to a region of adiabatictemperature lapse. Experimentally, the cillations at the near subsolar Viking 1 site. However, the lapserate remainsstable, in both the late afternoon and morn- direct solar heating of the upper atmosphere should also be ing profiles, down to the lowest altitude of observation, 1.5 greater at this location, and a diurnal effect (late afternoon km. Linear extensionof the measuredtemperature profilesto versusearly morning) may also contribute to the differencein the ground agreeswith the landed temperatures,sensed on sol upper-atmospherictemperatures. 1 at the sametime of day, to within 2.5ø on Viking 1 and 1.5ø In the lowest 5 km there is the diurnal difference referred to on Viking 2. If these comparisonsare error free, they would earlier. Thus we can summarize three differences between the admit an adiabatic lapseregion in the lowest 1.5 km of Viking temperatureprofiles at the two landing sites:(1) diurnal differ- 1 and the lowest 0.4 km of Viking 2. ences near the surface, (2) a small temperature difference However, there is a clear changein slopeof the profilesa few (•3ø-10 ø) below 35 km and in mean temperature up to 120 kilometersabove the surface,especially in the Viking 1 profile km due to season and latitude, and (3) a 25 ø temperature at 4 km, which suggeststhat a convectiveregion occursnear differenceabove 120 km, possiblycontrolled by dynamics. the surface.Since the temperatureprofile doesnot admit natural It will now be of interestto comparethese findings with pre- (thermal) convection,the data suggestthe presenceof turbu- Viking theoretical expectations. lent forced convection due to winds and a boundary layer thickness of 6 km, extending to 4 km above the reference COMPARISONSWITH THEORY, THEORETICALIMPLICATIONS ellipsoid. In the boundary layer the temperaturesare near adiabatic, indicatingthe occurrenceof vertical mixing, while Mean TemperatureProfiles aboveit they veer sharplyaway from the adiabat. Sincepoten- Processesgoverning the temperature profiles in the atmo- tial temperature increaseswith height in the boundary layer, sphere of Mars were studied theoretically by Gieraschand the forced convectiontransports heat downward. Goody[1967, 1968]. In the 1967paper (paper A) they calculate Forced convection can explain an adiabatic profile, but radiative equilibrium profiles,and in the 1968paper (paper B) some further explanationis neededfor the subadiabaticpro- they incorporate effects of free convectionand the diurnal filesobserved. Stone [1972] has indicatedthat stablelapse rates radiative wave emanatingfrom the surface,while arguingthat will occur in winds driven by baroclinic instability. Blumsack planetary-scalecirculation is not a first-orderconsideration in et al. [1973] incorporatean empirical dynamic vertical heat determining temperatures. Although dynamical oscillations flux term in their model and presentan examplein which the were not treated,they were alludedto as a possiblysignificant lapserate becomessubadiabatic roughly 1 scaleheight above phenomenon for Mars. the surface. Perhapsthese kinds of processesare responsible SEIFE AND KIRK: STRUCTURE OF THE ATMOSPHERE ON MARS 4375

TABLE 6. Measured Characteristicsof the Temperature Wave Structure

Viking I Viking 2

Peak No. z, km /XT, øK /Xz,km X, km z, km /XT, øK /Xz,km X, km

I 44.5 -3.5 +0.75 li 33 -5 +1.2 31 2 50 +4 - 1.0 12 48.5 + 14.5 -3.4 22 3 56 -7 + 1.7 20 59.5 -8 + 1.8 16 4 66 +17 -4.2 20 67.5 +6.5 -1.5 13 5 76 -10 +2.2 6 74 -10.5 +2.4 8 6 79 -2.5 +0.7 6 78 -9 +2.0 4 7 82 -8 + 1.8 9 80 - 10 +2.1 17 8 86.5 +6 -1.6 12 88.5 +21.5 -5.3 15 9 92.5 -9 +2.1 14 96 + 14 -3.6 8 10 99.5 + 12 -3.2 17 100 + 12 -2.8 20 11 108 +2.5 -0.9 13 110 -18.5 +4.2 8 12 114.5 +7.5 -1.8 23 114 -17 +3.7 8 13 126 -32 +7.5 68 118 -22 +4.9 19 14 160 +40 - 12.4 127.5 + 5 - 1.3 18 15 136.5 -7.5 +1.8 15 16 144 +9 -2.4 46 17 167 -25 +7.0

for stable lapse rates in the lowest 5 or 6 km of Mars atmo- amplitude.Their omissionfrom Table 6 would increaseX at 74 sphere. km to 12 km and at 88.5 km to 23 km. They are suggestiveof a The effectof the ground temperaturecycle in coolingthe tendencyfor a minor peak to appear from a mode locally out atmosphereduring the night and warmingit during the day of phase with the fundamentalmode. The reality of these was predictedin paperB to be limitedto the lowestlevels of detailsis not clear to us, but we are interpretingthem literally, theatmosphere, having little effectabove 5 km andlarge effect as measured.The most prominent of theseout-of-phase peaks only below2 km. This phenomenonis seenin the comparison is at 79 km on Viking 1. of Viking 1 and 2 near-surfacedata to extendup to --4 km There appearto be two or three peaks(not includedin the above the surface,and it is apparentlyvery much as antici- table) in the wave structureof the Viking 1 soundingbelow the pated. The heat exchangeis radiative,so that dust in the 45-km peak. These suggestthat the wave structure persists atmospherewould perhaps be expected to enhanceand extend down to the level of the boundary layer edge.The temperature the regionof diurnal variation in temperature. amplitudeis initially small(a few degrees),then increaseswith The CO•. condensationboundary has beenincluded in Fig- altitude to the order of 15ø or 20 ø, then is damped somewhat ure 12. In both the morningand late afternoonprofiles there is before increasingto very large valuesabove 100 km. a minimum margin of --20øK betweenatmospheric temper- Zurek has calculatedthat horizontal velocitiesexcited by the ature and condensation. In view of the lack of diurnal varia- diurnal heating cycle are as large as 150 m/s, above 70 km, tion of the mean profileabove the boundarylayer it appears under clear air conditions. Vertical flow velocities are about 2 that onlya largenegative amplitude of the thermaltide could ordersless, up to 1.5 m/s. If adiabaticcompression and expan- condenseCO•. and that hazes and clouds seen in the Mars sionresulting from the verticalflow componentare assumedto atmospherein the summerseason below polar latitudesare be responsiblefor the temperaturewaves, the amount of verti- most probably water ice. cal movementthus implied by the observedpeaks is given in Table 6 under the heading Az. Vertical excursionsof a few Wave Structure kilometers are sufficientto producethe observedtemperature We have previouslydiscussed the relationshipof the wave structure. Vertical motion at 0.1 m/s can account for the structurein the Viking 2 temperatureprofile to the tidal model smallerdisplacements in 4 hours (1.44 km), while 1 m/s for 4 of Zurek [1976] [Seiff and Kirk, 1976]. The Viking 1 wave hours (14.4 km) would account for the largestdisplacement. structureis generallysimilar to that of Viking 2, with differ- Thesevelocity magnitudes are compatiblewith the theoretical encesin phaseand amplitudeassociated with latitudeand time model. of day (Figure 15). The wavesappear ro be a complexsuper- Horizontal winds of the magnitude described,in the pres- positionof modes.Table 6 listsapproximately the temperature enceof wind shear,can be expectedto break down into turbu- amplitudesand wavelengthsobtained relative to the mean lence and to contribute to mixing of the atmosphere.The temperaturecurve drawn throughthe data (Figure 12). The larger velocitiesand greaterrange of motion observedat the wavelengthsare measuredover half a cycle,from onepeak to higher altitudes suggesta more vigorous turbulent mixing the nexthigher peak. The significanceof the/Xzcolumn will be there. The possiblerelationship of this dynamical turbulent explainedbelow. mixing processto the observedphotochemical stability of the The wavelengthvaries from 4 to 31 km below 100 km and atmospherehas been pointed out by Zurek and others. growsto a maximumin the uppermosthalf cycleof each Finally, Zurek has discussedthe effect of terrain on tidal sounding.For comparisonthe theoreticalmodel has indicated oscillations and concludes that it will have first-order effects, wavelengthsof 22-24 km. The wavelengthvalues depend, of addingmodes and varyingthe contributingmodes with longi- course,on just how smalla disturbanceis consideredto define tude. We suspectthat someof the modal complexityobserved a peak.For example,the Viking2 'peaks'at 78 km and96 km, in our data is the effect of the terrain, which for Viking 1 was a which lead to two of the smallerwavelengths, are of very small rapidly descendingrolling surface,near the center of a deep 4376 ENTRY SCIENCE

Fig. 16. Shadowgraphof a modelof theViking entry configuration in a laboratorytest flight. The atmosphere isCO2, the model's velocity is 3.4 km/s, and the Reynoldsnumber is 8 X 10•. In this figurethe model is at the Viking equilibriumflight attitude,a • -I I ø

basin.The theory showsthat low basinsenhance the velocities to V• and Vr, respectively.Subscript I denotesan inertial ref- and the temperatureamplitude (see, for example, the results erence frame, and subscriptr denotesa referenceframe an- for 120øW longitude, at the equator and at 19øN, in Zurek's choredin the atmosphererotating with the planet.Note that [1976] paper). • and • 0 ø, while •. and • • 90 ø. Inertial flight path angle APPENDIX A: DATA ANALYSIS dq/,/dt= -{[Vt/(R + z)] - (g/V•)}cos q/• + (a•,/V•) (8) The equationsof motion usedto reconstructthe trajectory were as follows: Gravitational acceleration Inertial velocity g = goR•'/(R + z)•' (9)

dV•/dt = g sin 3/• - as, (6) Altitude

Resolution of accelerations dz/dt = -V,• sin -y• (10) as,= (axcos c•+ azsin c•) cos • (7) Downrange angle - (ax sin a - az cos a) cos •. dtS/dt = (V• cos 'y•)/(R + z) (11) aL,= -(ax sina - a• cosa) cos•3 + (axcos a + a• sina) cos•4 Relative velocity wheree, is the anglebetween V• and Vr; e•.,the anglebetween Vr•' = Vf' + V,••' - 2V•V,• cos 3/• sin X• (12) V• and Lr; ea,the angle betweenL• and Lr; and e4,the angle betweenL• and Vt. L• and Lr are the lift vectorsperpendicular Velocity of atmosphererotating with planet SEIFE AND KIRK: STRUCTUREOF THE ATMOSPHEREON MARS 4377

Va = (R + z) cocos ß (13) P. F. Intrieri, personal communication, 1976]. The tests were designedto define the effects of gas composition,angle of Hydrostatic equilibrium attack, Reynolds number, and velocity on drag coefficient. dp/dt = gpV/sin •,/ (14) Accuratelymade scalemodels of the Viking entry configuration were fired from light-gasguns through an atmosphereof Here, as, is the acceleration in the V• direction, R is the local carbon dioxide in an enclosed test range, at velocities and radius of the planet (measuredto the referenceellipsoid), •,• is Reynolds numbers selectedto lie along the Viking entry tra- the flight path anglebelow horizontal,a is the angleof attack, jectory.Reynolds number was controlled by selectionof gas b is the range angle subtendedat the planet center from entry pressurewithin the test range. Drag coefficientswere deter- to time t, X• is the trajectoryheading angle (0 ø is due north), co mined from precisemeasurements of the model retardationin is planetary rotation rate (7.08821765 X 10-5 rad/s), and cI,is flight(see, for example, Canning et al. [1970]).In addition,the latitude. lift, staticand dynamicstability, and trim angleof attack were The data analysis was programed for computer solution. determined. The accelerationand altitude data were processedby the pro- A shadowgraphpicture of one of the models in flight is gram to yield the trajectory and the properties of the atmo- reproducedin Figure 16 to showthe flow configurationtypical sphere.The iterative procedureused follows. of the high entry speedsand attitude. An exampleof the drag 1. First approximations of the initial conditions (inertial data is givenin Figure 17. It showsthe accuracyof the data to velocity, flight path angle, altitude, latitude, and heading be within 1%. The effectof angle of attack is well defined.The angle) are made on the basis of the expected,or mission comparisonwith air data shows a 4% effect on Co of the nominal, trajectory. These conditionsare for a selectedarbi- changein gascomposition at the flight attitude. Test data for trary time prior to encounteringthe sensibleatmosphere. CO2, slightlycontaminated by air leakage,were usedin reduc- 2. A table of altitudes measuredby the radar altimeter is ing the Viking flight data. A more complete report of these stored in memory as a function of time. tests is planned. 3. Differential equations(6) and (8) are solvedsimultane- ously, supported by auxiliary equations(7) and (9). Altitudes Acknowledgments.Theauthors are indebted toman•, people WhO, are calculatedfor eachof the timesspecified in step2. (NOte overthe: years of preparationof this experiment,contributed signifi- that in (7), ax and az are the measured accelerationsand that cantly to its development, implementation, and analysis. Unfortu- the angle of attack, a, is calculated from their ratio through nately, we cannot acknowledgeall who contributedhere, but in par- ticular we wish to thank Robert C. Blanchardof the Langley Research the experimentallydetermined lift and drag coefficients.) Center Viking Project Office (VPO) and Fred Hopper of Martin 4. When a specifiedfinal altitude is reached,a differential Marietta Corporation (MMC) for invaluable contributions to the corrections process [Chapmanand Kirk, 1970] is applied to trajectory reconstruction effort; Simon C. Sommer and David E. yield correctionsto the initial conditions.This involvessolving Reeseof Ames ResearchCenter (ARC) for major contributionsto the another set of differential equations in which partial deriva- demonstrationof the concept; Robert Corridan and Carl•on S. James (ARC) for laboratory studiesof the instruments;and Roy Duckett tives of velocity, flight path angle, etc., with respectto the and Brooks Drew (VPO) and Sid Cook, Tony Knight, and Ernie initial conditions, are determined. Given a new set of initial Carlston(MMC) for contributionsto the experiment integration in conditions, the processis repeated until a best fit in a least 'the spacecraftand operationsplanning; and finally, Roland Dupree squaressense is obtained to the altitude data. Normally three (Kennedy Space Center) and Sally Rogallo (ARC) for invaluable assistancein the computer analysisof the flight data. or four iterations lead to convergence. 5. Relative velocity is determined as a function of time REFERENCES from (12), and the densityis then determinedfrom (3). Pres- Blumsack,S. L., P. J. Gierasch, and W. R. Wessel,An analytical and sure and temperature are computed from the assumptionof numerical study of the Martian planetary boundary layer over hydrostaticequilibrium (equation (14)) and from the gas law. slopes,J. Atmos.Sci., 30, 66-82, 1973. The mean molecular weight used for the mixed lower atmo- Canning, T. N., A. Seiff, and C. S. James (Eds.), Ballistic range spherein this step was 43.49, correspondingto 2.7 mol % N2, technology,Rep. 138, Adv. Group for Aeronaut. Res. and De- velop., Brussels,1970. 1.6 mol % Ar, and 0.15 mol % 02. Chapman, G. T., and D. 13.Kirk, A method for extracting aerody- APPENDIX B: DRAG COEFFICIENT DETERMINATION namic coefficientsfrom free flight data, AIAA J., 8, 753-758, 1970. Christensen, E. J., Martian topography derived from occultation, Continuum flow drag coefficientswere measured in a series radar, spectral, and optical measurements,J. Geophys.Res., 80, of experimentsconducted at Ames ResearchCenter in a ballis- 2909-2913, 1975. Gierasch, P. J., and R. M. Goody, An approximatecalculation of tic range with CO2 as the test medium [Intrieri et al., 1977; radiativeheating and radiativeequilibrium in the Martian atmosphere,Planet. SpaceSci., 15, 1465-1477, 1967.

VIKING ENTRY CONFIGURATION Gierasch, P. J., and R. M. Goody, A study of. the thermal and dynamicalstructure of the Martian lower atmosphere,Planet. Space Sci., 16, 615-646, 1968. CO2 Gierasch, P. J., and R. M. Goody, The effect of dust on the temperature of the Martian atmosphere,J. A tmos.Sci., 29, 400-402, 1971. CD1'6• - Hanel, R., 13. Conrath, W. Hovis, V. Kunde, P. Lowman, W. Ma- 1.4- V = 3.4 km/sec - guire,J. Pearl,J. Pirraglia,C. Prabhakara,and B. Schiachman, REYNOLDS NO. = 8 x 105 Investigationof the Martianenvironment by infraredspectroscopy on Mariner 9, Icarus, 17, 423-442, 1972. 1.2 - FLIGHT ATTITUDE - Hanson, W. 13.,S. Sanatani, and D. R. Zuccaro, The Martian iono- sphereas observedby the Viking retardingpotential analyzers, J. Geophys.Res., 82, this issue, 1977. 0 2 4 6 8 2 14 16 ANGLE OF ATTACK,(3, deg Hess,S. L., R. M. Henry, C. 13.Leovy, J. A. Ryan, J. E. Tillman, T. E. Chamberlain, H. L. Cole, R. G. Dutton, G. C. Greene, W. E. Simon, Fig. 17. Representativedata from laboratorymeasurements of drag and J. L. Mitchell, Preliminary meteorologicalresults on Mars from coefficient. the Viking 1 lander, Science,193, 788-791, 1976a. 4378 ENTRY SCIENCE

Hess, S. L., R. M. Henry, C. B. Leovy, J. A. Ryan, J. E. Tillman, T. E. Nier, A. O., W. B. Hanson, M. B. McElroy, A. Seiff, and N. W. Chamberlain, H. L. Cole, R. G. Dutton, G. C. Greene, W. E. Spencer,Entry scienceexperiments [for Viking, 1975, Icarus, 16, Simon,and J. L. Mitchell, Mars climatologyfrom Viking 1 after 20 74-91, 1972. sols, Science; 194, 78-81, 1976b. Nier, A. O., W. B. Hanson,A. Seiff, M. B. McElroy, N. W. Spencer, Intrieri, P. F., C. E. De Rose, and D. B. Kirk, Flight characteristicsoff R. J. Duckett, T. C. D. Knight, and W. S. Cook, Compositionand probesin the atmospheresoff Mars, Venus,and the outer planets, structureoff the Martian atmosphere:Preliminary results [from Vik- Acta Astronaut., in press, 1977. ing 1, Science, 193, 786-788, 1976. Kerzhanovich, V. V., Mars 6: Improved analysisoff the descentmod- Owen, T., and K. Biemann, Compositionoff the atmosphereat the ule measurements, Icarus, 30, 1-25, 1977. surfaceoff Mars: Detection off argon 36 and preliminaryanalysis, Kliore,A. J., D. L. Cain, G. Fjeldbo,B. L. Seidel,and M. J. Sykes, Science, 193, 801-803, 1976. The atmosphereoff Mars from Mariner 9 radio occultationmeasure- Seiff, A., Some possibilities[for determining the characteristicsoff the ments, Icarus, 17, 484-516, 1972. atmospheresoff Mars and Venus from gas dynamicbehavior off a Masson, D. J., D. N. Morris, and D. E. Bloxsom, Measurements off probe vehicle, NASA Tech. Note, D-1770, 1963. sphere drag from hypersoniccontinuum to [free-moleculeflows, in Seiff, A., The Viking atmospherestructure experiment--Techniques, Rarified Gas Dynamics,edited by L. Talbot, p. 643, Academic, New instruments, and expected accuracies,Space Sci. Instrum., 2, York, 1961. 381-423, 1976. Michael, W. H., Jr., A. P. Mayo, W. T. Blackshear, R. H. Tolson, Seiff,A., and D. B. Kirk, Structureoff Mars' atmosphereup to 100km G. M. Kelly, J.P. Brenkle, D. L. Cain, G. Fjeldbo, D. N. Sweet- from the entry measurementsoff Viking 2, Science,194, 1300-1303, nam, R. B. Goldstein, P. E. MacNeil, R. D. Reasenberg,I. I. 1976. Shapiro,T. I. S. Boak, M.D. Grossi, and C. H. Tang, Mars dynam- Seiff,A., D. E. Reese,S.C. Sommer,D. B. Kirk, E. E. Whiting,and ics, atmospheric,and surface properties:Determination from Vik- H. B. Niemann,Paet, An entry probeexperiment in the earth's ing tracking data, Science, 194, 1337-1338, 1976. atmosphere,Icarus, 18, 525-563, 1973. Mutch, T. A., A. B. Binder, F. O. Huck, E. C. Levinthai, S. Liebes, Jr., Stone, P. H., A simplifiedradiative-dynamical model [for the static E. C. Morris, W. R. Patterson,J. B. Pollack, C. Sagan, and G. R. stabilityoff rotating atmospheres, J. Atmos.Sci., 29, 405-418, 1972. Taylor, The surface off Mars: The view [from the Viking 1 lander, Zurek, R. W., Diurnal tide in the Martian atmosphere,J. Atmos.Sci., Science, 193, 791-801, 1976. 33, 321-337, 1976. Nier, A. O., and M. B. McElroy, Structure off the neutral upper atmosphereoff Mars: Resultsfrom Viking 1 and Viking 2, Science, 194, 1298-1300, 1976. Nier, A. O., and M. B. McElroy, Composition and structure offMars (Received April 13, 1977; upper atmosphere:Results from the neutral massspectrometers on revised June 6, 1977; Vikings I and 2, J. Geophys.Res., 82, this issue, 1977. acceptedJune 6, 1977.)