Results of the Mars Pathfinder atmospheric structure investigation

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 104, NO. E4, PAGES 8943-8955, APRIL 25, 1999

Results of the Mars Pathfinder atmospheric structure investigation

Julio A. MagalhSes • Space Science Division, NASA Ames Research Center, Moffett Field, California

John T. Schofield

Jet Propulsion Laboratory, California Institute of Technology, Pasadena

Alvin Seiff •

Space Science Division, NASA Ames Research Center, Moffett Field, California

Abstract. We report on a thorough analysis of the Mars Pathfinder atmospheric structure investigation (ASI) accelerometer data spanning the altitude range 161-8.9 km. Entry, descent, and landing occurred within 850 km of the Viking 1 lander and somewhat later in northern summer. The early morning entry (0300 hours) provided the first opportunity to study Mars' nighttime atmospheric structure; the close proximity to the Viking 1 site has permitted a search for changes in atmospheric structure during the 21 years between the landings. Our results confirm and refine the major features of the atmospheric structure discovered in the initial analysis of the ASI results reported by Schofield et al. [1997]. The current analysis has yielded a much better definition of the temperature structure above 90 km altitude. Pathfinder measured a thermospheric peak temperature of 153øK at 134 km, which is 30øK colder than the value found by Viking 1. Between 110 and 88 km, Pathfinder found a broad, nearly isothermal plateau at 127øK, which correlates very well with a similar structure evident in Viking 1 data at the same pressures, although the Pathfinder layer is 25øK colder. At levels above 88 km, wavelike oscillations with a wavelength --•5 km and amplitudes of 2-3øK are evident, possibly reflecting gravity or planetary wave activity. Between 90 and 60 km the average temperature is 20-30øK cooler than Viking 1 values. Large-amplitude (10-20øK) long-wavelength (20-40 km) oscillations, which show a remarkable correspondence to equivalent structures found in the Viking 1 profile at the same pressures, occur in this region and are likely due to a diurnal tidal mode. Between 85 and 77 km a minimum of one oscillation results in

temperatures up to 7øK below the saturation temperature of CO2, well outside the uncertainties in the measurements and the vapor pressure curve and comparable to observed supersaturations of water in Earth's mesosphere. Between 55 and 16 km, temperatures are close to or warmer than Viking 1 values; superposed long-wavelength oscillations correspond well with similar structures observed by Viking 1. Between 16 and 9.9 km the temperature profile shows an unexpected strong thermal inversion, which may reflect radiative cooling due to a water cloud. At the base of the inversion, temperatures begin to increase abruptly until the last measurement at 8.9 km. The Viking-like temperatures in the lower atmosphere are consistent with the Viking-like dust optical depths observed by the Mars Pathfinder imager. The cool temperatures in the middle and upper atmosphere may be indicative of significant nighttime cooling at these levels, although other interpretations are possible.

1. Introduction

The entry, descent, and landing (EDL) of the Mars Path- finder spacecraft on July 4, 1997, provided the first opportunity to make in situ measurements of Martian atmospheric structure since the 1976 Viking mission. The Mars Pathfinder atmospheric structure investigation (ASI) provides a detailed

•Also at San Jose State University Foundation, San Jose, California.

Copyright 1999 by the American Geophysical Union.

Paper number 1998JE900041. 0148-0227/99/1998JE900041 $09.00

snapshot of the density, pressure, and temperature of the Mar- tian atmosphere over a wide range of altitude extending from the thermosphere down to the lower atmosphere along one trajectory and at one time. These in situ measurements com- plement atmospheric temperatures derived from infrared spectrometers on orbiters, which provide global coverage of the lower atmosphere over an extended period of time at lower spatial resolution, and orbiter aerobraking measurements which make in situ measurements of density and temperature in the upper atmosphere near the thermosphere. These observations are further complemented by meteorological measurements from landers which provide an extended time series of high-accuracy measurements at one location at the surface.

8943

8944 MAGALH?•ES ET AL.: PATHFINDER ATMOSPHERIC STRUCTURE INVESTIGATION

Atmospheric structure experiments have previously investigated the atmospheres of Earth (Planetary Atmosphere Ex- periments Test Probe (PAET) [Seiff et al., 1973]), Mars (Vi- king landers [Seiff and Kirk, 1977]), Venus (Pioneer Venus probes [Seiff et al., 1980]), and Jupiter (Galileo probe [Seiff et al., 1996]). The PAET probe, which entered Earth's atmosphere in June 1971, demonstrated the accuracy and reliability of the reconstruction procedure by comparing the derived atmospheric structure with nearly simultaneously acquired stan- dard meteorological soundings [cf. Seiff et al., 1973]. All of these experiments as well as Mars Pathfinder utilized the same basic principles to determine atmospheric density, pressure, and temperature structure. An atmospheric probe protected by an aeroshell enters a planetary atmosphere with a velocity of the order of 10 km/s and is rapidly decelerated by aerodynamic drag. During this "entry phase," accelerometers in the spacecraft are used to measure the probe's deceleration, which is directly related to the atmospheric density. When the speed of the vehicle has decreased to close to the speed of sound, a parachute is deployed and the heat shield is dropped, exposing temperature and pressure sensors to the ambient atmosphere.

The USSR spacecraft Mars 6 obtained the first in situ measurements of planetary atmospheric structure during its entry into the Martian atmosphere in 1974 [Kerzhanovich, 1977], confirming remote sensing observations of a 5.45 mbar surface pressure and estimating the lapse rate in the lower and middle atmosphere. The Atmosphere Structure Experiment (ASE) on the two 1976 Viking landers [cf. Seiff, 1976] provided the first high vertical resolution and high accuracy profiles of temperature, pressure, and density from 120 km down to the surface at two locations on Mars [Seiff and Kirk, 1977]. Measurements obtained by the Viking upper atmosphere mass spectrometer (UAMS) instrument [Nier and McElroy, 1977] allowed profiles of density, pressure, and temperature to be extended up to an altitude of 200 km in the case of Viking 1 and up to 175 km in the case of Viking 2 [Seiff and Kirk, 1977]. The Viking 1 lander descended to 22.3øN latitude, 48øW longitude at 1615 local time (LT) on July 20, 1976, and the Viking 2 landed at 47.6øN, 226øW at about 1000 LT on September 3, 1976. Both landers arrived during early northern Martian summer (Viking 1 at Ls = 96 ø; Viking 2 atLs = 117 ø; Ls is the areocentric longitude of the Sun, where L s = 0 ø corresponds to the northern spring equinox).

Mars Pathfinder landed at a latitude and longitude (19.1øN, 33.5øW) close to Viking 1 and somewhat later in northern summer (Ls = 143ø). The early morning entry (0258 local Mars time) provided the first opportunity to study Mars' nighttime atmospheric structure. By landing in close proximity to the Viking 1 landing site (--•850 km) and at a similar season, the opportunity was created to look for changes in the atmosphere during the 21 years since the Viking 1 entry. The Path- finder project was originally created to demonstrate a novel four-stage deceleration subsystem to safely land on a variety of terrains after entering the atmosphere directly from an inter- planetary trajectory [cf. Golombek et al., this issue]. The ASI benefited from this direct entry, since the higher entry velocity (7.4 km/s for Pathfinder, 4.5 km/s for Viking) increased sensitivity to the tenuous upper reaches of the Martian atmosphere. In addition, the higher digital resolution of the Pathfinder accelerometers and the high sampling rate yielded improved sensitivity to the upper atmosphere and higher vertical resolution (400-80 m). Almost all of the velocity decrease of the lander occurred while it was enclosed in its aeroshell during

the entry phase. To enable a safe landing, further velocity reduction was obtained by deploying a parachute (at about 9 km altitude), firing a rocket (at about 100 m altitude), and by deploying shock absorbing air bags for the impact with the surface [cf. Golombek et al., this issue].

Many processes with a wide range of scales can potentially affect the structure of the Martian atmosphere, and evidence for these processes can potentially be detected with the high resolution of the ASI measurements. The atmosphere of Mars responds quickly to changes in radiative forcing due to its low mass and its radiatively active principal constituent [Goody and Belton, 1967]. The variable atmospheric dust content plays an important role in atmospheric heating through its direct absorption of sunlight [cf. Zurek et al., 1992], and aerosol particles (dust and condensates) can also produce enhanced radiative cooling of the atmosphere. The vertical and horizontal motion fields associated with the global and regional circula- tions exert an important influence on the thermal structure [cf. Haberle et al., 1993a; Wilson, 1997; Zurek et al., 1992]. Atmo- spheric waves with a wide range of scales, e.g., thermal tides, gravity waves, and planetary waves, can directly perturb the thermal structure and can also indirectly influence the structure through the momentum and energy they transport vertically and meridionally [cf. Barnes, 1990]. Thermal tides are expected to be particularly strong due to the low mass and dustiness of the atmosphere [Zurek and Haberle, 1988; Wilson and Hamilton, 1996]. Convection associated with static and shear instabilities can also be important locally. By adding another atmospheric structure profile to the set collected more than 21 years ago and by entering at a very different time of day and a slightly different season, Pathfinder allows us to improve our understanding of the processes determining the thermal structure of the Martian atmosphere.

An initial report on the Pathfinder ASI results was presented by Schofield et al. [1997]; this preliminary report was based on a subset of the accelerometer data. Here we report on an improved analysis using all of the accelerometer data from the entry phase. Improvements include a better treatment of the aerodynamic properties of the vehicle, of the gravity field, and of the instrument response function and a better assessment of the uncertainties in the resulting profiles. The new analysis has resulted in a much better definition of the atmospheric structure above 90 km altitude and has extended the profile to a slightly lower altitude. This analysis confirms and better defines all of the major features of the thermal structure below 90 km altitude reported by Schofield et al. [1997]. Smaller amplitude structures in the profile can now be more confidently identified as well. Section 2 presents a description of the ASI experiment and of the data acquired. Section 3 describes the analysis procedure used to reconstruct the profiles of density, pressure, and temperature. Section 4 presents the improved density, pressure, and temperature profiles. Section 5 discusses the results and their possible implications for our understanding of phenomena in the Martian atmosphere.

2. Instrument and Data Description The Mars Pathfinder atmospheric structure investigation/

meteorology (ASI/MET) instrument package is described in detail by Seiff et al. [1997]. Here we provide a brief description to aid in understanding the results from the ASI experiment. During most of the entry, descent, and landing (EDL) of the Mars Pathfinder lander, it was fully enclosed in a heat shield.

MAGAL•S ET AL.: PATHFINDER ATMOSPHERIC STRUCTURE INVESTIGATION 8945

During this "entry phase," the ASI experiment relied on measurements of the aerodynamic deceleration of the entry vehicle from three science accelerometers. The entry phase ended when the velocity of the entry vehicle was slow enough (less than 2 times the local speed of sound) to allow safe deployment of a parachute to further decelerate the lander. After parachute deployment and heat shield separation,•Ihe accelerometer data were supplemented by measurements from the met- erology package's (MET) pressure and temperature sensors. Because of the poor coupling of the temperature sensor to the atmosphere, the observations from it principally sensed the internal temperature of the lander, as anticipated by the design team [Seiff et al., 1997]. Reconstruction of atmospheric structure using the accelerometer and pressure sensor measurements from the parachute descent phase has thus far not been possible due to the complex motion of the lander on the parachute. Here we report on results derived from the accelerometer measurements acquired during the entry phase.

All the science accelerometers were Allied Signal QA-3000- 003 units, which sensed acceleration by electromagnetically restricting a test mass to a precise null position. The three accelerometers were mutually orthogonal and parallel to the lander's x, y, and z axes, where the z axis was along the axis of symmetry of the entry vehicle. The science accelerometers were all within 15 mm of the z axis of the vehicle and within

155 mm of the center of mass (CM) of the vehicle, which was along the z axis to high accuracy. The close proximity of the CM and the z axis accelerometer to the entry vehicle's symmetry axis ensured that the measurements of the axial accelerations were largely free of signal due to vehicle motions about the CM. In addition, the placement of the CM on the symmetry axis of the vehicle ensured a small angle between the z axis and the velocity vector (angle of attack a) during the atmospheric entry of Pathfinder.

Each accelerometer included three gain states with dynamic ranges of _ 16 mg, ___800 mg, and ___40 g. Digitization of the signal to 14 bits yielded digital resolutions of 2/ag, 100/ag, and 5 mg, respectively. Changes in gain state were commanded by an onboard data management subsystem, which monitored the magnitude of the decelerations during EDL. During the entry phase, upward changes in scale from the _+ 16 mg setting were commanded when readings on a given scale reached 7/8ths of full scale. Twenty-two seconds after parachute deployment, the z axis accelerometer was commanded to shift back down to the

800 mg scale. Eleven seconds before impact, all accelerometers were switched to the 40 g scale to record the impacts with the surface. These commandable range changes yielded a wide dynamic range of sensitivity (7 orders of magnitude), spanning the detection of the tenuous upper reaches of Mars' atmosphere to the vehicle's deceleration peak at 15.89 # and the similarly high accelerations accompanying the impacts with the surface.

The accelerometers recorded data continuously starting about 14 min before atmospheric entry until about I min after impact, resulting in a total of 13,346 accelerometer measurements from each axis during this period. During the freefall phase prior to entry, accelerometer readings were sampled at the rate of 1 Hz. The freefall measurements allowed the offsets

at zero acceleration to be accurately determined and permitted us to empirically determine the effects of the small precession of the rotating entry vehicle (rotating at a rate of 1.93 rpm) on the accelerometer readings. With the accurate background subtraction enabled by these measurements, we were able to

fully utilize the instrument's intrinsic high sensitivity to detect the atmosphere at the highest possible altitude. During EDL, accelerometer measurements were sampled at the rate of 32 Hz. With a vertical velocity at entry of about 2 km/s, this implies an altitude resolution of better than 60 m throughout EDL. However, a low-pass filter in the accelerometer electronics attenuated signal frequencies above 5 Hz to suppress the effects of noise and spacecraft dynamic motion, resulting in a vertical spatial resolution of 400-80 m. The effects of the frequency response of the accelerometer electronics have been removed using a Newtonian damping law with a time constant of 0.0245 s, which reproduces the frequency response of the instrument satisfactorily. Comparison of surface acceleration measurements of 3.716 m s -2, with the value of 3.717 m s -2 calculated for the lander location and height [Folkner et al., 1997], provided a verification of the accelerometer gain cali- bration on the 800 mg scale. During testing of the accelerometers, noise levels in each gain state were measured at 1-2 counts or less, so that the uncertainty in the measurements is •iog•e to the digital resolutions.

Figure 1 presents the deceleration history of Mars Path- finder as determined from the three science accelerometers

during entry and descent. Times in these figures and elsewhere in this paper are referenced to July 4, 1997, 1651:12.28 UTC. This time was chosen, since it was the navigation team's pre- diction for the time at which the Mars Pathfinder spacecraft would cross a radial distance of 3597.2 km from the center of

gravity of Mars (--•207 km above landing site radius). This distance was far enough from Mars that the upper atmospheric densities were below the threshold of the ASI experiment and yet close enough to the time of entry that high-order gravitational contributions are not needed for an accurate reconstruc-

tion of the trajectory during EDL. Data are displayed up to the last measurement before impact of the lander (impact at t = 343.41 s) with the Martian surface. The displayed deceleration values have been fully calibrated and validated. Data dropouts (two measurements) and short-lived (less than 1 s) transients associated with instrument gain changes have been removed. Zero offsets and precession of the vehicle based on cruise and freefall data have been subtracted from the obser-

vations as well.

3. Reconstruction Procedure

The procedure for the reconstruction of planetary atmospheric structure was first described by Seiffet al. [1973], and a more detailed description of the procedure appeared in the work by Seiff and Kirk [1977]. The work described in these publications has since been applied to Venus [Seiffet al., 1980] and Jupiter [Seiff et al., 1996]. Although our analysis of Mars Pathfinder ASI data has utilized the same basic deterministic

approach, we present a somewhat detailed accounting of the analysis steps, since our analysis algorithm and software have been independently developed to refine and extend the atmospheric structure reconstruction procedure and since no detailed published account has previously been given.

Atmospheric density p is related to the aerodynamic deceleration of a spacecraft through the aerodynamic drag equation:

2m a v

where a v is the acceleration along the flight path relative to the atmosphere, VR is the probe velocity relative to the atmo-

8946 MAGAL•S ET AL.: PATHFINDER ATMOSPHERIC STRUCTURE INVESTIGATION

115s0

i i ! i i i

_. ,F"/ t t

50 100 150 200 250 300

'rime (seconds) aEer R= 3597.2 km

Figure 1. Deceleration of Mars Pathfinder as recorded by the science accelerometers during the entry and parachute descent phases. Times are referenced to July 4, 1997, 1651: 12.28 UTC, which corresponds to the predicted time of cross- ing a radial distance of 3597.2 km from the center of gravity of Mars (-207 km above landing site radius). Last time shown immediately precedes the impact of Mars Pathfinder with the surface. Note the detection of the atmosphere at t = 29 s when the 2/•g threshold of the instrument is exceeded. Note the abrupt drop in deceleration at t = 209 s due to the mortar firing which deployed the parachute. The abrupt large increase in deceleration after parachute deployment is evident beginning at t = 210.5 s. High-frequency fluctuations due to oscillatory motions on the parachute are evident at nearly all later times. The small rise in deceleration near t = 229 s is asso-

ciated with heat shield separation. At t = 249 s, note the abrupt drop in deceleration associated with the unreeling of the Pathfinder lander from the backshell. Near t = 334 s the

fluctuations in acceleration are associated with air bag deployment. The firing of the solid rocket motors is evident beginning at t = 337 s. The abrupt drop in deceleration at t = 339 s is due to the freefall of the lander after the bridle connecting the lander to the backshell (to which the solid rocket motors and parachute are attached) is cut. Altitude above the landing site and velocity relative to the surface at the times of key events are also shown; •/is the flight path angle below horizontal at the moment of atmospheric detection.

sphere, m is the probe mass, C r) is the drag coefficient of the probe, and A is the probe's cross-sectional area. The drag coefficient Cr) varies during the entry, and this variation can be accounted for iteratively using aerodynamic databases com- piled from preflight experiments and numerical simulations, as discussed further below. During the entry phase, the total mass of the Mars Pathfinder entry vehicle was m = 585.3 kg and its area was A = 5.526 m 2.

With knowledge of the external forces acting on the spacecraft, the velocity and position of the probe are determined by integrating the equations of motion starting with an initial condition provided by the navigation team. The equations of motion written in a planet-centered spherical coordinate system rotating with the planet [cf. Fetter and Walecka, 1980] were used for the computations. The acceleration due to gravity is not directly measured by the accelerometers during passage through the atmosphere. To account for the effects of gravity, we have used a gravity model that includes the first zonal harmonic coefficient (•2) in the normalized spherical harmonic expansion of the gravity field [cf. Hubbard, 1984]. For

Mars •2 = 8.759 x 10 -4 [Smith et al., 1993]. Higher order harmonics are of much smaller magnitude [Smith et al., 1993] and are not important over the short time interval of EDL. The aerodynamic drag on the vehicle can be directly obtained from the three-axis science accelerometer measurements. Because

of the small angle of attack during the Pathfinder entry [cf. Braun et al., 1995] and because of the close proximity of the z axis accelerometer to the axis of symmetry, the measured z axis accelerations during entry are very close (generally within 0.02%) to the true deceleration along the flight path (a v).

Initial conditions for the integration were provided by the Mars Pathfinder navigation team in the form of an entry velocity and entry location at a prescribed time. This so-called "entry state" is based on observations of range and rate of motion along the line of sight derived from radiometric tracking of the spacecraft combined with trajectory solutions based on high-order models of the gravitational forces acting on the vehicle due to solar system bodies [cf. Kallemyn et al., 1996]. The entry state for July 4, 1997, 1651:12.28 UTC with 10- uncertainties listed is r = 3597.2 _+ 1.7 km, 0 = 23 ø +_ 0.04øN areocentric latitude, & = 343.67 ø _+ 0.01øE longitude, V/• = 7444.7 _+ 0.7 m/s, 3/= 16.85 ø +- 0.02 ø, ½ = 255.41 ø -+ 0.02 ø, where r is the radial distance from the center of mass of the

planet, V/• is the entry speed, •/is the flight path angle below horizontal, and ½ is the flight path azimuth measured clockwise from north (all in a Mars-fixed, i.e., rotating, coordinate system).

This initial state was marched forward in time using a fourth- and fifth-order Runge-Kutta-Fehlberg integrator with auto- matic step-size control [cf. Press et al., 1992]. We have con- ducted experiments to determine the numerical accuracy of our trajectory reconstruction procedure. The entry of Mars Pathfinder into an atmosphere with specified density structure was simulated, and the resulting deceleration histories were then analyzed with our reconstruction software. Positional errors were found to be -<3 m, and errors in velocity were -<0.3 m/s. The high sampling rate of the accelerometer data provides good vertical resolution and thus facilitates the direct integration of the accelerometer data to obtain good accuracy in the trajectory solutions. In this paper, we have used the full 32 Hz data set. However, with knowledge of the approximate analyt- ical form of the aerodynamic deceleration of the vehicle, properly chosen numerical methods [cf. Acton, 1990] can yield quite accurate integrations using data sampled at much less frequent intervals. The ASI results described in our first report [Schofield et al., 1997] were based on the application of such numerical methods to the data sampled at 1 Hz.

Figure 2 presents the altitude z, areocentric latitude 0, east longitude &, and total velocity V of the Mars Pathfinder relative to the planet's surface during EDL. The positions are referenced to the landing site location, which has been accurately determined by monitoring the lander's radio signal during the landed mission [Folknet et al., 1997]. The lander is located at 3389.715 km from the center of mass of Mars, 19.09øN areocentric latitude, and 326.48øE longitude. Using this reference point for the trajectory, our reconstructed entry altitude, latitude, and longitude at the time of entry are within the uncertainties in the entry state positions provided by the navigation team. Uncertainty envelopes based on the 30-uncertainties in the entry velocity and the effects of digitization are displayed as well. For the quantities plotted versus altitude in this figure as well as in other figures in this paper, the displayed envelopes represent the uncertainties at a particular

MAGAL•S ET AL.' PATHFINDER ATMOSPHERIC STRUCTURE INVESTIGATION 8947

200

180

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100 8o 60

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0 0 •0 •b0 150 200 250 300

Time (seconds)

160[

I 8o 6O

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200 [ ......... 180[ ( 160[

.... 140 I N

• •o 60

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326 328 330 332 334 336 338 340 342 344

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180[ (d) Velocity 160[

.-. 140[ N

oo! • 80

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0 1000 2000 30•)0 40•)0 50'00 60'00 70b0 Velocity (m/s)

Figure 2. Trajectory of the Mars Pathfinder lander during EDL as reconstructed from the science accelerometer data. (a) Altitude above the landing site versus time. (b) Areocentric latitude versus altitude. (c) East longitude versus altitude. (d) Total velocity relative to the surface of Mars versus altitude. Uncertainty envelopes include the ___3(r uncertainties in the entry state and digitization effects. Since the landing site location is known much more accurately than the position at entry, all positions have been referenced to the landing site location determined by Folkher et al. [1997].

time in the trajectory and do not include the altitude uncertainty presented in Figure 2a. The altitude uncertainties would appear as a slowly and smoothly varying vertical displacement of the overall profile. During the 343.41 s covered by Figure 2a, Pathfinder covered 205 km in altitude. Note from Figures 2b and 2c that in that time the lander also moved significantly in horizontal position (4.8 ø in latitude, 16.5 ø in longitude, which corresponds to a total horizontal distance of about 1020 km) prior to reaching about 15 km altitude.

During the entry phase down to 60 km, very little decrease in the entry velocity of 7.4 km/s occurs, and in fact, a small increase due to angular momentum conservation is evident in Figure 2d. The total velocity of the lander then decreases down to V - 377 m/s immediately before parachute release at 8.6 km altitude. This speed is far greater than the magnitude of winds (<15 m/s) predicted by general circulation model calculations for this location and season [cf. Haberle et al., 1997]. Thus, since the velocities in Figure 2d are large relative to the modeled winds and since we have no direct measurements of

the winds, we use the velocities relative to the surface to evaluate the atmospheric density using (1). Between 1.36 km and 388 m altitude, the Mars Pathfinder radar altimeter measured the vertical motion of the lander. The measurements from the

radar altimeter provide a valuable basis for evaluating accumulated errors in the trajectory reconstruction. At 1 km altitude the radar altimeter data indicate the lander was descend-

ing at a rate of 66 m/s. At this same altitude, 57 m/s is the

velocity indicated by our trajectory reconstruction. Relative to the entry velocity of 7400 m/s, this 9 m/s difference indicates an integrated accuracy of 0.1%. However, 9 m/s is outside the formal uncertainty of 2 m/s we have evaluated based on the entry state uncertainties and digitization effects, as shown in Figure 2d. Scale factor errors on the 40 g scale of the accelerometer and/or errors in modeling the complex motion of the lander on the parachute (cf. Figure 1) likely contribute to this difference. The main effect of this accumulated error is the

possibility of up to 1 km offsets in the absolute altitudes we have derived. Nevertheless, the 0.1% integrated error is small compared to uncertainties in Co, as discussed next, and has little effect on the derived state variables.

The aerodynamic properties of the Mars Pathfinder entry vehicle have been determined from experimental data and computational fluid dynamic simulations, and these data have been used to create an aerodynamic database [Braun et al., 1995]. Co varies during the entry and depends on the velocity of the vehicle, a, the Knudsen number Kn, and the Mach number Ma. Since Kn depends on the atmospheric density and Ma depends on the atmospheric temperature, an iterative procedure is required to accurately determine the atmospheric density and aerodynamic coefficients. Initial density, pressure, and temperature profiles were evaluated by assuming a constant value of Co. From these profiles, Kn and Ma as a function of time were determined and used to evaluate im-

proved values of Co from the aerodynamic database reported

8948 MAGALHAES ET AL.: PATHFINDER ATMOSPHERIC STRUCTURE INVESTIGATION

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Figure 3. Aerodynamic drag coefficient Cr• of the Pathfinder entry vehicle versus altitude.

by Braun et al. [1995]. This procedure was continued until successive iterations yielded minor change in the atmospheric structure. Two iterations beyond the initial profiles were found to yield excellent convergence. Figure 3 presents the variation of Cr• with altitude as determined from our reconstruction effort. Between 160 and 125 km, free molecular flow aerodynamics determines a C r• of 2.02. At lower altitudes as atmospheric densities increase, the transition to hypersonic continuum aerodynamics (so-called hypersonic transitional flow) leads to a decrease in Cry. During hypersonic continuum flow, Cr• remains fairly constant. The final rise and drop occur as the vehicle velocities enter the supersonic flow regime. Uncertain- ties in C r• at the small a of the Pathfinder lander are from 1 to 3% JR. A. Mitcheltree, private communication, 1998; Braun et al., 1995].

Atmospheric pressure p is then derived from the density by integrating the equation of hydrostatic equilibrium, and the atmospheric temperature T is determined from the ideal gas law with knowledge of the mean molecular weight/• as in the following equations:

p(z) = -p(z0)# •zz In p - p# dz (2) z0 0

p(z) = (3) T(z) p(z)R

where R s is the universal gas constant and # is the local acceleration of gravity. The initial value of p at Zo is estimated from the density and density scale height at this level; this boundary term assumes variations in T(z) and/•(z) are small compared to variations in p(z). Uncertainty in this initial condition can have a significant influence on thep and T values at the start of the profile, but values at lower levels are insen- sitive to the initial condition.

We have assumed the atmosphere below about 100 km altitude has a mean molecular weight of 43.49 as determined from the Viking 1 and 2 lander mass spectrometer measurements at the surface [Owen et al., 1977]. Some variability of the mean molecular weight in this altitude range may be possible as a result of poorly understood mixing rates in an atmosphere whose major constituent condenses in the polar regions [cf. Owen, 1992]. At higher altitudes, photodissociation and diffu- sive separation lead to a gradient with altitude of the molecular

weight. We have created a model for the variation of molecular weight with pressure based on the Viking 1 UAMS results [Nier and McElroy, 1977; Seiff and Kirk, 1977]. Figure 4 presents the molecular weight model we have used. The National Center for Atmospheric Research (NCAR) Mars thermospheric general circulation (MTGCM) model of the upper atmosphere [cf. Bougher et al., 1990] indicates that substantial diurnal variation in the molecular weight profile can occur (S. W. Bougher, personal communication, 1998). To assess the possible errors associated with these diurnal variations, molecular weight profiles from the MTGCM (S. W. Bougher, personal communication, 1997) runs for local times around the Pathfinder landing have been used as well.

4. Results

Figure 5 displays atmospheric density as a function of altitude derived from the Pathfinder accelerometer data taken

prior to parachute deployment. The uncertainty envelope includes the trajectory uncertainties described earlier, digitization error, and uncertainties in Cry. Densities from the Viking 1 ASI [Seiff and Kirk, 1977] and UAMS [Nier and McElroy, 1977; Seiff and Kirk, 1977] experiments have been plotted for comparison. The atmosphere was first sensed by the science accelerometers at an altitude of 160 km where p - 2 x 10 -• kg/m3; at these levels the uncertainty envelope is dominated by digitization error. Upper atmospheric densities down to -90 km altitude were from a factor of about 5 to about 3 times

lower than the values found by Viking 1. Between 90 and 65 km the Pathfinder values quickly converge to the Viking 1 values. At lower altitudes the atmospheric densities remain -10-30% lower than the Viking 1 values over most of the

101 ........

100

• • Viking 1 UAMS values

..... MTGCM predict for 0300 LT MTGCM predict for 0500 LT

Figure 4. Models of mean molecular weight variation with pressure used to reconstruct temperature profile. Viking 1 UAMS values from Nier and McElroy [1977] and Seiff and Kirk [1977]. Combined NASA Ames Mars general circulation model and Mars thermospheric general circulation model (MTGCM) results [cf. Bougher et al., 1998] from S. W. Bougher (personal communication, 1998). Predictions for 0300 and 0500 LST are included to allow for uncertainties in phasing of diurnal variations in the model. Note that at the starting pressure of the Pathfinder entry profile (5 x 10 -8 mbar), the spread in the displayed mean molecular weights is 38.9-37.6, yielding a maximum effect on derived temperatures of -3.5%.

• 16 2

.13 d3 •E1 ß d 4

• d s

ld 7

28 30 •2 34 •6 •8 4•0 4•2 44 Mean molecular weight (amu)

MAGALHAES ET AL.' PATHFINDER ATMOSPHERIC STRUCTURE INVESTIGATION 8949

remaining profile. At the end of the entry phase, p = 8.1 x 10 -3 kg/m 3.

Figure 6 displays the atmospheric pressure profile. The pressure profile begins at z = 140 km to minimize the uncertainty in the starting value for pressure, which is based on the slope of the density (see (2)). At z = 140 km, p = 0.05 nbar. Because of the low upper atmospheric densities, upper atmospheric pressures are similarly lower than the Viking 1 values by factors of ---5 to ---3 down to an altitude of 85 km. The rate of increase of pressure then abruptly speeds up and quickly brings the pressures to ---10% below the Viking 1 value by 60 km altitude. At lower levels the pressures remain 10-30% below the Viking 1 values until the end of the entry phase profile, which ends with a pressure of 2.9 mbar at an altitude of 8.9 km. The reduced atmospheric pressures relative to Viking 1 in the lower atmosphere and at the surface are consistent with the seasonal variation in surface pressure and hence atmospheric mass observed by Viking 1 [Tillman, 1988] and the later season of Pathfinder's landing. This seasonal variation in atmospheric mass results from the condensation and sublima- tion of CO2 in the polar regions [cf. Zurek et al., 1992]. The annual pressure minimum occurred soon after the Pathfinder landing [Schofield et al., 1997], indicating the maximum areal extent of the south polar cap had been reached.

Figure 7 presents the thermal structure from Pathfinder as a function of altitude along with measurements from Viking 1. The Martian thermosphere, where temperature increases rapidly with altitude due to heating by solar EUV radiation [cf. Barth et al., 1992], is present as an increase in temperature between z = 125 and 134 km with a peak at T = 153øK. Note that between 110 and 88 km, a deep nearly isothermal layer (T = 127øK) is present. Observe that from 90 km altitude down to 55 km, large-amplitude (10-20øK) long vertical wave-

,40[ 120 -

100 -

E ,.. 80- N

: 60

40

20

! ! ! - ß

Pathfinder ASI ..... Viking 1 ASI and UAMS

'%, . m . i . i . ß

168 lC• 6 164 162 100 Pressure (mbar)

Figure 6. Atmospheric pressure profile from entry phase of Mars Pathfinder. See Figure 5 for details.

length (20-40 km) oscillations dominate the profile. The minimum temperature of the profile (92.6øK) occurs at the minimum of one of these oscillations at z = 85 km. The CO2 saturation curve from James et al. [1992], which is based on a fit to an extensive body of data on the vapor pressure of CO2 down to 100øK, has been plotted for comparison. The temperature profile is at or below the CO2 saturation curve between 85 and 77 km, with an average supersaturation of 4.8øK and a

140

160

140

120

100

80

60

40

20

! - .

•"•"' ' ' Pathfinder ASI •"• '... Viking 1 ASI and UAMS

I. m I I I I ß ' 0 10 -8 -6 -4 lO lO lO lO lO

Density (kg/m 3)

Figure 5. Atmospheric density profile from entry phase of Mars Pathfinder. An uncertainty envelope is also displayed and is based on the _+ 1 o-uncertainties in the entry state, the effects of digitization, and uncertainties in the aerodynamic drag coefficient as discussed in the text. Densities from the Viking 1 ASI [Seiff and Kirk, 1977] and UAMS [Nier and McElroy, 1977; Seiff and Kirk, 1977] experiments are plotted for comparison. Surface values measured by the Pathfinder MET instrument (circle) [cf. Schofield et al., 1997] and the Viking 1 lander (cross) [cf. Seiff and Kirk, 1977] are displayed as well.

120

lOO ...;;-

__--'-:'- 80 -',

'" .•,.

60 C02 saturation

40 '"-,-.

Pathfinder ASI 20

.... Viking 1 ASI and UAMS

100 120 140 160 180 200

Temperature (Kelvins) Figure 7. Atmospheric temperature profile versus altitude from entry phase of Mars Pathfinder. See Figure 5 for details. Note that individual points have been plotted for the central profile. Saturation temperatures for CO2 from James et al. [1992] are displayed as well.


140

130

15 120 N

• 11o

lOO

90

ß , ß ß , ß i •..,.,...•,... i l

'•"x> Viking 1 UAMS values (16:15 LT) • M• --- TGCM predict for 0300 LT

' ' ' , , , , , • • 105 110 115 120 125 130 135 140 1 5 1 0 155

Temperature (Kelvins)

Figure 8. Upper atmospheric temperature profiles and effects of assumed mean molecular weight profile. The three curves display the temperature profiles resulting from the use of the mean molecular weight profiles displayed in Figure 4. Note that differences in the upper atmospheric temperatures resulting from the molecular weight profiles are _<5øK, which is much smaller than the uncertainty envelope due to other sources shown in Figure 7. Above 115 km, the principal source of uncertainty is the digitization error.

maximum supersaturation of 7.4øK at 81 km. Note that the Pathfinder profile also touches the saturation curve at 65 km altitude.

Below 55 km altitude, a subadiabatic monotonic increase in temperature down to 16 km is interrupted with weak thermal inversions at 55, 38, and 28 km. At 16 km an unexpected strong thermal inversion is present in which temperature decreases from 199øK at this altitude down to 183øK at 9.9 km. Temper- atures then abruptly increase to 188øK at the last measurement at 8.9 km (p -- 2.9 mbar). Further work is needed to determine if the smallest amplitude waviness (amplitude _<IøK) below 55 km is a real structure in the atmosphere. At these levels of the atmosphere, aerodynamic instabilities [cf. Braun et al., 1995] can lead to high-frequency small-amplitude angular oscillations of the spacecraft which could be causing this ap- parent waviness.

Figure 8 presents an expanded view of the temperature structure above 85 km altitude and illustrates the uncertainties

introduced by the possible range of molecular weight profiles at these levels. The uncertainty envelope in this figure includes only the effects of the different molecular weight profiles shown in Figure 4. To the extent that the three molecular weight models correctly span the possible range of mean molecular weights, the introduced uncertainty decreases with decreasing altitude from -4øK at z = 140 km down to zero at z = 100 km. Note this uncertainty is much smaller than the uncertainty envelope in Figure 7, which is dominated by the effects of signal digitization at these altitudes. Observe the oscillations in temperature with vertical scales of -5 km and amplitudes of-2-3øK which are evident throughout this region.

Since pressure rather than altitude is the physically mean- ingful variable related to radiative transfer and since the pressure structure of the Pathfinder and Viking 1 profiles is significantly different at a wide range of altitude, the temperature

profiles from these two missions are best compared on constant pressure surfaces. Figure 9 displays temperature versus atmospheric pressure from Pathfinder and Viking 1. Note the striking effect on the comparison of the thermospheric temperatures. Both the Pathfinder and Viking 1 profiles show peaks corresponding to the thermosphere at p - 1 x 10 -7 mbar, but the Pathfinder peak is 25øK cooler than the Viking 1 values at the same pressure. At lower levels of the upper atmosphere and in the middle atmosphere, the comparison on constant pressure surfaces leads to very good alignment of the isothermal layers and of the extrema of the large temperature swings occurring in both profiles. On average, the atmosphere betweenp = 8 x 10 -6 mbar (90 km) andp = 0.01 mbar (60 km) is 20-30øK cooler than the atmosphere at the time of Viking 1, with much larger differences near the peaks of the oscillations. Fromp - 0.01 mbar (55 km) down top = 1.42 mbar (16 km) the Pathfinder temperatures are on average quite close to or warmer than the Viking 1 values, with appar- ent superposed oscillations which appear anticorrelated between Pathfinder and Viking 1. Below this level, the thermal inversion causes Pathfinder temperatures to diverge significantly from the Viking 1 profile.

Figure 10 displays the static stability (dT/dz + #/%) com- puted from the temperatures in Figure 7. The Cp for pure CO2 has been evaluated by fitting a quadratic polynomial in temperature to experimental data presented by Hilsenrath et al. [1960] and Keenan et al. [1983]. The presented data cover the range of Martian temperatures and include data taken at p = 0.01 atm. A small correction to the actual composition of the Martian atmosphere [Owen et al., 1977] resulted in the following expression for Cp (based on data covering 100-270øK): Cp = 0.0033T 2 - 0.2716T + 656.30, where Cp is in mks units. The static stability provides a measure of the stability of

10 '5 10 '4

13_ '2 lO

10 '1

10 0

C02 saturation

Pathfinder ASI

.... Viking 1 ASI and UAMS

100 120 140 160 180 200

Temperature (Kelvins) Figure 9. Entry phase temperature profile as a function of pressure. See Figure 7 for details.

MAGALHfid•S ET AL.: PATHFINDER ATMOSPHERIC STRUCTURE INVESTIGATION 8951

the atmospheric structure to small vertical displacements when no wind shear is present. Significant variations with altitude are clearly present. In particular, observe the broad region of low stability at 52-65 km. Note the two narrow regions of high stability near 68 and 85 km as well. At the base of the profile the static stability is negative over a narrow altitude range near 9 km, reflecting the abrupt increase in temperatures at the base of the thermal inversion. Note the small-scale oscillations in

the stability as well, possibly indicative of atmospheric wave activity. Recall from Figure 2 that significant horizontal motion of the lander occurred above at3out 15 km altitude, so that Figure 10 may be sampling horizontal gradients in static stability and/or temperature as well.

Table 1 presents the derived atmospheric entry profiles in numerical form on a 2 km altitude grid. The full entry profiles and associated trajectory information are available on the Planetary Data Subsystem's (PDS) Mars Pathfinder CD-ROM.

5. Discussion

5.1. Mean Structure

The large decrease in atmospheric densities and pressures between z --- 60 and ---85 km coincides with the very low temperatures measured in the middle atmosphere. Cold temperatures yield reduced density and pressure scale heights, which cause the overlying surfaces of constant density and pressure to drop in altitude. At the temperature minimum of 92øK the density scale height is 5 km, which is significantly smaller than the 7.6 km scale height corresponding to the 140øK of the Viking 1 profile at these levels. Thus over an altitude range of 15 km, an atmosphere at 92øK would decrease in density by a factor ---20, while an atmosphere at 140øK would drop in density by a factor of ---7.4, yielding a relative drop in density of a factor of ---3. To more carefully investigate this drop in the constant pressure surfaces of the atmosphere observed by Pathfinder, we have taken the base pressure observed by Pathfinder at 60 km and evaluated the resulting density and pressure structure at higher altitudes using the

lOO

90

80

70

E 6O

N

e 50

ß • 40

30

20

10

I

0 I I I I I I -5 0 5 10 15 20 25

Ida+ g] (Kelvins/km) Cp

Figure 10. Static stability (dT/dz + g/½p) as a function of altitude derived from the temperatures in Figure 7. Neutral static stability is marked by a dashed line. The lapse rates are derived by differentiating a marching cubic polynomial in altitude fit to points within a 5 km box about each point.

Table 1. Atmospheric Structure Profiles

z, km p, mb T, øK p, kg/m 3

140.00 5.60e-08 143.30 1.84e- 10 138.00 7.02e-08 144.66 2.32e- 10 136.00 8.80e-08 145.98 2.92e- 10 134.00 1.10e-07 152.42 3.53e- 10

132.00 1.38e-07 144.20 4.72e-10 130.00 1.79e-07 127.26 7.00e- 10 128.00 2.36e-07 122.02 9.73e- 10 126.00 3.17e-07 115.05 1.40e-09 124.00 4.34e-07 110.37 2.02e-09 122.00 6.00e-07 111.23 2.79e-09

120.00 8.28e-07 111.53 3.86e-09 118.00 1.15e-06 107.14 5.60e-09 116.00 1.6 le-06 109.22 7.69e-09 114.00 2.22e-06 117.07 9.89e-09 112.00 3.00e-06 123.29 1.27e-08 110.00 4.02e-06 126.28 1.66e-08

108.00 5.31e-06 132.85 2.09e-08 106.00 7.06e-06 125.21 2.95e-08 104.00 9.43e-06 127.35 3.87e-08 102.00 1.26e-05 125.55 5.27e-08 100.00 1.69e-05 125.64 7.03e-08

98.00 2.26e-05 127.31 9.27e-08 96.00 3.01e-05 126.31 1.25e-07 94.00 4.04e-05 127.27 1.66e-07 92.00 5.37e-05 133.09 2.11 e-07 90.00 7.11 e-05 130.48 2.85 e-07

88.00 9.41e-05 133.70 3.68e-07 86.00 1.27e-04 107.63 6.15e-07 84.00 1.85e-04 94.52 1.02e-06 82.00 2.73e-04 97.24 1.47e-06 80.00 4.02e-04 96.83 2.17e-06 78.00 5.86e-04 101.07 3.03 e-06

76.00 8.37e-04 108.25 4.04e-06 74.00 1.17e-03 114.13 5.37e-06 72.00 1.61 e-03 121.11 6.95 e-06 70.00 2.17e-03 127.16 8.93e-06

68.00 2.90e-03 127.47 1.19e-05 66.00 3.96e-03 112.01 1.85e-05

64.00 5.52e-03 116.71 2.47e-05 62.00 7.53e-03 124.60 3.16e-05 60.00 1.01 e-02 130.22 4.06e-05

58.00 1.34e-02 138.15 5.07e-05 56.00 1.74e-02 146.67 6.22e-05 54.00 2.24e-02 151.74 7.73e-05 52.00 2.86e-02 159.05 9.40e-05 50.00 3.61 e-02 163.44 1.15e-04

48.00 4.56e-02 162.44 1.47e-04 46.00 5.76e-02 163.85 1.84e-04 44.00 7.24e-02 166.39 2.28e-04 42.00 9.07 e-02 169.36 2.80e-04 40.00 1.13e-01 172.08 3.44e-04 38.00 1.4 le-01 174.22 4.23 e-04

36.00 1.76e-01 171.44 5.36e-04 34.00 2.19e-01 171.89 6.68e-04

32.00 2.74e-01 176.46 8.11 e-04 30.00 3.38e-01 181.77 9.74e-04 28.00 4.17e-01 182.11 1.20e-03 26.00 5.14e-01 185.22 1.45 e-03 24.00 6.33e-01 185.32 1.79e-03 22.00 7.78e-01 187.18 2.17e-03 20.00 9.54e-01 191.55 2.60e-03 18.00 1.17e + 00 194.15 3.14e-03 16.00 1.42e+00 198.45 3.74e-03 14.00 1.73e + 00 194.68 4.64e-03 12.00 2.1 le + 00 188.96 5.85e-03

10.00 2.60e+00 185.01 7.35e-03

Read 5.60e-08 as 5.60 x 10 '8.


Viking 1 thermal structure and the assumption of hydrostatic balance. The resultirig density and pressure profiles agree very well with those observed by Viking 1. Therefore the low densities and pressures observed above 85 km and the rapid drop in these quantities over the 60-85 km altitude range can easily be accounted for by the cold middle and upper atmospheric

km, the Pathfinder entry profile reveals temperatures that are very similar to or somewhat warmer than values in the Viking 1 profile. At these levels of the atmosphere the abundance of suspended dust has an important effect on the thermal structure [cf. Gierasch and Goody, 1972; Pollack et al., 1979; Haberle et al., 1997]. After landing, the Imager for Mars Pathfinder

temperatures observed by Pathfinder. (IMP) determined the dust optical depth •-and the dust scale As can be seen in Figure 9, the average temperature of t'he height in the Martian atmosphere by observing the intensity of

region from the top of the profile down to the middle atmosphere is -20-30øK cooler than the same levels in the Viking 1 profile. Seasonal variation in the diurnally averaged solar flux between the two entries is of the wrong sign to account for these cooler temperatures. Temperatures in the thermosphere are influenced by solar EUV flux, which is modulated by the 11-year solar cycle as well as by seasonal variations [cf. Bougher et al., 1990]. Both entries occurred close to a minimum in the solar cycle, so variations in solar EUV flux are unlikely to account for the lower thermospheric temperature measured. Haberle et al. [1997] investigated the circulation of the atmosphere below 65 km altitude for the time of the Pathfinder landing. They found the average thermal structure at this location and season to be influenced by the rising branch of a cross-equatorial Hadley cell for dust optical depths like the values observed by Viking and Pathfinder. Over the L s range between the Viking 1 and Pathfinder landing, the circulation and its effects on the mean thermal structure are expected to be similar [Haberle et al., 1993a; Magalhges, 1987].

The very different local times of the entries (0258 LST for Pathfinder; 1615 for Viking 1) and the 21 years between the two entries suggest diurnal variations and/or secular or interannual variations in thermal structure could be important in accounting for the cold upper and middle atmosphere. Tem- peratures predicted for this region for the time of the Path- finder entry using a general circulation model (GCM) were -20-30øK warmer than the observations [Haberle et al., 1997]. At the pressures at these altitudes, local thermodynamic equilibrium (LTE) is not achieved, and a detailed computation of the populations of the energy levels and transitions must be performed to properly model the thermal structure. L6pez- Puertas and L6pez-Valverde [1995] have performed such a non- LTE calculation for the Martian atmosphere and found high infrared cooling and heating rates in the middle and upper atmosphere of Mars. The altitude range over which their calculations show solar IR heating rates of over 30øK per day agrees very well with the altitude range over which the Path- finder temperature profile is significantly cooler than the Vi- king 1 profile. Since the calculations are somewhat sensitive to the assumed thermal structure, further work to apply these calculations to the Pathfinder profile is needed. Haberle et al. [this issue] find that dynamical effects are important in cooling this region of the atmosphere. Clancy and Sandor [1998] observed cold daytime mesospheric temperatures using ground- based disk-averaged microwave observations of Mars taken around the time of the Pathfinder landing. They use these observations as well as other data sets, including the Pathfinder profile, to argue that a decrease in the dust loading of the mesophere of Mars since the time of the Viking 1 entry is the cause of the cold mesopheric temperatures. Therefore the existing work appears to suggest that both diurnal (radiative and dynamical) and secular/interannual variations could potentially be important in understanding the thermal structure of the upper and middle atmosphere of Mars.

In the lower atmosphere below 60 km altitude down to 16

the Sun at a range of zenith angles [Smith and Lemmon, this issue; Smith et al., 1997]. Daily values of •- - 0.4-0.6 were observed during most of the landed mission, and the scale height of the dust was found to be very close to the gas scale height (-10 km). These values are essentially identical to the values deduced from similar imaging observations obtained by Viking 1 at this season [Pollack et al., 1979]. The similarity in the dust opacities and scale heights is in very good agreement with the similarity between the Pathfinder and Viking 1 temperature profiles of the lower atmosphere.

5.2. Thermal Tides

Global-scale oscillations of the atmosphere induced by the diurnally varying solar heating (thermal tides) are known to be important on Mars due the low mass of the atmosphere and the direct absorption of sunlight by suspended dust [cf. Zurek et al., 1992]. Two dominant propagating tidal modes on Mars (as on Earth) are believed to be a diurnal mode (period equal to the length of the Martian day and wavelength equal to the circumference of Mars) and a semidiurnal mode (with period equal to one-half Martian day and wavelength equal to half the planetary circumference) as discussed by Zurek [1980]. Classi- cal tidal theory, which models tides as linear disturbances to a motionless background state with temperature varying only with altitude and with no topography included, yields the following expression for the vertical wavelength of a tidal oscillation [cf. Andrews et al., 1987]:

2rrH

Xz = (FH2/rhn _ 1/4)•/2 (4) where H is the pressure scale height, T is temperature, F is the static stability of the background state, and h,• is the so-called equivalent depth of each tidal mode and corresponds to eig- envalues of Laplace's tidal equation, which defines the horizontal structure of the tides. The dominant diurnal mode has

h,• = 0.485 km, and the dominant semidiurnal mode has h,• - 5.52 km [Zurek, 1980].

Figure 9 shows large-amplitude long-wavelength oscillatory structures in both the Pathfinder and Viking 1 profiles. Note the high degree of correlation of the structures in the Path- finder and Viking 1 profiles between 1 x 10 -7 mbar (135 km altitude) and 1 x 10 -4 mbar (90 km altitude). At higher pressures a good anticorrelation of the extrema of the undulations is evident all the way down to 0.2 mbar (-40 km) and possibly down to 0.8 mbar (-25 km). The approximate vertical wavelengths and amplitudes of the structures in the Pathfinder profile (the Viking 1 values are similar) are presented in Table 2. Table 2 also presents the vertical wavelengths derived from (4). Since the linear analysis used to derive (4) assumes the tides propagate through a "background" thermal structure, we have evaluated the vertical wavelengths using a background thermal structure derived by applying a low-pass digital filter with a 60 km box width to the observed temperatures in Figure 7.

For two entry profiles taken at the same location but 13

MAGALHAES ET AL.' PATHFINDER ATMOSPHERIC STRUCTURE INVESTIGATION 8953

Table 2. Comparison of Observed Properties of Large-Amplitude Oscillations in Pathfinder and Viking 1 Entry Profiles to Tidal Mode Vertical Wavelengths Predicted by the Classical Theory of Tides

Observed Mode

Pressure, Altitude z, Amplitude, Wavelength, Suggested mbar km øK km by Phasing

Theory

Diurnal

Mode, km Semidiurnal

Mode, km

10 -7 135 12 20 semidiurnal 4 x 10 -6 110 12 45 semidiurnal 2 x 10 -4 82 16 24 diurnal 0.004 65 10 20 diurnal

0.08 45 10 34 diurnal 0.8 25 3 20 diurnal

29 200

20 120

21 120 20 80 22 90 26 110

hours apart (which corresponds to the local time difference between the Pathfinder and Viking 1 profiles), a diurnal tidal mode would result in approximately anticorrelated oscillation peaks in the two profiles. Table 2 shows that such diurnal modes would have vertical wavelengths of approximately 20 km. The oscillatory structures with extrema at p = 2 x 10 -4 mbar (z = 82 km)andp = 4 x 10 -3 mbar (z = 65 km) clearly display both the phase relationship and vertical wavelengths expected for the diurnal tidal mode. The structures centered atp = 0.08 mbar (z = 45 km) andp - 0.8 mbar (z = 25 km) have the correct phase relationship, and the wavelengths are within 50% of the values expected from classical tidal theory. Haberle et al. [this issue] present GCM simulations, which fully include tides without the approximations of classical tidal theory, of the Pathfinder ASI profile fromp = 10 -4 mbar down to the surface. Their results show diurnal

temperature oscillations with similar vertical scales and amplitudes as the features in the ASI profile.

Over the same 13 hour local time difference, a semidiurnal tidal mode would produce correlated oscillatory structures. As can be seen in Table 2, a vertical wavelength of ---120-200 km is expected for the semidiurnal mode based on the classical tidal theory. Although the phase relationships of the structures at p = 1 x 10 -7 mbar (z = 135 km)andp = 4 x 10 -6 mbar (z = 110 km) are correct for a semidiurnal mode, the wavelength does not agree with the predictions of classical tidal theory. Classical tidal theory may not provide an adequate description of tides at these levels of the atmosphere. Alter- nately, the correlated structures at these upper levels could simply represent the mean structure of this region of the atmosphere and not reflect the signature of a semidiurnal tidal mode. Recall that the rise in temperature at pressures less than 10 -6 mbar (z > 120 km) corresponds to the thermosphere of Mars.

The amplitudes of the extrema at p = 0.8 and 0.08 mbar follow the expected p-i/2 rise for an undamped vertically propagating wave. However, at lower pressures the amplitudes vary little with height and indicate that damping of the vertically propagating tidal modes must be occurring. As waves propagate vertically and increase in amplitude, the lapse rates induced by such waves can exceed the adiabatic lapse rate and induce eddy mixing, which can damp the additional growth of the waves [Lindzen, 1981]. The reduced static stabilities between 50 and 80 km in Figure 10 suggest the amplitudes of the tidal modes are limited by breaking. Using the expression of Lindzen [1981] as a basis, the induced eddy diffusivity required to limit the amplitude growth is ---10 4 m 2 s -•, which agrees with Zurek [1976]. In addition, L6pez-Puertas and L6pez- Valverde [1995] have found high infrared cooling and heating

rates in the middle and upper atmosphere of Mars and radiative damping could potentially damp vertically propagating waves with diurnal timescales.

Therefore comparison of the large-amplitude structures in the Pathfinder and Viking 1 profiles suggests that a diurnal tidal mode can account for the large-amplitude oscillatory structures in these two profiles. Due to the expected long vertical wavelength of the semidiurnal mode and the gimilarity of the phasing of the semidiurnal mode in profiles taken 13 hours apart in local time, it is difficult to identify unambigu- ously the signature of the semidiurnal mode in the profiles. The similarity of the oscillatory structures in the two entry profiles, even though they were taken 21 years apart, suggests the structure of the tidal oscillations is strikingly robust during times away from global dust storms.

5.3. Thermal Inversion

The pronounced decrease in temperature with decreasing altitude below z = 16 km was unexpected [cf. Haberle et al., 1997, 1993b; Gierasch and Goody, 1968]. Near-surface thermal inversions in which temperatures decrease with decreasing altitude in the lowest few kilometers of the nighttime Martian atmosphere have been predicted by radiative-convective models [Gierasch and Goody, 1968; Haberle et al., 1993b]. The short radiative time constant of the thin Martian atmosphere and the low thermal inertia of the surface result in a much stronger and deeper near-surface thermal inversion during nighttime than is produced on Earth. The feature in the Pathfinder profile is much too high to be the predicted near-surface inversion. Us- ing our observed temperature at z = 8.9 km and the temperature ineasured at the surface [SchofieM et al., 1997], the surface temperature can easily be achieved with subadiabatic lapse rates. In addition, allowing for one of the predicted near-surface inversions, which would raise the temperature within a few kilometers of the ground, subadiabatic or adiabatic lapse rates can again reach the top of one of these low-level inversions.

Haberle et al. [this issue] find that the enhanced radiative cooling due to the presence of a cloud layer could produce the observed thermal inversion. The observed abrupt 5øK increase in temperature at the ba;e of the inversion between 9.9 and 8.9 km is also suggestive of the effects of a cloud layer. Indeed, images acquired by the IMP have shown clouds on the eastern horizon well before and soon after sunrise [Smith and Lem- mon, this issue; Smith et al., 1997]. In addition, Hubble Space Telescope observations of Mars in recent years and historical ground-based observations have also revealed white clouds near the morning terminator of the planet [James et al., 1996].

8954 MAGAL•S ET AL.: PATHFINDER ATMOSPHERIC STRUCTURE INVESTIGATION

These observations have been interpreted as evidence for early morning water ice clouds, although the altitudes of these observed clouds have not yet been uniquely determined.

The mechanism causing a cloud to form at these levels is still unknown. Dynamical mechanisms associated with horizontal or vertical advection of fluid could in principle lead to a thermal perturbation which would begin the cloud formation pro- cess. In the nighttime boundary layer, finite amplitude gravity waves can be excited by even quite small topographic obstacles [cf. Magalh•es and Young, 1995], and the required cooling of the fluid relative to Viking 1 is of the right amplitude to be produced by vertical adiabatic displacement by a finite amplitude gravity wave or other dynamical mechanism resulting in vertical motion. Alternate explanations involving vertical gradients in the dust opacity (and hence temperature) of the atmosphere produced by a local dust storm which occurred in Vallis Marineris immediately preceding the Pathfinder landing have also been suggested (R. T. Clancy, personal communication, 1998). Further work is needed to properly address the genesis of the thermal inversion.

5.4. CO2 Supersaturation

Temperatures in the Pathfinder profile between 85 and 77 km altitude are below the CO2 saturation curve by up to 7øK, which is well outside the uncertainty envelope of the ASI profile. The uncertainties in the saturation vapor pressure curve for CO2 are very small [cf. James et al., 1992] and at most introduce 0.4øK uncertainty in the curve. Therefore the Path- finder measurements clearly indicate atmospheric temperatures near 82 km are at and below the saturation temperature of CO2. The possibility of CO2 cloud formation on Mars has previously been discussed for the winter polar night in the lower atmosphere near the surface (cf. James et al. [1992] for a review and Forget et al. [1995]). However, formation of CO2 clouds in the middle atmosphere of the summer tropics is a new possibility which has not previously been explored. If CO2 clouds are forming near 82 km, the mean molecular weight of the atmosphere at these levels could potentially be increased by the presence of solid CO2 particles. Our derivation of temperature depends on the molecular weight (see (3)), so that the actual temperature of the atmosphere in the region of supersaturation could be somewhat higher than the displayed values. However, of course, T could not be larger than the saturation temperature itself, since the perturbation of the mean molecular weight would then not occur.

In Earth's mesosphere, noctilucent water ice clouds are observed to form and have been extensively modeled [cf. Jensen, 1989; Jensen et al., 1989]. High supersaturations of -> 10øK can occur in Earth's mesosphere; in addition, the low temperatures and low abundances of condensation nuclei at these altitudes

can significantly modulate cloud particle formation. These features of the terrestrial case (for example, the supersaturations we have detected) are likely also to be relevant to the formation of CO2 clouds in the Martian mesosphere even though the condensing molecule has different properties and is the major constituent of the atmosphere rather than a minor constituent. Further modeling of the microphysics of CO2 cloud formation and improved estimates of the abundance of condensation nuclei at these levels are clearly needed to assess if CO2 clouds could form in the middle atmosphere of the summer tropics.

High-altitude detached condensate hazes have previously been imaged by the Viking orbiters [cf. Jaquin et al., 1986] and detected by solar occultation measurements [cf. Chassefibre et

al., 1992] at a broad range of latitudes and seasons. Near the location and season of the Pathfinder landing, the tops of the observed detached condensate hazes occur at about 50-60 km

[Jaquin et al., 1986]. Although these tops are ---20 km lower than the region we have observed to be supersaturated, these observations indicate that narrow condensate layers do form in the middle atmosphere of Mars. Moreover, few observations exist of the morning terminator, and at the low pressures near 82 km, the signature of any condensate hazes may be too small to be visible in the limb images and occultation measurements. Herr and Pimental [1970] reported observations by the Mariner 6 and 7 infrared spectrometers of scattered sunlight in the 4.3 /am spectral feature of solid CO2 when the instrument was pointed at low latitudes, although the altitude corresponding to the observations is somewhat uncertain. Based on their

ground-based microwave observations and other data sets, Clancy and Sandor [1998] have proposed that the Herr and Pimental observations sampled CO2 ice clouds in the Martian daytime middle atmosphere (z •- 60-80 km). As discussed above, we have associated the temperature minimum at 82 km with the diurnal tide. If this interpretation is correct, this cold temperature and the associated supersaturation would only occur during nighttime. However, the local temperature maximum at p = 2 x 10-3 mbar (z •- 70 km), if it represents a different phase of the diurnal tide, would become a minimum 12 hours later. Whether such a minimum would cross the CO2 saturation curve depends on the extent of the warming of the middle atmosphere during daytime (see section 5.1). Should clouds form about these temperature minima, the narrowness of these minima suggests the clouds would appear as detached limb clouds.

Acknowledgments. We thank Bobby Braun and Dave Spencer for providing us with the Pathfinder aerodynamic database in digital form, and we thank Bob Mitcheltree for information on the uncertainties in

the aerodynamic coefficients. We thank Steve Bougher for allowing us to use the upper atmospheric molecular weight profile predictions from his Mars Thermospheric General Circulation model calculations for the time of the Pathfinder entry; these have proved quite valuable in deriving the upper atmospheric temperatures. We thank two review- ers for very helpful comments.

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(Received April 1, 1998; revised November 24, 1998; accepted November 25, 1998.)

Results of the Mars Pathfinder atmospheric structure investigation

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