THE PHOENIX ATMOSPHERIC STRUCTURE EXPERIMENT …sirius.bu.edu/withers/pppp/pdf/withersippw2010proc.pdfTHE PHOENIX ATMOSPHERIC STRUCTURE EXPERIMENT (ASE): DATA PROCESSING AND SCIENTIFIC

THE PHOENIX ATMOSPHERIC STRUCTURE EXPERIMENT (ASE): DATAPROCESSING AND SCIENTIFIC RESULTS

Paul Withers1 and D. C. Catling2

1Center for Space Physics, Boston University, 725 Commonwealth Avenue, Boston, MA 02215, USA ([email protected])2Department of Earth and Space Sciences, University of Washington, Box 351310, Seattle, WA 98195-1310, USA

ABSTRACT

The purpose of this report is to highlight certain aspectsof the data processing and scientific results associatedwith the Atmospheric Structure Experiment (ASE) of thePhoenix Mars lander. This experiment presented someunique challenges because its hardware was essentiallydesigned and built to fulfill engineering requirements be-fore the Phoenix mission began, meaning that the in-volvement of atmospheric scientists in the performanceof the experiment was extremely limited. Nonetheless,the reconstruction of the Phoenix trajectory and asso-ciated atmospheric structure was successfully accom-plished.

Key words: Mars; Atmosphere; Phoenix; EDL.

1. INTRODUCTION

NASA’s Mars Scout program selected the Phoenix mis-sion for flight in 2003. Its science mission focused “onproviding the ground truth for the 2002 Odyssey discov-ery of massive ice deposits hidden under surface soils inthe circumpolar regions” (Smith et al. 2008). The ob-jectives of this mission were: (1) to study the history ofthe ground-ice and its emplacement mechanisms, (2) toaddress the effect that subsurface ice has on the localsurface geomorphology, (3) to characterize the climateand local weather of the landing site, and (4) to addressthe habitability of the icy soil (Smith et al. 2008; Arvid-son et al. 2009; Smith et al. 2009). Much of the designof the Phoenix spacecraft, including those aspects rele-vant for cruise and entry, descent, and landing (EDL),derived from the mothballed “Mars Surveyor 2001 Lan-der” (Guinn et al. 2008; Desai et al. 2008; Grover et al.2008). Phoenix launched on 4 August 2007 and success-fully landed on Mars in the late afternoon (16.6 hrs) inthe Vastitas Borealis or northern plains region on 25 May2008 (Table 1). Data from its EDL have been used to ob-tain the first profile of atmospheric density, pressure, andtemperature from the martian polar regions with a verti-cal range in excess of 100 km and vertical resolution ofless than 1 km.

Table 1. Time and position of Phoenix landing.Time1 (UTC) 2008-05-25T23:38:24Aerocentric latitude2 (N) 68.21878± 0.00006Longitude2 (E) 234.24845± 0.000096Radius2 (km) 3376.2915± 0.0014Elevation3 (m) -4131Ls

4 (degrees) 76.6Local true solar time5 (hrs) 16.6

1Smith et al. (2009).2Martin-Mur (personal communication, 28 May 2008).The landed latitude, longitude and radius, which areshown with 1σ uncertainties, were determined fromDoppler tracking.3Elevation is with respect to the areoid de-fined by the Mars Orbiter Laser Altimeter(MOLA) investigation, specifically 16 pixelsper degree gridded MOLA data acquired fromhttp://geo.pds.nasa.gov/missions/mgs/megdr.html (Smithet al. 2003).4Calculated using http://www-mars.lmd.jussieu.fr/mars/time/martiantime.html.5Calculated from tabulated time and position usingSPICE tools provided by JPL’s Navigation and AncillaryInformation Facility (NAIF).

Table 2. Reconstructed conditions and their 1σ uncer-tainties at parachute deployment.

Altitude (km) 13.54 0.38Areocentric latitude (N) 68.265 0.030Longitude (E) 234.034 0.058Atmosphere-relative speed (m s−1) 390.9 1.5Angle of attack (deg) 4.90 0.71Mach number 1.703 0.015

Table 3. Reconstructed conditions and their 1σ uncer-tainties at first ground contact.

Altitude (km) 1.10 1.49Areocentric latitude (N) 68.237 0.029Longitude (E) 234.311 0.054Atmosphere-relative speed (m s−1) 6.1 3.6

The Experiment Data Records (EDRs, time series of ve-locity changes and angular velocities with 200 samplesper second) from the Phoenix Atmospheric Structure Ex-periment are available from the NASA Planetary DataSystem at http://atmos.nmsu.edu/PDS/data/phxase0001/(Catling et al. 2008). The Reduced Data Records (RDRs,reconstructed trajectory and atmospheric structure) fromthe Phoenix Atmospheric Structure Experiment are alsoavailable from the NASA Planetary Data System, thistime at http://atmos.nmsu.edu/PDS/data/phxase0002/(Withers et al. 2010). Production of the RDRs fromthe EDRs has been reported previously in Withers et al.(2010) and the first scientific results have been summa-rized previously in Withers & Catling (2010). Analy-ses of data from ASE for engineering purposes have alsobeen undertaken (Desai et al. 2008; Blanchard 2009).The unique contribution of the current work is to bringthose two themes together in a single package that is fo-cused on the interests of readers with a strong interest inthe technological challenges and scientific opportunitiesassociated with entry, descent, landing and flight in plan-etary atmospheres.

Figure 1 shows the time series of smoothed axial accel-erations recorded during entry. Unsmoothed axial ac-celerations only exceed their uncertainties below 65 km.Smoothing extends the vertical range of useful data up to128 km. The entry interface, defined to occur at a radialdistance of 3522.2 km, equivalent to an altitude of 145.9km, occurred att = 1857.733 seconds. All altitudes re-ported in this paper are radial distances above 3376.3 km,which is the radial distance to the landing site, not dis-tances relative to an equipotential surface. Peak deceler-ation was 84 m s−2. Parachute deployment is responsiblefor the sudden increase in the magnitude of the measuredacceleration neart = 2090 seconds and lander separationis responsible for the increase in the variance of the mea-sured acceleration neart = 2160 seconds. Other eventsthat occurred during EDL can be identified by careful in-spection of the acceleration measurements (Desai et al.2008). The reconstructed atmosphere-relative speed isshown in Figure 2. Table 2 reports the reconstructedconditions at parachute deployment and Table 3 reportsthe reconstructed conditions at first ground contact. Thespeed at first ground contact was6.1 ± 3.6 m s−1, whichcompares favourably with the design value of “a few ms−1” (Desai et al. 2008). This speed differs from zero byabout 0.1% of the entry speed of 5600 m s−1 (speed in aMars-centered inertial frame) and differs from the designvalue of “a few m s−1” by even less, suggesting that thetrajectory reconstruction process was extremely success-ful, including the reconstruction of Phoenix’s attitude.

The remaining sections of this work focus first on dataprocessing, then on scientific results. Section 2 demon-strates the importance of accurate knowledge of relevantreference frames. Section 3 demonstrates a novel methodfor reducing noise by averaging. Section 4 demonstratesan inconsistency between two independent determina-tions of the angle of attack history of Phoenix. Sec-tion 5 outlines a possible alternative method for determin-ing atmospheric density that is based on angle of attack

1800 1900 2000 2100 2200 2300 2400Time after 23:00:00.000 UTC (sec)

1E-5

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Figure 1. Smoothed axial accelerations (solid line) and1σ uncertainties (dashed line). Uncertainties change asthe width of the smoothing window decreases from 20seconds at entry to 0.32 seconds during peak decelera-tion.

0 1000 2000 3000 4000 5000 6000Atmosphere-relative speed (ms-1)

0

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itu

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)

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Figure 2. Atmosphere-relative speed as a function of al-titude. In this frame, speed increases from 5517 m s−1 atentry to a maximum value of 5552 m s−1 at 81 km alti-tude. Acceleration due to gravity is more significant thandeceleration due to aerodynamic drag in the rarefied up-per atmosphere.

Figure 3. Reconstructed angle of attack using either the“as designed” matrix (solid line) or the “as built” matrix(dashed line). The choice of transformation matrix hasdramatic implications for the reconstructed flight history.

oscillations. Section 6 outlines another possible alter-native method for determining atmospheric density thatuses Doppler-shifted radio transmissions during EDL.Section 7 presents and discusses the atmospheric resultsof the Phoenix Atmospheric Structure Experiment. Sec-tion 8 summarizes the findings of this work.

2. A GOOD SENSE OF DIRECTION

The time series of accelerations and angular velocitiesrecorded during EDL that were originally archived as Ex-periment Data Records (EDRs) by the PDS (Catling et al.2008) require a small correction (Withers et al. 2010).The raw data were transformed between several framesbefore being archived. One transformation matrix thatwas used in this process was based upon the spacecraft asdesigned, not as built. Elements of the “as built” matrixdiffer from the equivalent elements of the “as designed”matrix in the second or third decimal place. These appar-ently minor differences have major implications for thereconstructed trajectory and atmospheric structure. Al-titude at parachute deployment varies by over 2 km de-pending on which version of this matrix is used, as doesthe altitude of first ground contact. The reconstructed an-gle of attack at parachute deployment, which can lead tomission failure if it is large, is a few degrees with the “asbuilt” matrix, but over ten degrees with the “as designed”matrix (Figure 3). Clearly, experimenters working on at-mospheric structure experiments need to be aware of allaspects of their experiment and how uncertainties in eventhe least significant aspect can affect the accuracy of thefinal results. Requirements need to be defined, justified,and satisfied for every item that can affect the perfor-mance of the experiment and its results. This is perhapsmost challenging for atmospheric structure experimentsthat are initially conceived as serving limited engineeringpurposes and only transform into scientific investigationsat a late stage of their life cycle.

3. REDUCING NOISE

All atmospheric structure experiments work at their noiselimits at high altitudes. Finding ways to reduce noise,thereby increasing vertical range upwards, is a commonchallenge. Averaging is the obvious approach to pursue,but at the cost of reducing vertical resolution. Yet the sim-ple arithmetic mean is not appropriate here. The magni-tude ofa, the axial acceleration, increases exponentiallywith time at high altitudes (Figure 1). Thus:

a = a0 expt

τ(1)

wheret is time,a0 is the acceleration at timet = 0, andτ is the timescale, which equals the ratio of the atmo-sphere’s density scale height to the rate of change of alti-tude.

1880 1885 1890 1895 1900Time after 23:00:00.000 UTC (sec)

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Figure 4. Two time series of axial acceleration measure-ments before bias correction. Grey dots indicate smooth-ing with a 1024 point (5.12 sec) running mean and blackdots indicate smoothing with a 2048 point (10.24 sec)running mean.

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Figure 5. Two time series of axial acceleration measure-ments after bias correction. Grey dots indicate smooth-ing with a 1024 point (5.12 sec) running mean followedby correction using ratio to a 2048 point (10.24 sec) run-ning mean. Black dots indicate smoothing with a 2048(10.24 sec) point running mean followed by correctionusing ratio to a 4096 (20.48 sec) point running mean.

The mean acceleration betweent = −tX and t = tX ,amean, is not the same as the desired acceleration at thecentre of the time series unlesstX ≪ τ (Withers et al.2010):

amean = a0

τ

tXsinh

(

tXτ

)

(2)

Not only is the arithmetic mean a biased estimate of thedesired quantity, but transition from one smoothing win-dow to a different smoothing window (as might be ap-plied to retain a constant fractional error whilst maxi-mizing vertical resolution, for example) involves an un-physical discontinuous change in mean acceleration thatis extremely problematic to deal with. However, if thetimescaleτ can be determined, then the value ofa0 canbe found fromamean and tX . If a “long” average,aL,and a “short” average,aS , are calculated over the ranges

t = −2tS to t = 2tS andt = −tS to t = tS , respectively,then the ratio of the averages satisfies:

aL

aS= cosh

(

tSτ

)

(3)

Equation 3 can be rearranged using the trigonometric

identity cosh−1 (x) = ln(

x +(

x2 − 1)1/2

)

to yield:

tSτ

= ln

aL

aS+

√

(

aL

aS

)2

− 1

(4)

Thus the timescaleτ can be determined from the two re-lated means,aL andaS , and then used to find the trueacceleration at the centre of the series of data points. Fig-ure 4 illustrates differences betweenaL andaS for thePhoenix data. Figure 5 shows how these differences aredrastically reduced after application of the correction pro-cedure outlined above.

4. ANGLE OF ATTACK INCONSISTENCIES

Since Phoenix carried gyroscopes, its angle of attack canbe reconstructed directly,αD, as shown in Figure 3. Anindependent indirect estimate of the angle of attack,αI ,can also be obtained from the ratio of normal to axialacceleration (Withers et al. 2010). The indirectαI is of-ten used to support the trajectory and atmospheric struc-ture reconstruction for missions that carry accelerome-ters, but not gyroscopes (Spencer et al. 1999; Witherset al. 2003). Yet Figure 6 shows thatαI is typically1–2 degrees smaller thanαD. Note that this issue isdifferent from discrepancies betweenpredicted andre-constructed angles of attack addressed by Desai et al.(2008). Resolution of this issue is important for under-standing the flight dynamics of Phoenix and similar entryvehicles. Its precise implications are unclear, but theycould be significant.

5. ANOTHER ROUTE TO ATMOSPHERIC DEN-SITY

Figures 3 and 6 show small oscillations in the angle ofattack. They have amplitudes on the order of tenths ofa degree and periods of about two seconds. The periodof these oscillations depends on the atmospheric density(Schoenenberger et al. 2005):

Ω2 =−ρV 2ADCmα

2I(5)

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Figure 6. Time series of directly determined angle of at-tack,αD, (black line) and indirectly determined angle ofattack,αI (grey line). Results after parachute deploymentare not shown.

whereΩ is the angular frequency of the oscillations,ρis atmospheric density,V is atmosphere-relative speed,A is a reference area,D is a reference diameter,Cmα

is the derivative of the pitching moment coefficient withrespect to angle of attack, andI is a moment of inertia. Ifthe observed period of oscillations, reconstructed densityand speed, reference area ofπD2/4 whereD = 2.65 m(Catling et al. 2008), andCmα ∼ 0.1 rad s−1 (Edquistet al. 2008) are used with Equation 5 to calculateI, thenthe resultantI is within ∼ 10% of 200 kg m2 over muchof the trajectory (Withers et al. 2010). The actual momentof inertia is close to 200 kg m2 (Prince et al. 2008).

This technique can be inverted to obtain density estimatesfrom the period of these oscillations, moment of inertia,and pitching moment coefficient. Its accuracy is likely tobe worse than the standard “density from drag decelera-tion” method due to the potentially complex dynamics ofreal, not idealized, entry vehicles and uncertainties in thederivative of the pitching moment coefficient. Nonethe-less, the accuracy of the technique should be estimated bya detailed study. Even if the formal uncertainties are rel-atively large, the technique may still be valuable as an in-dependent verification of the results of the standard “den-sity from drag deceleration” method.

6. YET ANOTHER ROUTE TO ATMOSPHERICDENSITY

Many entry vehicles, including Phoenix, maintain adirect-to-Earth radio link during EDL or a similar radiolink to a receiver capable of recording the received fre-quency. These data serve as an important source of in-formation for understanding events during EDL, particu-larly in the event of mission failure during or shortly afterEDL.

The time series of received frequencies could be usedto perform a trajectory and atmospheric structure recon-struction independent of any accelerometer data recordedonboard the spacecraft during EDL. Near-real-time tra-

jectory and atmospheric structure reconstruction offers anumber of benefits. First, it provides a rapid estimate oflanding site location. Second, it provides a rapid assess-ment of the accuracy of the predicted atmospheric con-ditions. Third, it provides a set of immediate and tan-gible data products for the public to engage with. Pub-lic interest in the EDL phase of missions is intense, yetfew results are available for discussion until a day or solater. Results would be available even if the spacecraftexploded upon ground impact without returning any sci-ence data.

The Doppler effect can be used to determinev·l0 from thereceived frequency at a given time, wherev is the velocityof the spacecraft with respect to the known trajectory ofthe receiver andl0 is the unit vector along the line of sightfrom the spacecraft to the receiver. The velocity vector attime t1 = t0 + dt, v1, is related to the velocity vector attime t0, v0, via the acceleration vector,a:

v1 = v0 + a dt (6)

The acceleration vector,a, is the sum of the gravitationalacceleration,g, and the aerodynamic acceleration,aaero:

a = aaero + g (7)

Rearranging leads to:

aaero · l0 =1

dt

(

v1 · l0 − v0 · l0)

− g · l0 (8)

Under certain circumstances, it is reasonable to assumethat aaero = −k

(

v0 − vatm

)

, wherevatm is the veloc-ity of the rotating planetary atmosphere (Withers et al.2003). This is equivalent to the absence of lift on the en-try vehicle. Thus:

aaero =

(

v0 − vatm

)

(

v0 · l0 − vatm · l0) × (9)

[

1

dt

(

v1 · l0 − v0 · l0)

− g · l0

]

All of the quantities on the right-hand side of Equa-tion 9 are known, soaaero can be inferred. The trajec-tory and atmospheric structure reconstruction can pro-ceed as usual without needing any onboard accelerom-eter data. This concept has been applied to received fre-quencies recorded during the EDL of Opportunity, whichare shown in Figure 7. Note that the labels on the hori-zontal axis of Figure 7 are incorrect. Results are shown

Figure 7. Sky frequency observed by the NASA DeepSpace Network during the EDL of Opportunity. The ef-fects of atmospheric drag (frictional deceleration) areclearly visible. From Johnston et al. (2004).

0 1000 2000 3000 4000 5000 6000Atmosphere-relative speed (m s-1)

0

50

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150

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itu

de

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)

Figure 8. Atmosphere-relative speed determined fromOpportunity’s direct-to-Earth transmissions (black line)and from the accelerometer-based reconstruction ofWithers & Murphy (2009) (grey line) as functions of alti-tude.

in Figures 8 and 9. Given the inaccuracies introducedby extracting time and frequency data from Figure 7,the results are promising. It is clear that significantlygreater accuracy would be obtained if the actual timeseries of received frequencies was used instead. Twosteps are necessary before this technique can be reliedupon to support future entry probes formally. First, itshould be demonstrated using actual received frequen-cies, not values extracted from a published figure. Pos-sible test cases include the Pioneer Venus probes (Coun-selman et al. 1980), Pathfinder (Wood et al. 1997), Spirit,Opportunity, Phoenix (Kornfeld et al. 2008), the Galileoprobe (Atkinson et al. 1998), and Huygens (Bird et al.2005; Folkner et al. 2006). Second, sensitivity studiesand error analyses should be performed to quantify theexpected accuracy of its results.

7. SCIENCE

Figure 10 shows the reconstructed temperature profile forPhoenix (Withers & Catling 2010). The mesopause isclearly detected near 100 km, but temperature uncertain-

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itu

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Figure 9. Temperature determined from Opportunity’sdirect-to-Earth transmissions (black line) and from theaccelerometer-based reconstruction of Withers & Mur-phy (2009) (grey line) as functions of altitude.

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Figure 10. Vertical profile of reconstructed temperaturefor Phoenix (black solid line), with1σ temperature un-certainties shown by the grey envelope.

ties become very large at higher altitudes in the thermo-sphere. The middle atmosphere is dominated between 60km and 100 km by a large temperature maximum thatis 30 K warmer than its flanking temperature minima.This is caused by the sun-synchronous diurnal thermaltide, which a major component of the dynamics of the at-mosphere of Mars. Below 60 km, temperatures increasemore-or-less monotonically with decreasing altitude. Thesmall temperature maximum at 48 km may also be asso-ciated with the sun-synchronous diurnal thermal tide.

Figure 11 shows all six entry profiles obtained from themartian atmosphere to date. The overall impression isthat temperatures increase steadily with increasing pres-sure for pressures greater than 1 Pa, but vary significantlyfor smaller pressures.

These profiles are challenging to interpret due to theirsmall number. Orbital measurements offer much largernumbers of atmospheric profiles at a range of latitudes,local times, and seasons. These permit studies of thethree-dimensional structure of the martian atmospherethat the limited entry profiles do not. However, entryprofiles offer unique vertical range and resolution. In-deed, their vertical resolution is much better than typicalglobal-scale general circulation models, and hence many

100 150 200Temperature (K)

103102

101

100

10-1

10-2

10-3

10-4

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10-610-7

Pre

ssu

re (

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Figure 11. Six temperature-pressure profiles obtainedby Mars landers. Viking 1 is shown by the grey solidline marked with squares, Viking 2 by the grey solid linemarked with triangles, Pathfinder by the unmarked greysolid line, Spirit by the grey dashed line, Opportunity bythe grey dotted line, and Phoenix by the black solid line.

of the interesting phenomena contained in the entry pro-files are produced by “sub-grid-scale processes” that arerepresented parametrically in such models. The histori-cal division of many aspects of the atmospheric sciencesinto “lower atmosphere,” “middle atmosphere,” or “up-per atmosphere” topics has meant that many studies havenot taken full advantage of the ability of entry profiles tosample all these vertical regions at the same location andtime. Increasing recognition of the importance of cou-pling between atmospheric regions — and the resultantstimulus to develop “whole atmosphere” general circu-lation models with vertical ranges comparable to thoseof entry profiles — means that future analyses of entryprofiles may make greater use of their full vertical ex-tent. One-dimensional models are more able to match thevertical range and resolution of entry profiles, but cannotfully include the atmospheric dynamics that influence somany aspects of the observed thermal structure.

8. SUMMARY

Phoenix landed safely on the surface of Mars as designed.Measurements made during its entry have been used toreconstruct its trajectory and the atmospheric density,pressure, and temperature along this trajectory. Chal-lenges faced during the reconstruction process includeduncertainties in the relationship of key reference framesand noisy data. The results of the trajectory reconstruc-tion are self-consistent and consistent with other con-straints. Two different methods for determining the an-gle of attack during entry delivered significantly differ-ent results, the implications of which are not yet clear.Two alternative methods for finding atmospheric densityhave been discussed as possible complements to the es-tablished and robust “density from drag” method. The re-constructed temperature profile shows strong influencesof the sun-synchronous diurnal thermal tide in the mid-dle atmosphere. This is the sixth entry profile from theatmosphere of Mars and the first from the polar regions,

which play an important role in determining the climateof Mars.

ACKNOWLEDGMENTS

PW acknowledges support from NASA(NNX09AG16G). DC acknowledges past supportfrom the UK Science and Technology Facilities Council(STFC) awarded to the University of Bristol for Phoenixlander data reduction. PW and DC also acknowledgehelp and assistance from many people associated withthe Phoenix project.

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