David E. Smith

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David E. Smith

^a^,^∗

, Maria T. Zuber

^a

, Gregory A. Neumann

^b

, Erwan Mazarico

^b

, Frank G. Lemoine

^b

, James W. Head III

^c

, Paul G. Lucey

^d

, Oded Aharonson

^e

,

Mark S. Robinson

^f

, Xiaoli Sun

^b

, Mark H. Torrence

^g

, Michael K. Barker

^h

, Juergen Oberst

ⁱ^,^j

, Thomas C. Duxbury

^k

, Dandan Mao

^h

, Olivier S. Barnouin

^l

, Kopal Jha

^h

, David D. Rowlands

^b

, Sander Goossens

^m

, David Baker

^b

, Sven Bauer

ⁱ

, Philipp Gläser

^j

, Myriam Lemelin

^d

,

Margaret Rosenburg

ⁿ

, Michael M. Sori

^a^,^o

, Jennifer Whitten

^p

, Timothy Mcclanahan

^b

aDepartment of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

bSolar System Exploration Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA

cDept of Earth, Environmental and Planetary Sciences, Brown University, Providence, RI 02912, USA

dHawaii Institute of Geophysics and Planetology, University of Hawaii, Honolulu, HI 96822, USA

eDepartment of Earth and Planetary Sciences, Weizmann Institute of Science, Rehovot 76100, Israel

fSchool of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287, USA

gStinger Ghaffarian Technologies Inc., Greenbelt, MD 20770, USA

hSigma Space Corporation, Lanham, MD 20706, USA

iGerman Aerospace Center (DLR), Rutherfordstrasse 2, 12489 Berlin, Germany

jTechnical University Berlin, D-10623 Berlin, Germany

kSchool of Physics, Astronomy and Computational Sciences, George Mason University, Fairfax, VA 22030, USA

lSpace Department, The Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723, USA

mCenter for Research and Exploration in Space Science and Technology, University of Maryland, Baltimore County, Baltimore, 21250 MD, USA

nDivision of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125, USA

oLunar and Planetary Laboratory, University of Arizona, Tucson, AZ 85721, USA

pCenter for Earth and Planetary Studies, National Air and Space Museum, Smithsonian Institution, Washington, DC 20560, USA

a rt i c l e i nf o

Article history:

Received 14 March 2016 Revised 10 June 2016 Accepted 13 June 2016 Available online 25 June 2016 Keywords:

Moon surface

orbit determination

a b s t ra c t

InJune2009theLunarReconnaissanceOrbiter(LRO)spacecraftwaslaunchedtotheMoon.Thepayload consistsof7science instrumentsselectedtocharacterize sitesforfuture roboticandhumanmissions.

Amongthem,theLunarOrbiterLaserAltimeter(LOLA)wasdesignedtoobtainaltimetry,surfaceroughness,and reﬂectancemeasurements.Theprimaryphaseoflunarexplorationlastedoneyear,following a3-monthcommissioning phase.Oncompletion ofitsexploration objectives,the LROmissiontransi- tionedtoasciencemission.After7yearsinlunarorbit,theLOLAinstrumentcontinuestomapthelunar surface.TheLOLAdatasetisoneofthefoundationaldatasetsacquiredbythevariousLRO instruments.

LOLAprovided ahigh-accuracy globalgeodetic referenceframe towhich past,present and future lu- narobservationscanbereferenced.Italsoobtainedhigh-resolutionandaccurateglobaltopographythat wereusedtodetermine regionsinpermanentshadowatthelunarpoles.LOLAfurthercontributedto thestudyofpolarvolatilesthroughitsuniquemeasurementofsurfacebrightnessatzerophase,which revealedanomaliesinseveralpolarcratersthatmayindicatethepresenceofwaterice.Inthispaper,we describethemanyLOLAaccomplishmentstodateanditscontributiontolunarandplanetaryscience.

∗ Corresponding author.

E-mail address: [email protected] (D.E. Smith).

1. Introduction

The Lunar Reconnaissance Orbiter (LRO; Chin et al., 2007) was launched to the Moon on June 18, 2009 at 5:32p.m. EDT (Vondrak et al., 2010). The purpose of the LRO mission was to obtaindataabouttheMoonthatwillenablethefuturesafereturn of humans to the lunar surface, and to identifyand characterize http://dx.doi.org/10.1016/j.icarus.2016.06.006

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Fig. 1. The LOLA instrument (left) and the pattern of spots on the lunar surface (right). The red center spots are the areas illuminated by the laser and the green circles represent the ﬁelds of view of the corresponding detectors. (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article).

scientiﬁcallyinteresting landingsitelocations.Thesegoalsformed the basis ofthe selection of the instrument suite andthe initial spacecraft orbit. The Lunar Orbiter Laser Altimeter (LOLA; Smith et al., 2010) is one of the seven instruments onboard LRO, and was designed to acquire substantial topographic measurements in order to provide accurate relief information and a geodetic reference frame for all high-resolution datasets acquired by the spacecraft.

LOLA uses short pulses from a solid-state laser through a Diffractive Optical Element(DOE)to producea five-beam pattern thatilluminatesthelunarsurface(Smithetal.,2010).LOLAmakes four types of measurements: the range between the spacecraft and thesurface, the energyof the laser pulsereflected fromthe surface,thewidthofthereturnlaserpulse,andthesolarradiation reflected fromthelunarsurface. From thesebasicmeasurements, several scientific datasets are derived, including the topography, thealbedoatthewavelengthofthelaser(1064.4±0.1nm;Smith et al., 2010), theroughness ofthe lunar surface within the foot- print ofeach laser spot, andthe 1064-nmreflectance ofsunlight fromthelunarsurface.

In addition, LOLA enabled a Laser Ranging (LR) investigation (Zuberetal.,2010)by whichlaserpulsesfromEarth-based satel- lite laser ranging stations to LRO provided one-way range measurement. Asmall opticalreceiver mountedon theEarth-pointed high-gainantennareceivedthe532-nmpulses,whichwerepassed toLOLAforprecisetimingviaaﬁberopticcable.Thisexperiment providedadditionaltrackingforLROandenabled,fortheﬁrsttime, routinelasertrackingofaspacecraftinlunarorbit.

LROwasplacedinitscommissioning,near-polar,eccentricorbit withlowperiapsis(∼30-kmaltitudenearthesouthpole)onJune 27,2009.Threemonthslater, onSeptember27,thespacecraften- tered its 50-km, near-circular mappingorbit, whereit completed a one-year exploration mission for landing site characterization, andthenstarteditsscience-drivenmission.OnDecember11,2011, the spacecraft wasplaced back ina near-frozen orbit (near con- stantperiapse altitude andlocation)and altituderange of30km

Table 1

Instrument parameters and performance since start of opera- tions, July 3, 2009, until March 1, 2016.

LOLA operation, 2009–2016

Number of altimeter observations 6807,309,472 Number of laser ﬁrings 40 0 0,021,60 0

Initial laser output (mJ) 2.5

Laser pulse rate (Hz) 28

Laser pulse width (ns) 5

to200kmtosavefuel andextendthelifetimeofthe mission.In thespringof2015,theorbitperiapsiswasloweredto20–40km.

2. TheLOLAinstrument

TheLOLAinstrument,showninFig.1,isalaserrangingdevice thatsplitsapulsedlaserbeamintofiveoutputbeamsviaaDiffrac- tiveOptical Element(DOE),hasa singlereceiver telescope,anda detectorforeachofthebeams.TheLOLAgroundpatternprovides 5profilesspacedapproximately12mapartcross-trackwithmea- surementsseparatedby57malong-trackforeachprofile(fromthe average50kmaltitude).Fig.1showsthegroundpatternofobser- vations.Eachbeamprovidesameasurementoftheround-triptime of flight (range), pulsespreading (surface roughness), and transmit/returnenergy(surfacereflectanceatthelaserwavelength).The laserpulseenergy,thereceiveraperturesize,andthespacecraftal- titudelimittherangeprecisiontoabout10cmforaflatsurface.As aconsequenceofitstwo-dimensionalspotpattern,theinstrument provides an unambiguous determination of both along-track and cross-trackslopes alongthespacecraftgroundtrack(Fig.2).LOLA hasoperatednearlycontinuously(exceptionsdiscussedlater)since July3,2009(Table1).

Laser altimetry from orbit requires the position and attitude of the spacecraft, and the altimeter’s laser beam pointing with respect to the spacecraft coordinate system. To that end, several experiments were conductedto measure post-launch instrument

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Fig. 2. Derivation of slopes from two consecutive laser pulses shots from LOLA’s five-beam patterns showing an area 60 m ×100 m ². Successive laser pulse firings from a 50-km orbital altitude (dashed circles) each illuminate five spots, for which the ∼57 m along-track separation provides independent one-dimensional profiles (dashed lines). Various baselines (red) can be used to estimate bi-directional slopes over 25-m baselines. Residuals from planes fit to four or more closely-spaced spots provide root-mean-square roughness estimates. (For interpretation of the references to colur in this figure legend, the reader is referred to the web version of this article).

characteristics of LOLA including the laser boresight vector. In theseexperiments,LROpointedawayfromtheMoonandscanned the Earthin a raster pattern, as the LOLA laser actively fired. A groundstationon Earthreceived the1064nm pulses(the downlink),whileitfireditsownlasertoLRO(theuplink).Thedownlink pulsearrival timesanddigitizedwaveformswererecorded atthe groundstation,theGoddardGeophysicalandAstronomicalObser- vatory(GGAO) inGreenbelt,MD,andtheuplinkarrivaltimesand pulsewidthswererecordedbyLOLA’sfivedetectors.

Three successfulLOLAactiveEarthscanswere conducted:one in 2009, shortly after launch; one on Jan. 7, 2014; and another onMar. 24, 2014. The 1.2-mtelescope atGGAOwasequippedto record the 1064-nmdownlink pulsearrival timesandto digitize thepulse waveforms. Duringpost-processing, the energy ofeach downlink pulse could thus be measured by integrating the area underaGaussianﬁttothewaveform.Thespacecraftpositionand attitude were obtained from LRO project-supplied SPICE kernels.

Theﬁre timesandreceivetimesofthepulseswerematchedafter

tothe nominallaserboresightvector. Mazaricoetal.(2014) used thosetostudythelunarbodytide(Section3.8).Foreachcrossover, the 3-dimensional offsetvector between thetracks was adjusted untilitminimizedtheelevationresiduals.Theadjustmentreduced themedianRMSelevationresidualforallcrossoversfrom1.67mto 0.48m.Pointingerrorscauseperiodicvariationsinthetimeseries ofcross-trackandalong-trackoffsets(Fig.3).Thisperiodicbehav- ioriscorrelatedwiththeday/nightcycleandthesemiannualLRO yawﬂips(seeAppendix).Modelingofthiscrossoveroffsettimese- riesyieldsdaytimeandnighttimecorrectionstothenominalbore- sightintherangeof45to275

μ

^rad,^which^wereincorporatedinto theLOLAdataprocessingpipelineinJuly2014andintothesubse- quentLOLAPDSreleases.Thecorrectednighttimeboresightvector derivedfromthiscrossoveranalysisisinagreementwiththatde- rived fromtheEarthscans above.FutureEarth scanswhenLOLA isilluminatedwillbe usefultoascertainthepost-launch daytime boresight.

LOLA’snormalmode ofoperationisnadir-pointed,although it isalsooperatedoff-nadirwhenLOLAoranotherinstrumentistar- geted toa locationnot directlyunderthe spacecraftgroundtrack.

Off-nadirpointingisrathercommon,andpartofthenormaloper- ationsoftheLROspacecraft.LOLAcanacquiredataoverallregions oftheMoon,butbecausethegroundtracksare closerathighlat- itudesthanneartheequatorthespacingbetweenLOLAmeasure- ments ismuch smalleratthe poles thannearthe equator.Fig.4 showsthe average longitudinal coverage (distance betweenmea- surements) bylatitude.Theaverage coverageinlatitude isgener- ally on the order of 20 to 30m (along-track), as a result of the pulserateof28Hzandthe5proﬁles.

Fig. 3. Time series of (a) cross-track and (b) along-track LOLA beam offsets determined from crossovers. Black dots mark the semi-annual yaw ﬂips of the LRO spacecraft.

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Latitude

-80 -60 -40 -20 0 20 40 60 80

Meters

0 10 20 30 40 50 60 70 80 90 100

Fig. 4. LOLA’s longitudinal spacing as a function of latitude. The mean longitudinal spacing is calculated from all valid ground returns within 50 m of each latitude shown.

Locally, the spacingvariesandcan be severaltimeslarger (or smaller) than theaverageofa givenlatitude.In addition,theav- erageseparationoverthesouthern hemisphereisless,duetothe increased operation time during the eccentric orbitsboth during commissioningin2009andsincethefallof2012toconservefuel.

In the northern hemisphere, the present LROaltitude above the equator isgenerallygreater thanthe rangecapabilityofLOLA,so fewaltimetricmeasurementscanbeobtainednorthoftheequator.

3. Summaryofscienceresults 3.1. Globalshapeandtopography

LOLAaltimetry data havebeen assembledinto globalgrids in cylindricalandpolarstereographicprojections,atavarietyofres- olutions (Smith et al., 2015). Densely-spaced altimetric data are binned into uniformly-sampled maps by median ﬁltering to ex- cludenoise returns.Recognizingthat bothmanual inspection and automaticrejectionofnoisecanbeimperfectwhenthereturnrate islow(whenLROaltitudeishigh),an additionalcomparisonwith stereophotogrammetric tiles (Barker et al., 2016a) is sometimes usedintheeccentricorbittoexcludetheremainingoutliers.Data gaps in the mapsare ﬁlled by interpolation using splinesunder tension(SmithandWessel,1990).Theresultingmapsareprovided in multiple tiles at a resolution of 512 pixels per degree (ppd;

equivalentto∼59mresolutionattheequator),aswell ascoarser versionsre-sampledbypowersoftwo.(Aglobalgridat1024pix- els per degree wasdeemed toosparse overall andhas not been updated,althoughtherearesuﬃcientpointstobuild densergrids inmanyregions.)Whilethenear-polar LROorbityields thehigh- est arealdensityofgroundreturnsnearthe poles,the densityof samplingisroughly uniforminasimplecylindricalprojection.In- terpolationusingthisprojectiondoesnotperformwellinpreserv- ingshapesoflandformsnearthepoles,thushigh-latitude ground pointsarebinned,median-averagedandinterpolatedinconformal polarprojectionsaswell.Polarstereographicmaps,whichpreserve circularlandforms,areproducedatresolutionsfrom5to80mper pixel polewardof80°latitude,from 30to 120m per pixelabove 75°, from 60m to 240m per pixel above 60°, and from 100 to 400mperpixelpolewardof45°.TheLOLADigital ElevationMod- els (LDEMs), areindexed byshaded-reliefbrowse images,accom-

Table 2

Lunar spherical harmonic shape parameters. Values are given to four signiﬁcant ﬁg- ures or tenths of meters, whereas the expansion is carried out at higher precision.

Systematic errors on the order of 0.5 m are the dominant source of uncertainty.

Shape parameters from the PDS product LRO_2050_SHA.TAB ( Smith et al., 2015 ).

Parameter Unnormalized (km) ^aNormalized (km)

Mean radius C 00 1737.1513 ±0.0 0 05 Same

C 20(ﬂattening) −1.4937 −0 .6680

Polar radius (from C 20) 1735.6576 Equatorial radius 1737.8981

Center of figure (X), C 11 −1.7756 ±0.0 0 05 −1 .0251 Center of figure (Y), S 11 −0.7311 ±0.0 0 05 −0 .4221 Center of figure (Z), C 10 0.2396 ±0.0 0 05 0 .1383

C 21 −0.9933 −0 .7694

S 21 0.02245 0 .01739

C 22 0.0704 0 .1091

S 22 0.2473 0 .3832

aSpherical harmonics are normalized at degree l and order m as C lm= N lmC lm, where N lm= [{(2- δm,0)(2l + 1)(l-m)!}/(l + m)!] ^1/2.

paniedbycountmaps(LDEC)thatshowthenumberofreturnsin eachpixel(avalueof0whereinterpolationisnecessary).

Withthesteadilyimprovedknowledgeoflunargravityafforded by the Gravity Recovery And Interior Laboratory (GRAIL) Discov- eryMission(Zuberetal.,2013a),systematicerrorsinorbitaltracks have been largely eliminated (Mazarico et al., 2013), with the topographic uncertainty dominated by gaps in cross-track sampling. Such gaps are more frequent near the lunar limbs (90°E and270°E),becausespacecraftmaneuverswerepreferentiallyper- formed‘face-on’and precludedscience measurements. Spacecraft attitudeuncertaintyalsoaccountsforsomegeometricerrors,espe- ciallyduringslews.Atthe5-mresolutionofthepolarDEMs,small adjustmentsarestillnecessarytocompletelymatchadjacenttracks (Zuberetal.,2012;Gläseretal.,2014andthisissue).

Low altitude orbital surveys such as performed during the GRAIL missionend gamedemandedthe best possibleknowledge of topographic extremes to avoid prematurely impacting unsam- pledhigh-standing terrain.Prior to2009,the globalshapeof the Moon(Smithetal.,1997)wasuncertainbymanyhundredsofme- ters(Margotetal., 1999b),particularlyover thefarsidehighlands.

TheearlyresultsfromtheSELENEmission[Arakietal.,2009]gave a19.8kmrangeof topography,while LOLAtopographic extremes are about 19.92km. The longest physical diameter, 3486.014km, liesbetween25.9°N,204.15°Eanditsdiametricallyoppositepoint, while the shortest diameter, 3463.267km, lies at 67.1°S, 179.7°E, subtendinganangleof94.8°.RelativetotheIAU1737.4-km-radius spherical datum, the deepest point, −9.129km, lies at 70.36°S, 187.52°E, and the highest, 10.792km, lies at 5.341°N, 201.37°E.

Theequatorial radiusaveraged over a1°wide latitudinal band is 1738.133km.

Forcomparisonwith thedynamical axes of anearly-spherical body,itisconventional tousea sphericalharmonicexpansion to characterizetheprincipalparametersofshape,aslistedinTable2. Thedegree1un-normalizedcoefficientsrepresenttheoffsetofthe centeroffigure(COF)fromthecenterofmass,andyield1.935km, chieflyinthe-X(anti-Earth)direction(the longitudeoftheoffset projectedtotheequatorialplaneis202.38°E).Althoughareference ellipsoid of revolution (spheroid) has not been adopted, the degree(2,0)coefficientimpliesaflatteningof0.001289,considerably greaterthanthatofahydrostaticbodyundertheinfluenceofrota- tionalandtidalpotentials.Consideringthe degreeandorder(2,2) sectoralterms,theprincipalsemi-axisoftheshapeis1738.670km at143°longitude,and theintermediate semi-axis is1737.127km, alsooffsetfromtheprincipaldynamical axes.Atri-axial ellipsoid aboutthe center of figure has dimensions of 1739.146, 1737.394, and1734.928km,although such a form represents shape poorly,

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Fig. 5. Spherical harmonic topographic coeﬃcient root mean variance by degree (logarithmic scale). The root sums σl=[ C ²lm/(2l + 1)] ^1/2of normalized coeﬃcients are multiplied by degree for illustration.

witharoot-mean-squaremisﬁtof1.73km;itsmajoraxisistilted 27°withrespecttothepoleofrotation.Asweillustratebelow,the shapeisstronglyperturbedbylong-wavelengtheffects.

The topographic power spectrum of the Moon is shown in Fig.5. Sphericalharmonic coeﬃcientsofdegree 1–4 (dots) dom- inatethe shape. At wavelengths of ∼90 to 2000km (degrees 5–

120), topographic poweris diminished relative to the power law behavior at higher degrees, corresponding to a transition from complex craters to basin morphology and ﬂexural isostatic compensation.

Fig. 6a showstheglobaltopography oftheMoon centeredon 270°EwithOrientalebasinprominentbelowtheequator.Eachsuc- ceeding Fig. 6(b–d) removes successive low-degree terms up to 4. The nearside Mare Procellarum region and the farside South Pole-Aitkenimpactbasinaccountformuchofthelow-degreesig- nal(Garrick-Bethelletal.,2014;KeaneandMatsuyama,2014).The residualﬁgureisshapedbymorethan70basin-scaleimpactstruc- tures(Neumann etal., 2015) aswell asﬁner scale-positive-relief features — the topographic rims of craters or to a lesser extent thevolcanicfeaturessuchastheAristarchusandMariushills,and MontesRumker,Mairan,GruithuisenandCarpatus.Wrinkleridges andothertectonic features inthenearside mare regions alsoex- hibitpositiverelief.

3.1.1. Regionaltopography

Regional geologicalstudiesare enabledbyLOLAtopographyin regionswherepartialorpermanentshadowprecludeotherobser- vations,suchas overthe ﬂoorofthe 136-km-diameter Antoniadi Crateronthe southernfarside,ina regionofverythincrust.The topographyofthistransitional-typebasin, withterracedwalls, an interiorpeak ring anda small central peak, is shown in Fig. 7a.

Theareashowncoversabout0.06%oftheMoon.Thelowesteleva- tionoftheMoonliesatthebottomofa∼15-kmdiametersimple crater within Antoniadi at70.36°S, much of which exists in permanentshadow.Altimetry,however,revealsseveralfeaturesofits ﬂoor.Theseobservationsconstrainthescaleatwhichmorphologi- caltransitionsoccurinthisunusuallydeepregionoftheMoon.

WithinthevisibleportionsofAntoniadi,thelocationofanim- age(M154024477R) takenby theLROCNAC camera (Robinson et al.,2009) ofakm-sizedmound outcroppingfromthecrater ﬂoor is outlined by a small square (Fig. 7c). Fig. 7b and d illustrates howtheLOLAdataprovidecontextforinterpretationofsuchfea- tures.Herethe∼20mresolutionaffordedby manyclosely-spaced groundtracksallows proﬁlesandcontours to assessthe height of verysmall,unusualfeatures,andresolveafew-meters-deepmoat surroundingthe60-m-highmound.

-8 -6 -4 -2 0 2 4 6 8

km

d c

Fig. 6. (a) Global topography of the Moon in Mollweide equal-area projection, centered at 270 °E longitude, with the color scale at bottom superposed on hill- shaded relief. A black square denotes the highest point on the northern rim of Ko- rolev, while yellow triangles denote the axes of the greatest and smallest diameters through the center of mass. Subsequent ﬁgures show high-pass topography from (b) degree 3 (c) degree 4, and (d) degree 5 upwards. (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article).

3.2. Globalroughnessandsurfaceslopes

Quantiﬁcation andanalysis ofsurface roughnessproperties of theMoonatunprecedentedscalesandresolutionaremadepossi- blewiththe newglobalelevationdata.Surface slope andrough- nesscanbemeasuredatthe100-mscalewithabout10altimetric points(2LOLAframes),byﬁttingaplaneandmeasuringtheirscat- teraroundit(Fig.8).Rosenburgetal.(2011)furthermappedlunar surfaceslopeandroughnessusingarangeofparameters:median absoluteslope,bothdirectional (along-track)andbidirectional(in two dimensions); median differential slope; and Hurstexponent, over baselines ranging from ∼17m to ∼2.7km. Rosenburg etal.

(2011, 2015) found that the lunar highlands andthe mare plains display vastlydifferentroughness properties,withlessdistinctive variations within mare andhighlands. Most of the lunar surface exhibitsfractal-likebehavior (cf. Turcotte,1987),with asingleor twodifferentHurstexponentsoverthegivenbaselinerange;when atransitionexists,ittypicallyoccursnearthe1-kmbaseline,indi- catinga signiﬁcant characteristicspatial scalefor competingsur- face processes. Rosenburg et al.(2011) found that the Hurst ex- ponent is high within the lunar highlands, witha median value of 0.95, and lower in the maria (with a median value of 0.76).

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Fig. 7. (a) Shaded-relief topography of Antoniadi Crater, a 141-km-diameter impact feature that is the deepest feature of its size on the Moon. The white square outlines a small mound on the floor. (b) Contour plot at 5-m intervals showing the height of the mound from the LOLA LDEM_512_90S_45S_180_270 product, and profiles sampled from the gridded data record along N-S and E-W lines (vertical exaggeration 6:1). (c) The 3-km-diameter mound as seen by the LROC NAC (image M154024477R). (d) North-South profile across the mound showing individual LOLA returns (color indicates detector number) (vertical exaggeration 25:1). (For interpretation of the references to color in this figure, the reader is referred to the web version of this article).

Fig. 8. Surface slope (top) and roughness (bottom) at hectometer scale derived from pairs of LOLA shots ( ∼10 points).

Rosenburg et al. (2011) demonstrated that the median differen- tialslopeisapowerfultoolfordiscriminatingbetweenroughness unitsand isusefulin characterizing the ejectasurroundinglarge basins,particularlyOrientale,aswellastheraysystemssurround- ingyoung,Copernican-agecraters.Theyfurthershowthatmedian differentialslopeallowsaquantitativeexplorationoftheevolution ofsurfaceroughnesswithageonmaresurfaces.

In further analysis of the altimetry data, Kreslavsky et al.

(2013)presentedmapsofthetopographicroughnessoftheMoon athectometerandkilometerscalesderivedfromrangeprofilesob- tainedby LOLA.Asroughnessmeasures, they usedtheinterquar- tilerange ofprofile curvatureatseveral baselines,from115m to 1.8km,andplottedtheseina globalmap format.The mapspro- vide asynopticoverviewofvariationsof typicaltopographic tex- tures and utilize the exceptional ranging precision of the LOLA instrument. Kreslavsky et al. (2013) found that hectometer-scale roughness poorly correlates with kilometer-scale roughness, because the two scale lengths reflect different sets of processes andtime scales. Hectometer-scale roughness is controlled by re- golithaccumulationandmodificationprocessesandaffectedbythe mostrecent events (primarily,geologically recent(1–2Ga) mete- oriticimpacts).Kilometer-scale roughness, onthe other hand,re- flects major geological (impact, volcanic and tectonic) events in earliergeological history. Thedata presented by Kreslavsky etal.

(2013) also show that young large impact craters are rough, and their roughnessdecreases with increasing age.The globalrough- ness maps reveal a few unusually dense clusters of hectometer- and decameter-size impact craters that differ in their morphol- ogyandsettingsfromtypicalsecondarycraterclustersandchains;

theoriginofthesefeaturesiscurrentlyunknown.Kreslavskyetal.

(2013) mapscan also assist inthe geological mapping ofthe lu- narmariaby revealingcontactsbetweenvolcanicplainunits.The globalroughnessmapsalsoclearlyrevealcryptomaria,oldvolcanic plainssuperposedbyyoungermaterials,primarilycraterandbasin ejecta(WhittenandHead,2013,2015a,b).

Furthermore,thesedata can be successfullyapplied to understanding the dynamics of impact processes and their effects on surfacedegradation,evenatplanetaryscales.KreslavskyandHead (2012) showedthat thenewmapsofkilometer-scale topographic

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Fig. 9. Topography (a, c) and 100-m baseline surface slopes (b, d) of the lunar south and north poles, respectively. The topography clearly shows the variations in elevation while the slopes better define the edges of craters and ridges, and the flatness of crater floors. Both maps extend from 75 °to the pole.

roughnessandconcavity ofthe Moon reveal a distinctive roughness signature of the proximal ejecta deposits of the Orientale basin (the Hevelius Formation). They found that no other lunar impactbasin,eventhejust-precedingImbrium basin,ischaracter- ized by this type of signature although most have similar types ofejecta units and secondary crater structures. The preservation ofthisdistinctivesignature,anditslackinbasinsformedpriorto Orientale,wasinterpretedbyKreslavskyandHead(2012)tobethe resultofseismically-inducedsmoothingcausedbythislatestmajor basin-formingevent.IntenseseismicwavesaccompanyingtheOri- entalebasin-formingeventprecededtheemplacementofitsejecta in time and operated to shake and smooth steep and rough to- pographyassociatedwithearlierbasin depositssuch asImbrium.

Intheirinterpretation,Orientaleejectawasemplacedimmediately followingthe passage ofthe seismic wavesand thus formedthe distinctiveroughnesssignaturethathasbeenpreservedforalmost 4billionyears.

3.3.Polartopographyandslopes

Because of thedense spatialcoverage afforded by LRO’s polar orbit,thenorthandsouthpolarregionsarecharacterizedbyahigh densityofgroundtrackcoveragethat hasenabledhighresolution

maps.Fig.9showstopographyand100-mslopesforthenorthand southpolarregions.Thesetopographicmapsshownhaveaspatial resolution of60m that enablesgeologiccharacterization relevant for science analyses and exploration planning. The highest- resolutionpolarmaps(5m/pixelfrom87.5°latitudetoeach pole) met the missionrequirement of 30-mresolution for locationsof potentiallandingsitesorregionsofspecialscientiﬁcinterest.

LOLAhigh-resolutionDEMsenablegeologiccharacterizationas well ascratercountingandrelativeagedatingofthelunarpoles, including permanently shadowed areas. A prominent example is Shackleton crater, which is nearly coincident with the Moon’s south pole. Its interior receives almost no direct sunlight and is a perennial cold trap, making it a promising candidate location in which to seeksequestered volatiles. Previous orbital and Earth-based radar mapping andorbital optical imaging, however, have produced conflicting interpretations about the existence of volatiles (Nozette et al., 2001; Campbell et al., 2006; Haruyama et al., 2008; Spudis et al., 2013). The observations of Zuber etal.(2012)fromLOLADEMs,(Fig.10)revealedShackleton tobe an ancient,unusuallywell-preserved simplecraterwhoseinterior wallsarefresherthanitsfloorandrim.TheLOLADEMsshowthat Shackletonfloordepositsarenearlythesameageastherim,suggesting that little floor deposition has occurred since the crater

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Fig. 10. Topographic map and topographic image of Shackleton Crater using LOLA data. Topography and slopes are based on a 10-m spatial resolution grid of all available LOLA proﬁles that include collectively 16 million unique elevation measurements. Elevations are contoured at 5-m intervals ( Zuber et al., 2012 ).

formedmorethanthreebillionyearsago.AttheLOLAlaserwave- length,thefloorofShackletonisbrighterthanthesurroundingter- rain andthe interiors ofnearby craters, butnot as brightasthe interiorwalls. Zuberetal.(2012) interpretedthesecombined observations to be explainedprimarily by downslope movement of regolithonthewalls,exposingfresherunderlyingmaterial(Fassett andThompson, 2014). Therelatively brighter craterfloor is most simply explainedby decreased spaceweathering dueto shadow- ing,butaone-micrometer-thicklayercontainingabout20percent surficialicewascitedasanalternativepossibility.

LOLAhigh-resolution DEMs havealsobeen analyzedto assign agestoother Southcircumpolarpermanently-shadowedcraterin- teriors. Tye et al.(2015) studied the interiors ofthe lunar south circum-polarcratersHaworth,Shoemaker,Faustini,andShackleton, all ofwhich contain large permanently shadowed regions (PSRs) andall havebeeninterpreted tocontain sequesteredvolatilesin- cluding waterice. LOLAaltimetry data provided anew meansof examining the permanently shadowed interiors of these craters in unprecedented detail. Tye et al. (2015) used extremely high- resolutiongriddedLOLAdatatodeterminethesize-frequencydis- tributions and the spatial density of craters superposing their rims,inner slopes, andﬂoors. Onthebasis oftheir populationof superposed craters, Haworth, Shoemaker, and Faustini have pre- Nectarian formationages. Shackletonwasinterpreted ashavinga LateImbrianageonthebasisofcraterssuperposedonitsrim.Us- ing LOLAslopedata,Tyeetal.(2015) showedthatthe localden- sityofcratersisstronglydependentonslope;becauseofitssteep interior slopes, the lifetime of craters on the interior walls of Shackleton is limited. The slope-dependence of the small crater populationimpliesthat thepopulationinthesizerangeanalyzed iscontrolled primarilyby therateatwhichcraters aredestroyed, consistent withthe hypothesis that crater removaland resurfac- ingisaresultofslope-dependentprocessessuchasdiffusivemass wastingandseismicshaking.

3.4. Radiometry,reﬂectanceandalbedo

3.4.1. Normalalbedofromactiveradiometry

Owing to theimportance ofice asapotential resource atthe lunar poles, LOLAwas designedto search fordeposits of surface

frostinregionsofpermanentshadowthroughmeasurementofthe reﬂectanceofthesurfaceat1064nm(Smithetal.,2010).Because LOLAprovides its ownlight source, its measurements are partic- ularlyusefulbecausereﬂectance measurements within regions of permanentshadowcanbecomparedquantitativelytothoseofthe restoftheMoonwithouttheneedforcomplexphotometricmod- elsthatcorrectforvariablelighting,orinthecaseoftheregionsof permanentshadow,indirectlighting.ThisattributeofLOLAispar- ticularlyusefulforregionsinpermanentshadow,whoseonlynat- urallight sourceinthe visibleportionofthe spectrum,scattered light,ischallengingtomodelasitdependsonthetopographyand albedowithinandaroundtheshadowedregions.

Another useful feature of the LOLA reflectance experiment is thatitmeasuresthelunarsurfacereflectanceatzerophaseangle, thatistheanglebetweenthelight source(LOLA’slaser transmit- ter),thelunarsurface,andthereceiver(LOLA’sreceivertelescope) iszero(oreffectivelyso,thereisaminuteangleduetothetravel time of the light pulse to the lunar surfaceand back).With the Sunasa light source,this zerophase anglecondition cansome- timesbeobservedfromtheEarthandfromspace,butbecausethe angleof incidence systematically increases toward the poles, the surfaceisincreasinglyforeshortened andpassivezero-phasemea- surementsinpolarcratersarenotpossible.Foradarksurfacelike the Moon, measurements at zero phase are free of dependence upon topography, again enablingcomparison of reflectance mea- surementsamongterrainswithouttheneedforphotometricmod- els. Fig.11 showsthe lunar albedo at1064nm derived from the LOLAactivereflectancemeasurements.

TheinitialresultsfromtheLOLAreflectance experimentfound that the south polar crater Shackleton, mostly in permanent shadow, was locally unique in reflectance, being substantially brighterthanitssurroundings.Zuberetal.(2012) consideredsev- eralhypotheses forthis anomalous reflectance, includingbutnot limited to the presence of surface frost. Calibration of the first yearofLOLAobservationsdemonstratedthatregionsinpermanent shadowareingeneralabout15%brighterthanpolarareasthatre- ceivesomeilluminationandLuceyetal.(2014)suggestedthisgen- eralincrease wasduetoinhibitedspaceweatheringowingtolow temperatures,orpossiblesurfacefrost.

Reﬂectance data from LOLA were used by Hemingway et al.

(2015)andLemelinet al.(2016) to show that thelunar maria ex- hibit a latitude-dependent albedo. They suggested this was due to a variation inspace weatheringwith latitudeand average so- larincidenceangle,supportingasputteringsourceforlunarspace weatheringopticaleffects.LOLA’sdatauniquelysupportedthisin- vestigationbecauseofits immunityfromlatitude-dependentpho- tometriceffects.

LOLA’s measurements of the zero-phase reflectance are mir- rored on the planet Mercury with the Mercury Laser Altimeter data(Neumannetal.,2013).Comparisonofthesetwoexperiments show that the typical reflectance of Mercury is similar to that of the iron-rich lunar maria, despite the low-iron nature of the surface of Mercury. While this albedo difference was previously known,the laser experimentsprovide robust independentconfir- mation,andauniquephotometric geometryto supportinvestiga- tionsaimedatunderstandingthedifference.

Ongoing experiments with LOLA reflectance now center on a searchfortime-variablereflectancewhichwouldhelpidentifythe causeof increasedbrightnessin shadowed regions since anype- riodicvariation ismostlikely dueto transientsurfacefrost.Data fromDeepImpact,CassiniandChandrayaan-1indicatedthatspec- tralabsorptionduetowateristime-variable onthelunarsurface (Sunshineetal.,2009;Clark,2009;Pietersetal.,2009).LOLAmea- surementsof the reflectance ofsurfaces ata variety of tempera- turesmaybeabletodetectorplaceupperlimitsontheabundance ofmigratorywaterortime-variablesurfacefrost.

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Fig. 11. Normal albedo of the Moon at 1064 nm from active radiometry. The surface resolution is approximately 5 km in the global map (a) and 1 km in the south (b) and north (c) polar maps. Adapted from Lucey et al. (2014) .

3.4.2. Lunarphasefunctioninthenear-IRfrompassiveandactive radiometry

Althoughnotincludedintheoriginalinstrumentmissiongoals, wehave developeda second reflectance measurement technique, which leverages the LOLA noise-monitoring house-keeping data anduses them as a unique passive radiometryscience measure- mentoftheMoon.Insteadoflettingtheflightsoftwarecontrolthe thresholdstomaintainthenoiselevelto∼1–2%asduringnormal altimetricoperations,thethresholdscanbeheldfixedatverylow levelsto allow thousandsof noisecounts persecond tobe mea- suredandyield high-SNRreflectance measurements. Thisthresh- old settingistypically only employed whenthe spacecraftis too high to otherwise obtain any altimetric measurement (northern hemisphereinthenear-frozenellipticalorbit)andwhenthe beta angle(anglebetweentheprime meridianandtheSun) isnot fa- vorableconsideringtheLOLAthermalblanketanomaly(beta࣡80°) (seeAppendix).Thisdatasetisuniquebecauseitcoversanarrow spectral band, it is asprecisely geolocated asthe altimetry data, anditcomplementstheactivenormalalbedomeasurementmade withthelaser. Withpassiveradiometry,theinstrumentmeasures the solar photon rate reflected off the surface, which depends on the topography and viewing/illumination geometry. The so- called phase function describes the phase-angle portion of this dependence(Fig. 12). The phase function is ofinterest forbetter understanding the geologic and space weathering influences on regolith characteristics. A significant challenge has been to pre- dictthe observed variations in phase function with location and wavelengthfromfirstprinciples,becauseofthecomplexitiesofra- diativetransfertheoryappliedtolunarregolith.Theuniqueability ofLOLAto measurethe normalalbedothrough activereflectance provides new opportunities in this arena, because it allows for theremovalofmostoftheeffectsofsingleparticlealbedoonthe phasefunctionfromthoseofotherregolithproperties,suchasthe single particle backscattering strength and the opposition effect (OE,whichisthesurgeinbrightnessatphaseanglesnearzero).

Barker et al. (2016b) presented a method for calibrating the passiveradiometrydata andusedthe passiveandactive radiom- etrytostudythe near-IRphasefunction’s dependenceonvarious geologic parameters. On a global scale, they found that iron abundance and optical maturity were the dominant controlling parameters.Titanium abundance,surfaceroughnesson decimeter to decameter scales, and soil thermophysical properties had a smallereffect,andthelattertwowerecorrelatedwithopticalma- turity, indicating that exposure age wasthe driving force behind

Phase angle (deg)

0 15 30 45 60 75 90

RADF / An / LS

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

N per bin

10⁰ 10¹ 10² 10³ 10⁴ 10⁵

Fig. 12. 1064-nm highlands phase function from LOLA passive and active radiometry. Several phase functions for the highlands from the literature are overplotted and normalized at 30 °phase: Clementine 950-nm (dashed black line; Shkuratov et al., 1999 ), LROC WAC 689-nm (solid white line; Sato et al., 2014 ), Spectral Pro- filer 1068 nm (solid green line; Yokota et al., 2011 ), and Chandrayaan-1 M3 1070 nm (dashed blue line; Besse et al., 2013 ). The vertical axis is the radiance factor (RADF) divided by the normal albedo (An) and the Lommel–Seeliger (LS) relation. The radiance factor is the reflectance relative to a perfectly diffuse surface illuminated vertically. Dividing RADF by An and LS corrects, respectively, for different intrinsic reflectances of the observation locations and for the effects of varying incidence and emission angles ( Hapke, 2012b ). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).

their contribution. The phase function also exhibited a depen- denceonslope,possiblyduetomasswastingand/or reducedsky visibility. Geologically-inﬂuenced variationsof the phase function were observed, in particular associated with the dark halo of impact melt around the Copernican-aged Jackson crater and the ReinerGammaFormation(RG).ThephasefunctionofRGdeviated from the global average (for the same composition and optical maturity), suggesting that the unusual regolith evolution and properties at this location affect the visible-to-near-IR spectrum and phase function differently. From detailed modeling of the photometric function, Barker et al. (2016b) veriﬁed that several wavelengthtrendsobservedbySatoetal.(2014)withLROC inthe UV-VIScontinueintothenear-IR.Inparticular,themariaexhibited

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Permanent Shadow Average solar illumination Average Earth visibility

PSR non-PSR

%

0 20 40 60 80 100

Fig. 13. Solar illumination modeling results based on a 60 m/px LOLA topographic map, over 82.5 °S–90 °S. ( Mazarico et al., 2011a ).

decreased backscattering, a narrower OE angular width, and a smallerOE amplituderelative tothehighlands.It wasalsofound that thebackscatteringstrengthandOEwidthhavenosigniﬁcant correlationwithgeologiccontextwithinthemaria.

Theseresultsshedfurtherlightonthewavelengthdependence oftheMoon’sphotometricbehavior,somethingforwhichourthe- oretical understanding is presently incomplete (e.g.,Hapke et al., 2012a).Altogether,compositional variationsandspaceweathering haveimportanteffects ontheMoon’sphotometric behaviorapart fromtheir inﬂuenceonsingleparticlealbedo,aresultmadepos- sibleby LOLA’sunique abilitytodirectly measurenormalalbedo.

Thus, laser altimeters like LOLA can contribute to photometric studies thanks to their combined active and passive radiometry measurementsatallphaseangles.

3.5. Illuminationconditionsatthelunarpoles

OneofthemainobjectivesoftheLROmissionwastostudythe distribution of volatiles and the processes controlling their pres- enceandtheirpotentialtime-variabletransport.

Priorto theLROmission,theexistence ofareasin ‘permanent shadow’inthepolarregions,hypothesizedbyWatsonetal.(1961), wasthoughttobe directlyresponsible,throughcold-trapping, for all the volatiles observed by Lunar Prospector (Feldman et al., 1998). Spatiallyresolved observationsby theLENDinstrumenton LRO(Mitrofanovetal., 2010)showedthatthehypothesizedcorre- lation does not necessarily hold atsmall scales, and much work basedonthenewLROdatasetshasfocused onreﬁningmodelsof volatileproductionandloss(e.g.,Farrelletal.,2015)andtransport (SchorghoferandAharonson,2014).

Precise knowledge of the topography of the Moon is key in enabling these studies, as it directly impacts the illumination conditions and thermal environment of the lunar surface. The Clementine altimetric data(Smithetal., 1997) were not of suffi- cient quality toenable numericalsimulations ofthe illumination conditions,anddespitehighintrinsicresolution,Earth-basedradar data(e.g.,Margotetal.,1999) werelackinguniformcoverage due to the tidal lock of the Moon, resulting in significant coverage gaps and biases over a wide range of solar longitudes. While imagery-based studies did make progress in identifying areas of permanent shadow and of high illumination (Bussey et al., 1999), the laser altimeter data acquired by LALT (Araki et al., 2009) onboard SELENE enabled the first faithful simulation of illuminationconditionsbasedonatopographicmodelalone(Noda

et al., 2008). Soon after, the LOLA data substantially improved the quality and spatial extent made possible through numerical simulation,thanks to a longermission duration andhighermea- surementrate(140Hzeffective).Mazaricoetal.(2011a)presented results of solar insolation, permanent shadow regions (PSR) in- ventory, areas of highest illumination, and Earth visibility, over both poles (75–90°) at 240m/px.Instead of the more traditional ray-tracing method,they used a ‘horizon method’, more eﬃcient when investigatingillumination conditions at ﬁnertemporal resolution over long temporal baselines. Individual timestep results were validated with concomitant LROC WAC images (Robinson et al., 2009). Fig. 13 illustrates such results, from a more recent simulation performed in the 82.5°S–90°S region at 60m/px: av- eragesolarilluminationandEarthvisibilityover alunar nutation cycle(∼18.6years) andthe areasdeterminedtobe inpermanent shadow.

Whilespacecraftimagery ultimatelyprovidesgroundtruth for theillumination state (SpeyererandRobinson, 2013), camera ob- servationsarelimitedintemporalextent(bythemissionduration) andinspatialextent(byspacecraftorbitalphasingandinstrument field of view), and thus do not necessarily suffice to investigate long-termorsecular effects.The LOLA-derivedillumination maps are useful for the interpretation and analysis of scientific data acquiredby the other LROinstruments. For example, Mitrofanov et al. (2010) used the outlines of the PSRs defined by Mazarico et al. (2011a) to compute the statistical significance of the neutron suppression within them. The average illumination maps were leveraged in studies to better understand the distribution of volatiles in the near-subsurface, in particular by correlating the LEND measurements with illumination. Fig. 14 shows the high correlation between the general trends with latitude of decreasing average illumination poleward with the reduction in neutroncountsasmeasuredbyboththeLunarProspectorNeutron Spectrometer (LPNS)andthe Lunar ExplorationNeutron Detector (LEND)(Mazaricoetal.,2011a).Furtherstudiesfurtherestablished thislink,andshowedtheimportanceofmaximumslopeandslope azimuth on the presence of subsurface volatiles (McClanahan et al., 2015). Another derived product, the so-called sky visibility that describes the sky solid angle visible from the surface, was important to correct the Lyman Alpha Mapping Project (LAMP) observations andmeasure the surfacealbedo at UV wavelengths (Gladstoneetal.,2012).Simulationsoverlargerareasandathigher resolutions have since been performed. PSRs were identified at non-polar latitudes (Mazarico et al., 2011b), as low as 58.185°S

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Fig. 14. Examples of a peak-ring basin (A), protobasin (B), and ringed peak-cluster basin (C) on the Moon. Top panels show outlines of circle ﬁts to the basin rim crest and interior ring (dashed lines) on LOLA hillshade gridded topography. Bottom panels show LOLA colored gridded topography at 128 pixel/degree on LOLA hillshade gridded topography. (A) Schrödinger (326 km; 133.53_E, 74.90_S), a peak-ring basin, exhibits a nearly continuous interior ring of peaks with no central peak. (B) Antoniadi (137 km;

187.04_E, 69.35_S), a protobasin, has a less prominent peak ring surrounding a small central peak. (C) Humboldt (205 km; 81.06_E, 27.12_S) is a ringed peak-cluster basin with an incomplete, diminutive ring of central peak elements. From Baker et al. (2011) . (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article).

and 58.412°N (McGovern et al., 2013). Gläser et al. (2014) used LROCNAC-derived shape models in combinationwith LOLA data todeterminethebestSouthPolelocationsforlanders,intermsof solarpowerinputforfuturelunarexploration.

Continued work also showed that the total amount of area found to be in permanent shadow increases as the topographic mapqualityandthetopographicresolutionimprove.Fig.13sum- marizes the extent of permanent shadow in the polar regions fromvarious simulations. It illustrates that while Mazaricoet al.

(2011a)found that 7.03% and 9.82% oflatitudes poleward of 85° (NorthandSouth,respectively)wereinpermanentshadow,asim- ulationat the same resolution (240m/px) usingthe most recent LOLAmap (PDSrelease15,inJune2015)yields 7.75%and10.19%.

Higher resolutions (120m/px and 60m/px, with the same 2015 dataset)yield8.79%/10.74%and9.70%/11.41%,respectively.Ateven higher resolution, the trend continues, with ∼25% more area in permanentshadowet20m/pxthan at60m/px.Thisisconsistent withthefractalnatureoftopographicsurfaces(Turcotte,1987)and recentworkbyBandﬁeldetal.(2015)onthermalanisotropy.Con- versely,asresolutionincreases,themostilluminatedsitestendto shrink spatially and show lower solar illumination averages. No peakofeternallight, againhypothesizedbyWatson etal.(1961), exists on the Moon (Noda et al., 2008; Mazarico et al., 2011a;

Gläseretal.,2014).

3.6. Geology

3.6.1. Morphometriccharacterizationcratersandbasins

Of fundamental importance to the understanding of the geo- logicalevolutionofplanetsisthequantitativenatureoftheirland- formsandtheirrelationshiptothethermalevolutionoftheplanet.

LOLA data have provided the basis to undertake these types of analyses, andtoimproveour knowledgeof theoriginandevolu- tion oflandforms related to impactcrater volcanism andtecton- ism.

For example,a major question in the originand evolution of impact craters and basins is the nature of the transition, with increasing size, from simple, to complex, to peak-ring basins and ﬁnally to multi-ring basins. Baker et al. (2011) used LOLA and LROC data to document the relationship between complex craters with central peaks and multi-ring basins in protobasins (exhibiting a rimcrest andinteriorring plus acentral peak)and peak-ring basins (exhibiting a rim crest and an interior ring).

New data have permitted improved portrayal and classiﬁcation ofthese transitional features onthe Moon. Usinghigh-resolution LOLA gridded topographic data combined with image mosaics, Baker et al. (2011) conducteda survey of craters >50km indi- ameter on the Moon and updated the existing catalogs of lunar peak-ringbasinsandprotobasins(seealsoKalynnetal.,2013).

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Fig. 15. Histograms of the average illumination in the north (top left) and south (bottom left) polar regions. Each 1 °-latitude bin from 65 °to the pole is normalized to prevent lower-altitude areas from dominating the count numbers, and highlight the distribution of illumination at each latitude. The color scale is logarithmic. The right panels show the 5 °-median ‘average illumination’ (black), and the corresponding corrected LPNS and LEND epithermal neutron fluxes ( Feldman et al., 1998; Mitrofanov et al., 2010 ). The neutron data were each scaled linearly to fit the average illumination range, as indicated by their corresponding legends. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).

LOLAdatawerealsoessentialinthedetaileddocumentationof themorphologic transitionfromcompleximpact craters,to peak- ring basins,andto multi-ringbasinsandthemorphometricchar- acteristics oftheselandformsduetotheir large sizeandthelack ofglobalhigh-resolutiontopographydata.Bakeretal.(2012)used LOLA data to derive the morphometric characteristics of impact basinsontheMoon,assessthetrends,andinterprettheprocesses involvedintheobservedmorphologictransitions.Severalgeomet- rictrendsforpeak-ringbasinshavebeenobserved(Fig.15).Afac- tor of two reduction in the depth to diameter (d/D) ratio inthe transitionfromcomplex cratersto peak-ringbasinsmaybe char- acterizedbyasteepertrendthanknownpreviously.Thed/D ratio forpeak-ringbasinsdecreaseswithrim-crestdiameter,whichmay be dueto anon-proportional changeinexcavation cavitygrowth orscaling,asmayoccurinthesimpletocomplextransition,orin- creasedmagnitudeofﬂoorupliftassociatedwithpeak-ringforma- tion. Baker etal.(2012) found that newobservations ofgeomet- ric/morphometric properties of protobasins and peak-ring basins placesomeconstraintsontheprocessesthatcontroltheonsetand formation of interiorlandforms in peak-ringbasins. Comparisons

ofthegeometrictrendsoftheinnerringsofOrientalebasinwith those of peak-ring basins are generally consistent with a mega- terracemodelfortheformationofmulti-ringbasins.

In addition to quantifying the interior structure of impact cratersandbasins, LOLAdatahasalsobeenutilized toassessthe ejecta deposits and their thickness. Fassett et al. (2011) showed that quantifying theejecta distributionaround large lunar basins is importantto understanding the origin ofbasin rings, the vol- umeof the transientcavity, the depth of sampling, and the nature of the basin formation processes. Fassett et al.(2011) used LOLAaltimetry datatoestimate thethicknessofejectainthere- gion surrounding the Orientale impact basin, the youngest and best preserved large basin on the Moon. By measuring the size ofcraters progressivelycovered by Orientale ejectaasa function ofdistancefromthebasinrim,theirmeasurements yieldedejecta thicknesses of∼2900m nearthe CordilleraMountains, the topo- graphicrimofOrientale,decayingto∼1kminthicknessatarange of215km. These measurements imply a volume ofejecta in the regionfromthe Cordilleraring toa radial rangeof onebasin di- ameterof∼2.9×10⁶km³.

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Fig. 16. (A) Outline of craters mapped on the Moon from LOLA data superposed on a hillshade rendering of LOLA topography. (B) Crater densities on the Moon for craters

≥20 km in diameter, calculated in a neighborhood of radius 500 km. (Database from Head et al., 2010).

3.6.2. Agesandcraterdensity

LOLA data have provided unprecedented ability and opportunities to assess impact crater location, mapping and density (size-frequency) distributions, and to apply these data to mapping of lunar surface units, and fundamental lunar problems.

For example, previous analyses of the global distribution of lunar craters were compiled with images of different resolutions and viewing geometries. The availability of the LOLA global altimetry data set permitted the use of a consistent data set that could be illuminated from a variety of perspectives to gain un- precedentedviewsforcraterdetectionandgeometry.Using these high-resolutionaltimetricmeasurements ofthe Moon,Headetal.

(2010) produced acatalog ofall impact craters ≥20kmin diam- eteron the lunar surface(5185 in total) and analyzed their dis- tributionandpopulationcharacteristics.Fig.16showstheoutline

of thecraters (A)and their density inneighborhoods of500-km radius.(B).

They found that the most-densely cratered portion of the highlands reacheda state ofsaturation equilibrium. Furthermore, large impactevents,such asthe OrientaleBasin, locallymodiﬁed the pre-basin crater population to ∼2 basin radii from the basin center. Important impact basin stratigraphic markers in lunar history, such as Imbrium, Orientale, and Nectaris, are temporally distinguishable on the basis of crater statistics. Finally, the characteristics of pre- and post-mare crater populations support the hypothesis thatthere were twopopulations ofimpactors inearly Solar System history and that the transition occurred near the timeoftheOrientalebasin-formingevent.

LOLAdata also permitted an assessmentof the chronologyof lunar basins. Impactbasin formation isa fundamentalprocess in

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the evolution of the Moon and records the history of impactors in theearly SolarSystem. Inorder toassess thestratigraphy, sequence,andagesofimpactbasinsandtheimpactorpopulationas afunctionoftime,Fassettetal.(2012)usedtopographyfromLOLA to measurethe superposedimpactcrater size-frequencydistribu- tions for30lunarbasins(D≥300km).Thesedatagenerallysup- port the widely used (Wilhelms,1987) sequence of lunar basins, althoughFassettetal.(2012)foundsigniﬁcantlyhigherdensitiesof superposedcratersonmanylunarbasinsthanderivedbyWilhelms (1987)(50% higher densities).Their data also provide new insight into the timing ofthe transition between distinct crater popula- tionscharacteristicofancientandyounglunarterrains.Ontheba- sis oftheir data theywere able toshow that the transitionfrom a lunar impact ﬂux dominated by Population 1 to Population 2 occurred before themid-Nectarian. This isbefore the end ofthe period of rapid cratering, and potentially before the end of the hypothesizedLateHeavy Bombardment.LOLA-derivedcraterden- sitiesalso suggest that manyPre-Nectarianbasins, such asSouth Pole-Aitken,havebeencrateredtosaturationequilibrium.

3.6.3. Nature,emplacementandhistoryoflunarmaredeposits One of the mostfundamental problems inthe geological and thermal evolutionof theMoon isthe nature,modes ofemplace- ment,anddurationoflunar marebasaltdeposits.LOLAdatahave beenextremelyusefulincharacterizingmaredepositsandaddress relatedquestions. Forexample,Whittenet al.(2011),using LOLA andMoonMineralogyMapper(M3)imageandspectralreﬂectance data, to analyze mare basalt unitsin and adjacent to the Orien- talemulti-ringimpactbasin.Theyfoundthatmarebasaltemplace- ment on the western nearside limb began prior to the Orientale event as evidenced by the presence of cryptomaria. Whitten et al.(2011)foundthatthe earliestpost-Orientale-eventmarebasalt emplacement occurred in the center of the basin (Mare Orien- tale)andpostdatedtheformationoftheOrientaleBasinby about 60–100Ma.Over thenextseveralhundredmillionyears,theyre- ported that basaltpatches were emplaced ﬁrst alongthe baseof the OuterRook ring(LacusVeris) andthenalong thebaseofthe Cordillera ring (Lacus Autumni), with some overlap in ages. Ac- cording to Whitten etal. (2011), the latest basaltpatches are as youngassomeoftheyoungestbasaltdepositsonthelunarnear- side.

A major question in the analysis of the history of the Moon is the role of cryptomaria,ancient volcanic deposits obscured by superposed crater and basin impact ejecta. The timing of cryptomare deposition has implications for the duration and ﬂux of mare basalt volcanism. Whitten and Head (2015a) characterized light plainsunitsontheMoonthatmightbecandidatesforcryp- tomaria.Theyused LOLAaltimetryandroughnessdata,the presence of dark-halo impact craters associated with a mare basalt mineralogy, and high resolution Moon Mineralogy Mapper (M³) VNIR spectral data to determine cryptomare mineralogy as well as Lunar Prospector (LP) FeO and Th compositional measure- mentstoevaluatewhichancientigneousrocksareconsistentwith the mineralogical observations. Whitten and Head (2015a) observed signiﬁcant mineralogic variation for a few cryptomaria (e.g.,Schiller–Schickard,WestHumorum),hintingatheterogeneous mantlesource.Oftheancientigneousrocksinvestigated,Whitten andHead(2015a)foundthatcryptomarearemostconsistentwith typicalmarebasaltlithologies,suchaslow-Timarebasalts.

Whitten and Head (2015b) used LOLA and related data (M3, LROC, Diviner) to map the global distribution of cryptomaria, in ordertoprovideimportantinformationaboutthethermalandvol- canichistoryoftheMoon.Inaddition,knowingthedistributionof cryptomariacanprovideinformationaboutmantleconvectionand lunar magma ocean solidiﬁcation. The globalanalysis of Whitten and Head(2015b) identiﬁed and analyzed the general character-

istics(e.g.,topography,surfaceroughness,rockabundance,albedo, etc.)oflunarlightplainsinordertobetterdistinguishbetweenan- cientvolcanic deposits(cryptomaria)andimpactbasin andcrater ejectadeposits.Theyfound20discreteregionsofcryptomaria,cov- eringapproximately2%oftheMoon,whichincreasethetotalarea coveredbymarevolcanismto18%ofthelunarsurface.

Sorietal.(2016)combinedLOLAtopographyandGRAILgravity tomap the distributionofcryptovolcanic deposits.Theymodeled potential deposits as buried high-density rectangular prisms and estimateda volumeofcandidateburiedcryptovolcanismbetween 0.4×10⁶km³ and4.8×10⁶km³,dependingonassumptions about density and crustal compensation state. These deposits have an area between 0.50×10⁶km² and 1.14×10⁶km², which increases the amount of equivalent lunar surface containing volcanic de- positsfrom16.6%tobetween17.9%and19.5%.Theinferredvolume ofcryptovolcanismiscomparabletothesmallestestimatesofthe volumeofvisible marebasalts andup to ∼50%of thelargestes- timates.GRAIL andLOLAobservations thuscollectively showthat early(pre-3.8Ga)lunarvolcanismisanimportantelementoflunar thermalevolution. Alternatively, theburied material could repre- sentthepresenceofintrusiveMg-suitesillsorplutons.

3.6.4. Floor-fracturedcratersformationofintrusivestructures LOLAdata are critical to the interpretation of modification of cratersby marevolcanismandindetectingintrusivebodies,such assills andthe formationoffloor fracturedcraters. Forexample, floor-fractured craters (FFCs) are a class of lunar craters characterized by anomalously shallow floors cut by radial, concentric, and/or polygonalfractures;additionalinteriorfeatures are moats, ridges, and patches of mare material. Two formation mecha- nismshavebeenhypothesized—floorupliftinresponsetoshallow magmatic intrusion and sill formation, and floor shallowing in response to thermally-driven viscous relaxation. Jozwiak et al.

(2012) combined LOLA and LROC data to characterize and cate- gorize the population of FFCs andmap their distribution on the Moon.Theyfavorformationbyshallowmagmaticintrusionandsill formation.

Inan updatedstudyusingLOLAandGRAILdata,Jozwiaketal.

(2015) found that the distribution and characteristics of the FFC populationcorrelatedstronglywithcrustalthicknessandthepre- dictedfrequencydistributionofover-pressurizationvaluesofmag- matic dikes. Theyfound that for a typical nearside lunar crustal thickness,dikeswithhighover-pressurizationvaluesfavorsurface effusiveeruptions,medium values favorintrusion andsill formation, and low values favor formation of solidiﬁed dikes concen- tratedlowerinthecrust.

3.6.5. Contributionstothegeologyandsurfacecharacteristicsof futurelunarlandingsites

LOLAdatahelped establishthe geological context ofpotential futurelandingsitesfortheUnitedStatesandothernations.Ivanov etal.(2014) describedpotential landing sitesforthe Russian Lu- nar GlobMission tothe southcircumpolar region.The siteislo- cated in the southern part of the high topography surrounding the large South Pole–Aitken (SPA) basin. Photogeological analysis ofsurfaceLOLAtopographyandLROCimagesmadeitpossible to deﬁne groups of morphological units (area types): (1) related to theformationofrelativelyfreshimpactcraters;(2)associatedwith larger (>100km across) degraded craters including external and inner facies; and (3)occupying inter-craterspaces. The compari- son ofthegeological map withthe mapillustrating the distribu- tionofthe epithermalneutrons showsnocorrelation. The region plannedforinvestigations in thescope of theLunaGlob mission correspondstothetopographicriseofthelargest(and,likely,old- est)preservedbasin(SouthPole-Aitken)andoffersapotentialop-