Icarus 283 (2017) 70–91 Contents lists available at ScienceDirect Icarus journal homepage: www.elsevier.com/locate/icarus Summary of the results from the lunar orbiter laser altimeter after seven years in lunar orbit 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 a Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA b Solar System Exploration Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA c Dept of Earth, Environmental and Planetary Sciences, Brown University, Providence, RI 02912, USA d Hawaii Institute of Geophysics and Planetology, University of Hawaii, Honolulu, HI 96822, USA e Department of Earth and Planetary Sciences, Weizmann Institute of Science, Rehovot 76100, Israel f School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287, USA g Stinger Ghaffarian Technologies Inc., Greenbelt, MD 20770, USA h Sigma Space Corporation, Lanham, MD 20706, USA i German Aerospace Center (DLR), Rutherfordstrasse 2, 12489 Berlin, Germany j Technical University Berlin, D-10623 Berlin, Germany k School of Physics, Astronomy and Computational Sciences, George Mason University, Fairfax, VA 22030, USA l Space Department, The Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723, USA m Center for Research and Exploration in Space Science and Technology, University of Maryland, Baltimore County, Baltimore, 21250 MD, USA n Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125, USA o Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ 85721, USA p Center for Earth and Planetary Studies, National Air and Space Museum, Smithsonian Institution, Washington, DC 20560, USA a r t i c l e i n f 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 r a c t In June 2009 the Lunar Reconnaissance Orbiter (LRO) spacecraft was launched to the Moon. The payload consists of 7 science instruments selected to characterize sites for future robotic and human missions. Among them, the Lunar Orbiter Laser Altimeter (LOLA) was designed to obtain altimetry, surface rough- ness, and reflectance measurements. The primary phase of lunar exploration lasted one year, following a 3-month commissioning phase. On completion of its exploration objectives, the LRO mission transi- tioned to a science mission. After 7 years in lunar orbit, the LOLA instrument continues to map the lunar surface. The LOLA dataset is one of the foundational datasets acquired by the various LRO instruments. LOLA provided a high-accuracy global geodetic reference frame to which past, present and future lu- nar observations can be referenced. It also obtained high-resolution and accurate global topography that were used to determine regions in permanent shadow at the lunar poles. LOLA further contributed to the study of polar volatiles through its unique measurement of surface brightness at zero phase, which revealed anomalies in several polar craters that may indicate the presence of water ice. In this paper, we describe the many LOLA accomplishments to date and its contribution to lunar and planetary science. © 2016 Elsevier Inc. All rights reserved. ∗ Corresponding author. E-mail address: smithde@mit.edu (D.E. Smith). 1 w ( o o http://dx.doi.org/10.1016/j.icarus.2016.06.006 0019-1035/© 2016 Elsevier Inc. All rights reserved. . Introduction The Lunar Reconnaissance Orbiter (LRO; Chin et al., 2007 ) as launched to the Moon on June 18, 2009 at 5:32 p.m. EDT Vondrak et al., 2010 ). The purpose of the LRO mission was to btain data about the Moon that will enable the future safe return f humans to the lunar surface, and to identify and characterize D.E. Smith et al. / Icarus 283 (2017) 70–91 71 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). s t s e w i r s D t f a s r s t e p f ( l s h t p r w 2 t a a t s 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 t t 2 t t d 5 s a v o m l t a p c h J o r e cientifically interesting landing site locations. These goals formed he basis of the selection of the instrument suite and the initial pacecraft orbit. The Lunar Orbiter Laser Altimeter (LOLA; Smith t al., 2010 ) is one of the seven instruments onboard LRO, and as designed to acquire substantial topographic measurements n order to provide accurate relief information and a geodetic eference frame for all high-resolution datasets acquired by the pacecraft. LOLA uses short pulses from a solid-state laser through a iffractive Optical Element (DOE) to produce a five-beam pattern hat illuminates the lunar surface ( Smith et al., 2010 ). LOLA makes our types of measurements: the range between the spacecraft nd the surface, the energy of the laser pulse reflected from the urface, the width of the return laser pulse, and the solar radiation eflected from the lunar surface. From these basic measurements, everal scientific datasets are derived, including the topography, he albedo at the wavelength of the laser (1064.4 ± 0.1 nm; Smith t al . , 2010 ), the roughness of the lunar surface within the foot- rint of each laser spot, and the 1064-nm reflectance of sunlight rom the lunar surface. In addition, LOLA enabled a Laser Ranging (LR) investigation Zuber et al., 2010 ) by which laser pulses from Earth-based satel- ite laser ranging stations to LRO provided one-way range mea- urement. A small optical receiver mounted on the Earth-pointed igh-gain antenna received the 532-nm pulses, which were passed o LOLA for precise timing via a fiber optic cable. This experiment rovided additional tracking for LRO and enabled, for the first time, outine laser tracking of a spacecraft in lunar orbit. LRO was placed in its commissioning, near-polar, eccentric orbit ith low periapsis ( ∼30-km altitude near the south pole) on June 7, 2009. Three months later, on September 27, the spacecraft en- ered its 50-km, near-circular mapping orbit, where it completed one-year exploration mission for landing site characterization, nd then started its science-driven mission. On December 11, 2011, he spacecraft was placed back in a near-frozen orbit (near con- tant periapse altitude and location) and altitude range of 30 kmo 200 km to save fuel and extend the lifetime of the mission. In he spring of 2015, the orbit periapsis was lowered to 20–40 km. . The LOLA instrument The LOLA instrument, shown in Fig. 1 , is a laser ranging device hat splits a pulsed laser beam into five output beams via a Diffrac- ive Optical Element (DOE), has a single receiver telescope, and a etector for each of the beams. The LOLA ground pattern provides profiles spaced approximately 12 m apart cross-track with mea- urements separated by 57 m along-track for each profile (from the verage 50 km altitude). Fig. 1 shows the ground pattern of obser- ations. Each beam provides a measurement of the round-trip time f flight (range), pulse spreading (surface roughness), and trans- it/return energy (surface reflectance at the laser wavelength). The aser pulse energy, the receiver aperture size, and the spacecraft al- itude limit the range precision to about 10 cm for a flat surface. As consequence of its two-dimensional spot pattern, the instrument rovides an unambiguous determination of both along-track and ross-track slopes along the spacecraft ground track ( Fig. 2 ). LOLA as operated nearly continuously (exceptions discussed later) since uly 3, 2009 ( Table 1 ). Laser altimetry from orbit requires the position and attitude f the spacecraft, and the altimeter’s laser beam pointing with espect to the spacecraft coordinate system. To that end, several xperiments were conducted to measure post-launch instrument 72 D.E. Smith et al. / Icarus 283 (2017) 70–91 3 4 1 4 1 5 5 2 0 50 100 Distance (m) 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). a t w a k s i s b o s A q t t t u t 0 o i y r s t q d r i b i g O a o i m s s a pcharacteristics of LOLA including the laser boresight vector. In these experiments, LRO pointed away from the Moon and scanned the Earth in a raster pattern, as the LOLA laser actively fired. A ground station on Earth received the 1064 nm pulses (the down- link), while it fired its own laser to LRO (the uplink). The downlink pulse arrival times and digitized waveforms were recorded at the ground station, the Goddard Geophysical and Astronomical Obser- vatory (GGAO) in Greenbelt, MD, and the uplink arrival times and pulse widths were recorded by LOLA’s five detectors. Three successful LOLA active Earth scans were conducted: one in 2009, shortly after launch; one on Jan. 7, 2014; and another on Mar. 24, 2014. The 1.2-m telescope at GGAO was equipped to record the 1064-nm downlink pulse arrival times and to digitize the pulse waveforms. During post-processing, the energy of each downlink pulse could thus be measured by integrating the area under a Gaussian fit to the waveform. The spacecraft position and attitude were obtained from LRO project-supplied SPICE kernels. The fire times and receive times of the pulses were matched afterFig. 3. Time series of (a) cross-track and (b) along-track LOLA beam offsets determined pplying appropriate light time corrections. The time tags of the ransmitted and the received laser pulses at both LRO and GGAO ere used to solve for the LOLA bore-sight offset between the laser nd the receiver field of view. Note, this is not related to the Blan- et Anomaly discussed in Apendix where further details of the in- trument performance are provided. The use of altimetric crossovers provides another means to cal- brate the post-launch laser beam boresight vector. Compared to ingle beam altimeters, the novel cross-track information provided y LOLA’s multi-spot footprint allows a more accurate adjustment f crossover offsets, because each track’s profile forms a narrow urface onto which the other track’s points can be interpolated. sample of nearly 80 0,0 0 0 daytime and nighttime crossovers ac- uired in the 50-km circular orbit was used to derive corrections o the nominal laser boresight vector. Mazarico et al. (2014) used hose to study the lunar body tide ( Section 3.8 ). For each crossover, he 3-dimensional offset vector between the tracks was adjusted ntil it minimized the elevation residuals. The adjustment reduced he median RMS elevation residual for all crossovers from 1.67 m to .48 m. Pointing errors cause periodic variations in the time series f cross-track and along-track offsets ( Fig. 3 ). This periodic behav- or is correlated with the day/night cycle and the semiannual LRO aw flips (see Appendix). Modeling of this crossover offset time se- ies yields daytime and nighttime corrections to the nominal bore- ight in the range of 45 to 275 μrad, which were incorporated into he LOLA data processing pipeline in July 2014 and into the subse- uent LOLA PDS releases. The corrected nighttime boresight vector erived from this crossover analysis is in agreement with that de- ived from the Earth scans above. Future Earth scans when LOLA s illuminated will be useful to ascertain the post-launch daytime oresight. LOLA’s normal mode of operation is nadir-pointed, although it s also operated off-nadir when LOLA or another instrument is tar- eted to a location not directly under the spacecraft groundtrack. ff-nadir pointing is rather common, and part of the normal oper- tions of the LRO spacecraft. LOLA can acquire data over all regions f the Moon, but because the groundtracks are closer at high lat- tudes than near the equator the spacing between LOLA measure- ents is much smaller at the poles than near the equator. Fig. 4 hows the average longitudinal coverage (distance between mea- urements) by latitude. The average coverage in latitude is gener- lly on the order of 20 to 30 m (along-track), as a result of the ulse rate of 28 Hz and the 5 profiles. from crossovers. Black dots mark the semi-annual yaw flips of the LRO spacecraft. D.E. Smith et al. / Icarus 283 (2017) 70–91 73 Latitude -80 -60 -40 -20 0 20 40 60 80 M et er s 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. s e i c I e f 3 3 c o b c a i s u g t i e v e u i e s t i p p c p 7 4 e 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) a Normalized (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 a Spherical harmonics are normalized at degree l and order m as C lm = N lm C lm , where N lm = [{(2- δm,0 )(2l + 1)(l-m)!}/(l + m)!] 1/2 . p e b e h t p a f a c a ( G o p M t T a a l w s s 1 T 1 b c T c c p e g g t s a a a a Locally, the spacing varies and can be several times larger (or maller) than the average of a given latitude. In addition, the av- rage separation over the southern hemisphere is less, due to the ncreased operation time during the eccentric orbits both during ommissioning in 2009 and since the fall of 2012 to conserve fuel. n the northern hemisphere, the present LRO altitude above the quator is generally greater than the range capability of LOLA, so ew altimetric measurements can be obtained north of the equator. . Summary of science results .1. Global shape and topography LOLA altimetry data have been assembled into global grids in ylindrical and polar stereographic projections, at a variety of res- lutions ( Smith et al., 2015 ). Densely-spaced altimetric data are inned into uniformly-sampled maps by median filtering to ex- lude noise returns. Recognizing that both manual inspection and utomatic rejection of noise can be imperfect when the return rate s low (when LRO altitude is high), an additional comparison with tereophotogrammetric tiles ( Barker et al., 2016a ) is sometimes sed in the eccentric orbit to exclude the remaining outliers. Data aps in the maps are filled by interpolation using splines under ension ( Smith and Wessel, 1990 ). The resulting maps are provided n multiple tiles at a resolution of 512 pixels per degree (ppd; quivalent to ∼59 m resolution at the equator), as well as coarser ersions re-sampled by powers of two. (A global grid at 1024 pix- ls per degree was deemed too sparse overall and has not been pdated, although there are sufficient points to build denser grids n many regions.) While the near-polar LRO orbit yields the high- st areal density of ground returns near the poles, the density of ampling is roughly uniform in a simple cylindrical projection. In- erpolation using this projection does not perform well in preserv- ng shapes of landforms near the poles, thus high-latitude ground oints are binned, median-averaged and interpolated in conformal olar projections as well. Polar stereographicmaps, which preserve ircular landforms, are produced at resolutions from 5 to 80 m per ixel poleward of 80 ° latitude, from 30 to 120 m per pixel above 5 °, from 60 m to 240 m per pixel above 60 °, and from 100 to 00 m per pixel poleward of 45 °. The LOLA Digital Elevation Mod- ls (LDEMs), are indexed by shaded-relief browse images, accom-anied by count maps (LDEC) that show the number of returns in ach pixel (a value of 0 where interpolation is necessary). With the steadily improved knowledge of lunar gravity afforded y the Gravity Recovery And Interior Laboratory (GRAIL) Discov- ry Mission ( Zuber et al., 2013a ), systematic errors in orbital tracks ave been largely eliminated ( Mazarico et al., 2013 ), with the opographic uncertainty dominated by gaps in cross-track sam- ling. Such gaps are more frequent near the lunar limbs (90 °E nd 270 °E), because spacecraft maneuvers were preferentially per- ormed ‘face-on’ and precluded science measurements. Spacecraft ttitude uncertainty also accounts for some geometric errors, espe- ially during slews. At the 5-m resolution of the polar DEMs, small djustments are still necessary to completely match adjacent tracks Zuber et al., 2012; Gläser et al., 2014 and this issue). Low altitude orbital surveys such as performed during the RAIL mission end game demanded the best possible knowledge f topographic extremes to avoid prematurely impacting unsam- led high-standing terrain. Prior to 2009, the global shape of the oon ( Smith et al., 1997 ) was uncertain by many hundreds of me- ers ( Margot et al., 1999 b), particularly over the farside highlands. he early results from the SELENE mission [Araki et al., 2009] gave 19.8 km range of topography, while LOLA topographic extremes re about 19.92 km. The longest physical diameter, 3486.014 km, ies between 25.9 °N, 204.15 °E and its diametrically opposite point, hile the shortest diameter, 3463.267 km, lies at 67.1 °S, 179.7 °E, ubtending an angle of 94.8 °. Relative to the IAU 1737.4-km-radius pherical datum, the deepest point, −9.129 km, lies at 70.36 °S, 87.52 °E, and the highest, 10.792 km, lies at 5.341 °N, 201.37 °E. he equatorial radius averaged over a 1 ° wide latitudinal band is 738.133 km. For comparison with the dynamical axes of a nearly-spherical ody, it is conventional to use a spherical harmonic expansion to haracterize the principal parameters of shape, as listed in Table 2 . he degree 1 un-normalized coefficients represent the offset of the enter of figure (COF) from the center of mass, and yield 1.935 km, hiefly in the -X (anti-Earth) direction (the longitude of the offset rojected to the equatorial plane is 202.38 °E). Although a reference llipsoid of revolution (spheroid) has not been adopted, the de- ree (2,0) coefficient implies a flattening of 0.001289, considerably reater than that of a hydrostatic body under the influence of rota- ional and tidal potentials. Considering the degree and order (2,2) ectoral terms, the principal semi-axis of the shape is 1738.670 km t 143 ° longitude, and the intermediate semi-axis is 1737.127 km, lso offset from the principal dynamical axes. A tri-axial ellipsoid bout the center of figure has dimensions of 1739.146, 1737.394, nd 1734.928 km, although such a form represents shape poorly, 74 D.E. Smith et al. / Icarus 283 (2017) 70–91 Fig. 5. Spherical harmonic topographic coefficient root mean variance by degree (logarithmic scale). The root sums σ l = [ C 2 lm /(2l + 1)] 1/2 of normalized coefficients are multiplied by degree for illustration. -8 -6 -4 -2 0 2 4 6 8 km d c b a 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 ref- erences to color in this figure legend, the reader is referred to the web version of this article). 3 t b n p t s a t o ( d v e t a c f p o with a root-mean-square misfit of 1.73 km; its major axis is tilted 27 ° with respect to the pole of rotation. As we illustrate below, the shape is strongly perturbed by long-wavelength effects. The topographic power spectrum of the Moon is shown in Fig. 5 . Spherical harmonic coefficients of degree 1–4 (dots) dom- inate the shape. At wavelengths of ∼90 to 20 0 0 km (degrees 5– 120), topographic power is diminished relative to the power law behavior at higher degrees, corresponding to a transition from complex craters to basin morphology and flexural isostatic com- pensation. Fig. 6 a shows the global topography of the Moon centered on 270 °E with Orientale basin prominent below the equator. Each suc- ceeding Fig. 6 (b–d) removes successive low-degree terms up to 4. The nearside Mare Procellarum region and the farside South Pole-Aitken impact basin account for much of the low-degree sig- nal ( Garrick-Bethell et al., 2014; Keane and Matsuyama, 2014 ). The residual figure is shaped by more than 70 basin-scale impact struc- tures ( Neumann et al., 2015 ) as well as finer scale-positive-relief features — the topographic rims of craters or to a lesser extent the volcanic features such as the Aristarchus and Marius hills, and Montes Rumker, Mairan, Gruithuisen and Carpatus. Wrinkle ridges and other tectonic features in the nearside mare regions also ex- hibit positive relief. 3.1.1. Regional topography Regional geological studies are enabled by LOLA topography in regions where partial or permanent shadow preclude other obser- vations, such as over the floor of the 136-km-diameter Antoniadi Crater on the southern farside, in a region of very thin crust. The topography of this transitional-type basin, with terraced walls, an interior peak ring and a small central peak, is shown in Fig. 7 a. The area shown covers about 0.06% of the Moon. The lowest eleva- tion of the Moon lies at the bottom of a ∼15-km diameter simple crater within Antoniadi at 70.36 °S, much of which exists in per- manent shadow. Altimetry, however, reveals several features of its floor. These observations constrain the scale at which morphologi- cal transitions occur in this unusually deep region of the Moon. Within the visible portions of Antoniadi, the location of an im- age (M154024477R) taken by the LROC NAC camera ( Robinson et al., 2009 ) of a km-sized mound outcropping from the crater floor is outlined by a small square ( Fig. 7 c). Fig. 7 b and d illustrates how the LOLA data provide context for interpretation of such fea- tures. Here the ∼20 m resolution afforded by many closely-spaced groundtracks allows profiles and contours to assess the height of very small, unusual features, and resolve a few-meters-deep moat surrounding the 60-m-high mound. .2. Global roughness and surface slopes Quantification and analysis of surface roughness properties of he Moon at unprecedented scales and resolution are made possi- le with the new global elevation data. Surface slope and rough- ess can be measured at the 100-m scale with about 10 altimetric oints (2 LOLA frames), by fitting a plane and measuring their scat- er around it ( Fig. 8 ). Rosenburg et al. (2011) further mapped lunar urface slope and roughness using a range of parameters: median bsolute slope, both directional (along-track) and bidirectional (in wo dimensions); median differential slope; and Hurst exponent, ver baselines ranging from ∼17 m to ∼2.7 km. Rosenburg et al. 2011, 2015) found that the lunar highlands and the mare plains isplay vastly different roughness properties, with less distinctive ariations within mare and highlands. Most of the lunar surface xhibits fractal-like behavior (cf. Turcotte, 1987 ), with a single or wo different Hurst exponents over the given baseline range; when transition exists, it typically occurs near the 1-km baseline, indi- ating a significant characteristic spatial scale for competing sur- ace processes. Rosenburg et al. (2011) found that the Hurst ex- onent is high within the lunar highlands, with a median value f 0.95, and lower in the maria (with a median value of 0.76). D.E. Smith et al. / Icarus 283 (2017) 70–91 75 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 out- lines 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 pro- files sampled from the gridded data record along N-S and E-W lines (vertical ex- aggeration 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 inter- pretation 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). R t u b i d o ( a t t 1 v t i r c a g m o fl e ( t n a o t ( n g p e s s ( osenburg et al. (2011) demonstrated that the median differen- ial slope is a powerful tool for discriminating between roughness nits and is useful in characterizing the ejecta surrounding large asins, particularly Orientale, as well as the ray systems surround- ng young, Copernican-age craters. They further show that median ifferential slope allows a quantitative exploration of the evolution f surface roughness with age on mare surfaces. In further analysis of the altimetry data, Kreslavsky et al. 2013) presented maps of the topographic roughness of the Moon t hectometer and kilometer scales derived from range profiles ob- ained by LOLA. As roughness measures, they used the interquar- ile range of profile curvature at several baselines, from 115 m to .8 km, and plotted these in a global map format. The maps pro- ide a synoptic overview of variations of typical topographic tex- ures and utilize the exceptional ranging precision of the LOLA nstrument. Kreslavsky et al. (2013) found that hectometer-scale oughness poorly correlates with kilometer-scale roughness, be- ause the two scale lengths reflect different sets of processes nd time scales. Hectometer-scale roughness is controlled by re- olith accumulation and modification processes and affected by the ost recent events (primarily, geologically recent (1–2 Ga) mete- ritic impacts). Kilometer-scale roughness, on the other hand, re- ects major geological (impact, volcanic and tectonic) events in arlier geological history. The data presented by Kreslavsky et al. 2013) also show that young large impact craters are rough, and heir roughness decreases with increasing age. The global rough- ess maps reveal a few unusually dense clusters of hectometer- nd decameter-size impact craters that differ in their morphol- gy and settings from typical secondary crater clusters and chains; he origin of these features is currently unknown. Kreslavsky et al. 2013) maps can also assist in the geological mapping of the lu- ar maria by revealing contacts between volcanic plain units. The lobal roughness maps also clearly reveal cryptomaria, old volcanic lains superposed by younger materials, primarily crater and basin jecta ( Whitten and Head, 2013, 2015a,b ). Furthermore, these data can be successfully applied to under- tanding the dynamics of impact processes and their effects on urface degradation, even at planetary scales. Kreslavsky and Head 2012) showed that the new maps of kilometer-scale topographic 76 D.E. Smith et al. / Icarus 283 (2017) 70–91 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. m s r f r m p w i S s i t E h v e e a w S g roughness and concavity of the Moon reveal a distinctive rough- ness signature of the proximal ejecta deposits of the Orientale basin (the Hevelius Formation). They found that no other lunar impact basin, even the just-preceding Imbrium basin, is character- ized by this type of signature although most have similar types of ejecta units and secondary crater structures. The preservation of this distinctive signature, and its lack in basins formed prior to Orientale, was interpreted by Kreslavsky and Head (2012) to be the result of seismically-induced smoothing caused by this latest major basin-forming event. Intense seismic waves accompanying the Ori- entale basin-forming event preceded the emplacement of its ejecta in time and operated to shake and smooth steep and rough to- pography associated with earlier basin deposits such as Imbrium. In their interpretation, Orientale ejecta was emplaced immediately following the passage of the seismic waves and thus formed the distinctive roughness signature that has been preserved for almost 4 billion years. 3.3. Polar topography and slopes Because of the dense spatial coverage afforded by LRO’s polar orbit, the north and south polar regions are characterized by a high density of ground track coverage that has enabled high resolutionaps. Fig. 9 shows topography and 100-m slopes for the north and outh polar regions. These topographic maps shown have a spatial esolution of 60 m that enables geologic characterization relevant or science analyses and exploration planning. The highest- esolution polar maps (5 m/pixel from 87.5 ° latitude to each pole) et the mission requirement of 30-m resolution for locations of otential landing sites or regions of special scientific interest. LOLA high-resolution DEMs enable geologic characterization as ell as crater counting and relative age dating of the lunar poles, ncluding permanently shadowed areas. A prominent example is hackleton crater, which is nearly coincident with the Moon’s outh pole. Its interior receives almost no direct sunlight and s a perennial cold trap, making it a promising candidate loca- ion in which to seek sequestered volatiles. Previous orbital and arth-based radar mapping and orbital optical imaging, however, ave produced conflicting interpretations about the existence of olatiles ( Nozette et al., 2001; Campbell et al., 2006; Haruyama t al., 2008; Spudis et al., 2013 ). The observations of Zuber t al. (2012) from LOLA DEMs, ( Fig. 10 ) revealed Shackleton to be n ancient, unusually well-preserved simple crater whose interior alls are fresher than its floor and rim. The LOLA DEMs show that hackleton floor deposits are nearly the same age as the rim, sug- esting that little floor deposition has occurred since the crater D.E. Smith et al. / Icarus 283 (2017) 70–91 77 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 avail- able LOLA profiles that include collectively 16 million unique elevation measure- ments. Elevations are contoured at 5-m intervals ( Zuber et al., 2012 ). f l r i s r a s i s a t c a a c e i r t r s N L i s i S p i c i w 3 3 l f r L u p r e p t u l a t t t i t S t a s s t u s e L t s b e l y s c e t ( h t l w v t r d s o s k m t s c r f t ( s t oormed more than three billion years ago. At the LOLA laser wave- ength, the floor of Shackleton is brighter than the surrounding ter- ain and the interiors of nearby craters, but not as bright as the nterior walls. Zuber et al. (2012) interpreted these combined ob- ervations to be explained primarily by downslope movement of egolith on the walls, exposing fresher underlying material ( Fassett nd Thompson, 2014 ). The relatively brighter crater floor is most imply explained by decreased space weathering due to shadow- ng, but a one-micrometer-thick layer containing about 20 percent urficial ice was cited as an alternative possibility. LOLA high-resolution DEMs have also been analyzed to assign ges to other South circumpolar permanently-shadowed crater in- eriors. Tye et al. (2015) studied the interiors of the lunar south ircum-polar craters Haworth, Shoemaker, Faustini, and Shackleton, ll of which contain large permanently shadowed regions (PSRs) nd all have been interpreted to contain sequestered volatiles in- luding water ice. LOLA altimetry data provided a new means of xamining the permanently shadowed interiors of these craters n unprecedented detail. Tye et al. (2015) used extremely high- esolution gridded LOLA data to determine the size-frequency dis- ributions and the spatial density of craters superposing their ims, inner slopes, and floors. On the basis of their population of uperposed craters, Haworth, Shoemaker, and Faustini have pre- ectarian formation ages. Shackleton was interpreted as having a ate Imbrian age on the basis of craters superposed on its rim. Us- ng LOLA slope data, Tye et al. (2015) showed that the local den- ity of craters is strongly dependent on slope; because of its steep nterior slopes, the lifetime of craters on the interior walls of hackleton is limited. The slope-dependence of the small crater opulation implies that the population in the size range analyzed s controlled primarily by the rate at which craters are destroyed, onsistent with the hypothesis that crater removal and resurfac- ng is a result of slope-dependent processes such as diffusive mass asting and seismic shaking. .4. Radiometry, reflectance and albedo .4.1. Normal albedo from active radiometry Owing to the importance of ice as a potential resource at the unar poles, LOLA was designed to search for deposits of surfacerost in regions of permanent shadow through measurement of the eflectance of the surface at 1064 nm ( Smith et al., 2010 ). Because OLA provides its own light source, its measurements are partic- larly useful because reflectance measurements within regions of ermanent shadow can be compared quantitatively to those of the est of the Moon without the need for complex photometric mod- ls that correct for variable lighting, or in the case of the regions of ermanent shadow, indirect lighting. This attribute of LOLA is par- icularly useful for regions in permanent shadow, whose only nat- ral light source in the visible portion of the spectrum, scattered ight, is challenging to model as it depends on the topography and lbedo within and around the shadowed regions. Another useful feature of the LOLA reflectance experiment is hat it measures the lunar surface reflectance at zero phase angle, hat is the angle between the light source (LOLA’s laser transmit- er), the lunar surface, and the receiver (LOLA’s receiver telescope) s zero (or effectively so, there is a minute angle due to the travel ime of the light pulse to the lunar surface and back). With the un as a light source, this zero phase angle condition can some- imes be observed from the Earth and from space, but because the ngle of incidence systematically increases toward the poles, the urface is increasingly foreshortened and passive zero-phase mea- urements in polar craters are not possible. For a dark surface like he Moon, measurements at zero phase are free of dependence pon topography, again enabling comparison of reflectance mea- urements among terrains without the need for photometric mod- ls. Fig. 11 shows the lunar albedo at 1064 nm derived from the OLA active reflectance measurements. The initial results from the LOLA reflectance experiment found hat the south polar crater Shackleton, mostly in permanent hadow, was locally unique in reflectance, being substantially righter than its surroundings. Zuber et al. (2012) considered sev- ral hypotheses for this anomalous reflectance, including but not imited to the presence of surface frost. Calibration of the first ear of LOLA observations demonstrated that regions in permanent hadow are in general about 15% brighter than polar areas that re- eive some illumination and Lucey et al. (2014) suggested this gen- ral increase was due to inhibited space weathering owing to low emperatures, or possible surface frost. Reflectance data from LOLA were used by Hemingway et al. 2015) and Lemelin et al. (2016) to show that the lunar maria ex- ibit a latitude-dependent albedo. They suggested this was due o a variation in space weathering with latitude and average so- ar incidence angle, supporting a sputtering source for lunar space eathering optical effects. LOLA’s data uniquely supported this in- estigation because of its immunity from latitude-dependent pho- ometric effects. LOLA’s measurements of the zero-phase reflectance are mir- ored on the planet Mercury with the Mercury Laser Altimeter ata ( Neumann et al., 2013 ). Comparison of these two experiments how that the typical reflectance of Mercury is similar to that f the iron-rich lunar maria, despite the low-iron nature of the urface of Mercury. While this albedo difference was previously nown, the laser experiments provide robust independent confir- ation, and a unique photometric geometry to support investiga- ions aimed at understanding the difference. Ongoing experiments with LOLA reflectance now center on a earch for time-variable reflectance which would help identify the ause of increased brightness in shadowed regions since any pe- iodic variation is most likely due to transient surface frost. Data rom Deep Impact, Cassini and Chandrayaan-1 indicated that spec- ral absorption due to water is time-variable on the lunar surface Sunshine et al., 20 09; Clark, 20 09; Pieters et al., 2009 ). LOLA mea- urements of the reflectance of surfaces at a variety of tempera- ures may be able to detect or place upper limits on the abundance f migratory water or time-variable surface frost. 78 D.E. Smith et al. / Icarus 283 (2017) 70–91 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) . Phase angle (deg) 0 15 30 45 60 75 90 R AD F / A n / L S 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 N p er b in 100 101 102 103 104 105 Fig. 12. 1064-nm highlands phase function from LOLA passive and active radiom- etry. 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 ra- diance 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). t d v w i R f m p a p w U 3.4.2. Lunar phase function in the near-IR from passive and active radiometry Although not included in the original instrument mission goals, we have developed a second reflectance measurement technique, which leverages the LOLA noise-monitoring house-keeping data and uses them as a unique passive radiometry science measure- ment of the Moon. Instead of letting the flight software control the thresholds to maintain the noise level to ∼1–2% as during normal altimetric operations, the thresholds can be held fixed at very low levels to allow thousands of noise counts per second to be mea- sured and yield high-SNR reflectance measurements. This thresh- old setting is typically only employed when the spacecraft is too high to otherwise obtain any altimetric measurement (northern hemisphere in the near-frozen elliptical orbit) and when the beta angle (angle between the prime meridian and the Sun) is not fa- vorable considering the LOLA thermal blanket anomaly (beta  80 °) (see Appendix). This data set is unique because it covers a narrow spectral band, it is as precisely geolocated as the altimetry data, and it complements the active normal albedo measurement made with the laser. With passive radiometry, the instrument measures 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 of interest for better understanding the geologic and space weathering influences on regolith characteristics. A significant challenge has been to pre- dict the observed variations in phase function with location and wavelength from first principles, because of the complexities of ra- diative transfer theory applied to lunar regolith. The unique ability of LOLA to measure the normal albedo through active reflectance provides new opportunities in this arena, because it allows for the removal of most of the effects of single particle albedo on the phase function from those of other regolith properties, such as the single particle backscattering strength and the opposition effect (OE, which is the surge in brightness at phase angles near zero). Barker et al. (2016b) presented a method for calibrating the passive radiometry data and used the passive and active radiom- etry to study the near-IR phase function’s dependence on various geologic parameters. On a global scale, they found that iron abundance and optical maturity were the dominant controlling parameters. Titanium abundance, surface roughness on decimeter to decameter scales, and soil thermophysical properties had a smaller effect, and the latter two were correlated with optical ma- turity, indicating that exposure age was the driving force behindheir contribution. The phase function also exhibited a depen- ence on slope, possibly due to mass wasting and/or reduced sky isibility. Geologically-influenced variations of the phase function ere observed, in particular associated with the dark halo of mpact melt around the Copernican-aged Jackson crater and the einer Gamma Formation (RG). The phase function of RG deviated rom the global average (for the same composition and optical aturity), suggesting that the unusual regolith evolution and roperties at this location affect the visible-to-near-IR spectrum nd phase function differently. From detailed modeling of the hotometric function, Barker et al. (2016b) verified that several avelength trends observed by Sato et al. (2014) with LROC in the V-VIS continue into the near-IR. In particular, the maria exhibited D.E. Smith et al. / Icarus 283 (2017) 70–91 79 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 ). d s t c o o 2 h f s T s m 3 d e s w a 1 L l b v ( e c C c c d t g i o 1 2 i e t s s r v b r w o w e s e c s t s a fi l a a e e t w o t h d n S ( t a a t i o ( r n ecreased backscattering, a narrower OE angular width, and a maller OE amplitude relative to the highlands. It was also found hat the backscattering strength and OE width have no significant orrelation with geologic context within the maria. These results shed further light on the wavelength dependence f the Moon’s photometric behavior, something for which our the- retical understanding is presently incomplete (e.g., Hapke et al., 012a ). Altogether, compositional variations and space weathering ave important effects on the Moon’s photometric behavior apart rom their influence on single particle albedo, a result made pos- ible by LOLA’s unique ability to directly measure normal albedo. hus, laser altimeters like LOLA can contribute to photometric tudies thanks to their combined active and passive radiometry easurements at all phase angles. .5. Illumination conditions at the lunar poles One of the main objectives of the LRO mission was to study the istribution of volatiles and the processes controlling their pres- nce and their potential time-variable transport. Prior to the LRO mission, the existence of areas in ‘permanent hadow’ in the polar regions, hypothesized by Watson et al. (1961) , as thought to be directly responsible, through cold-trapping, for ll the volatiles observed by Lunar Prospector ( Feldman et al., 998 ). Spatially resolved observations by the LEND instrument on RO ( Mitrofanov et al., 2010 ) showed that the hypothesized corre- ation does not necessarily hold at small scales, and much work ased on the new LRO datasets has focused on refining models of olatile production and loss (e.g., Farrell et al., 2015 ) and transport Schorghofer and Aharonson, 2014 ). Precise knowledge of the topography of the Moon is key in nabling these studies, as it directly impacts the illumination onditions and thermal environment of the lunar surface. The lementine altimetric data ( Smith et al., 1997 ) were not of suffi- ient quality to enable numerical simulations of the illumination onditions, and despite high intrinsic resolution, Earth-based radar ata (e.g., Margot et al., 1999 ) were lacking uniform coverage due o the tidal lock of the Moon, resulting in significant coverage aps and biases over a wide range of solar longitudes. While magery-based studies did make progress in identifying areas f permanent shadow and of high illumination ( Bussey et al., 999 ), the laser altimeter data acquired by LALT ( Araki et al., 009 ) onboard SELENE enabled the first faithful simulation of llumination conditions based on a topographic model alone ( Nodat al., 2008 ). Soon after, the LOLA data substantially improved he quality and spatial extent made possible through numerical imulation, thanks to a longer mission duration and higher mea- urement rate (140 Hz effective). Mazarico et al. (2011a) presented esults of solar insolation, permanent shadow regions (PSR) in- entory, areas of highest illumination, and Earth visibility, over oth poles (75–90 °) at 240 m/px. Instead of the more traditional ay-tracing method, they used a ‘horizon method’, more efficient hen investigating illumination conditions at finer temporal res- lution over long temporal baselines. Individual timestep results ere validated with concomitant LROC WAC images ( Robinson t al., 2009 ). Fig. 13 illustrates such results, from a more recent imulation performed in the 82.5 °S–90 °S region at 60 m/px: av- rage solar illumination and Earth visibility over a lunar nutation ycle ( ∼18.6 years) and the areas determined to be in permanent hadow. While spacecraft imagery ultimately provides ground truth for he illumination state ( Speyerer and Robinson, 2013 ), camera ob- ervations are limited in temporal extent (by the mission duration) nd in spatial extent (by spacecraft orbital phasing and instrument eld of view), and thus do not necessarily suffice to investigate ong-term or secular effects. The LOLA-derived illumination maps re useful for the interpretation and analysis of scientific data cquired by the other LRO instruments. For example, Mitrofanov t al. (2010) used the outlines of the PSRs defined by Mazarico t al. (2011a) to compute the statistical significance of the neu- ron suppression within them. The average illumination maps ere leveraged in studies to better understand the distribution f volatiles in the near-subsurface, in particular by correlating he LEND measurements with illumination. Fig. 14 shows the igh correlation between the general trends with latitude of ecreasing average illumination poleward with the reduction in eutron counts as measured by both the Lunar Prospector Neutron pectrometer (LPNS) and the Lunar Exploration Neutron Detector LEND) ( Mazarico et al., 2011a ). Further studies further established his link, and showed the importance of maximum slope and slope zimuth on the presence of subsurface volatiles ( McClanahan et l., 2015 ). Another derived product, the so-called sky visibility hat describes the sky solid angle visible from the surface, was mportant to correct the Lyman Alpha Mapping Project (LAMP) bservations and measure the surface albedo at UV wavelengths Gladstone et al., 2012 ). Simulations over larger areas and at higher esolutions have since been performed. PSRs were identified at on-polar latitudes ( Mazarico et al., 2011b ), as low as 58.185 °S 80 D.E. Smith et al. / Icarus 283 (2017) 70–91 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). 3 3 l f L a t i i i a a c ( p N o L B a pand 58.412 °N ( McGovern et al., 2013 ). Gläser et al. (2014) used LROC NAC-derived shape models in combination with LOLA data to determine the best South Pole locations for landers, in terms of solar power input for future lunar exploration. Continued work also showed that the total amount of area found to be in permanent shadow increases as the topographic map quality and the topographic resolution improve. Fig. 13 sum- marizes the extent of permanent shadow in the polar regions from various simulations. It illustrates that while Mazarico et al. (2011a) found that 7.03% and 9.82% of latitudes poleward of 85 ° (North and South, respectively) were in permanent shadow, a sim- ulation at the same resolution (240 m/px) using the most recent LOLA map (PDS release 15, in June 2015) yields 7.75% and 10.19%. Higher resolutions (120 m/px and 60 m/px, with the same 2015 dataset) yield 8.79%/10.74% and 9.70%/11.41%, respectively. At even higher resolution, the trend continues, with ∼25% more area in permanent shadow et 20 m/px than at 60 m/px. This is consistent with the fractal nature of topographic surfaces ( Turcotte, 1987 ) and recent work by Bandfield et al. (2015) on thermal anisotropy. Con- versely, as resolution increases, the most illuminated sites tend to shrink spatially and show lower solar illumination averages. No peak of eternal light, again hypothesized by Watson et al. (1961) , exists on the Moon ( Noda et al., 2008; Mazarico et al., 2011a; Gläser et al., 2014 ). .6. Geology .6.1. Morphometric characterization craters and basins Of fundamental importance to the understanding of the geo- ogical evolution of planets is the quantitative nature of their land- orms and their relationship to the thermal evolution of the planet. OLA data have provided the basis to undertake these types of nalyses, and to improve our knowledge of the origin and evolu- ion of landforms related to impact crater volcanism and tecton- sm. For example, a major question in the origin and evolution of mpact craters and basins is the nature of the transition, with ncreasing size, from simple, to complex, to peak-ring basins nd finally to multi-ring basins. Baker et al. (2011) used LOLA nd LROC data to document the relationship between complex raters with central peaks and multi-ring basins in protobasins exhibiting a rim crest and interior ring plus a central peak) and eak-ring basins (exhibiting a rim crest and an interior ring). ew data have permitted improved portrayal and classification f these transitional features on the Moon. Using high-resolution OLA gridded topographic data combined with image mosaics, aker et al. (2011) conducted a survey of craters > 50 km in di- meter on the Moon and updated the existing catalogs of lunar eak-ring basins and protobasins (see also Kalynn et al., 2013 ). D.E. Smith et al. / Icarus 283 (2017) 70–91 81 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). t r a o L b i r t t a f b o c t r p f o t t c e t i u t L g b o o t g o r aLOLA data were also essential in the detailed documentation of he morphologic transition from complex impact craters, to peak- ing basins, and to multi-ring basins and the morphometric char- cteristics of these landforms due to their large size and the lack f global high-resolution topography data. Baker et al. (2012) used OLA data to derive the morphometric characteristics of impact asins on the Moon, assess the trends, and interpret the processes nvolved in the observed morphologic transitions. Several geomet- ic trends for peak-ring basins have been observed ( Fig. 15 ). A fac- or of two reduction in the depth to diameter ( d / D ) ratio in the ransition from complex craters to peak-ring basins may be char- cterized by a steeper trend than known previously. The d / D ratio or peak-ring basins decreases with rim-crest diameter, which may e due to a non-proportional change in excavation cavity growth r scaling, as may occur in the simple to complex transition, or in- reased magnitude of floor uplift associated with peak-ring forma- ion. Baker et al. (2012) found that new observations of geomet- ic/morphometric properties of protobasins and peak-ring basins lace some constraints on the processes that control the onset and ormation of interior landforms in peak-ring basins. Comparisonsf the geometric trends of the inner rings of Orientale basin with hose of peak-ring basins are generally consistent with a mega- errace model for the formation of multi-ring basins. In addition to quantifying the interior structure of impact raters and basins, LOLA data has also been utilized to assess the jecta deposits and their thickness. Fassett et al. (2011) showed hat quantifying the ejecta distribution around large lunar basins s important to understanding the origin of basin rings, the vol- me of the transient cavity, the depth of sampling, and the na- ure of the basin formation processes. Fassett et al. (2011) used OLA altimetry data to estimate the thickness of ejecta in the re- ion surrounding the Orientale impact basin, the youngest and est preserved large basin on the Moon. By measuring the size f craters progressively covered by Orientale ejecta as a function f distance from the basin rim, their measurements yielded ejecta hicknesses of ∼2900 m near the Cordillera Mountains, the topo- raphic rim of Orientale, decaying to ∼1 km in thickness at a range f 215 km. These measurements imply a volume of ejecta in the egion from the Cordillera ring to a radial range of one basin di- meter of ∼2.9 ×10 6 km 3 . 82 D.E. Smith et al. / Icarus 283 (2017) 70–91 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). o r h l t c h d a h S t l 3.6.2. Ages and crater density LOLA data have provided unprecedented ability and oppor- tunities to assess impact crater location, mapping and density (size-frequency) distributions, and to apply these data to map- ping of lunar surface units, and fundamental lunar problems. For example, previous analyses of the global distribution of lu- nar craters were compiled with images of different resolutions and viewing geometries. The availability of the LOLA global al- timetry data set permitted the use of a consistent data set that could be illuminated from a variety of perspectives to gain un- precedented views for crater detection and geometry. Using these high-resolution altimetric measurements of the Moon, Head et al. (2010) produced a catalog of all impact craters ≥20 km in diam- eter on the lunar surface (5185 in total) and analyzed their dis- tribution and population characteristics. Fig. 16 shows the outlinef the craters (A) and their density in neighborhoods of 500-km adius. (B). They found that the most-densely cratered portion of the ighlands reached a state of saturation equilibrium. Furthermore, arge impact events, such as the Orientale Basin, locally modified he pre-basin crater population to ∼2 basin radii from the basin enter. Important impact basin stratigraphic markers in lunar istory, such as Imbrium, Orientale, and Nectaris, are temporally istinguishable on the basis of crater statistics. Finally, the char- cteristics of pre- and post-mare crater populations support the ypothesis that there were two populations of impactors in early olar System history and that the transition occurred near the ime of the Orientale basin-forming event. LOLA data also permitted an assessment of the chronology of unar basins. Impact basin formation is a fundamental process in D.E. Smith et al. / Icarus 283 (2017) 70–91 83 t i q a t t p a s ( i t s a o p h s P 3 t m b r a d t m e a e t 6 p t C c y s i s t m l t e m V a m t s ( m a t L o c c l a i e c e e c t p e 0 d a t p o v t e t s 3 c a fl t a r n m r ( g M f ( p d m t e t t 3 f f e n c t o d t l i s t p c e he evolution of the Moon and records the history of impactors n the early Solar System. In order to assess the stratigraphy, se- uence, and ages of impact basins and the impactor population as function of time, Fassett et al. (2012) used topography from LOLA o measure the superposed impact crater size-frequency distribu- ions for 30 lunar basins (D ≥ 300 km). These data generally sup- ort the widely used ( Wilhelms, 1987 ) sequence of lunar basins, lthough Fassett et al. (2012) found significantly higher densities of uperposed craters on many lunar basins than derived by Wilhelms 1987) (50% higher densities). Their data also provide new insight nto the timing of the transition between distinct crater popula- ions characteristic of ancient and young lunar terrains. On the ba- is of their data they were able to show that the transition from lunar impact flux dominated by Population 1 to Population 2 ccurred before the mid-Nectarian. This is before the end of the eriod of rapid cratering, and potentially before the end of the ypothesized Late Heavy Bombardment. LOLA-derived crater den- ities also suggest that many Pre-Nectarian basins, such as South ole-Aitken, have been cratered to saturation equilibrium. .6.3. Nature, emplacement and history of lunar mare deposits One of the most fundamental problems in the geological and hermal evolution of the Moon is the nature, modes of emplace- ent, and duration of lunar mare basalt deposits. LOLA data have een extremely useful in characterizing mare deposits and address elated questions. For example, Whitten et al. (2011) , using LOLA nd Moon Mineralogy Mapper (M3) image and spectral reflectance ata, to analyze mare basalt units in and adjacent to the Orien- ale multi-ring impact basin. They found that mare basalt emplace- ent on the western nearside limb began prior to the Orientale vent as evidenced by the presence of cryptomaria. Whitten et l. (2011) found that the earliest post-Orientale-event mare basalt mplacement occurred in the center of the basin (Mare Orien- ale) and postdated the formation of the Orientale Basin by about 0–100 Ma. Over the next several hundred million years, they re- orted that basalt patches were emplaced first along the base of he Outer Rook ring (Lacus Veris) and then along the base of the ordillera ring (Lacus Autumni), with some overlap in ages. Ac- ording to Whitten et al. (2011) , the latest basalt patches are as oung as some of the youngest basalt deposits on the lunar near- ide. A major question in the analysis of the history of the Moon s the role of cryptomaria, ancient volcanic deposits obscured by uperposed crater and basin impact ejecta. The timing of cryp- omare deposition has implications for the duration and flux of are basalt volcanism. Whitten and Head (2015a) characterized ight plains units on the Moon that might be candidates for cryp- omaria. They used LOLA altimetry and roughness data, the pres- nce of dark-halo impact craters associated with a mare basalt ineralogy, and high resolution Moon Mineralogy Mapper (M 3 ) NIR spectral data to determine cryptomare mineralogy as well s Lunar Prospector (LP) FeO and Th compositional measure- ents to evaluate which ancient igneous rocks are consistent with he mineralogical observations. Whitten and Head (2015a) ob- erved significant mineralogic variation for a few cryptomaria e.g., Schiller–Schickard, West Humorum), hinting at heterogeneous antle source. Of the ancient igneous rocks investigated, Whitten nd Head (2015a) found that cryptomare are most consistent with ypical mare basalt lithologies, such as low-Ti mare basalts. Whitten and Head (2015b) used LOLA and related data (M3, ROC, Diviner) to map the global distribution of cryptomaria, in rder to provide important information about the thermal and vol- anic history of the Moon. In addition, knowing the distribution of ryptomaria can provide information about mantle convection and unar magma ocean solidification. The global analysis of Whitten nd Head (2015b) identified and analyzed the general character-stics (e.g., topography, surface roughness, rock abundance, albedo, tc.) of lunar light plains in order to better distinguish between an- ient volcanic deposits (cryptomaria) and impact basin and crater jecta deposits. They found 20 discrete regions of cryptomaria, cov- ring approximately 2% of the Moon, which increase the total area overed by mare volcanism to 18% of the lunar surface. Sori et al. (2016) combined LOLA topography and GRAIL gravity o map the distribution of cryptovolcanic deposits. They modeled otential deposits as buried high-density rectangular prisms and stimated a volume of candidate buried cryptovolcanism between .4 ×10 6 km 3 and 4.8 ×10 6 km 3 , depending on assumptions about ensity and crustal compensation state. These deposits have an rea between 0.50 ×10 6 km 2 and 1.14 ×10 6 km 2 , which increases he amount of equivalent lunar surface containing volcanic de- osits from 16.6% to between 17.9% and 19.5%. The inferred volume f cryptovolcanism is comparable to the smallest estimates of the olume of visible mare basalts and up to ∼50% of the largest es- imates. GRAIL and LOLA observations thus collectively show that arly (pre-3.8 Ga) lunar volcanism is an important element of lunar hermal evolution. Alternatively, the buried material could repre- ent the presence of intrusive Mg-suite sills or plutons. .6.4. Floor-fractured craters formation of intrusive structures LOLA data are critical to the interpretation of modification of raters by mare volcanism and in detecting intrusive bodies, such s sills and the formation of floor fractured craters. For example, oor-fractured craters (FFCs) are a class of lunar craters charac- erized by anomalously shallow floors cut by radial, concentric, nd/or polygonal fractures; additional interior features are moats, idges, and patches of mare material. Two formation mecha- isms have been hypothesized—floor uplift in response to shallow agmatic intrusion and sill formation, and floor shallowing in esponse to thermally-driven viscous relaxation. Jozwiak et al. 2012) combined LOLA and LROC data to characterize and cate- orize the population of FFCs and map their distribution on the oon. They favor formation by shallow magmatic intrusion and sill ormation. In an updated study using LOLA and GRAIL data, Jozwiak et al. 2015) found that the distribution and characteristics of the FFC opulation correlated strongly with crustal thickness and the pre- icted frequency distribution of over-pressurization values of mag- atic dikes. They found that for a typical nearside lunar crustal hickness, dikes with high over-pressurization values favor surface ffusive eruptions, medium values favor intrusion and sill forma- ion, and low values favor formation of solidified dikes concen- rated lower in the crust. .6.5. Contributions to the geology and surface characteristics of uture lunar landing sites LOLA data helped establish the geological context of potential uture landing sites for the United States and other nations. Ivanov t al. (2014) described potential landing sites for the Russian Lu- ar Glob Mission to the south circumpolar region. The site is lo- ated in the southern part of the high topography surrounding he large South Pole–Aitken (SPA) basin. Photogeological analysis f surface LOLA topography and LROC images made it possible to efine groups of morphological units (area types): (1) related to he formation of relatively fresh impact craters; (2) associated with arger ( > 100 km across) degraded craters including external and nner facies; and (3) occupying inter-crater spaces. The compari- on of the geological map with the map illustrating the distribu- ion of the epithermal neutrons shows no correlation. The region lanned for investigations in the scope of the Luna Glob mission orresponds to the topographic rise of the largest (and, likely, old- st) preserved basin (South Pole-Aitken) and offers a potential op- 84 D.E. Smith et al. / Icarus 283 (2017) 70–91 Fig. 17. (Left) Distribution of the adjusted radial, cross-track, and along-track relative track offsets. For clarity, the counts for the cross-track and along-track distributions are multiplied by five. (Right) Two-dimensional histogram of measured and predicted radial offsets (after subtracting the orbital errors estimated by least-squares). The red line is the 1:1 line, not a fit. (After Mazarico et al., 2014 ). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article). n a t s ( G c d r 1 a i m i W f 3 t T f w T b a f s t w i k a c s t m j portunity to analyze ancient material lunar crustal materials from depth, and to introduce important constraints into the spectrum of models proposed for explaining the Moon’s origin and early evolu- tion. 3.7. Orbit determination and spacecraft positioning Because of its exploration-driven goals, LRO carried high- resolution instruments, in particular its LROC NAC camera (0.5 m/px), which require accurate knowledge of the spacecraft tra- jectory in order to combine, compare, and analyze data at a ‘land- ing site’ scale. The levied requirement on orbit reconstruction was 50 m ( Chin et al., 2007 ). Unlike most planetary missions, LRO was not tracked by the Deep Space Network (DSN), but rather by a dedicated NASA station at White Sands, NM (with Ka-band down- link for large data volume requirements) with support by world- wide stations of the commercial Universal Space Network (USN) for telemetry and communication. The originally baselined S-band tracking precision was not of sufficient accuracy to achieve the re- quired orbit reconstruction precision, which motivated the addition of a laser ranging experiment (see Section 3.9 ). However, the sta- tion performance was significantly better than expected, both at the White Sands primary station ( ∼0.2–0.3 mm/s Doppler preci- sion, compared to 1 mm/s required) and at the USN sites ( ∼0.4– 0.5 mm/s, vs. 3 mm/s). Thus, the radiometric data could ultimately support the original position knowledge goals of the LRO mission. Mazarico et al. (2012) described the orbit determination method- ology that enabled the fulfillment of the geodetic requirements. The GEODYN orbit determination and geodetic parameter estima- tion software, developed and maintained at NASA/GSFC ( Pavlis et al., 2013 ), is used to integrate the spacecraft trajectory, analyze and fit available geodetic measurements. The use of LOLA data through altimetric crossovers was especially important early in the LRO mission to achieve high geodetic accuracy for the LRO orbits and the LOLA ground points, and define the “LOLA geodetic frame” to which the LRO datasets are now controlled. Orbit overlaps better than 20 m were achieved using the LOLA multi-beam crossovers ( Mazarico et al., 2012 ). The development of specially tuned grav- ity field solutions for LRO (e.g., LLGM-1) made it possible for radio tracking data-only orbit reconstruction to also meet the require- ments. With the advent of the GRAIL mission ( Zuber et al., 2013a ), the eed for crossover-enhanced orbit reconstruction was alleviated, nd they now only provide marginal improvements compared to he radio-only solutions ( Mazarico et al., 2013 ). The current orbit olutions produced by the LOLA team and archived on the PDS http://geo.pds.nasa.gov/missions/lro/rss.htm ) use the GRGM900C RAIL gravity field produced at GSFC ( Lemoine et al., 2014 ), trun- ated at degree and order 600 for computational reasons (and no emonstrated need to include higher terms). The accuracy of these econstructions is around 10 m in total position and better than m radially. In addition to an overlap analysis, these numbers were ssessed from the magnitude of the corrections necessary to align ndividual LOLA tracks to an existing high-quality LOLA topography odel (a crossover adjustment similar to the technique employed n Zuber et al., 2012 , and later by Gläser et al., 2014 ). A study by agner et al. (2016 , in this issue) of the positions of anthropogenic eatures on the Moon confirmed this level of orbit quality. .8. Detection of the lunar body tide Because of the gravitational perturbations by the Earth and Sun, he Moon experiences tides over monthly and yearly timescales. he Moon’s rigidity yields much smaller time-variable surface de- ormation than experienced by the Earth under smaller forcing, ith a maximum amplitude of ∼50 cm ( Williams et al., 2011 ). wo-way lunar laser ranging (LLR) to the corner-cube reflectors rought to the Moon by the Apollo and Lunokhod missions have llowed the precise monitoring of the Moon’s orbit and orientation or over 40 years, and the tidal deformation is part of the ranging ignal measured ( Williams et al., 2008, 2013 ). The detection of the idal deformation from orbit is a very challenging measurement, hich requires sub-meter accuracies for the spacecraft position- ng and altimetric ranges, as well as accurate instrument pointing nowledge or reconstruction ( Section 3 ). However, it can provide n independent measure of the tidal Love number h 2 , largely un- orrelated with the Moon’s orbit and inertial orientation. Mazarico et al. (2014) considered more than 5 billion mea- urements acquired in the low-altitude, circular LRO orbit (prior o December 2011), from which > 50 0,0 0 0 multi-beam crossover easurements were selected for co-registration. The relative ad- ustments required to co-align the track pairs were then utilized D.E. Smith et al. / Icarus 283 (2017) 70–91 85 Fig. 18. Schematic of the LRO laser ranging (LR) system. The Earth uplink signal is detected by the LR telescope mounted on the HGA, and sent to LOLA channel 1 for processing via the fiber optic bundle. Adapted from Zuber et al. (2010) . Fig. 19. LRO USO drift estimated by NGSLR LR data over several months (in blue) and by GEODYN processing with all LR data over two-week arcs converged with GRAIL gravity (GRGM900C, in red). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article). i L p c p a m h s j a m e K ( 3 L L ( k s L n a weighted least-squares filter, which jointly estimated the tidal ove number h 2 and additional spacecraft orbit and instrument ointing errors ( Section 3 ). Fig. 17 shows the distribution of radial, ross-track, and along-track offsets. The LOLA-derived value of h 2 =0.0371 ± 0.0033, and is com- atible with LLR-derived values ( h 2 = 0.03786 ± 0.0076, Williams et l., 2008 ). Other values predicted based on GRAIL-derived interior odels result in larger values ( h 2 ∼0.0423, Williams et al., 2014 ; 2 =0.0476 ± 0.0064, Williams et al., 2013 ). The detection of the lunar body tide from orbit with LOLA data hows the capabilities of laser altimeters for key geophysical ob- ectives, which can be important for other bodies ( Steinbrügge et l., 2015; Mazarico et al., 2015 ). Further studies of the LOLA data ay enable the first estimates of tidal distortion, which could for R xample help determine if the viscosity beneath the Procellarum REEP Terrain (PKT) region is reduced due to a thermal anomaly Wieczorek et al., 2006 ), and distinguish h 20 from h 21 and h 22 . .9. Laser ranging In order to improve Precision Orbit Determination (POD) of the RO spacecraft, a Laser Ranging (LR) experiment was added to the RO mission during development ( Zuber et al., 2010 ). Mao et al . 2016) describe in detail the LR experiment as well as the time- eeping and geodetic results. The goal of LR was to perform one-way time-of-flight mea- urements from Earth-based satellite laser ranging stations to LRO. aser pulses from the Earth were received by the LR telescope (LRT, amos-Izquierdo et al., 2009 ), mounted on and co-bore-sighted 86 D.E. Smith et al. / Icarus 283 (2017) 70–91 Fig. 20. Correlation between GRAIL free-air gravity and gravity derived from LOLA topography assuming a density of 2550 kg m −3 . The blue curve shows the corre- lation of a gravity field obtained from data up to November 9, 2012 and the red curve shows the correlation including the last month of low-altitude GRAIL data acquired prior to the spacecraft planned lunar impacts. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article). Fig. 21. Comparison of DEMs of the Chang’E 3 landing site (labeled red circle) in Mercator projection. (a) LOLA DEM with continuous curvature interpolation to fill gaps between tracks; (b) SLDEM2015, a lunar topographic model made from a com- bination of LOLA topography SELENE Terrain Camera (TC) images; and (c) LROC WAC GLD100 DEM. (For interpretation of the references to color in this figure leg- end, the reader is referred to the web version of this article). with the LRO High Gain Antenna (HGA). The LRT pointed at the Earth through a 3.81-cm diameter, off-center hole in the primary reflector of the HGA. With a 30-mrad ( ∼1.7 o ) field of view and a 19-mm diameter aperture, the LRT field of view covered nearly the entire Earth. The laser pulses intercepted by the LRT were trans- mitted via a ∼10-m multi-fiber-optic cable at the focal point of the LRT attached to the HGA running to the LOLA channel 1 detector as shown in Fig. 18 . The LOLA channel-1 detector was designed to re- ceive both the 1064-nm lunar return signals and the 532-nm Earth signals via two separate range windows within the 35.7-ms LOLA measurement cycle. NASA’s the Next Generation Satellite Laser Ranging (NGSLR) station at Greenbelt, Maryland, was the primary LRO-LR ground station. NGSLR was modified from its original design of performing two-way laser ranging to the retro-reflectors on Earth-orbiting satellites to enable tracking of both LRO and Earth-orbiting satel- lites. A sub-network of 9 SLR stations (McDonald, Texas, USA; Monument Peak, California, USA; Yarragadee, Australia; Harte- beesthoek, South Africa; Greenbelt in Maryland, USA; Zimmerwald, Switzerland; Wettzell, Germany; Herstmonceux, England; Grasse, France) of the International Laser Ranging Service (ILRS) ( Pearlman et al., 2007 ) provided global coverage for LRO-LR. The tracking sites were equipped with Rubidium (Rb), Cesium (Cs) or Hydrogen- maser clocks to maintain a stable time base. Near-real time (within 30 s) tracking feedback was provided to the sites to allow adjust- ment of their laser fire times and angular biases to mitigate orbit prediction errors. The LR station network demonstrated that close to 24-h per day tracking coverage was possible for ranging to LRO. Two methods were used to independently estimate the long term drift of the LRO Ultra-stable Oscillator (USO). One method di- rectly compares the LOLA receive MET times with the laser trans- mit times in UTC from main LR station NGSLR over a two to three- month time span during which there are no clock breaks at either NGSLR or LRO. The USO frequency drift and aging are obtained by removing the calculated light time from the out-going and received time difference and fitting a quadratic function to the residuals. The resulting USO drift is shown in the Fig. 19 in blue. Another method estimates the LRO USO frequency and aging in the orbit determination process using the GEODYN program. The GEODYN estimated USO drift values, plotted in Fig. 19 in red, agree well with those from the direct transmit-receive time comparison. Given appropriate clock synchronization ( Bauer et al., 2016a ), the LR observations have been demonstrated to improve LRO or- D.E. Smith et al. / Icarus 283 (2017) 70–91 87 Fig. A1. History of output energy from laser 1 and laser 2 as measured by the laser energy monitor. Table 3 Area in permanent shadow (km 2 ) based on illumination simulations with maps of varying resolution and topographic coverage density. North Mazarico et al. (2011), 240 m/px Updated LOLA map, 240 m/px Updated LOLA map, 120 m/px Updated LOLA map, 60 m/px Updated LOLA map, 20 m/px > 82.5 °N 9670 10,894 12,335 13,662 – > 85 °N 5088 5609 6365 7025 – > 87.5 °N 1811 1929 2137 2305 2830 > 89 °N 321 349 381 409 501 > 82.5 °S 12,491 13,217 14,180 15,374 – > 85 °S 7106 7377 7774 8260 – > 87.5 °S 3668 3735 3827 3928 4401 > 89 °S 428 441 463 488 572 b 2 3 G t s ( u e o g m t t n w t b 3 i t t d a s c n m t a e e t i 9 T g L ∼ i n d h e S t c t f ∼ r a T ∼ l e a T t l its, by a factor of two or better for arc overlaps ( Bauer et al., 016b ). .10. Synergy with gravity from the GRAIL mission While the LRO mission was in operation in lunar orbit, the RAIL mission ( Zuber et al., 2013a ) to the Moon was launched o obtain a high-resolution gravity of the Moon. The twin GRAIL pacecraft acquired accurate satellite-to-satellite range-rate data 0.03–0.05 μm/s precision over 1–2 s), which ultimately yielded an nprecedented resolution measure of the lunar gravity field ( Zuber t al., 2013b; Konopliv et al., 2013 ; Lemoine et al., 2013, 2014 ). One f the first scientific results from GRAIL was a spherical harmonic ravity solution that, when compared with the LOLA spherical har- onic model of topography, showed agreement at the 99% level in he degree band 120 to 600. Fig. 20 shows the correlation between he gravity and topography. This high correlation indicates that lu- ar gravity at those scales is primarily the result of the topography, hich can be explained by extensive fracturing of the lunar crust hat homogenized density variations in response to impact bom- ardment, particularly in early lunar history ( Zuber et al., 2013b ). .11. LOLA + TC combined topographic model The ability of laser altimeters to obtain global measurements ndependent of solar illumination conditions provides an advan- age over passive stereoscopic imaging, particularly at high lati- udes ( > 60 °) where such imaging is hindered by low solar inci- ence angles, shadowing and permanent shadow. In addition, laser ltimetry provides a more accurate geodetic framework to which tereo models can be controlled. On the other hand, stereo imaging an provide denser surface coverage than laser altimetry, especially ear the equator. Gaps in the LOLA coverage as wide as a few kilo- eters still persist near the equator, due to the very narrow cross-rack width of the individual LOLA profiles ( ∼50 m). Thus, the LOLA ltimetric dataset can benefit from the extensive cross-track cov- rage provided by camera data, such as the SELENE Terrain Cam- ra (TC) imagery. The TC was a push-broom stereo imager onboard he Kaguya spacecraft ( Haruyama et al., 2008 ) that acquired stereo maging with individual ∼30 km-wide swaths, and covered over 9% of the lunar surface with a spatial posting of 10 m. Barker et al. (2016a) presented a method for co-registering the C data to the latest, most accurate GRAIL gravity-derived LOLA eodetic framework, yielding 3–4 m RMS elevation residuals to OLA profiles and increasing the fraction of residuals < 5 m from 50% prior to registration, to ∼90% after registration. By combin- ng both datasets, gaps in the LOLA data could be filled without the eed for interpolation during map production. The resulting DEM, esignated as SLDEM2015, covers latitudes between ± 60 ° with a orizontal resolution of 512 ppd, and is available from the Plan- tary Data System LOLA data node ( http://imbrium.mit.edu/DATA/ LDEM2015/ ). The SLDEM2015 fills an important part of the resolu- ion/coverage/accuracy parameter space that previously was unoc- upied by most other commonly-used lunar DEMs. For example, he LROC WAC GLD100 covers latitudes within ± 79 ° with an ef- ective horizontal resolution ∼1 km and a mean vertical accuracy 10–20 m ( Scholten et al., 2012 ). The LROC NAC provides higher- esolution stereo DEMs (pixel scale ∼2–5 m), but NAC stereo im- gery covers only ∼2% of the surface ( Henriksen et al. (2016 )). herefore, with a ∼3–4 m accuracy and ∼60 m resolution covering 87% of the surface, the SLDEM2015 has many geophysical, geo- ogical, and cartographic applications in lunar science, as well as xploration and mission design. Studies requiring the high geodetic ccuracy of the LOLA data and the excellent spatial coverage of the C data will especially benefit. In particular, it will improve the or- horectification and co-registration of diverse lunar datasets to the atest LRO/LOLA/GRAIL geodetic system by avoiding the gaps nor- 88 D.E. Smith et al. / Icarus 283 (2017) 70–91 Fig. A2. Far-field patterns of both lasers measured prior to launch (bottom) and reconstructed from active Earth scans ∼5 years subsequent to launch (top). The white circle is the receiver field-of-view. A t r c w d K w t A i mally present between LOLA groundtracks. A comparison of these three DEMs is shown in Fig. 21. 4. Summary/conclusions The Lunar Orbiter Laser Altimeter will continue to acquire altimetry over the Moon during the LRO extended missions, as well as roughness and albedo data. As detailed herein, the results of mapping to date have demonstrably contributed towards site characterization and geodetic positioning required for future ex- ploration. The LOLA data will benefit all manner of analyses to advance understanding of lunar science. Knowledge of topography, slopes, roughness, and reflectance bear on numerous outstanding problems in lunar geology and geophysics, and LOLA has, to this point, provided the highest resolution and highest accuracy topo- graphic model for any solid planetary body in the Solar System. cknowledgments We would like to acknowledge the LOLA Engineering Team for he design and development of an outstanding instrument. We also ecognize the support of the Lunar Reconnaissance Orbiter space- raft and operations teams, and the Project Science Office without hom the LOLA investigation would not have been possible. In ad- ition, we gratefully acknowledge the contributions of Mikhail A. reslavsky, Caleb Fassett, Debra Hurwitz and Lauren Jozwiak to- ard making LOLA a success through their scientific utilization of he data to address important scientific problems. ppendix: Instrument. changes over time Immediately after the turn-on of LOLA, it was evident that the nstrument had an optical alignment problem when the space- D.E. Smith et al. / Icarus 283 (2017) 70–91 89 Table A1 LOLA instrument performance. Measurement LOLA performance, rms Altimetry 10 cm Radiometry, active 3%, after calibration Radiometry, passive 5%, after calibration Surface roughness 1.0 m, 5 m spot Slopes 0.5 m, 25 m baseline 0.3 deg, 25 m baseline 0.1 deg, 100 m baseline c w p i b w o s r t f o “ m m m t s r a p T l e s c g t w t m t s n a t f c t l i d  t f a t r R A B B B B B B B B B C C C F F F F F G G G H H H H H H raft passed from the sunlit side of the Moon to the dark side. It as subsequently recreated in the laboratory that the beam ex- ander (transmitter telescope) and the receiver telescope were be- ng pulled out of alignment due to the contraction of the thermal lanket that protects the instrument. All the spots were affected hen over the nighttime lunar surface, thus reducing the quantity f data acquired, but they quickly returned to proper alignment as oon as sunlight reached the spacecraft. Because of the specific di- ection and magnitude of the movement of the beams relative to he detectors, two out of the five spots became aligned with dif- erent receiver channels and could yield altimetric measurements ver the dark side. This effect has generally been referred to as the LOLA thermal blanket anomaly” and has persisted throughout the ission. As the laser output power decreased over time, the perfor- ance of the instrument has slowly deteriorated, limiting the aximum range to which LOLA could obtain an adequate re- urn signal. LOLA has 2 laser transmitters, and both have shown imilar decrease in output, although Laser 1 has decayed more apidly than Laser 2. At the present time, Laser 2 is the oper- tional laser of choice. Both lasers were designed for 1 billion ulses (shots) and both lasers have emitted over 2 billion pulses. he output of the two lasers since launch is shown in Fig. A1. In ate 2010, the energy of both lasers appeared to increase, how- ver this is believed to be an artifact of the laser energy monitor ystems. At the same time, the energy measured at the receiver, orrected for distance to the surface and surface reflectivity, be- an to decline. The received energy also drops sharply during the wice-yearly transition through a solar beta angle of 90 degrees, here the spacecraft constantly faces the relatively cold lunar erminator. From early in the mission, the experiments measured a ther- ally driven pointing anomaly, when LOLA is facing deep space or he cold side of the Moon. Averaging all 3 successful active Earth cans for all 5 spots and both lasers, the downlink data indicate a ighttime offset from the nominal boresight of X = 63 ± 35 μrad nd Y = −351 ± 57 μrad in the along-track and cross-track direc- ions, respectively. The downlink data also allowed reconstruction of the laser ar-field pattern ( Fig. A2 ). The primary lobe beam width has not hanged significantly from the pre-flight value of 100 μrad, but here is more energy spread among sidelobes, outside the primary obe, than in the pre-flight tests. The far-field pattern of Laser 1 s more dispersed and irregular than that of Laser 2. The uplink ata indicate an average nighttime receiver boresight correction of X = 0 ± 71 μrad and Y = 140 ± 28 μrad, possibly caused by the hermal blanket pulling on the receiver telescope. Comparing data rom such experiments shortly after launch and nearly 5 years later llows the direct measurement of changes in the laser characteris- ics and provides critical data to understand the laser behavior and efine the instrument calibration. Table 3 , Table A1 eferences raki, H., Tazawa, S., Noda, H., et al., 2009. Lunar global shape and polar topography derived from Kaguya-LALT laser altimetry. Science 323, 897–900. doi: 10.1126/ science.1164146 . andfield, J.L., Hayne, P.O., Williams, J.-P., et al., 2015. Lunar surface roughness de- rived from LRO diviner radiometer observations. Icarus 248, 357–372. doi: 10. 1016/j.icarus.2014.11.009 . aker, D.M.H., Head III, J.W., Fassett, C.I., et al., 2011. The transition from com- plex crater to peak-ring basin on the Moon: New observations from the Lunar Orbiter Laser Altimeter (LOLA) instrument. Icarus 214, 377–393. doi: 10.1016/j. icarus.2011.05.030 . aker, D.M.H., Head III, J.W., Neumann, G.A., et al., 2012. The tran- sition from complex craters to multi-ringed basins on the Moon: Quantitative geometric properties from Lunar Reconnaissance Orbiter Lu- nar Orbiter Laser Altimeter (LOLA) data. J. Geophys. Res. 117, E00H16. doi: 10.10.29/2011JE004021 . arker, M.K., Mazarico, E., Neumann, G.A., et al., 2016a. A new lunar digital elevation model from the lunar orbiter laser altimeter and SELENE terrain camera. Icarus http://dx.doi.org/10.1016/j.icarus.2015.07.039 . arker, M.K., Sun, X., Mazarico, E., et al., 2016b. Lunar phase function at 1064 nm from lunar orbiter laser altimeter passive and active radiometry. Icarus http: //dx.doi.org/10.1016/j.icarus.2016.02.008 . auer, S. , Hussman, H. , Oberst, J. , et al. , 2016a. Processing of one-way laser rang- ing data to LRO: Performance and calibration of spacecraft and ground station clocks. (Submitted for publication). Icarus . auer, S., Oberst, J., Dirkx, D., et al., 2016b. Demonstration of orbit determination for the Lunar Reconnaissance Orbiter using one-way laser ranging data. Planet. Space Sci. (Submitted for publication) esse, S., Yohota, Y., Boardman, J., et al., 2013. One Moon, many measurements 2: Photometric corrections. Icarus 226, 127–139. doi: 10.1016/j.icarus.2013.05.009 . ussey, D.B.J., Spudis, P.D., Robinson, M.S., 1999. Illumination conditions at the lunar South Pole. Geophys. Res. Lett. 26, 1187–1190. doi: 10.1029/1999GL900213 . ampbell, D.B., Campbell, B.A., Carter, L.M., et al., 2006. No evidence for thick deposits of ice at the lunar south pole. Nature 443, 835–837. doi: 10.1038/ nature05167 . hin, G., Brylow, S., Foote, M., et al., 2007. Lunar reconnaissance orbiter overview: The instrument suite and mission. Space Sci. Rev. 129, 391–419. doi: 10.1007/ s11214- 007- 9153- y . lark, R.N., 2009. Detection of adsorbed water and hydroxyl on the Moon. Science 326, 562–564. doi: 10.1126/science.1178105 . arrell, W.M., Hurley, D.M., Zimmerman, M.I., 2015. Solar wind implantation into lunar regolith: Hydrogen retention in a surface with defects. Icarus 255, 116– 126. doi: 10.1016/j.icarus.2014.09.014 . assett, C.I., Thomson, B.J., 2014. Crater degradation on the lunar maria: Topographic diffusion and the rate of erosion on the Moon. J. Geophys. Res. 119, 2255–2271. doi: 10.10 02/2014JE0 04698 . assett, C.I., Head III, J.W., Kadish, S.J., et al., 2012. Lunar impact basins: Stratigraphy, sequence and ages from superposed impact crater populations measured from Lunar Orbiter Laser Altimeter (LOLA) data. J. Geophys. Res. 117, E00H06. doi: 10. 1029/2011JE003951 . assett, C.I., Head III, J.W., Smith, D.E., et al., 2011. Thickness of proximal ejecta from the Orientale Basin from Lunar Orbiter Laser Altimeter (LOLA) data: Implica- tions for multi-ring basin formation. Geophys. Res. Lett. 38, L17201. doi: 10.1029/ 2011GL048502 . eldman, W.C. , Barraclough, B.L. , Maurice, S. , et al. , 1998. Major compositional units of the Moon: Lunar prospector thermals and fast neutrons. Science 281, 1483–1493 . arrick-Bethell, I., Perera, V., Nimmo, F., et al., 2014. The tidal-rotational shape of the Moon and evidence for polar wander. Nature doi: 10.1038/nature13639 . ladstone, G.R., Retherford, K., Egan, E., et al., 2012. Far-ultraviolet reflectance properties of the Moon’s permanently shadowed regions. J. Geophys. Res. 117, E00H04. doi: 10.1029/2011JE003913 . läser, P., Scholten, F., De Rosa, D., et al., 2014. Illumination conditions at the lunar south pole using high resolution digital terrain models from LOLA. Icarus 243, 78–90. doi: 10.1016/j.icarus.2014.08.013 . apke, B., Denevi, B., Sato, H., et al., 2012a. The wavelength dependence of the lunar phase curve as seen by the lunar reconnaissance orbiter wide-angle camera. J. Geophys. Res. 117, 0. doi: 10.1029/2011JE003916 . apke, B. , 2012b. Theory of Reflectance and Emittance Spectroscopy, second ed. Cambridge University Press, Cambridge . aruyama, J., Matsunaga, T., Ohtake, M., et al., 2008. Global lunar-surface map- ping experiment using the lunar imager/spectrometer on SELENE. Earth Planets Space 60, 243–255. doi: 10.1186/BF03352788 . ead III, J.W. , Fassett, C.I. , Kadish, S.J. , et al. , 2010. Global distribution of large lu- nar craters: Implications for resurfacing and impactor populations. Science 329, 1504–1507 . emingway, D.J., Garrick-Bethell, I., Kreslavsky, M.A., 2015. Latitudinal variation in spectral properties of the lunar maria and implications for space weathering. Icarus 261, 66–79. doi: 10.1016/j.icarus.2015.08.004 . enriksen, M.R. , Manheim, M.R. , Speyerera, E.J. , et al. , 2016. Extracting accurate and precise topography from LROC narrow angle camera stereo observations. (in this issue). Icarus . 90 D.E. Smith et al. / Icarus 283 (2017) 70–91 N P P P R R R R S S S S S S S S S S S S T T V W W W W W W Ivanov, M.A., Abdrakhimov, A.M., Basilevsky, A.T., et al., 2014. Geological con- text of the potential landing site of the luna-glob mission. Sol. Syst. Res. 48, 391–402 Russian: Astronomicheskii Vestnik 48, 423-435, doi: 10.7868/S0320930X14060024 . doi: 10.1134/S0038094614060021 . Jozwiak, L.M., Head III, J.W., Zuber, M.T., et al., 2012. Lunar floor-fractured craters: Classification, distribution, origin and implications for magmatism and shallow crustal structure. J. Geophys. Res. 117, E11005. doi: 10.1029/2012JE004134 . Jozwiak, L.M., Head III, J.W., Wilson, L., 2015. Lunar floor-fractured craters as mag- matic intrusions: Geometry, modes of emplacement, associated tectonic and volcanic features, and implications for gravity anomalies. Icarus 248, 424–447. doi: 10.1016/j.icarus.2014.10.052 . Kalynn, J., Johnson, C.L., Osinski, G.R., et al., 2013. Topographic characterization of lu- nar complex craters. Geophys. Res. Lett. 40, 38–42. doi: 10.1029/2012GL053608 . Keane, J.T., Matsuyama, I., 2014. Evidence for lunar true polar wander and a past low-eccentricity, synchronous lunar orbit. Geophys. Res. Lett. 41, 6610–6619. doi: 10.1002/2014GL061195 . Konopliv, A.S., Park, R.S., Yuan, D.-N., et al., 2013. The JPL lunar gravity field to spher- ical harmonic degree 660 from the GRAIL primary mission. J. Geophys. Res. 118, 1–20. doi: 10.10 02/jgre.20 097 . Kreslavsky, M.A., Head III, J.W., 2012. New observational evidence of strong seis- mic effects of basin-forming impacts on the Moon from Lunar reconnaissance orbiter lunar orbiter laser altimeter data. J. Geophys. Res. 117, E00H24. doi: 10. 1029/2011JE003975 . Kreslavsky, M.A., Head III, J.W., Neumann, G.A., et al., 2013. Lunar topographic roughness maps from Lunar Orbiter Laser Altimeter (LOLA) data: Scale de- pendence and correlation with geologic features and units. Icarus 226, 52–66. doi: 10.1016/j.icarus.2013.04.027 . Lemelin, M., Lucey, P.G., Neumann, G.A., et al., 2016. Improved calibration of re- flectance data from the LRO Lunar Orbiter Laser Altimeter (LOLA) and impli- cations for space weathering. Icarus 273, 315–328. doi: 10.1016/j.icarus.2016.02. 006 . Lemoine, F.G., Goossens, S., Sabaka, T.J., et al., 2013. High-degree gravity models from GRAIL primary mission data. J. Geophys. Res. 118, 1676–1698. doi: 10.1002/ jgre . Lemoine, F.G., Goossens, S., Sabaka, T.J., et al., 2014. GRGM900C: A degree 900 lunar gravity model from GRAIL primary and extended mission data. Geophys. Res. Lett. 41, 3382–3389. doi: 10.10 02/2014GL060 027 . Lucey, P.G., Neumann, G.A ., Riner, M.A ., et al., 2014. The Global Albedo of the Moon at 1064-nm from the Lunar Orbiter Laser Altimeter (LOLA). J. Geophys. Res. 119, 1665–1679. doi: 10.10 02/2013JE0 04592 . Mao, D. , McGarry, J.F. , Mazarico, E. , et al. , 2016. The laser ranging experiment of the lunar reconnaissance orbiter: Five years of operations and data analysis. (in this issue). Icarus . Margot, J.-L., Campbell, D.B., Jurgens, R.F., et al., 1999. Topography of the lunar poles from radar interferometry: A survey of cold trap locations. Science 284, 1658– 1660. doi: 10.1126/science.284.5420.1658 . Mazarico, E., Neumann, G.A., Smith, D.E., et al., 2011a. Illumination conditions of the lunar polar regions using LOLA topography. Icarus 211, 1066–1081. doi: 10.1016/ j.icarus.2010.10.030 . Mazarico, E. , Neumann, G.A. , Smith, D.E. , et al. , 2011b. Illumination conditions of the lunar poles to 65 degrees latitude from lunar orbiter laser altimeter data. In: Annual Meeting of the Lunar Exploration Analysis Group. Houston, Texas Abstract #51 . Mazarico, E., Rowlands, D.D., Neumann, G.A., et al., 2012. Orbit determination of the lunar reconnaissance orbiter. J. Geod. 86 (3), 193–207. doi: 10.1007/ s00190-011-0509-4 . Mazarico, E. , Lemoine, F.G. , Goossens, S.J. , et al. , 2013. Improved precision orbit de- termination of lunar orbiters from the GRAIL-derived lunar gravity models. In: 23rd AAS/AIAA Space Flight Mechanics Meeting. AAS. Hawaii, Kauai, pp. 13–274 . Mazarico, E., Barker, M.K., Neumann, G.A., et al., 2014. Detection of the lunar body tide by the lunar orbiter laser altimeter. Geophys. Res. Lett. 41, 2282–2288. doi: 10.1002/2013GL059085 . Mazarico, E., Genova, A ., Neumann, G.A ., et al., 2015. Simulated recovery of Eu- ropa’s global shape and tidal Love numbers from altimetry and radio tracking during a dedicated flyby tour. Geophys. Res. Lett. 42, 3166–3173. doi: 10.1002/ 2015GL063224 . McClanahan, T.P., Mitrofanov, I.G., Boynton, W.V., et al., 2015. Evidence for the sequestration of hydrogen-bearing volatiles towards the Moon’s southern pole-facing slopes. Icarus 255, 88–99. doi: 10.1016/j.icarus. 2014.10.001 . McGovern, J.A, Bussey, D.B., Greenhagen, B.T., et al., 2013. Mapping and characteriza- tion of non-polar permanent shadows on the lunar surface. Icarus 223, 566–581. doi: 10.1016/j.icarus.2012.10.018 . Mitrofanov, I.G., Sanin, A.B., Boynton, W.V., et al., 2010. Hydrogen mapping of the lunar south pole using the LRO neutron detector experiment LEND. Science 330, 4 83–4 86. doi: 10.1126/science.1185696 . Neumann, G.A., Cavanaugh, J.F., Sun, X., et al., 2013. Bright and dark polar deposits on Mercury: Evidence for surface volatiles. Science 339, 296–300. doi: 10.1126/ science.1229764 . Neumann, G.A., Zuber, M.T., Wieczorek, M.A., et al., 2015. Lunar impact basins re- vealed by gravity recovery and interior laboratory measurements. Sci. Adv. 1, 0852. doi: 10.1126/sciadv.1500852 . Noda, H., Araki, H., Goossens, S., et al., 2008. Illumination conditions at the lu- nar polar regions by KAGUYA, SELENE laser altimeter. Geophys. Res. Lett. 35, L24203. doi: 10.1029/2008GL035692 . ozette, S. , Spudis, P.D. , Robinson, M.S. , et al. , 2001. Integration of lunar polar remote-sensing data sets: evidence for ice at the lunar south pole. J. Geophys. Res. 106 (E10), 23253–23266 . avlis, D.E., J. Wimert, and J.J. McCarthy, 2013. GEODYN II System Description, vol. 1–5, contractor report, SGT Inc., Greenbelt, Md. earlman, M. , Noll, C. , Gurtner, W. , et al. , 2007. The International Laser Ranging Service and itd support for GGOS - monitoring and understanding a dynamic planet with geodetic and oceangrphic tools. Tregoning and Rizos, pp. 741–748 . ieters, C.M., Goswami, J.N., Clark, R.N., et al., 2009. Character and spatial distri- bution of OH/H 2 O on the surface of the Moon seen by M3 on Chandrayaan-1. Science 326, 568–572. doi: 10.1126/science.1178658 . amos-Izquierdo, L. , Stanley Scott III, V. , Connelly, J. , et al. , 2009. Optical sys- tem design and integration of the lunar orbiter laser altimeter. Appl. Opt. 48, 3035–3049 . obinson, M.S., Brylow, S.M., Tschimmel, M., et al., 2009. Lunar Reconnaissance Or- biter Camera (LROC) instrument overview. Space Sci. Rev. 150, 81–124. doi: 10. 1007/s11214-010-9634-2 . osenburg, M.A., Aharonson, O., Head, J.W., et al., 2011. Global surface slopes and roughness of the Moon from the lunar orbiter laser altimeter. J. Geophys. Res. 116, E02001. doi: 10.1029/2010JE003716 . osenburg, M.A., Aharonson, O., Sari, R., 2015. Topographic power spectra of cratered terrains: Theory and application to the Moon. J. Geophys. Res. 120, 177–194. doi: 10.10 02/2014JE0 04746 . ato, H., Robinson, M.S., Hapke, B., et al., 2014. Resolved Hapke parameter maps of the Moon. J. Geophys. Res. 119, 1775–1805. doi: 10.10 02/2013JE0 04580 . cholten, F., Oberst, J., Matz, K.-D., et al., 2012. GLD100: The near-global lunar 100 m raster DTM from LROC WAC stereo image data. J. Geophys. Res. 117, 0. doi: 10. 1029/2011JE003926 . chorghofer, N., Aharonson, O., 2014. The lunar thermal ice pump. Astrophys. J. 788 (169), 7. doi: 10.1088/0 0 04-637X/788/2/169 . hkuratov, Y.G., Kreslavsky, M.A., Ovcharenko, A .A ., et al., 1999. Opposition effect from Clementine data and mechanisms of backscatter. Icarus 141, 132–155. doi: 10.1006/icar.1999.6154 . mith, W.H.F. , Wessel, P. , 1990. Gridding with continuous curvature splines in ten- sion. Geophysics 55, 293–305 . mith, D.E., Zuber, M.T., Neumann, G.A., et al., 1997. Topography of the Moon from the Clementine lidar. J. Geophys. Res. 102, 1591–1611. doi: 10.1029/96JE02940 . Smith, D.E., Zuber, M.T., Jackson, G.B., et al., 2010. The lunar orbiter laser altimeter investigation on the lunar reconnaissance orbiter mission. Space Sci. Rev. 150, 209–241. doi: 10.10 07/s11214-0 09-9512-y . mith, D.E. , Neumann, G.A. , Jha, K. , et al. . LOLA PDS Archive, NASA Planetary Data System . ori, M.M., Zuber, M.T., Head, J.W., et al., 2016. Gravitational search for cryptovol- canism on the moon: Constraints on early igneous activity. Icarus, 273, pp. 284– 295. doi: 10.1016/j.icarus.2016.02.009 . peyerer, E.J., Robinson, M.S., 2013. Persistently illuminated regions at the lunar poles: Ideal sites for future exploration. Icarus 222, 122–136. doi: 10.1016/j. icarus.2012.10.010 . pudis, P.D., Bussey, D.B.J., Baloga, S.M., et al., 2013. Evidence for water ice on the Moon: Results for anomalous polar craters from the LRO Mini-RF imaging radar. J. Geophys. Res. 118, 2016–2029. doi: 10.1002/jgre.20156 . teinbrügge, G., Stark, A., Hussmann, H., et al., 2015. Measuring tidal deformations by laser altimetry. A performance model for the Ganymede laser altimeter. Planet Space Sci. 117. doi: 10.1016/j.pss.2015.06.013 . unshine, J.M., Farnham, T.L., Feaga, L.M., et al., 2009. Temporal and spatial variabil- ity of lunar hydration as observed by the deep impact spacecraft. Science 326, 565–568. doi: 10.1126/science.1179788 . urcotte, D.L. , 1987. A fractal interpretation of topography and geoid spectra on the Earth, Moon, Venus and Mars. J. Geophys. Res. 92, E597–E601 . ye, A.R., Fassett, C.I., Head III, J.W., et al., 2015. The age of lunar south circumpolar craters Haworth, Shoemaker, Faustini, and Shackleton: Implications for regional geology, surface processes, and volatile sequestration. Icarus 255, 70–77. doi: 10. 1016/j.icarus.2015.03.016 . ondrak, R., Keller, J., Chin, G., et al., 2010. Lunar Reconnaissance Orbiter (LRO): Observations for lunar exploration and science. Space Sci. Rev. 150, 7–22. doi: 10. 1007/s11214-010-9631-5 . agner, R.V., Nelson, D.M., Plescia, J.B., et al., 2016. Coordinates of anthropogenic features on the Moon. Icarus doi: 10.1016/j.icarus.2016.05.011 . atson, K. , Murray, B.C. , Brown, H. , 1961. The behavior of volatiles on the lunar surface. J. Geophys. Res. 66, 3033–3045 . hitten, J., Head III, J.W., Staid, M.I., et al., 2011. Lunar mare deposits associated with the Orientale impact basin: New insights into mineralogy, history, mode of emplacement, and relation to Orientale Basin evolution from Moon Mineralogy Mapper (M3) data from Chandrayaan-1. J. Geophys. Res. 116, E00G09. doi: 10. 1029/2010JE003736 . hitten, J.L., Head III, J.W., 2013. Detecting volcanic resurfacing of heavily cratered terrain: Flooding simulations on the Moon using Lunar Orbiter Laser Altimeter (LOLA) data. Planet Space Sci. 85, 24–37. doi: 10.1016/j.pss.2013.05.013 . hitten, J.L., Head III, J.W., 2015a. Lunar cryptomaria: Physical characteristics, dis- tribution, and implications for ancient volcanism. Icarus 247, 150–171. doi: 10. 1016/j.icarus.2014.09.031 . hitten, J.L., Head III, J.W., 2015b. Lunar cryptomaria: Mineralogy and composition of ancient volcanic deposits. Planet Space Sci. 106, 67–81. doi: 10.1016/j.pss.2014. 11.027 . D.E. Smith et al. / Icarus 283 (2017) 70–91 91 W W W W W W Y Z Z Z Z ieczorek, M.A., Jolliff, B.L., Khan, A., et al., 2006. The constitution and structure of the lunar interior. Rev. Mineral. Geochem. 60, 221–364. doi: 10.2138/rmg.2006. 60.3 . ilhelms, D., 1987 Geologic History of the Moon, US Geological Survey Professional Paper 1348 illiams, J.G. , Boggs, D.H. , Folkner, W.M. , 2008. DE421 Lunar Orbit, Physical Li- brations, and Surface Coordinates Rep. IOM 335-JW,DB,WF-20 080314-0 01. Jet Propulsion Laboratory, Pasadena, California . illiams, J.G., Turyshev, S.G., Folkner, W.M., 2011. Lunar Geophysics and Lunar Laser Ranging, Ground-based Geophysics on the Moon, p. 3038. illiams, J.G., Boggs, D.H., Folkner, W.M., 2013. DE430 Lunar Orbit, Physical Li- brations, and Surface Coordinates, Rep. IOM 335-JW, DB,WF-20130722-016, Jet Propulsion Laboratory, Pasadena, California. illiams, J.G., Konopliv, A.S., Boggs, D.H., et al., 2014. Lunar interior properties from the GRAIL mission. J. Geophys. Res. 119, 1546–1578. doi: 10.10 02/2013JE0 04559 . okota, Y., Matsunaga, T., Ohtake, M., et al., 2011. Lunar photometric properties at wavelengths 0.5-1.6 μm acquired by SELENE spectral profiler and their depen- dency on local albedo and latitudinal zones. Icarus 215, 639–660. doi: 10.1016/j. icarus.2011.07. 028 . uber, M.T., Smith, D.E., Zellar, R., et al., 2010. The lunar reconnaissance or- biter laser ranging investigation. Space Sci. Rev. 150, 63–80. doi: 10.1007/ s11214- 009- 9511- z . uber, M.T., Head, J.W., Smith, D.E., et al., 2012. Constraints on the volatile distri- bution within Shackleton crater at the lunar South Pole. Nature 486, 378–381. doi: 10.1038/nature11216 . uber, M.T., Smith, D.E., Lehman, D.H., et al., 2013a. Gravity Recovery and Interior Laboratory (GRAIL): Mapping the lunar interior from crust to core. Space Sci. Rev. 178. doi: 10.1007/s11214-012-9952-7 . uber, M.T., Smith, D.E., Watkins, M.M., et al., 2013b. Gravity field of the Moon from the Gravity Recovery and Interior Laboratory (GRAIL) mission. Science 339. doi: 10.1126/science.1231507 .