Surface Roughness at the Moon’s South Pole: The Influence of Condensed Volatiles on Surface Roughness at the Moon’s South Pole

Condensed volatiles within lunar permanently shadowed regions are of high scientific and resource utilization importance. Volatiles remain elusive and difficult to observe directly, due to low direct solar illumination. In this work, we investigate correlations between, as well as possible effects of, condensed volatiles and surface roughness. We analyze topographic roughness at 50 m and 30–120 m baselines of the lunar south pole (poleward of 85° S). We focus on six south polar craters of interest and their directly surrounding non-cold-trap areas: Faustini, Shoemaker, Haworth, Cabeus, Nobile, and an unnamed region. We further analyze six analogous equatorial craters to investigate the non-ice smoothing contributions: Morozov F, Rosenberger C, Van Maanen, Fraunhofer E, Brisbane, and Asclepi. Lastly, we compare a sunlit and a permanently shaded portion of the Amundsen crater floor. Utilizing data from the Lunar Reconnaissance Orbiter’s Lunar Orbiter Laser Altimeter (LOLA), Lyman Alpha Mapping Project (LAMP), Lunar Reconnaissance Orbiter Camera, and Diviner Lunar Radiometer Experiment, we find subdued roughness within cold traps but determine that roughness is not a unique identifier of condensed volatiles. However, a correlation between LOLA roughness, LAMP normalized Off-band/On-band albedo, temperature, and water-ice stability suggests possible terrain softening due to condensed volatiles, although we cannot rule out dust ponding and/or fairy castle structure contributions. We conclude that LAMP volatile signatures at the topmost ∼100 nm may be indicative of volatile deposits at depths beyond the LAMP sensing capabilities.


Introduction
Since the possibility of cold-trapped water ice at the Moon's poles was first recognized (Watson et al. 1961), many observational campaigns have attempted to detect and characterize possible condensed volatile populations.Permanently shadowed regions (PSRs) at the lunar poles result from the low obliquity of the Moon's spin axis relative to the ecliptic plane.The lack of solar illumination within PSRs (Mazarico et al. 2011) aids in sustaining low temperatures and creates environments known as cold traps capable of retaining condensed volatiles over geologically long time periods (e.g., Schörghofer & Williams 2020;Landis et al. 2022;Magaña et al. 2023).Condensed volatiles and PSRs are of great interest, both as a scientific record of the volatile history of the Earth-Moon system and for resource utilization.If volatiles should prove to be extractable from cold traps, they may be a valuable resource for future crewed and robotic lunar missions.
Interest in condensed volatiles and PSRs spans national boundaries.Many techniques have been employed to advance the understanding of condensed volatiles within PSRs, and PSR observations have been conducted by instruments whose initial goals did not include PSR investigations.For example, ground and orbital radar observations performed by Arecibo, Clementine, the Lunar Reconnaissance Orbiter (LRO), and Chandrayaan-1 (e.g., Simpson & Tyler 1999;Campbell & Campbell 2006;Spudis et al. 2010;Nozette et al. 2010;Patterson et al. 2017) have contributed to understanding condensed volatiles.Further, neutron spectroscopy has been employed by spacecraft such as Lunar Prospector and LRO (e.g., Feldman et al. 2001;Mitrofanov et al. 2010) to quantify hydrogen within PSRs.Imaging campaigns performed by LRO and Danuri (e.g., Speyerer & Robinson 2013;Robinson et al. 2017) and laser altimetry utilized by LRO, Kaguya, and Chang'e 1 (e.g., Araki et al. 2009;Ping et al. 2009;Li et al. 2010;Fisher et al. 2017) have been used to search for high albedos associated with PSR ices.In addition, far-ultraviolet (FUV) spectroscopy by LRO (e.g., Gladstone et al. 2012;Hayne et al. 2015;Magaña et al. 2022) and infrared observations by LRO and Chandrayaan-1 (Paige et al. 2010a;Li et al. 2018) have been utilized to identify spectral signatures associated with water ice within PSR cold traps.Lastly, an impact experiment by the Lunar Crater Observation and Sensing Satellite (LCROSS; Colaprete et al. 2010) was executed to inventory volatiles within the Cabeus PSR.These studies have been useful for constraining the abundance, depth, and heterogeneous nature of surface and near-surface ices within PSRs, such as generally enhanced hydrogen from neutron spectroscopy, spectral behavior consistent with ice, and direct detection of volatiles with LCROSS.However, many questions remain regarding the nature and distribution of ice.Plans for future missions are underway, such as NASA's Volatiles Investigating Polar Exploration Rover (VIPER; Vaughan 2020) mission, expected to launch in 2024, which will provide ground-truth observations of PSRs on Mons Mouton near the lunar south pole.
Although observations of condensed volatiles within PSRs have been successful despite low-illumination conditions (Li et al. 2018;Lemelin et al. 2021), another approach is to search for the effects of condensed volatiles.Recently, geomorphic characteristics of polar terrains have been studied to understand how the presence of condensed volatiles affects the landscape.For example, the depth-to-diameter (d/D) ratios of small (2-15 km diameter) craters were studied by Rubanenko et al. (2019) and Kokhanov et al. (2015), who suggested that craters with a lower d/D ratio may be indicative of buried volatileregolith mixture deposits, based on correlation with other evidence for subsurface ice deposits.Further analyses of topographic roughness at the Moon's poles have shown that some PSRs exhibit subdued roughness compared to adjacent warmer surfaces (Deutsch et al. 2021;Moon et al. 2021).Moon et al. (2021) analyzed topographic roughness (50-200 m scale) within the Scott-E crater PSR and found that the surface roughness was significantly lower in regions where ice is predicted to be thermodynamically stable compared to adjacent regions that do not support ice.Deutsch et al. (2021) analyzed topographic roughness (360 m scale) at 12 polar craters (<∼15 km) inside and outside of ice stability zones (ISZs).Deutsch et al. (2021) determined that 9 of the 12 craters analyzed had ISZs with meaningful subdued roughness in comparison to adjacent warmer areas where ice is not stable.In these studies, subdued roughness was proposed to be related to terrain softening caused by subsurface ice or to enhanced regolith transport.
The purpose of this work is to perform a comprehensive analysis of topographic roughness and its relationship to lunar cold traps within PSRs at the south pole utilizing four instruments on board LRO.Topographic roughness was measured by the Lunar Orbiter Laser Altimeter (LOLA), FUV albedo from the Lyman Alpha Mapping Project (LAMP), imagery from the Lunar Reconnaissance Orbiter Camera (LROC), and annual bolometric temperatures from the Diviner Lunar Radiometer Experiment (Diviner).We build on previous analyses to explore whether roughness can serve as an indicator for the presence of surface and subsurface ice reservoirs; we investigate topographic roughness at 50 m and 30-120 m baselines at all south polar cold traps (poleward of 85°S and larger than the roughness maps' spatial resolution) and focus on six regions of interest (ROIs).The six polar ROIs studied here enhance the inventory of sites previously evaluated by Deutsch et al. (2021) and Moon et al. (2021) and include Faustini (87°.18 S, 84°.31 E), Shoemaker (88°.14 S, 45°.91 E), Haworth (87°.45 S, 354°.83E), Cabeus (85°.33 S, 317°.87E), Nobile (85°.28 S, 53°.27 E), and an unnamed region (86°.73S, 22°.00 E).These ROIs were in part chosen as a result of their large size (>40 km) and based on their potential to harbor condensed volatiles, as predicted by their annual maximum bolometric temperatures.We additionally investigate roughness at Amundsen crater (84°.44 S, 83°.07 E), including portions of the permanently shaded and illuminated crater floor, to understand the effects of condensed volatiles on roughness, and we compare with Amundsen results by Deutsch et al. (2021).Lastly, we compare roughness with six analogous equatorial ROIs.Our analysis of the south pole has implications for future missions.Section 2 describes the LRO instrument data sets utilized in this study.Surface roughness maps and roughness values for the entire south pole (poleward of 85°S) and ROIs are given in Section 3. Section 4 explores processes that could affect surface roughness within craters/cold traps and their surrounding regions.Lastly, we discuss the implications of our results in Section 5 and summarize conclusions in Section 6.

Lyman Alpha Mapping Project (LAMP)
LAMP (Gladstone et al. 2010) is an FUV imaging spectrograph on board LRO with a bandpass of 57-196 nm.LAMP was designed in part to image and collect spectra of PSRs at the lunar poles by utilizing the faint illumination from UV-bright stars and the background Lyα hydrogen emission.The use of faint illumination sources requires accumulation of signal over many years and careful data processing.In this analysis, we utilize observations taken during pre-fail-safe door opening (pre-FDO) operations, spanning from the start of the LRO mission in 2009 through 2016 September.Post-FDO data are not considered in this analysis owing to a difference in operating mode and calibration procedures.Data are accumulated and processed as described in Magaña et al. (2022), including spectral binning to 2 nm scales and spatial binning to 4 km scales to increase the signal-to-noise ratio of data sets.
Volatiles within PSRs can be constrained by LAMP observations through the so-called Off-band/On-band ratio.The wave bands are defined based on the FUV spectral shape of water-ice reflectance.Off-band indicates the wavelength region where water ice is highly reflective in the FUV (175-190 nm), and On-band indicates the wavelength region where water ice has low reflectance (130-155 nm).Regions with elevated Off-band/On-band ratios relative to the surrounding regions may therefore indicate the presence of condensed water ice (Gladstone et al. 2012;Hayne et al. 2015;Magaña et al. 2022).Minor volatile species such as CO 2 (2wt% relative to H 2 O) and NH 3 (6wt% relative to H 2 O) may contribute to the observed Off-band/On-band ratio; however, delineation from H 2 O is challenging owing to overlapping regions of thermal stability and reduced statistics at CO 2 and NH 3 temperatures.Sine water ice is expected to be the major volatile component, we therefore only consider the H 2 O volatile population (Magaña et al. 2023).

Diviner Lunar Radiometer Experiment (Diviner)
The Diviner (Paige et al. 2010b) thermal radiometer on board LRO has a bandpass of 0.3-400 μm throughout nine spectral bands.The radiances from channels 3-9 (7.55-400 μm) are integrated to determine bolometric temperatures across the lunar surface.Diviner products utilized in this study include annual maximum and average bolometric temperatures.We binned these Diviner products to 240 m, 1 km, and 4 km resolution to provide a pixel-by-pixel comparison with LOLA and LAMP observations.Annual maximum bolometric temperatures (T max ; Figure 1(a)) are useful in identifying surface cold traps (Schörghofer & Williams 2020), regions where temperatures remain sufficiently low to support the accumulation of condensed volatiles on the lunar surface.Water-ice cold traps are commonly defined as regions where T max remains below ∼110 K (Vasavada 1999).Although sublimation rates provide a more accurate representation of cold-trapping areas (Schörghofer & Williams 2020), the maximum temperature method allows for a conservative analysis of cold traps and is implemented in this analysis.The mean surface bolometric temperature (T avg ; Figure 1(b)) approximately represents the temperature at 1 m depths (Schörghofer & Williams 2020).The instrument was therefore used to delineate ROIs to evaluate surface roughness within these regions; we consider annual average and maximum temperatures to investigate roughness correlations with surface and subsurface (1 m depth) temperatures.Surface roughness is explained in Section 2.4.

Lunar Reconnaissance Orbiter Camera (LROC)
LROC (Robinson et al. 2010) on board LRO is a system of two high-resolution Narrow Angle Cameras (NACs) and a multispectral Wide Angle Camera (WAC).Seven WAC color bands (two UV bands and five visible bands) span wavelengths 315-680 nm.The NACs provide images of the lunar surface at 0.5 m pixel −1 , while the WAC provides visible images of the surface at 100 m pixel −1 at 50 km altitude.
In this study, we utilize dynamic Quickmap layers consisting of NAC images and the WAC Global Morphologic basemap, which was created using updated camera pointing and a new photometric correction (Wagner et al. 2015).These products are used for context and available on the LROC QuickMap web interface (https://quickmap.lroc.asu.edu/).In this product, the high-resolution NAC images are laid over the WAC basemap.The south pole basemap is shown in Figure 2 where cold trap areas (Figure 1) are masked in white.

Lunar Orbiter Laser Altimeter (LOLA)
LOLA (Smith et al. 2010) on board LRO was designed to obtain altimetry, surface roughness, and reflectance measurements of the lunar surface.Global topographic information is achieved through a single laser firing at 28 Hz, which is split into five beams that form a cross pattern on the surface.We utilize previously derived polar surface roughness data sets at 240 m pixel −1 spatial resolution (30-120 m baseline; LDRM_75S_240M) and 1 km pixel −1 spatial resolution (50 m baseline; LDRM_40S_1000M and LDRM_32N) and equatorial surface roughness data sets at 1 km pixel −1 spatial resolution (50 m baseline; LDRM_32_N).
Surface roughness is a function of the measurement baseline and represents the deviation from the mean topography where the broad underlying slopes have been removed.Baseline refers to the horizontal length scale over which the roughness is determined.Several methods exist to quantify surface roughness, including the second derivative of elevation (also known as curvature; Kokhanov et al. 2019), the standard deviation of elevation gradients (Frankel & Dolan 2007), and the median differential slope (Kreslavsky & Head 2000).For this analysis, roughness (R) is the rms variation in height residual.The 1 km resolution polar and equatorial maps utilized in this study are calculated from the five spots returned from a single laser pulse, resulting in an effective baseline of ∼50 m (i.e., the diameter of a single five-spot footprint from the nominal mapping altitude of 50 km).The unbiased estimate of roughness (in meters) at the center of each laser shot is thus given by where n is the number of LOLA spots (5), v is the number of degrees of freedom (3), and z is the height residual for a given spot about a plane fit to the five-spot footprint.This map is then gridded to 1 km pixel −1 resolution such that each pixel represents average roughness.Noise is given by the mean statistical observations and is ∼0.15 m.Meanwhile, the 240 m resolution polar map is calculated from three successive laser shots with 5-15 profile returns, resulting in baselines that vary from ∼30 to 120 m.These roughness values are averaged and gridded to 240 m pixel −1 resolution.Equivalent 30-120 m baseline maps are available at higher (40 m pixel −1 ) resolution; however, we choose to utilize the gridded (240 m pixel −1 ) maps to increase the significance of sampling statistics (i.e., there are substantial data gaps in the 40 m pixel −1 maps).

Roughness across the South Pole
We focus our analysis on lunar south pole roughness maps (poleward of 85°S) at two different scales: 30-120 m baseline (240 m resolution) and 50 m baseline (1 km resolution).On the Moon, topographic roughness at the hectometer scale has been shown to be primarily affected by space weathering, micrometeorite bombardment, and regolith gardening, while baselines at the kilometer scale have been found to be primarily affected by major geological events such as impacts, volcanism, and tectonics (e.g., Kreslavsky et al. 2013).LOLA roughness maps for 30-120 m baseline (240 m resolution) and 50 m baseline (1 km resolution) are shown in Figure 3, with cold traps (T max < 110 K) denoted by contours.A binary slope mask is shown in Figure 3(a), with high slopes (greater than 10°) shaded white and low slopes (less than 10°) shaded gray.Roughness at high slopes is denoted by purple shades and roughness at low slopes is denoted by green shades in Figures 3(b)-(c).
We compare surface roughness for the entire map area at both baselines between the outlined cold traps and the noncold-trap regions.The non-cold-trap regions are defined as all areas with T max > 110 K and are outlined in black contours in Figure 3. Usable pixels are given in Table 1 and translate to over ∼8000 km 2 cold-trap areas and more than ∼80,000 km 2 non-cold-trap regions.At a baseline of 50 m, the average roughness within all cold traps in the map area (poleward of 85°S) is found to be 0.405 ± 0.02 m (median of 0.395 m), while the average roughness of all non-cold-trap areas is 0.428 ± 0.02 m (median of 0.419 m).At a baseline of 30-120 m, the average roughness within cold traps is found to be 0.825 ± 0.02 m (median of 0.734 m), while the non-coldtrap regions have an average roughness of 0.877 ± 0.01 m (median of 0.771 m).Therefore, south polar cold traps are ∼5% smoother (roughness is subdued) than the non-cold-trap surroundings, according to the ratios (cold-trap to non-coldtrap) of mean and median values for either scale size.Reported error estimates are based on standard deviation of roughness values.
We utilize the two-sided Kolmogorov-Smirnov (K-S) statistic (p-value) to test the statistical significance of smoothing (subdued roughness) within cold traps.We consider the null hypothesis where the two regions being compared are statistically similar, indicated by a p-value greater than 0.05.Similarly, a p-value less than 0.05 provides support for the two populations being distinct at a confidence level of 95%.Frequency distribution plots for both populations at 1 cm bins for all surface slopes are shown in Figure 4. Evidence of subdued surface roughness within cold traps is shown through a leftward shift in the cold-trap histograms relative to the surrounding region.We further find evidence that topographic roughness at the 50 m baseline and the 30-120 m baseline is different inside of polar cold traps than in the non-cold-trap regions through p-values less than 0.05 (p < 0.05).However, we note that cold-trap distributions are largely overlapped with the distribution of the non-cold-trap regions.This overlap indicates that while non-cold-trap surfaces are on average smoother than non-cold-trap regions, some non-cold-trap surfaces are just as smooth as cold traps at both baselines, and roughness is not a conclusive indicator of volatiles.In other words, while condensed volatiles may reduce surface roughness within cold traps, other processes may also serve to reduce roughness at cold traps and noncold traps alike.However, this does not rule out the effect of condensed volatiles within cold traps on surface roughness.

Roughness at South Polar Regions of Interest
In this subsection we investigate roughness within six polar ROIs and their respective surrounding non-cold-trap regions.The six ROIs are labeled in Figure 3 and are reported in Table 1.
The surrounding non-cold-trap regions are defined as areas of T max > 110 K directly surrounding the cold trap and are chosen to include more area than the cold-trap ROIs while avoiding neighboring ROIs.Figures 5 and 6 show the surface area analyzed, where cold traps are contained within black contours and their respective non-cold-trap surrounding regions are excluded by black contours.Figure 5 shows the 50 m baseline roughness, while Figure 6 shows the 30-120 m baseline roughness.As with Figure 3, surface roughness associated with high slopes is shaded in purple and roughness associated with low slopes is shaded in green.The number of pixels encompassed within each ROI and their respective surrounding regions are listed in Table 1.
It may not be appropriate to directly compare the roughness within one ROI to the roughness at a different ROI owing to salient physical differences between the two regions (e.g., Kreslavsky et al. 2013).Comparing one cold trap to a noncold-trap area with a different slope or different age is also not appropriate owing to differences in mass wasting and cratering histories, both of which can influence the roughness of a surface (Jawin et al. 2014;Wang et al. 2020;Deutsch et al. 2020;Rosenburg et al. 2011;Deutsch et al. 2021).Instead, we compare only roughness ratios, i.e., the ratio of the roughness within a cold trap to that of the immediately surrounding region (square; Figures 3 and 4).The roughness ratios for the six ROIs at the south pole, as well as the accumulation of all south pole cold traps (all cold traps poleward of 85°S; Section 3.1), are shown in Figure 7.We find that, in general, the roughness inside the cold traps of interest is reduced relative to their surrounding regions by ∼10% at both 50 m and 30-120 m baselines, as indicated by surface roughness ratio values less than unity (Figure 7).At both baselines, Faustini breaks from this trend, displaying increased roughness within the cold trap relative to the surrounding regions.Roughness ratios at Faustini remain greater than unity when we exclude the fresh crater located within the cold trap (87°.4 S, 82°.8 E; Mandt et al. 2016).Regardless of the Faustini exception, the correspondence between the other five ROIs and the larger regional value for the roughness ratios provides higher confidence in the assessment.
We further find that surface roughness ratios are similar at both baseline ranges for all ROIs, although individual roughness values are not.We investigate the influence of pixel scale on roughness ratio to determine whether roughness ratio differences can be explained by the difference in pixel scale.We first bin the 30-120 m baseline data set (240 m pixel −1 ) to a pixel resolution of 1 km pixel −1 .Next, we calculate the percent difference in roughness ratios of the rebinned 30-120 m baseline data set (1 km pixel −1 ) to the 50 m baseline data set (1 km pixel −1 ) and find percent differences within 3% at all ROIs.Differences in roughness ratios between ROIs at the 30-120 m baseline data set (240 m pixel −1 ) and ROIs at the 50 m baseline data set (1 km pixel −1 ) are up to ∼6%.Through our analysis of rebinning roughness maps we find that the differences in pixel scale cannot fully account for the slight differences in roughness ratios at 50 m and 30-120 m baselines; however, rebinning the elevation data from which the roughness maps are derived may result in a higher percent difference.

Hypothesis Analysis and Results
In this section we investigate three hypotheses to explain subdued roughness within ROIs: (1) mass wasting due to high slopes within craters, (2) impact melt and debris infill within  Mass wasting refers to the downward movement of material on sloped terrain, resulting in more efficient crater degradation (e.g., Tye et al. 2015) and the appearance of "elephant-hide" texture (e.g., Zharkova et al. 2020;Kreslavsky et al. 2021).We test whether the detected subdued roughness within polar cold traps could be attributed to mass wasting by implementing restrictions on the terrain slope.In this section we investigate all south pole areas poleward of 85°S.In the following section we focus on six cold-trap ROIs.If mass wasting is primarily responsible for subduing roughness by transporting materials  downward, then we expect to see higher roughness ratios at ROIs when we restrict our roughness analysis to areas with low slopes.It has been found that slopes steeper than ∼20°may promote the downward movement of material (Lucey et al. 2014).However, lower slopes may also be affected by downslope mass movement and "elephant-hide" texture (Xiao et al. 2013;Zharkova et al. 2020;Kreslavsky et al. 2021).Further, work by Tye et al. (2015) found evidence that slope correlates with crater retention, even at a few degrees.Nonetheless, we choose to analyze only regions of slopes 10°, where the slope baseline is 30-120 m, after Deutsch et al. (2021).For completion, we further compare with high-slope areas (slopes > 10°).Topographic roughness maps of the south pole (poleward of 85°S) are shown in Figure 3 at the 50 m and 30-120 m baselines, where regions with slopes greater than 10°a re shown in purple.
We reevaluate the surface roughness ratios with slope restrictions applied for the south pole map area (poleward of 85°S).Slope restrictions reduce the number of usable pixels by a factor of ∼2 such that cold-trap areas encompass more than ∼4000 km 2 while non-cold-trap regions encompass over ∼50,000 km 2 when only slopes less than 10°are considered.When only slopes greater than 10°are considered, the number of pixels considered is reduced to ∼4000 km 2 for cold traps and ∼30,000 km 2 for noncold traps.Frequency distribution plots binned to 1 cm are shown in Figure 4 for low slopes (less than 10°) in green and high slopes (greater than 10°) in purple.We find that the frequency distributions shift leftward and peak at lower roughness values at both 50 m and 30-120 m baselines when areas associated with lower slopes are considered.Indeed, when only high slopes (slopes >10°) are considered, we find average cold-trap topographic roughness of 0.424 ± 0.02 m (median = 0.415 m) and non-cold-trap roughness of 0.442 ± 0.01 m (median = 0.435 m) at 50 m baselines.When only low slopes (slopes <10°) are considered, the average topographic roughness within cold traps is reduced to 0.388 ± 0.02 m (median = 0.376 m) while non-cold-trap roughness is reduced to 0.419 ± 0.01 m (median = 0.408 m) at 50 m baselines.A similar trend is noted for 30-120 m baselines.For high slopes, average cold-trap topographic roughness is 0.825 ± 0.02 m (median = 0.764 m), while average non-cold-trap topographic roughness is 0.877 ± 0.02 m (median = 0.797 m).For low slopes, average topographic roughness within cold traps is reduced to 0.806 ± 0.02 m (median = 0.700 m) while non-cold-trap roughness is reduced to 0.861 ± 0.01 m (median = 0.749 m) at 30-120 m baselines.In other words, cold traps are found to be up to ∼7% smoother than their surrounding areas.P-values for cold-trap and non-  cold-trap regions are found to be p < 0.05 at both 50 m and 30-120 m baselines (at 1 cm bins) for both slope restrictions.Therefore, when comparing topographic roughness with and without slope restrictions, we find that roughness at these baselines is further subdued when only low slopes are considered, indicating that cold traps on shallow-sloped terrains (presumably crater floors) are smoother than steep-sloped terrains (presumably crater walls).We therefore conclude that mass wasting cannot account for subdued roughness within south pole cold traps.However, we cannot eliminate that mass wasting has occurred and contributed to the reduced roughness at the crater floor.

Mass Wasting (Slope Influence) at Polar Regions of Interest
Next, we further investigate roughness within the six polar ROIs and their respective surrounding non-cold-trap regions for slope restrictions of less than and greater than 10°.For slope restrictions, the numbers of pixels utilized in our ROI study are roughly reduced by a factor of two for both cold traps and surrounding regions.The numbers of pixels encompassed within each ROI and their respective surrounding region are given in Table 1.ROI roughness maps at 50 m and 30-120 m baselines are shown in Figures 5 and 6.
We compare the roughness ratios of the ROIs and total analyzed south polar map area.Roughness ratios for both baselines with slope restrictions applied are given in Table 2.With slope restrictions applied, roughness ratios at all ROIs and at both baselines remain below unity, indicating reduced roughness within cold traps, with the exception of Faustini.With slope restrictions applied, Faustini ratios remain above unity at both baselines.This may indicate that mass wasting is readily occurring but constrained to the crater walls such that materials are not transported to the crater floor.For comparison, roughness ratios for both baselines without slope restrictions applied are also given in Table 2.We find that percent differences in roughness ratios with and without slope restrictions are within 5% for all ROIs.

Mass Wasting (Slope Influence) at Equatorial Regions of Interest
We investigate roughness within and around six equatorial craters where condensed volatiles are not thermodynamically stable and compare to south pole cold traps where condensed volatiles are thermodynamically stable.This comparison allows for an analysis of non-volatile-related terrain softening.For this comparison we investigate the 50 m baseline (1 km resolution) global roughness map publicly available on the NASA Planetary Data System (PDS).This map is consistent with the 50 m baseline (1 km resolution) polar map analyzed in this study.
Equatorial craters of interest are chosen based on age, size, composition, and location.Similar to the south polar ROIs, the chosen equatorial craters were formed during the pre-Nectarian period and have d/D ratios near saturation (∼0.07;Wu et al. 2022).Further, diameters of the equatorial craters range from ∼40 to 60 km; south pole craters have diameters of ∼40 to ∼100 km.We ensure that the selected equatorial craters do not contain emplaced mare material by utilizing products by Nelson et al. (2014) available on the LROC QuickMap tool.Nelson et al. (2014) utilized LROC mosaics and Clementine color ratio products to map mare material.Lastly, equatorial craters are within 60°of the equator at sufficiently low latitudes to prevent the accumulation of condensed volatiles (Hayne et al. 2020).Six craters are found to satisfy these criteria (Figure 10 Average 50 m and 30-120 m Baseline Roughness and Roughness Ratios between the Cold Trap and Surrounding Non-cold-trap Region regions where slopes are greater than 10°and that are excluded from this study.Since most polar cold traps reside within crater floors, portions of the equatorial crater floors are chosen to represent ice-free regions for comparison with the south pole.The portions of the crater floors analyzed here are outlined in black. Table 3 gives the number of pixels on the crater floor for each ROI and the number of pixels encompassed by the surrounding region used for roughness ratio calculations.Roughness ratios for each ROI are also given in Table 3.We find that equatorial roughness ratios show evidence of subdued roughness at all equatorial ROIs.Rosenberger C, Fraunhofer E, Brisbane, and Asclepi show the greatest amount of smoothing and have average roughness ratios of 0.74 ± 0.03, 0.80 ± 0.04, 0.77 ± 0.03, and 0.76 ± 0.03, respectively.Morozov F and Van Maanen have average roughness ratios of 0.96 ± 0.04 and 0.89 ± 0.03, respectively.The average roughness ratio within equatorial craters is thus 0.82 ± 0.03 m (median = 0.78).The average ratio at equatorial ROIs is then ∼10% smoother than the average of south pole cold traps.Since we only consider regions with low slopes (<10°), this may indicate that processes other than mass wasting may be controlling roughness within equatorial craters, and we conclude that mass wasting alone cannot account for subdued roughness within equatorial craters.However, we acknowledge that some mass wasting/downslope creep likely occurred and aided in smoothing the crater floor.We also cannot rule out the influence of seismic shaking on smoothing ROIs.Further, since roughness within equatorial craters analyzed here is found to be more subdued than that in polar craters, processes that subdue roughness may be more prevalent at the equator than at the poles; we do not expect that cold traps prevent the regions from being smoother.We explore further nonthermal processes that may be influencing roughness at equatorial craters in the following section.

Impact Melt, Debris Infill, and/or Hummocky Ejecta at Equatorial ROIs
Next, we consider how surface roughness may be affected by the presence of light plains, impact melt, boulders, and/or hummocky ejecta within and around equatorial craters of interest.Since cold traps at the south pole reside within regions of poor illumination, we analyze the six analogous equatorial ROIs.
Light plains include deposits associated with local-and regional-scale impacts, nonmare volcanics, and impact melt deposits.We utilize a manually mapped global light plains map available on the LROC QuickMap tool (Meyer et al. 2020).This map was produced by analyzing LROC (Robinson et al. 2010) observations.We further utilize LROC WAC (100 m pixel −1 ) mosaics and NAC (0.5 m pixel −1 ) images available on the LROC QuickMap tool as shown in Figure 9 to perform our own inspection of infill and impact melt within  craters and hummocky ejecta in the surrounding regions.For identification of impact melt we search for classic features, including smooth surfaces, ponds or channel flows, cooling racks, and wrinkles.If hummocky ejecta surrounding the crater is primarily responsible for low roughness ratios, then we expect to see blocky/rough rims and primary ejecta.
We first analyze LROC WAC and NAC images for the six equatorial ROIs (Figure 9).Due to their pre-Nectarian age (e.g., Wilhelms et al. 1987), light plains material found within these craters is likely related to the Orientale and Imbrium basins.We find that Morozov F has a slightly higher rim on the right side of the crater, which could suggest that the rim was higher before mass wasting and crater infill.However, no light plains deposits were found within the crater.Clear evidence of ejecta outside of the crater and impact melt within the crater was also not found.Within Rosenberger C, a small patch of light plains is located on the northeast floor.We also find evidence of mass wasting on the crater walls, but we do not find any impact melt.Van Maanen is substantially degraded (the crater rim and shape are poorly defined), and light plains are not found within the crater.Fraunhofer E shows more cratering on the west side of the crater floor than the east, which may lead to asymmetrical roughness patterns, but neither light plains nor impact melt are found.On the other hand, Brisbane contains light plains throughout most of the crater floor, but no impact melt.Lastly, Asclepi also has light plains throughout most of the floor and central peak, but no impact melt.We thus find light plains within three equatorial craters (Rosenberger C, Brisbane, and Asclepi).Although light plains maps by Meyer et al. (2020) could include impact melt, we do not expect this to be the case for Rosenberger C, Brisbane, and Asclepi, from our visual inspection.Further, we find significant evidence of degradation, indicative of mass wasting and crater infilling.However, no clear evidence of hummocky ejecta is found surrounding the craters.
We therefore conclude that the old, pre-Nectarian equatorial craters analyzed here likely experience subdued roughness owing to a combination of regional-or basin-type light plains emplacement and other debris infill, as well as nominal degradation and mass wasting.It is therefore possible that the similarly aged south polar craters (Tye et al. 2015;Deutsch et al. 2020a) experienced abundant degradation and infill but to a lesser extent owing to higher roughness ratios at the south pole compared to the equatorial ROIs.However, we acknowledge that many differences exist between equatorial and polar craters.Equatorial roughness ratios show that the crater floors of our equatorial ROIs are ∼10%-20% smoother than the area directly surrounding the crater; polar roughness ratios show that PSRs on crater floors are 5%-6% smoother than the area directly surrounding the crater.In other words, equatorial ROIs are smoother compared to their surroundings despite their higher maximum slopes.Further, if light plains and crater infill were primarily responsible for the observed subdued roughness at crater floors, then equatorial craters would have received significantly more light plains and debris infill than polar craters as evidenced by smoother equatorial surface values.If most lunar light plains are related to Orientale and Imbrium basins, then this asymmetry may be possible owing to the high basin latitudes.However, this analysis indicates that the subdued roughness at polar ROIs could be explained by light plains infill/mass wasting.Unfortunately, visual images of polar ROIs are difficult to analyze owing to poor illumination conditions.

Amundsen Crater
Amundsen crater (84°.44 S, 83°.07 E; 103 km diameter) provides a case study for comparing roughness between sunlit and permanently shaded surfaces within a single crater.That is, we compare roughness between surfaces that do and do not support ice.If condensed volatiles are primarily responsible for subdued roughness at south polar ROIs, then we expect the permanently shaded region of the Amundsen crater floor to be smoother than the sunlit portion.
An LROC QuickMap image of Amundsen (NAC and WAC) is shown in Figure 10.The Amundsen PSR (outlined in orange) is located at the southeast portion of the crater floor and extends to the crater wall.Views within the PSR are provided by LROC NAC long-exposure images.We first search for light plains within Amundsen and find light plains throughout the illuminated portion of the crater floor outlined in white (Figure 10; Meyer et al. 2020).Indeed, the illuminated crater floor appears smooth with small overlain impact craters.However, light plains within the PSR cannot be confidently mapped owing to a reduction in illumination and subsequent decrease in data quality.Therefore, subdued roughness at the PSR due to light plains cannot be eliminated.
As with the equatorial study, we analyze 50 m baseline roughness for Amundsen.We further restrict our analysis to the portion of the PSR with slopes <10°and annual maximum temperatures below 110 K.This cold-trap ROI is outlined (black) in Figure 11 and encompasses ∼245 km 2 .To compare the permanently shadowed floor to the illuminated floor, we choose an analogous illuminated portion of the SW crater floor.
To ensure that the illuminated portion is as analogous to the permanently shaded floor as possible, we choose a region of approximately equal area, of approximately equal proximity to the crater wall, and of similar slope (i.e., relatively flat, ensuring similar solar wind weathering effects that may affect physical regolith properties; Byron et al. 2019).This illuminated ROI encompasses ∼220 km 2 and is outlined (black) in Figure 11.
We find an average cold-trap roughness of 0.433 ± 0.015 m (0.413 m median) and average illuminated crater floor roughness of 0.657 ± 0.024 m (0.651 m median).In other words, the Amundsen cold trap is ∼35% smoother than the nearby illuminated crater floor.Using the same approach as before, we utilize the K-S statistic to test the significance in the roughness change between the illuminated and shadowed populations at 2.5 cm bins and find a p < 0.05, indicating that roughness values between the sunlit and shadowed regions are two significantly different populations and that the cold-trap roughness is subdued relative to the roughness of the nearby illuminated terrain (Figure 12).This result is consistent with findings by Deutsch et al. (2021), who analyzed a variation of the Vector Ruggedness Measure (VRM * ) on scales of 20-120 m at the lunar poles, where VRM * represents the characteristic angle of surface normal variation such that low VRM * represents a smooth surface.This study analyzed six north polar and six south polar craters, including Amundsen crater.This study found mean VRM * values of 1.45 +/−1.11 and 1.88 +/−1.36 for inside and outside of ISZs at Amundsen, respectively.In other words, the region where water ice would be thermodynamically stable within Amundsen crater (T max < 112 K) was found to be ∼30% smoother than the surrounding warmer region.Amundsen was one of 9 of the 12 craters that Deutsch et al. (2021) found to have ISZs that were relatively smoother than the surrounding regions (and the crater with the most subdued ISZ).

South Pole Roughness Comparisons with LAMP
Finally, we compare south pole roughness ratios with LAMP normalized Off-band/On-band ratios (Magaña et al. 2023).Normalized Off-band/On-band ratios serve as an indicator for condensed H 2 O within the topmost ∼100 nm.Magaña et al. (2023) further suggest that the Off-band/On-band ratio may indicate other condensed volatile species such as CO 2 and NH 3 .However, due to the challenges in delineating volatile populations and evidence that CO 2 and NH 3 abundances are significantly lower than H 2 O, we consider only sublimation loss rates for H 2 O in our analysis.
The sublimation loss of ice residing on the lunar surface (in vacuum) is primarily controlled by temperature and can be estimated by the annual maximum temperature.Subsurface ice experiences reduced sublimation loss owing to the overlying regolith and the decreased maximum temperatures at depth (Schörghofer & Williams 2020).In this analysis, we determine sublimation rates for surface condensed H 2 O as described in Magaña et al. (2023) and Siegler et al. (2011), by considering the saturation vapor pressure.Modeling results by Schörghofer & Williams (2020) show that sublimation rates at 1 m depths are decreased by a factor of 10 4 assuming a vertical mean free path of 100 μm for diffusion of a water molecule between regolith grains.Further, the annual average temperature (T avg ) was found to be representative of the temperature at 1 m depths (Schörghofer & Williams 2020).
We grid the polar 50 m baseline (1 km resolution) roughness maps to the same resolution as our LAMP maps (4 km) to allow for a pixel-by-pixel comparison between surface roughness and LAMP Off-band/On-band. Figure 13 shows topographic roughness and LAMP normalized Off-band/On-band ratios as a function of temperature (T max and T avg ) and corresponding sublimation rates (surface and at 1 m depths).We consider 5179 4 km pixels in this analysis.The south pole LAMP data set utilized here is described in Magaña et al. (2022), and normalized Off-band/On-band-temperature data and surface sublimation rates are described in Magaña et al. (2023).Normalized Off-band/On-band ratios are denoted by colored symbols, where the color scale has a threshold at a minimum of 1.0, indicating ice-free regions; ratios of 1.1 are consistent with ∼0.1 wt.% water ice (Magaña et al. 2022).Albedo ratios and roughness have been smoothed to 1 K bins, and sublimation rates of 1 km m −2 Gyr −1 and 1 kg m −2 Myr −1 are denoted by vertical dashed lines.Consistent with previous results, we find decreased roughness values (subdued roughness) at cold-trap temperatures.Further, as shown by Magaña et al. (2023), Off-band/On-band ratios are increased at these cold-trap temperatures.Therefore, a trend between surface roughness, Off-band/On-band ratio, temperature, and sublimation rates is evident.Of note, Deutsch et al. (2021) found subdued ISZs at craters that both do and do not host surface water-ice exposures (Li et al. 2018), as well as that water-ice exposures (identified by Chandrayaan-1ʼs Moon Mineralogy Mapper) were not indicative of subdued roughness.However, it is not possible that the relatively small amount ice at the optical surface detected by LAMP is responsible for the observed subdued roughness at the investigated baselines.Larger concentrations of subsurface ice are likely necessary to result in the observed softening of topography.That is, the subsurface ice would have to be of sufficient quantities and close enough to the surface to cause a measurable reduction in roughness (Deutsch et al. 2021).Determining the depth and abundance of subsurface ice required to explain the observed smoothing is beyond the scope of this study, but it is an important next step in understanding how ice may alter the polar landscape.Meanwhile, the correlation between LAMP volatile signatures and subdued surface roughness may provide insight on locations to search for subsurface ice, as well as to better understand the relationship between surface and subsurface ice.

Discussion
Sufficiently abundant condensed volatiles within lunar polar cold traps may serve to subdue surface roughness (Deutsch et al. 2020b(Deutsch et al. , 2021;;Moon et al. 2021); however, subdued roughness is not unique to condensed volatiles.We find that some ice-free regions are just as smooth as regions where ice is thermodynamically stable.We also analyze roughness ratios (i.e., the ratio of roughness inside a crater to that in the surrounding region) and find decreased ratios within five out of six south polar cold traps.However, condensed volatiles, mass wasting, crater infill, and hummocky ejecta may all lead to decreased ratios within cold traps and other crater floors alike.Indeed, subdued roughness is also found even more prominently at equatorial craters where temperatures do not support the accumulation of condensed volatiles.
We find subdued roughness within south polar cold traps both when we do and when we do not consider slope restrictions, where roughness is more subdued when all slopes are considered.Therefore, we conclude that mass wasting alone cannot explain the subdued roughness within polar cold traps.We similarly find subdued roughness within equatorial craters when we consider only slopes <10°.Since condensed volatiles are not thermodynamically stable at equatorial latitudes, this result indicates that mechanisms other than mass wasting and the condensation of volatiles contribute to decreased surface roughness inside craters.Indeed, Deutsch et al. (2021) also found subdued roughness in polar craters that do not achieve temperatures cold enough to accumulate ice over geologically long timescales.
Although we chose six equatorial ROIs that best represent the six south polar ROIs (e.g., pre-Nectarian, >∼40 km diameters, and highlands composition), several differences may persist between polar and equatorial craters that could affect surface roughness (e.g., solar wind weathering).For example, equatorial regions likely receive different amounts of infill from nearby impacts, including debris associated with impacts that created Orientale and Imbrium basins, whereas the south pole likely includes more Schrödinger material.Of the six equatorial ROIs studied here, three show evidence of light plains and all six show evidence of heavy degradation.No clear evidence of ejecta is found surrounding these craters.Nonetheless, the difference in the degree of smoothing between equatorial and polar craters may provide an indication of the degree of smoothing associated with volatiles.Equatorial craters have an average roughness ratio (ratio of crater floor roughness to the roughness of the region surrounding the crater) of 0.82 ± 0.03 m.Conversely, the six south pole ROIs have an average ratio of 0.93 ± 0.02 m at 50 m baselines and an average ratio of 0.94 ± 0.02 m at 30-120 m baselines when only low slopes are considered.When only high slopes are considered, the six south pole ROIs have an average ratio of 0.96 ± 0.02 m at 50 m baselines and an average ratio of 0.94 ± 0.02 m at 30-120 m baselines.
Another test for condensed volatiles and light plains comes from comparing the roughness ratio of the Amundsen cold trap to an illuminated portion of Amundsen's crater floor.We find light plains material at Amundsen's illuminated floor.Light plains at the shaded floor are not investigated.We also find subdued roughness at the cold trap relative to the illuminated ROI at the crater floor.This result suggests that condensed volatiles may be partially responsible for the reduction of roughness at cold traps.However, we cannot eliminate roughness differences owing to differences in infill or nominal degradation at the shaded versus illuminated crater floor.Further, differences in the thermodynamic environments may also affect roughness.For example, LAMP results show evidence of increased regolith porosity/fluffiness (i.e., conversely a lower photometric compaction parameter) through a decrease in albedo at polar cold traps (Gladstone et al. 2012;Magaña et al. 2022).Increased regolith porosity (decreased compaction) from dust ponding effects and enhanced fairy castle structuring of the regolith at cold traps cannot be eliminated, as a layer of fluffy regolith within cold traps compared to their surrounding non-cold-trap regions may lead to reduced roughness ratios.However, the vertical extent (depth) of regolith with increased porosity at cold traps cannot be quantified by LAMP.
A comparison with LAMP Off-band/On-band albedos further indicates a relationship between topographic roughness and surface condensed volatiles (and possible dust ponding/ fairy castle structuring) at temperatures where condensed water is stable over geologically long timescales.We find subdued roughness at regions where Off-band/On-band ratios are elevated, indicative of condensed volatiles.However, the presence of condensed volatiles at the topmost ∼100 nm is unlikely to cause the observed reduction in roughness at the investigated baselines.Instead, our results may be indicative of a relationship between surface and subsurface volatiles at the south pole.Further evidence for this comes from a correlation between roughness and temperature at regions where Offband/On-band ratios do not suggest the presence of condensed volatiles (Figure 13).In this case, the increasing trend between roughness and temperature could be due to the presence of buried volatile populations at depth beyond the sensing depth of LAMP.A correlation between roughness and volatiles was also found by Deutsch et al. (2021) and Moon et al. (2021).Deutsch et al. (2021) studied polar craters and found subdued roughness in craters that both do and do not host surface ice.
In this study we find that the differences in vertical relief within cold traps compared to non-cold-trap regions are on the scale of centimeters.While infill due to light plains materials, degradation/regolith gardening, and mass wasting likely contribute to the observed smoothing within cold traps, the correlation of roughness with surface volatile signatures (LAMP Off-band/On-band ratio) and temperature and the observed reduced roughness at Amundsen's shadowed floor compared to the illuminated floor point to some degree of softening as a result of condensed volatiles.In this case, LAMP volatile signatures at the topmost ∼100 nm may be indicative of volatiles at depths beyond the sensing capabilities of LAMP.Several future lunar missions plan to target south pole cold-trap observations, such as VIPER.These future observations will aid in understanding the relationship between topographic roughness and condensed volatiles.

Summary and Conclusions
LRO-LAMP, LOLA, Diviner, and LROC observations are studied in conjunction to understand surface roughness characteristics at the lunar south pole and how condensed volatiles within cold traps may affect surface roughness at 50 m and 30-120 m baselines.We consider the south pole as a whole (poleward of 85°S) and focus on six ROIs: Faustini, Shoemaker, Haworth, Cabeus, Nobile, and an unnamed region.We further compare with six similarly sized pre-Nectarian equatorial craters, used as ice-free analogs to polar craters: Morozov F, Rosenberger C, Van Maanen, Fraunhofer E, Brisbane, and Asclepi.
We investigate three hypotheses to explain the observed subdued roughness within polar ROIs: (1) mass wasting due to high slopes within craters, (2) impact melt and debris infill within craters and/or hummocky ejecta in the regions surrounding craters, and (3) condensed volatiles within cold traps.We consider modification due to mass wasting by placing slope restrictions, debris/light plains infill by analyzing LROC images of equatorial craters, and volatile contributions by performing a case study at Amundsen.Roughness changes due to condensed volatiles are also investigated by analyzing LAMP Off-band/On-band albedo ratios with temperature, sublimation rate, and surface roughness.From hypothesis 1 we find that mass wasting cannot fully account for subdued roughness measured within polar and equatorial ROIs.From hypothesis 2 we find that regional-or basin-type light plains emplacement and other debris infill, as well as nominal degradation and mass wasting, likely explain the reduced roughness within equatorial ROIs.These processes likely affect and have implications for polar cold traps.From hypothesis 3 we find correlations between roughness and surface volatile signatures and temperature, as well as reduced roughness at Amundsen's shadowed floor compared to the illuminated floor.These results suggest some degree of terrain softening due to condensed volatiles with polar ROIs, as well as a relationship between surface and subsurface volatiles.South pole analyses such as the study presented here will aid future missions planned for the lunar south pole.Through this analysis we further conclude the following: 1.Although absolute roughness values depend on baseline, corresponding roughness ratios at 50 m and 30-120 m baselines are consistent with one another across all ROIs investigated here.2. Surface roughness at 50 m and 30-120 m baselines is reduced within five of six pre-Nectarian south polar cold traps relative to their surroundings and within six of six pre-Nectarian equatorial craters relative to their surroundings, i.e., surface roughness inside craters is reduced independent of thermodynamic stability of condensed volatiles.Roughness inside the analyzed equatorial ROIs is on average more subdued than for south pole ROIs.3. Surface roughness of Amundsen's permanently shadowed crater floor is subdued relative to its illuminated (presumably ice-free) crater floor by ∼35%.Reduced roughness may result from the presence of volatiles or from differences in temperature-dependent properties such as porosity (decreased compaction), or from differences in composition, infill, etc. 4. A correlation exists between LAMP Off-band/On-band ratio, surface roughness, temperature, and sublimation rate.Terrain softening due to the presence of condensed volatiles may be occurring within some polar cold traps, and LAMP observations of the topmost ∼100 nm may provide insight into where deeper ice may be accumulated, if surface ice is linked to subsurface ice.

Figure 1 .
Figure 1.Annual (a) maximum and (b) average bolometric temperature for the lunar south pole.Cold traps (T max <110 K) are outlined in black.

Figure 2 .
Figure 2. LROC mosaic of the lunar south pole provided by the LROC QuickMap tool.Cold-trap areas (T max <110 K) are masked in white.

Figure 3 .
Figure 3. (a) South pole map of the lunar south pole (poleward of 85°S), where high slopes (greater than 10°) are shown in white and low slopes (less than 10°) are shown in gray.Surface roughness maps at (b) 50 m baseline (1 km resolution) and (c) 30-120 m baseline (240 m resolution).Cold traps (T max < 110 K) are outlined in black, and selected ROIs are labeled.Latitude is given by concentric circles at 1°increments.Maps are in polar stereographic projection.

Figure 4 .
Figure 4. Frequency distribution of topographic roughness at the lunar south pole (poleward of 85°S) at 50 m baselines (left) and 30-120 m baselines (right) at 1 cm roughness bins for cold traps (top) and surrounding non-cold-trap regions (bottom).High slopes (greater than 10°) are shown in purple, low slopes (less than 10°) are shown in green, and all slopes (no restrictions) are shown in blue.

Figure 5 .
Figure 5. 50 m baseline (1 km resolution) surface roughness maps of the lunar cold traps of interest and the directly surrounding non-cold-trap regions for (a) Faustini, (b) Shoemaker, (c) Haworth, (d) Nobile, (e) Cabeus, and (f) an unnamed region.Cold-trap areas (T max < 110 K) are outlined in black contours.

Figure 6 .
Figure 6.30-120 m baseline (240 m resolution) surface roughness maps of the lunar cold traps of interest and the directly surrounding non-cold-trap regions for (a) Faustini, (b) Shoemaker, (c) Haworth, (d) Nobile, (e) Cabeus, and (f) an unnamed region.Cold-trap areas (T max < 110 K) are outlined in black contours.

Figure 7 .
Figure 7. Surface roughness ratios for six ROIs and for the average of all south pole cold traps.Roughness ratios below unity (horizontal dashed line) indicate that a cold trap is less rough than its directly surrounding regions.

Figure 8 .
Figure 8. Surface roughness map at 50 m baseline (1 km resolution) in equidistant cylindrical projection for six equatorial craters that serve as comparisons with polar ROIs: (a) Morozov F, (b) Rosenberger C, (c) Van Maanen, (d) Fraunhofer E, (e) Brisbane, and (f) Asclepi.ROIs are outlined in black contours.

Figure 10 .
Figure 10.QuickMap LROC images of Amundsen shown in stereographic projection.The orange circle denotes the crater rim, and the white contour encircles light plains deposits identified in Meyer et al. (2020).The thin pink contour indicates the PSR.

Figure 12 .
Figure 12.Frequency distribution of topographic roughness at 50 m scales and 2.5 cm bins.Cold traps are shown in the darker-green shade, and non-cold-trap regions are shown in the lighter-green shade.

Figure 13 .
Figure 13.South pole (poleward of 85°S) surface roughness (50 m baseline) vs. temperatures, where the colored points correspond to the normalized LAMP Offband/On-band ratio and have a minimum threshold of 1.0.Slopes greater than 10°are not included.Vertical dashed lines represent 1 Gyr and 1 Myr lifetimes of surface and subsurface condensed H 2 O. Red trend lines represent a linearly increasing best fit between 70 K < T max < 110 K and 150 K < T max < 250 K.

Table 1
Number of Pixels Analyzed for Each ROI and the Surrounding Non-cold-trap Region for 50 m and 30-120 m Baselines

Table 3
Average 50 m Baseline Roughness and Corresponding Area for Each Equatorial Region of Interest