Depth-to-diameter Ratios of Fresh Craters on the Moon and Implications for Surface Age Estimates

The depth-to-diameter (d/D) ratios of small lunar craters (D < 400 m) can be used to determine important properties of the upper regolith, specifically material strength or thickness. The d/D is also an important component of topographic diffusion models that describe how different erosive processes influence and change the topography of a surface over time, and these models have been applied to estimate surface ages. These models must make assumptions regarding rates of erosion and the initial d/D of a crater. Previous works investigating d/D of small craters, which use various methodologies to calculate depth, typically assume that a fresh appearing crater is a young crater. Work presented here provides d/D measurements of known—rather than assumed—young, meter-scale craters to provide better constraints on small crater depths and to help further our understanding of lunar surface ages and upper regolith properties. Given the interest in impact crater modification at small, human scales on the Moon and the wide range of assumptions built into topographic diffusion models and their predictions, understanding whether the results for initial d/D from past work hold up under different analyses is critical. We observed no distinct trends in d/D for small, young craters and report a wide range of d/D from 0.08 to 0.215, in contrast with past work that derived different averages based on crater size. The variation in d/D may correspond to heterogeneous regolith properties or be a result of a data source artifact.


Introduction
Impact cratering is a dominant geologic process seen on solid surfaces throughout the solar system (e.g., Melosh 1989;Osinski & Pierazzo 2012).Surfaces of bodies that lack an atmosphere (e.g., the Moon) are inundated with impacts, resulting in impact craters that influence the topography of the surface.On airless bodies throughout the solar system, smaller meter-scale impacts are much more common than larger impacts, and therefore sub-kilometer-scale impacts control more of the degradation and erosion of the lunar surface over time when compared to kilometer-scale impacts (Xie et al. 2017;Fassett et al. 2022;O'Brien & Byrne 2022;Fassett & Thompson 2014;Ross 1968;Soderblom 1970;Craddock & Howard 2000;Howard 2007).
Impact ejecta material is known to be a significant contributor to topographic diffusion and landscape evolution on the Moon (Minton et al. 2019) because the emplacement of ejecta from small impacts causes mass transport, primarily in the downslope direction (e.g., Soderblom 1970).The rate of erosion on the Moon is dependent on the number and size of impacts and the volume of material ejected during an impact.Morphometric properties of impact craters, like their depth-todiameter ratio (d/D), can be used to estimate the amount of material ejected from an impact and the amount of erosion that an impact crater has experienced.The d/D of a crater generally correlates with the estimated age and degree of degradation of a surface (e.g., Oberbeck & Quaide 1968;Basilevsky 1976;Holsapple 1993;Stopar et al. 2017).The rate of erosion of small craters provides constraints on rates of topographic diffusion on the Moon, which is a primary constraint on models used for interpreting ages of the lunar surface.Additionally, estimates of the depth of a small impact crater at the time of its formation are necessary to properly determine subsequent erosion.
Previous work focusing on degradation of small craters investigated the d/D of "fresh appearing" craters, but the actual ages of these craters are unknown (e.g., Daubar et al. 2014;Stopar et al. 2017).In this study, we investigated the d/D of impact craters with ages <1 Myr to test previous work that based work on "fresh appearing" craters.We calculated the d/D of impact craters formed in the past ≈15 yr identified from Lunar Reconnaissance Orbiter Camera (LROC) data (Robinson et al. 2010) and of "cold spot craters"-those previously identified using data from the Lunar Reconnaissance Orbiter (LRO) Diviner instrument, which are interpreted to have experienced little or no observable degradation, appear cold at night (Bandfield et al. 2014;Williams et al. 2018), and are estimated to have formed <1 million years ago (Mya).If the measured d/D of these very young impact craters is different from previously published d/D trends of "fresh appearing" craters that have no known age, then models of topographic diffusion and erosion that use formational d/D values from that previous work may yield inaccurate estimates of the rates of erosion and ages of the lunar surface.For example, if the initial d/D of small craters has been overestimated, then previous work may have overestimated rates of topographic diffusion, which would affect interpretations of crater ages (e.g., Fassett et al. 2022).
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Background
Utilizing crater morphometry (i.e., quantitative measurements) and investigating morphology (i.e., qualitative properties) have been used to study the near-surface structure of the Moon (e.g., Oberbeck & Quaide 1967, 1968).Variations in crater shapes and d/D for small craters (<400 m) are thought to be a result of varying material strength or thickness of the upper regolith (Oberbeck & Quaide 1967, 1968).This is because small craters (<400 m) on the Moon form in the strengthdominated regime entirely in the upper regolith, and therefore the shape and diameter of these craters are primarily a result of the strength and thickness of the regolith (Housen & Holsapple 1999).Small lunar craters <400 m have been used to estimate regolith depth and infer layering of material at the site of impact (e.g., Oberbeck & Quaide 1967;Quaide & Oberbeck 1968;Bart et al. 2011;Bart 2014).Scaling laws have been used to estimate morphometric properties of impact craters that form in the strength-dominated regime (D < 400 m; Housen & Holsapple 1999).Conversely, the morphometry of larger craters that form in the gravity-dominated regime are not as controlled by the material properties of the upper regolith, and a systematic review of the literature showed that they have a linear d/D close to 0.2, independent of crater diameter and regardless of target body (Robbins et al. 2018).
In addition to using d/D to characterize lunar regolith properties, measurements of d/D have also been important to further knowledge of lunar surface ages, and a model of pristine d/D is a necessary component of topographic diffusion models.Topographic diffusion models, which are used to describe how different erosive processes influence and change the topography of a surface over time, were first implemented to estimate ages of the lunar mare (Soderblom & Lebofsky 1972) and have subsequently been applied to estimate surfaces ages of other moons (e.g., Craddock & Howard 2000).Topographic diffusion on the Moon may be a result of several different diffusive processes, including thermal expansion and seismic shaking, but the dominant process is thought to be topographic degradation from small impact craters (e.g., O'Brien & Byrne 2022).To use a lunar topographic diffusion model, assumptions must be made regarding the initial d/D of small lunar craters (e.g., Fassett & Thomson 2014;Speyerer et al. 2016;Stopar et al. 2017;Xie et al. 2017;Mahanti et al. 2018;Fassett et al. 2022;O'Brien & Byrne 2022).Variations seen in d/D values of craters can be caused by many different factors, including the presence of volatiles in the target material (e.g., Boyce et al. 2005 for craters on Mars); variations in the target strength and material properties (e.g., Herrick & Hynek 2017;Krüger et al. 2018;Osinski et al. 2019); postimpact surface modification, degradation, or infilling of the crater (e.g., Fassett & Thomson 2014); and/or velocity of the impactor (e.g., Silber et al. 2017;Prieur et al. 2018).Recent work indicates that degradation and topographic diffusion for craters D < 200 m are size dependent (Fassett et al. 2022), and so it is essential to quantify the initial d/D of small craters to refine and update topographic diffusion models.Additionally, previous work (e.g., Basilevsky et al. 2014;Daubar et al. 2014;Stopar et al. 2017;Mahanti et al. 2018) used digital terrain models (DTMs) to investigate the d/D of small lunar craters (D < 400 m) and found that small craters are shallower than predicted in crater scaling relationships by Pike (1977).The unexpected morphometry of these shallow craters could be due to fast-acting degradation processes that affect the crater immediately after formation (i.e., landslides or mass wasting; Basilevsky et al. 2014), or to incorrect assumptions regarding the initial morphometry of small craters.
Within the literature, a wide range of measurement techniques have been used to obtain d/D values for craters.Table 1 summarizes the d/D of small lunar craters from previous research, techniques used to measure d/D, and key conclusions of each study.There are many studies that investigated regional and global variations in d/D for small craters but differed in their approach and results.However, each of these studies had a different focus, and there was no consistent methodology between studies that is reflected in the different results.The different results have led to varying interpretations about the lunar surface and small impact craters.Daubar et al. (2014) utilized the three-point "crater helper" tool extension in ArcMap (Kneissl et al. 2011), which is a tool where a researcher places three points along the crater rim and then the tool fits a circle.The diameter was calculated from the area of the circle as D 2 A = p , and the rim elevation was calculated as the mean of the elevation points along the crater rim circle.The lowest point in the DTM was identified as the crater floor and was subtracted from the average elevation to get depth.Mahanti et al. (2018) used Cratertools (Kneissl et al. 2011) to identify the crater rim and then created a mask in the DTM 3× the crater radius around the crater of interest, attached elevation data onto the remaining pixels, binned the data, and reduced the crater of interest into a matrix in which each pixel value is the elevation.The matrix was then analyzed between 0.8 and 1.2 crater radii to identify a maximum elevation value, and the depth is then calculated by subtracting the lowest bin data value from the maximum elevation (Mahanti et al. 2018).Stopar et al. (2017) used a different approach and identified rim and floor elevations using two to five crater profiles of each individual crater and calculated depth as the measured rim to floor.It is important to note differences in methodologies because the way in which data are collected can affect the results.Thus, assuming that results that use different methodologies are directly comparable is not necessarily true (Robbins et al. 2018).
It is important to further understand results reported in Stopar et al. (2017) since several studies use their results for modeling, which has implications for lunar surface degradation rates and ages (e.g., Minton et al. 2019;Xie et al. 2019;O'Brien & Byrne 2022;Fassett et al. 2022).Stopar et al. (2017) expanded on previous work to more thoroughly investigate variations in d/D based on degradation states and to more rigorously investigate minimally modified, and therefore assumed-to-be-young, craters.They completed a morphometric investigation of 930 globally distributed impact craters <400 m diameter.Results are summarized in Figure 1.Stopar et al. (2017) classified craters based on degradation state, classifying craters such that classes A, AB, and B were all considered fresh craters.Class A craters were noted as the freshest, with sharp rims and with observable ejecta.Class B craters had prominent rims, but the ejecta is less obvious, and Class AB craters appeared to be in a transition from Class A to Class B. Shown in Figure 1 are their data for the average d/D ratios for all degradation classes, which varied from 0.11 to 0.17, and they concluded that the d/D decreased with decreasing diameter.They concluded that craters D < 100 m had a d/D of 0.12 and that craters 100 m < D < 200 m had a d/D of 0.15.Stopar et al. (2017) also assessed apparent crater degradation based on the presence of interior melt ponds and the interior crater wall slope, where a steeper slope was used to infer a younger crater.Utilizing this approach, they found no differences in crater wall slope or d/D for the youngest and freshest appearing craters (A and AB craters) at any diameter sizes, indicating that degradation has not significantly affected the d/D of these craters.Stopar et al. (2017) also investigated small craters emplaced on Tycho ejecta, inferring a maximum impact age of 110 Mya, and they found that the d/D varies from 0.12 to 0.22, with the freshest appearing craters having a d/D of ∼0.15-0.16.Interestingly, the d/D of small craters (<200 m) around Tycho were shown to be relatively deeper than observed global averages, and they concluded that this may be a result of different target properties (i.e., ejecta) around Tycho compared to elsewhere on the Moon.However, around Tycho the d/D did not vary based on terrain, including melt ponds or brecciated ejecta, and they concluded that the d/D for very small craters may be more controlled by crater diameter than terrain.No statistical analysis was conducted to identify differences in d/D between variations in diameter size, terrain, or degradation class.

Data Sets
In order to obtain the most accurate initial d/D values for small craters, we investigated 10 of the youngest craters that we could identify to ensure as little degradation as possible, all craters being <1 Myr and 40% being <10 yr at the time the topography data were generated.This is in marked contrast with all past work, which used craters that had the appearance of youth but lacked direct evidence for recent formation.The first set of craters we used are newly observed impact craters identified by the LROC (Speyerer et al. 2016).The second set of craters were cold spot craters, which were mapped and cataloged using the Diviner Lunar Radiometer instrument aboard LRO (Bandfield et al. 2011).The first set, new lunar impact craters, were identified by comparing LROC Narrow Angle Camera (NAC) spatial pairs, taken at different times, to identify changes in the surface (Speyerer et al. 2016).The second set, cold spot craters, are a type of crater that has a distinct ejecta deposit that displays evidence of granular flows, appears cold at night, and extends 10-100 crater radii from the rim (Bandfield et al. 2011).The ejecta of cold spot craters at distances of 10-100 crater radii appear to be "fluffed up" and exhibit fine-scale flow features that are quickly degraded on the lunar surface (Bandfield et al. 2014).Using crater-counting techniques of craters superimposed on cold spot crater ejecta, Williams et al. (2018) determined that cold spot craters that still exhibit continuous ejecta are no older than 0.5-1 Myr, far younger than the larger, rayed lunar craters that are Copernican in age (<∼1 Gyr).Because cold spots quickly degrade, any crater that still exhibits these features is part of the youngest and most recent impact population on the Moon (Williams et al. 2018).In fact, the larger (>40 m) members of the population of new craters observed by LROC were observed to form cold spots, indicating that this is a ubiquitous feature of fresh impact craters (Powell et al. 2021).
The craters we used from Speyerer et al.  we restricted cold spot craters from Williams et al. (2018) to D < 400 m too.We down-selected that list based on craters that had overlapping NAC DTMs without significant artifacts around or within the crater of interest.We further down-selected craters that were superimposed on a relatively surrounding surface.Using these criteria, we identified four new craters from the new impact crater list (Speyerer et al. 2016) and six cold spot craters from the Williams et al. (2018) database.Our final data set for this study consisted of 10 new impact craters, summarized in Table 2.An overview of craters measured in our study is shown in Figure 2. The topographic profiles of each crater show that the methodology accurately resolves variations in morphology for small, young craters.

Morphology
The morphology of small craters that form in the strengthdominated regime is largely a result of the material strength of the regolith (e.g., Daubar et al. 2014).Daubar et al. (2014), based on equations from Melosh (1989), estimated that the transition diameter from the strength-to gravity-dominated regime on the Moon is between 210 amd 430 m.Lab experiments investigating small impact craters (<300 m) conducted by Oberbeck & Quaide (1967) indicated that impacts into layered material with varying material strengths produced varying crater morphologies.Results of these experiments have been extrapolated to make interpretations regarding small impacts into the lunar surface and thickness of regolith overlying megaregolith (e.g., Bart 2014).A bowlshaped crater would indicate that the crater formed entirely in the upper regolith, while a flat floor crater would indicate a crater excavated to the boundary between a lower strength regolith layer and an underlying surface with higher strength (e.g., bedrock or megaregolith; Quaide & Oberbeck 1968;Bart 2014).
Crater diameters in our study are <210 m, and thus we assume that they all form in the strength-dominated regime.We therefore also assume that the thickness and strength of regolith at the target site will affect the morphology of the final crater.To identify variations in regolith and classify the morphology, we visually inspected topographic profiles drawn through the center of the crater (Table 2) and classified each crater as having a normal bowl shape or a flat floor.

Depth Measurements
We calculated crater depths by determining the average of the highest rim elevations and the average of the deepest floor elevations following the method of Robbins et al. (2021).Our methodology is different from shadow measurements because we are using DTMs and have none of the assumptions required with using shadows (i.e., assuming that the crater rim is relatively flat and horizontal; Robbins et al. 2018).This is also different from utilizing topographic profiles because we are using all of the available topography data to understand the topography along the entire rim and within the entire floor, rather than profiles that are restricted to one deepest floor point and one or two points along the rim, depending on whether a radius or diameter profile is drawn.The likelihood that a few cardinal profiles will sample the highest point along a rim is very low.Because our methodology utilizes all available DTM information, it will provide more accurate rim-to-floor depth measurements by minimizing effects of anomalous crater data when compared to other techniques since the whole crater floor and rim are considered.From the entire data set for the crater, we can derive a measurement for the highest rim points and lowest floor points, which are likely to be the most original.
Our technique allows for a semiautomated or manual extraction of these data.NAC DTMs, along with the location and diameter of each crater, were first loaded into Wavemetrics' Igor Pro software.Within Igor, we first drew a polygon along the approximate location of the crater rim, visible in the NAC DTM.A polygon was then drawn as an annulus around the outside of the crater rim, at approximately two to three crater radii, to encompass the surrounding surface.A third polygon is drawn within the crater floor.Once the surrounding surface, crater rim, and crater floor are manually identified, an automated code is run to identify all points from the NAC DTM that lie within the surface and floor polygons.For the surrounding surface and crater floor, this was a pointswithin-a-polygon calculation.All DTM points within the polygon for the floor were identified, the mean (μ) and standard deviation (σ) were calculated, and a standard sigmarejection (e.g., Grubbs 1969) was applied where all points > μ -σ are rejected.This rejection eliminates the highest value points, which are more likely to represent post-impact processes such as mass wasting, while retaining the deepest ∼16% of points, which are more likely to represent the true, unmodified crater floor.From the remaining points, the μ and σ are recalculated and stored in a data table.The surrounding surface is a simple μσ calculation.For the crater rim, the code searched radially outward from the crater center to identify the highest points along the crater rim within a small buffer from the originally drawn polygon.Those highest points along the full rim were extracted.Again, a sigma-rejection was applied where points <μ + σ were rejected.This rejection eliminates the lowest value points, which are more likely to represent erosion and dampening of the crater rim, while retaining the highest ∼16% of points, which are more likely to represent the

Uncertainties
Understanding the formal uncertainties of these measurements is necessary when comparing our results to other results from methods such as topographic profiles or shadow measurements.The uncertainty on each elevation measurement for crater rim, crater floor, and surrounding surface elevation can be estimated as N N 2 s , where σ is the standard deviation and N is the number of points used in the elevation measurements.Calculating the σ for each elevation measurement must include any error from the DTM elevation points and from the standard deviation of the elevation measurements collected.The NAC DTMs used in this study were created in SOCETSET by the LROC Team, and uncertainties of the elevation data are reported in the PDS label files as vertical precision values, which have a reported range of 0.99-3.399m.To properly propagate uncertainty, these errors were added in quadrature so that ), where σ 1 is standard deviation from the DTM and σ 2 is standard deviation from the elevation measurements.Uncertainties are reported in Table 2 and average ±19% with a median of ±10%.

Results
Our d/D measurements are summarized in Table 2 and shown in Figure 3.For all measured craters, the average d/D is 0.133, while the average d/D for only craters on the mare unit is 0.123, and the singular measured crater on the highlands has a d/D of 0.215.For only the craters on the mare, the average d/D for craters <100 m is 0.122, and for craters 100-200 m the d/D is 0.125.In addition, for only craters on the mare, the average d/D for flat floor craters is 0.116, and the average d/D for normal bowl-shaped craters is 0.129.One should keep in mind when looking at these numbers that our median uncertainty in d/D was ±10%.NEWCRATER3 has a large error bar that is due to the quality and lower resolution of the NAC DTM (e.g., 3.4 m pixel −1 resolution compared to 0.8 m pixel −1 resolution for the highest-resolution DTM used in this study) and the small number of points measured within the crater floor (five points).Because of the resolution, the uncertainty in the floor measurement is ±6 m.Although our calculated error is high, we think that five data points is still sufficient for our measurements; thus, they are still reported.
Comparison of the present measurements to those used in previous studies is shown in Figure 3.Our average d/D for known new craters <100 m is the same as reported in Stopar et al. (2017), d/D ≈ 0.12.The d/D we measured from known new craters >100 m is 0.125, slightly lower than the 0.15 reported by Stopar et al. (2017).We also observe no distinct difference in d/D as a function of diameter, implications of which are discussed in the next section.

Discussion and Conclusions
Our crater measurements indicate that most new craters have a d/D < 0.2 but are variable between 0.08 and 0.215.Craters with 10 m < D < 400 m form in a strength-dominated regime, and their morphologies are dictated by the thickness of the upper regolith, which can be up to 13 m deep on the mare, with an average thickness of 5 m (Bart 2014).Unfortunately, we only have one measurement for the highlands, so we cannot discuss the implications of just one data point.However, the regolith in the highlands is known to be thicker, which may be an explanation for a higher d/D for this singular crater (McKay 1991).
The average d/D of our measured craters >100 m differs from that of Stopar et al. (2017) slightly (0.125 vs. 0.15, respectively), but our reported values have a similarly large range of reported d/D (0.09-0.2 and 0.08-0.215,respectively).We did not identify a trend showing a shallowing or a difference in average d/D for craters D < 100 m and 100 < D < 200 m as was reported by Stopar et al. (2017).Although our work only investigated 10 craters, we think that our results are robust owing to our crater selection criteria and methodology for crater measurements.Slight differences between data sets are present between our work and Stopar et al. (2017), but our range of data is generally consistent, and we think that the chances of identifying only anomalous data in our data set are low.Additionally, it is not uncommon for researchers to draw different conclusions from the same data set (Breznau et al. 2022).
The lack of trend with diameter could indicate that any variation of d/D seen between individual craters is due to terrain and the rheological properties of the upper regolith as opposed to a generalizable diameter-dependent trend (e.g., Oberbeck & Quaide 1967;Quaide & Oberbeck 1968).Previous work has established that crater morphologies are influenced by layer thickness and strength independent of velocity (Oberbeck & Quaide 1967;Quaide & Oberbeck 1968).The upper regolith layer is heterogeneous, a result of local topography and regolith production (Wilcox et al. 2005), and those variations may contribute to differences seen in small crater morphologies.
More recent work suggests that the slight variations in d/D may represent variations in impactor velocity (e.g., Silber et al. 2017;Prieur et al. 2018).Impactor velocities are known to influence d/D for larger, transitional craters (D = 10-26 km; Silber et al. 2017).However, the influence of impactor velocity independent of surface properties, especially for small craters D < 400 m, is less constrained.Prieur et al. (2018) conducted a numerical model to investigate the influence of varying target properties and impactor velocity.Prieur et al. (2018) found that for craters <400 m the thickness of and friction within the upper layer, the strength of each subsequent layer, the amount of energy transmitted into the surface during impact, and the impactor velocity all contributed to the final morphology of the impact crater.Prieur et al. (2018) found that crater rim diameter is more closely linked to upper regolith thickness as opposed to variations in impactor velocity (ranging from 5.0 to 12.7 km s −1 ), while the crater morphology and depth are influenced by a combination of surface strength and thickness and impactor velocities.Although much research has shown that the material strength of the upper regolith is an important factor for final crater morphology (e.g., Oberbeck & Quaide 1967;Quaide & Oberbeck 1968;Daubar et al. 2014), more research is necessary to determine the relative influence of impactor velocity.
Another reason for these slight variations may be crater selection or measurement methodology.The trend observed by Stopar et al. (2017) could also be due to data source artifacts: Our own work has shown that when DTMs are used for crater depth measurements for craters <∼20-30 pixels, it can lead to artificially shallower crater depths (e.g., Robbins & Hynek 2013;Robbins et al. 2021;Hoover et al. 2023).The trend in Stopar et al.ʼs data (Figure 1) is very similar to that artifact we observe at all crater diameters when the resolution is ∼20-30 DTM pixels, and NAC DTMs are produced at scales of ∼1-4 m pixel −1 .
It is also important to note the large range of crater d/D for both "fresh appearing" and new impacts, meaning that reporting averages for small crater impacts does not encapsulate the true nature of their depths.It is known that smaller crater morphometry is more sensitive to infilling and erosion and that the d/D of small craters will more rapidly change owing to degradation processes when compared to larger craters (D > 500 m; e.g., Fassett & Thomson 2014;Stopar et al. 2017).Stopar et al. (2017) also measured two craters formed this century, calculating depth using shadow length measurements.They found a d/D of 0.17 and 0.18 for craters with a diameter of 26 and 43 m, respectively, while we found, using our methods, 0.184 ± 0.037 and 0.14 ± 0.129 (Figure 3).The ∼15% maximum variation in d/D is most likely due to variations in methodology but also underscores a need to report uncertainties.Because these two new craters had a deeper d/D (0.11-0.12) than they had otherwise found for craters <100 m, they concluded that it is possible that small craters form with a d/D closer to 0.2 and quickly degrade to the shallower observed d/D.This supported earlier work by Basilevsky et al. (2014) that found that small craters (D < 60 m) with a d/D > 0.14 degrade an order of magnitude more quickly than shallow craters of similar diameter.Conversely, our results indicate that craters D < 400 m can form with a range of d/D from 0.080 to 0.215, and thus we cannot assume that small craters with a d/D ∼ 0.1 are degraded.Indeed, two of the four craters studied that formed in the past decade had d/D of ∼0.08, and they are very unlikely to have undergone significant modification in the past 10 yr (Fassett et al. 2022).
As shown in Figure 3, the average d/D for our measured craters differs from previously reported d/D values.However, the d/D of our craters greatly varies between 0.080 and 0.215, with no distinct trend with diameter.The variation in d/D of craters <400 m is likely dependent on regolith thickness and is therefore spatially variable.These differences are important because it has been shown that increasing the d/D from 0.1 to 0.2 would triple a modeled diffusion rate (O'Brien & Byrne 2022).An increase in initial d/D in modeled diffusion rates would result in higher rates of erosion, affecting interpretations of the lunar surface by underestimating ages.If we do not account for these variations, then ages derived from topographic diffusion models will overestimate or underestimate surface ages.Our results indicate that assumptions about ages based on crater morphology or morphometry may introduce errors.Similarly, it may be inaccurate to assume that a crater with a shallow d/D has undergone modification; conversely, one cannot assume that a crater is young because it has a minimally modified appearance.Additional depth measurements of newly formed impact craters would greatly increase our knowledge of the morphometry of young craters and variations in regolith across the lunar surface and would enable improved topographic diffusion models and therefore estimates of the ages of lunar surfaces.
(2016) are all D < 400 m, and to compare more directly with Stopar et al. (2017),

Figure 1 .
Figure 1.Summary of d/D results reported in Stopar et al. (2017).Panel (a) shows data for all "fresh" craters, panel (b) displays only the freshest craters (A craters), and panels (c) and (d) show fresh craters with increasing evidence of degradation (AB and B craters, respectively).Note that their publicly available data are quantized to two decimal points.

Figure 2 .
Figure 2. The 10 craters used in our study.The left image in each panel is one of the NAC orthoimages used in the creation of the DTM, and the right image is the DTM overlying the NAC image.Beneath the pair is a single topographic profile.Panels (a)-(d) are new crater impacts observed by LROC, and panels (e)-(j) are cold spot craters observed by DIVINER.

Figure 3 .
Figure 3.The d/D of craters measured in this study (red squares for mare craters and red circle for the highlands crater) compared to ranges estimated or measured by previous workers (black circles and pink diamonds).Pink diamonds indicate measurements made from shadows of new crater detections in previous work.Error bars shown are calculated using the standard deviation and the number of points used in the elevation measurements, which is discussed in Section 3.4.Averages from our data (red lines) and past work (black lines) are overlaid.The average d/D for craters <100 m is similar between this study and previous studies, but the average differs for craters >100 m.

Table 1
Summary of Previous Work That Measured d/D of Small Young Craters, or Work That Required d/D Values for Their Models Crater floor elevation determined by the lowest elevation in a cropped NAC DTM encompasses the crater of interest.Crater diameter determined using the three-point circle tool in ArcMap crater helper tools.
Assumed d/D based on work from Stopar et al. (2017) and Xie et al. (2017).

Table 2
Overview of Crater Data Including the Measured d/D, DTM Images Used, Geologic Unit, and Crater Shape URLs for the DTMs are provided in the Appendix.Crater indices M, L, E, A are the newly detected craters, while the CS# craters are cold spot crater detections.To highlight differences in methodologies between studies, the final columns shows shadow measurements from previous work for two of the craters measured in this study.

Table A1
URL of NAC DTMs Used in This Work