The Search for Topographic Correlations within the Reiner Gamma Swirl

Lunar swirls have been traditionally considered to be unaffected by topographic changes. Yet, correlations between areas of high albedo and lower elevations are observed in regions of the Mare Ingenii swirl. Here, we apply similar techniques used at Mare Ingenii to determine if correlations between swirl units and topography also exist within Reiner Gamma. We generate topography using the techniques of stereophotoclinometry to Lunar Reconnaissance Orbiter Camera Narrow Angle Camera images to derive meter- to submeter-scale topography. We choose a 50 km2 study region with a 2.6 m ground sample distance (GSD), and within this region there is a 1 km2 subregion with a 0.8 m GSD. We use surface reflectance data at multiple viewing geometries to classify these regions into different swirl units using machine learning techniques. Statistical analyses of the data show mean height variations between on- and off-swirl of ∼4 m, with on-swirl at a lower elevation. It is not clear how this scale of elevation difference influences the formation of swirl units, but it supports postulations of dust migration and magnetic sorting contributing to their formation.


Introduction
Lunar swirls are bright albedo markings unique to the Moon.Their shapes range from single features to groupings of complex loops and ribbons, the scales of single features being typically tens of kilometers with groupings extending 10 times that size (Denevi et al. 2016).An example swirl from Reiner Gamma is shown in Figure 1.Swirls consist of bright "onswirl" regions surrounded by dark lanes or darker "off-swirl" regions.Notably, the swirl locations are frequently correlated with magnetic anomalies (Hood et al. 1979;Hood & Schubert 1980), although not all magnetic anomalies exhibit swirls (Blewett et al. 2011) nor do the albedo markings always overlay magnetic regions (Syal & Schultz 2015).Some spectral characteristics of the swirls are similar to fresh impacts or ejecta, across the UV-IR spectral range (e.g., Hood et al. 1979;Blewett et al. 2011;Kramer et al. 2011;Denevi et al. 2014;Glotch et al. 2015;Hendrix et al. 2015).However, swirl spectra have been found to be inconsistent with immature regolith and to display distinctive properties that are unique to swirls (Pieters et al. 2014;Pieters & Noble 2016).In some cases, onswirl regions have also been found to have more compact regolith than their surroundings (Hess et al. 2020).Multiple mechanisms have been proposed for swirl formation, such as magnetic shielding from the solar wind (e.g., Hood & Schubert 1980), cometary impacts (e.g., Schultz & Srnka 1980), electrostatic dust levitation and transport (e.g., Garrick-Bethell et al. 2011), and magnetic sorting (e.g., Pieters & Garrick-Bethell 2015).However, no mechanism explains all of the observed characteristics or has emerged as the single controlling factor for swirl formation.
Few lunar swirl studies have included topography as a potential factor in swirl formation because there was little evidence to support it.For example, Denevi et al. (2016) examined many lunar swirls but did not find any topographic correlation using the 100 m raster digital terrain model (DTM) from the Lunar Reconnaissance Orbiter Camera (LROC) Wide Angle Camera (WAC; Scholten et al. 2012).Higher-resolution DTMs such as SLDEM2015 (Barker et al. 2016) and those generated with the SOftCopy Exploitation Toolkit (SOCET SET; Henriksen et al. 2017) or the Lunar Orbiter Laser Altimeter (LRO; Mazarico et al. 2012) have thus far not been used to examine topographic correlations.Recent work by Domingue et al. (2022Domingue et al. ( , 2023, in revision) , in revision) utilized much higherresolution DTMs (0.7 and 0.8 m) and found statistically significant topographic correlations between swirls and elevation in two regions of the Mare Ingenii swirl.Although the elevation difference was not obvious in a general sense, onswirl portions had a statistically significant 2-5 m lower elevation compared to off-swirl portions in these two specific regions.Thus, the role of elevation is significant and cannot be ruled out, particularly at higher resolutions where the differences in surface detail are apparent (Figure 2).However, we note that elevation cannot be used to predict whether a patch of ground is on-or off-swirl and that such elevation differences do not necessarily apply to all swirls on the Moon.If elevation differences are contributing to the formation of swirls, then this information may provide a better understanding of how swirls form.At the very least, we may be able to rule out some formation mechanisms, or increase the likelihood of other mechanisms.Domingue et al. (2022Domingue et al. ( , 2023, in revision) used the stereophotoclinometry (SPC) software suite to generate topography from the LRO Narrow Angle Camera (NAC) images at Mare Ingenii.The regions of on-and off-swirl were mapped based on visual albedo contrast, with each region consisting of up to tens of millions of data points.The statistical analysis of Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
the elevation was performed for each region by testing the differences between cumulative distributions and by calculating mean heights with a 95% confidence interval.This study furthers the initial investigations of Domingue et al. (2022Domingue et al. ( , 2023, in revision) , in revision) by examining the correlations between on-and off-swirl with elevation within a portion of the Reiner Gamma swirl.We apply similar techniques for generating SPC data products and determine the statistical correlations as in Domingue et al. (2022Domingue et al. ( , 2023, in revision), in revision).However, in this study we have applied both supervised and unsupervised machine learning (ML) techniques, used by Chuang et al. (2022) to classify and map swirl units.As the Reiner Gamma study region here is identical to that in Chuang et al. (2022), we adopt the same unit maps from their study.
We choose to examine Reiner Gamma (center: 7.4°N, 301°E) since it is the archetypical example of lunar swirls within basaltic maria.Located on the lunar near-side along the western edge of Oceanus Procellarum, the study region is slightly south of the central "eye" and contains bright onswirl areas separated by dark lanes (see Figure 1).This region is optimal for our study because it contains on-and off-swirl units in a small area, and has images with a range of incidence and emission angles.The on-swirl area gradually reduces in albedo as it transitions to off-swirl.These transition areas were identified by Chuang et al. (2022) and termed as "diffuse-swirl."Here, we examine the correlations between topography and the three swirl units (on-swirl, off-swirl, and diffuse-swirl) within the Reiner Gamma study region as mapped earlier by Chuang et al. (2022).

Overview
Prior studies by Domingue et al. (2022Domingue et al. ( , 2023, in revision) , in revision) demonstrated that the elevation differences between on-and off-swirl areas in Mare Ingenii are at the meter scale.Thus, our approach to investigating the elevation differences in Reiner Gamma follows the same convention by first generating highresolution topographic data using the techniques of SPC.SPC generates topography in the form of DTMs using overlapping spacecraft images.This DTM can have a vertex spacing or ground sample distance (GSD) equal to the image pixel scale with accuracies at the 1 or 2 pixel level (Weirich et al. 2022).The accuracy for both the vertical and horizontal directions is the same.Other methods of generating DTMs from stereo images, such as the NASA Ames Stereo Pipeline (ASP), often have a GSD 3 to 5 times larger than the image pixel scale, even in best-case scenarios (Beyer et al. 2018).In this study, we have produced DTMs from SPC at two different spatial resolutions in order to identify the subtle elevation differences that might exist at Reiner Gamma (see Figure 2).The topography for the main study region of Reiner Gamma was created at 2.6 m GSD, and is referred to as the "low-resolution DTM," or the "study region."A high-resolution DTM strip at 80 cm GSD was created for a portion of the study region.We examine this strip of topography at both the 2.6 m low and 80 cm high resolutions (Figure 2), and refer to these data sets as the "subregion" and "high-resolution subregion," respectively (Figure 1).
This study is not focused on swirl formation processes, but rather on localized topography.In order to examine local elevation differences within the DTMs, we first remove any broad, regional slope change across the low-resolution study region.This is followed by the masking of morphologic features that cause localized extreme topographic variations, such as large impact craters, troughs, and localized peaks.These often have extreme high and low elevations that may skew the overall statistical results for each swirl unit.Many of the large features cross swirl unit boundaries, skewing the results of all units.There is one large trough spanning over 4 km in length and two peaks containing the highest elevation values along the northwest edge of the study region (see Figure A1) that were masked from the slope-removed DTM.No other morphologic features, besides impact craters, were masked as there was no obvious correlation of topographic low or high values with features either in the non-slope-corrected DTM, the slope-corrected DTM, or in the surface reflectance images (see next section), regardless of size.The slope removal and feature masking is also done for the high-resolution DTM within the subregion.Next, we identify the location of on-swirl, off-swirl, and transitional diffuse-swirl units directly from the brightness variations in the spacecraft images.We apply two different ML algorithms to both classify and map the swirl units to ensure robust results (Chuang et al. 2022).Using the mapped units, we then extract the elevation values from the slope-corrected and feature-masked topography for each unit.Lastly, we perform statistical analyses of the elevation differences between the on-swirl, off-swirl, and diffuse-swirl units.The entire methodology, including new data products and maps, are described in detail below.

Stereophotoclinometry Digital Terrain Models and Surface Reflectance Data
The SPC software, as implied by the name, combines the techniques of stereo positioning with multi-image photoclinometry.Stereo positioning is performed by using multiple spacecraft images of the same patch of surface, each with the spacecraft in a different location with respect to the surface.These images are aligned to each other using a common feature, such as a boulder or crater.A vector is then projected out from each spacecraft position toward the common feature, and the intersection of these vectors determines its elevation.This is a highly robust and accurate method to determine elevation, and DTMs are often generated using only this technique.Examples of stereo DTMs include those generated by the NASA ASP and the SOCET SET.However, as stated above, stereo-only DTMs have a limited GSD (Beyer et al. 2018), which is why SPC also uses photoclinometry.
Before discussing photoclinometry, we provide term definitions to avoid confusion when referring to certain features.In this paper, a single elevation value within a DTM is termed a "vertex" and the spacing between these elevation values as the "ground sample distance" (GSD).A single brightness value within an image is a "pixel.""Pixel" also refers to a horizontal distance measurement on the surface.It is often inconvenient to refer to elevations and their uncertainties in absolute units, so we refer to them in terms of vertex units (DTM centric) or pixel units (image centric).To further complicate matters, DTMs can be generated at any GSD and the GSD can be larger (undersampling the image), smaller (oversampling the image), or the same as the pixel distance.Hence, we will refer to distances in terms of the number of vertices, and other times in terms of the number of pixels, depending on the application.
Photoclinometry is a technique that uses the brightness of each pixel in an image to determine slope.Essentially, surfaces that slope toward the Sun are brighter, while surfaces sloping away from the Sun are dimmer.Albedo can also cause brightness variations, so for photoclinometry using a single image the albedo is assumed to be constant across the DTM.SPC, however, does not assume constant albedo.Using multiple images from a range of illumination angles, along with the lunar-Lambert photometric function (McEwen 1991), the slope and albedo for each DTM vertex can be determined based on the image brightness variations.SPC testing has shown different photometric functions have no effect on the final slope of each vertex, though different functions will determine how quickly the solution converges (E.E. Palmer et al. 2023, in preparation).To turn a slope measurement into an actual height, at least one of the DTM vertices needs an associated height.In SPC, this height is determined using a stereo position.Starting at the stereo position, the slope at each vertex can be integrated to produce a height for each vertex.Thus, SPC combines the accurate 3D positioning determined from stereo with the vertex-to-image pixel resolution from photoclinometry.
The basic unit of SPC centers around a 99 by 99 vertex DTM, called a "maplet."The elevation at the center of this maplet is defined by stereo positioning, with the remaining vertices defined by photoclinometry.Maplets with the same GSD are positioned to overlap, so the distance between stereo points is 70 vertices.Hundreds to thousands of overlapping maplets, with varying vertex spacing, are used to cover the region, and these maplets are processed and combined into a single DTM.Aside from generating topography, the overlapping maplets are also used to correct the position and pointing of the spacecraft for each image.This capability is essentially the reverse of stereo positioning.Each maplet position and the alignment of an image in that maplet is used to determine the position and pointing of the spacecraft when the image was taken.Thus, the topography can improve the spacecraft position and pointing, which can further improve the topography.While it is possible to condition the SPC heights using other DTMs, this was not done for the DTMs in this study.Further details of the SPC process can be found in Gaskell et al. (2008Gaskell et al. ( , 2023) ) and Palmer et al. (2022).
SPC-generated DTMs safely guided the OSIRIS-REx spacecraft to touch the surface of asteroid Bennu and collect a sample in 2020 (Lauretta et al. 2021).NASA Class B software validation for SPC determined the error of SPC-generated models (Craft et al. 2020;Weirich et al. 2022).Normally, it is not possible to determine the error of an SPC model because there is no truth model to compare it against.As part of the validation, Weirich et al. (2022) used a measure of the internal consistency of an SPC model, which is called the formal uncertainty (FormU).FormU is essentially the rms uncertainty of the stereo positions.By comparing SPC models at various stages of development to a truth model, Weirich et al. (2022) found the FormU was always within a factor of 2 of the actual rms error.Weirich et. al. (2022) and E. E. Palmer et al. (2023, in preparation) analyzed how various image sets affected the SPC error.Applying the same logic of Weirich et al. (2022) to the Reiner Gamma image set, SPC has the ability to generate topography with an uncertainty of 1-2 image pixels if the DTM GSD is equal to the image pixel distance.However, since generating a DTM over large areas at high resolution with SPC is a time-intensive process involving up to millions of vertices, we often generate topography that undersamples the images.In these cases, which includes Reiner Gamma, SPC DTMs have an uncertainty of 1 to 2 times the DTM GSD.As discussed in Section 3, the low-resolution DTM for Reiner Gamma has a GSD of 2.6 m and the high-resolution DTM has a GSD of 0.8 m, so the uncertainty for these DTMs will be 2.6-5.2m and 0.8-1.6 m, respectively.Stereo points are spaced every 182 m for a GSD of 2.6 m, and every 56 m for a GSD of 0.8 m.
In addition to DTM elevation data, we generate surface reflectance data from LROC images for the classification and mapping of swirl units.As albedo is a function of incidence angle, we select images at a range of incidence angles to input into the ML algorithms.The purpose of using multiple reflectance images is to consider a wide range of possible angles as representative of the image coverage for a given region.Because there is no limit on the number of data sets used by the algorithm, having more available data gives a more robust result in terms of the unit mapping.Additionally, images with different incidence angles helps account for photometric variability.If a single image did not cover the full study region, we use both the left (L) and right (R) camera images for complete coverage.Because both cameras collected data simultaneously, the Sun position is the same in the L and R images.The full-coverage LROC images are then projected onto the SPC DTM, and undersampled to the same resolution as the SPC DTM, either 2.6 m or 0.8 m GSD.
For both the low-and high-resolution SPC DTMs, we use the following combined images, which were acquired at three different incidence angles: M1149901166L/R images at 18°, M1145205753L image at 42°, and M1112203387L/R images at 66°.

Regional Slope Removal and Feature Masking
To remove the regional slope and mask out high-relief features, both of which can bias the statistical analyses, we import the SPC DTMs as well as surface reflectance data at various incidence angles into the Environmental Systems Research Institute ArcGIS for Desktop ® 10.4 (ArcGIS) software.ArcGIS is a commercial Geographic Information Systems package with a robust set of tools for image processing, mapping, 3D viewing and geostatistical analysis of both raster-and vector-based data.
A regional slope of less than 0.5°is apparent from NW-SE profiles across the 2.6 m low-resolution DTM of the study region.To remove the slope, we first create a raster "subtraction" surface in ArcGIS based on the actual elevation values in the DTM and then subtract it from the original topography to produce a final slope-removed DTM (see Domingue et al. 2022).For the high-resolution DTM subregion at 80 cm, we rescale the subtraction surface to the higher resolution before performing the slope removal.Because the topographies generated at the different resolutions are derived from the same core SPC results based on the GSD, there is no change to the inherent data, regardless of resolution.Details on the specific steps used to remove slope can be found in the A.1.
The subtraction surface introduces minor step functions in the elevation values, which appear as seams in the sloperemoved DTM.We use tools within ArcGIS to smooth the slope-removed DTM in reducing the appearance of these seams.Statistical analysis of the smoothed versus unsmoothed topography produces the same results within error.Thus, the smoothing process has no effect on the results.Further details and figures of the smoothing process can be found in the A.1.
To avoid areas with extreme reflectance due to positive-or negative-sloping features, we examine the DTMs, LROC/ WAC mosaic, and reflectance images to identify impact craters and other regionally large features such as troughs and peaks that are many hundreds to thousands of meters across.We manually trace the outer margins of these features using circular and elliptical drawing tools in ArcGIS.Impact craters smaller than 50 m in diameter were not included as their relief and size altogether do not have a significant effect on the statistical numbers for each swirl unit.Removing these craters would also result in less information for the image classification and potentially overskew the statistical data analyses.The reflectance data within these features were then nulled in both the high-and low-resolution DTMs, as well as the reflectance images used for mapping swirl units.We note that for the highresolution subregion, we masked an additional 53 craters with diameters of 17-92 m.The higher-resolution topography allowed for additional craters to be identified.

Machine Learning: Classification of Swirl Units
Using surface reflectance image data undersampled to the same resolution as the topography, we apply two independent methods to identify and map swirl units within the Reiner Gamma study region.These methods were introduced previously by Chuang et al. (2022), but here we discuss their application to this study.We note that no changes have been made to these methods in the time since the study by Chuang et al. (2022).The first method used is the K-means algorithm, a common unsupervised ML algorithm that can identify underlying clusters, here referred to as units, within a data set without the use of examples or data labeled by a user.Unit identification by K-means is an iterative process that partitions all of the data values in multidimensional parameter space into K numbers of distinct units defined by the user.We apply Kmeans using several different values of K for the unit maps.A secondary tool is used to determine the optimal value of K.For this purpose, we use the common elbow method that calculates the within-cluster sum of squares, a measure that yields the total variability across all units as a function of K units.The plot of the calculated values versus K units produces a monotonically decreasing function where the inflection point, or "elbow," is defined as the optimal number of K units.The selection of this point is automated using the so-called "Kneedle" algorithm (Satopaa et al. 2011).
The second method applied to the reflectance data was the maximum likelihood classification (MLC) algorithm, available as part of the Spatial Analyst Tools extension package in ArcGIS.The MLC algorithm is a supervised ML algorithm that requires labeled data, i.e., user-defined values, to establish a quantitative definition for each unit.In ArcGIS, unit definitions are established during a training phase, where a user selects sets of data samples that are representative of each unit.In the case of both the study region (2.6 m pixel −1 ) and subregion (80 cm pixel −1 ) reflectance data, we choose a set of training areas for each unit based on the K-means map.The selected data are then evaluated and stored in a signature file that contains information such as the mean, number of data points, and the variance-covariance matrix for each unit.This file is then used to classify every data point in the image to produce a unit map.In addition, the MLC algorithm also produces a probability map of how well each data point is classified based on the training sample data used.More details about this can be found in Chuang et al. (2022).

Statistical Analysis for Topographical Correlations
We use three different methods to explore the potential correlation between topography and each of the swirl units: cumulative distributions, mean heights with confidence intervals, and fitted histograms.The cumulative distributions give a complete visual representation of the data, the mean heights with confidence intervals reduce the data into a single number with a range, and the fitted histograms are used to confirm the overall trend given by the mean heights (i.e., the fitted histogram data provides a quantitative measurement at lower accuracy and is used here qualitatively; see Section 3).
First, we examine the cumulative distributions of heights.Unlike histograms, in which data are placed into bins, cumulative distributions retain the full data resolution and provide a visual representation of key characteristics and distribution shapes.The statistical significance of the topographic differences between on-, diffuse-, and off-swirl regions was determined using the Kolmogorov-Smirnov (K-S) test (e.g., Press et al. 2007).We use the function from Python SciPy (Virtanen et al. 2020) for the two-sample K-S test, scipy.stats.ks_2samp.We also consider Kuiper's variation of this test using astropy.stats.kuiper(Astropy Collaboration et al. 2013, 2018), which is more sensitive to the tails than the standard K-S test.
Second, we calculate the mean height for each unit.The uncertainty on the mean height is proportional to the inverse of the number of data points; therefore, the mean height of each swirl unit can reach millimeter accuracy even though the uncertainty on individual points is at the meter scale.We determine the mean heights using confidence intervals and assuming independent samples with unknown but equal population variances.We use the Z score, based on the cumulative standard normal distribution, to calculate the differences in mean heights for a 95% confidence interval.The mean height difference, Δh, between two data sets, h 1 and h 2 , with N1 and N2 points in each data set is calculated by where a -1 is the percentage confidence interval (here α = 0.05), z α/2 is the reliability factor (here z 0.025 = 1.96), and σ p is a pooled estimate of the combination of the standard deviations of the two data sets (σ h1 and σ h2 ): From this analysis, Equation (1) returns a mean value and a range in which there is 95% confidence that the true mean value lies.
Third, for completeness, we create histograms of each region.We set the number of bins for each data set, between 17 and 22, using Sturges' rule (Sturges 1926).In order to estimate the mean heights and errors for comparison with the confidence-interval results, we then fit Gaussian distributions to the histograms using the equation where x is the height, and the fitted parameters are the constant a, the mean height μ, and the standard deviation σ.We fit the Gaussian distributions using the Python function scipy.optimize.curve_fit,which uses a least-squares method and returns a covariance matrix (Virtanen et al. 2020).The error on each fitted variable is the square root of the respective covariance value, corresponding to one standard deviation.
The difference in heights between two distributions with Gaussian best-fit means μ 1 and μ 2 , each having fitted errors of err μ1 and err μ2 , is The histograms are based on binned data and therefore return less accurate results than the confidence-interval analyses.We consider the histograms as a second visualization of the data and as a check on any height trends.

Topography
Using SPC, we generate a 7 × 7 km DTM with a 2.6 m GSD for the study region within the Reiner Gamma swirl (Figure 3(A); see also Chuang et al. 2022).The study region DTM is built using 29 images taken with the LRO/NAC.A list of these images is provided in the A.2.The images used have resolutions ranging from 1.3 m pixel −1 to 0.5 m pixel −1 .A total of 2198 maplets are generated with a GSD of 40 m to 2.6 m, with most of the maplets having the latter GSD.The RMS uncertainty of the stereo positions (also called FormU; see Section 2.2) of the best maplets is 3.9 m in the study region DTM, which is 1.5 times the best maplet GSD.The corresponding 2.6 m GSD DTM for the subregion (Figure 2(B)) is extracted from the study area DTM.We note that the difference in resolution from the SPC DTMs compared to the 100 m GSD LROC/WAC topography for the Moon is significant (see Figure 2), and we propose the higher resolution is necessary to detect the topographic correlations within swirls (Domingue et al. 2022(Domingue et al. , 2023))).
A second, 0.6 × 2.3 km DTM was generated at higher spatial resolution for the subregion within the study region (Figure 2(C)).The subregion has a 0.8 m GSD and was generated using 998 maplets with a GSD ranging from 40 m to 0.8 m maplets.This subregion contains portions of both onand off-swirl.The FormU of the best maplets in the highresolution subregion is 1.4 m, which is 1.7 times the best maplet GSD.When the heights of the hi-and low-resolution DTMs are subtracted, the resulting height difference of the individual vertices is at most ∼5 m, which is within the stated uncertainty of 2 times the GSD of 2.6 m.
All stereo solutions are independent of each other, and thus the relative error of the heights does not depend on the distance between the stereo solutions.Photoclinometry height errors cannot be directly measured, but we expect them to be similar to the stereo height errors.The results of the final SPC DTMs that are slope-removed and feature-masked for both the study region and subregion, respectively, are shown in Figures 3(A), 4(A), and 5(A).

Swirl Unit Maps
The K-means algorithm identified three units for the study region at 2.6 m pixel −1 based on the optimal number of groups from the elbow method.This establishes the presence of a third unit, diffuse-swirl, in addition to the definitive on-and off-swirl units for Reiner Gamma (Figure 3(C); see Chuang et al. 2022).The detection of this third unit in both Reiner Gamma (Chuang et al. 2022; this study) and Mare Ingenii (Chuang et al. 2022) indicates that the swirl regions on the lunar surface may be more complex than previously indicated.
The relative amounts of each unit in the study area based on the K-means analysis are on-swirl 33%, off-swirl 28%, and diffuse-swirl 39% (see Table 1).Using reflectance values from training areas (Figure 3(B)) based on the K-means results, the three-unit map from the MLC algorithm shows a different distribution, with a lesser amount of off-swirl and greater amount of on-swirl compared to the K-means map: on-swirl 43%, off-swirl 19%, and diffuse-swirl 38% (Figure 3(D)).Analysis of the subregion using the same 2.6 m pixel −1 lowresolution unit maps are shown in Figures 4(C) and (D).
Using the reflectance data at 0.8 m pixel −1 from the subregion only, the K-means algorithm produced a two-unit map based on the elbow method grouping optimization, onand off-swirl (Figure 5(C)).Comparison of the study region three-unit map at 2.6 m pixel −1 (Figure 4(C)) to this two-unit map shows that the vast majority of diffuse-swirl was reclassified as on-swirl, with the off-swirl unit distribution remaining similar.The MLC algorithm produced a very similar unit map to the K-means with minor differences in the relative amounts of on-and off-swirl (Figure 5(D)).
To test how differences in both surface coverage and data resolution can affect the ML results, we explicitly set the number of units to three in the K-means algorithm for the highresolution subregion reflectance data.Accordingly, we then select training areas for three units in the MLC algorithm (Figure 6(B)).The resulting high-resolution K-means map has a different distribution compared to the low-resolution K-means map with more on-swirl and diffuse-swirl coverage in the highresolution than in the low-resolution (on-swirl, 37% high resolution versus 25% low resolution; off-swirl, 27% high resolution versus 33% low resolution; diffuse-swirl, 36% high resolution versus 42% low resolution; see panel C in Figures 4  and 6).However, when comparing the high-and low-resolution MLC maps, the distribution among the three units remains nearly identical (see Table 1).
The distribution of units in the ML maps as a function of aerial coverage (study region versus subregion) have two important implications.First, there is a definite difference in the distribution of on-and off-swirl units between the low-and high-resolution reflectance data.Although the difference in spatial resolution between the two data sets results in nearly 10 times more pixels at high resolution, the difference in distribution is more closely related to differences in aerial coverage rather than resolution.This is supported by the fact that the MLC and K-means maps show little change in the unit amounts between low and high resolution, particularly for the subregion (data sets B and C in Table 1).This result underscores the importance of context in terms of the amount of data coverage of a swirl for classifying units by ML.
A second implication is that the K-means algorithm is potentially more sensitive to differences in the data values than the MLC algorithm.The use of training areas and the consistency in relative unit amounts from low to high resolution for the MLC subregion maps suggests that the algorithm closely follows the training values in classifying units.Conversely, the K-means algorithm classifies without following any range of defined values or "labeled" data.Therefore, if the value range changes significantly, such as focusing on a smaller area like the subregion in this study, the results could be very different, as shown here.Note how the percentage of MLC on-swirl changes by less than 1% from the three-unit low-resolution subregion to the three-unit high- resolution subregion only, whereas the percentages change for all three units using K-means (data sets B and D in Table 1).We also note that while the K-means and MLC maps are visually comparable to where on-, off-, and diffuse-swirl units are generally defined, the fact that they are not identical lends additional support to the importance of mapping context.

Statistical Analysis
Table 1 contains the numbers of DTM data points and the percentages of the totals, by swirl unit classification, in each data set.
When comparing on-, diffuse-, and off-swirl units in each data set, the K-S statistic ranged between 0.08 and 0.43, with zero probability in all cases that the compared samples were derived from the same parent distribution.Kuiper's statistic ranged from 0.16 to 0.52, again with zero probability that any of the compared samples were from the same parent distributions.The cumulative distributions on which these results are based are presented by specific data set below.

Full Data Sets of the Study Region
For the data sets of the 7 × 7 km study region, the cumulative distributions and histograms of heights are shown in Figure 7.The mean height differences are listed in Table 2, based on the confidence-interval analysis for the cumulative distributions and the Gaussian fits to the histograms.The binning required to produce the histograms creates a lowerresolution analysis compared to the cumulative distributions, and this is reflected in the order-of-magnitude larger error bars.In fact, the fitted mean heights, μ, are in the thousands of meters with fitted errors, err μ , being tenths of meters.Following standard error propagation (Equation ( 4)), these relatively small fitted errors become larger relative to the meterlevel differences in mean heights.Because the histogram analyses have such large inherent error, the weighted average (where the weighting is equal to the inverse square of the errors) of the mean height differences of both the confidenceinterval and histogram analyses returns average height differences that are the same as the confidence-interval results within the errors to the second decimal place (Table 2).Essentially, the histograms provide a useful qualitative check to the more comprehensive cumulative distribution results and confidence-interval analyses.
The numerical results are commensurate with what is observed in the plots.The histograms show that the highest elevation unit is the diffuse-swirl area in both the K-means and MLC definitions.The K-means histogram shows on-swirl as being slightly lower than off-swirl, while the MLC histogram displays the opposite (off-swirl is slightly lower than on-swirl); however, the errors encompass the mean heights being the same, and any difference is difficult to see by eye in the plots.The cumulative distributions show the same relative height order between the two ML unit definitions: on-swirl is lowest, diffuse-swirl is highest, and off-swirl is intermediate.
The highest-quality result, from the confidence-interval analysis, is that diffuse-swirl is the highest of the three regions, at an average of 1 or 1.5 m higher than on-swirl.Diffuse is also higher than off-swirl by an average of 0.4 or 0.7 m.On-swirl is thus lower than off-swirl by 0.6 or 0.8 m.The different values stem from using the two different ML classification methods.The lower-resolution histogram analyses agree that the diffuseswirl data are the highest on average and do not detect any statistical difference between on-and off-swirl heights; the onand off-swirl height differences from the Gaussian fits are consistent with zero, within the error bars.Therefore, at the DTM spatial resolution of 2.6 m GSD the diffuse-swirl unit appears to be an elevated area separating the on-and off-swirl units.
The K-means and MLC methods classify points slightly differently.Approximately the same number of points are diffuse-swirl for each method.However, MLC finds more onswirl points than K-means and fewer off-swirl points (by a few hundred thousand; see Table 1).Even so, the two methods return roughly similar results when analyzing the correlations between swirl units and topography.The K-means cumulative distributions for each classification unit are slightly more separated than the MLC, as is visually apparent in Figure 7.The K-means confidence-interval results reflect this difference, with slightly lower mean heights on-swirl and slightly higher mean heights off-swirl than MLC.

Comparison of the Subregion Topography at Low and High Resolution
The subregion was examined at two different spatial resolutions.In the low-resolution case, the swirl unit definitions are those derived from examining the 7 × 7 km study region at 2.6 m GSD.In the high-resolution case, two different approaches were taken for defining the swirl units.The first approach used the unit definitions from the low-resolution 7 × 7 km ML results and resampled the units at the higher spatial resolution.The second approach used the reflectance data resampled at the higher spatial resolution and applied the ML techniques to just the reflectance values from this high-resolution subregion data set.Here, we focus on the first approach.We discuss the second approach in the next section.
Considering unit definitions from the study region, for both low-and high-resolution topography, the MLC method classifies more on-swirl points and fewer diffuse-and off-swirl points than K-means (by 5%-18% of the total; see Table 1).Each ML method returns a similar percentage of the total for each swirl unit at the two different resolutions.
The cumulative distributions and histograms of heights for the subregion are shown in Figures 8 and 9. Starting with lowresolution topography, visually the distributions suggest that onswirl is the lowest, with off-and diffuse-swirl being similar.Comparing the two ML methods, the shapes of the distributions look similar, though there is a slight shift toward lower heights in the diffuse unit for K-means relative to MLC.This trend is confirmed by the mean height differences from the confidenceinterval analysis shown in Table 2.The height differences between on-and off-swirl match at 0.4 m, however K-means Unsupervised K-means clustering algorithm map with three units defined: on-swirl (blue), diffuse-swirl (yellow), and off-swirl (red).(D) Supervised MLC algorithm map of on-swirl (blue), diffuse-swirl (yellow), and off-swirl (red) units.Note how similar, though not identical, the MLC map is to the K-means map both in this highresolution subregion-only data and the low-resolution study region data in Figure 4. returns significantly smaller height differences than MLC (by roughly 0.5 m) for on-and off-swirl versus diffuse-swirl.
Like the 7 × 7 km study region, the units from low to high are on-, off-, and diffuse-swirl.For this subregion in lowresolution topography (top panels in Figures 8 and 9) relative to the study region (Figure 7), the confidence-interval height differences between (i) on-and diffuse-swirl are significantly smaller for K-means and similar for MLC; (ii) diffuse-and offswirl are smaller for K-means and slightly larger for MLC; and (ii) on-and off-swirl are slightly smaller for both methods.
For the subregion in high-resolution topography with study region unit classification, the distributions in Figures 8 and 9 visually indicate that on-swirl is the lowest, then diffuse-swirl, and then off-swirl.Comparing the two ML methods, the shapes of the on-and off-swirl distributions look somewhat similar, but there is an obvious shift toward lower heights in the diffuse-swirl unit for K-means relative to MLC.These trends are confirmed by the confidence-interval analysis as listed in Table 2.For both K-means and MLC, on-swirl is lower than diffuse-and off-swirl, but, unlike the majority of the low-resolution subregion and full region results, diffuse-swirl is the same or lower than off-swirl.The confidence-interval height difference between on-and offswirl is 4.1 or 4.4 m (slightly smaller for MLC than K-means).Kmeans returns 1.7 m of this height difference as being between diffuse-and off-swirl, while MLC has no difference in heights for these units.The trend here is thus, from low to high, on-, diffuse-, then off-swirl.
For this subregion in high-resolution topography (bottom panels in Figures 8 and 9) relative to the 7 × 7 km study region (Figure 7), the confidence-interval height differences between (i) on-and diffuse-swirl are significantly larger for both methods; (ii) diffuse-and off-swirl are significantly larger for K-means (and in the opposite direction, with diffuse-swirl being lower than off-swirl) and nonexistent for MLC; and (ii) on-and off-swirl are significantly larger (by multiple meters) for both methods.These plots show that the distribution of heights in the diffuse-swirl unit is shifted to higher elevations with respect to on-and off-swirl.The off-swirl unit is similar to on-swirl, although it has more data points at higher elevations.The results from the two ML techniques are similar, with K-means showing slightly larger differences between the units.Bottom: histograms of heights for the 7 × 7 km region for each of the swirl units as identified by each of the two ML techniques: MLC (left) and K-means (right).Gaussian fits to each unit, G(x, a, μ, σ), are shown as dotted lines.Variations in color shading indicate where populations overlap.As shown in the top plots, although less clearly, the distributions of heights are shifted to higher elevations for the diffuse-swirl unit relative to on-and off-swirl.The on-and off-swirl histograms are similar, with the fitted mean for on-swirl being slightly lower than off-swirl in MLC and slightly higher in K-means.The different sample sizes of the units in each ML technique are apparent in these plots.

Comparison of the High-resolution Subregion with Two versus
Three Swirl Units When performing swirl classification based solely on the subregion reflectance data at 0.8 m pixel −1 , the K-means method determined that the optimal number of units was two.For comparison, a three-unit classification using only the subregion reflectance data are also analyzed.Figures 10 and 11 show the cumulative distributions and histograms of heights for these different classifications.Most of the points that are classified as diffuse-swirl in the three-unit data set (a few hundred thousand) are classified as on-swirl in the two-unit data set, although some of a Histogram data sets are the differences between the mean heights with extrapolated errors from fitted Gaussians, Δh G , following Equation (4).All others are height differences, Δh, with 95% confidence intervals from Equation (1).Negative values mean the former swirl unit is lower than the latter.Items in bold are for on-versus off-swirl units from the most accurate, confidence-interval analysis.the off-swirl points (a few tens of thousands) also move to diffuseswirl (see Table 1).
Figures 10 and 11 visually show that on-swirl is lower than off-swirl.When the third, diffuse-swirl unit is considered, it falls in between these two units.The diffuse-swirl unit shifts to slightly lower heights for K-means relative to MLC.These trends are confirmed by the mean height differences from the confidence-interval analysis shown in Table 2.
Comparing K-means and MLC for this subregion with different numbers of units, the height difference between onand off-swirl is roughly the same at -2.7 m (two-unit case) or -3.9 m (three-unit case).Both methods return that the diffuseswirl is intermediate in height between on-and off-swirl: the height difference is 1.2 m (K-means) or less than half a meter (MLC).The overall trend, from low to high, is on-, diffuse-, and off-swirl.
For the subregion in high-resolution topography and with subregion unit classification (bottom of Figures 10 and 11) relative to the high-resolution topography with study unit classifications (bottom panels in Figures 8 and 9), the height differences between (i) on-and diffuse-swirl are similar; (ii) diffuse-and off-swirl are smaller for K-means and slightly larger (and negative) for MLC; and (ii) on-and off-swirl are slightly smaller for both methods.The two-unit method (top of Figures 10 and 11) has height differences between on-and offswirl that are ∼1.5-2m smaller than the three-unit method, presumably because the higher diffuse-swirl units have been grouped with the lower on-swirl units.

Discussion
In this study, our objective is to determine whether correlations exist between swirl units and topography that are similar to those seen previously in Mare Ingenii (Domingue et al. 2022(Domingue et al. , 2023, in revision), in revision).The confidence-interval analysis shows that a similar trend is observed in the high-resolution data at Reiner Gamma as seen in Mare Ingenii, where on-swirl is the lowest elevation unit, followed by diffuse-swirl, and then off-swirl.The mean heights for the high-resolution subregion- only data with three units, where units are defined based on the 7 × 7 km study region, provide the most compelling statistical results (Table 2, D, three units).The on-swirl unit is 3-4 m lower than the diffuse-swirl unit, and the diffuse-swirl unit is 0-1 m lower than the off-swirl unit.Overall, the on-swirl unit is ∼4 m lower than the off-swirl unit.
However, the trend of increasing mean height from on-to diffuse-to off-swirl in Reiner Gamma is resolution dependent.In the low-resolution data, the diffuse-swirl is statistically the highest unit, not off-swirl as indicated in the high-resolution data.This is due to a refinement in the shape of the surface derived by SPC when going to a higher spatial resolution.When SPC is used to generate higher-resolution topography, it is not simply adding a finer grid to the lower-resolution topography.Additional refinement in the shape of the surface (i.e., x, y, and z directions) always occurs.The high-resolution topography is based on a larger number of highly accurate stereo points and improved spacecraft position and pointing, thus more information is extracted from each image.These refinements result in actual changes to the heights and distances (i.e., shape), and provide a higher level of confidence in the high-resolution topography than the low-resolution topography, despite the similar height difference uncertainties in the two resolutions.
The errors for the height differences with 95% confidence intervals in Table 2 are small, around a few centimeters for the nonhistogram values.These errors are small because the large number of vertices in each DTM lead to high precision.However, this does not imply that the heights are uniform across a unit.Quite the contrary: there are many vertices classified as on-swirl that are higher than other vertices classified as off-swirl.For example, the lower right corner of Figure 5(A) is classified as on-swirl by all algorithms and the topography is colored yellow, while the topography in the upper left corner of the same panel is always classified as offswirl by all algorithms yet is a blue color.Nonetheless, the mean height differences between units show the on-swirl topography trends lower (Table 2).The surface in each unit is not smooth, the terrain is rugged with many height variations.The statistical analyses demonstrate that the mean surface of each unit is characterized by a different height, with the ruggedness overlaid on this mean surface.
Multiple transects across the study region (i.e., profiles) do not show an obviously consistent trend such as high elevation in the off-swirl, intermediate elevation in the diffuse-swirl, and low elevation in the on-swirl.While the mean elevations are consistent with the elevation differences between the units (Table 2), the ruggedness of the lunar surface is much more apparent in the profiles.However, since the multiple statistical approaches show consistent trends, it lends credence to the onswirl unit truly having a lower elevation than the other units.
Our understanding of SPC DTMs and ML results point toward the high-resolution topography with three swirl units providing the more accurate description of the surface heights and unit correlations.Whether the three units are determined using the study region reflectance data at a 2.6 m GSD or the subregion reflectance data at a 0.8 m GSD, the mean height differences of the units remain relatively unchanged (i.e., difference of a meter or less; Table 2, C and D).Determining the units based on the larger study region provides greater context.The overall trend of mean heights forms a consistent pattern in that the on-swirl mean heights are always lower than the off-swirl and diffuse mean heights.This pattern is consistent regardless of the spatial resolution of the topography or the presence/absence of the diffuse-swirl unit.
The unit maps above (Figures 3 and 5) show the importance of selecting a large study region for ML.Chuang et al. (2022), analyzing the study region, showed the K-means elbow method finds three distinct units.Limiting the analysis to a smaller region, for example by only analyzing the subregion, only two swirl units would have been indicated in Reiner Gamma (i.e., on-and off-swirl).Alternatively, if we had only generated the low-resolution topography for the study region, we would not have discovered the multimeter mean height difference between on-and off-swirl.Only when combining a large area with high-resolution topography do the meter-scale height differences confidently manifest.
Are these ∼4 m mean height differences between on-and off-swirl meaningful, or are they merely coincidental and only occur in our study region?Since we see the same trend of lower on-swirl at two locations in Mare Ingenii (Domingue et al. 2022(Domingue et al. , 2023, in revision), in revision), it would suggest this elevation difference is not coincidental.How could a mean elevation difference of ∼4 m affect the on-swirl locations?Although the process is still being studied, Domingue et al. (2022Domingue et al. ( , 2023, in revision) , in revision) provides an overview of how bright dust transport into regions with low elevation can increase the reflectance.In brief, dust can be lofted by various mechanisms, such as by electrostatic forces or even by impacts.Lateral transport of the dust can occur due to interactions with magnetic fields or inside of a photoelectron sheath.Various properties of the dust such as size, composition, and magnetic susceptibility may play a role in this transport and the likelihood of being trapped in a low elevation, as well as influence the eventual reflectance of the surface.Additional properties of the dust, such as its compaction state, can also affect the reflectance.The role of dust transport and/or sorting is beyond the scope of this On-swirl is lower than off-swirl in all cases, with diffuse at an intermediate height between the two when it is considered as a separate unit.Two units are optimal when classifying based on the subregion-only data; however, classifications based on the larger study region reveal that a third unit is present and needs to be considered.
project, but provides a means of how the bright on-swirl unit would be more likely at lower elevations relative to off-swirl units, and helps define future areas of study.
Whatever the reason for on-swirl units correlating with elevation that trends lower, we have already noted that some patches of the topography do not follow this trend.Processes that are elevation independent are also shaping the swirl, but none of the mechanisms proposed thus far fully satisfy all the observations.In a single swirl, perhaps some regions of the swirl are dominated by these elevation-independent processes, but when these processes are absent or subdued dust transport into low elevations is dominant.Thus, swirl units could be shaped by elevation differences, but are not characterized by elevation differences.

Conclusions
SPC has, for the first time, enabled the examination of swirl topography on submeter scales for areas in two swirl regions, Mare Ingenii (Domingue et al. 2022(Domingue et al. , 2023, in revision) , in revision) and Reiner Gamma (this study).Both studies establish that there are topographic correlations within the swirl units, with the finding here that the on-swirl unit at Reiner Gamma is ∼4 m lower than the off-swirl unit, based on the most accurate statistical analyses and considering three units.The results depend on which algorithm and statistical analysis technique are used: if only two units are considered, the height difference between on-and off-swirl is reduced to ∼3 m, and low-resolution data return on-to off-swirl height differences of less than a meter.Thus, while these correlations are marginal in the low-resolution topography at 2.6 m GSD, they are enhanced in the high-resolution topography at 0.8 m GSD.This difference suggests generating the submeter topography is needed to tease out the subtle elevation differences found in swirls, and, until it is shown that these elevation differences can be detected in low-resolution DTMs, analyzing high-resolution topography at a meter or less should be considered for future studies.
In addition to the topographic correlations, we use unsupervised and supervised ML of the reflectance data to find a third swirl unit, termed diffuse-swirl, which supports the findings in Chuang et al. (2022).This diffuse-swirl unit is always found between and adjacent to on-and off-swirl units, and is either the same height or lower than the off-swirl unit (for the most accurate, high-resolution analyses).Small areas such as the subregion in this study are not always sufficient for the algorithms to identify the diffuse-swirl unit.Thus, larger surface areas are better suited to identify the subtle reflectance differences.The diffuse-swirl unit may represent a transition zone between on-and off-swirl.
Dust transport into low elevations could enhance the reflectance of the surface and shape the location of on-versus off-swirl units.However, many of the observations required to confirm this possibility, such as a compositional difference between on-swirl and off-swirl, are only now being explored.What is known is that none of the swirl-formation hypotheses proposed thus far, such as magnetic shielding, can explain all the observations.We propose that a combination of these processes, which include dust transport into low elevations, is required to form lunar swirls.10.The on-swirl heights are lower than off-swirl heights in all cases.The differences in heights between units is more pronounced when three units are considered.
The low-resolution DTM for Reiner Gamma will soon be available from the Imaging and Cartography PDS Node.The low-resolution reflectance data and mask layer can be found as a data set archive on Zenodo at https://doi.org/10.5281/zenodo.7967459.The high-resolution subregion DTM and the high-resolution reflectance data and mask layer can be found as a data set archive on Zenodo at 10.5281/zenodo.7967916.

Figure 1 .
Figure 1.Top: lunar swirls in Reiner Gamma on the near-side of the Moon.The full study region (red box) is located just south of the central "eye."The image is from a portion of the 100 m pixel −1 global LROC WAC mosaic.North is to the top.Bottom: 42°incidence angle surface reflectance image with bright on-swirl areas separated by dark lanes.A separate narrow subregion within the study region is indicated by the blue box.

Figure 2 .
Figure 2. Comparison of the difference in surface detail between the global LROC/WAC and SPC DTMs.Although other data sets exist at this location, these are the only sets in the literature that have been examined for topographic correlations.(A) Portion of the 100 m GSD LROC/WAC DTM covering the subregion within the Reiner Gamma study region (i.e., blue box in Figure 1).(B) Portion of the low-resolution (2.6 m GSD) SPC DTM for the study region covering only the subregion.See Figure 1 for context.(C) High-resolution (80 cm GSD) SPC DTM covering only the subregion.North is to the top.The subtle statistical correlations of the lowest elevations within on-swirl regions (see Statistical Analysis section), both in this study and those prior have only been detected using high-resolution SPC DTMs.

Figure 3 .
Figure 3. Data sets generated for the Reiner Gamma study region at 2.6 m pixel −1 resolution.The location of the subregion is outlined by the dark blue box.North is to the top.Scale bar is shown in panel A. (A) Slope-removed SPC DTM using a color stretch based on a 2.5 standard deviation about the mean; see Figure A1 for unmasked topography with no slope correction.(B) Surface reflectance at 18°incidence angle with on-swirl (blue), diffuse-swirl (yellow), and off-swirl (red) training areas used by Chuang et al. (2022) for the supervised MLC algorithm.Reflectance data are undersampled to align with the 2.6 m GSD topography.(C) Unsupervised K-means clustering algorithm map with three defined units based on the elbow method optimization: on-swirl (blue), diffuse-swirl (yellow), and off-swirl (red).(D) Supervised MLC algorithm map from Chuang et al. (2022) of on-swirl (blue), diffuse-swirl (yellow), and off-swirl (red) units.

Figure 4 .
Figure 4. Reiner Gamma study region data and unit maps extracted from Figure 3 at 2.6 m pixel −1 of the subregion with craters masked.(A) Slope-corrected SPC DTM with the same color stretch as in Figure 3. (B) Surface reflectance at 18°incidence angle.Reflectance data undersampled to align with 2.6 m GSD topography.(C) Unsupervised K-means clustering algorithm map with on-swirl (blue), diffuse-swirl (yellow), and off-swirl (red) units.(D) Supervised MLC algorithm map of onswirl (blue), diffuse-swirl (yellow), and off-swirl (red) units.

Figure 5 .
Figure5.Reiner Gamma high-resolution subregion-only data and unit maps at 80 cm pixel −1 with craters masked, with two swirl units.Due to the higher resolution, additional craters were masked along with those identified in the lower-resolution data.(A) Slope-corrected SPC DTM using a color stretch based on a 2.5 standard deviation about the mean.(B) Surface reflectance at 18°incidence angle with on-swirl (blue) and off-swirl (red) circular training areas used for the supervised MLC algorithm.Reflectance data undersampled to align with 80 cm GSD topography.(C) Unsupervised K-means clustering algorithm map with two defined units based on the elbow method optimization: on-swirl (blue) and off-swirl (red).(D) Supervised MLC algorithm map of on-swirl (blue) and off-swirl (red) units.

Figure 6 .
Figure 6.Reiner Gamma high-resolution subregion-only data and unit maps at 80 cm pixel −1 with craters masked, with three swirl units.(A) Slope-corrected SPC DTM using a color stretch based on a 2.5 standard deviation about the mean.Same as Figure 5(A).(B) Surface reflectance at 18°incidence angle with on-swirl (blue), diffuse-swirl (yellow), and off-swirl (red) circular training areas used for the supervised MLC algorithm.Reflectance data are the same as Figure 5(B).(C)Unsupervised K-means clustering algorithm map with three units defined: on-swirl (blue), diffuse-swirl (yellow), and off-swirl (red).(D) Supervised MLC algorithm map of on-swirl (blue), diffuse-swirl (yellow), and off-swirl (red) units.Note how similar, though not identical, the MLC map is to the K-means map both in this highresolution subregion-only data and the low-resolution study region data in Figure4.

Figure 7 .
Figure7.Top: cumulative distributions of heights for the 7 × 7 km low-resolution study region for each of the on-swirl (blue), diffuse-swirl (tan), and off-swirl (pink) units as identified by each of the two ML techniques: MLC (left) and K-means (right).The lighter-shaded areas surrounding each cumulative frequency distribution line represent the 3.9 m FormU error bars on each measurement; slight color variations indicate where error bars overlap.These plots show that the distribution of heights in the diffuse-swirl unit is shifted to higher elevations with respect to on-and off-swirl.The off-swirl unit is similar to on-swirl, although it has more data points at higher elevations.The results from the two ML techniques are similar, with K-means showing slightly larger differences between the units.Bottom: histograms of heights for the 7 × 7 km region for each of the swirl units as identified by each of the two ML techniques: MLC (left) and K-means (right).Gaussian fits to each unit, G(x, a, μ, σ), are shown as dotted lines.Variations in color shading indicate where populations overlap.As shown in the top plots, although less clearly, the distributions of heights are shifted to higher elevations for the diffuse-swirl unit relative to on-and off-swirl.The on-and off-swirl histograms are similar, with the fitted mean for on-swirl being slightly lower than off-swirl in MLC and slightly higher in K-means.The different sample sizes of the units in each ML technique are apparent in these plots.
b A: associated with Figure 3. B: associated with Figure 4. C: associated with Figure 5(A) and Figures 4(B)-(D).D: two units associated with Figure 5; three units associated with Figure 6.
a A: associated with Figure 3. B: associated with Figure 4. C: associated with Figure 5(A) and Figures 4(B)-(D).D: two units associated with Figure 5; three units associated with Figure 6.

Figure 8 .
Figure 8. Cumulative distributions of heights for the subregion in low (top) and high (bottom) resolution for the MLC (left) and K-means (right) methods.The swirl unit classifications were performed using the 7 × 7 km study region.The lighter-shaded areas surrounding each cumulative frequency distribution line represent the error on an individual measurement; slight color variations indicate where error bars overlap.The high-resolution data show more of a spread in heights between the swirl units than the low-resolution data, with on-swirl data being at the lowest heights.

Figure 9 .
Figure 9. Histograms of heights for the subregion in low resolution (top) and high resolution (bottom) for each of the swirl units as identified by MLC (left) and Kmeans (right).The swirl unit classifications were performed using the 7 × 7 km study region.Gaussian fits to each unit, G(x, a, μ, σ), are shown as dotted lines; variations in color shading indicate where populations overlap.These histograms are based on the data shown in Figure 8.The height progression from low to high for on-, to diffuse-, to off-swirl is apparent.

Figure 10 .
Figure10.Cumulative distributions of heights for the high-resolution data of the subregion with two (top) and three (bottom) swirl classification units for the MLC (left) and K-means (right) methods.The unit classifications were performed using the subregion-only data.The lighter-shaded areas surrounding each cumulative frequency distribution line represent the error on an individual measurement; slight color variations indicate where error bars overlap.On-swirl is lower than off-swirl in all cases, with diffuse at an intermediate height between the two when it is considered as a separate unit.Two units are optimal when classifying based on the subregion-only data; however, classifications based on the larger study region reveal that a third unit is present and needs to be considered.

Figure 11 .
Figure 11.Histograms of heights for the high-resolution data of the subregion with two (top) and three (bottom) swirl classification units for the MLC (left) and Kmeans (right) methods.The unit classifications were performed using the subregion-only data.Gaussian fits to each unit are shown as dotted lines; variations in color shading indicate where populations overlap.These histograms are based on the data shown in Figure10.The on-swirl heights are lower than off-swirl heights in all cases.The differences in heights between units is more pronounced when three units are considered.

Figure A2 .
Figure A2.Results from the regional slope correction across the study region but only within the subregion.(A) Original SPC DTM at 2.6 m GSD.(B) Sloperemoved topography with impact craters and large features masked.(C) Slope-removed topography with step-wise seams smoothed out.Note the significant reduction in seams in panel C as compared to panel B.

Table 2
Mean Height Differences between Swirl Units a

Table 1
Statistics for Different Data Sets by Swirl Units