The Surface Texture of Martian Lava Flows as Inferred from Their Decimeter- and Meter-scale Roughness

Extensive lava flows are found in the equatorial region of Mars, shaping the surface in a very distinct way. In radar images (at the decimeter scale), these flows are bright, with circular polarization ratios greater than one. This is a typical characteristic of extremely rough, blocky lava flows on Earth. Although the source of the extreme dm-scale roughness of Martian lava flows is unknown, their surface roughness can be constrained at the meter scale in an effort to infer their emplacement style. Here, we utilized high-resolution HiRISE images of Mars to construct digital terrain models of 35 lava flows, and measure their surface roughness parameters at a scale never before examined. Our results show that at the meter scale, Martian lava flows are smoother than blocky flows seen on Earth, and similar in roughness to terrestrial pāhoehoe and rubbly flows, as well as young lunar lava flows. However, these latter flows are much smoother at the decimeter scale than Martian lava flows. The differences observed in the surface roughness of Martian lava flows compared to analog lava flows on Earth and the Moon might be the result of: (1) the differences in the emplacement style of the lava flows, and/or (2) the differences in post-emplacement modification processes on the surface of the lava flows.


Introduction
Volcanism on Mars is considered an important crust-forming process on the planet, which may still be active in the present time (Greeley & Spudis 1981;Greeley et al. 2000). Volcanic features such as massive volcanoes and flood lavas are spread across the planet, shaping its surface in a very distinct way (Greeley & Schneid 1991;Keszthelyi & McEwen 2007). As a result, it is important to understand how Martian lavas were emplaced, and what their physical and chemical characteristics are. This can often be inferred from the lava flows' surface texture. Previous work done by Jaeger et al. (2010) and Keszthelyi et al. (2006Keszthelyi et al. ( , 2004Keszthelyi et al. ( , 2000 suggest that most of the Amazonian lava flows located within the Amazonis, Elysium, and Tharsis volcanic regions are likely pāhoehoe flows with a "platy-ridge" texture ( Figure 1). This texture is thought to form when surges of lava disrupt a solidified pāhoehoe sheet flow. It is seen in parts of the Laki lava flow in Iceland, the closest terrestrial analog to Martian flood lavas yet identified (Keszthelyi et al. 2004).
However, ground-based radar observations of Mars at S-band (12.6 cm wavelength; 3 km spatial resolution) revealed that the roughness properties of these lava flows differ from platy-ridged flows on Earth at the decimeter scale (Harmon et al. 2012;Neish et al. 2017; Figure 2). Volcanic features observed near the Martian equator (i.e., Marte Vallis, Tharsis region, Elysium region) produce extremely bright radar returns with circular polarization ratios (CPR) greater than one. These are most analogous to blocky, andesitic lava flows seen on Earth, such as in Craters of the Moon National Monument and Preserve in Idaho (COTM; Neish et al. 2017) and SP Crater in Arizona (Campbell 2012; Figure 3). The cause of the extreme decimeter-scale roughness of Martian lava flows has yet to be identified. We can, however, constrain their surface roughness at additional scales in an effort to infer their emplacement style. In particular, we can use highresolution images of Mars that have been acquired by the High-Resolution Imaging Science Experiment (HiRISE) instrument on board the Mars Reconnaissance Orbiter (MRO). This instrument acquires optical images at up to 0.25 m pixel −1 , which can be used to produce digital terrain models (DTMs) at 1-2 m pixel −1 Kirk et al. 2008).
Surface roughness is defined as the topographic expression of a surface over different horizontal scales (i.e., centimeters, meters, kilometers) (Shepard et al. 2001). Previous work has sought to measure the surface roughness of lava flows at different scales on different planetary bodies, because they give clues about the emplacement style of the lava flows and the interior processes of the planetary body (MacDonald 1953;Gregg & Fink 1995;Shepard et al. 2001;Sehlke et al. 2014;Neish et al. 2017;Tolometti et al. 2020). On Mars, previous work (i.e., Kreslavsky & Head 1999Garvin & Frawley 2000;Aharonson et al. 2001;Kirk et al. 2003;Neumann et al. 2003;Cord et al. 2007;Kim & Muller 2008;Campbell et al. 2013) has focused on its global surface roughness over the decameter-to-kilometer scale. These studies suggest a scale-dependent roughness for the geological units of the planet. At these scales, Martian volcanic plains are generally smoother than other geological units on Mars (Kreslavsky & Head 2000). Other work has examined the meterscale roughness of the Martian surface to find appropriate landing sites for future Martian lander missions (Kirk et al. 2003;Beyer & Kirk 2012;Beyer 2017). No previous work, however, has looked at the meter-scale roughness of Martian lava flows to infer its emplacement style.
Here, we measured the surface roughness of Martian lava flows at the decimeter and meter scale in an effort to understand why Martian lava flows are so rough in radar data when compared to most other lava flows in the solar system (Harmon et al. 2012). To achieve this goal, we produced high-resolution topographic data sets (1-2 m pixel −1 ) of Mars Kirk et al. 2008). These data sets allow us to quantify the roughness of large areas of lava flows on Mars at a scale never before attempted. The objectives of this study are: (1) to measure and constrain the surface roughness parameters of Martian lava flows using highresolution topographic data sets of Mars, (2) to compare these   (S-band). Terrains with bright radar returns (i.e., Elysium, Marte Vallis, Tharsis) represent volcanic regions of the planet (modified from Harmon et al. 2012). Here, the gray scale has a maximum radar reflectivity of 0.30. The Doppler equator is seen as a radar-dark band located at −10°latitude. The bright region located at roughly −10°and 240°is an artifact due to the foldover of radar-bright regions Arsia Mons and Daedalia Planum across the Doppler equator. results to the surface roughness parameters of terrestrial and lunar lava flows, and (3) to infer the emplacement style of Martian lava flows to have a better understanding of the volcanic processes present on Mars.

Methodology
In this study, we used data sets from MRO-HiRISE and the Mars Global Surveyor (MGS) Thermal Emission Spectrometer (TES) instruments to constrain the surface roughness of Martian lava flows. More specifically, we processed HiRISE stereo-pairs into DTMs using a combination of ISIS3 (ISIS:http://isis. astrogeology.usgs.gov) and NASA's Ames Stereo Pipeline (ASP) software (Beyer et al. 2018). (Refer to Beyer et al. 2018 for details on the workflow of HiRISE DTM generation.) We then extracted the average rms slope and Hurst exponent of 48 portions of Martian lava flows at the meter scale from the DTMs. To aid in the interpretation of our results, we also extracted the MGS-TES Dust Cover Index (DCI) for each of the lava flows studied. This is a measure of the relative abundance of the spectrally obscuring dust across the surface of Mars (Ruff & Christensen 2002). Finally, we linked the meter-scale roughness obtained in this work to the decimeter-scale roughness of terrestrial lava flows derived from the Uninhabited Aerial Vehicle Synthetic Aperture Radar (UAVSAR) and Airborne Synthetic Aperture Radar (AIRSAR) data sets. This will help us to better understand the emplacement style of Martian lava flows (Evans et al. 1986;Hensley et al. 2005).
Here, we chose flows that: (1) were located within the radardark and radar-bright areas of the Arecibo S-band radar images provided in Harmon et al. (2012), (2) had stereo-pairs available to produce HiRISE DTMs using ASP, and (3) did not have obvious artifacts in the HiRISE DTMs that could have affected the results. In most cases, we used only one representative region within each lava flow, 200 m by 200 m in size, to extract the roughness parameters of the 100 m long topographic profiles. In seven of the DTMs, however, we extracted several regions for study.

Quantifying the Surface Roughness
As mentioned in Section 1, surface roughness is the topographic expression of a surface over different horizontal scales (Shepard et al. 2001). To quantify this value, we need topographic data that show the differences in height along a surface (i.e., DTMs). There are different parameters that can be used to quantify surface roughness of various geologic surfaces (Shepard et al. 2001). Here, we used Shepard et al.ʼs (2001) suggestion to use the rms slope and Hurst exponent metrics to report these values. The rms slope refers to the average slope along a two-dimensional profile, and it depends on the scale at which it is measured (Shepard et al. 2001). The Hurst exponent describes how the roughness of the surface changes with scale (Turcotte 1997). The Hurst exponent ranges from zero to one, where values closer to zero represent surfaces that become smoother or rougher as the scale increases, and values closer to one represent surfaces that maintain their roughness or smoothness as the scale increases (Turcotte 1997;Shepard et al. 2001).
We extract the rms slope using the Allan variance (v 2 ) (Equation (1)), which samples the topographic profile (z) (Figure 4) at every step (x i ) and calculates the rms slope as follows: Here, n is the number of sample points, x is the step size, and z x i ( ) is the height of the surface at point x i . From Equation (2), we get the rms slope, S rms .
The Hurst exponent can be calculated using Equation (3). Typically, the Allan variance is plotted versus the step size in log-log space, and the Hurst exponent is inferred from the slope of the line ( Figure 5).
Here, x 0 is the reference scale (we use 2 m because it is the highest resolution of our topographic data), and C s is the rms slope at the reference scale.
In this work, we used HiRISE DTMs to extract 100 m long topographic profiles of Martian lava flows in two perpendicular directions (downflow and cross-flow). First, we removed the best-fit linear function from the topographic profile. We do this to avoid the effects of slopes that occur over large scales, because they can introduce biases into our results (Shepard et al. 2001;Campbell 2002). Then, we calculated the Allan variance at 2 m intervals for each step size between a range of 2 m and 12 m. We used this range because the length of the profile should be a minimum of ∼10 times the length of the scale being studied (Shepard et al. 2001). Finally, we determined the Hurst exponent and rms slope from fits to the resulting variogram. We repeated these calculations using a starting point that increased by one pixel, until we reached the end of the first row (or column, for the perpendicular flow) of the DTM. We repeated this procedure for every row (or column) until each pixel of the profile had an associated rms slope and Hurst exponent (minus the last 100 m of every row or column) ( Figure 6).
In an effort to find a terrestrial emplacement style with similar roughness properties at the meter and decimeter scale to those observed in the Martian lava flows studied here, we compared (1) the meter-scale roughness (rms slope and Hurst exponent) obtained in this work and the (2) decimeter-scale roughness of Martian lava flows obtained from radar observations at S-band (12.6 cm wavelength), to the (3) meter-scale roughness of terrestrial lava flows from topographic profiles acquired in the field and the (4) decimeter-scale roughness of terrestrial lava flows derived from UAVSAR and AIRSAR radar data sets. These data sets were acquired at L-band (24 cm wavelength); no S-band data are currently available for terrestrial lava flows. UAVSAR and AIRSAR are two fully polarimetric imaging radar systems operated by NASA/JPL (Evans et al. 1986;Hensley et al. 2005). Please refer to Neish et al. (2017) for a detailed description of how UAVSAR and AIRSAR data sets were acquired and processed.
From these data sets, we calculated the CPR. CPR is defined as the ratio of SC to OC returns, where SC represents the same circular polarization as the transmitted signal, and OC represents the opposite circular polarization of the transmitted signal. When a circularly polarized radar wave is transmitted and backscatters off an interface, the polarization of the wave changes; as a consequence, smooth surfaces will tend to have high OC returns and low CPR values (0-0.4), because the radar wave will only backscatter off a single interface, flipping its polarization. Moderately rough surfaces, on the other hand, will tend to have equal OC and SC returns and moderate CPR values (0.5-1), because the radar wave will backscatter off multiple interfaces, which will randomize the polarization. Blocky surfaces, however, will have high SC returns and therefore high CPR values (>1), because the radar wave will encounter natural corner reflectors, causing double bounce backscattering (Neish & Carter 2014).

Results
We used a total of 41 HiRISE DTMs of volcanic surfaces on Mars to quantify the surface roughness of 48 portions of Martian lava flows (39 portions are radar-bright, and the other 9 portions are radar-dark). Six of the DTMs were processed by the HiRISE team in SOCET- SET (McEwen et al. 2007), and posted for public use on NASA's Planetary Data System ( Table 1). We generated the other 35 DTMs using ISIS3 and ASP ( Table 2). These are posted for public use here: doi:10.5281/zenodo.3770870. The surface roughness parameters extracted from these data sets range from 0°to 7°for the rms slope and 0.4-0.9 for the Hurst exponent. We also extracted the TES DCI for each lava flow studied in this project and found 44 dust-covered lava flows and 4 dust-free lava flows. A detailed explanation of our results can be found in the following subsections.

HiRISE Digital Terrain Models
In this work, we utilized 8 HiRISE DTMs of radar-dark volcanic surfaces, and 33 DTMs of radar-bright volcanic surfaces at S-band (12.6 cm wavelength; 3 km per pixel). HiRISE stereo images typically have a spatial sampling of 25-50 centimeters, providing us with DTMs of 1-2 m per pixel. We converted the HiRISE stereo-pair ID for each product into its proper DTM ID using the NASA Planetary Data System product-naming convention for HiRISE DTMs ( To validate the DTM values extracted from the ASP, we took the difference between two DTMs of the same region produced by the two different software packages (SOCET-SET and ASP) (Figure 7). At first sight, there is a notable difference between the two DTMs. The ASP-derived DTM, which was controlled to the Mars Orbiter Laser Altimeter (MOLA) topographic data set and projected onto a sphere, shows a linear trend that is not present in the SOCET-SET-derived DTM. We do not think this should affect our results, though, because we remove linear trends from our profiles prior to extracting the surface roughness. In addition, the ASP-derived DTM shows more variation in elevation than the SOCET-SET-derived DTM The black region at the right side of D and E represents the last 100 m of the row; because each pixel represents the roughness parameters extracted from one 100 m long profile, we cannot extract parameters in this region. Note. Here, * represents radar-dark DTMs.  (a standard deviation of 15 m versus a standard deviation of 5 m). This is not surprising, given that the SOCET-SET software requires manual editing when geo-referencing the stereo data set, resulting in a more detailed DTM. ASP was designed to process multiple data sets more quickly and efficiently than is possible with manual editing. The elevation difference map showed a minimum of −58 m, a maximum of 41 m, and a standard deviation of 14 (Table 3). In the end, the effect of these differences is minimal when calculating the surface roughness, as the surface roughness values obtained for the same lava flow are identical within errors (H: 0.85±0.08 versus 0.82±0.10, Cs: 2°.1±1°.1 versus 2°.2±1°.0). Additionally, we removed the long-baseline slope of both DTMs to identify small-scale similarities and differences between them, as well as noise patterns and artifacts (see Figure 8). We noticed that at a small scale, the DTMs are  It is well known that different artifacts can be present in HiRISE DTMs regardless of the software used to produce them. These include: (1) boxes:square areas with 0.5-1 m differences in elevation from their surrounding areas, caused by the processing algorithms in SOCET-SET; (2) CCD seams: visible lines along the DTM where two CCD frames overlap; (3) faceted areas: areas with an approximate terrain shape due to their low contrast and signal; and (4) manually interpolated areas: geometric patterns caused by the manual editing of the HiRISE image Kirk et al. 2008). The DTMs utilized in this project, however, showed only obvious CCD seam lines (Figure 7), which are created when the HiRISE image is being mosaicked from the multiple CCD detectors. It is very difficult to remove these artifacts from the HiRISE images Kirk et al. 2008), so to avoid a discrepancy in our results, we avoided the seams when identifying regions from which to extract surface roughness.
Finally, in an effort to better understand the effective resolution of an ASP-derived DTM, and hence the sensitivity of our roughness results, we generated HiRISE images with reduced resolutions (2 and 4 m pixel −1 ) of a small portion of a Martian lava flow. We then compared these reduced-resolution images with a shaded-relief image of the ASP-derived HiRISE DTM of this area (see Figure 9). We did this because previous studies (Henriksen et al. 2017;Neish et al. 2017;Kirk et al. 2018) found that the effective horizontal resolution of DTMs may be lower than what is stated by the DTM software. For example, Neish et al. (2017) found that when reducing the effective resolution of a topographic profile, the Hurst exponent tended to increase, while the rms slope tended to decrease. Here, we found that the effective resolution of an ASP-derived DTM may be closer to 2 m pixel −1 than 1 m pixel −1 , because we can identify features in the shaded-relief image and in the image reduced to a resolution of 2 m pixel −1 with the same accuracy. These results, however, could vary between DTMs and the software used to generate them (e.g., Tebolt et al. 2020). The shaded-relief image used for this comparison did not show much noise and/or artifacts compared to other shaded-relief images derived from ASP-and SOCET-SET DTMs. This likely played an important role in identifying the effective resolution of the DTM. Future work should study this topic in more depth.

Surface Roughness
We used 41 HiRISE DTMs of 33 radar-bright and 8 radardark volcanic surfaces on Mars to determine the surface roughness (rms slope and Hurst exponent) for 48 portions of lava flows (some DTMs contained multiple lava flows). For each lava flow, we extracted the rms slope and Hurst exponent from multiple 100 m long topographic profiles in two perpendicular directions: downflow (expressed as CsX and HX), and crossflow (expressed as CsY and HY). We then calculated the average rms slope and Hurst exponent within each area, and their standard deviation ( Table 4). The rms slope values obtained for these surfaces ranged from 0°to 7°, with á ñ CsX =1°.7±0°.9, and á ñ CsY =1°.5±0°.7. The Hurst exponent ranged from 0.4 to 0.9, with an average value of 0.7±0.1 in both directions ( Table 4). The rms slope for the majority of these lava flows cluster around 0°-2°, with a Hurst exponent that clusters around 0.7-0.9.
We classified the lava flows as either radar-bright or radardark features from the S-band images provided in Harmon et al. (2012). Unfortunately, the radar data for Mars has not been made publicly available. Thus, we are limited to using the pixel values from the images provided in Harmon et al. (2012) to qualitatively infer radar backscatter. Here, we interpret darkgray to black pixels as radar-dark features, and light-gray to white pixels as radar-bright features. We observed that both radar-dark and radar-bright features share similar rms slopes at the meter scale. Intriguingly, the highest rms slope values obtained in this study (∼6°) correspond to 3 radar-dark flows (smooth at the dm scale) (Figure 10). These results may be due to differences in the emplacement style and/or post-emplacement modification processes. We address such possibilities in Section 4.

TES DCI
We extracted the TES DCI values of the 48 Martian lava flow portions using the map sampling tool in the Java Mission-planning and Analysis for Remote Sensing (JMARS) software. JMARS is a software suite that permits the visualization and analysis of spacecraft data from different planetary bodies in our solar system. The map sampling tool in JMARS gives us the DCI value for each of the 48 lava flow portions studied. To extract these data, we created custom shape files for each portion of the lava flows studied and extracted the DCI parameter for the area. The TES DCI map scale is 3.5 km per pixel; our shape files are smaller than a single TES pixel, so there is no standard deviation reported for our values.
For the 48 Martian lava flow portions, we found a range of TES DCI values from 0.92 to 0.98 ( Table 4). The majority of the DCI values for these flows (both radar-bright and radardark) cluster around 0.93-0.94. This means that they are mostly covered in dust (most dust-covered surfaces have DCI<0.95). However, two radar-bright flows appear to have relatively dustfree surfaces with a DCI of ∼0.97 (dust-free surfaces range from 0.95 to 1.00) (Ruff & Christensen 2002). Our results also show that radar-dark flows are typically dust covered, although their average DCI is higher (0.946±0.003) than the radarbright flows (0.937±0.003) (Figure 11). The flows with the highest rms slopes (5°-7°) at the meter scale appear dust covered and radar-dark at the decimeter scale. Figures 12 and  13 show the surface roughness and DCI results of an example dust-covered Martian lava flow and an example dust-free Martian lava flow.

Discussion
The Martian lava flows studied in this work have rms slopes that range from 0°to 7°and Hurst exponents that range from 0.4 to 0.9 at the meter scale. The majority of these flows are "smooth" at the meter scale, because their rms slopes cluster around 0°-2°. They also have Hurst exponents that range from 0.7 to 0.9 over the range of 2-12 m, indicating that they maintain their smoothness as the scale increases to the decameter scale. Previous studies (i.e., Kreslavsky & Head 2000;Campbell et al. 2013) have observed that the roughness of Martian lava flows at the decameter scale is smooth (<1°), and tend to decrease as the scale increases to the kilometer scale. At the decimeter scale, however, many of these flows are extremely rough (radar-bright) in Arecibo S-band (12.6 cm) images. Conversely, those lava flows that appear smooth (radar-dark) at S-band have the highest rms slopes at the meter scale found in this study. In general, we find examples of Martian lavas that are: (1) smooth at the meter scale and rough at the decimeter scale, (2) smooth at both scales (meter and decimeter), and (3) rough at the meter scale and smooth at the decimeter scale. None of the lava flows studied is rough at both the meter scale and the decimeter scale.
The differences in the observed roughness could be due to (1) a difference in the emplacement style of the lava flows, (2) a difference in post-emplacement modification processes on the Note. The DTMs studied in this work are all smaller than a single TES pixel, so there is no standard deviation in the DCI values. Here, * represents radar-dark flows.
surface of the lava flows, and/or (3) the limitations of the technique used to characterize the lava flows. We discuss each possibility below.

Difference in the Emplacement Style of Martian Lava Flows
The emplacement style of lava flows plays a significant role in their observed surface roughness. Different lava morphologies often have different surface roughness values, which vary with scale (Shepard et al. 2001;Neish et al. 2017). Thus, the surface roughness of one particular flow will likely change when observed at different scales (i.e., decimeter-size textures not visible at the meter scale) (MacDonald 1953;Gregg & Fink 1995;Sehlke et al. 2014;Tolometti et al. 2020). It is thus possible that the differences in surface roughness observed in our work (i.e., smooth at the meter and decimeter scale, versus smooth at the meter scale and rough at the decimeter scale) are due to the emplacement style of the lava flows on Mars. Some rubbly pāhoehoe flows on Earth, for example, are seen to be rough at the decimeter scale and smooth at the meter scale (Neish et al. 2017). This flow morphology is a potential analog to Martian lava flows observed in our work that are smooth at the meter scale but rough at the decimeter scale. Hawaiian smooth pāhoehoe flows, on the other hand, are smooth at both scales (decimeter and meter) (Neish et al. 2017), and could be a potential analog morphology for those Martian flows with similar roughness characteristics observed in our work. Finally, some terrestrial blocky flows have meter-sized blocks (Bulmer & Campbell 1999;Bulmer et al. 2005). These appear smooth at the decimeter scale and rough at the meter scale, resulting in a potential analog to those Martian lava flows studied in this work.
There is also a relationship between the chemical composition of lava flows and their surface roughness values. Tolometti et al. (2020) suggest that flows with high components of SiO 2 , Na 2 O, and K 2 O, and low components of TiO 2 , Fe 2 O 3 , CaO, and MgO (which are typically blocky and block-'a'ā flows), have high CPR values approaching one at L-band (24 cm wavelength). Conversely, lava flows with high components of TiO 2 , Fe 2 O 3 , CaO, and MgO, and low components of SiO 2 , Na 2 O, and K 2 O (which are typically pāhoehoe flows), have low to moderate CPR values. There are, however, some exceptions to this relationship. Emplacement style is a function of several factors, of which chemical composition is just one. For example, mechanically fractured lavas (i.e., rubbly flows) with low silica content exhibit moderate CPR values; these lavas may be initially emplaced as smooth pāhoehoe, which are later fractured by surges of lava. In addition, some siliceous lavas (i.e., block-'a'ā) do not have high CPR values, because they lack natural corner reflectors on their surfaces, which are necessary for the double bounce backscatter that produces high CPR (Campbell 2012;Neish & Carter 2014).
Finally, evidence of (1) water ice in the shallow subsurface of Mars at multiple latitudes (including the mid-latitudes) (e.g., Feldman et al. 2004;Byrne et al. 2009;Smith et al. 2009;Vincendon et al. 2010), (2) hydrovolcanic explosions (e.g., Rice et al. 2006;Ennis et al. 2007;Keszthelyi et al. 2010), and (3) phreatomagmatic activity on the surface of Mars (e.g., Wilson & Head 2004) suggest that hydrovolcanism was active on Mars. As a consequence, the surface roughness of those Martian lava flows located where hydrovolcanism was active may have been affected by these processes. There are 29 lava flows in our study that are smooth at the meter scale (rms slope <5°) and rough at the decimeter scale (radarbright) (Figure 14). Previous work done by Jaeger et al. (2010) and Keszthelyi et al. (2000Keszthelyi et al. ( , 2004Keszthelyi et al. ( , 2008 qualitatively described the emplacement style of Martian lavas as basaltic fluid flow sheets with a "platy-ridge" texture. This is based on surface morphology comparisons between images from the Mars Orbiter Camera (MOC) instrument on board the MGS spacecraft, and field work and aerial photographs of terrestrial lava flows. As mentioned in Section 1, "platy-ridge" flows are thought to form when surges of lava disrupt a solidified pāhoehoe sheet flow through mechanical fracturing. Therefore, one interpretation for the extreme roughness of Martian lava flows at the decimeter scale is that their nearsurface texture consists of decimeter-sized textures created by mechanical fracturing of pāhoehoe surfaces, creating "rubbly" or "slabby" textures.
Can this explain the observed meter-scale roughness of Martian lava flows? At the meter scale, the surface roughness properties of Martian lava flows are (1) smoother than the blocky flows seen on Earth at COTM, (2) similar to pāhoehoe and rubbly flows observed in Hawaii and Iceland respectively, and (3) similar to the Ina D lava flows on the Moon. The radar properties of the Martian lavas at the decimeter scale (L-band: 24 cm for terrestrial flows and S-band: 12.6 cm for Martian/lunar flows), however, are similar to blocky flows seen on Earth, which also have larger rms slopes at the meter scale (Neish et al. 2017). The only similar lava flow observed on Earth is one rubbly pāhoehoe observed at the 2014-15 Holuhraun flow in central Iceland, which is smooth at the meter scale and moderately rough at the decimeter scale (CPR=0.5) ( Figure 15). However, in general we do not observe lava flows that are emplaced with high dm-scale roughness and low m-scale roughness on Earth. Either there is a different emplacement style occurring on Mars, or there is another process (possibly post-emplacement processes discussed below) that is affecting the observed surface roughness.

End-case 2: Smooth at Both Scales (Meter and Decimeter)
We observe 6 lava flows emplaced with low m-and dm-scale roughness on Mars, which share similar roughness behavior with  Figure 17).
Martian lava flows have slightly lower roughness (rms slope: 0°-2°) at the meter scale than those pāhoehoe flows seen in Hawaii (rms slope: 5°), but post-emplacement modification  processes such as dust infilling could be responsible for these small differences. We discuss this possibility in Section 4.2.

End-case 3: Rough at the Meter Scale and Smooth at the Decimeter Scale
We also observed 3 lava flows with relatively high m-scale roughness and low dm-scale roughness on Mars ( Figure 18). This is a relatively rare surface texture among terrestrial lava flows. However, there is one particular blocky flow of the Sabancaya volcano in Peru that exhibits ∼6 m size blocks on its surface. Although incredibly rough at the meter-todecameter scale (Bulmer & Campbell 1999;Bulmer et al. 2005), its texture is "smooth" at decimeter scales, which results in low CPR at those scales (CPR: ∼0.3 at L-band) (Figure 19). Those Martian lavas with a rough m-scale roughness and smooth dm-scale roughness could share similar emplacement styles to the andesitic to dacitic lava flows observed in Peru at the Sabancaya volcano. However, it is important to note that the roughest lava flows in our study have an rms slope of only 7°at the meter scale; the m-scale roughness of the Sabancaya flow is 26°. Such difference in surface roughness could be due to differences in the size and composition of the blocks, as well as dust infilling in the Martian flows.
In summary, the emplacement style of Martian lava flows may be similar to those rubbly pāhoehoe flows seen in Iceland (moderate dm-scale and low m-scale roughness); smooth pāhoehoes in Hawaii (smooth at both scales); or blocky flows seen in Peru (high dm-scale and low m-scale roughness). However, there could be other emplacements styles not observed on Earth at work on Mars. Alternatively, postemplacement processes occurring on Mars, and/or limitations to the data sets used in this work, might be affecting the observed surface roughness of Martian lava flows. We explore those possibilities in the following subsections.

Difference in Post-emplacement Modification Processes on the Surface of the Lava Flows
Martian lava flows, like any other geological feature on its surface, are affected by post-emplacement modification processes. These processes (i.e., impact cratering, aeolian deposition, surface erosion, atmospheric processes) need to be considered when interpreting our surface roughness results at multiple scales. One important process currently operating on the surface of Mars is dust deposition (Ruff & Christensen 2002). This process could explain the surface roughness differences observed in this project, because the dust is not uniformly distributed around Mars.
The 48 portions of lava flows studied here show some differences in their TES DCI, although 92 percent (44 flows) are dust-covered surfaces (DCI from 0.88 to 0.949), and only 8 percent (4 flows) are relatively dust-free surfaces (DCI from 0.950 to 1.00). Eighty-four percent (37 flows) of the dust-covered flows are smooth at the meter scale and rough at the decimeter scale, while 11 percent (5 flows) are smooth at both scales (meter and decimeter), and 5 percent (2 flows) are rough at the meter scale and smooth at the decimeter scale (Table 5). On the other hand, 50 percent (two flows) of the relatively dust-free flows are smooth at the meter scale and rough at the decimeter scale, 25 percent (1 flow) are smooth at both scales (meter and decimeter), and 25 percent (1 flow) are rough at the meter scale and smooth at the decimeter scale (Table 5). Here we define "smooth" at the meter scale as any lava flow with an rms slope <5°and "rough" as any lava flow with an rms slope 5°. We interpret the radar-dark lava flows to be smooth at the dm scale, while radarbright flows are interpreted to be rough at the dm scale.
It is possible that the difference in dust coverage on the surface of the lava flows could be controlling our surface roughness results at the meter scale, making them appear "smoother" than they were when they were emplaced. This is because optical and infrared cameras, like the one that the HiRISE instrument uses to scan the surface of Mars, are sensitive only to the top few microns of a surface . It is impossible to see buried surfaces (in this case the different lava flow textures buried by the Martian dust) with  optical and infrared cameras, which may result in the observed "smooth" surfaces at the meter scale when extracting the surface roughness using HiRISE data sets.
At the decimeter scale, however, the roughness of the Martian lava flows is not affected by the dust cover on the surface. Radar wavelengths can penetrate into the near subsurface and sense the different textures of buried surfaces (Harmon et al. 2012). If the dust cover has similar properties to the lunar regolith, the penetration depth could be as much as 10 times the radar wavelength (Campbell 2002), about a meter in our case. Thus, the radar data tell us how "smooth" or "rough" the surface of the lava flow may have been at the decimeter scale when it was first emplaced, even if the lava flow surface is currently buried by dust.

Limitations of the Technique Used to Characterize the Lava Flows
Even though we utilized the highest-resolution topographic data sets of the Martian surface to extract the surface roughness of Martian lava flows in this work, there are some limitations to our method. For example, the surface roughness of Martian lava flows derived from this work are limited to the meter scale (or larger). We currently have no instrument capable of producing large-scale topographic maps of the Martian surface at the decimeter scale (or smaller). This may influence our results and lead to misinterpretations about the lava flows' properties and how these flows were emplaced. For example, previous work done by Neish et al. (2017) found that when the resolution of the data sets (i.e., one-dimensional topographic  profiles) is reduced, the Hurst exponent increases and the rms slope decreases.
As a result, our work is limited to only a qualitative interpretation of the roughness of Mars at the decimeter scale, using low-resolution S-band radar images from Harmon et al. (2012). These images convolve the roughness from both surface and subsurface sources, making the source of the roughness ambiguous. There is also a difference in the spatial resolution of the HiRISE and Arecibo data sets of three orders of magnitude (HiRISE: 2 m; Arecibo 3 km). This limited our roughness interpretations of Mars at the dm scale, because our regions of interest are far smaller than a single Arecibo pixel. In addition, there are no radar data sets of terrestrial lava flows at S-band, which limits direct comparisons between Martian and terrestrial lavas at these wavelengths. Such limitations could lead to misinterpretations about the surface characteristics of Martian volcanic flows. However, NASA and ISRO plan to launch a dual L-and S-band radar into Earth's orbit in 2022 (Rosen et al. 2015). Such data sets will be critical to better understand the emplacement of lava flows on Earth and other planetary bodies.
Our work was also primarily limited to ASP-derived DTMs, which are different from those produced using the SOCET-SET software (see Section 3.1). Even though our surface roughness results derived from two DTMs generated by different software (ASP and SOCET-SET) were the same, it is possible they may not be the same for other flows. More comparison between ASP-derived DTMs and SOCET-SET-derived DTMs are needed in future work. Future work could also compare the surface roughness of multiple Martian lava flows using DTMs generated by the two software packages. This will improve our knowledge about (1) the limitations of different software packages when generating DTMs, and (2) how compatible the surface roughness of Martian lava flows is using DTMs derived from different software.
Finally, our work was also limited to remote-sensing data of Mars, because Mars does not have a lander and/or rover near any of these rough volcanic surfaces. Generally, it is judged too dangerous to land on or near such surfaces. The roughness of lava flows varies within scales (see Figure 16), and may often be misinterpreted without appropriate data sets. This is why further study of this topic would benefit greatly from (1) a radar remote-sensing instrument on board a Martian spacecraft with high spatial resolution, and/or (2) an in situ suite analyzing and acquiring data (e.g., visual images, chemical composition of the surface) of different volcanic surfaces on Mars.

Conclusions
It is evident that volcanic processes have been active throughout the geologic history of Mars. However, it is still not known how many of these flows were emplaced. Examining the surface roughness of Martian lava flows at multiple scales can provide clues to this process. Martian lava flows appear to have extremely unusual roughness properties compared with terrestrial analogs. The radar characteristics of most Martian lava flows show that they have extremely rough surfaces at the decimeter scale, similar to blocky lava flows on Earth, but are smooth at the meter scale, most similar to pāhoehoe flows on Earth. In addition, most blocky lava flows on Earth are highly silicic, while most lava flows on Mars are basaltic in composition, which do not typically produce blocky surfaces.
In this work, we found for the first time that Martian lava flows are mostly smooth at the meter scale. Their surface roughness has a range of 0°-7°(rms slope), with an average of 1°.7±0°. 9. These results are most similar to the "smooth" pāhoehoe surfaces observed in Hawaii, which also typically have low CPR values at the decimeter scale, unlike the Martian flows. However, 92 percent of these flows have their surfaces covered in dust (DCI<0.95), and only 8 percent have a relatively dust-free surface (DCI>0.95). Thus, the surface roughness of many of these flows could be explained by the emplacement of a fractured lava flow being later infilled by dust.
However, in some cases the roughness of the flows at the decimeter and meter scale might be indicative of the emplacement process, especially in the few dust-free examples we identified in this work. In these cases, the emplacement style of Martian lava flows may be similar to rubbly pāhoehoe flows seen in Iceland (moderate dm-scale and low m-scale roughness), smooth pāhoehoe flows in Hawaii (smooth at both scales), and blocky flows in Peru (high dm-scale and low m-scale roughness). There could be, however, emplacement styles and post-emplacement processes occurring in Mars that are alien to our knowledge, as well as limitations to the data sets utilized for this study that might be affecting the observed surface roughness of Martian lava flows.