Objectives

To test the CO 2 block hypothesis, in the context of pit formation, we first conducted a short survey of Martian linear gully terminal pits and detached pits on dunes in Russell, Proctor and Matara Craters. The objectives of this study were to (i) characterise the different terminal pit morphometries, (ii) investigate if there was any evidence of a link between these terminal pit morphometries and detached pits and (iii) investigate the range of block sizes which may be reactivating and widening linear gully channels seasonally.

To further test the CO 2 hypothesis, in the context of pit formation, we performed experiments to examine whether sliding and hence partially buried CO 2 ice blocks would form morphologies comparable to Martian linear gully primary terminal pits and detached pits.

To test the cryoventing hypothesis, in the context of furrow formation, we performed a second set of experiments with two aims: (i) to study the erosion patterns resulting from the interaction between a gently placed CO 2 block and granular substrate and compare these features to a pre-existing Martian furrow network classification12; (ii) to study the factors which constrain furrow pattern type and furrow density.

Survey of Linear Gully Pits in Proctor, Russell and Matara Craters

High Resolution Imaging Science Experiment (HiRISE) Digital Terrain Models (DTMs) DTEEC_003080_1325_004077 and DTEEC_007018_1255_007229 and corresponding orthophotos were employed to survey linear gully pits in Proctor Crater and Russell Crater, respectively. The polygon tool in ArcMap 10.4 was used to measure the area of individual terminal pits (along the levée apex), taking the diameter of this circle as the pit width. Terminal pit area was calculated by squaring the pit radius and multiplying by π. Pit depths were measured using the Interpolate Line tool, by drawing a line across the pit centre and extending this to the surrounding dune surface. Depth was estimated as the difference in elevation between a pit floor and the surrounding dune surface on each side and averaging these values.

The Russell Crater DTM (DTEEC_007018_1255_007229) has an estimated vertical precision of 1.2 m28. The relatively low estimated vertical precision is attributed to a low convergence angle (or sum of emission angles) between the stereo pair used to develop the DTM, which reduces vertical precision. Horizontal accuracy of this DTM was given by post spacing, which was 1 m/pixel. The Proctor Crater DTM (DTEEC_003080_1325_004077) has an estimated vertical precision of <0.5 m28 and a horizontal accuracy of 1 m/pixel. Pit widths in both locations were generally much wider than 1 m and so horizontal accuracy should not significantly affect our measurements. Both sites were dark dunes and so noise in the DTMs may have affected our measurements to a small degree. We have estimated an upper limit of this effect by taking 10 linear cross sections close to pit locations in both DTMs. We detrended these cross sections, averaged them and calculated the standard deviation as an estimate of noise29. In Russell Crater this value was 1.7 m and in Proctor Crater, the value was 1.08 m and so depths <1.7 m were not reported in Russell Crater and depths less than 1.08 m were not reported in Proctor Crater. Horizontal measurements from orthophotos at both locations may have been affected by atmospheric dust and detector noise which was at the pixel level and would affect our horizontal measurements by one pixel at most.

A time-series of HiRISE images was used to determine whether there may be a link between detached pit and terminal pit formation. We propose that larger pit sizes (that indicate larger ice blocks) have a higher probability of generating detached pits. Terminal pit areas were measured as outlined above and the number of detached pits surrounding them were counted. Detached pits were identified as low albedo depressions. Negative topography was confirmed using the Interpolate Line tool to generate topographic profile data across the feature in the corresponding DTM where possible. Smaller features that may have been artefacts of dune surroundings (e.g. shadows in ripples), were not included. HiRISE images taken at the same location (−54.3°, 12.9–13°) on the Russell megadune and Matara Crater dunes (−49.5°, 34.7° and −49.5°, 34.6°) allowed us to identify new or widened terminal pits and new detached pits. Suitable data were not available for Proctor Crater.

The Russell Crater observations ranged over 4 Mars years (MY) between MY 29 and 32. The images used were ESP_012213_1255, ESP_020784_1255, ESP_029764_1255 and ESP_039153_1255 for MY 29, 30, 31 and 32 respectively. These images have emission angles of 8.2°, 5.1°, 3.8° and 3.8° respectively. Emission angle is the angle between the HiRISE camera and a normal drawn perpendicular to the surface, where 0° is known as nadir). Roll directions (obtained by comparing image centre longitude and subspacecraft longitude) were from west, east, east and west, respectively. For Matara Crater the survey extended over 2 MY between MY 30 and 31 (HiRISE images ESP_020414_1300, ESP_029750_1305 for sites at −49.5°, 34.7°. These images have emission angles of 4.7° looking from west and 0.4° looking from east respectively. ESP_021759_1300 and ESP_030528_1300 were examined for sites at −49.5°, 34.6°. These images had emission angles of 9.7° looking from east and 12.2° looking from east, respectively. Differences in lighting were accommodated for by adjusting contrast and brightness in the overlapping images. New detached pits were identified as circular depressions of low albedo that were not in the previous MY image and which surrounded a terminal pit. The extent to which pits were widened (if any) was measured by fitting a circular polygon to the same terminal pit for two consecutive Mars years, calculating area as outlined above, and differencing these data. Early spring images were examined for each location in order to measure high albedo features thought to be CO 2 blocks within channels. This was done by zooming in to optimal pixel resolution and using the Measure tool to record their width and length.

The images were taken at similar L s , or solar longitude (the Mars/Sun angle, measured from the northern hemisphere spring equinox where L s = 0, a measurement used to quantify Martian seasons). Images were also selected based on the emission angle. To minimise the effect of geometric distortions, single colour RDR images were used in each case. These are radiometrically-corrected images which are map projected. The radiometric correction adjusts for instrument offset, dark current and gain and then converts pixel values to \(\frac{Intensity}{Flux}\) reflectance. Geometric processing corrects for optical distortion and projects the image from spacecraft viewing to a map coordinate system. The MOLA (Mars Orbiter Laser Altimeter) DTM is used to improve the camera pointing intercept position on the Martian surface. Orthorectification corrects for distortions that may occur in off-nadir images where the spacecraft roll angle causes pixel foreshortening in the cross-track direction30. The images we used were not orthorectified, and so disparities may occur when comparing images with different observation geometry. To minimise this effect, images close to nadir were chosen and care was taken to select images with less than a 5° difference in emission angle. Because such differences are small, we can neglect parallax distortions31. A correction was made for any minor deviations however by dividing x-direction measurements by the cosine of the emission angle30. In each case the distortions are within tens of centimetres and thus fall within errorbars for our measurements.

Experimental Setup

In order to investigate the CO 2 block hypothesis for pit formation21 and the cryoventing hypothesis for furrow formation11 we performed laboratory experiments. Initial pilot work, under ambient terrestrial conditions, revealed that water in the atmosphere had a significant effect as it formed frost on the surface of the block and on the bed. This affects the heat budget, the permeability of the bed and the mobility of the grains and must be avoided. Additionally, this frost would later melt and erase the surface microtopography. Therefore, we performed our experiments in a low humidity chamber. The chamber was erected on a level surface in a constant temperature (ΔT ≈ 3 K) laboratory. A plastic container (460 × 675 × 400 mm) was filled with dehumidifying silica gel beads. A smaller plastic container (300 × 520 × 370 mm) was placed inside, forming a silica gel bead moat which surrounded the interior container. A perspex lid was fitted on top of the chamber and vacuum bagging gum sealant tape was added at the interface between the container and lid to ensure the chamber was air-tight. A sealed trap door was constructed within the perspex lid in order to minimise exposure to atmospheric water vapour when placing blocks inside.

Prior to each experimental run, three CO 2 ice blocks were placed upon the silica bead moat and were given time to sublimate. These generated dense CO 2 gas which flushed out the original gaseous content, thus removing any water vapour. This reduced the relative humidity sufficiently so that there was no noticeable frost formation during the experiments on the ~−80 °C CO 2 ice blocks.

Though grain sizes at linear gully and furrow locations on Mars have not been constrained, we used the preliminary data collected by the Curiosity Rover in the Bagnold dune setting on Mars to optimise the range of grain sizes employed in our experiments. We estimated a scale factor of 0.61 (see Supplementary Material, Experimental Scaling) by which to reduce grain size to compensate for the disparity in gravity between Mars and Earth. Grain sizes detected in the Bagnold dunes ranged from fine to coarse sand32, with many passing through a <150 μm sieve. The average grain size detected in the Bagnold dunes was between 200 and 300 μm 32. When scaled, these ranges fall between <90 μm and 122–183 μm, respectively. Therefore, Guyson Honite Glass Spheres of four grain diameter ranges (4–45 μm, 45–90 μm, 75–150 μm and 160–212 μm) were used for sixteen separate experimental runs.

Experimental Protocol

In the low humidity environment, pure CO 2 ice blocks were slid onto beds of glass spheres of each grain size range. We define “sliding” as a gentle motion nudging the block onto the bed surface — sliding is a motion which has enough force to slightly disrupt the granular surface. Sublimation then transports the grains underneath and near the edge of the block. We used Structure from Motion33 (SfM) to build Digital Elevation Models (DEMs) of the resultant morphologies from each experiment. We then compared these morphologies and morphometries with Martian terminal and detached pits measured using HiRISE images and DTMs.

A second set of experiments was designed to study the formation of furrows. The blocks were placed as gently as possible on a flat granular bed in order to generate CO 2 gas flow beneath the block. The aim was to investigate whether such a layer of gas at the interface between CO 2 ice and a granular substrate could form furrow networks on an initially smooth and level bed. SfM was again employed to build high resolution DEMs of the features produced and the resulting furrow morphologies were compared with the well-characterised furrow networks on Martian dunes11,12.

Each granular sample was dried and sieved to disaggregate material prior to each experiment. The sample was then poured into the inner container and levelled using a spirit level. A time-lapse camera was positioned inside the chamber to record sublimation rate. A digital hygrometer placed on top of the bed indicated depression of relative humidity in real-time. Once relative humidity decreased sufficiently, the trap door was opened and a CO 2 ice block of mass <1 kg (Table 1) was either placed or slid onto the bed. The chamber was immediately sealed and the block in each case was allowed to sublimate and interact with the granular substrate. This sublimation process lasted ~7–11 hours for each block depending on its mass and whether it burrowed. Videos of the initial sublimation dynamics in each case were recorded with an iPhone 6S 12 megapixel camera from outside the chamber, in order to avoid accumulation of grains on the lens which would hamper video quality.

Table 1 Laboratory experiment controlled and measured parameters: Full size table

Digital Elevation Model Development

All features resulting from CO 2 sublimation were modelled in three dimensions by SfM33 using Agisoft Photoscan. SfM is a technique for reconstructing three dimensional structures from two dimensional image sequences. Agisoft Photoscan is commercially available software which can photogrammetrically process digital images to create 3D spatial data. Each feature produced was imaged at many overlapping positions. In order to establish scale in the DEMs, coded markers were placed within the scene. Agisoft Photoscan finds the exact centre of coded markers enabling the production of highly accurate DEMs and the accurate measurement of features in the scene. Agisoft recommend that three or more scale bars are optimal. Therefore, a local coordinate system composed of three coded markers at known distances apart from one another, was used for scale definition34 to develop our 3D models. This local coordinate system was composed of three black and white circular 12-bit coded markers which were printed on three 6.8 × 8 cm sheets of paper. The centres of these markers were positioned on a flat wooden triangle (of 75 cm2 area) and the markers themselves were laminated with a thin layer of plastic34. The (x, y, z) coordinates of the marker centres were carefully measured with an Engineer’s Scale prior to placement in the scene34 and these were later entered in Agisoft Photoscan to develop scale bars for reference within the models. These coordinates (in metres) were: (0, 0, 0), (0.064, 0.115, 0) and (0.131, 0, 0) and these have accuracy <1 mm. The scale was in a constant location relative to the experimental chamber in each case, the centre of the nearest target on the scale was 15 cm from the chamber. This was close enough so that it could be seen in multiple overlapping images. This served as a reference for scale definition and also helped the processing tool to align images accurately. Constancy was assured by the remote nature of the laboratory — external vibrations were minimised. Care was taken when moving around the region of interest not to cause vibrational disturbances. In order to ensure a vertical orientation of the z-plane, the local coordinate system was placed flat on the laboratory bench during each experiment. The planar arrangement of the coded markers was confirmed using a spirit level to ensure the bench was level and the laminate nature of the markers ensured they did not bend.

The images were captured at a maximum distance of ~1 m from the bed surface and minimum distance of ~0.05 m at a variety of angles with respect to the image subject in each case. Camera positions were not recorded, as Agisoft Photoscan can compute accurate estimates. The focal length on the camera and aperture were fixed at 4.15 mm and f2.2 respectively and otherwise, the camera was not calibrated. Between 41 and 100 images were captured for each experiment, depending on whether fine detail such as furrow patterns were to be captured, or whether primary pit dimensions alone would be measured. The images were then aligned and referenced in Agisoft Photoscan, to build a point cloud, mesh and generate a DEM and corresponding orthophoto of each feature (resolutions in Table 1). The dimensions of each pit were then measured in ArcMap 10.4, using the DEM and orthophoto.

Differencing before and after DEMs in order to estimate pit depth was not possible due to the high albedo of the initial flat bed. We approximated the initial level surface by taking an average of 5 linear cross sections of the flat bed surrounding (but farthest from) the pit in ArcMap 10.4. In each case brighter regions where distortions were expected were avoided when taking these transects. A line was interpolated across the primary pit to these locations and the difference in height between the original bed surface and the depression formed by the CO 2 ice block was determined. An average and standard deviation of these values were taken in each case and standard deviations fall within the uncertainty margins outlined in Supplementary Material, Digital Elevation Model Uncertainty Estimates. Levées were measured in a similar manner by taking average values of the difference between the average flat surface and levée height. Maximum and minimum levée height were recorded in each case.

The area of furrows produced on each bed surface was recorded using polygonal mapping in ArcMap 10.4. The area of the flat pit floor in each case was determined by zooming in to optimal pixel resolution on the orthophoto overlain above the DEM and using the free-hand tool to mark the line where the inner slope of levées ended and the flat pit floor began. The pit floor is defined as the reasonably flat area directly below where the incident block was for which the perimeter is identified as the line between where the inner levée slope ended at 1 pixel resolution. The area of the space between furrow networks was determined by zooming in to optimal pixel resolution and mapping the outer edge of each furrow. This total area was differenced from the total pit floor area to get the area covered by furrow networks. The area covered by furrows was then expressed as a percentage of the total pit floor area. A complete discussion of the DEM uncertainties presented in this paper is available in Supplementary Material.

Data Availability

The datasets generated and analysed during the current study are available from the corresponding author on request.