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. Author manuscript; available in PMC: 2020 Sep 1.
Published in final edited form as: Icarus. 2019 Apr 1;329:197–206. doi: 10.1016/j.icarus.2019.03.041

Vertical and Horizontal Heterogeneity of Atmospheric Dust Loading in Northern Gale Crater, Mars

Casey A Moore a, John E Moores a, Claire E Newman b, Mark T Lemmon c, Scott D Guzewich d, Michael Battalio c
PMCID: PMC6662233  NIHMSID: NIHMS1530234  PMID: 31359883

Abstract

This paper updates the record of atmospheric dust loading within northern Gale Crater, Mars, by providing line-of-sight extinction (LOS-Ext) measurements of the intervening dust between the rover and the crater rim. These measurements are derived from images taken with the Navigation Cameras (Navcam) onboard the Mars Science Laboratory (MSL) rover, Curiosity. The observations span 2.44 Mars years, from Mars Year (MY) 31 at a solar longitude (LS) of 208° to t LS = 7° of MY34, sols 100 – 1701 of the MSL surface mission. This work examines the dataset for seasonal trends of the LOS-Ext in addition to horizontal variations and the vertical structure of LOS-Ext. The LOS-Ext has a repetitive pattern with a single peak in the latter half of the Mars year. The atmosphere in the crater is well mixed horizontally but not vertically as larger LOS-Ext is seen nearer the crater floor than at higher altitudes within the crater. The results allow a discussion on whether or not Gale Crater is a sink for atmospheric dust or a source of atmospheric dust in the current era.

Keywords: Mars, Atmospheric Dust, Extinction, Opacity, Sedimentation

1. Introduction

The quantification and characterization of dust in the Martian atmosphere remains an important area of study as suspended atmospheric dust is the dominant force behind atmospheric circulation in the Martian atmosphere. Dust is the largest contributing factor in how much solar radiation is absorbed and scattered in Mars’ atmosphere, therefore affecting the thermal properties of the Martian atmosphere.

The opacity of an atmosphere is a quantifiable measure of suspended dust and aerosols. Opacity is wavelength dependent and the amount of opacity at different wavelengths can be used to distinguish between different aerosol species, such as dust and ices (H2O, CO2), along with their microphysical properties.

Several studies have examined the temporal and geographic variability of Mars’ atmospheric opacity (Colburn et al., 1989; Smith et al., 1997; Smith and Lemmon, 1999; Markiewicz et al., 1999; Lemmon et al., 2004; 2015; Smith et al., 2008; 2016, etc.). Landed assets, individually, allow temporal variations in atmospheric opacity above their local landing site to be studied. Meanwhile orbital missions allow temporal variability to be seen on a global scale. Contemporaneous measurements of atmospheric opacity are common (e.g. Colburn et al., 1989; Lemmon et al., 2015; Moores et al., 2015).

This paper examines the geographic and temporal variability of dust within Gale Crater, Mars. This is quantified as an extinction value, which is the opacity due to dust divided by a path length and has units of inverse length. Extinction is typically used to study the distribution of dust/ices within the atmospheric column; such is the case with the lidar on the Phoenix lander (Whiteway et al., 2009; Dickinson et al., 2011; Komguem et al., 2013) or those of orbital spacecraft examining the limb of the Martian atmosphere (e.g. Määttänen et al., 2013; Kleinböhl et al., 2015). The opacity of dust between the rover and crater rim is calculated using an analytical approximation. Reporting the line-of-sight extinction (LOS-Ext) value instead of an opacity allows the measurements to be compared to one another as the distance between the rover and the crater rim is not static. The LOS-Ext reported in this paper are average values over the entire optical path between the rover and the crater rim.

LOS-Ext values in Gale Crater have been reported three times before. Moores et al. (2015) discusses the first 360 sols of MSL atmospheric monitoring movies and examines LOS-Ext briefly. Moore et al. (2016) discuss the seasonality of LOS-Ext as it included over a Mars years’ worth of data. In Moores et al. (2016), the opacity of dust plumes raised during the landing phase of the mission were measured.

This study provides a multi-dimensional view of the LOS-Ext in northern Gale Crater. Since the timescales involved in this dataset are long, on order of seven sols between observations, this dataset cannot pick up short-term (i.e., of order minutes-to-hours in duration) dust events such as dust devils or active lateral transport. However, it should be possible to detect long-term dust transport via horizontal variations in the LOS-Ext. This has the potential to show where dust enters the crater from downslope winds (Rafkin et al., 2016) and spread laterally throughout the crater. Variations in the vertical LOS-Ext profile have the potential to show seasonal dust lifting and, along with Mastcamera (Mastcam) column opacity measurements, can help approximate a sedimentation rate for dust into the crater.

Section 2 discusses the dataset and the methodology to derive LOS-Ext. Section 3 presents the results of LOS-Ext examined seasonally, horizontally, and vertically within Gale Crater. Section 4 presents a discussion of the results and how they help assess the recent record of atmospheric conditions local to Gale Crater. Section 5 provides a conclusion to this study.

2. Datasets and Updated Analysis Method

2.1. The Navigation Cameras

Navcam is an engineering camera onboard MSL consisting of four cameras mounted on the Remote Sensing Mast. Scientific applications of Navcam datasets include studies of Martian clouds (Kloos et al., 2016; Kloos et al., 2018), dust (Moores et al., 2015; Moore et al., 2016) and dust events (Moores et al., 2015; Lemmon & Newman et al., 2017).

Summarizing critical information for this study, Navcam has: (1) a square footprint with a 45° field-of-view, (2) a CCD size of 1024 × 1024 pixels, (3) a signal-to-noise ratio of up to 200:1 for well-exposed images, and (4) a spectral range of 600–800 nm.

For complete technical specifications of the engineering cameras produced for MSL, see Maki et al. (2012). For information on the performance of the Mars Exploration Rover (MER)-derived optics used in Navcam see Maki et al. (2003).

2.1.1. Imagery; Dust Devil Search Movies and North Crater Rim Extinction

The dataset consists of radiometrically calibrated images from two Navcam imaging sequences termed the Dust Devil Search Movies (DDSM) and the North Crater Rim Extinction (NCRE) observations. Both sequences have a northward pointing slightly above the horizon (azimuth ≃ 0°, elevation ≃ 5°) allowing the foreground, the distant crater rim, and the sky to be imaged.

The DDSMs are composed of four images with identical pointings and are sub-framed to 1024 pixels in width and 512 pixels in height. Elapsed time between each image allows a movie to be constructed. The first image of a DDSM is used in the derivation of LOS-Ext. The DDSMs were acquired to assess dust devil activity north of the rover, however, only one marginal detection has been made (Moores et al., 2015; Kahanpää et al., 2016) using these observations. Recently, numerous dust devils have been detected south of the rover towards Aeolis Mons with Navcam (Lemmon & Newman et al., 2017), effectively retiring the DDSM observation.

To continue the LOS-Ext record, the DDSM observation has been replaced with the NCRE observation. The NCREs are equivalent to one image in a DDSM that has been down sampled 2:1 to further reduce data volume.

The LOS-Ext dataset consists of 153 images from the DDSMs and 7 NCRE images, spanning sols 100 – 1701, (MY31, LS = 208° to MY34, LS = 7°), approximately 2.44 Martian years. On average, there are 10 sols between each DDSM and 13 sols between each NCRE in the LOS-Ext dataset.

The LOS-Ext dataset is a subset of the DDSM and NCRE observations that meet the following requirements in that the image must: (1) have been acquired within two hours of local noon and (2) have a direct line-of-sight to the crater rim.

2.2. Digital Elevation Model

It is necessary to calculate the distance between the rover and the crater rim to obtain the LOS-Ext. Between landing and sol 1701 the rover traversed nearly 16.5 km, generally to the southwest, which amounts to a total straight-line distance of nearly 9 km from Bradbury Landing. The previous work in Moore et al. (2016), assumed a constant 30 km distance between the rover and the crater rim, an assumption which is no longer valid. This study made use of a digital elevation model (DEM) of Gale Crater and the rover’s localization data to approximate distances to the crater rim. The DEM is derived from observations of Gale Crater made with the High/Super Resolution Stereo Camera (HRSC) on the Mars Express orbiter. The DEM has a 50-m/pixel resolution covering all of Gale Crater and the outlaying topographic environment.

The rover localization data (latitude and longitude) is used to approximate the rover’s position on the DEM to the nearest pixel. The relatively low-resolution of the DEM introduces uncertainties in the assumed rover location and thus the derivation of distances. However, these uncertainties have a negligible effect on the calculated LOS-Ext, as the distances involved are on the order of 30 km. For an in-depth overview of how distances are determined, the reader is directed to Appendices A and B.

2.3. LOS-Ext Methodology

In Moore et al. (2016), opacities were derived for the center of the image and divided by a static 30 km path length to yield the LOS-Ext. The work presented here addresses pointing drift of the Navcam and the rover’s mobility between observations to create a more consistent LOS-Ext record. As such, the images are rectified to one another and this process is detailed in Appendix C.

2.3.1. Line-of-Sight Extinction

As derived in detail in Moores et al. (2015) and extended in Moore et al. (2016), the line-of-sight optical depth between the rover and crater rim can be obtained from Navcam images using the approximation:

τ≈−ln(1−ISIMIGIM−ISIM), (1)

where IS, IM, and IGare mean radiance values for patches of the sky, mountain (crater rim) and (fore)ground, respectively. Radiometrically calibrated data products from the Navcam image processing pipeline are used, and hence the values of the pixels are indeed measures of radiance. In general terms, this approximation comes about by comparing the radiance obtained by looking through paths with near infinite (sky), near zero (foreground), and a medium (crater rim) opacity.

This method works because the crater rim, the foreground, and the dust in the atmosphere are illuminated similarly by the Sun through a low opacity atmosphere and the photons received by the Navcam are close to horizontal. Additionally it is assumed that the material making up the foreground and the crater rim are the same and that this material exhibits a Lambertian reflectance so that there are only minimal deviations in the phase function of the reflected light. For the full derivation the reader is directed to Moores et al. (2015).

Radiative transfer simulations were run at Texas A&M University in order to validate Eq. (1) for a range of line-of-sight and column optical depths using the geometry of the Navcam image set. The radiative transfer model and analytical expression agree to within 4%, with the analytical expression typically yielding a slight underestimate of dust loading along the line-of-sight (Moores et al., 2015). The LOS-Ext is then determined by dividing the opacity by the pathlength between the rover and the crater rim,

LOS−Ext=τ/d, (2)

where τ is approximated using Eq. (1), and the distance in kilometers, d, has been estimated for every image in the dataset and detailed in Appendix C.

2.3.2. Algorithm Applications

Equations (1) and (2) are implemented in different algorithms that are used to derive: 1) a mean-valued LOS-Ext for each image, 2) a regionally dependent LOS-Ext value for a specific geographical location on the crater rim, 3) a horizontal strip broken into 16 × 8 pixel regions along the crater rim, 4) a mean-valued vertical profile of LOS-Ext values for a 48-pixel tall section on the crater rim, which corresponds to an elevation change of roughly 1.1 km.

The first method uses Eqs. (1) and (2) in a straightforward way: IM is the average radiance of a 16-pixel tall region of the crater rim with a width determined by the horizontal coverage of the crater rim. IS and IG are the mean radiance values of a patch of sky and ground that are of the same width (e.g. same horizontal pixel values) of the crater rim patch but with vertical sizes of 30 and 40 pixels, respectively. The distance used is the mean-valued distance for all the pixels within the patch of the crater rim.

The second method isolates a specific 664-pixel wide geographic region on the crater rim common between images and derives the LOS-Ext similarly to method 1.

The third method breaks up the horizontal coverage of the crater rim in each image into 16 × 8 blocks. The mean radiance values for the sky, ground and crater rim are all calculated for 8-pixel wide sections in the image and evaluated using Eq. (1). The distance, d, in Eq. (2) is the mean-valued distance for each 16 × 8-pixel region on the crater rim. This produces a horizontal profile of the LOS-Ext for each image, and is also used to provide a 95% confidence interval for our measurements.

The fourth method produces a vertical profile of LOS-Ext for each image. Here, 48 patches each with a height of one pixel are used to determine the vertical profile of LOS-Ext. The distances are the mean-valued distance for each horizontal strip. Further, since this method requires a larger vertical view of the crater rim, the LOS-Ext values are additionally scaled as if the dust were to fall off with altitude, as pressure would.

2.3.3. Associated Errors

The images are radiometrically calibrated and the radiance received by Navcam is dependent on a number of variables, illumination being just one of them. Illumination effects, such as shadows, can affect how much light is received by the Navcam. As such, the dataset is restricted to images obtained in a four-hour window centered around local noon. This restriction in solar elevation reduces sources of error from shadowing on the crater rim. This is inferred by near identical standard deviations of the radiance values for the patch on the crater rim and that of the sky above.

The most dominant source of error in the derivation of LOS-Ext using the method outlined above is due to the variegated terrain local to the rover. This source of error is comprised of two components: the topography and the geomorphology local to the rover. The differences in topography in the foreground introduces inconsistent illumination effects, such as shadowing, between each image. Differences in geomorphology counteract the assumption that the crater rim is composed of the same materials found local to the rover. Combined, these two effects contribute to a systematic error upwards of 15% (Moores et al., 2015). These systematic errors are on the order of the differences between method 1 and method 2 of calculating the LOS-Ext in each image. As such, the reported LOS-Ext herein will be that of method 1 unless specified to be from method 3 or 4.

A 95% confidence interval is derived for each image by measuring the LOS-Ext multiple times in each image. This is done by dividing the crater rim into n distinct 8 pixel wide by 16-pixel tall regions. The size of the region was chosen to optimally negate effects due to image compression while still allowing a significant number of measurements, n > 80, within each image. The LOS-Ext is calculated for the n regions and the intervals are determined by: CI=1.96σ/n, where σ is the standard deviation of n measurements of the LOS-Ext for each image. The confidence intervals

3. Results

3.1. Seasonality

Year-over-year the LOS-Ext values have a similar pattern, as seen in Figure 1, which presents the LOS-Ext with the 95% confidence intervals time-folded over one Mars year.

Figure 1: Mean LOS-Ext versus LS.

Figure 1:

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The data presented here are the mean LOS-Ext per image as a function of solar longitude. MY31 is shown with black triangles, MY32 is shown with red squares, MY33 is shown with blue circles, and MY34 is shown with a cyan diamond. Seasonally low LOS-Ext (less dust) occurs near LS = 90° and seasonally high LOS-Ext (more dust) occur in the LS = 270–315° range.

Seasonal patterns are observed for the entire dataset with minimal LOS-Ext in the first half of the year and maximal values occurring in the second half of the year. For the two full Mars years in which data has been collected, MY32 and MY33, annual minimum and maximum LOS-Ext occur near LS = 90° and LS = 300°, respectively. Between LS = 90° and LS = 300° the trend for

LOS-Ext is to increase, while the trend between LS = 300° and LS = 90° of the next Mars year is a decreasing one.

It appears that a trend of slightly higher valued LOS-Ext exists as time progresses. The values derived for MY33 are typically larger than those for MY32 and values derived for MY32 are typically larger than those for MY31. This interannual variability suggests that while the LOS-Ext values indeed follow seasonal trends, the values themselves will differ for the same solar longitude for different Mars years.

Significant differences in LOS-Ext are seen between MY32 and MY33 during the LS = 0–180° seasons. Since large sol-to-sol variations in the LOS-Ext are not seen in the data, it can be suggested that within Gale Crater, MY33 was statistically slightly dustier during the southern winter than it was in MY32.

Outside of this timeframe, e.g. during the LS = 180–360° seasons, again differences in LOS-Ext are seen with the LOS-Ext values for MY33 being slightly elevated compared to those for MY32, but the confidence intervals are larger during this season.

These trends do not correlate with the interannual variability in the Mastcam column opacity measurements for MY32 and MY33, or those seen at the MER locations (Montabone et al., 2015; Lemmon et al., 2015). The column opacity measurements are typically double peaked in the later half of the year around LS = 240° and LS = 320° with a seasonal low around LS = 120°. The LOS-Ext is instead shown to be singly peaked over multiple Mars years.

3.2. Horizontal (Geographic) Variation

Figure 2 shows the LOS-Ext as a function of lateral position on the crater rim, e.g. method 3. The data in Figure 2A is interpolated to fill in the temporal gaps and is presented as Figure 2B. On average, cooler colors, indicating lower LOS-Ext values, are seen between LS = 0 – 180° implying high visibility during southern autumn and winter; on average, warmer colors, indicating higher LOS-Ext values, are seen between LS = 180 – 360° implying low visibility during southern spring and summer.

Figure 2: LOS-Ext Horizontal Variations.

Figure 2:

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LOS-Ext values versus relative location on the crater rim for the period of the observations covering 2.44 MY. The LOS-Ext value is displayed with the color axis. The horizontal axis are degrees from north, with north being 0°. Time is conveyed on the y-axis and reads top to bottom. The three frames represent the 3 different Mars years this data spans: MY31 on the left, MY32 in the middle and MY33 on the right. A) Shows only the data for the images used in this study. B) Interpolates the data in A) to fill in temporal gaps.

It is worth noting that as time progresses, the changes in LOS-Ext across the crater rim appear to change as one. That is, the colors tend to get brighter and darker, indicating increases and decreases in LOS-Ext, as one. This can be seen in the non-interpolated data in Figure 2A, which is suggestive of minimal lateral transport of dust, which would present itself as a spreading out of higher valued LOS-Ext from a singular point. These differences in LOS-Ext across the crater rim are likely due to features on the crater rim itself affecting the illuminating conditions, and not due to varying dust loads across the image. As such, it can be said that the dust suspended within the crater is indeed well-mixed horizontally.

3.3. Vertical Variations

Figure 3 shows the variations in LOS-Ext as a function of height on the crater rim, e.g. method 4. Figure 3A shows this for the images in the dataset and Figure 3B interpolates the data to fill in the temporal gaps.

Figure 3: LOS-Ext Vertical Variations.

Figure 3:

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Vertical distribution of LOS-Ext values as a function of solar longitude for MY32 and MY33. The LOS-Ext value is represented with the color axis, while vertical location on the crater rim is displayed on the y-axis, in meters relative to the crater floor. A) Shows only the data for the images used in this study. B) Interpolates the data in A) to fill in temporal gaps.

Looking at the raw data in Figure 3A it is possible to see some vertical structure but interpolating over the un-sampled times provides a better visualization and is displayed in Figure 3B. Interpolation is a good-enough approximation as to what this dataset would look like if the frequency of observations increased to a per sol basis. This is justified by noticing the gradual increase or decrease in the LOS-Ext seen in the seasonal trend in Figure 1.

Notice in Figure 3B for nearly the entire dataset the LOS-Ext values are maximal at minimal altitude and have a slight gradient of decreasing LOS-Ext with increased altitude. This makes sense as the atmosphere is the thickest at the lowest altitudes, thus a greater capacity to suspend dust at these lower altitudes.

One of the most interesting take-aways from this plot is that the dusty season in MY32 is bookended by a point in time where the LOS-Ext is seasonally low at low altitudes (LS = 200°) and a point in time where the LOS-Ext is seasonally high at low altitudes (LS = 300°). This warrants further investigation as the same phenome does not occur in MY33 on the same magnitude as only a small inversion is seen in MY33 at LS = 215°. This inversion could be suggestive of dust being uplifted from the crater floor and thrown to higher altitudes during the most convective time of day or possibly dust being injected into the crater from the atmosphere above.

4. Discussion

4.1. Geographic Heterogeneity in Line-of-Sight Extinction

Initially, it was thought that variations in the LOS-Ext in a single image would reveal regions in which dust enters and/or leaves the crater. Such locations would have been identified on the plots of Figure 2 as a horizontally spreading of warmer or cooler colors indicating dust entering or leaving the crater, respectively. However, this horizontal movement is not apparent in the dataset and would tend to support the hypothesis that the dust in the northern part of the crater is well mixed horizontally. The variations that do remain likely mark changes in the reflectance from one spot to another on the crater rim. This is more easily seen in Figure 2B where interpolation is used to obtain approximate LOS-Ext values for times in which data is missing.

The same geographic location on the crater rim separated in time should not exhibit seasonal reflectance differences. The data tends to reproduce statistically similar normalized extinction values, meaning higher or lower LOS-Ext are seen in similar locations, suggesting that the horizontal variations in LOS-Ext are due to the features on the crater rim itself. This is further supported by the fact that two regions near each other on the crater rim can vary in LOS-Ext by an order of 50% when comparing a fully illuminated and fully shadowed section of the crater rim. As such, the horizontal variations in LOS-Ext are not considered to be variations in the dust loading of the atmosphere within the crater, but instead due to the physical differences of the crater rim.

It might be possible to resolve this issue by mapping the reflectance along the crater rim on a dust free sol and normalize each image to this map, but it would be difficult as different sunlight geometries have the potential to vary sub-pixel shadows on the crater rim. Further investigation is needed to resolve this issue, and at the moment it is being left as for future study.

4.2. Comparisons to Mastcam

The column opacity from the Mastcam Tau observation at 880 nm are used to determine the amount of dust above the crater. The Mastcam Tau observations are similar to those reported for the Mars Exploration Rovers (Lemmon et al., 2015) and are shown as a function of solar longitude in Figure 4A. The similarity in opacity over the MER Opportunity location in Meridani Planum and MSL is interesting because Curiosity is lower in elevation than Opportunity (Squyres et al., 2004; Vasavada et al., 2014). One would expect that the opacities observed in Gale Crater would be elevated compared to those of the MER sites because MSL is looking through ~2 km more atmosphere but in reality, they are similar valued (Vicente-Retortillo et al., 2016). This has led to the idea that the atmosphere within Gale Crater itself is relatively dust free.

Figure 4: LOS-Ext vs Column-Averaged Extinction.

Figure 4:

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A) Mastcam opacity as a function of solar longitude. B) PBL Depth as a function of solar longitude from MarsWRF simulations. C) Colmun-averaged extinction and LOS-Ext as a function of solar longitude.

We make use of the average peak PBL depths which are derived from MarsWRF (Richardson et al., 2007; Toigo et al., 2012) and the values reported by Guzewich et al. (2017) are used here, which are similar to other models (e.g. Fonseca et al., 2017). These are derived from the high spatial resolution “B” grid MarsWRF simulation described by Newman et al. (2017) for increments of 30° in LS and shown in Figure 4B.

Within the PBL, the extinction is assumed to be constant and are the reported values of LOS-Ext. Multiplying the LOS-Ext by the depth of the PBL gives a proxy for the opacity of dust within the PBL. The opacity due to dust above the crater is determined by subtracting the opacity within the PBL from the Mastcam Tau opacities. This value is then divided by the scale height for dust above the PBL to derive an averaged extinction value for dust above the crater. The dust scale height was determined from observing occultations of Phobos and is on the order of 8.5 km (Mark Lemmon, personal communication).

Figure 4C compares the mean valued LOS-Ext to that of the column-averaged extinction as a function of solar longitude. The LOS-Ext is shown to be slightly less than the column-averaged extinction for the majority of the Martian year save for southern summer LS = 270 – 360° and periods in which the two values converge, seen around LS = 135° and LS = 180° for MY32 and MY33.

The analysis shown here suggests that the atmosphere within Gale Crater is indeed less dusty than the atmosphere above the crater during most seasons, but the opposite is true during southern summer.

4.3. Is Gale Crater a source or a sink for dust in the current era?

Treating Gale Crater as a purely diffuse system it is possible to approximate the rate of diffusion of dust into or out of the atmosphere within the crater.

From Fick’s first law:

J=−Ddϕdx, (4)

where J is the diffusion flux (m−1 s−1), D is the Eddy diffusivity coefficient (m2 s−1), and dϕdx is the change in concentration of dust particles (m2) with depth (m) of the PBL.

In this instance, the eddy diffusion rate is the most important factor to consider as it has the ability to affect the resulting diffusion flux the most. Rodrigo et al. (1990) suggest using a constant value on the order of 2000 m2 s−1 for the Eddy diffusivity coefficient for middle latitudes for altitudes below 90 km. Later, Taylor et al. (2007) ran a 1D PBL simulation to derive Eddy diffusivity as a function of time and altitude in the Martian atmosphere. The study showed that the peak Eddy diffusivity lasted several hours, on order of 20% of a sol, for near-polar latitudes. As such, if the constant value of 2000 m2 s−1 from Rodrigo et al. (1990) is typical of noon-time peak Eddy diffusivity over Gale Crater, and if this peak diffusivity lasts on the order of 20% of a sol in equatorial latitudes as it does in polar latitudes, the average Eddy diffusivity is approximately 400 m2 s−1 sol−1.

A doubling and adding radiative transfer code (Moores et al., 2007) is used to establish a relationship between particle density and observed extinction (or opacity). This assumes the distribution of dust particles can be modeled by a modified Gamma distribution (Hansen and Travis, 1975) which has been used with success on Mars, e.g. using an effective radius of a = 1.6 μm and b = 0.2 would put the modal radius of optically active particles at 0.5 μm (Tomasko et al., 1999).

The derivative,dϕdx, is treated as a constant within the PBL, dϕ is the difference between the extinction above and within the crater, while, dx is the modeled depth of the PBL. A settling rate is obtained from the diffusion flux by assuming the dust would fall out into a simple cubic packing regime, effectively assuming a static atmosphere.

The analysis performed here is shown in Figure 5 as a diffusion rate per sol as a function of solar longitude. Positive and negative rates of diffusion are seen in both Mars years. A positive diffusion rate implies dust is settling into the crater while a negative diffusion rate implies dust lifting. In MY32 were the inversion is seen in the vertical profile around LS = 200° the diffusion rate is positive suggesting dust lifting in this season, whereas in the small inversion seen in MY33 around LS = 215° the diffusion rate is negative suggesting dust being injected into the crater.

Figure 5: Diffusion rate of dust into or out of Gale Crater.

Figure 5:

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A diffusion rate for dust is calculated for Gale Crater by comparing the LOS-Ext and the column-averaged extinction. Cumulative deposition of dust into the crater is seen with approximately 3.5 and 2.7 μm MY-1 for MY32 and MY33 respectively.

Integrating the rate of diffusion yields 3.5 μm per Martian Year (μm MY−1) of dust accumulation within Gale Crater for MY32 and 2.7 μm MY−1 accumulation for MY33. These values are much lower than sedimentation rates obtained at the Mars Pathfinder (40 – 80 μm MY−1; Johnson et al., 2003) and Phoenix (>40 μm MY−1; Drube et al., 2010) landing sites and what the Mars Exploration Rovers, Spirit and Opportunity saw, reporting values on order of 20 μm MY−1 and 16 μm MY−1 for their respective landing sites (Kinch et al., 2007).

Lewis and Aharonson, (2014) suggest 10–100 μm MY−1 for the formation of rhythmites and Borlina et al., (2015) suggest 8–37 μm MY−1 deposition rates were required to create Aeolis Mons.

The accumulated deposition into Gale Crater calculated here seems inconsistent with rates estimated to have existed in the past to match observations seen within Gale Crater, but this is to be expected, as the exercise is looking at the most convective time of day and still sees net positive deposition into the crater.

The exercise shows that within a given year, Gale Crater can have both positive and negative diffusion rates. In the current era, Gale Crater acts as both a sink and a source for dust during the most convective time of day depending on the season.

5. Conclusion

The line-of-sight extinction in the northern portion of Gale Crater is reliably repeatable on an interannual basis. This suggests that the mechanisms responsible for the dust-loading environment of the crater (topography and wind patterns) are consistent, year-over-year. The visibility within the crater is high (e.g. low LOS-Ext) during southern autumn and winter (LS = 0–179°) and low (e.g. high LOS-Ext) during southern spring and summer (LS = 180–359°).

By analyzing the vertical distribution of dust within the crater during the most convective time of day, dust is seen to be lifting from the crater floor. Dust within Gale Crater is not well mixed during the most convective time of day, as a gradient in LOS-Ext exists, exhibiting lower concentrations of dust at higher altitudes within the crater than those near the crater floor.

Comparisons between LOS-Ext and the column-averaged extinction imply a greater dust-mixing ratio exists in the atmosphere above the crater than the air inside the crater for the duration of the Mars year. During each Mars year, similar values between the LOS-Ext and column-averaged extinction are seen near LS = 135° and LS = 180° with LOS-Ext being larger than the column extinction during southern summer (LS = 270–360°). Furthermore, this time frame corresponds to a negative diffusion rate, suggesting that during this season Gale Crater is acting as a source for atmospheric dust.

Highlights.

  • Line-of-sight extinction measurements at Gale Crater, Mars over a span of 2.44 Mars years.

  • Measurements are derived from radiance calibrated Navcam data products from the Mars Science Laboratory.

  • Vertical and horizontal dust profiles are derived for the atmosphere within the crater.

  • Back of the envelope calculation indicative of a sedimentation rate of a few μm MY−1, during the most convective time of day.

6. Acknowledgements

C.A. Moore would like to acknowledge the contributions of the Mars Science Laboratory Participating Scientists Program for access to the science team and rover operations and of the Canadian Space Agency for providing funding for this work.

Appendix

The methods used to aggregate a geographically consistent and distance corrected LOS-Ext dataset are discussed further in this section as they add little to the discussion to the LOS-Ext values and their role in the air within Gale Crater. Appendix A discusses how a virtual camera is created using a digital elevation model. Appendix B discusses how images from the virtual camera and Navcam are compared to arrive at distance zto pixels in another image.

A. Virtual Image

A virtual Navcam image using the Digital Elevation Model (DEM) from HRSC onboard Mars Express is constructed on a per location basis to quantify the path length between the rover and the crater rim. Ideally, these virtual images will look similar to the landscapes portrayed by Navcam. This section will detail the process to create the virtual images, show how well the virtual images are able to recreate the Martian landscape from the rover’s point-of-view.

It is possible to determine the pixel position of the rover on the DEM for every observation. Due to a resolution of 50-m/pixel for the DEM, multiple observations can be represented as the same location on the DEM. As such, a list of unique rover locations on the DEM is compiled, and henceforth referred to as zones. A virtual image is made for the entire dataset. The dataset spans 72 zones.

A subset of the DEM is read into Matlab for each zone consisting of a 45° wedge radiating to the north with the “camera” located at the vertex. To recreate a Navcam Image the DEM is projected onto the surface Mars and elevation data is transformed from physical size to angular size.

The DEM is a flat projection of a curved surface. As such, the effects of Mars’ curvature must be considered as the landscape bends away from the point-of-view of an observer on the surface. In the north-south direction Mars’ polar radius, r♂,p = 3375 km, is used to correct the elevations with the following formula:

ZNS(i,:)=z(i,:)−r♂,p(1−cosθi), (A.1)

where z is the elevation data, (i,:) references the row of the DEM matrix, and the θi term refers to the angle made in reference to the center of Mars from the observation point to the rows in the DEM.

Elevations in the East-West direction are corrected for in a similar way using:

ZEW(:,j)=ZNS(:,j)−r♂,4.6°(1−cosθj), (A.2)

only this time, the radius of a great circle on Mars at the MSL latitude, e.g. r♂,4.6° = 3385 km, is used, j references the columns, and hence θj is the angle made in reference to the center of the great circle between the observation point and the column in the DEM.

To obtain a Martian landscape that an on-the-ground observer may see, the elevation data are converted into angular size. Smaller features close to the observer may have a larger angular size than a large feature at a greater distance. The elevation data are converted to angular size calculated on a pixel-by-pixel basis using:

δ(x,y)=tan−1Δzd(x,y), (A.3)

where, x and y refer to the pixel position (with the set pair [x, y] = [1,1] being the top left corner of the DEM), z is the elevation data from the DEM, Δz is the difference in elevation between the observation point (virtual camera) and the reference point, e.g. Δz = |z(x, y) − z(x◦, y◦)|, and d(x, y) is the distance from the observation point to the reference point, calculated using the Pythagorean theorem and multiplying by the spatial resolution of the DEM.

The last step is to stretch the 45° wedge to fill the virtual camera frame using interpolated elevation values to fill in the gaps. Figure A1 shows the end result, a near perfect representation of the Martian landscape and compares it to that of a Navcam image taken from the same zone. The virtual image and the Navcam image are very similar, albeit offset from one another.

Figure A1: Virtual Image + NCAM DDSM Frame.

Figure A1:

Open in a new tab

This is an example showing how the DEM was able to reproduce the landscape displayed in a DDSM frame. The background (black and white image) is the first frame of the DDSM taken on sol 635. The red line outlining the crater rim is composed of the DEM derived maximum rim height. Above that, floating in the sky is the virtual image generated by the DEM.

B. Derivation of Distances

A correlation between the Navcam frames and the virtual images can be made. The point with the largest angular size within the Navcam frame matches the point with the largest angular size within the virtual image, as seen in Figure A1. An algorithm to determine the distance to specific pixels in the Navcam image is detailed below:

The region starts a known number of pixels below the highest point of the crater rim in the image. The highest peak in the Navcam image is the same as the highest angular size determined from the DEM. As such, to find the region of interest on the DEM, the rows of pixels on the Navcam image need to be converted into an angular elevation using:

δn=δmax−ΘΔhn, (B.1)

here n are the rows from the image we are interested in δmax is the maximum angular height from the DEM, Θ is the vertical angular resolution of the Navcam image, and Δhn = |hmax − hn| is the difference in pixel number between the largest feature and the row of interest.

A series of contour maps are created using the δn as the elevation. Column-by-column, the contour for each elevation closest to the observation point is recorded and a distance is attributed to it, again, using the Pythagorean theorem and the resolution of the DEM.

C. Manual Image Processing Techniques

Due the rover pitch, yaw, and tilt, Navcam may be pointing slightly east or west instead of due north or even tilted up to 10°. This effect on the derived LOS-Ext was determined to be small, as the algorithm collects a mean radiance value from large portions of the image and the variation in the retrieved LOS-Ext was seen to be relatively uniform across the width of each image (Moore et al., 2016). This paper aims to extract a geographically consistent LOS-Ext from the image dataset, as such, it becomes necessary to correct for these offsets. A method of manually rectifying the images to one another is developed which preserves the geography of the crater rim detailed below.

Images are offset from one another in two ways that are easily corrected: rotation and translation. Manual image processing is completed using a combination of Matlab and an open-source image-processing program, GNU Image Manipulation Program (GIMP). The horizon spanning the image is not always parallel to the Navcam optical axis. Thus, it becomes necessary to rotate the images. The images are then translated to align common features to a base image, effectively rectifying the images to one another creating a dataset that is geographically consistent.

The rotation and translation are recorded and fed into Matlab when the images are processed. Figure C1 shows the base image, sol 635, being used to align an image from sol 227. Sol 635 is used as the base image due to its clarity and sharp contrast between the top of the crater rim and the sky.

Curiosity’s general direction of travel is to the southwest away from the north crater rim. As such, the Navcam field-of-view is capable of detecting a larger footprint of the crater rim (approximately 27.5 km on sol 1701 compared to that of approximately 23.5 km on sol 100). This, in turn, decreases the angular height of the crater rim from ≃ 3.5°, or 80 pixels, in the beginning of the mission to ≃ 2.7°, or 62 pixels, as of sol 1701. The change in vertical angular size is not taken into account.

Figure C1: Navcam Image Rectification.

Figure C1:

Open in a new tab

All images in this dataset are aligned to a base image, sol 635. (Top) Sol 635 DDSM image overlays sol 227 DDSM image. (Bottom) Sol 227 DDSM image overlays sol 635 DDSM image. Images were differenced and manually aligned using the GIMP software package.

Footnotes

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