Exploring morphology, layering and formation history of linear terrestrial dunes from radar observations: Implications for Titan

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Exploring morphology, layering and formation history of linear terrestrial dunes from radar observations: Implications for Titan Priyanka Sharmaa,⁎, Essam Heggya,b, Tom G. Farra a b

Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, United States Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089, United States

A R T I C L E I N F O

A B S T R A C T

Keywords: Sahara Dunes Aeolian processes Geomorphology Geophysics Radar SIR-C Radar sounding/Ground Penetrating Radar Radar imaging Titan

Understanding the morphology and internal layering of large aeolian dune fields through radar observations can provide unique insights into the climatic and geophysical conditions that led to their formation. In this study, we perform a large-scale characterization of the morphology and internal layering of linear dunes in hyper-arid areas on Earth, through utilizing multiple complementary radar datasets (SIR-C imaging, SRTM interferometryderived elevations and radar sounding or Ground Penetrating Radar (GPR)). Linear dune fields in the Egyptian desert are of special interest, due to their significance as planetary analogs to dunes on Mars and Saturn's largest moon, Titan. Satellite radar imagery and elevation data of the region show significant variance in the geomorphology of different dune fields in Egypt. In addition, GPR probing of the first few meters suggests different inner settings in the layering of dunes of different ages in eastern and western Egypt, reflecting different paleoclimatic regimes that led to their formation. Furthermore, our radiometric analysis suggests that dunes with different inner layering arrangement also exhibit different radar backscatter returns as a function of their heights. For relatively younger dunes with a homogeneous inner structure, like the ones in eastern Egypt in the Qattaniya dune field, we observe that sigma0 does not change as a function of the dune height. For relatively older dunes in western Egypt like the Great Sand Sea (Northern (Siwa) and Southern dune fields), we observed a linear correlation between sigma0 and the dune height. Thus, surface properties of dunes like morphology and backscatter variation with height are related to inner characteristics like arrangement of internal layering, relative ages and can be used to infer their depositional history. Linear dunes discovered in the equatorial regions of Titan by the Cassini-Huygens mission are morphologically very similar to these linear dune fields in the Egyptian Sahara. Hence, assessing the variability of morphology and radar backscatter properties of Titan's dunes as a function of their heights can help constrain the ambiguities associated with their internal structure and formation history and provide insights into Titan's paleowind regimes.

1. Introduction The Egyptian Sahara occupies the north-eastern edge of the Sahara Desert in Africa. This desert occupies an area of almost 700,000 km2, stretching from the Egyptian-Libyan border on the west to the Nile river on the east, from the Mediterranean Sea in the north to the border of Egypt-Sudan in the south (El-Baz, 1992; Bubenzer et al., 2007a, 2007b; Besler, 2008; Abouelmagd et al., 2012; Telfer and Hesse, 2013). Linear dune fields in the Egyptian desert are key elements in reconstructing recent paleo-climatic winds that steered moist Atlantic/Mediterranean air masses, north of the limit of tropical monsoonal rainfall at 20°N (Brookes, 2003), sustaining early Holocene lakes and playas in the region. The Egyptian Sahara has been extensively studied as an analog to

⁎

planetary aeolian environments (El-Baz, 1981, 1992; El-Baz et al., 1979; Gaber et al., 2009; Kröpelin, 1993; Paillou et al., 2003). Both radar imaging and sounding data have been used for comparisons of terrestrial surface features in the Egyptian Sahara with Mars (Grandjean et al., 2006; Hugenholtz et al., 2012), including dunes (Breed et al., 1979; El-Baz et al., 1979), aeolian bright and dark-colored streaks (ElBaz and Maxwell, 1979), yardangs (El-Baz et al., 1979), dry channels (Breed et al., 1982), surface rock morphology (Garvin et al., 1981) and pits and flutes formed in rocks by wind erosion (McCauley et al., 1979). The Egyptian Sahara thus provides an excellent terrestrial analog for studying planetary aeolian processes and their roles in planetary paleoclimatic reconstruction. Radar characterization of these analogous terrestrial dunes provides crucial field comparisons for planetary dunes

Corresponding author. E-mail addresses: [email protected] (P. Sharma), [email protected] (E. Heggy), [email protected] (T.G. Farr).

http://dx.doi.org/10.1016/j.rse.2017.10.023 Received 15 May 2017; Received in revised form 29 September 2017; Accepted 14 October 2017 0034-4257/ © 2017 Elsevier Inc. All rights reserved.

Please cite this article as: Sharma, P., Remote Sensing of Environment (2017), http://dx.doi.org/10.1016/j.rse.2017.10.023

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Fig. 1. Landsat visible imagery showing locations of three sites of analogous dune fields in Egypt. (1) Southern Great Sand Sea (central/south-western Egypt); (2) Northern Great Sand Sea (Siwa dunes in north-western Egypt) and (3) Qattaniya dunes (northeastern Egypt; west of Cairo). Corresponding SIR-C radar backscatter scenes are also shown.

to be ~5000 years BP, and this provides an upper estimate on the age of the dunes in the Qattaniya dune field which lie to the west of the Nile river valley (Mohamed, 2012). Terrestrial dune fields have been studied in the past with imaging radars (Blom and Elachi, 1981, 1987; Hugenholtz et al., 2012; Lancaster et al., 1992; McCauley et al., 1982). Along with radar images, Ground Penetrating Radar (GPR) or radar sounding data, which rely on the propagation of microwaves through the surface to deduce subsurface layering, have also been used extensively to study the layering and migration of terrestrial dunes (Bristow et al., 2000, 2005, 2007a, 2007b, 2010a, 2010b; Harari, 1996; Heggy et al., 2006a). Radar sounding instruments have also been used on planetary missions (Heggy et al., 2006b; Seu et al., 2007; Picardi et al., 2004; Ono et al., 2010) to examine the subsurface characteristics, especially subsurface water, on Mars and Earth's Moon.

(mostly observed with radar), and can therefore provide unique insights into understanding their geomorphological characteristics, internal layering and formation history, in the absence of in-situ ground validation data for these planetary bodies. We focus on three sites of dune fields in the Egyptian Sahara: 1) Southern Great Sand Sea in central/south-western Egypt, 2) Northern Great Sand Sea (Siwa) dunes in north-western Egypt and 3) Qattaniya dunes in north-eastern Egypt (~ 200 km west of Cairo). Fig. 1 shows the locations of these terrestrial analog dune fields. These large, linear dunes in the Egyptian Sahara have heights of tens of meters to ~100 m, widths of up to a few kilometers and lengths of up to hundreds of kilometers (Lancaster, 1995; Radebaugh et al., 2010). They are thus comparable in size and morphology to the linear dunes observed on Saturn's largest moon, Titan, with the Cassini radar instrument. Although linear dunes have also been observed on Mars, they are not as widespread, compared to other dune types, as on Titan (Edgett and Blumberg, 1994; Bourke et al., 2010). We will therefore only discuss the comparison of terrestrial linear dunes with those on Titan in this study. OSL and radiocarbon dating indicate dunes in the Great Sand Sea to be older (~ 15,000–20,000 years as reported by Bubenzer et al., 2007a, 2007b; INQUA Dunes Atlas project, 2011) compared to the Qattaniya dunes (dune fields in the vicinity of the Nile valley, including the SouthRayan dune field and the neighboring Qattaniya dune field, date back to ~5000 years B.P., based on geomorphological evidence (Mohamed, 2012; Mohamed and Verstraeten, 2012; Verstraeten et al., 2014, 2017)). Although radiocarbon/OSL dating has not been done for the Qattaniya dunes, geomorphological and anthropogenic evidence can be used to prove that these dunes are relatively younger compared to the Great Sand Sea. The Nile river's discharge has reduced drastically several times in its history, but the last time that this occurred is estimated

2. Instruments and datasets For our SAR characterization of the dunes in the Egyptian Sahara, we used C-band (5.8 cm wavelength) backscatter data from the Spaceborne Imaging Radar (SIR)-C, in Multi Look Complex (MLC) format in HH polarization, with a range resolution of 50 m and azimuth resolution of 50 m. A more detailed description of the SIR-C data can be found in Jordan et al. (1995) and Stofan et al. (1995). We have also utilized elevation data with a resolution of 1 arc-second (~ 30 m) from the Shuttle Radar Topography Mission (SRTM) (Blumberg, 2006; Farr et al., 2007). Table 1 shows details of the SIR-C scenes and the corresponding SRTM Digital Elevation Models (DEMs) used for this study. We collected GPR/radar sounding data for the Qattaniya and Siwa dunes (Northern Great Sand Sea) in Egypt during a site visit in 2

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Table 1 SIR-C scenes and corresponding SRTM DEMs used for studying Egyptian dunes. Analog site name Southern Great Southern Great Southern Great Northern Great Qattaniya

Sand Sand Sand Sand

Sea Sea Sea Sea (Siwa)

SIR-C scene ID

Center location coordinates of SIR-C scene

SIR-C incidence angle (°)

SRTM DEM

PR15994/15995 PR15976/15977 PR16160/16161 PR15554/15555 PR46897/46898

26°14′02″N, 26°18′32″N, 25°31′44″N, 28°01′44″N, 30°11′06″N,

24.8 50.38 65 25 54

N26E026 N25E026, N25E026, N27E025, N29E029,

26°44′52″E 26°48′10″E 27°07′30″E 26°10′58″E 30°12′03″E

N26E026, N25E027, N26E027 N25E027 N28E025, N27E026, N28E026 N30E029, N29E030, N30E030

Fig. 2. (a) Location of GPR data profiles over dunes in the Qattaniya and Siwa (Northern Great Sand Sea) dune fields in the Egyptian Sahara.

Qattaniya Siwa

Fig. 3. Field images from site visit to Qattaniya and Siwa dunes in September, 2010 provide views of largescale size of dunes under consideration in this study. Dunes in the Great Sand Sea in Egypt are 50–100 m in height, while the Qattaniya dunes are 10–50 m in height. The image in the bottom right demonstrates the GPR data collection and equipment used (photo credit: Jani Radebaugh and Stephen Phillips).

September 2010. The model of GPR unit used in the field was a RAMAC X3M unit with 500 and 800 MHz antennae, both produced by Mala Inc. GPR data were collected using pulse repetition ground-coupled radar, operating at a central frequency of 0.8 GHz, with bandwidth equal to half of the central frequency, allowing 5 cm vertical resolution and a

penetration depth of 8 m into the dunes. The 0.8 GHz frequency band was associated with a shielded dipole ground coupled antenna. Surface coupling on the dunes was optimal which allowed data collection with high signal-to-noise ratio (SNR). Furthermore, the remote location of the field site allowed very little electromagnetic interference in the 3

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(a) Southern Great Sand Sea

(b)Northern Great Sand Sea (Siwa)

(c) Qattaniya dune field

Fig. 4. Selected topographic profiles across Egyptian dunes. Each inset consists of the SIRC (C-HH) radar backscatter image with profile across dune shown in red. (a) Southern Great Sand Sea (PR15994/15995) (b) Northern Great Sand Sea (Siwa dunes; PR15554/15555) (c) Qattaniya dunes (PR46897/46898) and (d) Corresponding SRTM elevation profiles (meters ASL) are shown. As can be seen in the elevation profiles, the Southern Great Sand Sea dunes lie atop an elevated bedrock compared with the Siwa and Qattaniya dune fields in the lower oases. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

(d) Fig. 5. Figure a shows a GPR radargram at 0.8 GHz for a section of a dune in the Siwa (Northern Great Sand Sea) dune field in western Egypt and Figure b shows a GPR radargram for a dune in the Qattaniya dune field in eastern Egypt. The GPR penetration depth of ~ 8 m is based on average radar ground wave velocity of 0.13 m/ns using a dielectric constant of Ɛeff = 4. In the top figure for the Siwa dune, the radargram shows complex, non-uniform sedimentary structure in the arrangement of layers. In the bottom figure for the Qattaniya dune, we observe the layers to be more homogeneously arranged. Internal layering observed is marked out explicitly in Figures (c) and (d) for the Siwa and Qattaniya dune, respectively.

(a)

(b)

(c)

(d)

4

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Fig. 6. Example of stacked, geo-referenced SIR-C backscatter (PR15994 (L-band)/PR15995 (C-band)), SRTM elevation (N26E026) and SRTM backscatter (Cband) (N26E026) data for dunes in the Southern Great Sand Sea in Egypt (center coordinates of SIR-C scene: 26°14′02″N, 26°44′52″E).

Fig. 7. Example profile across an individual dune in the Southern Great Sand Sea. (a) SIR-C backscatter image (PR15995) of the region with the profile shown in red; (b) Landsat visible imagery of the region; (c) Variation of normalized SIR-C C-band backscatter (C-HH σ0 in dB) and SRTM elevation (in meters) with horizontal distance along profile (in meters); (d) Variation of normalized SIR-C C-band backscatter (C-HH σ0 in dB) with SRTM elevation (in meters) (profile start and end coordinates are 26°23′6″N, 26°40′31″E and 26°23′6″N, 26°40′54″E, respectively). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

(with a greater number of taller dunes, having heights of ~50–100 m) and relatively older (~ 15,000–20,000 years old) as compared to the Qattaniya dune field in eastern Egypt with smaller dunes (fewer dunes and dunes of shorter heights of ~ 10–50 m) that are relatively younger (upper estimate of their age is approximately 5000 years). The Qattaniya dunes are fewer, smaller and more widely spaced from each other and appear to lie directly on the bedrock. This is distinct from the dunes in the Great Sand Sea which we studied, which are encompassed within large sand seas, wherein dunes lie atop a sandy substrate (although even sand seas can have rocky interdunes and bare bedrock, as observed in some other parts of the Saharan sand seas). A diverse set of morphologies are observed on comparison of SIR-C radar images of the dunes in the Northern Great Sand Sea (Siwa) with those in the Southern Great Sand Sea and the Qattaniya dunes. In particular, dunes in the Northern Great Sand Sea (Siwa) are highly irregular in form and not very parallel, long or straight. This may be an effect of the Siwa Oasis nearby, in the form of possible disruption of the dune forms through fluid interactions or the result of a variable wind regime. In contrast, dunes in the Southern Great Sand Sea are more

collected data, resulting in good radiometric accuracy of the subsurface reflectors. GPR profiles were collected perpendicular to the long axis of the dunes, obtained from one interdune to the summit along the slope. Fig. 2 shows locations where the GPR data were collected in the field. The GPR profiles cross over the easternmost dune of the Qattaniya field (centered at ~29.85°N, 30.28°E) and also over one of the dunes in the Siwa field (centered at ~28.87°N, 25.20°E). Fig. 3 shows some field images from our visit to the Siwa and Qattaniya dune fields. We processed the GPR data using the Reflexw geo-physical near-surface processing and interpretation package, produced by Sandmeier Geophysical Research. 3. Geomorphology and internal layering of dunes in the Egyptian Sahara The three terrestrial sites in Egypt under consideration in this study were carefully chosen to provide a fair comparison of terrestrial dunes of different sizes with dunes on Titan. Dunes in the Great Sand Sea (Southern and Northern (Siwa) dune fields) in western Egypt are larger 5

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Fig. 8. Example profile across multiple dunes in the Southern Great Sand Sea. (top left) SIR-C backscatter image (PR15995) of the region with the profile shown in red; (top right) Landsat visible imagery of the region; (bottom) Variation of normalized SIR-C C-band backscatter (C-HH σ0 in dB) and SRTM elevation (in meters) with horizontal distance along profile (in km); (profile start and end coordinates are 26°14′18″N, 26°39′1″E and 26°14′50″N, 26°50′47″E, respectively). From the plots at the bottom, we can deduce that the dunes (higher elevations) correspond to lower radar backscatter or dips in the σ0 versus distance plot and thus dunes appear darker in SIR-C backscatter images. On the other hand, the inter-dunes (lower elevations) correspond to higher radar backscatter or peaks in the σ0 versus distance plot and thus, inter-dunes appear brighter in SIR-C backscatter images. It is to be noted that dune peaks appear brighter in comparison with the rest of the dune due to orientation effects. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Siwa (Northern Great Sand Sea)

Southern Great Sand Sea

(a)

(b)

Fig. 9. Variation of SIR-C normalized (C-HH) radar backscatter (σ0 in dB) with SRTM elevation (in meters). (a) Southern Great Sand Sea (PR15994/15995; inc = 24.8°); (b) Siwa (Northern Great Sand Sea) dunes (PR15554/ 15555; inc = 25°); and (c) Qattaniya dunes (PR46897/46898; inc = 54°). Reflections from slip faces of dunes contribute to the scatter observed in the plots. Relatively older and larger dunes in the Northern and Southern Great Sand Sea with more crossbedded internal layering (as observed in our GPR data), encounter relatively more reflective interfaces at any depth, and thus demonstrate increasing radar backscatter with increasing height along dune profile. On the other hand, relatively younger and smaller dunes like the ones in eastern Egypt in the Qattaniya dune field, have a more homogeneous arrangement of inner sedimentary layers and show little to no variation in the backscatter with dune height.

Qattaniya

(c) linear and regular in form. Fig. 4 shows high-resolution topographic profiles (from the Shuttle Radar Topography Mission (SRTM)) across some example dunes in the Egyptian desert. The summits of the

Qattaniya Dunes are modified into crescents along the dune long axis from dominant, northerly winds operating on a NNW-trending crestline. In the Great Sand Sea of western Egypt, the gross morphology of 6

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0.047

the dunes appears to have formed in the late Pleistocene under a different climate regime, while the upper parts of the dunes exhibit complex active slip faces (Haynes, 1982; Lancaster, 1995). Radar images of these dunes are very sensitive to the geometry of the slip faces and lower-angle exposed base or plinth, which reflect specularly depending on illumination direction and incidence angle (Blom and Elachi, 1981, 1987). Some of the radar energy also appears to penetrate the dry sand, a process most likely taking place on Titan as well (Lorenz et al., 2006; Paillou et al., 2014). GPR surveys of terrestrial linear dunes, combined with trench digging on site, have provided insight into the stratigraphy within these aeolian features on Earth (Bristow et al., 1996, 2000; Heggy et al., 2006a). Subsurface reflections observed in GPR radargrams are a result of multiple sand deposition and erosion events that form each dune. The observed layering and inner stratigraphic characteristics indicate the dune formation episodes as a function of the wind regimes, amplitudes and directions (Bristow et al., 1996). The inferred layering can be interpreted based on cross-cutting relationships and law of superposition, to deduce the order of deposition of strata (Bagnold, 1941; Bristow et al., 2000, 2005, 2007a, 2007b; Hesse, 2016; McKee and Tibbitts, 1964; Rubin and Hunter, 1985; Rubin, 1990; Tsoar, 1982). This implies that at any depth, dunes that have a more complex arrangement of internal layers reflect formation over multiple sedimentation episodes. This would be in contrast to dunes that would have an inner layering with a more uniform arrangement of layers at the same depth, indicating that these dunes have experienced fewer variations in wind regimes (Bristow et al., 2000; Heggy et al., 2006a). The GPR data collected by our team provide evidence for this difference in the internal sedimentary structures between relatively older dunes in western Egypt in the Siwa (Northern Great Sand Sea) dune field and younger dunes in eastern Egypt in the Qattaniya dune field. GPR radargrams over a section of a dune in the Siwa dune field and a dune in the Qattaniya dune field in Egypt are shown in Fig. 5. Both dunes are observed to be layered in the first 8 m of the subsurface (penetration depth for the GPR data); however, the internal layers in the dune in the Siwa dune field are observed to be more inclined and cross-bedded, and arranged in a more non-uniform manner, indicating wind reversals and a more complex formation history, as compared to the dune in the Qattaniya dune field with layers arranged almost parallel to one another, indicative of a more consistent wind regime. These different radargrams clearly show stratigraphic differences between dunes of different relative ages from different dune fields.

1253

1692

1200

24.8

25

54

Southern Great Sand Sea (PR15994/15995) Siwa (Northern Great Sand Sea) (PR15554/15555) Qattaniya (PR46897/46898)

− 40.71 ± 4.0 − 40.09 ± 0.48 − 0.004 ± 0.003

− 0.038

0.039 − 24.58 ± 3.7 − 32.72 ± 0.69 0.058 ± 0.005

0.277

0.046 − 25.98 ± 4.7 − 47.07 ± 1.78 0.065 ± 0.005

0.32

Normalized radar backscatter (dB) Regression intercept Regression slope Number of data point pairs (N) Incidence angle (°) Dune field site

Table 2 Statistical parameters for variation of SIR-C (C-HH) normalized radar backscatter (σ0 in dB) and SRTM elevation (in meters) for terrestrial dunes.

Pearson's correlation coefficient (ρobs) for backscatter-height dependency

Critical values of Pearson's correlation coefficient (ρcrit) at significance level (α) = 0.05, N > 1000

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4. Variation of SAR backscatter with elevation across dunes We used the ENVI software for processing all of the radar imaging datasets used in this study. Depending on the spatial extent of the SIR-C scenes, we first mosaicked multiple SRTM DEM tiles to cover the same area. We then used SRTM C-band backscatter data (1 arc-second/30 m resolution) to provide Ground Control Points (GCPs) and co-register the SIR-C scenes with the SRTM DEMs (the SRTM DEMs could not be directly used for the co-registration due to the difficulty with visually colocating tie points from elevation data). Next, we warped the SIR-C image onto the SRTM DEM mosaic, resulting in backscatter and elevation data at the same resolution. Finally, we stacked layers of the SIRC C-band backscatter data, SRTM elevation data and SRTM C-band backscatter data (Fig. 6 shows an example stack for dunes in the Southern Great Sand Sea). For each site, we then selected 35 profiles traversing individual dunes and extracted the corresponding backscatter and elevation data (‘profile’ refers to a selection of radar backscatter and corresponding elevation measurements). The radar backscatter data was normalized (divided by incidence angle cosine, assuming a horizontal surface) to take into account the effect of the incidence angle (Clapp, 1946; Ulaby et al., 1982). We then examined the variation of the C-band backscatter data in HH polarization with elevation across the dunes. Figs. 7 and 8 7

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inc = 24.8°

Fig. 10. Effect of incidence angle on variation of SIR-C normalized (C-HH) radar backscatter (σ0 in dB) with SRTM elevation (in meters). (a) Great Sand Sea (PR15994/15995; inc = 24.8°); (b) Great Sand Sea (PR15976/15977; inc = 50°); (c) Great Sand Sea (PR16160/16161; inc = 65°). We find the overall correlation between backscatter and height along dune profile remains positive, irrespective of the change in incidence angle.

inc = 50°

a

b inc = 65°

c

exact number of data point pairs used for each site). To test for positive correlation in the case of Southern and Northern (Siwa) Great Sand Sea dunes (at different incidence angles), we employed a one-tailed or directional test with the null hypothesis (H0): ρactual ≤ 0 and the alternate hypothesis (H1): ρactual > 0. For each of these positive correlation cases, we found ρobs > ρcrit, which allowed us to reject the null hypothesis and confirm the statistical significance of the observed positive correlation. In fact, there is less than 0.05% probability that our calculated ρobs values would be observed by chance, for each of our positive correlation cases. At the other end of the spectrum, for the smaller Qattaniya dunes with a slightly negative trend of backscatter versus dune height, we first carried out a one-tailed or directional test in the opposite direction, with the null hypothesis (H0): ρactual ≥ 0 and the alternate hypothesis (H1): ρactual < 0. We found ρobs > − ρcrit, which implies that the null hypothesis cannot be rejected with certainty. We followed this up with a two-tailed or non-directional test, with the null hypothesis (H0): ρactual = 0 and the alternate hypothesis (H1): ρactual ≠ 0. We found │ρobs│ < │ρcrit│, which again does not allow for rejection of the null hypothesis and suggests there is no/minimal correlation between the observed backscatter and height along dune profile for the Qattaniya dunes. This radar backscatter analysis, along with the statistical tests performed, thus shows a difference in the observed radar backscatter for dunes of different ages in different dune fields in Egypt, in addition to the difference in internal sedimentary layering observed in our GPR data, as described in the previous section.

show the variation of SIR-C backscatter and SRTM elevation with distance along the profile across an example individual dune and multiple dunes, respectively. In total, we delineated 170 profiles over dunes in Egypt: 105 in the Southern Great Sand Sea (35 each corresponding to three different incidence angles, to test the effect of varying incidence angle on backscatter-height dependency), 35 over Siwa dunes in the Northern Great Sand Sea and 30 over Qattaniya dunes. Along with examining the variation of radar backscatter with elevation over small scales for individual profiles, we also collated our measurements for dunes in each of the three different fields and investigated the relation between backscatter and elevation over regional scales. Fig. 9 shows our results corresponding to each SIR-C scene in each of the three dune fields. We found that for the relatively older dunes in western Egypt with heights of 50–100 m or so, like the ones in the Great Sand Sea (Southern and Northern Siwa), the backscatter shows a positive dependence on elevation (indicated by the positive regression slope and positive Pearson's correlation coefficient (ρobs)). On the other hand, for relatively younger Qattaniya dunes in eastern Egypt, the backscatter shows very weak/ almost no variation with elevation (indicated by the small negative regression slope and negative Pearson's correlation coefficient (ρobs)). Table 2 lists values of the slope, intercept and Pearson correlation coefficient for the relation between the C-HH radar backscatter and elevation for each of these cases. Backscatter-height relations for dunes in the Southern Great Sand Sea observed at different incidence angles are quantified in Fig. 10 and Table 3, and we find varying incidence angle to have minimal effect on the regression slope, while the correlation coefficient is not affected at all. To assess the statistical significance of the correlation between backscatter versus dune height, we compared our calculated Pearson correlation coefficients (ρobs) with critical values of the coefficient (ρcrit) at a certain required level of significance (α) (Press et al., 2007). A probability of occurrence by chance of 5% (α = 0.05) is considered the usual cutoff for statistical significance. An estimate of the Pearson correlation coefficient higher than the critical value, combined with a small α, indicates strong correlation (positive or negative, depending on the sign of the Pearson correlation coefficient) between the two datasets. For each of our terrestrial sites, more than 1000 pairs of backscatter-height points were used for the analysis (Tables 2 and 3 list the

4.1. Possible hypothesis for observed difference in inner layering and radar backscatter of terrestrial dunes Each individual sand dune consists of multiple aeolian deposits or sets of cross-stratification, with each unit corresponding to a period of active deposition due to a consistent wind regime. The bounding surfaces of these sets indicate periods of reversal of predominant wind direction and slower or non-deposition of sand (Bristow et al., 1996, 2005, 2007a, 2007b). With time, as climate and predominant wind directions change, more sets of cross-stratification build up, with the strata at the top being the youngest, and those at the bottom being the oldest (assuming there is minimal lateral migration of the dune). We hypothesize that the difference in the internal layering of dunes 8

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0.044

influences the observed surface radar backscatter (assuming the SIR-C penetration depth to be ~10 times the C-band wavelength, i.e., ~60 cm) (Elachi, 1987; Campbell, 2002). The internal layers encountered by the incident microwaves would lead to variation in the observed backscatter with changing height along the dune topographic profile. As suggested in Fig. 11, for dunes consisting of inclined and/or cross-bedded internal sedimentary layers arranged in a more complex/ heterogeneous manner (like the ones in western Egypt in Northern Great Sand Sea (Siwa) and Southern Great Sand Sea), the observed radar backscatter should vary with dune height due to reflections from multiple interfaces between the layers. In the case of dunes with a more homogeneous arrangement of internal layers, and thus probably formed by fewer variations in paleo-wind regimes (like the ones in eastern Egypt in the Qattaniya dune field), the incident radar waves will encounter fewer or no layer interfaces for the same penetration depth, resulting in negligible variation of the radar backscatter with changing dune height. As a result, the observed radar backscatter should exhibit a strong positive correlation with height along the dune profile for more heterogeneously-layered dunes, while the backscatter-height dependence will be negative or non-existent for dunes with substrates arranged more or less parallel to each other. In other words, complex paleo-climatic conditions that consist of multiple variations in the wind regimes, lead to heterogeneous inner layering in dunes, which then leads to variable observed radar backscatter with height. Our analysis of SIR-C radar backscatter data for dunes in the Egyptian Sahara does indeed demonstrate this pattern, indicating that variations in dune morphology/backscatter characteristics are related to differences in internal dune setting and layering. Thus, by examining the variation of SAR backscatter with elevation along dunes, it might be possible to qualitatively assess their internal layering and constrain the ambiguities associated with the occurrence and succession of paleo-wind regimes that led to their formation. There are some inherent assumptions associated with the hypothesis that we state here. Firstly, we assume that our selected backscatterheight profiles are representative of all dune fields under consideration in this study, including the Southern and Northern Great Sand Sea and Qattaniya dune fields on Earth. We mitigate the effect of this assumption by selecting a large number of profiles (170 over terrestrial dunes in Egypt), each consisting of tens of data point pairs. Next, we assume negligible liquid/salt content, which would affect the effective dielectric constant, for both the terrestrial and Titanian dunes under consideration in this study. Liquid and salt content only play an important role in affecting the radar backscatter for coastal dunes, not for dunes like the ones in the Egyptian Sahara, which are desiccated with negligible water content (El-Baz, 1992). The low dielectric constant for Titan's dunes measured through Cassini scatterometry/radiometry (Paganelli et al., 2007; Wye et al., 2007) also indicates no significant liquid component for Titan's dunes. Finally, we assume that along the short length of our profiles across the dunes, no factors other than the volume scattering (which primarily depends on the number of internal layers encountered by the incident microwaves) vary substantially. This is because surface ripples are constant along dune profiles and thus there is not any appreciable change in surface roughness at the radar wavelength scale that could affect the observed backscatter. Surface scattering will therefore not vary much along the dune profile length and as a result, any variation that we observe in the radar backscatter with height across dune profile should primarily come from variation in the volume backscatter. Thus, by combining the backscatter data with elevation at several points along the dune profile, we can investigate the internal sedimentary structures of dunes on Earth and validate it with GPR measurements.

−64.7 ± 3.9 1405 65

0.013 ± 0.002

− 70.57 ± 0.73

0.21

0.046 −44.44 ± 5.5 1253 50

0.065 ± 0.006

− 65.71 ± 2.11

0.27

0.046 −25.98 ± 4.7 1253 24.8

Great Sand Sea (PR15994/15995) Great Sand Sea (PR15976/15977) Great Sand Sea (PR16160/16161)

0.065 ± 0.005

− 47.07 ± 1.78

0.32

Critical values of Pearson's correlation coefficient (ρcrit) at significance level (α) = 0.05, N > 1000 Pearson's correlation coefficient (ρobs) for backscatter-height dependency Normalized radar backscatter (dB) Regression intercept Regression slope Number of data point pairs (N) Incidence angle (°) Dune field site

Table 3 Effect of variation of incidence angle on measured radar backscatter is demonstrated in this table. Statistical parameters for variation of SIR-C (C-HH) normalized radar backscatter (σ0 in dB) and SRTM elevation (in meters) for dunes in the Southern Great Sand Sea (for different incidence angles) are shown. We find that although the regression slope of the backscatter versus height dependence varies slightly with changing incidence angle (this is expected because of normalization by cosine of the incidence angle), the overall correlation remains positive and confirms the robustness of the increasing trend of the backscatter with height along dune profile for larger and relatively older dunes in the Southern Great Sand Sea.

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5. Conclusions The aim of this study was to investigate the morphology and internal layering of linear terrestrial dunes, through the use of 9

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Fig. 11. Effect of internal layering on relation between observed radar backscatter and dune height. Dunes with different internal structures are considered (left panel). Zoomed-in view of GPR data for top 2 meters of dunes from Fig. 5 is shown, to focus on internal layering corresponding to SIR-C penetration depth of ~ 60 cm. (Middle panel) Model for inner layering of dunes is presented, based on GPR data (Right panel) Hypothesis for variation of radar backscatter versus elevation for different types of dunes. For relatively older dunes with a complex arrangement of inner layering formed my multiple wind regime changes, more interfaces would be encountered by incident radar waves, leading to more reflections and greater variation in the observed backscatter. In the case of younger dunes with homogeneous arrangement of internal layers formed by a relatively consistent wind regime, there would be little to no increase in the number of layer interfaces encountered by the incident microwaves with increasing height along a dune profile, and so the backscatter would not vary significantly with elevation. Fig. 12. Dunes on Titan observed in Cassini SAR swaths. (Top) Planetary photojournal product ID PIA14500 acquired during the T77 Titan flyby on June 21, 2011. Image covers 350 km by 930 km, centered at 11°N, 74°W. Incidence angle varies between 15°–30°. (Bottom) Planetary photojournal product ID PIA11802 acquired during the T49 Titan flyby on Dec 21, 2008. Image covers 220 km by 170 km, centered at 19.2°S, 257.4°W. Incidence angle is ~ 25°. Resolution in both images is ~ 350 m/pix. Image credit: NASA/JPLCaltech/ASI/Space Science Institute.

these dune fields are accompanied by differences in internal sedimentary structures observed in our Ground Penetrating Radar (GPR) survey data. GPR data show contrast between the inner layering of relatively older dunes in the Siwa dune field in western Egypt versus the younger Qattaniya dunes in eastern Egypt, with the Siwa dunes consisting of

complementary radar datasets (imaging, interferometry-derived elevations and radar sounding). We focused on three sites of linear dune fields in the Egyptian Sahara: Northern (Siwa) and Southern Great Sand Sea in western Egypt and the Qattaniya dune field in eastern Egypt. Geomorphological differences based on SIR-C radar imagery amongst 10

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Egypt. © 2017 California Institute of Technology. Government sponsorship acknowledged.

internal layers arranged in a more complex and heterogeneous manner, as compared to the Qattaniya dunes at the same depth. This indicates more variations in the paleo-climatic regimes that formed the Siwa dunes than the Qattaniya dunes. In addition, we compared the variation of SIR-C SAR backscatter with SRTM-derived elevation along dune profile over individual dunes. Older dunes in the Great Sand Sea (Southern and Northern) show a strong positive correlation between backscatter and height while the relatively younger dunes in the Qattaniya dune field exhibit a weaker negative correlation. Based on this analysis, we propose that dune age and depositional history are related to and can be inferred from differences in internal sedimentary layering and variation of observed radar backscatter with height along dune profile. The technique developed in this study for examining the linear dunes on Earth could have implications for investigating the internal layering, relative ages and formation history of dunes on other planets and moons, most notably, the analogous linear dunes on Titan. Images obtained by the Cassini Synthetic Aperture Radar (SAR) (Elachi et al., 2004), Visual and Infrared Mapping Spectrometer (VIMS) (Brown et al., 2004) and Imaging Science Subsystem (ISS) (Porco et al., 2005) have depicted the manifestation of aeolian or wind-driven processes at work, in the form of extensive dune fields in Titan's equatorial regions (Arnold et al., 2012; Barnes et al., 2008; Lancaster, 2006; Le Gall et al., 2011; Lorenz and Radebaugh, 2009; Lorenz et al., 2006; Neish et al., 2010; Radebaugh et al., 2008, 2010). The near-parallel, radar-dark linear features on Titan have a typical spacing of ~1–2 km, with heights of ~ 100–150 m, lengths of many tens of kilometers and slopes of 6° to 10° from radarclinometry (Arnold et al., 2011; Lorenz et al., 2006; Mills et al., 2012) (Fig. 12). These features have been classified as linear dunes and compared with terrestrial longitudinal dune fields like the ones in Namib desert in western Africa (Lancaster, 2006; Neish et al., 2010; Radebaugh et al., 2008, 2010). This comparison is based on the overall parallel orientation of Titan's dunes to the predominant wind direction on Titan, their superposition on other features and the way they wrap around topographic obstacles. Based on areal extents determined from radar (SAR) and visible (ISS) images, the largest dune fields on Titan have been named as Aztlan, Belet, Fensal, Senkyo and Shangri-La (Le Gall et al., 2011, 2012; Arnold et al., 2011, 2012). Although the morphology of Titan's dunes has been studied from Cassini SAR images, it has not been possible to investigate their internal layering and the paleo-climate that formed them in detail as of yet. The single polarization (HH, implying the instrument transmits and receives Horizontal polarization), Ku-band (13.7 GHz, 2.17 cm wavelength), Cassini SAR data currently available for Titan, solely do not provide enough information to examine the layering and consequently, formation history of the dunes on Titan. Recent studies attempting to model SAR backscatter of Titan's dunes point to differences in morphology and physical characteristics of not only dunes from different dune fields, but also between dune and interdune areas (Le Gall et al., 2014; Paillou et al., 2014). Such backscatter modeling studies could be complemented in the future by application of the technique presented in this article. Variations in morphologies and radar backscatter-elevation dependence between dunes from different aeolian fields on Titan could potentially be used to predict differences in internal layering of these dunes, and by extension, contribute to a better understanding of the paleo-climatic variations that led to their formation.

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Acknowledgements We are grateful to the Keck Institute of Space Studies for their financial support for this study. Part of this work was supported by NASA Planetary Geology and Geophysics grant, NNXZ08AKA2G. The research described here was carried out in part at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. We thank Jani Radebaugh and Stephen Phillips for providing their in-situ images from the site visit to 11

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