Comparison of Morphological Characteristics of Terrestrial and Martian Barchans

Abstract

<p>Barchans represent a common dune type found on Earth and Mars. Their morphological characteristics are singular and easily recognized. Their formation is favored on relatively immobile substrates with near-unidirectional winds that sculpt the distinctive crescentic, aerodynamic morphology. Barchans often occur isolated from one another, although they can occur in organized sets or barchanoid dune fields.  Long and Sharp (1964) and Bourke and Goudie (2009) measured attributes of barchan morphology and identified four archetypal shapes based on the ratio of the length of the stoss slope to the distance between the ends of the horns.</p><p>            In this study, we report findings based on measurements of 3,406 barchans: 2,686 from 20 terrestrial dune fields and 720 from 10 Martian dune fields. Barchan morphology was characterized by six metrics: body length (L1), measured from the upwind nose of the barchan to the nearest base of the slipface; total length (L2) measured to the (average) ends of the horns; body width (W1), measured on a line perpendicular to L1 and intersecting at the base of the slipface; horn-to-horn width (W2), measured perpendicular to L2 and parallel to W1; and horn lengths (H1 and H2) measured perpendicular to W1. The morphometric data were used to develop three new shape metrics as a basis for barchan shape characterization: 1) a width ratio (WR: W1/W2); 2) a length ratio (LR: L1/L2); and 3) a symmetry ratio (SR: longer horn length/shorter horn length). The barchan stereotype (Type 1) was defined as meeting three criteria: SR between 1.0–1.2, WR between 0.95-1.58 (mean value +/- one standard deviation) and LR between 0.52–0.76. Cluster analysis was used to define three additional characteristic shapes. Type 2 barchans are moderately symmetrical ( =1.47), uniform in width (  = 1.01), and elongated (  = 0.53). Type 3 barchans are moderately symmetrical (  = 1.4), with converging horns (  = 1.56), and compact (  = 0.74). Type 4 barchans are asymmetric (  = 3.46) uniform in width (  = 1.15) and average elongation (  = 0.64).</p><p>            We found that, on average, terrestrial barchans are shorter, proportionately wider, and more symmetric than those on Mars. Most barchans are Type 1, 2, or 3 (26%, 32%, and 35%, respectively), and relatively few are Type 4 (8%). The distributions of types, however, is quite different for the two planets. On Earth, most barchans are Type 2 (38%) and Type 1, stereotypical barchans comprise 30% of our samples. Type 4 barchans are least common (6%). On Mars, most barchans are Type 3 (64%). The distributions of Types 1, 2, and 4 are similar. Type 1, stereotypical barchans, the least common on Mars, comprise 11% of our samples, and Types 2 and 4 each represent 13% of our samples. These results indicate that most barchans do not conform to our idealized morphological image on either Earth or Mars. In our sample, Martian barchans are larger than terrestrial, with shapes characterized largely by asymmetric, converging horns.</p>

A Simple Agent‐Based Model That Reproduces All Types of Barchan Interactions

“…The parameter λ 1 is the proportionality constant relating the length and width of the main body. Based upon field data (Sherman et al., 2021) we set λ 1 = 1.5. The dunes' central axes are fixed parallel with the dominant wind direction, the positive x ‐direction.…”

“…Downwind of the body, each flank extends into a horn, with the streamwise distance from toe to the horn‐tip proportional to the flank‐width L l , r = λ 2 W l , r . From field data (Sherman et al., 2021) we set λ 2 = 2.5 The y ‐coordinate of the horn‐tip extends half a horn‐width H l , r from the respective edge of the dune. We use an existing expression for the scaling of horn and flank‐widths $$${H}_{l,r}=\alpha {W}_{l,r}+{\Delta }/2,$$$ with α = 0.05, and Δ = 4.6 m (Hersen et al., 2004; Worman et al., 2013).…”

Barchan swarm dynamics from a Two-Flank Agent-Based Model

“…The size of the dune is represented by the widths W p,s of the port and starboard flanks. The widest point of the dune occurs a distance λ 1 (W p + W s )/2 downwind of the toe, where we use λ 1 = 1 based on comparison with an existing dune dataset (Sherman et al, 2021). The total lengths of the flanks, from toe to tip of the horn, are assumed to be proportional to their widths L p,s = λ 2 W p,s where we use λ 2 = 1.8 based on real-world dunes (Sherman et al, 2021).…”

“…The widest point of the dune occurs a distance λ 1 (W p + W s )/2 downwind of the toe, where we use λ 1 = 1 based on comparison with an existing dune dataset (Sherman et al, 2021). The total lengths of the flanks, from toe to tip of the horn, are assumed to be proportional to their widths L p,s = λ 2 W p,s where we use λ 2 = 1.8 based on real-world dunes (Sherman et al, 2021). The width of each horn is a linear function of the flank-width H p,s = αW p,s + ∆/2 with α = 0.05 and ∆ = 4.6m (Hersen et al, 2004;Worman et al, 2013).…”