of 29
Supplementary Materials for
Wave ripples formed in ancient, ice-free lakes in Gale crater, Mars
Claire A. Mondro
et al.
Corresponding author: Claire A. Mondro, cmondro@caltech.edu
Sci. Adv.
11
, eadr0010 (2025)
DOI: 10.1126/sciadv.adr0010
This PDF file includes:
Supplementary Text S1 to S4
Figs. S1 to S6
Tables S1 and S2
References
Supplementary Text
S1. Instruments and Imaging
Curiosity imaged the Prow outcrop in detail from multiple positions, including up
-close
orthogonal views of the cm-scale ripples in two locations. All Mast Camera (Mastcam) image
mosaics included in this manuscript were processed by Malin Space Science Systems (MSSS)
using the routine workflow that is applied to all Mastcam mosaics, which includes standardized
radiometric and geometric calibrations and a color balance correction as part of the mosaicking
process (
5
8
).
Morphology measurements on Mars Hand Lens Imager (MAHLI) and Chemistry &
Camera (ChemCam) long distance Remote Micro Imager (LD-RMI) image data (
59
) were made
in pixels and converted to distances by the pixel resolution of each image. Pixel resolutions of
the MAHLI images were calculated from the image scale bar that is provided on images
processed by the MAHLI team. Pixel resolutions of the LD-RMI images were calculated from
the ChemCam camera instantaneous field of view (iFOV) and the distance from camera to target.
The orientation of ripple crests was estimated using Navigation Camera (Navcam)
stereomesh data products (
60
). Ripple crest orientations were estimated along the top of each
outcrop in plan view (uncertainty of ±10°). The orientation of the Amapari Marker Band (AMB)
and Prow outcrops at the locations where ripples were observed was measured on georeferenced
High Resolution Imaging Science Experiment (HiRISE) orbiter image data (uncertainty of ±10°)
displayed in the Multi-Mission Geographic Information System (MMGIS) program (
61
-6 3
).
Identification and measurement of grain size was performed using MAHLI image data.
The lower limit of resolution of MAHLI images in ~60 μm/pixel (
36
) and the smallest grain size
that is confidently detectable in these images is ~180 μm in diameter, or the size of fine sand. If
no grains are detectable in MAHLI images, the grain size is assumed to be < 180 μm.
S2. Ripple Measurements
AMB grains are not detectable in MAHLI images but must be large enough to form
ripples (i.e. larger than silt-size). Therefore, the grain size of the AMB ripples is assumed to be
between 60
180 μm, or very fine to fine sand. Individual sand grains are visible in the MAHLI
images of the Sumuru target at the Prow (Fig S4).
Point counting within a subset of the highest-
resolution image produced a grain size range of 140
1000 μm (D
50
= 389 μm; medium sand).
Ripple crest orientation was only visible and measurable in one location along the Prow
and at two adjacent locations at the AMB. The Prow ripple crest orientation was measured within
the same layer that contains the ripples used for morphologic analysis, but ~2 m away from
where ripple morphology was measured. The AMB ripple crest orientation was measured along
the top of the uppermost ripple layer ~4 m away from the ripples used for morphologic analysis,
along which a visual assessment of outcrop character indicates that the ripple orientation is
largely consistent. At both the Prow and AMB locations, ripple crest orientation is approximately
orthogonal to outcrop orientation (Tables S1, S2).
Ripple wavelength (λ) is defined as the horizontal distance between adjacent ripple crests,
measured parallel to bedding. Wavelength measurements, including mean and range for each
ripple population, are included in Tables S1 and S2. Because ripple crests at both the AMB and
the Prow are approximately orthogonal to the orientation of the outcrop, the measured
wavelength is very similar to the true wavelength. Non-orthogonal wavelength measurements
would increase the measured wavelength (
λ
m
) relative to
the true wavelength (λ
t
). Assuming a
maximum potential uncertainty in orientation measurements of up to 20°, we calculated the
percent change in wavelength to assess the effect of the orientation uncertainties on wavelength
measurements. A 20° change in the angle between ripple crest and outcrop orientation produces
a λ
t
that is 6% smaller than the
λ
m
, where
cos
(
20°
)
=
λ
t
λ
m
(1)
and therefore
λ
t
= λ
m
×0. 94
.
(2)
For the AMB ripples, this correction shifts the wavelength range to 3.6 cm
5.0 cm
(mean λ
t
= 4.18 cm). For the Prow ripples, this correction shifts the wavelength range to 3.27 cm
– 5.5 cm (mean λ
t
= 4.4 cm). The corrected wavelengths do not contribute to any significant
change in the morphology interpretation of the ripples. Because the difference is small and the
corrections are based on the maximum combined uncertainty from the orientation measurements,
where the true correction within that range is unknown, we use the measured wavelengths
throughout the manuscript text to describe ripple morphology.
The symmetry index of a ripple is defined as the horizontal distance from trough to crest
on the left side, divided by the horizontal distance from trough to crest on right side, where
distances are measured laterally, parallel to bedding. Symmetry index is often measured as a
ratio of the stoss side to lee side (
3
9
) but in the case of the AMB and the Prow, the ripples are
symmetric enough that the stoss and lee sides are not immediately discernible. Therefore, we
kept the measurements consistent as left over right within the view angle towards the outcrop.
Keeping the ratio consistent in this way also allowed us to confirm that there is no consistent
direction of asymmetry.
Wave ripples have a symmetry index of < 1.5, combined flow ripples have a symmetry
index between 1.5 and 3.0, and current-dominated ripples have a symmetry index >3.0 (
3
9
).
These values assume the symmetry index is measured as the ratio of stoss to lee side (where the
minimum possible value is 1.0). When stoss and lee sides are not differentiated, wave ripples
have a symmetry index between 0.7 and 1.5. Symmetry index measurements for the AMB and
Prow ripples, including range and mean for each ripple population, are included in Tables S1 and
S2. Symmetry index values do not directly correspond with individual ripple wavelengths
because wavelength is measured crest to crest and symmetry defines a single ripple as trough to
trough.
Ripple height (
h
) is defined as the maximum vertical distance from trough to crest,
measured perpendicular to the ripple layer. Ripple aspect ratio (
h
/λ) was calculated for each
corresponding ripple wavelength and height (Tables S1, S2). The aspect ratio would also be
affected by uncertainty in the wavelength measurements as a result of uncertainty in the
orientation measurements. If λ
t
is up to 6% smaller than
λ
m
, the true corrected aspect ratio (
h
t
)
would be up to 6% larger than the measured aspect ratio, where
λ
t
=
m
×0. 94)
.
(3)
For the AMB ripples, this correction shifts the measured aspect ratio range from 0.1
0.17 (mean = 0.13) to a maximum corrected aspect ratio range of 0.106
0.18 (mean = 0.14)
which is still consistent with orbital ripples. For the Prow, this correction shifts the measured
aspect ratio range from 0.06
0.09 (mean = 0.074) to a maximum corrected aspect ratio range of
0.064
0.095 (mean = 0.078) which is still lower than typical for orbital ripples but falls within
the transition zone where suborbital ripples can form.
The ratio of wavelength to median grain size (λ/D
50
) can be used to characterize orbital
versus anorbital ripples. Anorbital ripples consistently have a λ/D
50
ratio that falls within the
range of 400
600, while orbital ripples can have a much larger rang
e of λ/D
50
(~100
2000,
inclusive of 400
600;
35
). The wavelength to grain size ratio can indicate that ripples are
not
anorbital, if it falls outside the anorbital range, but within that range ripples can be either
anorbital or orbital.
We
used the average measured wavelength for each the AMB and Prow
ripple populations to calculate the wavelength-grain size ratio. In the AMB, because grain size is
not detectable, we applied the range of possible grain sizes (60
180 μm) to estimate a λ/D
50
range of 750
250. This range is non-diagnostic and could correspond to either anorbital ripples
(at the smaller end of the possible grain size range) or orbital ripples (throughout the possible
grain size range. In the Prow, we used the median grain size calculated from point counts, along
with the mean measured wavel
ength, to calculate a λ/D
50
value of 118. This ratio is inconsistent
with anorbital ripple formation. Substituting the corrected
mean λ
t
for both the AMB and Prow
does not significantly change the wavelength-grain size ratio values for either ripple population.
S3. Wave Ripple Modeling
The wave ripple paleohydraulic reconstructions follow previous work (
54, 56
), and codes
are available in supplementary material from (
56
). We calculated the significant wave heights
,
H
,
and wave periods,
T
, for a given wind fetch,
F
, wind speed
,
U
w
, and water depth
,
h
, using a semi-
empirical wave forecasting model applicable for shallow and deep water (
42
),
퐻 =
2
0. 283 tanh
(
0. 53 h
0. 75
)
푡푎푛ℎ(
0.00565퐹
1/2
tanh (0. 53h
0. 75
)
)
(4)
푇 =
7. 54 tanh
(
0. 833 h
3/8
)
푡푎푛ℎ(
0.0379퐹
0. 33
tanh (0. 833h
3/8
)
)
(5)
in which
=
푔퐹
2
is the dimensionless fetch,
=
푔ℎ
2
is the dimensionless water depth,
U
A
is a
wind stress factor (units m/s),
g
is the acceleration of gravity. The model explicitly incorporates
gravity through dimensional analysis due to the important role that gravity plays as the restoring
force in wind wave (i.e., surface gravity wave) kinematics.
The model u
ses a wind stress factor (also called an adjusted wind speed factor), rather
than wind speed directly, because as water waves evolve, they change the roughness at the
water-air interface which influences the boundary stress for a given wind speed. Wind drag
becomes increasingly large at fast wind speeds due to boundary roughness created by surface
gravity waves. Coastal Engineering Research Center (
5
5
) used an empirical relation to relate
wind speed,
, measured at 10 m elevation above the water surface, to the wind stress factor,
, where both velocities are given in m/s,
=0. 71푈
1. 23
(6 )
Equation (6) is applicable to terrestrial conditions, but it requires modification for Mars because
it does not explicitly include a term for atmospheric density,
, which should strongly influence
the boundary stress for a given wind speed. Eq. (6) also does not explicitly include gravity
,
which affects wave heights (as shown in Eq. 4), and therefore would influence drag at the
boundary.
To adapt Eq. (6) to martian conditions, we developed an alternate version that allows the
wind speed to be converted into a wind stress factor wit
h explicit consideration of gravity and
atmospheric density by following turbulent boundary layer theory. Our derivation follows a
scaling relation for the log-law for turbulent boundary layers (
6
4
), in which wind speed at
elevation
z
is
(
)
(7 )
where
is the boundary shear stress,
is the boundary roughness height and
n
is a constant that
approximates the natural logarithm. For the case of wind generated waves,
is set by the wave
height, which in turn scales with
2
/푔
(Eq. 4) or equivalently
(
)/푔
because
휏 ∝휌푈
2
.
Therefore, we set
∝(
)/푔
in Eq. (7), which yields
∝(
)
0.5−푛
(푧푔)
(8 )
where
n
was found to be
n
= 0.0935 to match the dependencies in Eq (6
) for terrestrial
conditions. To find the wind speeds on Mars, or any planet, that produce the equivalent stresses
on the water surface as on Earth, we took Eq. (8), rearranged it as an expression for
, specified
a
generic scenario (subscript
m
) and an Earth scenario (subscript
e
) and set
equal between the
two scenario resulting in
푤푚
=푈
푤푒
(
)
0.5−푛
(
)
(9 )
in which we assumed any constants in Eq. (8)
(e.g., von Kármán’s constant) are indeed
constants, and therefore cancel out in Eq. (9), and the height above the water surface,
z
, is the
same under both scenarios (i.e.,
z
= 10 m). Setting
=
푤푒
in Eq. (6
) and combining
it with Eq.
(9 ) results in a prediction of the wind stress factor for any values of atmospheric density and
gravity that is mathematically equivalent to Eq. (6) for terrestrial conditions
,
=0. 71푈
푤푚
1. 23
(
)
−0. 115
(10
)
We used Eq. (10) in place of Eq. (6
) in the wave forecasting model (Eqs. 4 and 5)
. In preliminary
tests, we found that the relatively simple wave forecasting model we used provided
quantitatively similar results to the SWAN wave model implemented in Delft-3D modeling suite
that was adjusted for martian conditions (
11
).
With wave height and wave period calculated from the wave forecasting model, we used
Airy wave theory for intermediate-depth waves to find the near-bed wave orbital diameter,
d
o
,
and the wave orbital velocity,
U
o
. By Airy wave theory,
=퐻/sinh (
2휋ℎ
)
(11)
=
휋푑
(12)
in which
L
is the wavelength of the wave given by
퐿 =
푔푇
2
2휋
푡푎푛ℎ(
2휋ℎ
)
.
(13)
We used an iterative scheme to solve Eq. (11-13), and we did not report a solution where waves
were expected to break, which violates Airy wave theory. The breaking criteria is (e.g.,
65
)
퐻 >0. 142
2휋퐿
2
푔푇
2
(14)
Airy wave theory is a linear theory for the motion of gravity waves that can be derived
from first principles and therefore the dependencies on gravity are known. The theory assumes
potential flow (inviscid and irrotational) and, despite its simplicity, compares well to
observations of waves in oceans and lakes. Non-linear wave theories are also well established,
but the improvement they offer is minimal in comparison to other uncertainties inherent in a
paleo-environmental reconstruction of this type.
To predict the wavelength of orbital wave ripples, we used
휆=0. 65푑
(e.g.,
6
6
). In
addition to creating waves with the appropriate wave orbital diameter, the near bed oscillations
must be of sufficient strength to move sand and produce ripples. The grey shaded zone in Fig. 4
shows the range in which ripples are expected to develop based on sediment transport constraints
(
5
7
), where we assumed a median grain diameter of
D
50
= 100 μm (for the AMB ripples), density
of sediment of
=
3000 kg/m
3
, consistent with a mafic lithology, and water density of
=
1000 kg/m
3
. The criteria of (
57
) uses a dimensionless particle diameter,
=(푅푔퐷)
0.5
퐷/(4휈)
(15)
where
= 10
-6
m
2
/s is the kinematic viscosity of water, and
푅 =(휌
−휌
)/휌
. They found that
the wave orbital velocity that corresponds to the onset of different bedform regimes is
=2 휋퐶
[
1+5(
3푇
0
)
2
]
−1/4
(16)
in which
C
and
T
0
are empirical variables that vary for different bed states. For the onset of
ripples, You and Yin (
41
) found that
퐶 =5.5(
)푠
0. 78
and
0
=169
2
−1. 64
. We set the
upper bound on ripples to their sheet flow regime given by
퐶 = 13.5(
)푠
0. 78
and
0
=
30
2
−1.3
, beyond which hummocks or plane bed is likely to form.