Icarus 228 (2014) 54–63
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Icarus
journal homepage: www.elsevier.com/locate/icarus
Formation of lobate debris aprons on Mars: Assessment of regional ice
sheet collapse and debris-cover armoring
James L. Fastook a,⇑, James W. Head b, David R. Marchant c
a
University of Maine, Orono, ME 04469, USA
Department of Geological Sciences, Brown University, Providence, RI 02912, USA
c
Department of Earth & Environment, Boston University, Boston, MA 02215, USA
b
a r t i c l e
i n f o
Article history:
Received 16 April 2013
Revised 29 August 2013
Accepted 25 September 2013
Available online 5 October 2013
Keywords:
Mars, climate
Mars, surface
Mars, polar geology
Mars, polar caps
a b s t r a c t
Lobate debris aprons (LDA) are lobate-shaped aprons surrounding scarps and isolated massifs that are
concentrated in the vicinity of the northern Dichotomy Boundary on Mars. LDAs have been interpreted
as (1) ice-cemented talus aprons undergoing viscous flow, (2) local debris-covered alpine-like glaciers,
or (3) remnants of the collapse of a regional retreating ice sheet. We investigate the plausibility that LDAs
are remnants of a more extensive regional ice sheet by modeling this process. We find that as a regional
ice sheet collapses, the surface drops below cliff and massif bedrock margins, exposing bedrock and regolith, and initiating debris deposition on the surface of a cold-based glacier. Reduced sublimation due to
debris-cover armoring of the proto-LDA surface produces a surface slope and consequent ice flow that
carries the armoring debris away from the rock outcrops. As collapse and ice retreat continue the debris
train eventually reaches the substrate surface at the front of the glacier, leaving the entire LDA armored
by debris cover. Using a simplified ice flow model we are able to characterize the temperature and sublimation rate that would be necessary to produce LDAs with a wide range of specified lateral extents and
thicknesses. We then apply this method to a database of documented LDA parameters (height, lateral
extent) from the Dichotomy Boundary region, and assess the implications for predicted climate conditions during their formation and the range of formation times implied by the model. We find that for
the population examined here, typical temperatures are in the range of 85 to 40 °C and typical sublimation rates lie in the range of 6–14 mm/a. Lobate debris apron formation times (from the point of bedrock exposure to complete debris cover) cluster near 400–500 ka. These results show that LDA length and
thickness characteristics are consistent with climate conditions and a formation scenario typical of the
collapse of a regional retreating ice sheet and exposure of bedrock cliffs. This scenario helps resolve many
of the unusual characteristics of lobate debris aprons (LDA) and lineated valley fill (LVF). For example, the
distribution of LVF is very consistent with extensive flow of glacial ice from plateau icefields, and the
acquisition of a debris cover in the waning stages of retreat of the regional cover as the bedrock scarps
are exposed. The typical concentric development of LDA around massifs is much more consistent with
ice sheet retreat than insolation-related local accumulation and flow. We thus conclude that the retreating ice-sheet model is robust and should be investigated and tested in more detail. In addition, these
results clearly show that the lobate debris aprons in the vicinity of the Dichotomy Boundary could not
have attained temperatures near or above the ice melting point and retained their current shape, a finding that supports subzero temperatures for the last several hundred million years, the age of the LDA surfaces. A further implication is that the LDA ice has been preserved for at least several hundred million
years, and could potentially contain the record of the climate of Mars, preserved since that time below
a sublimation lag deposit.
Ó 2013 Elsevier Inc. All rights reserved.
1. Introduction
Models of ice sheets on Mars (e.g., Fastook et al., 2008) have
helped to identify and interpret glacial deposits observed from
⇑ Corresponding author.
E-mail address: fastook@maine.edu (J.L. Fastook).
0019-1035/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved.
http://dx.doi.org/10.1016/j.icarus.2013.09.025
orbit (Head and Marchant, 2003), while also testing climate scenarios that may have been responsible for their formation (Forget
et al., 2006). In many of these cases it is possible that the ice sheets
themselves existed only in the past during periods of different
climate dictated primarily by dramatic changes in obliquity (Forget
et al., 2006; Madeleine et al., 2009). Here we examine possible
formation mechanisms for lobate debris aprons (LDA).
J.L. Fastook et al. / Icarus 228 (2014) 54–63
LDAs in the Deuteronilus Mensae region in the fretted terrain
along the Dichotomy Boundary (Sharp, 1973) have been thought
to involve significant amounts of water ice since the time of Viking
observations (Carr and Schaber, 1977; Lucchitta, 1984), but controversy over the amount of water ice involved has ranged from very
low (20–30%, ice assisted talus flow; Squyres, 1978, 1979), to
medium (30–80% rock-glaciers; Li et al., 2005: Mangold et al.,
2002), and to high (>80% debris-covered glaciers; Colaprete and
Jakosky, 1998; Kargel, 2004; Head et al., 2005, 2006a, 2006b;
Parsons et al., 2011). In addition, the low number of craters on
the LDA surfaces requires mid-to-late Amazonian ages for formation and movement cessation (e.g., Chuang and Crown, 2005).
Recently, the SHARAD subsurface radar sounding experiment
on the Mars Reconnaissance Orbiter (MRO) (Seu et al., 2007) has
confirmed that many, if not most, of the LDAs contain relatively
pure water ice covered only by a thin layer of debris shed from
adjacent scarps (Holt et al., 2008a, 2008b; Plaut et al., 2008,
2009). The requirement that the valley floor extend undistorted
beneath the observed LDAs dictates a dielectric constant consistent
with pure (<10% contaminant) water ice. In addition, the surface
debris layer can be constrained to be less than 10 m due to the
lack of a shallow soil–ice interface in the radar data, but must be
greater than 0.5 m to explain the lack of a hydrogen signal in gamma ray/neutron data (Boynton et al., 2007; Feldman et al., 2004;
Mitrofanov et al., 2002).
Fig. 1 shows a radargram and ground track from Plaut et al.
(2009) for a LDA at 39.1N, 24.2E in the Deuteronilus Mensae region
(see Head et al., 2006b). Focusing on the feature in the left-hand
side of the track where it crosses between two mesas, one observes
a profile showing a classic convex shape often indicative of viscous
flow (Fig. 1b). Li et al. (2005) demonstrated that LDA profiles could
be reasonably approximated with a plastic rheology defined by a
yield stress with resulting parabolic profiles, and used this to
categorized them into Types I, II, and III (convex and close to the
plastic profile, convex but below the plastic profile, and convex
but with much more deviation from the plastic parabolic profile)
that reflected their degree of post-formation modification. Parsons
et al. (2011) and Parsons and Holt (2013) proposed a formation
mechanism whereby the current profiles evolved through viscous
flow of predominantly pure ice from a shorter and much thicker
deposit, and then used the estimated age of the LDAs to constrain
the temperature, the grain size, and dust fraction manifest in their
defined ice rheology. We choose a very different approach, with
the assumption that the LDAs are remnant features of a larger,
regional ice sheet.
2. Formation hypothesis
Of the three major interpretative frameworks for LDAs, (1)
ice-cemented debris aprons undergoing viscous flow, (2) local debris-covered alpine-like glaciers, or (3) remnants of the collapse of a
regional retreating ice sheet, significant evidence has recently
accumulated that supports the regional ice sheet model. This evidence includes (1) the existence of glacial highstands that suggest
that many of these features are part of a larger glacial landsystem
with ice being several km thick regionally (Dickson et al., 2008,
2010), (2) the presence of distal ice-rich deposits well beyond
the distal margins of lobate debris aprons (Baker et al., 2010), (3)
an integrated pattern of exposures that suggest regional glacial
landsystems (Head et al., 2010), (4) global climate models that
support regional snow and ice accumulation rather than local
accumulation that would favor alpine-type valley glaciers (Madeleine et al., 2009), and (5) glacial flow models that are consistent
with both the climate models and the geological evidence (Fastook
et al., 2010). On the basis of this evidence, we investigate the
55
Fig. 1. SHARAD Radargram 719502 from Plaut et al. (2009) for a LDA at 39.1N,
24.2E in the Deuteronilus Mensae region. (a) Vertical dimension as time delay. (b)
Vertical dimension converted to depth assuming a subsurface dielectric constant of
water ice (3.2). (c) Simulated radargram showing the expected positions of off-nadir
clutter echoes. (d) MOLA topography along the ground track. Focusing on the
feature in the left-hand side of the track in (b) where it crosses between two mesas
(the two left-hand arrows), one observes a profile showing a classic convex profile
often indicative of viscous flow.
plausibility that LDAs are remnants of a more-extensive regional
ice sheet by modeling this process.
In our scenario, as the regional ice sheet collapses, the surface
drops below cliff and massif bedrock margins, exposing bedrock
and regolith, and initiating debris deposition. Reduced sublimation
due to debris-cover armoring of the LDA, which initially is focused
near exposed bedrock cliffs, produces a relative increase in the
slope of distal (exposed) ice that with consequent ice flow along
the entire glacier, carries the armoring debris further away from
the base of the cliff. As collapse continues, the debris train eventually reaches the glacier snout, leaving the entire LDA armored by
debris cover. This armored LDA, with its considerably reduced sublimation rate, could persist for a long period of time. Indeed, even
here on Earth, the oldest known ice may be preserved beneath an
analogous armored layer in the Dry Valleys of Antarctica, where
preserved ice is known to be several million years old (Marchant
et al., 2007; Kowalewski et al., 2011). Ice, being a non-Newtonian
fluid, exhibits behavior where for low stresses, deformation, and
hence flow, is reduced by orders of magnitude from that which
would be produced by a linear flow law. We would expect these armored LDAs to continue to deflate, albeit much more slowly with
the reduced sublimation rate, until their surface profile reaches a
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J.L. Fastook et al. / Icarus 228 (2014) 54–63
configuration where the slope and thickness product provide such
a low driving stress that movement, for all intents and purposes,
would cease. As this configuration might be attained at different
times and places along the profile, one might expect differential
movement resulting in longitudinal compression of the debris
layer that might appear as ridges transverse to the down-slope
direction.
Specifically, the formation mechanism, shown schematically in
Fig. 2, begins with a larger regional ice sheet that completely buries
the underlying terrain (Fig. 2a) (Fastook et al., 2010; Head et al.,
2010; Madeleine et al., 2009). As this ice sheet collapses in an
ablating environment, its surface drops below the level of the
scarps where current LDAs are found (Fig. 2b). At this point debris
from the scarps begins to accumulate on the ice sheet surface. As
with our terrestrial analog, the Mullins Glacier in the Dry Valleys
of Antarctica (Marchant and Head, 2005, 2007; Marchant et al.,
2007; Shean et al., 2007), this debris cover armors the surface
(Fig. 2c) and reduces ablation by orders of magnitude (Kowalewski
et al., 2006, 2011). As the initial armoring begins at the base of the
scarps, the ice sheet will begin to evolve a surface slope down away
from the scarp (Fig. 2d). This surface slope will continue to carry
surface debris away from the scarp, expanding the armored area.
As the sheet continues its collapse, at some point the surface debris
will reach the glacier snout and the entire profile will be completely armored by debris (Fig. 2d), leaving behind a LDA with a
particular thickness and lateral extent that depends on the choice
of certain parameters within the model. We now take this conceptual model and explore a quantitative formulation.
3. Modeling
The model is a 1D flowband shallow-ice formulation simplified
by assuming isothermal conditions, i.e., a specified uniform temperature in the flowband interior equal to the mean annual surface
temperature (Fastook, 1987; Millour et al., 2011). This simplification is reasonable given that the low flow velocities will produce
little shear heating and the typical thicknesses of LDAs of a few
hundred meters will provide little insulation of the already low
geothermal flux (for reference see treatments in Fastook et al.,
2008, 2011; Fastook and Head, 2012). The model uses Glen’s Flow
Law (Glen, 1955; Paterson, 1994), and while newer rheologies exist
that account for dust and ice grain size (e.g., Goldsby et al., 2013),
these defining properties are poorly constrained in the current
LDAs. Future analysis of LDA radar properties (e.g., Holt et al.,
2008b; Plaut et al., 2009) might provide minimum estimates of
dust/debris content, and analysis of terrestrial cold-base glacier
flow textures could provide additional clues (e.g., Marchant et al.,
2010). Other parameters in the model besides temperature, which
determines flow rates in the evolving LDA, include the debris-free
sublimation rate, the limiting debris-covered sublimation rate, the
debris accumulation rate at the base of the scarp, a factor relating
the depth of debris cover to the reduction in sublimation rate, and
the height of the scarp at which debris begins to accumulate. Using
this model, we now explore the parameter space to assess the
model predictions and to identify the most sensitive parameters.
4. Experiments
Fig. 2. Schematic of proposed formation mechanism. (a) Larger regional ice sheet
that completely buries the underlying terrain. (b) As this ice sheet collapses in an
ablating environment, its surface drops below the level of the scarps and debris
from the scarps begins to accumulate on the ice sheet surface. (c) This debris cover
armors the surface and reduces ablation by orders of magnitude. (d) As the initial
armoring begins at the base of the scarps, the ice sheet will begin to evolve a surface
slope down away from the scarp that carries surface debris away from the scarp,
expanding the armored area. As collapse continues, the entrained debris reaches the
glacier snout and the entire profile is completely armored by debris, leaving behind
a LDA with a particular thickness and lateral extent that depends on the choice of
temperature and debris-free sublimation prescribed in the model.
Extensive model runs with randomly chosen values for the various input parameters yield a suite of final configurations, each
with a resulting thicknesses and lateral extent. After extensive
examination of the parameter space we find that the most sensitive parameters are temperature, debris-free sublimation rate,
and scarp height. Since scarp height is well constrained by MOLA
topography, we examine in detail the effects of temperature and
debris-free sublimation rates. Fig. 3 shows plots of margin distance
and thickness as functions of temperature (horizontal axis, °C) and
debris-free sublimation rates (vertical axis, mm/a). Each colored
dot (they appear as irregular clusters due to the very large number
of randomly-generated simulations) represents one of the 50,000
model runs generated with temperature and debris-free sublimation rates provided by a range-constrained pseudo-random number generator. One can clearly see that warmer temperatures and
lower sublimation rates lead to greater margin extent, while warmer temperatures and larger sublimation rates lead to thinner
LDAs. This is to be expected since warmer ice is softer and supports
faster flow for a given surface slope, allowing the armoring debris
to be carried further before reaching the glacier snout, resulting in
a completely armored LDA. On the other hand, higher sublimation
rates reduce the overall thickness faster, typically leaving much
thinner LDA for the same lateral extent.
Armed with our database of results from particular input
parameters, we can specify a ‘‘target’’ configuration (i.e. thickness
J.L. Fastook et al. / Icarus 228 (2014) 54–63
57
Fig. 3. (a) Margin distance and (b) thickness as functions of temperature (horizontal axis, °C) and debris-free sublimation rates (vertical axis, mm/a). Each colored dot
represents one of the 50,000 model runs. Warmer temperatures and lower sublimation rates lead to greater margin extent, while warmer temperatures and larger
sublimation rates lead to thinner LDAs. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
and margin extent), and ask what climatic conditions (i.e. temperature and debris-free sublimation rate) could have produced that
configuration. We define a ‘‘distance’’ metric that is a measure of
the goodness of the result to the desired target, where T0 and M0
are the target thickness and the margin extent respectively.
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 2
T T0
M M0
D¼
þ
T0
M0
Fig. 4 shows envelopes of candidate temperatures and debrisfree sublimation rates that would produce specific target configurations. Shown here are solutions whose ‘‘distance’’ metric is less
than 0.32 (100.5, indicated by color in the figure by its base-10
logarithm and chosen arbitrarily to show the envelope of ‘‘nearby’’
conditions that yield solutions close to the target margin extent
and thickness). Fig. 4a targets a configuration with a margin extent
of 13 km and a thickness of 370 m, the mean values of the catalogued LDAs considered here (Chuang and Crown, 2005; Ostrach,
2007). For this target configuration, the best fit at the center of
the ‘‘bullseye’’ is obtained for a temperature of 64.2 °C and a debris-free sublimation rate of 8.9 mm/a. A thinner and smaller target
configuration, 10 km in extent and 200 m thick is shown in Fig. 4b.
The best fit now requires a slightly warmer temperature of
58.2 °C but a larger sublimation rate of 10.2 mm/a. Fig. 4c and
d are for target configurations one standard deviation larger in extent (20 km) and one standard deviation thinner (4c at 200 m) and
thicker (4d at 550 m). The larger but thinner configuration of
Fig. 4c requires much warmer temperatures, 36.4 °C, but a considerably reduced sublimation rate, 7.1 mm/a. The larger but thicker configuration of Fig. 4d is obtained with virtually the same
sublimation rate, 7.1 mm/a, but much colder temperatures,
54.5 °C.
As we repeat the procedure for different target margin extents
and thicknesses, we find the following behavior shown in Fig. 5.
Lines of constant thickness trend from lower left to upper right
(200 along the lower right to 900 along the top at 50 m intervals
shown with colors from the left-hand vertical scale bar). Lines of
constant margin extent display an ‘‘L-shaped’’ pattern (with 5 km
on the left and 50 on the upper right at 5 km intervals shown with
colors from the right-hand vertical scale bar). Also shown in Fig. 5
are the resulting temperatures and debris-free sublimation rates
for the LDAs listed in Appendix A of Ostrach (2007) where here
the absolute ‘‘distance’’ metric (not Log10 as in Fig. 4) for the closest
fit is shown by colors from the horizontal scale bar along the top of
the figure. Most achieved reasonable fits with the conspicuous
exception of the LDAs thinner than 200 m, all of which, regardless
of extent, had unreasonably large ‘‘distance’’ metrics. A possible
explanation for this is that the thinner LDAs have undergone continued deflation subsequent to the complete armoring, a process
not included here. For the rest, with the exception of a few very
thick outliers, most of the LDAs lie along a curved line trending
from low temperature, high sublimation rates (90 °C and
15 mm/a) for those with the smallest lateral extent (5 km) to warmer, lower sublimation rates (25 °C and 5 mm/a) for those with
larger lateral extents (30 km). Given our proposed formation
mechanism, this makes sense in that cold ice flows less readily,
so debris is not carried as far during the time interval in which
the higher sublimation rate is deflating the ice. Conversely, warmer
more easily deformed ice will carry the debris much farther during
the longer time interval provided by the lower sublimation rate.
This observation has implications for the relative humidity during
the formation episodes, since normally warmer temperatures at
the same pressure and humidity would be expected to produce
higher sublimation rates. The results in Fig. 5 provide us with a
‘‘mapping,’’ or transformation, that we can use to convert any measured LDA’s thickness and extent into a climatic record of the temperature and debris-free sublimation rate present at the time the
LDA formed.
5. LDA inventory
With this mapping from LDA extent and height to temperature
and debris-free sublimation rate provided by our database of
50,000 model runs and illustrated in Fig. 5, we can now apply this
transformation to specific measurements of LDA extent and height
in order to assess what climatic conditions might have been present at the time of formation of specific LDAs.
An inventory of LDAs (Ostrach, 2007) for a region near the
Dichotomy Boundary provided tabulated locations, thicknesses,
and lateral extents for over 200 LDAs, some 80 of which are in
the region shown in Fig. 6. The distribution of tabulated LDA thicknesses and margin extents is shown in Fig. 6a and b respectively.
Thicknesses range from 42 to 890 m, with a mean and standard
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J.L. Fastook et al. / Icarus 228 (2014) 54–63
Fig. 4. Envelopes of candidate temperatures and sublimation rates that would produce specific target configurations for solutions whose ‘‘distance’’ metric is less than 0.32
(10–0.5, indicated by color in the figure by its base-10 logarithm). (a) Targets a margin extent of 13 km and a thickness of 370 m, the mean values of the catalogued LDAs, with
best fit for a temperature of 64.2 °C and a sublimation rate of 8.9 mm/a. (b) Targets a thinner and smaller target configuration (10 km in extent and 200 m thick) and
requires a slightly warmer temperature of 58.2 °C but a larger sublimation rate of 10.2 mm/a. (c) Targets one standard deviation larger in extent (20 km) and one standard
deviation thinner (200 m). (d) Targets one standard deviation larger in extent (20 km) and one standard deviation thicker (550 m). The larger but thinner configuration of (c)
requires much warmer temperatures, 36.4 °C, but considerably reduced sublimation rate, 7.1 mm/a. The larger but thicker configuration of (d) is obtained with virtually the
same sublimation rate, 7.1 mm/a, but much colder temperatures, 54.5 °C. (For interpretation of the references to colour in this figure legend, the reader is referred to the
web version of this article.)
deviation of 372 and 179 m respectively. Margin extents range
from 2 to 47 km, with a mean and standard deviation of 13 and
9 km. Our mapping predicts a temperature of 64.2 °C and a sublimation rate of 8.94 mm/a for the mean thickness and extent.
Reducing thickness by one standard deviation requires 13 °C warmer temperature, but no change in the sublimation rate. Increasing
thickness by one standard deviation requires 4.6 °C colder temps,
and again no change in sublimation. Reducing the extent by one
standard deviation requires 30 °C colder temperatures and an increase in sublimation of 7.6 mm/a. Increasing the extent by one
standard deviation requires temperatures 18 °C warmer and sublimation reduced by 2 mm/a. These results are summarized in
Table 1.
An example profile detailed in Ostrach (2007) from orbit
12123.2, located at 29.43E, 41.27N is shown in Fig. 7. The lateral
extent and thickness is listed at 26 km and 636 m. For comparison,
also shown is the model-generated profile identified from our
mapping of Fig. 5 for its tabulated extent and thickness. The best
match to extent and thickness is for a temperature of 50.2 °C
and debris-free sublimation rate of 6.4 mm/a. Given the simplifications in the ice sheet model, the match between the observed and
modeled profile is reasonable. Since the model profile is for the instant the debris train reaches the glacier snout and the whole LDA
is armored, it is not unexpected that the measured profile would
fall below the modeled profile. Even at this temperature there
would be some continued movement subsequent to the entrained
debris reaching the glacier snout that would lower the profile. The
presence of a slightly concave profile at the toe of the LDA is perhaps indicative of continued sublimation, even beneath the debris
armoring.
With the tabulated distribution of LDA characteristics and our
mapping of LDA thickness and extent into climatic information,
we can ask the question: What is the distribution of derived climatic conditions predicted by the distribution of LDA characteristics? Fig. 8 shows the properties derived from the LDAs of Ostrach
(2007). Fig. 8a and b show temperatures and debris-free sublimation rates respectively. While we are aware of the dangers of interpolation (and more so extrapolation) of unevenly spaced data, it is
59
J.L. Fastook et al. / Icarus 228 (2014) 54–63
Table 1
Predicted temperature and debris-free sublimation rate for the mean LDA thickness
and lateral extent with the range in response for a range of plus or minus one
standard deviation from the means.
Thickness (m)
Extent (km)
Temperature (°C)
Sublimation rate (mm/a)
Predicted temperature and sublimation for mean thickness (372 m) and extent
(13 km) ± one standard deviation
193
4
82.5
16.4
372
4
93.2
16.60
551
4
99.4
16.48
193
13
50.0
8.75
372
13
64.2
8.94
551
13
67.6
8.82
193
22
31.4
6.77
372
22
46.4
6.71
551
22
50.6
6.71
Fig. 5. Best fit contours for thickness and margin extent with LDAs from Ostrach
(2007). Lines of constant thickness trend from 200 m at the lower left to 900 m at
the upper right at 50 m intervals with colors from the left-hand vertical scale bar.
Lines of constant margin extent display an L-shaped pattern with 5 km on the left
and 50 on the upper right at 5 km intervals with colors from the right-hand vertical
scale bar. The absolute ‘‘distance’’ metric for the best-fit temperatures and debrisfree sublimation rates for the LDAs listed in Appendix A of Ostrach (2007) are
shown by stars with colors from the horizontal scale bar along the top of the figure.
(For interpretation of the references to color in this figure legend, the reader is
referred to the web version of this article.)
still worthwhile to visualize the spatial distribution. Contours in
Fig. 8c and d are cubic-spline fits to the LDA results for temperature
and debris-free sublimation, generated using Generic Mapping
Tool (GMT). While there are clear north–south and topographic
trends in the temperature results, with temperatures colder at
higher latitudes and warmer at higher elevations, the debris-free
sublimation rates do not display similar simple trends. For sublimation, a saddle of medium rates separates two eastern and western patches of high sublimation and two northern and southern
patches of low sublimation, with no clear association with either
latitude or elevation. These preliminary results are meant to show
broad candidate trends. When more LDA and LVF data are collected
and ages for the various occurrences are determined this approach
can become a potentially robust description of the climate during
formation.
In Fig. 9 we examine the duration of the formation process, specifically the time from the moment the surface drops to the level of
the cliff top and armoring debris begins to accumulate on the ice
surface until the transported debris train reaches the glacier snout
and the LDA is completely armored (between Fig. 2b and d). Fig. 9a
shows the formation time as a function of temperature and debrisfree sublimation rate and includes the LDAs of Ostrach (2007). For
cold temperatures we observe a monotonically decreasing formation time for increasing debris-free sublimation rate, as would be
expected since with cold, and therefore very hard ice, the rate at
which the surface lowers depends primarily on this sublimation
rate. As we move to warmer temperatures, an inversion occurs,
where for sublimation rates between 5 and 6 mm/a we observe a
secondary maximum in formation times exceeding 700 ka. This occurs because the faster flow of the warmer, and hence softer ice is
able to carry the debris farther from the base of the cliff retarding
ultimate formation time. From Fig. 3 it is clear that this occurs for
LDAs with thickness of 100–250 m and margin extent of 20–
30 km. The only LDA that falls into this category is one at 29.89E,
45.56N with a thickness of 154 m, an extent of 20.1 km, and a formation time of 745 ka. Excluding this and the two with formation
times greater than 1 Ma (both anomalously thick and large, requiring very low sublimation rates), the mean formation time is 422 ka
Fig. 6. Location maps for Dichotomy Boundary LDAs from Ostrach (2007) (a) Thickness (m), ranging from 42 to 890 m, with a mean and standard deviation of 372 and 179 m
respectively. (b) Margin extent (km), ranging from 2 to 47 km, with a mean and standard deviation of 13 and 9 km.
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J.L. Fastook et al. / Icarus 228 (2014) 54–63
Fig. 7. LDA profile from Orbit 12123.2 (Ostrach, 2007) and model-generated profile
for 50.2 °C and 6.4 mm/a sublimation. The extent is listed as 26 km and thickness
is 636 m.
with a standard deviation of 88 ka. Clearly flow due to the softening temperature effect in the ice is insignificant below 80 °C and
becomes progressively more important only as one approaches the
melting point.
Fig. 9b shows the distribution of LDA formation times in the
Dichotomy Boundary region. The two white stars correspond to
the outliers in Fig. 9a at 100 °C, 0.24 mm/a and 55 °C,
0.8 mm/a. These are the only two with formation times greater
than 1 Ma and correspond to very thick (>800 m) and relatively
large extents (16.5 and 47 km). With the exception of the orange
star that corresponds to the LDA described above that lie in the
inversion, the rest all have formation times close to 400 ka.
Finally, Fig. 10 summarizes the frequency distributions of the
LDA configurations used as input to our analysis: (Fig. 10a) LDA
thickness and (Fig. 10b) LDA extent. Also shown are frequency distribution histograms for the properties derived by our modeling
exercise: (Fig. 10c) predicted temperatures, (Fig. 10d) predicted
debris-free sublimation rates, and (Fig. 10e) formation times. In
each of these a red bar with a width of one standard deviation is
centered on the mean value. LDA thickness shows two clusters
around 100–150 and around 300–450 m. LDA extent is clustered
towards smallest sizes declining rapidly in frequency as one moves
to larger extents. The temperature frequency distribution resembles LDA extents, whereas formation time resembles LDA
thickness. The sublimation rate frequency distribution, with the
exception of a cluster around 8 mm/a, appears to be more of a
normal distribution about the mean.
Fig. 8. (a) Modeled temperature and (b) modeled debris-free sublimation rate for the LDAs from Ostrach (2007). (c) Cubic-spline fitted temperature and (d) cubic spline-fitted
sublimation rate for the data of (a and b). Cubic splines are generated using Generic Mapping Tool (GMT). The data is first preprocessed with the GMT routine blockmean at a
resolution of 0.1° and then gridded with the GMT routine surface with a tension setting of 0.25 (a tension setting of zero gives the ‘‘minimum curvature’’ solution, which can
cause undesired oscillations and false local maxima or minima, whereas a tension setting of one yields a harmonic surface, i.e. no maxima or minima are possible except at
control data points).
J.L. Fastook et al. / Icarus 228 (2014) 54–63
61
Fig. 9. Formation time: the time from the moment the ice surface drops to the level of the cliff top and armoring debris begins to accumulate on the ice surface until the
transported debris train reaches the snout and the LDA is completely armored. (a) As a function of derived temperature and debris-free sublimation rate with LDAs from
Ostrach (2007). (b) Distribution of LDA formation times in the Dichotomy Boundary region. The two white stars are the outliers in (a) at (100 °C, 0.24 mm/a) and (55 °C,
0.8 mm/a), the only two with formation times greater than 1 Ma, corresponding to very thick, relatively large LDAs.
Fig. 10. Frequency distribution histograms for the input to our analysis (a) LDA thicknesses and (b) LDA extents, as well as for the properties derived by the modeling
exercise, (c) predicted temperature, (d) predicted debris-free sublimation rate, and (e) formation time. For each of these a red bar with a width of one standard deviation is
centered on the mean value. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Given the generally cold temperatures predicted by the model
and shown in Fig. 10c, we would expect little supraglacial melting
to have taken place, with the dominant ablation mechanism in the
form of direct sublimation. There is evidence, however, for at least
some limited melting that was capable of producing small glaciofluvial valley systems outside the current limits of some LDAs.
These systems, as described by Fassett et al. (2010), are small
and indicative of cold-based glaciers, and what melting did occur
resulted from ‘‘preferred insolation geometries’’ such as cliff faces
and solar-heated surface debris alongside exposed glacier ice.
6. Conclusions
LDAs have been interpreted as (1) ice-cemented talus aprons
undergoing viscous flow, (2) local debris-covered alpine-like
glaciers, or (3) remnants of the collapse of a regional retreating
ice sheet. We investigated the plausibility that LDAs are remnants
of a more extensive regional ice sheet by modeling this process.
The model is a 1D flowband shallow-ice formulation simplified
by assuming isothermal conditions, i.e., a specified uniform temperature in the flowband interior equal to the mean annual surface
temperature (Fastook, 1987; Millour et al., 2011). Other parameters in the model besides temperature, which determines flow
rates in the evolving LDA, include the debris-free sublimation rate,
the limiting debris-covered sublimation rate, the debris accumulation rate at the base of the scarp, a factor relating the depth of debris cover to the reduction in sublimation rate, and the height of the
scarp at which debris begins to accumulate.
Our model results suggest a clear relationship between temperature and debris-free sublimation rates at the time of ice formation
and the resulting thickness and lateral extent of LDA’s. We found
62
J.L. Fastook et al. / Icarus 228 (2014) 54–63
that warmer temperatures and lower sublimation rates led to
greater margin extent (Fig. 3b), while warmer temperatures and
larger sublimation rates led to thinner LDAs (Fig. 3a). With the definition of a ‘‘distance’’ metric that allows us to assess the goodness
of our fit to the desired target LDA’s thickness and lateral extent, we
observed an envelope of temperatures and debris-free sublimation
rates that could have produced the target LDA configuration (Fig. 4).
We then compared model results to observations and found
that: (a) modeled profiles compare well with observed LDA profiles
(Fig. 7); (b) an inventory of LDAs along the Dichotomy Boundary
observed and characterized by thickness and lateral extent (Ostrach, 2007) yielded a map of temperatures and debris-free sublimation rates showing geographic and topographic trends in our
results (Fig. 8); (c) a typical formation time from when the ice
surface drops below the cliff top to when the LDA is completely
armored for the cataloged LDAs of 400–500 ka is observed
(Fig. 9), suggesting that these LDAs could have formed relatively
rapidly during the collapse of the ice sheet.
These results show that observed LDA length and thickness
characteristics are consistent with climate conditions and a formation scenario typical of the collapse of a regional retreating ice
sheet and exposure of bedrock cliffs.
The collapse of a regional retreating ice sheet helps resolve
many of the unusual characteristics of lobate debris aprons (LDA)
and lineated valley fill (LVF). For example, the distribution of LVF
is very consistent with extensive flow of glacial ice from plateau
icefields (e.g., Head et al., 2006a, 2006b; Head et al., 2010; Fastook
et al., 2010), and the acquisition of a debris cover in the waning
stages of retreat of the regional cover (Dickson et al., 2008, 2010)
as the bedrock scarps and regolith are exposed. The typical concentric development of LDA around massifs is much more consistent
with ice sheet retreat than insolation-related local accumulation
and flow of alpine-type glaciers. In addition, results from GCMs
(Forget et al., 2006; Madeleine et al., 2009) that predict widespread
areas of positive accumulation rates are consistent with the formation of regional ice sheets whose collapse would leave these features as remnants.
Martian ice sheets, in their colder and drier environment, might
never attain full equilibrium configurations as ice sheets do on the
warmer and wetter Earth. However, our LDA formation mechanism
indicates that regional ice sheets that completely bury the terrain
are very likely to form. During collapse in response to changing climate, this ice sheet is controlled by the basic conservation of mass
and momentum framework on which the ice sheet model is based.
Given our results, we thus conclude that the retreating ice-sheet
model is a reasonable LDA formation scenario and should be investigated and tested in more detail.
Further, we conclude that LDAs in the along the Dichotomy
Boundary could never have experienced temperatures near or
above the ice melting point and still retain their current shape, a
finding that supports subzero temperatures for the last several
hundred million years. One might then expect to potentially find
preserved below the sublimation lag deposit, ancient ice that contains a record of the climate of Mars when the LDAs formed.
Acknowledgments
We thank the National Aeronautics and Space Administration
(NASA) for financial assistance to support this work through a Mars
Data Analysis Program Grant (NNX11AI81G) to J.W.H.
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