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Accepted Manuscript
The Formation and Stability of Buried Polar CO2 Deposits on Mars
Curtis V. Manning, Carver Bierson, Nathaniel E. Putzig,
Christopher P. McKay
YICAR 12970
To appear in:
Received date:
Revised date:
Accepted date:
6 April 2018
22 June 2018
26 July 2018
Curtis V. Manning,
Carver Bierson,
Nathaniel E. Putzig,
Christopher P. McKay, The Formation and Stability of Buried Polar CO2 Deposits on Mars, Icarus
(2018), doi:
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? The Clancy effect allows burial of CO2 deposits to preserve them during higher obliquity
? Further stabilization of buried CO2 occurs at
depth by close-off of pore space.
? The deepest CO2 deposits approach the triple
point temp. making basal melting possible.
The Formation and Stability
of Buried
Polar CO2 Deposits on Mars
In the shelter of some of those scarps and troughs,
deposits have been found that are thought to consist
of solid CO2 covered by a layer of insulating water ice
(Phillips et al., 2011; Bierson et al., 2016 ? hereafter,
Curtis V. Manninga , Carver Biersonb , Nathaniel
Recent radar observations of the southern polar cap
with SHARAD, the Shallow Radar sounder, on the
E. Putzigc and Christopher P. McKaya
NASA-Ames Research Center, MS 245-3, Moffett Field, CA
Mars Reconnaissance Observer (MRO) have revealed
94035-1000, USA
radar ?reflection-free zones? (RFZ) that require mab
U.C. Santa Cruz, 1156 High St. Santa Cruz, CA, 95064
terial with a dielectric constant close to that of solid
Planetary Science Institute, 1546 Cole Blvd., Lakewood, CO
CO2 in order for the depth analysis to render under80401
lying water-ice layers flat in radargrams (Phillips et
al., 2011), in continuity with abutting layers. Further
Draft version August 18, 2018
investigations show the presence of sublimation pits
in the unit known as Aa3 of the residual cap (Kolb
and Tanaka, 2006; Tanaka et al., 2007) that overlies
that pure
Shallow Radar soundings of the south polar layered depositsthe
have revealed
with as many as three distinct layers separated by thinner layers of 2water ice (Bierson et al., 2016). This
layering is suggestive of formation by cyclical processes such as obliquity, eccentricity and advance of
of COto
on Mars (Putzig et
2 have
perihelion. If obliquity is the main driver, then there were manyexchangeable
opportunities inventory
for CO2 deposits
layers, bounded by
formed within the last 3.5-4 Myr. To persist, however, CO2 deposits must be followed by the deposition
to three CO2 layof an insulating layer of porous water ice that can seal in the CO2 to survive the obliquity maxima
that follow. We suggest that the existing deposits were formed within the last 350 kyr. Each obliq- The maximum
of theindeposits
is a little
over one kilometer
uity minimum was quickly followed by a period in which perihelion
the northern
(southern winter) solstice. Under these conditions, an enhanced deposition of low porosity, fine-grained of depositional
cycles, likely
by the
oscillawater ice could occur on the winter pole. A similar series of depositions
and dominated
burials by water
have occurred between 2.75 and 2.2 million years ago, but these deposits were unlikely to have survived
the many high obliquity swings that occurred between 2.2 Ma and 400 ka. The formation and burial
formaof CO2 ice could also have occurred in similar fashion earlier during the last ? 100 Myr in which the
of deposits
during flux
the may
last be
? 3.5
southern polar layered deposits were formed. Although at current
the geothermal
too to 4 Myr of low
low to cause basal melting of CO2 deposits, in earlier times, deposits formed in deeper scarps and valleys 1.
in these
deposits suggests
could have led to basal CO2 melting and sequestration into the While
and sequestration in the regolith may provide an explanation for the fate of the thick CO2 atmosphere kyr obliquity
cycle, they may also be dependent on other factors,
(pCO2 >
? 0.5 bar) implied by climate models of early Mars.
such as eccentricity or the seasonal timing of perihelion. In particular, the survival of a CO2 deposit
depends on their being sealed by a blanket of insuMars, polar caps, basal melting, obliquity cycles
lating porous water ice before the subsequent rise in
the obliquity causes the ambient surface temperature
to rise above the frost point of CO2 . Another reThe Martian south polar ice cap consists of 3 comquirement for deposit stability is that the water-ice
ponents, the seasonal cap, the residual cap, and the
deposit should be deep enough that the thermal grasouth polar layered deposits (SPLD). The seasonal
dient would accelerate the sintering process near the
cap is composed CO2 ice less than about 1 meter
bottom of the deposit to the extent that the ice grains
thick. The residual cap is composed of CO2 which
compress to the point that the pores are cut off from
survives the summer, and is about 10 meters thick.
each other so that CO2 vapor cannot diffuse out.
The SPLD is a more extensive deposit of water ice
The temporal variations of obliquity, eccentricity
with a small amount of dust, and some layers with a
and perihelion advance, each with different cadences,
high fraction of dust. It is approximately 3.5 km thick
may result in CO2 and water-ice deposition cycles
at its thickest (Tanaka, Kolb and Fortezzo, 2007).
that, for a given low-obliquity excursion, may or may
The layered deposits have scarps, gullies and troughs,
not be synchronized in a way to form and seal a
formed during periods of strong ablation (Milkovich
CO2 ice deposit. The availability of the Laskar et
and Plaut, 2008), although it remains possible, by
al. (2004) calculations of obliquity and orbital paanalogy to the northern cap, that the chasmata and
rameters of Mars for the last 20 Myr allows a detroughs may be constructional features formed during
tailed assessment of opportunities for the formation
accretion (Holt et al., 2010; Smith and Holt, 2010)).
We have noted that the existence of today?s buried
CO2 deposits in the SPLD depend on the subsequent
burial by an insulating boundary layer while the surface CO2 cap is still stable to ambient temperatures.
The conditions for transport of water southward
are sensitive to the orbital parameters. According
to Clancy et al. (1996), water ice could accumulate
in the south when perihelion occurs in the northern
summer at rates approaching a solid ice-equivalent
of up to 10 mm per year. If we assume an average rate half of that, then during a ? 10 kyr period
during which perihelion occurs in the northern summer (southern winter), an equivalent of 50 m of zeroporosity ice could accumulate. However, some of this
layer would be lost during the subsequent southern
summer, during which ablation would dominate in
the south. Given a 30 m deposit (the average of BL1
or BL2 ) of pure ice after an obliquity cycle, then before compaction the high porosity snow could have
initially been ? 100 m thick if it had a porosity of
70%. However, many processes could have driven this
porosity down, including sintering and compaction
due to the overburden of the seasonal cap. The current top boundary layer, BL3 , is less than 20 m thick,
some of which is mostly buried by unit Aa4 (Tanaka
et al., 2007). However, it is very doubtful that BL3
is as compacted as the boundary layers below it, and
so is likely to have a lower water content.
In B2016, the Shallow Radar instrument on the
Mars Reconnaissance Observer (MRO) was used to
collect a total of 429 radar scans of the SPLD. These
were used to analyze the layered deposits at latitudes
north of 87? S (see B2016 Fig. 1a). The RFZs are
detected within the residual ice cap, and taken to be
CO2 .
In Table 1, we reproduce data from Table 1 of
B2016. In the first column are shown the layer designations (naming conventions of units set by Tanaka
et al., 2007), in column two are the compositions.
These units are divided vertically into three sections
separated by horizontal lines. The top section is the
residual cap. The middle section is what could be
called the upper SPLD composed of the alternating
layers of RFZs and boundary layers, which are numbered from the bottom up. Below the bottom line
is the lower SPLD with two units of water ice that
extend down to the regolith. In column 3 are posted
the averaged thicknesses in meters of each layer. We
note that the round numbers presented in Table 1
mask irregularities in the thickness of the RFZs and
boundary layers, and not all layers are present at each
location. As a result, adding the layer thicknesses
from the top to the bottom of layer Aa3a , one finds
a thickness of 1.2 km, although the deepest part of
the CO2 deposit is only a little over 1 km in depth
current cap (Nye et al., 2000). On current Mars, CO2
deposits need to be contained, or else they will flow
on geologically short time scales. Radargrams presented in B2016 show that the deposits are exposed
in scarps and troughs. Radargrams also show the
details of the layering of the water-ice cap that contain the deposits. Below some of the CO2 deposits,
horizontal layering in the water ice can be seen. Elsewhere, there are apparent signs of differential settling
and locations of unconformity in the water-ice layering, often aligning with the scarp slopes that contain
the deposits, extending into lower water-ice units.
and burial of CO2 deposits on Mars.
Below, we present the B2016 data on RFZs (�,
followed, in � by a discussion of the factors affecting the deposition and preservation of buried CO2
deposits in recent, and the less-recent past. In � we
touch on the possibility of basal melting of CO2 ice.
Basal melting is strongly limited by the geothermal
flux, the depth of the deposit and, to a lesser extent,
by the conditions within the top boundary layer (Mellon, 1996). We discuss our results and present conclusions in �
Table 1: Layering data (B2016)
Unit name Composition Unit thickness (m)
CO2 /H2 O
? 10
H2 O
< 20
H2 O
< 700
H2 O
H2 O
H2 O
Because of the unusually low viscosity of CO2 , a
cap of pure CO2 could not support the profile of the
3.1. The Clancy effect(1996)
Currently, Mars is near aphelion in the northern
late spring to summer season, Lp = 251? . Under
these conditions, with perihelion near the southern
summer solstice, the transport of water vapor is generally northward (Clancy et al., 1996). However,
about 25 kyr ago, the longitude of perihelion was in
the northern summer (Lp = 71? ), and when this occurs, conditions are optimal for southward transport
during the southern winter. Under such conditions,
especially when the eccentricity is large, temperatures rise, water sublimes from the northern cap, and
moves toward the equator. When perihelion occurs in
high obliquity, a switch to low obliquity would likely
provide a substantial source for both poles, regardless
of eccentricity. Breaks in a continuity of episodes of
delivery can also occur during periods of high polar
insolation (e.g., Putzig et al., 2009).
The Clancy effect implies that the accumulation of
water-ice layers on the north and south poplar layered deposits should not have a direct correspondence
with each other since the timing of periods in which
net accumulation could be expected are separated by
? 25 kyr, by which time eccentricity and obliquity
will have changed significantly. However, the major depositional breaks between sets of deposits (e.g.,
Milkovich and Plaut, 2008) very likely correspond between north and south, being sensitive both to high
obliquity and or low eccentricity. If a correspondence
between these ablative breaks that define the sets of
layers is made, then the variation of layers within
the respective sets (both north and south) can be
modeled if these sets are properly correlated with the
Laskar et al., (2004) obliquity and orbital data. Then
the details of the corresponding sets could provide insight into the details of accumulation and ablation on
the respective polar layered deposits.
According to Levrard et al., (2007), ice migrates to
the poles either from equatorial regions or the higher
latitudes of either hemisphere. It is likely that at 5
Ma, before which the obliquity was high, the equatorial regions would have had a significant amount of
water while the higher latitudes would have had little. After millions of years of low obliquity, however,
the low-latitude source of water ice has probably been
depleted. Generally, therefore, the rate of growth of
the polar caps during a long-term period of low average obliquity should decline in time, with seasonal
exchanges driven primarily by the Clancy effect.
Judging from the estimated cratering age of the
SPLD, there must have been a significant period of
low obliquity, ending between about 30 and 100 or
so Myr (Koutnik, Byrne and Murray, 2002) in which
much of the equatorial ice was transported to the
poles. Following that there must have been a period
of high obliquity to dessicate the poles, leaving a thick
lag at Promethei Lingula, followed, during the last 5
Myr, by a new low-obliquity stage. It would appear
that the 300 m of water ice accumulated in the lower
SPLD was added during the last 5 Myr since it shows
no sign of having had an extended period of ablation.
While we can know little of the obliquity and orbital parameters beyond 10 or 20 Myr, we have detailed information for the last 10 Myr. This can be
used to diagnose the forces which formed and buried
the CO2 deposits in the upper section of the SPLD.
the northern summer, atmospheric water vapor concentrations can be an order of magnitude greater than
at aphelion (Clancy, 1996). Since the temperature in
the northern hemisphere is from 20 to 25 K greater
under these conditions than at aphelion, the altitude
at which the saturation of water vapor would occur is
25 or 30 km. This vapor can then be caught up in the
ascending branch of the Hadley circulation and taken
southward. When perihelion occurs in the southern
summer, conditions are reversed; temperatures in the
northern summer are lower, and the saturation of water vapor occurs at altitudes of about 10 km, below
the reach of the Hadley circulation. The water vapor
nucleates on dust, freezes and gravitationally settles.
Thus, perihelion advance can very broadly control the
growth and ablation of the respective ice caps. Simulations of the south polar ice cap by Montmessin
et al. (2007) confirm this view for both phases of
the perihelion cycle. An exception to this pattern
may occur when global dust storms cause the atmosphere to warm during the northern aphelion, such as
in 1976 and 1978 (during the Viking mission), to the
point that higher concentrations of water occurred,
allowing the vapor to rise to high altitudes and become entrained in the Hadley circulation (Clancy et
al., 1996).
The precession-induced variability in water vapor transport is called the ?Clancy effect? (e.g.,
Montmessin et al., 2007). Because the perihelion
advance is a 51,000 year cycle, it reverses direction every 25,500 yr. High eccentricities enhance
the net yearly transport of water since it enhances
the north/south temperature asymmetry, helping to
magnify the Clancy effect. According to the modeling
work of Levrard et al. (2007; Fig. 2) higher obliquities may stifle net yearly transport since summer
ablation at the aphelion would increase more rapidly
with obliquity than the accumulation rate at perihelion. Under higher obliquity water tends to move
toward the lower latitudes. However, for moderately
high obliquity, this effect may be may be effectively
counter balanced if the eccentricity is high since, if
aphelion is in the southern summer, a large eccentricity can reduce polar insolation to a level normally
delivered only at a lower obliquity.
While the short-term variability of the eccentricity
has a 25,500 kyr period, there is a longer 1.8 Myr period over which the eccentricity moves from a high of
' 1.2 to zero and back again (Ward, 1979). When
the eccentricity is near zero, there is a cessation of accumulation at the poles (Clancy et al., 1996), producing a break in a series of layers, as seen in the NPLD.
However, this conclusion must depend on there being
only a small rate of delivery of water from the low latitudes, as is the case today, but after a long period of
3.2. The recent past
3.2.1. The last 520 kyr
To give a picture of the conditions during which the
CO2 deposits on the SPLD were formed, we present,
in Figure 2, the recent historical trends in orbital parameters and obliquity (Laskar et al., 2004) in correspondence with our simulated evolution of CO2 inventories over the last 520 kyr. To chart the evolution of CO2 inventories we use the Mars Evolution Code (MEC; Manning et al., 2006). MEC is a
yearly averaged energy balance model of CO2 evolution to which the many sources and sinks are fully
coupled, and driven by the modeled obliquities of
Laskar et al. (2004). The upper three panels of
Fig. 2 show the trends in eccentricity, longitude of
perihelion, and obliquity, respectively. The horizontal line in the obliquity plot shows the approximate
obliquity (? ' 26? ), at which a surface CO2 ice cap
would sublime away. The bottom panel of Fig. 2
shows simulation results, initialized so that the current atmospheric pressure (orange ?+? sign) can be
reached. The running atmospheric partial pressure of
CO2 , PCO2 , is in black, the regolith content is in red,
and the surface CO2 ice deposit is shown in blue.
The calculation of polar temperatures in MEC are
based on a model of Marinova et al. (2005), developed
to account for the meridional advection of heat from
equator to pole. This is in turn based on an analytical approximation of an advection parameter, ?, by
Gierasch and Toon (1973). Meridional adevection of
heat plays an important role in determining the obliquity at which the atmosphere may collapse. However, recent general climate model studies by Soto et
al. (2015) claim that models of meridional transport,
such as Gierasch and Toon, (2015), Marinova et al
(2005), and Manning et al. (2006; see Eq. A32), may
overestimate the magnitude of heat transport, causing an underestimation of the obliquity below which
atmospheric collapse may be triggered.
Polar temperatures are calculated using yearly
averaged solar insolation, greenhouse warming and
meridional advection. The latter is based on the
equator to pole thermal gradient (Haberle et al.,
1994). The calibration procedure for MEC is to adopt
an average polar albedo, then adjust the magnitude
of the advection parameter to achieve an atmospheric
pressure of ? 6.5 mbars under the current obliquity,
as well as to arrange for the disappearance of the
cap when the obliquity rises to approximately 27.5?
(Francois et al., 1990). We have found that reducing
the advection parameter to one tenth of that used in
our study can be compensated by a relatively small
reduction of the albedo (i.e., Ap ' 0.700 reduced to
Ap = 0.686. Results show that for atmospheric pressures visited by the simulation in Fig. 2, the obliquities at which the atmosphere both collapses and
re-sublimes would be increased by less than one degree of arc for an advection parameter reduced by
a factor of ten. This difference has an insignificant
affect our results, primarily because the response of
calibration to a reduction in the advection parameter
is to lower the albedo, which tends to stabilize pole
temperatures. Also, for smaller advection parameter
values, greenhouse warming dominates the advective
heat transport, so that further reduction of the advection parameter produces smaller changes. However,
for significantly higher atmospheric pressures (e.g.,
? 100 mbars), the reduction of advective transport
can have a significant effect on both collapse and resublimation obliquities.
Note that the Manning et al. (2006) model includes an active regolith which releases CO2 when
the atmosphere collapses (Zent & Quinn, 1995; Toon
et al., 1980). This serves to make CO2 caps more
massive than would be the case when ignoring the
regolith content since the decline in atmospheric pressure causes the regolith to outgas. Our parameterization of the regolith is presented in Manning et al.
(2006), Fig. 2 of Appendix 6, where the current regolith content was assumed to be 50 mbars. However, according to Zent and Quinn (1995), without a
very deep powdered regolith (e.g., 100 m), the most
likely exchangeable inventory is between about 1 and
4 kPa. We scaled the regolith content to 60% of our
previous value so that the adsorbed inventory would
be ? 30 mbars at the current averaged temperature
and pressure of Mars (see Eq. A21 of Manning et
al., 2006). With an active regolith, if a 12 mbar atmosphere were to collapse to PCO2 = 1.0 mbar, we
find that the CO2 ice cap thereby formed is equivalent to about 26 mbar atmospheric. This only includes 11 mbars from the atmosphere, so the other
15 mbars must come from the regolith. This result
implies that the regolith strongly buffers the atmospheric pressure. Thus, with an active regolith, if the
current inventory of frozen CO2 within the RFZs (? 7
mbars; Putzig et al., 2018) were to sublime, the atmosphere (? 6.5 mbar) would pick up only about 2.9
mbar of CO2 making it 9.4 mbars while the regolith
would pick up about 4.1 mbars.
The vertical lines in Fig. 2 are aligned with particular longitudes of perihelion; red (dot-dashed line)
for LP = 90? , and blue (short-dashed lines) for the
flanking values, LP = 0? and 180? . These are intended to help the eye in judging the synchronization of the southward transport of water with the
The obliquity and orbital parameter simulations of
Laskar et al. (2002; 2004) provide an opportunity to
study the effects of obliquity, perihelion advance and
eccentricity on the residual cap.
B2016 as the top and bottom of the water-ice layer.
However, the analysis above suggests an alternative
interpretation. We propose these two reflections may
be two distinct water-ice layers with thicknesses below the ? 15 meter resolution of SHARAD separated
by a thin CO2 layer of about 10 meters. If true, it
would help remove any ambiguity associated with the
suggested B2016 obliquity associations of the respective CO2 deposits.
Looking a little further back in time, we note that
in Fig. 2, the obliquity minimum at ? 450 ka has no
corresponding deposit in the SPLD under our suggested interpretation, although perihelion occurs in
the northern summer within the time that the CO2
ice cap is still massive. We find two possible reasons why this unit might be missing. First, the eccentricity is relatively low and declining while perihelion is in the southern winter, suggesting that the
Clancy effect could have been weak, producing a relatively thin insulating layer of snow. Another factor could be that, following the burial of the deposit,
the obliquity reaches about 30? . A thin water-ice cap
and a relatively strong period of ablation could therefore explain its absence. Simulations with the LMD
Martian Global Climate Model (Forget et al., 1999;
Montmessin et al., 2004) by Levrard et al., (2007) of
the north polar layered deposits (NPLD; Figure 1),
suggest that at this obliquity, ? = 30? , the ablation
of a couple of millimeters per Mars year is likely. In
principle this result is applicable to the south over a
perihelion cycle, since the two caps appear to be in a
near depositional equilibrium. We note that the ablation of two millimeters per Mars year, summed over
10 kyr of ablation is still the equivalent of about ten
meters of zero porosity ice lost over a perihelion cycle. Considering a possibly thin water-ice layer, this
may be significant.
It is similarly notable that the deposit at 320 ka,
here assumed to be Aa3a , also has the perihelion
rather optimally placed relative to the obliquity minimum. Nevertheless, this deposit has a rather spotty
presence on the SPLD. As can be seen in B2016 Fig.
1b, RFZs are generally localized in three separate locations, low on the cap, high on the cap, and in between. The deposit of greatest area, layer Aa3a is
low on the cap, but it is relatively thin. The CO2
deposits half way up the cap have no representative
of unit Aa3a (just Aa3b and Aa3c ). There is only a
small unit Aa3a deposit high on the cap. We note,
however, that the high-obliquity period that followed
(240 ? t ? 300 ka) barely exceeds the 26? limit of
surface CO2 stability, suggesting that ablation should
not have been a serious threat to its stability. On the
other hand, the eccentricity during southern winter
solstice is relatively low and declining during the pe-
formation of the buried CO2 caps. Horizontal bars
are placed between these vertical lines at an ice cap
pressure-equivalent at the southern winter solstice for
each potential CO2 ice burial.
In the calculation of the evolution of CO2 shown in
Fig. 2, it was assumed that 10% of frozen CO2 was
buried each time the CO2 cap forms. In defense of
this, we note that existing buried CO2 is only found in
sheltered regions of the SPLD that amount to about
10% of its surface area, suggesting that the more exposed CO2 sublimes when obliquities rise. This is
a convenient way to simulate the progressive burial
of some of the CO2 cap. In actuality, burial may depend on the seasonal dust storms, trends in eccentricity with time, and the availability of deep sheltered
spaces for CO2 deposits, as well as the variable longitude of perihelion, eccentricity and obliquity (Clancy
et al., 1996). The CO2 ice deposits represented in
Fig. 2 are surface caps since MEC does not currently
model their burial.
In B2016 it was suggested that the CO2 deposits
in the SPLD may have formed during the last 340
kyr; unit Aa3a at 340 ka, unit Aa3b at 200 ka and
unit Aa3c at 22 ka. Figure 2 shows that in each case,
the minima in obliquity are followed by a period in
which perihelion occurs in the northern summer, as
we are led to believe should be the case for CO2 burial
(Clancy et al., 1996). To these three deposits, we
now suggest another; in Figure 3 we show an enlargement of the radargram from the upper-right corner
of B2016 Fig. 2a, showing that the boundary layer,
BL2 , shows two separate reflections, with a RFZ in
between. If this deposit (let us provisionally call it
Aa3b0 ) is indeed a CO2 deposit, then there must be
an obliquity minimum following the 200 ka unit Aa3b ,
and perihelion in northern summer must quickly follow that. Reference to Fig. 2 shows that all conditions are met, as there is a small obliquity minimum
at ? 125 ka, followed shortly afterwards by perihelion in the northern summer. The possible bifurcation of BL2 can be seen at other locations of B2016
Fig. 2a and 2b that show BL2 , but this double layer
is not apparent in other boundary layers. In their
Fig. 2b (upper right), this same locale (see the paths
of the two radar scans in Fig. 1b of B2016) has an
irregular BL2 with the two reflections erratically distributed, as though the depth of the boundary layer
varied within the footprint of the radargram. We
must note, however, that the eccentricity is low during the ? 10 kyr period at ? 125 ka in which BL2b
would be expected to have formed, suggesting a possibly thin water-ice layer. However, the obliquity that
follows this period barely exceeds 26? , thus minimizing ablation from the following summers.
The two reflections of BL2 were interpreted by
of 6.5 mbar (dotted) and 12 mbar (solid line), and the
figure shows the effect both on the atmosphere and
regolith at obliquities ? >
? 26 . The situation is in
fact quite comparable to the last 350 kyr, including
the presence of what could plausibly produce a double
water-ice layer with CO2 in between. In the comparison, it would also be necessary to explain the absence
of the first possible deposit at ? 2.7 ka. However, the
high obliquities near t = 1 and 2 Ma augur for high
rates of ablation of the upper boundary layer and the
sublimation of any near-surface CO2 deposits. We
suggest these deposits could not have survived the
much more intensive insolation that was to follow.
3.2.4. Opportunities for basal melting in the last
? 100 Myr
Although the above analysis only pertains to the
last ? 3.5 Myr, the southern polar layered deposits
are thought to be many millions of years old, judging
from crater retention ages (Koutnik, Byrne & Murray, 2002). It is reasonable to consider whether, during the extended period of their construction, there
could have been opportunities for similar atmospheric
collapses, with CO2 deposits in crevasses and scarps,
buried under snow, similar to the deposits in the
SPLD. Indeed, shallow radar studies have found numerous RFZs within the lower section of the SPLD
(Phillips et al., 2011, supplementary material). These
RFZs are not confirmed as CO2 since we do not yet
have a good means to establish their dielectric constant since no favorable layering geometries have been
The stratigraphic study of Milkovich and Plaut
(2008) finds that the southern polar layered deposits
are composed of three major sequences or units. The
second unit, P LL, which is exposed in Promethei
Lingula, consists of a sequence of sets of layers that
are interrupted by unconformities suggestive of periods of ablative climate change. This sequence ends
with a strong period of ablation that produced deep
scarps and the curvilinear valleys (Milkovich and
Plaut 2008). PLL has a domed shape of height ? 3
km above the southern plains (Tanaka et al. 2007;
Milkovich and Plaut, 2008). According to Koutnik
et al. (2002), the crater-retention age of this unit is
between 30 and 100 Myr of age. We suggest that
during the construction of P LL and of the following ? 300 meters of layered deposits upon which the
lower SPLD is placed, there may have been many opportunities for the deep burial of CO2 deposits some
of which could have resulted in the basal melting of
CO2 .
riod in which the Clancy effect would otherwise have
been active, suggesting weak water transport. We
suggest that other, perhaps mesoscale factors, may
have affected the distribution of CO2 deposits, or subsequent water-ice deposits.
We note also that the top boundary layer, BL3 , is
thin (< 20 m), especially considering that it is unlikely to have been compacted as much as the lower
boundary layers. The buried boundary layers are
likely to have been sintered at depth (a temperaturesensitive process), and crushed by the overburden of
hundreds of meters of CO2 and water ice. The sublimation pits in BL3 (B2016) may be a sign of the
permeability of the layer, suggesting that not all of
unit Aa3c will long endure.
While the deposits Aa3b (200 ka), Aa3c (22 ka),
and the proposed deposit at Aa3b0 (125 ka), seem to
obey the general criteria for CO2 deposits outlined
earlier, the obliquity fluctuation at 450 ka, and to a
lesser extent, 340 ka, show a lack of proportionality
in their resulting deposits with respect to obliquity
minimum and perihelion placement. The variability
of the Aa3a deposit size with position on the SPLD
suggests that the value and trend of eccentricity may
be a significant factor in determining the thickness
of the boundary layer. To help disentangle the relative strengths of obliquity and eccentricity and perihelion in determining water transport will take a
more detailed model of atmospheric evolution such
as a zonal/seasonal model or a GCM.
3.2.2. Obliquity variations between 520 ka and 1 Ma
For obliquity variations between 520 ka and 1.0 Ma,
there are few situations in which the proper relative
positioning of perihelion and obliquity minima occur.
One case at ? 800 ka finds the relative perihelion
and obliquity minimum ideally placed for a strong
Clancy effect, but evidence for that deposit is lacking in the SHARAD data. We note that the lowobliquity excursion at ? 800 ka was followed by a
high-obliquity excursion in excess of ? 35? (see Fig.
1). According to Figure 1 of Levrard et al. (2007), in
the northern summer season, ablation can far exceed
the winter accumulation rate at such high obliquity,
suggesting that a hypothetical deposit of water ice
would not survive a subsequent obliquity maximum
of ? ? 35? , allowing the just-buried CO2 deposit to
sublime. Again, this model of the NPLD ought to,
under averaged conditions, accurately approximate
the response on the south pole.
3.2.3. Opportunities at 2.75 ? t ? 2.2 Ma
In Figure 4, we explore another period of time in
which the variations are minimal ? those between 2.2
Ma and 2.75 Ma. We ran the MEC at initial pressures
?T =
4.1. The effective thermal conductivity of the upper
boundary layer
Although we are neglecting the water ice of the inner boundary layers, we cannot neglect the thermal
effect of the insulating upper boundary layer. Mars
conditions are ideal for forming a very low thermal
conductivity upper boundary layer; moisture delivered in the Hadley circulation could condense around
sub-micron sized dust as nucleation sites, freeze, and
fall to the residual cap, forming dry, particulate snow.
On the other hand, it is theoretically possible that
saturated air advected into the area close to the
residual cap could be directly deposited on the residual cap, forming something akin to hoarfrost, which
could have a significantly greater thermal conductivity. Under the conditions of a relatively rapid deposit
delivered by Hadley circulation, we assume that a dry
snow is the more likely initial result.
We assume the boundary layers are composed of
frozen water that was condensed around dust grains
as nucleation sites. We assume the snow particles
have a diameter of approximately 50 祄. Terrestrial
observations of the thermal conductivity of dry snow
suggest a lower bound of about k = 0.078 W m?1 K?1
(e.g., Mellon, Ferguson and Putzig, 2008). However,
when the mean free path of molecules is greater than
the pore sizes, the thermal conductivity is controlled
by the atmospheric pressure. For dust-nucleated
snow with a size of ? 50 祄, the thermal conductivity is reduced by over an order of magnitude
at current Martian pressures (Mellon, McKay, and
Grant, 2015; Edgett & Christensen, 1991), suggesting
?1 ?1
that kH2 O <
? 0.0078 W m K . However, the sintering process, principally produced by grain boundary
diffusion and sublimation-condensation, can change
the effective grain size at temperature-sensitive time
scales, causing an increased surface area of contact
between grains, and a higher thermal conductivity.
The process of sintering can fuse individual grains
together, increasing the thermal conductivity of the
material. In an experimental study by Kaempfer and
Schneebeli (2007), they recorded the advance of the
sintering process at a range of temperatures over periods of up to a year. They used a parameter called
the specific surface area (SSA), which is the surface
H = 20 (� mW m?2 ,
where ?z is the slab thickness in meters, and H is
the geothermal flux (Mellon, 1996). The canonical
value of H is 30 mW m?2 (Clifford, 1987; Heldmann
et al., 2005), however recent studies with SHARAD
suggest that there has been very little isostatic compensation (less than 100 m) in the Gemina Lingula
lobe of the NPLD (Phillips et al,., 2008), or the
main lobe of the NPLD (Putzig et al., 2009), implying an elastic thickness greater than about 300 km
(Phillips et al., 2008; supplementary material). This
appears to limit the value of the geothermal flux at
the north pole to H ? 13 mW m?2 (Dehant et al.,
2012). However, stagnant lid models suggest that
there is significant variability in the thermal flux over
the planet, some of which suggest a south polar value
near H ? 20 mW m?2 (Dehant et al., 2012). Thus,
we consider that the south polar geothermal flux is
in the range,
perspective, but this is not particularly important for
understanding the issues of basal melting. Because
boundary layers, BL1 and BL2 , are relatively thin
and their thermal conductivity is likely to be high, the
temperature difference due to their presence would
add to only a little over 1 K at the bottom of the
CO2 slab. In the following analysis, we simplify the
problem by considering a pure CO2 slab of arbitrary
Here we examine the possibility of basal melting,
and under some conditions, sequestration into the regolith.
In equilibrium, the temperature shift across a layer
of thermal conductivity, k, is
W m?1 K?1 ,
kCO2 (T ) =
although the global average appears close to
30 mW m?2 . Please note that, for the convenience
of presentation, we have given H in units mW m?2 ,
but it must be converted into W m?2 our equations.
Below, we study the thermal structure of CO2 slabs.
The thermal conductivity of CO2 is a function of
temperature, well-modeled by the following function,
where T is the temperature in Kelvins (Kravchenko
and Krupskii 1986). For instance, a moderately thick
upper boundary layer could result in a temperature
T = 165 K at the top of the CO2 slab, for which the
thermal conductivity would be k = 0.566 W m?1 K?1 ,
while at the triple point of CO2 , T ' 217 K, k =
0.43 W m?1 K?1 . Substituting Eq. 3 into the differential form of Eq. 1, one finds the following integrable
For the melting of a thick CO2 slab to occur, it
must reach a temperature of 216.67 K at its base.
We round this up to 217 K for our calculations.
The fact that the CO2 ice is interspersed with layers of water ice is interesting from the stratigraphic
and the thermal gradient within the top boundary
layer would accelerate the diffusion of CO2 from the
deposit. Such conditions could lead to a permanent
feature being formed, such as the sublimation pits
seen overlying the RFZs today (Phillips et al., 2011).
Finally we suggest that seasonal frost could affect
the surface of the top boundary layer by penetrating
and binding the snow particles together, increasing
conductivity at the surface if the boundary layer is
not covered with seasonal/permanent CO2 ice. However, we believe this is unlikely to penetrate to a significant portion of the top 5 meters, so we neglect this
If we assume that both BL1 and BL2 have a porosity near zero (note that at only 90 meters under a CO2
cap on Mars, the pressure would exceed 5 bars), then
we may get an estimate of their thickness when they
were first formed. The lowest boundary layer, BL1 ,
which is observed to be ? 20 m (Table 1), would be
67 meters if it originally had a porosity of 70%. However, as we have seen, this maximal porosity may not
last long. If we accept that BL2 is actually two layers
of water ice, each 15 meters (and CO2 ice of thickness 10 m), then this would convert to 45 meters
each. However, these differences in thickness would
not significantly affect the temperture jump since, as
we suggest above, below about 10 m of the top waterice layer, the conductivity would increase to the point
that it would not significantly impede thermal conduction.
The southern cap is said to currently have a permanent cap of CO2 , less than about 10 m thick overlying the SPLD, which can survive the summer due
to its high albedo. In this case, the surface temperature would remain near the current frost point
of CO2 , about 150 K. Under a higher obliquity, this
CO2 surface cap would most likely disappear during
the summer season, and seasonal changes of surface
temperature would accelerate the sintering process.
The seasonal skin depth would vary from about 0.54
m (for k = 0.01 W m?1 K?1 and ? = 300 kgm?3 ) and
1.1 m (for k = 0.1 W m?1 K?1 and ? = 700 kgm?3 ).
But during the last 400 kyr, obliquities were low, and
a permanent CO2 cap could have persisted.
We summarize these results as follows. For the
current Mars, we judge that the top boundary layer
can be decomposed into three layers. Starting from
the top, a 5 meter layer of snow, then a 5-meter
layer of moderately sintered snow, and below that,
a high-conductivity layer, which contributes little to
the temperature jump between the top and bottom
of the top boundary layer. We assume a geothermal flux, H = 20 mWm?2 (Eq. 2). For the top
layer,with k = 0.008 W m?1 K?1 , the thermal gradient is dT /dz ? H/k = 2.5 Km?1 , or 12.5 K
area of snow accessible to gases per unit volume. Experiments measured the deformation and densification of grains of snow as small as 50祄 for a range
of temperatures. We found that measured rates were
proportional to the vapor pressure over ice. At 219 K
they report that the decline of the SSA is about 19%
in a year.
By calculating the partial pressure over water ice
at temperatures down to 150 K, we were able to approximate the time scale of sintering as a function of
temperature. We found that at 150 K, it would take
about 4 � 105 years for the SSA to decline by 20%,
roughly three obliquity cycles, and hence a negligible
rate for a south polar surface boundary layer. On the
other hand, at Martian atmospheric pressures, newly
formed snow at this temperature would have a very
?1 ?1
low thermal conductivity (kH2 O <
? 0.008 W m K ).
In this case, there is a substantial thermal gradient
dT /dz ' 2.5 K m?1 at equilibrium for a geothermal
flux of H = 20 mW m?2 . Under these conditions, if
the surface temperature were 150 K, at a depth of
five meters, the temperature would rise to ? 163 K
at current Martian atmospheric pressures.
At 163 K, the rate of the sintering process is about
1.5 orders of magnitude greater than that at 150 K,
so that the SSA would decline by 20% in only about
15 kyr, roughly the length of the period in which
perihelion aligns with northern summer. Thus, with
the Clancy effect, the great majority of the upper
boundary layer would be deposited within this sintering time scale.
Below 5 meters, however, the thermal conductivity of the top boundary layer could be significantly
affected. We suggest that between 5 and 10 meters
depth, the thermal conductivity could be increased to
k ' 0.02 W m?1 K ?1 , only moderately higher than at
5 meters depth since our initial assumption is that the
boundary layer for unit Aa3c formed about 22 ka, not
much longer than the sintering time-scale of 15 kyr
at that depth.
Below 10 meters depth, we expect that the effects of the overburden pressure on the density and
the thermal conductivity, would become relevant,
accelerating grain boundary diffusion, sublimationcondensation, and densification. We suggest that
?1 ?1
the thermal conductivity k >
? 1.0 W m K , and
that at some point, the sintering process will cause
the pores to close, preventing the diffusive venting
of CO2 . This pore blockage may be a crucial aspect of the stability of buried CO2 deposits which, on
Earth, occurs between snow densities of 820 and 840
kgm?3 (Herron and Langway, 1980). Sintering would
have to proceed to this point in a time-scale less than
about 10 kyr since obliquity is generally rising after
the CO2 deposit is formed, and rising temperatures
would just reach the triple point temperature is,
z ? = 1265 meters for H = 20 mW m?2 . The extremal values for H = 20 (� mW m?2 , and from
Eq. 5, yield are z ? = 936 m and z ? = 1816 m for
the upper and lower bounds of H, respectively. We
note here that, on the basis of this, basal melting is a
reasonable possibility during the previous ? 5 My of
growth of the residual cap. Note, however, that the
thermal gradient in the CO2 slab is, dz/dT = k/H,
?1 ?1
where we let kef
f = 0.5 Wm K , (the value of k
at 187 K). We find dz/dT = 25 mK?1 for the central
value, 33 mK?1 for H = 15 mWm?2 , and 20 mK?1
for H = 25 mWm?2 . Thus, if our estimate of the
temperature at the bottom of the upper boundary
layer was high by, say, 5 K, then z ? would be greater
by approximately five times the above values ? 125
meters for H = 20mWm?2 .
4.2.2. Deposits with z 0 > z ?
over 5 meters. For the zone (k = 0.02 W m?1 K?1 ),
5 ? z ? 10 m, dT /dz ' 1.0 Km?1 , or 5 K over
the next 5 meters. For the remainder of the top
boundary layer (k = 1.0 W m?1 K?1 ), we estimate
dT /dz = 0.02 Km?1 , or dz/dT = 50 mK ?1 . At this
thermal conductivity, over 20 meters there would be a
thermal jump of 0.4 K. Summing these temperatures
we find that the temperature rise from the top of BL3
to its bottom would be about 18 K. For a surface temperature of 150 K, this would imply a temperature of
168 K at the top of the unit, Aa3c . Applying the
extrema of our estimate of the geothermal flux at the
south pole (see Eq. 2), we find that the temperature
at the top of the CO2 slab would be approximately
= 168 K.
It is, however, likely that in time, such as the 20
kyr since we believe unit Aa3c formed, sintering will
advance and raise the thermal conductivity of the top
boundary layer. Thus, we suggest that 168 K is likely
an upper limit. We believe that Ttop = 163 K could
reasonably represent the minimum. An average of
the extremes gives,
= 165.5 �4 K,
where we use the extremal values of H (Eq. 1) to
generate the errors.
4.2. The thermal structure of a CO2 slab
Here we treat the CO2 deposit as a single slab. We
have a top temperature, Ttop = 165.5 � 3.4 K, and a
bottom temperature Tbott ? 217 K, where the upper
limit is the triple point of CO2 . As a simplification,
we neglect the boundary layers that divide the CO2
slab, since they have negligible impact on the thermal gradient of the CO2 . We consider two cases,
first of which is a CO2 slab whose thickness is less
than or equal to that at which can melting can be
approached. Following that, we consider the melting
rate with a still deeper deposit.
4.2.1. Depth of melting
Let us consider a single slab of thickness z ? such
that the temperature at the bottom just reaches the
triple point of CO2 without causing any melting. In
this case, the slab would transmit the full value of the
geothermal flux, H. Integrating Eq. 3, and solving for
thickness, z ? , we have,
z =
Substituting the central value of the temperature,
Ttop = 165.5 K, from Eq. 5, and Tbott = 217
K into Eq. 6, the thickness of a CO2 slab that
For a CO2 slab of thickness z 0 > z ? , we expect
basal melting to occur. In this case, the geothermal
flux through the slab at equilibrium, H 0 , would be
less than the current average value, assumed to be
H = 20 (� mW m2 , since the thermal gradient at
equilibrium would be more gradual,
?T kef f
where ?T is the difference between the triple point
and the temperature, Ttop , at the top of the CO2
slab. We let kef f = 0.5 Wm?1 K?1 , as above. Since
the heat flux that is devoted to melting CO2 ice is
H ? H 0 , the melting rate can be expressed as follows,
?T kef f 1
d2 MCO2
H ? H0
, (8)
dA dt
?f us H 0
?f us H 0 z ? z 0
H0 =
where the heat of fusion for CO2 is ?f us H 0 =
8347 J mol?1 or 1.897 � 105 J kg?1 . By dividing Eq.
8 by the density of CO2 (? 1600 kg m?3 ), we have
the vertical melting rate at depth z 0 > z ? . Results
for a range of z 0 under the three conditions discussed
above, are shown in Figure 5, where respective line
types are listed in Column 3 of Table 2. Melting
rates are given in millimeters per year. In reality,
the uneven topography containing the RFZs guarantees that each deep deposit would have a distribution
of melting rates, so that the weighted mean melting
rates of a deposit would likely be significantly smaller
than at the deepest parts.
Table 2 Minimal slab thickness for basal melting
H (mW m?2 ) ?T Ttop
z ? (m)
12.1 162.1
15.5 165.5
18.9 168.9
Our analysis of CO2 ice deposit survival is based on
observations of B2016, the analytical work of Clancy
et al. (1996), and simulations from the Manning et al.
(2006) model of atmospheric evolution. This analysis shows the consistency of the identifications of the
obliquity minima in the last 350 Ma with the layers
suggested by B2016. It should be noted, however,
that it is still possible that the series at 2.6 ? t ? 2.3
Ma could theoretically be the source of the deposits,
but many of the the series of high-obliquity excursions
between 2.2Ma and 500 ka would likely have ablated
and sublimed the deposits, leaving the scarps exposed
for the later series of obliquity minima at t <
? 400 ka.
In addition, the idea of the bifurcated boundary layer,
BL2 , suggests that the essentially zero porosity 40 m
layer suggested by B2016 analysis is actually two layers of water ice, perhaps 15 m thick each, plus one
layer of CO2 about 10 m thick. In this case, we would
have three boundary layers of thickness ?
< 20 m composed of very low porosity ice (not counting BL3 ).
Correcting for 70% porosity when they were the dry
snow was first formed, they would have been from
45 to 67 meters thick.
While the Clancy effect correctly predicts the
preservation of the CO2 deposits we do find, it may
be less efficient in predicting the absence of the one
at 450 ka, and the relatively less-robust deposit of
350 ka. It may be that these failures are due to the
relatively low and declining eccentricity during the
perihelion period at northern summer (southern winter) solstice, which would generally reduce the net
transport of water. However, the moderately high
obliquity maximum (? ' 30? ) following deposition of
the 400 ka layer may also have helped to erode what
may have been an already thin layer of snow. The
cause of the variability of the deposit size of unit Aa3c
with altitude on the cap cannot be fully explained by
eccentricity or other orbital factors since the obliquity maximum that followed its emplacement barely
exceeded 26? . For this, we may have to consider
mesoscale effects.
The analysis of the thermal structure of the top
boundary layer suggests that most top boundary layers of water ice, when first formed, could have been
significantly thicker than the current one, perhaps
40 to 75 meters thick, given an initial 70% porosity.
However, the time scale for densification may be rapid
(e.g., ? ? 14 kyr) due to temperature-accelerated sintering and compression in the lower half of the layer.
For CO2 deposits, the thermal gradient is very sensitive to the geothermal flux. However, for the central
value, H = 20 mWm?2 , the pont where basal melting begins is only about 200 meters below the current
deepest CO2 deposit (B2016). For depths in excess
of that at which temperatures just reach the triple
point of CO2 , the temperature gradient of the slab
(and thermal flux) is less, with the excess devoted
to basal melting. Although the limits on H suggest
that it is not likely that basal melting is currently
occurring, it is not excluded. Several million years
ago, during the construction of the SPLD, there could
have been troughs and valleys deep enough to accommodate significant basal melting. The opportunity
for sequestration into the regolith would be limited
by whether the deposits touched or approached the
underlying regolith. In that case, the exchangeable
inventory of CO2 on Mars could have been significantly diminished by earlier episodes of the formation of deep frozen CO2 deposits, especially at a time
when the geothermal flux was greater, as noted by
Kurahashi-Nakamura and Tajika(2006)
We have analyzed the conditions under which buried
CO2 ice caps could occur, considering Shallow Radar
probes of existing deposits, their thermal structure,
and the possibility of basal melting of CO2 within
the context of a declining atmospheric pressure and
geothermal flux. Based on this we reach the following
1. The Clancy effect, in which the alignment of perihelion with northern summer when the obliquity
has reached a minimum and a CO2 deposit has been
formed, can explain the burial and stabilization of
the CO2 layers in the SPLD.
2. A second important stabilization factor for CO2
deposits is the sintering and densification of the top
boundary layer with depth to a density greater than
the ? 800 kg m?3 pore cut-off limit, which seals in the
CO2 . This allows the deposit to survive the following
high-obliquity phase of quasi-periodic oscillations,
when the CO2 ice would otherwise be unstable.
3. The depth at which basal melting may occur
under the current geothermal flux is possibly only
about 200 meters deeper than the deepest of the
current deposits, opening up the possibility of basal
melting and sequestration of CO2 , both in the recent
and distant past. This has implications for the evolution of the Martian atmospheric pressure with time.
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Fig. 1.? The Laskar et al. (2002) values for the obliquity during the last 4 Myr. The ?plus? sign marks the present obliquity.
Red (short-dashed) line indicates the approximate obliquity at which a 12 mbar atmosphere would collapse. Green (long dashed)is
the collapse obliquity for a 140 mbar atmosphere. The blue solid line shows the obliquity at which a perennial CO2 ice cap becomes
unstable. The positions of the colored lines are based on the model of Manning et al., 2006 (see below).
Time (Myr)
Fig. 2.? The last 0.52 Myr of Mars evolution. From top down, panels show the eccentricity, the angle of perihelion, Lp , and the
obliquity, all from from Laskar et al. (2004), and on the bottom, a simulation of the atmospheric evolution model MEC (Manning
et al., 2006) showing the trends of atmospheric pressure, in black, the regolith content, in red, and the CO2 ice in blue. The current
pCO2 is denoted by the orange ?+? sign. Vertical lines are at Lp values 0? (blue; short-dash), 90? (red; dot-dash), and 180? (blue;
short-dash) intended to guide the eye for alignment with obliquity and CO2 ice cap. The RFZ unit names corresponding to buried
deposits are shown in the bottom panel, and in Table 1. See text for discussion.
Fig. 3.? Radargram from B2016 Fig. 2a (SHARAD observation 5968-01). The maximum depth of RFZs is a little over 1 km.
Note the bifurcation of BL2 , suggesting that the little obliquity dip at ? 125 ka has produced some buried CO2 .
Time (Myr)
Fig. 4.? Same as Figure 2 except that we explore the time range, 2.75 Ma < t < 2.20 Ma, when obliquity variations are small
(see Fig. 1). We show results for two different atmospheric pressures, PCO2 = 6.5 mbar and 12 mbar; the traces corresponding to
a maximum 6.5 mbar atmospheric inventory have dotted lines.
Fig. 5.? The vertical melting rates derived from Eq. 8 for H = 15, 20, and 25 mW m?2 (long-dash, short-dash and solid lines,
respectively). The dotted lines around the short-dashed lines are the result of applying the maxima and minima of Ttop of Eq.
5 to Eq. 6 and then to Eq. 8. The ordinate gives vertical melting rate in mm/yr. To transform vertical melting rates to areal
melting rates, multiply by ?CO2 ' 1600 kg m?3 .
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