Accepted Manuscript

Ancient melting of mid-latitude snowpacks on Mars as a water sourcefor gullies

K.E. Williams, O.B. Toon, J.L. Heldmann, M.T. Mellon

PII: S0019-1035(08)00439-9DOI: 10.1016/j.icarus.2008.12.013Reference: YICAR 8849

To appear in: Icarus

Received date: 9 July 2008Revised date: 17 October 2008Accepted date: 11 December 2008

Please cite this article as: K.E. Williams, O.B. Toon, J.L. Heldmann, M.T. Mellon, Ancient melting ofmid-latitude snowpacks on Mars as a water source for gullies, Icarus (2009), doi:10.1016/j.icarus.2008.12.013

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Ancient melting of mid-latitude snowpacks on Mars as a water source for gullies.

K. E. Williams1

, O. B. Toon1

, J. L. Heldmann2

, M.T. Mellon3

1

Dept of Atmospheric and

Oceanic Sciences & Laboratory for Atmospheric and Space Physics (LASP UCB 392,

University of Colorado, Boulder, CO 80309-0392 kaj.williams@colorado.edu ) 2

NASA

Ames Research Center, Division of Space Sciences and Astrobiology, Moffett Field, CA

94035 3

Laboratory for Atmospheric and Space Physics,UCB 392, University of

Colorado, Boulder, CO 80309-0392.

38 Pages

12 Figures

1 Table

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Proposed running head: Ancient Snowmelt and Gullies On Mars

Direct editorial correspondence to:

Kaj Williams

NASA – Ames

Mail Stop 245

Moffett Field, CA 94035-1000

kaj.e.williams@nasa.gov

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Abstract

We hypothesize that during past epochs of high obliquity seasonal snowfields at

mid-latitudes melted to produce springtime sediment-rich surface flows resulting in gully

formation. Significant seasonal mid-latitude snowfall does not occur on Mars today.

General Circulation Model (GCM) results, however, suggest that under past climate

conditions there may have been centimeters of seasonal mid-latitude snowfall (Mischna

et al. 2003). Gully locations have been tabulated by several researchers (e.g. Heldmann

and Mellon, 2004; Heldmann et al. 2007; Malin and Edgett 2000) and found to

correspond to mid-latitude bands. A natural question is whether the latitudinal bands

where the gullies are located correspond to areas where the ancient snowfalls may have

melted, producing runoff which may have incised gullies. In this study we model thin

snowpacks with thicknesses similar to those predicted by Mischna et al. (2003). We

model these snowpacks under past climate regimes in order to determine whether

snowmelt runoff could have occurred, and whether significant amounts of warm soil

(T>273K) existed on both poleward and equatorward slopes in the regions where gullies

exist. Both warm soil and water amounts are modeled because soil and water may have

mixed to form a sediment-rich flow. We begin by applying the snowpack model of

Williams et al. (2008) to past climate regimes characterized by obliquities of 35° (600 ka

before present) and 45° (5.5 ma before present), and to all latitudes between 70° N and

70° S. We find that the regions containing significant snowmelt runoff correspond to the

regions identified by Heldmann and Mellon (2004), Heldmann et al. (2007) and Malin

and Edgett (2000) as containing large numbers of gullies. We find that the snowmelt

runoff (>1 mm, with equivalent rainfall rates of 0.25 mm/hr ) and warm soil ( >1 cm

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depth) would have occurred on slopes within the gullied latitudinal bands. The snowfall

amounts modeled are predicted to be seasonal (Mischna et al. 2003), and our modeling

finds that under the previous climate regimes there would have been meltwater present on

the slopes in question for brief periods of time, on the order of days, each year. Our

model provides a simple explanation for the latitudinal distribution of the gullies, and

also suggests that the gullies date to times when water migrated away from the present

poles to the mid-latitudes.

Keywords: Ices, Mars, surface

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Introduction and background

Gully-like landforms exist in both the northern and southern hemispheres of Mars

(Heldmann et al. 2007; Heldmann and Mellon, 2004; Malin and Edgett, 2000; Balme et

al. 2006; Dickson et al. 2007). The characteristics of the gully forms vary considerably

(Malin and Edgett, 2000; Treiman, 2003). One type of gully includes a well-defined

alcove, an incised channel and a debris apron (Malin and Edgett, 2000), as shown in Fig.

1. In this study, we look for correspondence between gully occurrence and predicted

localities where surface liquid water could be explained by snowmelt.

(Figure 1 here)

Christensen (2003) hypothesized that after equatorward movement of ice occurred

during past high obliquity periods, surface ice or snow remained stable long enough to

begin melting and producing meltwater runoff under the subsequent lower obliquity

periods. The meltwater runoff was then suggested as a source for gullies. Williams et al.

(2008) have shown that snowsheets at midlatitudes on present-day Mars will melt or

sublimate quickly, often in only a few seasons depending on snowpack thickness and

slope geometry. These results indicate that exposed layers of snow are not preserved

from previous epochs of high obliquity, when extensive movement of ice away from the

permanent polar caps may have occurred (e.g. Jakosky et al. 1993).

Midlatitude snowsheets are expected to have been present in the past on Mars

when the obliquity was higher than now (Mischna et al. 2003; Levrard et al. 2004). We

propose that such snow sheets melted during the spring and summer season to form the

gullies. Other researchers have proposed a link between ancient snowfall and valley

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channels (Clow, 1987; Fassett and Head, 2006; Fassett and Head, 2007; Gulick, 2001;

Gulick et al . 1997). Our idea, proposed in this paper, focuses on gullies and unites

multiple concepts, including the concept of Christensen (2003) that snowsheets will melt,

the work of Mischna et al. (2003) showing that significant snowfall will occur at

midlatitudes under higher obliquity conditions, the observations that gullies are relatively

young (Malin and Edgett, 2000; Heldmann et al. 2007) and the polar caps are relatively

young (~ 4 ma) with predictions that the obliquity of Mars was high (≥ 35°) about 4.5

million years ago (e.g. Laskar, 2004; Milkovich et al. 2008). In addition, our theory

provides a natural explanation for the latitudes in which gullies are found.

There has been disagreement in the scientific literature over the characteristics of

the fluid responsible for Martian gully formation. While a CO2 gaseous flow has been

posited by Hoffman (2002) in order to explain polar gullies, the thermodynamic

difficulties of getting CO2to form on mid-latitude slopes of arbitrary orientation prevents

the explanation of Hoffman (2002) from being applied to low and mid-latitude gullies.

Alternative erosive agents for Mars that have been suggested have included debris flows

(Malin and Edgett, 2000), liquid CO2 (Musselwhite et al. 2001; later refuted by Stewart

and Nimmo, 2002), dry material (Treiman, 2003), salty brines (Knauth and Burt, 2002) or

mostly pure water (Heldmann et al. 2007). Our work suggests that erosional flows may

occur in environments on Mars, charged by the modest amounts of water supplied by

seasonal deposition of snow.

Martian gullies are relatively common between 30° to 70° in both the northern

and southern hemispheres (c.f. Heldmann et al. 2007; Heldmann and Mellon, 2004;

Balme et al. 2006; Dickson et al. 2007). The orientation and inclination of gully-bearing

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slopes for both hemispheres has been studied and appear to encompass all aspect

orientations (Heldmann and Mellon, 2004; Heldmann et al. 2007), though in some

locations such as the southern mid-latitudes there appears to be a poleward preference

(Dickson et al. 2007; Balme et al. 2006). The majority of gully-bearing slopes appear to

have slope inclination angles between 12 and 38° for the northern hemisphere and 5 to

40° for the southern hemisphere (Heldmann et al. 2007; Heldmann and Mellon, 2004;

Dickson et al. 2007). In this paper we have elected to model 20° slopes facing toward

and away from the equator.

(Figure 2 here)

The climate of Mars is believed to have undergone extensive fluctuations (c.f.

Milkovich et al. 2008) driven primarily by fluctuations of orbital parameters (e.g. Ward,

1974). The planetary obliquity (axial tilt) and the orbital eccentricity are commonly

analyzed in this context. Dynamical calculations by Laskar (2004) have determined the

variations of obliquity and eccentricity for the past several million years (Fig. 2). A

noteworthy feature of Fig. 2 is that prior to about 4.5 million years ago the mean

obliquity was above 35°, with excursions to 45°. More recently there have been periods

of time with high obliquity. According to GCM studies of Mars, there were considerable

amounts of seasonal snowfall and atmospheric water vapor present when the obliquity

was > 35° (Mischna et al. 2003). According to the calculations by Laskar (2004) (and in

Fig. 2) the obliquity was most recently 35° approximately 600 ka before present (bp).

The obliquity was 45° approximately 5.5 ma bp.

In this study we attempt to explain a subset of the observed gullies on Mars,

namely those with features suggestive of fluvial activity (Malin and Edgett 2000;

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Heldmann and Mellon, 2004; Heldmann et al. 2005). To do so we assume that various

snowfall amounts occurred over latitudes suggested by Mischna et al. (2003), and then

run the snow melt model of Williams et al. (2008) under two past climate regimes

(characterized by 35° and 45° obliquities). We wish to investigate the question of

whether snowmelt runoff and warmed soil occurred in sufficient quantities to provide

enough material for surface flows. Unfortunately other Martian paleo- GCM simulations,

such as the Levrard et al. (2004) study, provide insufficient data regarding latitudinal

distribution of seasonal snowfall for high obliquity cases, and thus we were unable to use

their data for this study.

We do not explore longitudinal distributions of gullies in this paper because the

existing Martian paleo-General Circulation Model (GCM) simulations disagree with

regard to residual ice cap placement and the longitudinal occurrences of stable ice.

Levrard et al. (2004) found that while the transport of polar ice to midlatitudes does occur

under high obliquity (>30°) conditions, they were unable to obtain a stable (residual) ice

cap at mid-latitudes for high obliquities. On the other hand, the Mischna et al. (2003)

simulations produced stable surface ice at mid-latitudes for similar high obliquities. In

addition, in order to study the longitudinal occurrences of gullies it would also be

necessary to minutely examine each geological setting for gullies to determine the

topographic features that might control local snowfall. Hence the correlation of

longitudinal location of gullies with paleo -GCM simulations is an open research question

that we do not address.

Model Description

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For this study we use the snowpack model of Williams et al. (2008). No salts or

brines are included in the modeling process. A general overview of the snowpack model

follows. The model utilizes a finite-volume solver in order to compute the energy and

mass transport within the snowpack. Mass loss is permitted to occur from the top of the

snowpack (as sublimation) or runoff from the bottom of the snowpack. Meltwater

percolation and refreezing is also permitted within the snowpack. The model itself is

solved on a mass grid, rather than a spatial grid, in order to make mass and energy

conservation tractable. The snowpack layers are permitted to grow and shrink, but are

initially set to 1 mm thickness since we are interested in modeling relatively thin

snowpacks (< 10 cm).

(Figure 3 here)

The surface energy balance in our model consists of the following components

(Fig. 3): latent heat flux due to mass loss/gain, atmospheric infrared emission to the

snow, sensible heat flux, infrared emission from the snow, solar absorption by the snow

and infrared emission from an adjacent surface to the snow.

The energy for the surface layer is evolved by the following expression:

∂U

∂t= −k(T)

∂T

∂z bottom

−εσT 4 + (F−1/ 2 − F+1/ 2) + AH + SH + Fir − L∂M

∂t (1)

Here it is understood that the right-hand side terms are each averaged over a time interval

greater than or equal to the integration timestep. The integration timestep for Eq. 1 was

set at 0.25 seconds. The choices of various parameters in Eq. 1 are summarized in

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Williams et al. (2008), but with several exceptions for past climate regimes (outlined

below). The quantity mCpTU = is the area-normalized energy of the surface layer of

ice/dust/liquid mixture of mass m. Again the equations are solved on a mass grid; when

required, layer thickness zΔ is determined from the layer mass since the relative mass

contributions of liquid water, dust and ice are tracked for each layer. The

−k(T)∂T

∂z bottom

term is the heat conducted out of the bottom face of the top layer. The

−εσT 4 term is the infrared radiation emitted by the surface. The

2/12/1 +−

− FF term is the

average net solar flux absorbed by the surface layer (direct and scattered radiation) for the

timestep. The AH term is the downwelling atmospheric infrared heat flux density, and

H

S is the atmospheric sensible heat flux density. The Fir term is the infrared heat flux

density contribution from a planar surface at the foot of the slope and

t

M

L

∂

∂

is the latent

heat loss. Each of these terms is described in detail by Williams et al. (2008).

Aside from the capability of being run at different latitudes, the snowpack model

is run for a given slope inclination and aspect. We have used the equivalent slope

concept (as outlined in Dingman, 2002) to account for slope geometry (Williams et al.

2008). This concept accurately represents the solar flux on a plane parallel semi-infinite

slope, and makes no approximations other than ignoring shadowing and other three-

dimensional issues. These limitations are discussed in Williams et al. 2008.

Our model uses the two-stream shortwave radiative transfer code of McKay et al.

(1994) to simulate energy deposition within the snow. The two-stream radiative transfer

code simulates solar energy distribution in a snow column with a non-homogeneous dust

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distribution. The dust is initially homogeneously mixed into the snow, but the model

permits a concentrated dust layer (lag) to form on the surface as the snow ablates.

The snowpack model computes the temperature profile within the soil underlying

the snowpack (i.e. the soil substrate). In addition, the temperature profile is computed in

an adjacent soil column, which is not covered by snow. The adjacent soil column

temperature profile is used to infer the air temperature above the snow. The adjacent soil

column temperature profile is solved with a simple finite-difference model, and is solved

over a uniform grid of 1 cm layers. The soil temperature model has been described in

Williams et al. (2008).

The adjacent soil column model is also used for another purpose. As a snowpack

gradually ablates on a slope, we presume that bare patches of soil are present on the slope

as well. The temperature of the topmost soil layer is of interest because the soil may

provide mobile sediment to be incorporated in a flow. Soil cohesion, as well as other

physical properties related to the potential of a soil to be mobilized in a flow, are largely

unknown for the Martian slopes. As a rough estimate of the potential for a layer of soil

to be mobilized, we have elected to use the temperature of the soil layer; if the soil

temperature is > 273K we assume it may be easily mobilized in a flow, whereas

otherwise the meltwater runoff might simply freeze upon contact with cold (< 273K) soil.

We have therefore modeled the temperatures of a bare soil column colocated with the

snowpacks on slopes in order to determine how much “warm” soil (soil with

temperatures > 273K) is available for transport. Hence, by our definition, “warm” soil

has units of depth, and is defined to be soil with temperature greater than 273K. The

instant that runoff is produced from a given snowpack, we check the adjacent soil model

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on the slope and determine how much warm soil exists at the soil surface. The melting

and runoff occurs only over a few days, and occur during late spring. Hence the depth of

“warm” soil will not change significantly during melting and runoff, other than diurnal

variations in the soil temperature during those several days. The soil column is much

darker than the snow, and warms up much more quickly than the snow. According to our

model, by the early afternoon (at which time the snow is melting), the soil is as warm as

it ever will be for that day. We also compute the temperature of the soil substrate beneath

the snowpack.

The model parameter settings have been described in Williams et al. (2008), with

several exceptions. Since in the present study we are modeling freshly fallen snow that

begins melting after settling and aging for >100 Mars days, we have elected to follow

Clow (1987) and set the snow density to 400 kg/m3

and the snow grain radius to 1 mm.

A snow density of 400 kg/m3

corresponds to terrestrial wind-packed snow (Paterson,

1994). The dust mixture is initially set to 10 parts per million by weight (ppmw). The

amount of atmospheric dust which would have been deposited in seasonal snowfalls

under past climate regimes is unknown, but it seems reasonable that there would have

been at least small amounts of dust present. Given Viking Lander estimates of

atmospheric dust optical depth to be between ~0.1 and 3.0 (Toigo et al. 2002), we

estimate the amounts of dust swept out of the lower atmosphere and incorporated within

the snow to be between 10 and 500 ppmw. For sensitivity tests, discussed below, we

varied the amount of dust in the snow between 10 and 500 ppmw.

We have set the ground thermal inertia to 250 J m-2

K-1

s-1/2

which corresponds to

the median of the thermal inertia values observed in regions where gullies occur

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(Heldmann et al. 2007; Heldmann and Mellon, 2004). Our soil albedo is set to 0.13,

which falls within the range of values observed around the gully sites (Heldmann et al.

2007; Heldmann and Mellon, 2004).

The orbital parameters in this study include the present-day longitude of

perihelion (250.87°), eccentricity values of 0.08403 (for 35° obliquity) to 0.0367 (45°

obliquity), and obliquities of 35 and 45°. For sensitivity tests, the longitude of perihelion

was varied by 360° in 90° increments.

The seasonal snowfall was presumed to have occurred at midwinter (Ls=90° for

the southern hemisphere and Ls=270° for the northern hemisphere), and in a single

episode. No additional precipitation is allowed to occur during the springtime. It is of

course likely that ancient snowfalls may have occurred differently, including multiple

snowfalls per season. It is the aim of this study, however, to determine the

thermodynamic feasibility of melting and runoff, as well as potential for flows and not to

address the infinite number of meteorological scenarios that were possible at all latitudes.

The model parameter settings relevant to the present study are summarized in Table 1.

The snowfall amounts modeled include 1 – 5 cm depths. Mischna et al. (2003)

predicted that the snowfall amounts for 35° obliquity were approximately 1.0 cm for mid-

latitudes, and approximately 2.0 cm for 45° obliquity at midlatitudes. However, Erickson

et al. (2005) suggest that winds can cause considerable snow depth variations to occur on

terrestrial slopes, with depth variations between 0x and >5x. Therefore we feel the 1-5

cm snowfall depths modeled are in accordance with the snowdrift depth variation

suggested by Erickson et al. (2005). It is also possible that snowdrifts may have occurred

on Martian hillslopes in a manner similar to terrestrial nivation hollows. In terrestrial

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situations, nivation hollows can develop on hillslopes when seasonal snowpatches erode

the underlying soil (Christiansen 1998). Subsequent seasonal snow deposits tend to

accumulate in such hollows, providing regions where snow can form deeper drifts

(Christiansen 1998). It is possible a similar process would have occurred on Mars,

creating regions where snowdrifts preferentially form (in this case, the nivation hollow

would correspond to the gully alcove). The nivation concept is discussed again below.

Model Results

We have run the snowpack model of Williams et al. (2008) under two past

climate regimes (characterized by 35° and 45° obliquities) in order to determine whether

seasonal melts of small amounts of snow could have yielded meltwater runoff on slopes.

In general, all of our modeled snowpacks lasted less than one Mars year, eventually

disappearing by late spring. Sublimation was the dominant mass loss process. Melting,

if it occurred, only was present during the last several days of the snowpack lifetime,

when then snow was very thin and dusty.

(Figure 4 here)

Many gully images indicate episodic gully activity, since superposed fans, cross-

cutting channels and superposed alcoves are relatively common. A cartoon of one

possible process is depicted in Fig. 4. It should be noted that even if only a few mm of

runoff are produced (a few liters / m2

), that the total meltwater volumes could still be

significant when taken over the extent of the gully alcoves as discussed below.

Therefore it is possible that the gully erosion and sediment deposition could occur due to

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meltwater alone, without need for the example in Figure 4. Nevertheless it seems

extremely unlikely that the meltwater in the channel would be devoid of sediment since

clearly sediment transport is required for gully incision. It is also possible that the

meltwater flowed in pre-existing gully channels.

We do not know the extent to which the meltwater runoff might infiltrate the soil

on Martian slopes. For terrestrial cases, Dingman (2002) suggests that infiltration rates

for grass-covered standard soil and moderate slopes (16°) can be close to 50% of the

water input rate, however other work suggests that infiltration rates are negligible for

terrestrial Arctic slopes (Heldmann et al. 2005). Nevertheless, even if infiltration was

extensive there could likely still be significant meltwater volumes remaining. For

example, if a given gully alcove containing snow has an area of 300 x 300 m = 9x104

m2

,

and if there was 1 mm of meltwater runoff produced, the total volume of meltwater

produced within the alcove would be 90 m3

. Even if the majority of the meltwater was

consumed via infiltration, there could potentially still be 10s of cubic meters of meltwater

runoff left. According to our simulations, the snow sublimated over ~150 days but the

meltwater runoff is produced over only 1 – 2 days, and only in the afternoon. The actual

meltwater production occurs only after the majority of snow has sublimated.

Restricting our attention to the latitudinal bands where gullies appear to be

common (30°-70°), GCM model estimates by Mischna et al. (2003) for 35° obliquity

indicate that the amounts of zonally averaged atmospheric water vapor could have been

greater than 200 prμm (precipitable microns) during summer and the seasonal extent of

surface ice extended as far south as 10° N in northern winter and as far north as 20° N in

the southern winter. As will be discussed below, the ice extents are not hemispherically

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symmetric due to the longitude of perihelion occurring during southern hemisphere

summertime in the simulations. The seasonal snow depths at mid-latitudes given by the

model of Mischna et al. (2003) ranged from 0.5 cm under 35° obliquity to 1 cm under 45°

obliquity, though it should be stressed that these numbers are only rough estimates. Note

that given our modeled snow density of 400 kg/m3

, the Liquid water Equivalent Depth

(LED) of a 1 cm snowpack is 0.4 cm.

(Figures 5 and 6 here)

Figs. 5 and 6 show the amounts of runoff produced for various amounts of

snowfall as a function of latitude on 20° slopes facing toward and away from the equator,

for an obliquity of 35°. The data have been smoothed via cubic polynomial regression.

Note that in our columnar model meltwater runoff amounts (mm) convert immediately to

liters/m2

. According to Figs. 5 and 6, most of the slopes in the latitudes considered are

warm enough to produce runoff, with the exception of the 50° - 60° N and 70° S polar

slope locations. The model results suggest that a 5 cm snowpack would produce a

maximum of approximately 2.5 mm (2.5 liters / m2

) of runoff at 60° S latitude for an

equatorward slope, and that for poleward slopes a similar (maximum) runoff amount

occurred at 10° S latitude. As expected, in general the equatorward slopes were warmest,

and hence produced slightly larger amounts of runoff for a given latitude than poleward

slopes. The mesh area indicates the region covered by a perennial cap (where runoff is

not expected), and the hatched area covers the area where significant seasonal snowfalls

are not expected to occur, based on the results of Mischna et al. (2003).

(Figures 7 and 8 here)

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We also model the thermal structure of the soil substrate (beneath the snow

column). In all of the cases where snowpack melting occurred, the topmost 1 mm of the

soil substrate under the snow column was above 273K, whereas the remainder of the soil

substrate column was below 273K. We believe that the topmost 1 mm of the soil

substrate being warm makes it unlikely that the meltwater runoff would simply refreeze

at the base of the snow column. According to Figs. 7 and 8, the amount of warm soil

available on the same slope as the snowpack ranges from 1-2 cm for the obliquities of

35°. The 70° N location for poleward slopes is slightly cooler than the equatorward slope,

and hence neither runoff nor warmed soil was present at that location. It should be noted,

however, that the models and parameters used here are imperfect (as are all models and

parameter estimates), and hence the 70° N region should not be considered a “hard” limit.

(Figures 9 – 12 here)

As can be seen in Fig. 9-12, the 45° obliquity cases are similar to the 35°

obliquity cases in that there is a maximum runoff of ~ 2.1 mm on equatorward slopes for

60° S and ~2.0 mm on poleward slopes for 20° S. Depending on the initial snowfall

amounts, in the southern hemisphere on both slope azimuths we find that 1 cm warm soil

amounts are fairly common but less so in the northern hemisphere. For deeper snowpacks

(5 cm snow, or 2 cm LED), however, we find 2 – 3 cm warm soil amounts are common

in the latitudinal ranges in question. The greater amounts of warm soil present on slopes

when a 5 cm (2 cm LED) snowpack is melting is a consequence of the fact that 5 cm

snowpacks melt later in the springtime, by which time the soil surface has become

warmer.

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Fig. 10 shows that for equatorward slopes under 45° obliquity, and excluding

areas of insufficient snowfall or a permanent cap, the runoff amounts from a 5 cm

snowpack (2 cm LED) are less than the runoff amounts produced by thinner snowpacks.

Thicker snowpacks have a longer lifetime than thinner snowpacks, however the amount

of runoff produced can vary depending on factors such as the snow dust content,

remaining snow thickness and season (insolation) when the melting occurs. The reason

the 5 cm snowpack produces less meltwater runoff than a thinner snowpack is that the

thicker snowpack is able to survive long enough that insolation begins to decline (for this

particular slope and latitude), whereas the thinner snowpack expires when insolation is

still relatively intense.

For both obliquities, and again restricting our attention to the latitudinal bands in

question, it is apparent from the model results that the thinnest snowpacks (< 3 cm) do

not consistently yield meltwater runoff at all latitudes. Nevertheless the deeper

snowpacks (3-5 cm) do melt and produce runoff at all latitudes considered, yielding

between 1-2.5 mm of runoff depending on the slope geometry and latitude.

We have conducted extensive sensitivity tests of our snowpack model, which are

summarized elsewhere (Williams et al. 2008), where we concluded the most sensitive

parameters were slope geometry, orbital characteristics and dust content. Under current

Mars conditions (obliquity 25.19°, eccentricity ~0.09 and longitude of perihelion ~250°)

the snowpack is most sensitive to slope geometry and dust content. Poleward slopes

generally greater than 40° were found to be sufficiently steep (at least at mid-latitudes)

that no melting could occur. The dust sensitivities were more pronounced when initial

snowpack dust amounts exceeded 100 ppmw. We have also varied the slope inclination

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between 10 and 30° in order to measure the effect on the amount of meltwater produced.

The effect on the lifespan of the snowpack was somewhat significant (as Williams et al.

2008 also showed), however in this case the effect on meltwater amounts produced were

negligible.

We conducted three new sensitivity tests on the snowpack model under the 35°

climate regime. Specifically, we varied the atmospheric water amounts between 100-300

precipitable microns, the snow dust content between 10 and 500 ppmw and the longitude

of perihelion from 0 – 360°. The result of varying the atmospheric water was very small;

assuming a base case of a 3 cm snowfall on an equatorward slope at 50°S, we found that

varying the atmospheric water in the range specified produced only a small change (0.017

mm) in the amount of runoff, which corresponds to approximately 15% by volume of the

total runoff.

The effect of increasing the snow dust content was to both shorten the snowpack

lifetime and to reduce the amount of meltwater runoff. At 10 ppmw (our base case) the

snow surface was relatively cool in springtime, inhibiting sublimation and therefore

extending the snowpack lifetime to early summer. In the 500 ppmw case, however, the

snow surface was relatively warm in the spring season, and thus sublimated vigorously.

By summertime the 500 ppmw snowpack was almost gone, and hence only a tiny amount

of meltwater was produced when the more intense summer heating began.

The effect of varying the longitude of perihelion was significant; varying the

longitude of perihelion by +/- 45, 90, 180° affected the runoff amounts by as much as 100

% (increases of as much as +/- 0.5 mm). The sensitivity tests indicate that the runoff

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amounts are sensitive to our parameter choices, but not enough to affect the conclusions

of this study that runoff will occur.

Note that a comparison of Figs 10 and 11 with Figs. 5 and 6 show that, according

the modeling by Mischna et al. (2003), obliquity dramatically affects the availability of

snowfall in the southern hemisphere for the longitude of perihelion being considered. As

with any complex model, GCM predictions are not infallible. It is difficult to know even

what degree of confidence to attach to a variable such as snowfall depth. Nevertheless we

feel that the amounts predicted by Mischna et al. are plausible.

Discussion and Conclusion

We have found that the modest snowfalls similar to those predicted by Mischna et

al. (2003) for obliquities of 35 and 45o

, can melt over a few day time period and release

mm of runoff each year. We have also found that exposed soil, on the same slope as the

snow, will have temperatures > 273K to depths of 1-2 cm each spring. We suggest this

combination of snowmelt runoff and warm soil provide material which may be mobilized

each spring, and that this admixture may have incised gullies.

We have chosen not to posit a more specific erosional or depositional flow

mechanism for gully incision in this study. Possible types of flow that may be relevant

include debris flows, mudflows, hyperconcentrated streamflows, or open channel flows.

The rheologies and other characteristics of these types of flows are vast and complicated

subjects. As one possible example however, we consider terrestrial snowmelt-induced

debris flows.

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The amounts of water required to form the initial slope failure for terrestrial

snowmelt-induced debris flows are presently poorly constrained and depend greatly on

the properties of the material. However some Mars researchers have suggested that

Martian debris flows could form with water concentrations as small as 10% by volume

(Malin and Edgett, 2000). Several debris flows in the Swiss Alps during 1987 were

analyzed by Roesli and Schindler (1990), who found that the soils were remarkably

sensitive to water content in the sense that the addition of 3-4% (weight) of water was

enough to change the slope material from the plastic to the liquid regime. Our study

suggests that similar liquid/sediment ratios may be possible on the Martian slopes, given

that our model indicates mm of liquid runoff and cm of warm soil occur on the slopes.

The question remains of how, given initially thin (e.g. 0.5-1.0 cm) snowfalls, a

sufficiently thick (e.g. 5 cm) snow patch might develop that could produce significant

meltwater runoff. One possible mechanism is that they may have developed in a manner

similar to that of terrestrial nivation hollows. As mentioned previously, snowdrifts may

develop, often several times thicker than the initial snowfall (Erickson et al. 2005). In

terrestrial research, it has been noted that nivation often begins with the formation of

snowdrifts on the leeward side of ridges (Cain 1995; Christiansen 1998). Once the

snowdrifts begin seasonally melting, erosion at the edges begin to excavate a hollow,

often producing backwall erosion and alluvial fan deposition (Christiansen 1998). Once

even a very shallow hollow develops, positive feedbacks can occur whereby the nivation

hollow accumulates greater amounts of snow in subsequent seasons, producing even

more melting and subsequent hollowing (Mark Williams, private comm., Christiansen

1998). An interesting observation related to nivation is that the locations of nivation

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hollows are often controlled more by prevailing winds and snowfall amounts, and less by

slope aspect (Christiansen 1998). Hence the locations of the Martian gully alcoves may

not be controlled solely by slope insolation amounts as others have suggested (c.f.

Dickson et al. 2007), but rather by wind direction. Similarly, Erickson et al (2005) found

that of the several modeled parameters (elevation, slope, radiation, wind sheltering and

wind drifting), that wind sheltering had the greatest effect on predicted snow depth.

The results in Fig. 5 and 6 show a marked asymmetry in that both the runoff

amounts and the available warm soil amounts are generally greater in the southern

hemisphere than in the north. The asymmetry is due to the generally greater solar

irradiation amounts in the southern hemisphere in our simulation, leading to generally

higher surface temperatures. Higher surface temperatures are due to the fact that the

longitude of perihelion falls at approximately Ls=250°, and therefore the periapse occurs

during the southern summer. Given that the longitude of perihelion is expected to vary

with the 50 ka precession cycles, which is of shorter duration than obliquity variations,

we expect that the hemispherical asymmetry in runoff to be temporary. By varying the

longitude of perihelion in our model, we are able to reverse the hemispheric asymmetry

in slope runoff amounts, favoring the northern hemisphere. Some research, such as that

of Heldman et al. (2007), suggest that there is roughly the same number of gullies in both

hemispheres. Our modeling results in this case provide a natural explanation for this

hemispheric parity, as long as the gully formation mechanism would have occurred over

equal or greater timescales than a precession cycle.

Combining the work of Milkovich et al. (2008) and Mischna et al. (2003), as well

as the meltwater runoff potential from our snowpack model, leads us to suggest that some

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of the mid-latitude gullies were formed (or resurfaced) by flows under previous climate

epochs with high obliquity. One implication of this hypothesized mechanism is that

some of the gullies should have about the same age as the top of present polar ice sheets,

because once the ice sheets started to re-form in the polar areas the obliquity must have

been near its present value, ending the gully formation period. It is possible that the last

gullies formed (or the last erosion occurred) as the ice sheets (residual caps) returned to

present locations within the last 100 ka. Recent work by Milkovich et al. (2008),

however, suggest that the top 300 m of the polar layered deposits may be less than 100

ka old, overlying older ice. If true, one possible inference would be that the 300 m of ice

of the top part of the Polar Layered Deposits could have also been redistributed to lower

latitudes in the form of atmospheric water (snowfall) since the last obliquity cycle, along

with the overlying ice sheet.

From the model results, there appears to be availability of > 1 mm of runoff, as

well as the availability of > 1 cm of warm soil on both equatorward and poleward slopes

between 60° and 30° S, as well as approximately 20° and 60° N. Assuming an adequate

seasonal supply of snow (2-5 cm), we argue that the meltwater runoff could have incised

the gullies, as well as contributed material to debris aprons during both of the past climate

regimes studied (35° and 45° obliquity).

It should be emphasized that the modeled process is capable of large amounts of

erosion and deposition, given that it is both a seasonal and cumulative process. Such

repetitive erosive and depositional events would almost certainly leave direct geologic

evidence for us to observe in current and future spacecraft missions.

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Acknowledgements

The authors wish to thank Mark W. Williams for helpful discussions regarding terrestrial

nivation, and to thank Trinity Allen for assistance with the gully images. Ginny Gulick

and an anonymous reviewer provided very helpful suggestions as well.

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Table 1. A summary of the model parameters which were relevant to the present study.

Atmospheric water and longitude of perihelion parameters were varied for sensitivity

testing over the stated range. For other parameters, see Williams et al. (2008).

Parameter Value

Snowpack density 400 Kg/m3

Snow grain radius 1 mm

Snowpack depths 1 – 5 cm

Snowpack dust content 10-500 ppmw

Dust and soil albedo 0.13

Soil thermal inertia 250 J m-2

K-1

s-1/2

Obliquity 35°, 45°

Eccentricity 0.084 (35° obl.), 0.0367 (45°obl.)

Longitude of perihelion 0°- 360°

Season of Snowfall deposition Ls = 90° for southern hemisphere

Ls = 270° for northern hemisphere

Slope inclination 10, 20, 30°

Slope aspect (measured clockwise from N) 0°, 180°

Atmospheric water content 100 - 300 mprμ

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Fig. 1. An example of gully morphology. This HiRISE image is located at 49.0° S

latitude and 268.1° E longitude. The photo was taken at Ls=164.4° (southern winter) at

3:51 pm local Mars time. The gully slope faces approximately equatorward. HiRISE

image credit: NASA/JPL/University of Arizona.

Fig. 2. Eccentricity and Obliquity for Mars for the last 6 million years. (data from

Laskar, private comm.)

Fig. 3. The energy terms used in our snowpack model.

Fig. 4 A possible mechanism for sediment movement and deposition. Arrows indicate

the flow of meltwater.

Fig. 5 The meltwater runoff amounts computed for poleward slopes and 35° obliquity.

The hatched region indicates latitudes where insufficient snowfall is expected to allow

runoff and the meshed area indicates latitudes where a perennial cap is expected to occur

which will prevent melt. The data have been smoothed by polynomial regression. Note

that in our columnar model meltwater runoff amounts (mm) convert immediately to

liters/m2

.

Fig. 6. The meltwater runoff amounts computed for equatorward slopes and 35°

obliquity. The hatched region indicates latitudes where insufficient snowfall is expected

for runoff to occur and the meshed area indicates latitudes where a perennial cap is

expected to occur. The data have been smoothed by polynomial regression.

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Fig. 7. Depth of soil with temperatures > 273K at start of melt season, for poleward 20°

slope inclination and 35° obliquity. The grid spacing of the soil model is 1 cm.

Fig. 8. Depth of soil with temperatures > 273K at start of melt season, for equatorward

20° slope inclination and 35° obliquity.

Fig. 9 The water runoff amounts computed for poleward slopes and 45° obliquity. The

hatched region indicates latitudes where insufficient snowfall is expected to allow runoff

and the meshed area indicates latitudes where a perennial cap is expected to occur

preventing melting. The data have been smoothed.

Fig. 10 The water runoff amounts computed for equatorward slopes ,and 45° obliquity.

The hatched region indicates latitudes where insufficient snowfall is expected to allow

runoff and the meshed area indicates latitudes where a perennial cap is expected to occur

preventing melting. The data have been smoothed.

Fig. 11. Depth of soil with temperatures > 273K at start of melt season, for poleward 20°

slope inclination and 45° obliquity.

Fig. 12. Depth of soil with temperatures > 273K at start of melt season, for equatorward

20° slope inclination and 45° obliquity.

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