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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112, E08001, doi:10.1029/2006JE002881, 2007
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Hydrological modeling of outflow channels and chaos regions on Mars
Jeffrey C. Andrews-Hanna1,2 and Roger J. Phillips1
Received 15 December 2006; revised 6 March 2007; accepted 11 May 2007; published 2 August 2007.
[1] The Martian outflow channels were carved by the eruption of catastrophic floods from
groundwater aquifers. This study models the time evolution of a typical outflow channel
flood originating within a chaos region. The flood initiates when superlithostatic pore
pressures within a confined aquifer lead to the propagation of hydrofractures through the
confining cryosphere to the surface. The peak discharges are modulated by diffusion of the
flood pulse within the chaos region, resulting in a rapid rise in discharge immediately
after flood initiation. Later flow is limited by diffusion through the aquifer and is sensitive to
the variation of the hydraulic properties with changing pore pressure. After the termination
of the flood by freezing within the chaos region much of the aquifer remains pressurized.
Diffusion of the excess pressure from the undrained portions of the aquifer back toward
the chaos region triggers a second flood, ultimately resulting in a periodic series of floods.
For Iani Chaos at the source of Ares Valles, modeled peak discharges on the order of 106 to
107 m3 s1 were obtained, with total volumes of individual floods ranging from 600 to
5000 km3 and a minimum period between successive floods of 44 years. The cumulative
flood volume depends upon the number of floods, which is a function of the volume of
pressurized aquifer or the duration of recharge from distant sources. These results suggest
that individual channels were likely carved by large numbers of floods and were unlikely to
have experienced bankfull flow in their final state.
Citation: Andrews-Hanna, J. C., and R. J. Phillips (2007), Hydrological modeling of outflow channels and chaos regions on Mars,
J. Geophys. Res., 112, E08001, doi:10.1029/2006JE002881.
1. Introduction
[2] The circum-Chryse outflow channels (Figure 1)
record the largest and most dramatic flooding events observed in the Solar System. The channels were discovered
in Mariner 9 images, which revealed enormous fluvial
features tens to hundreds of kilometers across, a kilometer
or more deep, and hundreds to thousands of kilometers in
length [Baker and Milton, 1974]. The outflow channels date
primarily from the Hesperian epoch (3.7 to 3.0 Ga
[Hartmann and Neukum, 2001]) [Baker, 1982], after a
dramatic cooling of the climate led to the growth of a thick
cryosphere [Carr, 1996a]. A number of features within
these channels, such as streamlined islands and deep scour
marks, are indicative of the catastrophic flow of water
[Baker, 1979, 1982]. The immense scale of the channels
is made even more enigmatic by the fact that the individual
outflow floods apparently emerged fully formed from the
ground at discrete sources. Most outflow channels originate
either from a broad region of disrupted terrain, referred to as
a ‘‘chaos region,’’ or from within a tectonic canyon. The
chaos-sourced channels are thought to have formed through
the catastrophic eruption of water directly from a pressurized
1
McDonnell Center for the Space Sciences and Department of Earth and
Planetary Sciences, Washington University, St. Louis, Missouri, USA.
2
Now at the Department of Earth, Atmospheric, and Planetary Sciences,
Massachusetts Institute of Technology, Cambridge, Massachusetts, USA.
Copyright 2007 by the American Geophysical Union.
0148-0227/07/2006JE002881$09.00
groundwater aquifer trapped beneath the thick confining
cryosphere [Carr, 1979, 1996a], while the canyon-sourced
channels have been interpreted as evidence of the overtopping and catastrophic drainage of an enclosed canyon
lake that had been filled by groundwater [Robinson and
Tanaka, 1990].
[3] Most studies of the outflow channels have focused on
interpretations of the surface geomorphology, applying our
understanding of the hydraulics and fluvial geomorphology
of terrestrial floods to the Martian outflow channels. The
individual outflow floods have been estimated to have total
volumes of up to 106 km3 of water [Rotto and Tanaka,
1992] and peak discharges, assuming bankfull conditions,
approaching 109 m3 s1 in some cases [Komatsu and Baker,
1997]. These discharges are approximately 7 orders of
magnitude greater than the largest terrestrial groundwater
springs, and 2 orders of magnitude greater than the largest
catastrophic floods on the Earth [Baker, 1982]. However,
these estimates commonly rely upon a number of assumptions that have not been adequately tested, including the
assumption that the channels formed in single events and
experienced bankfull flow in their current state. Mapping
studies have delineated the relative erosional histories of the
main circum-Chryse channels [Nelson and Greeley, 1999],
but the detailed history of flooding within the individual
channels remains poorly understood.
[4] We take a different approach, and attempt to model
numerically the formation and evolution of the outflow
channel floods at their sources in regions of chaotic terrain.
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diameter of 10 cm, thus assuming that the majority of the
sediment was composed of cobbles and boulders and likely
underestimating the carrying capacity. Clearly, large uncertainties remain in the flood volumes required to carve the
outflow channels. Nevertheless, the simple approach of
assuming a maximum sediment load provides a reasonably
firm lower limit on the flood volumes and a valuable
constraint for hydrologic modeling.
[6] The peak discharges are commonly estimated by
applying the Chezy-Manning equation [Knighton, 1998]
scaled to Mars gravity:
1
gMars 1=2
Q ¼ w d 5=3 S gEarth
n
Figure 1. Mars Orbiter Laser Altimeter (MOLA) shaded
relief map of outflow channels in the circum-Chryse region.
Beginning with the a priori assumption of a pressurized
aquifer, we utilize a hydrological model of the Martian
megaregolith [Hanna and Phillips, 2005] combined with a
model of flow through the chaos region in order to simulate
the flow of water through the aquifer to the surface at the
flood source, so as to reconstruct the evolution of the
discharge and flood volume as a function of time. We take
Iani Chaos at the source of Ares Valles as our case study of
a typical chaos outflow source. Using the insight gained into
the nature of the floods, we then reconsider some of the
basic assumptions of the geomorphic studies based on our
model results. In particular, we focus on the implications of
the model results for the number, duration, evolution of
discharge, and erosional history of the outflow channel
floods.
2. Previous Studies
2.1. Fluvial Geomorphology
[5] Previous estimates of the volumes and peak discharges of the floods came from interpretations of the
channel geomorphology. Flood volume estimates were
calculated from the measured channel volumes by assuming
a maximum volumetric sediment load, above which turbulent flow is no longer possible and the flood will become a
debris flow, and calculating the volume of sediment-laden
water required to remove the requisite volume of rock
[Carr, 1987; Komar, 1980; Rotto and Tanaka, 1992].
Assuming a volumetric sediment fraction of 0.4, this
method yields total flow volumes for the individual outflow
channels of approximately 105 to 3 106 km3. However,
this assumed sediment load serves only as an upper limit,
and thus provides a lower limit on the flood volume.
Plausible sediment loads could range from values typical
of terrestrial rivers, on the order of 0.001, up to this upper
limit of 0.4, leaving an uncertainty of a factor of 400.
Recent work has emphasized the likelihood of much lower
sediment loads than those typically assumed [Kleinhans,
2005]; however, that study assumed that only the bed load
was significant, thus ignoring the significant capacity of the
floods to carry suspended loads. Furthermore, sediment load
calculations were done using a median sediment particle
ð1Þ
where Q is the discharge, n is the roughness coefficient
(typically taken to be in the range of 0.015 to 0.035
[Robinson and Tanaka, 1990]), w is the channel width, d is
the channel depth (assumed to be much less than the width),
S is the hydraulic slope (commonly taken to be the bed
slope), and g is the acceleration of gravity. More recently,
Wilson et al. [2004] argued that the Darcy-Weisbach
equation more accurately represents the mean flow velocity
and discharge:
Q ¼ w d 3=2 ð8gMars S=fc Þ1=2
ð2Þ
where fc is the friction factor, which depends primarily on
the nature of the channel bed and the ratio of the bed
roughness elements to the flow depth.
[7] It can be seen in equations (1) and (2) that the
discharge scales with either the 5/3 or the 3/2 power of
the flow depth, though there is an additional dependence on
depth in the friction factor in equation (2). For the Martian
outflow channels, we have no way of measuring the depth
of flow at the time of peak discharge. It has commonly been
assumed that the channels in their present configuration
were bank full during their final stage of flow [e.g.,
Komatsu and Baker, 1997], though more recent studies
have considered the likelihood that channel flow was less
than bank full [Mitchell et al., 2005] based on the observation of small inner channels within some of the outflow
channels [Williams et al., 2000; Williams and Malin, 2004;
Leask et al., 2007]. Typical maximum discharge estimates
based on the bankfull assumption are on the order of 108 to
109 m3 s1 for Ares Valles [Komatsu and Baker, 1997]. The
sensitivity of the discharge to the flow depth introduces a
significant degree of uncertainty into the estimations of the
discharge. The calculation of the channel discharge is
complicated further by the observation of level or even
uphill slopes along the channel beds in the downstream
direction for distances of hundreds of kilometers [Williams
and Phillips, 1999; Skinner and Tanaka, 2000], leading to zero
or negative discharges by simple application of equations (1)
and (2), and calling into question the reliability of any discharge estimate based on channel slope and cross section.
[8] An added complication arises from the fact that the
friction factor used in equation (2) is generally taken from
empirical expressions based on terrestrial channel observations, which are parameterized in terms of the flow depth
and the channel bed roughness. However, analytical expressions for the friction factor demonstrate its dependence on
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the Reynolds number, which is a function of the flow depth,
fluid density, and viscosity. The high concentrations of
suspended sediment and ice commonly invoked for the
Martian outflow channels would result in significant
changes to the density and viscosity. For example, the
maximum volumetric sediment load of 0.4 would increase
the viscosity by a factor of 16 [Bargery et al., 2005] and
the density by a factor of 2. If we simply assume that the
dependence of the friction factor on flow depth [Wilson et
al., 2004] reflects its dependence on the Reynolds number,
the resulting effect would be to decrease the discharge for a
given flow depth by 33%. However, since both the actual
sediment load and the dependence of the friction factor on
the Reynolds number are poorly constrained, we do not
attempt to correct for this effect in our calculations.
[9] These shortcomings in the quantitative geomorphology approach to studying the outflow channels are discussed not to discount the usefulness of such approaches,
but rather to suggest that caution must be taken with respect
to the application and interpretation of these methodologies.
The goal of this study is to supplement such geomorphic
approaches through the use of numerical models of the
outflow channel floods at their sources, and thereby gain
insight not only into the properties of the floods at the
surface, but also the subsurface processes driving their
formation.
2.2. Modeling Studies
[10] In a seminal study, Carr [1979] modeled the discharge of an outflow channel source region using the onedimensional hydraulic well approximation of Jacob and
Lohman [1952], assuming spatially and temporally uniform
aquifer properties. The chaos source region was represented
as a cavity extending through both the confining layer and
the aquifer to the impermeable basement beneath, a geometry
that may be more representative of the canyon sourced
outflow channels. It was found that peak discharges comparable to those inferred for the outflow channels could be
generated by flow through the aquifer. However, the peak
discharges occurred at the onset of the floods and then
decreased with time as a power law, implying that the
maximum discharges would have been short-lived and
would have coincided with the earliest immature channel.
This early peaking of the discharge clearly has implications
for the validity of the assumption that the channels in their
final form could ever have been bank full [Wilson et al.,
2004], an issue that we will address in light of this study in a
later section.
[11] More recently, Carr [1996b] suggested that the
floods are not limited by the permeability, but rather are
able to achieve high discharges by the disruption and
entrainment of the aquifer materials themselves, thus circumventing the gradual diffusion of pore pressures through
the aquifer. However, we note that the water to rock ratios in
typical aquifers (1:9, assuming a porosity of 0.1) are much
lower than the minimum water to rock ratio in the floods
(3:2, assuming a maximum volumetric sediment fraction of
0.4). Thus, in order to disrupt and entrain the aquifer host
material in the floods, the pore water contained within the
disrupted aquifer could constitute at most 7% of the total
floodwater, with the remainder being supplied by diffusion
through the intact aquifer. Alternately, erosion and removal
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of the outermost drained portions of the aquifer could
increase the hydraulic gradient in the remaining aquifer,
but the flood would still be diffusion limited. We further
note that the volumes of water inferred to be necessary to
carve the channels greatly exceed the volume of water that
can be contained in the aquifers underlying their sources,
thus requiring disruption and removal of an aquifer of much
greater extent than the observed chaos regions.
[12] Several more recent works have modeled the outflow
channel sources under the assumption that the flow through
the aquifer was driven by a uniform hydraulic gradient that
was related to the observed regional topographic slope [e.g.,
Head et al., 2003]. This approach assumes implicitly that
the outflow channels were driven by steady flow through
the aquifer in equilibrium with a constant recharge at
distance, in conflict with the understanding of the floods
as the product of the catastrophic drainage of a highly
pressurized aquifer. Manga [2004] recognized this, and
demonstrated the importance of the time variation of the
flow from a pressurized aquifer for channels originating
within linear tectonic sources.
[13] We here build upon the existing body of work by
simulating the origin of outflow channel floods within chaos
regions, using the hydrological model of Hanna and Phillips
[2005] and taking into account the variation of the hydraulic
parameters with depth and pore pressure. This study sheds
new light on the initiation and termination of outflow channel
floods, the nature of the flow through the source aquifers, the
number and duration of the floods, the variation of the
discharge and total flood volume with time, and the erosive
history of the channels.
3. Hydrological Model
3.1. Model Overview and Constraints
[14] We take the existence of a pressurized aquifer as an a
priori condition, and focus on the evolution of the discharge
from such a pressurized aquifer at a chaos source. We model
the flow of water to the surface as it passes through both the
aquifer (section 3.2) and the disrupted confining layer in the
chaos region (section 3.3). Section 3.4 considers the minimum discharge that can be maintained against freezing,
which ultimately causes the termination of the floods. The
implementation of the model and its specific application to
Iani Chaos and Ares Valles are discussed in section 3.5.
[15] While the results of this study can be applied to any
chaos-sourced outflow channel, we tailor the model to apply
to Iani Chaos, at the source of Ares Valles, allowing us to
compare the model results with the geomorphic estimates of
the discharge and flood volume for this channel. Iani Chaos
has an area of 1.5 105 km2, corresponding to an effective
radius of approximately 200 km in a cylindrically symmetric model. The chaos region is drained by Ares Valles, with
a channel depth of approximately 1 km, width of 20 km,
and average bed slope from Mars Orbiter Laser Altimeter
topography [Smith et al., 2001] of 0.001. As discussed
previously, the discharge of Ares Valles under bankfull
conditions has been estimated to be approximately 108 to
109 m3 s1 [Komatsu and Baker, 1997], though values
several orders of magnitude lower are possible for more
conservative flow depths. The total channel volume of Ares
Valles is estimated at approximately 8 104 km3 [Carr,
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ity are calculated on the basis of the inferred abundance of
breccia and fractures, and on the known properties of
terrestrial and lunar analogues to these materials. The
permeability in this model under hydrostatic pore pressures
ranges from 1011 m2 at the surface, down to 1015 m2
at depths greater than 5 km, while the compressibility
ranges from 2 109 to 1.5 1010 Pa1. All of the
hydraulic properties are highly sensitive to the effective
stress state of the aquifer as determined by the combination
of the lithostatic pressure and the fluid pore pressure. For
example, as the pore pressure increases, the fracture apertures widen, resulting in an increase in the permeability,
which depends on the cube of the aperture width. This pore
pressure dependence will be particularly important for the
outflow channels, in which large and rapid variations in the
pore pressure during the drainage of the aquifer are
expected.
Figure 2. MOLA shaded relief map of Iani Chaos
(centered on 342°E, 0°N).
1987], corresponding to a minimum total flow volume of
1.2 105 km3 for a maximum volumetric sediment load of
0.4. However, Ares Valles has four major sources, including Iani, Margaritifer, and Aram Chaos regions, as well as
a drainage system flowing northward from the Argyre
basin. Assuming that one quarter of the flood volume
originated from Iani Chaos, this leaves a minimum volume
of 3 104 km3 of water. Again, we emphasize that this
estimated flood volume is only an extreme lower limit.
3.2. Aquifer Model
[16] Transient flow within an aquifer is governed by the
diffusion equation [Domenico and Schwartz, 1990]:
@h
1
r ðkrhÞ
¼ @t m nbw þ bpore
ð3Þ
where h is the hydraulic head (m), k is the spatially and
temporally variable intrinsic permeability of the aquifer
(m2), m is the fluid viscosity (Pa s), n is the porosity, b w is
the compressibility of water (Pa1), and b pore is the
compressibility of the aquifer matrix. The hydraulic head
is a potential term, which includes both the elevation z of a
fluid parcel above a datum, as well as the aquifer pore
pressure Ppore:
h¼
Ppore
þz
rw g
ð4Þ
where rw is the density of water. Thus the hydrological
model must specify the porosity, permeability, and compressibility of the aquifer materials.
[17] The outflow channel source regions occur primarily
within the Noachian aged crust and Hesperian volcanics
east of Tharsis. We adopt the megaregolith aquifer model of
Hanna and Phillips [2005], which assumes a thick regolith
overlying the fractured and partially brecciated basement
rock beneath. The porosity, permeability, and compressibil-
3.3. Chaos Model
[18] There is a wide range in chaos region morphologies
on Mars. On one end of the spectrum, chaos regions such as
Aromatum Chaos at the head of Ravi Valles show clear
evidence of tectonic or structural control, and also seem to
have experienced significant collapse of the subsurface
[Leask et al., 2004]. This morphology suggests both strongly
heterogeneous and likely anisotropic subsurface properties,
as well as dramatic changes to the surface and subsurface
structure during the course of the flooding. At the other end
of the spectrum, chaos regions such as Iani Chaos at the head
of Ares Valles manifest themselves in the form of distributed
fractures and fissures over a broad region, with no clear
evidence for either collapse or tectonic control. While both
types of chaos are important in understanding the nature of
outflow channel flood generation, and there are undoubtedly
similarities in the processes involved in the flooding from
both, the latter is much more amenable to the modeling
approach of this study.
[19] As stated earlier, it is generally thought that chaos
regions at the sources of outflow channels formed when the
fluid pore pressure within a confined aquifer reached or
exceeded the lithostatic pressure at the base of the cryosphere [Carr, 1979]. At this time, the excess pore pressure
would expand the fractures within the aquifer and allow
their propagation into the frozen crust above. If the outflow
channels formed under cold climate conditions similar to
those that prevail on the planet today, these fluid filled
fractures would need to propagate through a cryosphere
thickness of 1 to 3 km, assuming a surface temperature of
220 to 250 K, a thermal conductivity of 2 to 3 W m1 K1,
and a heat flux of 50 mW m2 [Hauck and Phillips, 2002].
This flow from the aquifer to the surface through the chaos
region has a diffusive effect on the flood pulse in the early
stages of flow, as will be demonstrated in the sections that
follow.
[20] In order to construct a hydrological model of the
chaos region, we first look at the structure within and
around Iani Chaos (Figure 2). Toward the periphery of the
chaos region, isolated and branching flat-floored valleys
penetrate the surrounding undisrupted surface. These
valleys appear to be structurally controlled, and are likely
the surface manifestations of fractures. Within the main
chaos region, the valleys intersect and increase in number,
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Figure 3. Wide- and narrow-angle Mars Orbiter Camera
(MOC) images of a fissure (arrows) between mesas in
Hydraotes Chaos (MOC images M09-03791 and M0903790, left and center, respectively). A portion of the narrowangle MOC image (white box) has been enlarged at right.
dissecting the surface into a large number of flat-topped
mesas of relatively undisturbed country rock. These mesas
range in size from approximately 1 to 10 km across. Most of
the intermesa valleys have flat smooth floors, presumably
because of erosional widening and infilling with sediments
and debris. In places, however, it is possible to see the
bedrock structure at the base of these valleys, in which the
surface trace of a fissure that parallels the mesa walls can be
seen (Figure 3, in nearby Hydraotes chaos). We propose that
these fissures are in fact the hydrofractures that served as
conduits for the flow in the outflow channel events. While
the valleys between mesas have widths on the order of 1 km,
and the surface manifestations of these fissures have widths
on the order of 100 m, the actual subsurface conduits were
likely much smaller than their eroded surface manifestation.
[21] Over much of the chaos area, the mesas grade into
regions of more heavily disrupted terrain with a hummocky
appearance, in which rounded hills are separated by flat,
dune-filled valleys with a spacing ranging between a few
hundred meters and 1 km (Figure 4). The outlying linear
valleys, mesas and hummocky terrain appear to be members
of a continuum, with the hummocky terrain representing the
eroded remnants of hydrofracture-bound mesas. The difference in appearance is attributed to the closer spacing of the
hydrofractures in the hummocky terrain, which would result
in both a smaller lateral extent of the mesas, as well as a
greater flux of water to the surface and increased erosion.
[22] We envision the following scenario for chaos formation. In the initiation of the outflow event, hydrofractures
begin to propagate upward through the cryosphere from the
aquifer beneath. Rather than propagating new fractures
through solid rock, it is more likely that existing icecemented fractures within the cryosphere will be activated
and used as conduits for flow to the surface. These randomly oriented fluid filled fractures will intersect and
coalesce as they propagate upward, similar to patterns of
magma migration [Hart, 1993]. To a first approximation,
the spacing of the hydrofractures when they reach the
surface should be comparable to the thickness of the cryo-
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sphere through which they have propagated, to within a
factor of order unity, depending on the statistical distribution of fracture orientations. Thus the typical valley spacing
within the chaos region, and by inference the surface
hydrofracture spacing, of 1 km is in agreement with the
expected cryosphere thickness of 1 to 3 km.
[23] The hydrological properties of the chaos region are
based on the inferred spacing and width of the hydrofractures. We make the simplifying assumption of a uniform
hydrofracture spacing with depth, with a spacing of 1 km
based on surface observations. Observations of terrestrial
faults and hydrofractures suggest widths in the range of
104 to 9 103 m are typical immediately after a faulting
or hydrofracturing event [Gudmundsson et al., 2001], much
greater than the typical preexisting fracture width within the
aquifer of 1 –2 104 m [Hanna and Phillips, 2005].
However, the large and sustained flux of water through the
chaos region hydrofractures would likely lead to some
degree of erosional widening. We consider a range of
hydrofracture apertures of 5 103 to 5 102 m. While
this model is a gross oversimplification, it will later be seen
that the resistance to flow within the chaos region is
significantly less than that in the aquifer, such that the
hydraulic properties of the chaos region do not significantly
impede the flow except during the initial flood pulse, and do
not affect the flow hydrograph at later times.
[24] Thus flow occurs within two types of fractures on its
path to the surface: water within the aquifer passes through
the narrow-aperture fractures and joints that permeate the
crust; while water within the chaos region passes through
freshly generated macroscopic hydrofractures. While flow
within the narrow-aperture fractures within the aquifer will
be laminar, the flow will become turbulent as it is focused
into the wider chaos hydrofractures draining to the surface.
Flow through a conduit in the turbulent regime is modeled
as [Head et al., 2003]
q¼
1=2
g wfiss
rh
wfiss Nfiss
fw
ð5Þ
Figure 4. MOC narrow-angle image of rounded hills in
the hummocky terrain within Iani Chaos (portion of MOC
image E01-00637, centered on 341.6°E, 4.1°S).
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where q is the discharge (m s1), g is the acceleration of
gravity, wfiss is the fissure width (m), fw is the dimensionless
friction factor (here taken to be 0.025 for a water filled
fracture [French, 1985]), and Nfiss is the spatial number
density of fissures (m1). Note that the discharge is now
proportional to the square root of the gradient in hydraulic
head, and so the conventional concept of permeability does
not apply. Time-dependent flow through the chaos region is
solved for by balancing the divergence of the flow with the
change in hydraulic head:
@h
1
rq
¼
@t
rw g nbw þ bpore
"
#
1=2
g wfiss
1
r
¼
rh
wfiss Nfiss
fw
rw g nbw þ bpore
[27] The transition from turbulent to laminar flow conditions for pipe flow occurs for critical Reynolds numbers
Recr of 2000 to 4000 [Tritton, 1988]. For flow through a
conduit, the Reynolds number is calculated as
Re ¼
3.4. Flood Termination
[25] Since the discharge to the surface is limited by the
diffusion of the water through the aquifer, it is expected that
the discharge will decrease with time as a power law, as
found by Carr [1979]. In the waning stages of the flood, the
flow would no longer be maintained against freezing in the
cold Martian climate, and would be terminated. Clow
[1994] assumed that the flood is limited by freezing within
the channel and estimated the minimum discharges that
could be maintained for conditions appropriate for the
outflow channels under the present climate to be on the
order of 100 m3 s1, though the actual value will depend on
the slope and channel geometry. However, terrestrial experience demonstrates that rivers that freeze to their bottom do
not cease flowing, but rather break out through the ice layer
upstream of the constriction and flow across the top of the
ice, building up thick deposits of overflow ice or aufeiss in
the process. For the outflow channels, freezing of the
channel downstream of the chaos region cannot affect the
flow through the aquifer and its release to the surface, and
thus is not an effective means of terminating the floods.
[26] Alternatively, we suggest that the limiting factor in
the termination of the floods is the freezing of the water
within the chaos region hydrofractures. In order to reach the
surface, the aquifer water must pass through the cryosphere
thickness of 1 to 3 km within a network of narrow conduits.
Throughout this transit, the water will lose heat conductively to the surrounding cryosphere, which ranges in
temperature from 273 K at its base to approximately 220 K
at the surface for the present-day climate. Under conditions
of turbulent flow, the conductive heat loss will result in the
formation of suspended frazil ice particles [French, 1985]
which can remain in the flow and be advected out of the
system to the surface, allowing the flow to be maintained
against freezing. However, as the discharge wanes and the
flow in the chaos region becomes laminar, the conductive
heat loss will result in the nucleation of ice directly onto the
hydrofracture walls, and the conduits will rapidly freeze
shut.
wfiss ur
m
ð7Þ
where u is the average flow velocity. The critical Reynolds
number can be used in (7) to calculate the critical flow
velocity, ucr, and discharge, Qcr, from the chaos region as a
whole at the point at which flow to the surface becomes
laminar:
ð6Þ
Expansion or contraction of these wide-aperture hydrofractures proceeds at the expense of the surrounding rock
mass, and thus a compressibility of 1010 Pa1 is assumed,
representative of fractured bedrock or ice cemented regolith.
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Qcr ¼ ucr wfiss Achaos Nfiss
m Achaos Nfiss
¼ Recr
r
ð8Þ
where Achaos is the area of the chaos region, and Nfiss is the
typical hydrofracture density in the chaos region (m1).
Note that the dependence upon the actual hydrofracture
width drops out of the final form of equation (8), thereby
removing the least constrained parameter from the equation.
For a 200 km radius chaos region with a typical
hydrofracture density of 103 m1 (typical spacing of
1 km), a water viscosity of 103 Pa s, and a critical
Reynolds number of 2000, we calculate a minimum
discharge of 2.5 105 m3 s1. The increased turbulence
resulting from the roughness of the hydrofracture walls and
the advection of heat from deeper portions of the aquifer
may delay the termination of the flood, so we consider
minimum discharges of 104 to 105 m3 s1. When the
discharge decreases to this level, the flow through the chaos
region hydrofractures will become laminar and the conduits
will become choked with ice, thereby terminating the flood.
Smaller chaos regions will have proportionately lower
minimum discharges. This approach results in a higher
cutoff value for the discharge than estimated by Clow
[1994], precluding the long period of sustained low-level
flow that would otherwise ensue. This result is in agreement
with the observation that the outflow channels are
dominated by catastrophic erosional landforms, with little
evidence for extended periods of later, lower energy flow.
Smaller inner channels consistent with low discharge latestage flow are observed in some of the outflow channels
[Williams et al., 2000; Williams and Malin, 2004], but do
not appear to dominate their erosive history.
3.5. Model Implementation
[28] Flow is modeled using a fully explicit, two-dimensional, finite difference model to solve equations (3) and (6)
on an axisymmetric nonuniform mesh representing a cylindrically symmetric chaos region underlain by a laterally
extensive aquifer subject to no-flow conditions at the top
(beyond the chaos region), bottom, and edge (beyond the
hydraulic influence of the flood event). We represent Iani
Chaos as a 200 km radius chaos region in a 1 to 3 km thick
cryosphere, with a hydrofracture spacing of 1 km and hydrofracture widths ranging from 5 103 to 5 102 m. The
base of the aquifer is set at 20 km depth, and its hydrological
properties are modeled after Hanna and Phillips [2005]. We
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ANDREWS-HANNA AND PHILLIPS: MARTIAN OUTFLOW CHANNEL FLOODS
Figure 5. Discharge as a function of time in the early
stages of a flood from a 200 km radius chaos region for
different cryosphere thicknesses and aquifer overpressures
(baseline model represented by the solid line), as well as for
a model in which the permeability and compressibility of
the aquifer are held constant in time.
also consider the possibility of greater fracture apertures by a
factor of two within the aquifer. The model mesh extends out
to a distance of 2000 km from the chaos region center, well
beyond the hydraulic influence of the discharge and aquifer
depressurization at the chaos region. After each time step, the
aquifer properties are updated to reflect their dependence
upon the changing hydraulic head. For initial conditions, we
assume a uniformly pressurized aquifer, such that the pore
pressure at the base of the cryosphere exceeds the lithostatic
pressure by an amount ranging from 2 to 10 MPa. The exact
threshold for outflow channel initiation is unknown, and will
depend upon the material properties of the confining layer
and the details of the flood onset. Hydrofractures can begin
to propagate once the pore pressure reaches the lithostatic
pressure, but the rate of propagation must be sufficient to
prevent freezing of the fluids within, suggesting pore pressures in excess of the lithostatic pressure are likely required.
We note that 10 MPa is comparable to the tensile strength of
basalt [Peck and Minakami, 1968], and so pore pressures
greater than this are unlikely. Flooding is initiated by
applying a constant head boundary condition to the top of
the chaos region, set equal to the surface elevation, thus
allowing the pressurized aquifer to drain to the surface
through the chaos hydrofractures. The flood continues until
a minimum discharge is reached, here assumed to be
between 104 and 105 m3 s1.
4. Model Results
4.1. Individual Floods
[29] We first look at the model results for individual
outflow channel floods, turning later to the possibility of
repeating floods. The discharge at the surface as a function
of time for the early stages of flow is shown in Figure 5 for
our baseline model, assuming a 20 km thick aquifer overlain
by a 2 km thick cryosphere, a pore pressure excess of 5 MPa
E08001
above the lithostatic pressure, and an assumed hydrofracture
width in the chaos region of 5 103 m. Also shown are a
simulation with a 1 km thick cryosphere, and a simulation
with an excess pore pressure of 2 MPa. The peak discharge
for the baseline model of approximately 7.6 106 m3 s1 is
reached after an elapsed time of 2.4 104 s (6.7 hours) after
outflow initiation. The discharge drops quickly after the
peak value is reached. The minimum discharge of 105 m3 s1
is reached after 2.1 106 s (23 days), at which point a total
flood volume of 1.0 103 km3 has been debauched.
Alternatively, if a minimum discharge of 104 m3 s1 is
assumed, the flood terminates after 3.6 107 s (417 days)
after having released 1.8 103 km3 of water to the
surface. Thus decreasing the minimum discharge results
in a dramatic increase in the duration of the flood, but only
a modest increase in the total flood volume.
[30] The results from model runs for a variety of aquifer
parameters and initial conditions are given in Table 1. Peak
discharges range from 8.2 105 to 1.6 107 m3 s1, and
flood volumes range from 614 to 2850 km3. For different
sized chaos regions, the peak discharges will scale linearly
with the area, while the total flood volumes will scale nearly
linearly. The results show that higher peak discharges are
possible for greater chaos hydrofracture widths, though
there is a tradeoff between the magnitude and the duration
of these peak values. Increasing the cryosphere thickness
results in a decrease in the peak discharge due to the greater
diffusion of the flood pulse through the thicker cryosphere,
while resulting in an increase in the total flood volume due
to the greater pore pressure required to disrupt the thicker
cryosphere. An increase in the excess pore pressure required
for outflow channel formation increases both the peak
discharge and the total flood volume.
[31] In order to highlight the importance of the dependence of the hydraulic parameters on the pore pressure, the
simulation was repeated with the aquifer parameters held
constant throughout the simulation at their initial values for
the pressurized aquifer. A similar peak discharge of 8.3 106 m3 s1 was obtained at a time of 3.1 104 s. However,
as a result of the maintenance of higher permeability
throughout the aquifer despite the decreasing pore pressure,
the discharge decreases much more slowly with time
(Figure 5) and the minimum discharge is reached later in
the simulation, at 7.7 107 s. Thus the dependence of the
aquifer properties on the pore pressure provides for a more
sharply peaked flood and a more rapid termination.
[32] We now look below the surface at the aquifer
response to the outflow event. In order to better visualize
the patterns of flow within the aquifer, we consider a scaleddown model consisting of a 5 km radius chaos region in a
1 km thick cryosphere overlying a 1 km thick aquifer. The
hydraulic head and permeability have been plotted in
aquifer cross section at three different times (Figure 6). In
the earliest stages of flow (t = 103 s), the discharge is
dominated almost entirely by vertical flow from immediately beneath the chaos area. As the aquifer drains, the
decrease in hydraulic head is accompanied by a decrease in
permeability. After 104 s, there begins to be a significant
component of lateral flow from the region peripheral to the
chaos area. At this time the permeability has dropped by
more than an order of magnitude in the upper portions of the
aquifer beneath the chaos. At 105 s, the lateral flux from the
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ANDREWS-HANNA AND PHILLIPS: MARTIAN OUTFLOW CHANNEL FLOODS
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Table 1. Effect of Cryosphere Thickness, Excess Pore Pressure, and Chaos Hydrofracture Width on the Discharges, Volumes, and
Durations of Model Outflow Channel Floods
ym,a
km
Ppore,b
MPa
wfiss,
m
2
2
2
1
3
2
2
2i
2j
5
5
5
5
5
2
10
5
5
2.5 102
5 103
5 102
2.5 102
2.5 102
2.5 102
2.5 102
2.5 102
2.5 102
Qmax,c
m3 s1
7.55
8.22
1.58
9.24
5.91
5.74
9.42
7.55
8.33
106
105
107
106
106
106
106
106
106
tmax,
s
2.4
3.8
5.0
7.7
3.6
1.5
3.3
2.4
3.1
d
104
105
103
103
104
104
104
104
104
V(104 m3 s1),e
km3
1.79
1.78
1.75
1.41
2.01
1.22
2.85
1.77
4.85
103
103
103
103
103
103
103
103
103
t(104 m3 s1),f
s
3.6
3.6
3.5
2.4
4.4
2.8
4.9
3.5
7.7
107
107
107
107
107
107
107
107
107
V(105 m3 s1),g
km3
1.02
1.02
9.95
8.92
1.08
6.14
1.81
1.01
3.16
103
103
102
102
103
102
103
103
103
t(105 m3 s1),h
s
2.1
2.3
2.0
1.7
2.2
1.5
2.9
2.0
4.5
106
106
106
106
106
106
106
106
106
a
Cryosphere thickness.
Pore pressure in excess of lithostatic.
Peak discharge.
d
Time of peak discharge.
e
Flood volume after minimum discharge of 104 m3 s1 is reached.
f
Time to reach minimum discharge of 104 m3 s1.
g
Flood volume after minimum discharge of 105 m3 s1 is reached.
h
Time to reach minimum discharge of 105 m3 s1.
i
Aquifer model with fracture apertures greater by a factor of 2.
j
Aquifer properties held constant at initial values throughout the simulation.
b
c
chaos periphery is much greater than the vertical flux
beneath the chaos region, though for large chaos areas the
total discharge will still be dominated by the vertical flux of
water from beneath the chaos region. The permeability at
this time has decreased by more than 2 orders of magnitude
in the upper portion of the aquifer beneath the chaos, such
that the permeability is at a nearly constant value in the
upper kilometer of the aquifer. At this time, the hydraulic
head in the top 100 m of the aquifer has approached the
hydrostatic value of 2 km relative to the base of the
aquifer, suggesting that the chaos region presents little
resistance to the flow. As a result, the discharge is determined primarily by diffusive flow through the aquifer,
which is independent of the chaos region properties. In
full-scale simulations, the pressure wave from the initiation
of the flood (i.e., the maximum depth at which the decrease
in hydraulic head as a result of the discharge to the surface
is noticeable) reaches a depth of only about 6 km by the
flood termination at approximately 107 s, as a result of the
decreasing permeability with depth. Thus the discharge and
volume of a single flood is unaffected by the aquifer
properties at greater depths than this.
Figure 6. (left) Hydraulic head in meters and (right) permeability in m2 within an aquifer during an
outflow event from a small (5 km radius) chaos area at 103 s, 104 s, and 105 s after initiation of flow. The
1 km thick aquifer is overlain by a 1 km thick confining layer (not shown), breached by a chaos region
extending from radii of 0 to 5 km. Superimposed over the hydraulic head are arrows representing the flow
velocity vectors (normalized relative to the maximum velocity within each plot).
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ANDREWS-HANNA AND PHILLIPS: MARTIAN OUTFLOW CHANNEL FLOODS
[33] These modeled peak discharges fall significantly
below the Ares Valles peak discharge estimate of 108 to
109 m3 s1 assuming bankfull flow, though we will argue
below that this bankfull assumption results in gross overestimates of the discharge. Using equation (2), we calculate
the flow depth during peak discharge for the baseline model
flood to be only 54 m, significantly less than the channel
depth of 1 km. The flood volumes also fall significantly
short of the minimum volume required to carve Ares Valles,
and in the next section we discuss the likelihood that the
individual outflow channels actually formed through a large
number of episodic floods.
4.2. Multiple Floods
[34] Following the termination of the flood by freezing,
much of the aquifer remains pressurized because of the low
permeability of the deep portions of the aquifer and the
large lateral length scales involved (Figure 6). After the
flood termination, the pressurized fluid in these distal
portions of the aquifer will continue to diffuse toward the
drained portions, resulting in a repressurization of the
aquifer beneath the chaos region. Eventually, the pore
pressures beneath the chaos region will again reach superlithostatic levels, triggering a second flood. This cycle of
flood termination, repressurization, and flood recurrence
will repeat until the aquifer is sufficiently drained to be
unable to generate additional flooding events.
[35] We model the repressurization of the aquifer beneath
the chaos region by continuing the simulated flow through
the aquifer after the discharge through the chaos hydrofractures has been terminated. Figure 7 shows the evolution
of the discharge to the surface, the integrated flood volume
as a function of time, and the pore pressure at the base of
the cryosphere beneath the chaos region over a series of
three floods for the baseline model. As discussed above, the
main period of peak discharge in the first flood lasts several
days, and the total flood duration is on the order of a year
(Figures 7a and 7b). The initial drop in pore pressure as the
aquifer drains during the first flood is collapsed onto the y
axis in Figure 7c. Following the termination of the first
flood, the pore pressure in the aquifer just beneath the chaos
region rises relatively rapidly over the first few tens of
years, as the pressures from greater depths beneath the
chaos region diffuse upward. This vertical diffusion is
sufficient to eventually bring the pore pressure at the base
of the cryosphere back up to lithostatic values in order to
initiate a second flood after 1.4 109 s (44 years), and a
similar pattern of aquifer depressurization and discharge to
the surface ensues. Following the second flood, the deep
aquifers beneath the chaos region have been sufficiently
drained that vertical diffusion alone is not sufficient to
trigger a third flood. Thus, after the initial period of rapid
increase in pore pressure driven by vertical diffusion, the
pore pressure continues to rise more slowly because of
the lateral diffusion from the distal undrained portions of
the aquifer, until a third flood is initiated at 9.7 109 s
(310 years) after completion of the second.
[36] The time between subsequent floods increases
throughout the sequence, as more distal portions of the
aquifer must be tapped to repressurize the aquifer beneath
the chaos region. Erosion within the chaos region during
subsequent floods will both reduce the thickness of the
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confining cryosphere and result in its structural weakening,
thereby decreasing the threshold pore pressure necessary for
flood reactivation and increasing the likelihood of subsequent flood outbursts. While this model has not explicitly
included the erosion of the chaos region, the effect of such
erosion would be to decrease the time between subsequent
floods relative to our model results, particularly after a large
number of floods have ensued. Since the model only
represents the first few floods in the series, the effects of
chaos erosion at this early stage in the flooding history are
likely to be small. We have here simply assumed that the
first flood occurs at some threshold pore pressure (5 MPa)
above the lithostatic pressure, and subsequent floods are
triggered when the pore pressure reaches the lithostatic
pressure. The period of time between floods is also dependent on the assumed initial aquifer pore pressure. Greater
initial pore pressures result in a shortened interflood period,
particularly early in the simulations when the high pore
pressures at great depth beneath the chaos region are able to
repressurize the drained portions of the aquifer above.
[37] For comparison, if we ignore the minimum discharge
and allow a single flood to continue indefinitely, an arbitrarily large flood volume can be achieved for a flood of
long enough duration. However, the majority of the flood
occurs at exceedingly low discharge. For the baseline
model, one year after initiation of the flood, the discharge
has dropped by a factor of nearly 700 below the peak value,
and a total flood volume of 1741 km3 has been released.
After ten years, the discharge has dropped by a factor of
3200 below the peak value, with a total flood volume of
2880 km3. After 100 years, the discharge has dropped to
only 700 m3 s1, a factor of more than 10,000 lower than
the peak value, and a total flood volume of 6110 km3 has
been released. A series of periodic floods would release
nearly the same volume of water over a given period of
time, but the flow would be concentrated in short bursts of
high discharge flow, with the average discharge during
periods of flooding inordinately greater than that of a single
prolonged flood.
[38] These results have assumed that an area much larger
than the chaos region was initially pressurized to superlithostatic levels. Alternatively, it has been proposed that the
outflow channels were driven by a steady source of recharge
from precipitation and melting of ice deposits high on the
Tharsis rise [Harrison and Grimm, 2004, 2005], or from a
combination of the passive drainage of aquifers and a steady
flux of water being ejected from deeply buried aquifers
beneath Tharsis [Hanna and Phillips, 2006]. This same
result of periodic outbursts as the chaos region is gradually
repressurized would result from such a steady source of
recharge, relaxing the requirement for the pressurization of
the aquifer to superlithostatic levels over an area many times
larger than the chaos region. The period of time between
successive floods for the case of steady distant recharge
will be dependent upon the recharge rate. The global hydrological models of Harrison and Grimm [2004, 2005] and
Hanna and Phillips [2006] suggest average discharge rates
over geologic timescales at the outflow channel sources to
be on the order of several m3 s1. For comparison, the
periodic floods modeled here have mean discharge rates
averaged over the flood and interflood periods on the order
of 100 to 1000 m3 s1. In order for these periodic floods to
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ANDREWS-HANNA AND PHILLIPS: MARTIAN OUTFLOW CHANNEL FLOODS
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Figure 7. Evolution of the (a) discharge, (b) flood volume, and (c) subchaos pore pressure as a function
of time for periodic floods from a 200 km radius chaos region representative of Iani Chaos at the source
of Ares Valles. Note the different timescales used in each plot and discontinuities along the time axis in
Figures 7a and 7b.
be maintained by a global-scale aquifer recharge rate of
1 m3 s1, the individual flood volume of 1000 km3
requires an interflood period of order 104 years. If the
global-scale hydrology succeeded in pressurizing a regional aquifer to lithostatic pressures, then the floods would
initially recur over short timescales (102 years) as
suggested in this work, with the interflood periods gradually lengthening as the regional aquifers drained, until an
interflood period capable of being sustained by the globalscale flow was achieved. The total flood volume in either
case will depend on the number of flood episodes, which
in turn depends on either the extent of the pressurized
aquifer or the duration and rate of distant recharge. In
order to achieve the estimated minimum flood volume
from Iani Chaos of 3 104 km3, the flood volumes given
in Table 1 would require a minimum of between 6 and 49
individual floods. If the sediment loads carried by the
floods were less than the maximum value of 0.4 assumed,
the number of floods required would increase accordingly.
4.3. Erosive History and Geomorphic Implications
[39] As stated earlier, a common assumption in many
studies of the outflow channels is that they were formed in
single floods with peak discharges occurring under bankfull
conditions in the observed channel. Our results suggest that
both of these assumptions are gross oversimplifications for
outflow channels originating within chaos regions. The
discharges in these floods would have peaked early in the
flood, followed by long periods of lower discharge until
the floods terminated as a result of freezing within the chaos
region. Similarly, the rate of channel erosion should peak
early in the floods, but be followed by extended periods of
decreasing erosion in the later stages of the floods. As a
result, the channels during the peak discharge of the first
flood will only be a fraction of their final size. Furthermore,
the observed channels were likely carved by a large number
of floods, with each flood only responsible for a fraction of
the erosion, and with successive floods decreasing in
magnitude as the aquifer depressurizes and the threshold
for outflow reactivation decreases because of erosion in the
chaos region.
[40] There is currently no generally accepted and universally applicable relationship between channel flow dynamics
and erosion within a bedrock channel. Most models relate
the erosion rate, e_ , to either the stream shear stress on
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ANDREWS-HANNA AND PHILLIPS: MARTIAN OUTFLOW CHANNEL FLOODS
the bed, t, or the stream power, w [Sklar and Dietrich,
1998]:
e_ ¼ Kt t ¼ Kt rw gdS
ð9Þ
e_ ¼ Kw w ¼ Kw tu
ð10Þ
where S is the hydraulic slope, u is the flow velocity, d is the
flow depth, and Kt and Kw are dimensional parameters that
are poorly constrained and highly dependant upon the
mechanism of erosion and the rock type. Whipple et al.
[2000] argued that the erosion rate is best represented as
e_ ¼ Kt t a
ð11Þ
where the exponent a is dependent upon the erosive
process. Considering the physical processes behind the key
erosive mechanisms, they estimated exponent values of 3/2,
5/2, and up to 7/2 for plucking, abrasion by suspended load,
and cavitation, respectively. The cavitation model was
poorly constrained, and they noted a lack of direct
observational evidence for cavitational erosion within the
bedrock channels of their study. Furthermore, Wilson et al.
[2004] found that the supercritical flow required for
cavitation was not likely to have occurred during the
outflow channel floods. It has been argued that erosion by
plucking was important for both the Channeled Scablands
of eastern Washington State and the outflow channels
[Baker, 1979; Baker and Milton, 1974], suggesting that a
shear stress exponent of 3/2 is most representative of the
erosion in the outflow channels. However, the longitudinal
striations and streamlined islands observed in some
channels [Baker and Milton, 1974] are likely the result of
scouring by suspended load, suggesting a shear stress
exponent of 5/2.
[41] The current understanding of erosion in terrestrial
bedrock channels, in particular the value of the proportionality constants Kt and Kw, is insufficient to be able to
directly calculate the erosion rate expected to result from the
modeled outflow channel hydrographs. However, the relationships in equations (9) through (11) allow us to gain
insight into the variation of the relative erosion rate during
an outflow flood. We calculate the normalized erosion rate
as a function of time for the baseline outflow flood model,
considering the shear stress erosion models with stress
exponents of 1, 3/2, 5/2, and 7/2. The flow velocity and
depth as a function of time are calculated from the discharge
curve using equation (2) and the observed geometry of
Ares Valles. The normalized integrated eroded depths are
plotted in Figure 8 alongside the normalized flow depth
for our baseline flood model with a minimum discharge of
104 m3 s1. As expected, the channels are only partially
eroded at the time of peak discharge. For the median shear
stress exponents of 3/2 and 5/2, the channel has only
reached only 5% to 22% of its final depth at the time of
peak discharge. By the time the discharge has dropped by
a factor of 10 below its peak value, the channel will have
reached 26% to 78% of its final depth. Stated another way,
if one were to make the simplistic and unwarranted
assumption that the channel was carved in a single flood
and was exactly bank full at the time of peak discharge,
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these results suggest that the flow depth and channel depth
at this time would have been between 5% and 22% of the
observed final channel depth. Note that for this simple
scenario of bankfull flow during peak discharge, the high
water marks would be coincident with the channel top, but
the channel base at the time of this peak discharge would
have been situated well above its final value.
[42] The above treatment neglects a number of complicating factors. As demonstrated in section 4.2, the outflow
channels were likely carved in multiple events, with diminishing flood discharges and volumes for successive events.
Each event would carve the channel deeper, and thus each
successive flood would fall further short of the bankfull
condition. On the other hand, the ability of a single flood to
transport sediment of a given size is proportional to the
square of the flow velocity [Whipple et al., 2000]. Thus, as
the discharge decreases by approximately 2 orders of
magnitude from its peak value to the waning stages of the
flood, the larger sized fractions of the suspended and bed
load will settle out of the flow and could form an armoring
deposit over the channel bed. This effect could diminish the
erosive effectiveness of the flood in the later stages, and
result in a focusing of the erosion in the early stages.
[43] This analysis is not meant to quantitatively reproduce
the erosion during an outflow channel event, but rather to
illuminate the general pattern of the erosive history of the
channels. The results suggest that the assumption of bankfull flow within the final observed channel is a gross
overestimate, both because of the continued erosion of the
channel after attainment of peak discharges and the likelihood of multiple floods. It also suggests that the use of high
water marks in the reconstruction of the flow is unreliable,
since the correlation of a particular high water mark with a
known channel base level is not generally possible.
4.4. Channeled Scabland Analog
[44] While the conclusion that the individual outflow
channels were likely carved in a large number of discrete
events conflicts with the classical paradigm of their formation through one or several floods, the concept of a series of
repeating catastrophic floods has precedent in the terrestrial
literature. The Channeled Scablands of eastern Washington
State are commonly held as the best terrestrial analog to the
Martian outflow channels [Baker and Milton, 1974], and we
here extend that analogy to the number and nature of the
floods.
[45] Early interpretations of the Channeled Scablands
assumed that they were carved by the release of one, or
perhaps several, catastrophic floods of water [Bretz, 1923;
Bretz et al., 1956]. However, later evidence suggested that
they had in fact been carved by a large number of floods,
perhaps as many as 89, in a periodic succession [Wait, 1980,
1984, 1985]. The evidence for this series of many floods
came not from erosional features, but rather from depositional features, in which the deposits from individual floods
are preserved in backwaters and separated by varved lake
sediments (Figure 9). This record preserves both the number
and timing of the floods, suggesting that individual floods
were separated by periods of several to tens of years. The
periodic nature of the floods is a result of the mechanism for
the flood generation. The Channeled Scabland floods are
thought to have formed because of the catastrophic drainage
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combination of steady recharge with a threshold for release
is predicted to result in an episodic flooding history.
5. Discussion and Conclusions
Figure 8. Plot versus time of the normalized flow depth
and normalized erosional depth for the baseline flood model
during the early stages of the flood for different dependences of the erosion rate on the shear stress (t).
of glacial Lake Missoula, formed when a lobe of the
Cordilleran ice sheet dammed a major drainage network
[Alt, 2001]. The river water ponded behind the glacier until
it reached a sufficient depth to float the ice sheet, and then
flowed out from underneath in a jökulhaup-style flood. The
first flooding event was followed by a period of several tens
of years as the river water again pooled behind the glacier,
until it reached a sufficient depth to again float the glacier
and initiate a second flood. This process would continue as
long as the glacier dammed the river outlet and the fluvial
system upstream of the dam persisted.
[46] The analogy between the repeating floods in the
Channeled Scablands and the outflow channel floods is
twofold. First, the Channeled Scablands demonstrate that it
can be difficult to distinguish between a single flood and a
large number of floods based on the resulting erosional
landforms alone. The geomorphic signatures of the two can
be indistinguishable. This suggests that evidence of the
number and timing of the Martian outflow channel floods
may be found in the associated sedimentary deposits rather
than in the erosional record of the channels. Second, there is
a strong analogy between the nature of the processes
responsible for the recurring floods on Earth and Mars.
For both cases, there is a steady buildup of water until a
threshold is reached and flooding ensues, followed by a
period of recharge until the threshold is again reached and
the process repeats. For the terrestrial case, the threshold is
the attainment of a lake level sufficient to float the glacial
dam, and the recharge is a result of the continued drainage
of the upstream areas and flow through the river to the
dammed glacial lake. For the Martian case, the threshold is
the attainment of superlithostatic pore pressures in the
aquifer beneath the confining cryosphere, and the recharge
is the steady flow through the aquifer from the undrained
and still pressurized portions of the aquifer to the drained
portions at the source of the floods. In both cases, this
[47] Detailed modeling of the process of outflow channel
initiation and the aquifer response to an outflow event has
led to predicted maximum discharges and total flow volumes that are consistent with the observed channel geomorphology. We find that the discharge from a chaos source
is dominated by vertical flow from directly beneath the
chaos. The predicted discharges decrease rapidly after
the peak discharge, consistent with the interpretations of
the outflow channel floods as catastrophic and short-lived
events. During a single flood, continued erosion after the
attainment of peak discharges would have continued to
increase the channel depth by a factor of 5 to 20. After
termination of the flood, the high pore pressures diffuse
from the undrained portions of the aquifer back toward the
chaos region, resulting in a repressurization that triggers
additional episodes of flooding. Individual floods persist for
months to years, and are separated by minimum interludes
of 10s to 100s of years. Thus the outflow channels were
likely carved by large numbers of floods over long periods
of time, and the channels in their final form were not likely
to have ever experienced bankfull flow. For Iani Chaos at
the source of Ares Valles, the model predicts a minimum of
6 to 49 floods with peak discharges on the order of 106 to
107 m3 s1. This scenario is consistent with the observation
of small inner channels within some outflow channels
[Williams et al., 2000; Williams and Malin, 2004], which
is suggestive of multiple flooding events. Nevertheless, we
suggest that the observed erosional record may belie the true
number of floods, as in the Channeled Scablands.
[48] The outflow channels pose a curious conundrum: the
geomorphic evidence suggests they were carved by catastrophic floods from groundwater sources, and yet groundwater flow is an inherently gradual and diffusive process.
While transient high discharges can be produced from
groundwater flow [Carr, 1979], they are followed by long
periods of much lower discharges that decrease with time as
Figure 9. Sediment layers (rhythmites) deposited in a
backwater environment during multiple floods in the
Channeled Scablands of eastern Washington State (photograph by J. Andrews-Hanna).
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ANDREWS-HANNA AND PHILLIPS: MARTIAN OUTFLOW CHANNEL FLOODS
a power law. The periodic series of floods proposed here
would deliver the same volume of water to the surface as a
single sustained long-duration flood, but in a series of highdischarge bursts punctuated by long periods with no flow,
increasing the net catastrophic nature of the floods.
[49] The volumes and durations of the floods forming
the outflow channels have significant implications for the
volatile evolution of Mars. It has been suggested that the
outflow channels played a key role in delivering volatiles to
the surface of Mars during the Hesperian, possibly filling a
northern ocean or driving climate change [Gulick et al.,
1997]. These results suggest that individual outflow channels did not form all at once, but rather in a series of several
to hundreds of individual floods, separated by periods of
tens to hundreds of years. Such a flooding history would
make the generation of a northern ocean or a significant
climate change more difficult, as suggested by Williams et
al. [2000]. Under the present climatic regime, the comparatively small volumes of the individual floods may be more
likely to freeze, sublimate, and condense onto the poles,
rather than pond to form an ocean [Kreslavsky and Head,
2002]. The ultimate fate of the outflow channel effluents is
essential to our understanding of the volatile and climate
history of Mars during the Hesperian, but the channel
geomorphology alone does not sufficiently illuminate the
nature and history of the floods to reveal this fate. This work
suggests that understanding the hydrology of outflow channel genesis is crucial to understanding their impact on the
Martian environment.
[50] Acknowledgments. We would like to thank Keith Harrison and
an anonymous reviewer for comments that helped to improve and clarify
the manuscript. This work was supported at Washington University by
grants NNG05GQ81G and NNX06AB92G from NASA. The authors
acknowledge the use of Mars Orbiter Camera images processed by Malin
Space Science Systems that are available at http://www.msss.com/moc_
gallery/.
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J. C. Andrews-Hanna, Department of Earth, Atmospheric, and Planetary
Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139,
USA. (jhanna@mit.edu)
R. J. Phillips, Department of Earth and Planetary Sciences, Washington
University, St. Louis, MO 63130, USA.
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