JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL. 98, NO. E6, PAGES 10,973-11,016, JUNE 25, 1993
A Model for the HydrologicandClimaticBehaviorof Water on Mars
STEPHEN M. CLIFFORD
Lunar and Planetary Institute,Houston,Texas
Paststudiesof the climaticbehaviorof wateron Mars haveuniversallyassumedthat the atmosphere
is the sole
pathwayavailablefor volatileexchange
betweenthe planet'scrustalandpolarreservoirs
of H20. However,if the
planetary
inventoryof outgassed
H20 exceeds
theporevolumeof thecryosphere
by morethana few percent,thena
subpermafrost
groundwater
systemof globalextentwill necessarily
result.The existenceof sucha systemraisesthe
possibilitythatsubsurface
transport
maycomplement
long-termatmospheric
exchange.
In thispaper,thehydrologic
response
of a water-richMarsto climatechangeandto thephysicalandthermalevolutionof its crustis considered.
The analysisassumes
thatthe atmospheric
leg of the planet'slong-termhydrologiccycleis reasonably
described
by
current models of insolation-drivenexchange.Under the climatic conditionsthat have apparentlyprevailed
throughout
mostof Martiangeologichistory,thethermalinstabilityof groundice at low- to mid-latitudeshasled to
a netatmospheric
transport
of H20 fromthe "hot"equatorialregionto the colderpoles.Theoreticalarguments
and
variouslinesof morphologic
evidencesuggest
that thispolewardflux of H20 hasbeenepisodicallyaugmented
by
additionalreleasesof water resultingfrom impacts,catastrophic
floods,and volcanism.Given an initially icesaturated
cryosphere,
thedepositionof materialat thepoles(or anyotherlocationon the planet'ssurface)will result
in a situationwherethelocalequilibriumdepthto themeltingisothermhasbeenexceeded,meltingice at thebaseof
the cryosphere
until thermodynamicequilibriumis onceagain established.The downwardpercolationof basal
meltwaterintotheglobalaquiferwill resultin the riseof thelocal watertablein the form of a groundwater
mound.
Given geologically
reasonable
valuesof large-scale
crustalpermeability(i.e., >•10-2 darcies),the gradientin
hydraulicheadcreatedby the presenceof the moundcouldthendrivetheequatorwardflow of a significantvolume
of groundwater
(>•108km3) overthecourseof Martiangeologichistory.At temperate
andequatoriallatitudes,the
presenceof a geothermalgradientwill then resultin a net dischargeof the systemas water vapor is thermally
pumpedfrom the highertemperature(highervapor pressure)depthsto the colder (lower vapor pressure)nearsurfacecrust.By thisprocess,
a gradientassmallas 15 K km-1 coulddrivethe verticaltransportof 1 km of water
to thefreezingfrontat thebaseof the cryosphere
every106-107 years,or theequivalentof -102-103 km of water
overthe courseof Martian geologichistory.In thismanner,muchof the H20 that hasbeenlost from the crustby
the sublimationof equatorialgroundice, impacts,and catastrophicfloods may ultimately be replenished.The
validity of this analysisis supportedby a detailedreview of relevantspacecraftdata, discussions
of lunar and
terrestrialanalogs,andtheuseof well-established
hydrologicmodels.Amongthe additionaltopicsdiscussed
are the
thermalandhydrologicpropertiesof thecrust,the potentialdistributionof groundice and groundwater,the thermal
evolutionof theearlycryosphere,
therechargeof thevalley networksand outflowchannels,the polarmassbalance,
anda reviewof severalimportantprocesses
that are likely to drive the large-scaleverticaland horizontaltransport
of H20 beneaththe Martian surface.Givena geologically
reasonable
description
of the crust,and an outgassed
inventoryof waterthatexceedsthe porevolumeof the cryosphere
by just a few percent,basicphysicssuggests
that
thehydrologicmodeldescribed
herewill naturallyevolve.If so, subsurface
transporthaslikely playedan important
rolein thegeomorphic
evolutionof theMartiansurfaceandthelong-termcyclingof H20 betweentheatmosphere,
polarcaps,andnear-surface
crust.
CONTENTS
Introduction ................................................................
10,974
The Geophysical Basis for a Global Groundwater
System on Mars ...........................................................
Porosity Versus Depth ............................................
10,974
10,975
Thermal Structure ..................................................
10,976
The Distribution of Groundwater ...............................
10,978
Terrestrial Analogs: The Occurrence of Groundwater
and the Permeability of the Earth's Crust .........................
The Occurrence of Groundwater ...............................
10,980
The Stability and Replenishment of Equatorial H20 ...........
The Stability of Equatorial Ground Ice .......................
Other Crustal Sources of Atmospheric Water ..............
Evidence of Ground Ice Replenishment ......................
Processesof Replenishment .....................................
Transport Through the Cryosphere ............................
Polar Deposition, Basal Melting, and the Physical
Requirementsfor Pole-to-Equator Groundwater Flow ......... 10,995
Polar Basal Melting .................................................
10,995
10,981
The Large-Scale Permeability of the Earth's Crust ....... 10,981
Local and Regional Groundwater Flow ......................
10,983
Examples of Large-Scale Terrestrial Groundwater
Flow Systems ........................................................
10,983
10,985
10,985
10,987
10,988
10,989
10,993
Growth of a Polar Groundwater Mound ......................
10,997
The Effect of Crustal Permeability on Pole-to-Equator
Groundwater Flow ..................................................
11,000
The Large-Scale Permeability of the Martian Crust ...... 11,001
The Early Evolution of the Martian Hydrosphere
and Climate .................................................................
The Evolution of the Early Martian Climate and the
Initial Emplacementof Crustal H20 ..........................
The Hydrologic Responseof Mars to the Thermal
Evolution of Its Early Crust .....................................
Copyright1993 by the AmericanGeophysical
Union
Papernumber93JE00225.
0148-0227/93/93JE-00225505.00
10,973
11,002
11,002
11,003
10,974
CLIFFORD:
HYDROLOGIC
ANDCI_IMATICBEHAVIOROFWATERONMARS
Further Considerations ..................................................
11,006
Recharge of the Valley Networks and
Outflow Channels ...................................................
meltwaterbeneaththe polar capswill then resultin the rise of
the localwatertablein the form of a groundwater
mound.Given
11,007
The Polar Mass Balance and High Obliquities .............
11,008
geologically
reasonable
valuesof crustalpermeability,
the gradientinhydraulic
headcreated
bythepresence
of themound
will
Qualifications and Potential Tests ....................................
11,009
Conclusions .................................................................
11,010
Notation .....................................................................
11,011
1. INTRODUCTION
Virtually all past studiesof the climaticbehaviorof water on
Mars have focusedon the potential for insolation-drivenexchangebetweenthe regolith, atmosphere,and polar caps [e.g.,
Leighton and Murray, 1966; Toon et al., 1980; Fanale et al.,
1982, 1986]. Implicit in this work has beenthe assumptionthat
the atmosphereis the sole pathway available for volatile ex-
change.
However,if the planetary
inventory
of outgassed
H20
exceedsby morethana few percentthe quantityrequiredto saturate the pore volumeof the cryosphere(that regionof the crust
where the temperatureremainscontinuouslybelow the freezing
point of water), then a subpermafrostgroundwatersystemof
global extent will necessarilyresult. As discussedby Clifford
[198lb, 1984], the existenceof sucha systemmay have playeda
criticalrole in the long-termclimaticcyclingof wateron Mars.
This paper examinesthe potentialhydrologicresponseof a
water-richMars to both climate changeand to the physicaland
thermalevolutionof its crust.It is basedon the ad hoc assumption that Mars possesses
a globalinventoryof water sufficientto
both saturatethe pore volume of the cryosphereand create a
groundwatersystemof global extent. Evidencefor sucha large
inventoryis providedby a long list of Martian landformswhose
morphologyhas been attributedto the existenceof subsurface
volatiles [Rossbacher and Judson, 1981; Carr, 1986, 1987;
then drive the flow of groundwateraway from the poles and
towardsthe equator.At equatorialand temperatelatitudes,the
presenceof a geothermalgradientwill result in the local dischargeof the systemas water vapor is thermally pumpedfrom
the higher temperature(higher vapor pressure)depths to the
colder(lower vaporpressure)near-surfacecrust.In this fashion,
muchof the groundice and groundwaterthat has been removed
from the crust by impacts, catastrophicfloods, and long-term
sublimation,may ultimatelybe replenished.
Variousaspectsof this model, includingthe inherentinstability of equatorialgroundice [Clifford and Hillel, 1983], and polar
basal melting [Clifford, 1987b], have been discussedin detail
elsewhere.The focusof this paperwill thereforebe on thoseaspectsof the hydrologicresponseof Mars to climate changethat
have sofar receivedlittle or no attention,with particularemphasis on the potentialrole of subsurface
transport.Amongthe topics discussedare the thermal and hydrologicpropertiesof the
crust, the potentialdistributionof groundice and groundwater,
the stabilityand replenishmentof equatorialgroundice, basal
meltingandthe polarmassbalance,the thermalevolutionof the
early cryosphere,
the rechargeof the valley networksand outflow
channels,and a review of several processesthat are likely to
drivethe large-scale
verticalandhorizontal
transport
of H20
within the crust.Throughoutthis discussionit is assumedthat
the atmosphericleg of the long-termhydrologiccycle is reasonably describedby currentmodelsof insolation-drivenexchange
[Toonet al. 1980;Fanale et al. 1982, 1986]. Therefore,this paper will emphasizethe geologicrequirementsand actualphysics
of subsurface flow.
Finally, it shouldbe stressedagain that this is a theoretical
Squyres,1989]. In particular,it is supportedby the existenceof
the outflowchannels,whosedistribution,size,andrangeof ages, analysis,onewhosescopeis purposelyrestrictedto consideration
suggeststhat a significantbody of groundwaterhas been pres- of the hydrologicevolutionof a water-richMars. For this reason,
ent on Mars throughoutmuch of its geologichistory [Baker, no attempthasbeenmadeto conclusivelydemonstratethat Mars
an inventoryof water
1982; Tanaka, 1986; Tanaka and Scott, 1986; Carr, 1986, 1987; is indeedwater-rich,or that it possesses
Mouginis-Mark, 1990; Baker et al., 1992]. Based on a conserva- sufficientlylargeto form a groundwatersystemof globalextent.
tive estimateof the dischargerequiredto erodethe channels,and Rather,the volumeof water requiredto satisfythis conditionis
explored.
the likely extent of their original sourceregion, Carr [1986, estimatedand its potentialhydrologicconsequences
1987] estimatesthat Mars may possessa crustal inventoryof The resultsof this analysissuggestthat, given a geologically
reasonabledescriptionof the physicalpropertiesof the planet's
waterequivalentto a globalocean0.5-1 km deep.
Under the climatic conditionsthat have apparentlyprevailed crustand an inventoryof water that exceedsthe pore volumeof
by as little as a few percent,the hydrologicmodel
on Mars throughoutmostof its geologichistory,groundice is un- the cryosphere
transport
stablewith respectto the water vaporcontentof the atmosphere describedhere will naturallyevolve.If so, subsurface
at latitudesequatorwardof +40ø [Toonet al., 1980; Clifford and has likely playedan importantrole in the geomorphicevolution
andthelong-term
cyclingof H20 between
Hillel, 1983; Fanale et al., 1986]. As a result, the inventoryof of theMartiansurface
the
atmosphere,
polar
caps,
and
near-surface
crust.
equatorialgroundice is thoughtto haveexperienceda steadydecline. Becausethe cold polar regionsare the dominantthermo-
dynamic
sinkfor anyH20 released
to theatmosphere,
thereis a
preferential
transferof H20 fromthecomparatively
'Not"equatorial regionto the colderpoles.Theoreticalargumentsand variouslinesof morphologicevidencesuggestthatthis polewardflux
2. THE GEOPHYSICAL BASIS FOR A GLOBAL
GROUNDWATER SYSTEM ON MARS
The existenceof a globalgroundwatersystemon Mars is nec-
of H20 hasbeenaugmented
throughout
the planet's
historyby essarilysubjectto certaingeologicconstraints;the mostobvious
additionalreleasesof water resultingfrom impacts,catastrophic of whichis thattheremustexist a suitablyporousandpermeable
floods, and volcanism.The subsequentdepositionof dust and layer in which the groundwatercan reside. In this sectionthe
the existenceof sucha layeris summarized.
H20 at the poleswill ultimatelyresultin a situation
wherethe evidencesupporting
thermalequilibriumdepthto the meltingisothermhas been ex- In addition,severalrelevantparametersare discussed,
including:
ceeded.In responseto this deposition,melting will begin and the variationof porositywith depth,the thermalstructureof the
continueat the base of the polar cryosphereuntil thermal equi- crust, and how these two factors interact to influence the state
librium is onceagain established.The downwardpercolationof anddistributionof waterwithin the crust.
•ORD:
HYDROLOGIC
ANDCLIniC
BEHAVIOR
OFWATERONMARS
10,975
2.1. Porosity VersusDepth
Toddet al., 1973;Siegfriedet al., 1977]. Still greaterpressures
(>>10 kbar) are often necessary
to eliminateprimaryporosity,
Impactprocesseshave played a major role in the structural
suchas vesiclesin basaltor the intergranularporespaceof sedievolution of the Martian crust [Soderblom et al., 1974; Gurnis,
1981]. Field studiesof terrestrial impact craters [Shoemaker,
mentaryrock [Birch, 1961; Gold et al., 1971; Todd et al., 1973;
1963; Short, 1970; Dence et al., 1977] and theoreticalmodelsof Siegfriedet al., 1977]. Thus, any estimateof crustalporosity,
the crateringprocess[Melosh, 1980, 1989; O'Keefeand Ahrens, basedon the assumptionof a 1 kbar closurepressure,is nec1981] have shownthat impactsmodifythe structureof a plane- essarilyconservative.
BinderandLange[1980]suggest
thatthe seismicproperties
tary surfacein at leasttwo importantways:(1) by the production
by anexponential
declinein
and dispersalof large quantitiesof ejecta, and (2) throughthe of thelunarcrustarebestdescribed
porosity
with
depth,
a
relationship
that
is
consistent
with that
intensefracturingof the surroundingand underlyingbasement.
in manygeologicenvironments
on Earth [e.g.,Athy,
Fanale [1976] has estimated that over the course of Martian observed
andGautier,1988].Accordingto thismodel,the
geologichistory,the volumeof ejectaproducedby impactswas 1930;Schmoker
sufficientto createa globalblanketof debrisup to 2 km thick. porosityat a depthz is givenby
As notedby Carr [1979], it is likely that this ejecta layer is interbeddedwith volcanicflows, weatheringproducts,and sedimentarydeposits,all overlyingan intenselyfracturedbasement
(Figure 1). This descriptionof the Martian crust is essentially
identical to that proposedby Hartmann [1973, 1980] for the
near-surfaceof the Moon, where the early period of intense
bombardmentis believedto have resultedin the productionof
a blocky, porous "megaregolith"that extends to considerable
depth,a view that is supportedby the seismicpropagationcharacteristicsof the lunar crust [Toks6z et al., 1972, 1974; Toks6z,
1979].
For the near-surface of the moon, P wave velocities increase
ß (z) -- cI)(O)exp(-z/K)
(1)
where•(0) is the porosityat the surfaceandK is the porosity
decayconstant.
Assuming
thatthe densityof the Martiancrustis comparable
to its lunarcounterpart,
the inferredvalueof the lunarporosity
decayconstant
(-6.5 km) canbe gravitationally
scaledto find the
appropriatevalue for Mars, i.e.,
K Mars- 6.5 km (g Moon/ g Mars)
= 2.82 km.
with depthuntil they reacha local maximumat about20-25 km
where
gMoon
(=1.62ms-2)andgMars
(=3.71ms-2)arethegravi-
ity with increasinglithostaticpressure.The transitionbetween
Two potentialporosityprofilesof the Martian crustare illus-
[Toks6zet al., 1972, 1974; Simmonset al., 1973; Toks6z, 1979]. tational accelerationsat the surfaceof the Moon and Mars, reThis behavior is consistentwith a reduction in crustal poros- spectively.
tratedin Figure 2. The first is basedon a surfaceporosityof
for theMoonby BinderandLange
with the beginningof the constantvelocity zone at a depth of 20%, thesamevalueassumed
well with the measured
-20 km, where the lithostaticpressureis thoughtto be sufficient [1980], and one that agreesreasonably
fractured
and coherent
lunar basement
is believed
to coincide
(>1kbar-- 108Pa) to closevirtuallyall impact-generated
pore porosityof lunar breccias[Warren and Rasmussen,1987]. This
space[Toksb'zet al., 1972, 1974; Toks6z,1979].
A closurepressureof 1 kbar is consistentwith mostlaboratory
studiesof fracturedigneousrock [Birch, 1961; Siegfriedet al.,
1981], but pressuresin excessof 5 kbar are sometimesrequired
to ensurethe closureof all fractureopenings[Gold et al., 1971;
modelyieldsa self-compaction
depth(the depthat which crustal
porosityfallsbelow1%) of approximately
8.5 km. By integrating
theporosityof thecrustdownto thisdepth,thetotalporevolume
is foundto be sufficientto storea globallayerof waterapproximately540 m deep[Clifford, 198l a].
In the secondprofile, a surfaceporosityof 50% is assumed,a
valueconsistent
with estimatesof the bulk porosityof Martian
Crater ejecta
Volcanic
Increasing
depth
ß.•......: C5
'.:.'..L..-.'.1....
:.:•...:•
..r•'.
.• ...................
3!57:
ß.:.
flows
Weathering products
Sedimentary deposits
I
I
I
Self-compactiondepth
Fig. 1. An idealized stratigraphiccolumnof the Martian crust Clifford
[1981a, 1984].
(PERCENT)
20
30
40
50
•,(o) = 50%
fractured
in situ.
I
10
= 20%
..
Basement
I
POROSITY
00
-10
Fig. 2. Theoreticalporosityprofilesof theMartiancrustbasedon the lunar
modelof Binder and Lange [1980]. The curvebasedon a surfaceporosity
of 20% is simplythelunarmodelof Binderand Lange [1980] gravitationally scaledto Mars.The curvecorresponding
to a surfaceporosityof 50% is
includedto accountfor thepossibility
thatvariousprocesses
of physicaland
chemicalweathering
andlarge-scale
ice segregation
may havesubstantially
increasedthe availableporespacein theoutercrust[Clifford, 1984, 1987a].
10,976
CLI•ORD: HYDROLOGIC
ANDCLIMATICBEHAVIOROFWATERONMARS
soil as analyzedby the Viking Landers[Clark et al., 1976]. A formationof extensivebodiesof subpermafrost
groundwater
surfaceporositythislargemaybe appropriate
if the regolithhas [Clifford,1981b, 1984].The fateanddurationof groundwater
on
undergone
a significantdegreeof weathering[e.g.,Malin, 1974; Mars is thereforecriticallydependenton both the size of the
Huguenin,1976; Gooding,1978] or if it containslarge segre- planetary
inventory
of H20 andtotalporevolumeof the frozen
gatedbodiesof groundice. The self-compaction
depthpredicted crust.
by this modelis roughly11 km, while its total porevolumeis
equivalentto a globaloceansome1.4 km deep[Clifford,! 984]. 2.2. Thermal Structure
This pore volumeis likely an upperlimit, for it seemsdoubtful
The Martiancryosphere
is definedas that regionof the crust
that weatheringor large-scaleice-segregation
will affect more
where
the
temperature
remains
continuously
belowthe freezing
thantheupperfew kilometersof thecrust.Belowthisdepth,the
point of water(Figure3) [Fanale, 1976;Rossbacherand Judson,
porosityprofile will most likely resemblethe gravitationally
a solute-free
freezingpointof
scaledlunar curve. The physicalcharacteristics
of both models 1981;Kuzmin,1983].If we assume
273 K, thenat thesurface
thiscondition
is satisfiedat everylatiare summarized in Table 1.
The presenceof groundwatercould affect estimatesof the tudebelowthediurnalskindepth,thusdefiningthe cryosphere's
self-compaction
depthand total porevolumein severalways. upper bound.However,becauseneither the magnitudeof the
heatflux northethermalconductivity
of the:'
As discussed
by Hubert and Rubey[1959] and others[Byeflee Martiangeothermal
crust
are
known,
the
depth
to
the
lower
bound
of
the
cryosphere
and Brace, 1968; Brace and Kohlstedt,1980; Thompsonand
is considerably
lesscertain.
Cormoily,1992],the hydrostatic
pressure
of waterwithina pore
The depthto thebaseof the cryosphere
canbe calculatedfrom
can partially offset the lithostaticpressureacting to close it.
the steadystateone-dimensional
heatconduction
equation,where
Thus,for a "wet"Mars, crustalporositymay persistto depths
roughlya third greaterthanthoseindicatedby the "dry"models
in Figure2. However,groundwater
canalsoreducecrustalporosz = •
(2)
ity by solution,compaction,and cementation[Maxwell, 1964;
Qg
Rittenhouse,
1971]. Suchprocesses
are of greatestsignificance
under conditionsof high temperatureand pressure[Maxwell,
1964; Petrijohn, 1975]. Currently, these conditionsare likely to
exist only at great depth on Mars, where their impact on the
overall porosityof the megaregolithis expectedto be small.
However, conditionswere almostcertainlydifferent in the past.
For example,modelsof the thermalhistoryof Mars suggestthat
4 billion yearsago the planet'sinternal heat flow was some35 times greaterthan it is today [Toksrz and Hsui, 1978; Davies
and Arvidson, 1981; Schubertand $pohn, 1990]. In addition,the
existenceof an early atmosphericgreenhousemay have permitted liquid waterto existat or nearthe surface,whereit mayhave
reactedwith atmospheric
CO2 to formextensive
carbonate
depositswithin the crust[Kahn, 1985; Postawkoand Kuhn, 1986;
Kasting, 1987; Pollack et al., 1987]. The extent to which such
processes
may have affectedthe porosityand depthof the megaregolithis unknown.
Whether Mars oncepossessed
a warmer,wetter climate [Masurskyet al., 1977; Pollack et al., 1987], or a climate that has alwaysresembledthe conditionswe observetoday[Soderblomand
Wennet, 1978], as the interior of the planet graduallycooled,a
fleezing-frontdevelopedwithin the crustthat propagateddownward with time [Cart, 1979] (see also section6.2). If the total
pore volumeof this frozen region grew to exceedthe planetary
inventory of water, then eventually all of the water on Mars
should have been cold-trappedwithin the frozen near-surface
crust [Soderblomand Wennet, 1978]. Alternatively, if the pore
volumeof this regionis lessthan the planetaryinventoryof outgassedwater (defined here as the sum total of chemicallyunboundwater presentin the planet'satmosphere,on its surface,or
andwhere
•cisthethermal
conductivity
ofthecrust,
Trap
isthe
meltingtemperature
of theground
ice,Tinsis themeanannual
surface
temperature,
andQgisthevalue
ofthegeothermal
heat
flux [Fanale,1976].At present,
onlythecurrentlatitudinalrange
of mean annualsurfacetemperatureis knownto any accuracy
(-154-218 K +5 K), while the remainingvariableshave associated uncertaintiesof 20-50%. Plausiblerangesfor each of
these variables are discussed below.
2.2.1. Thermalconductivity.Fourprincipalfactorsinfluence
the thermalconductivity
of terrestrialpermafrost,theyare:bulk
density,degreeof poresaturation,particlesize, andtemperature
[Clifford and Fanale, 1985]. The effect of an increasein bulk
density(and/orpore saturation)on the thermalconductivityof
permafrostis readily understoodbecausethe conductivitiesof
rockandice are significantly
higherthanthe conductivity
of the
air theydisplace.However,the effectsof particlesize and temperatureare a bit morecomplicated.
Experiments have shown that thin films of adsorbedwater
remainunfrozenon mineralsurfacesdownto verylow temperatures[Andersonet al., 1967;Andersonand Tice, 1973], particularly in the presenceof potentfleezingpointdepressors
suchas
NorthPolarCap
_..
SouthPolarCap
..............
....,.
...............
............
...........
;.......................
......
_....... ................
.::;?i!?.;.:);.{'::;i':i:•':i
Cyosphe
e
........
:.:;!::::;:t;i.?;?;'•
?'?'•"•'
• Melting
Isotherm
• •'•"":•:';'?'•?.ii•.';;?:'.::.;
withinitscrust),thentheexcess
H20 should
haveresulted
in the
TABLE 1. CalculatedMegaregolithCharacteristics
Surface
Porosity Self-Compaction Storage
Capacity
(I)(0),%
Depth,
km
20
8.5
5O
11.0
x107km3
7.8
20
mH20
540
1400
Fig. 3. A pole-to-polecrosssectionof the Martian crust illustratingthe
theoreticallatitudinalvariationin depthof the freezingfront at the baseof
thecryosphere.
Notethatgroundice canexistin equilibriumwith the atmosphereonlyat thoselatitudesanddepthswherecrustaltemperatures
arebelow
the frostpoint of atmospheric
water vapor [-198 K, Farmer and Doms,
1979].Outsidetheselocations,
groundicecanonlysurviveif it is diffusively
isolatedfromthe atmosphere
by a regolithof low gaseous
permeability[e.g.,
Smoluchowski,1968; Clifford and Hillel, 1983; Fanale et al., 1986].
FigureadaptedfromFanate[ 1976]andRossbacher
and Judson[ 1981].
•ORD:
HYDROLOGICAND CLIMATIC BEHAVIOR OF WATER ON MARS
NaC1andCaCI2 [BaninandAnderson,
1974].Because
thethermalconductivity
of unfrozen
water(-0.54 W m-I K-I [Penner,
1970])is significantly
lowerthanthatof ice(2.25W m-l K-I at
10,977
/2
3b
273 K), its presencewill necessarilydecreasethe effectivethermal conductivityof silicate-icemixtures. Since the quantity of
14a
•5
16
H20 adsorbed
per unit surface
areais roughlyconstant
for all
7
8a
mineral soils [Puri and Murari, 1963], it follows that the con-
Frozen
8b
Soil
ductivityof a frozen soil will be proportionalto its contentof
high specificsurfaceareaclay. However,as the temperatureof a
frozen soil declines, so too does its content of adsorbed water
[Andersonet al., 1967; Andersonand Tice, 1973]. This results in
19c
10a
lob
11
an increasein the soil'seffectiveconductivity,an increasethat is
compounded
by the strongtemperaturedependenceof the ther-
12a
12b
mal conductivity
of ice, whichrisesfrom2.25 W m-1 K-I at
273K, to 4.42W m-1 K-1 at 160K [Ratcliffe,1962].
Basalt
114
115
I
I
I
I
I
1
2
3
4
5
6
Althougha directmeasurement
of the bulk thermalconductiv- o
ity of the Martian megaregolithis lacking,a likely rangeof valThermal Conductivity(W m K
ues can be inferredby consideringterrestrialanalogs.Imagesof
the surfacetaken by the Viking spacecraftsuggestthat the li- Fig. 4. Thermalconductivities
of frozensoil and basalt[Cliffordand
thology
of theupperfewkilometers
of thecrustvariesfroma Fanale,
1985].
loosefine-grainedregolithto meter-sizedblocksof ejecta, all intercalatedwith a significantquantityof volcanics[Greeleyand
Spudis,1981; Greeley, 1987; Arvidsonet al., 1989]. If so, then
thermalpropertiesof the megaregolithshouldbe closelyapproximatedby thoseof terrestrialfrozensoil andbasalt.
Laboratorymeasurementsof the thermal conductivityof 144
samplesof frozen soil and 301 samplesof basaltare summarized
in Table 2 and Figure 4. The samplesvary in composition,lithology, porosity,and degree of pore saturation,but all represent
conditionsthat are likely to exist somewherewithin the top
10 km of the Martian
crust. The thermal
conductivities
of the soil
samples
rangefrom0.08-4.0W m-1 K-1, withanaverage
value
of-1.66 W m-1 K-i; while the basaltconductivities
exhibit a
greaterspread,
0.09-5.40W m-1 K-1, withan average
valueof
-2.06 W m-1 K -1.
If our assumptionsabout the structureand lithology of the
outercrustare correct(i.e., Figure 1), thenthe thermalproperties
of the megaregolithwill be moststronglyinfluencedby basalt.If
so, the data in Table 2 suggest a column-averagedthermal
conductivity
of-2.0 (_1.0)W m-l K-1, withlowervalueslikely
TABLE 2. ThermalConductivityof MegaregolithAnalogs
Number
Group
Description
of
Samples
ConductivityRange,
W m -1 K -1
Frozen Soil
la
b
2
3a
b
4a
b
5
6
7
8a
b
c
Sandysoils,50-100% saturation[Sanger, 1963]
Sandysoils,3-45% saturation[Sanger,1963]
Poorlygradedcleansand,100% saturation[Lachenbruchet al., 1982]
Clay soils,50-100% saturation,T= 263 K [Sanger, 1963]
Clay soils,15-45% saturation,T= 263 K [Sanger, 1963]
Generic silt soil, 100% saturation[ Lachenbruch, 1970]
Genericclay soil, 100% saturation[Lachenbruch,1970]
Clay soil,nearlysaturated[Slusarchukand Watson, 1975]
Ledaclay andSudburysilty clay soils,100% saturation,T = 253 K [Penner,1970]
Fairbankssilty clay loam, 5-100% saturation,T = 269 K [Kersten,1963]
Black cultivatedsoil,0-100% saturation,T = 268 K [Higashi, 1953]
Brownsubsoil,0-100% saturation,T = 268 K [Higashi, 1953]
Yellow brownsubsoil,0-100% saturation,T = 268 K [Higashi, 1953]
18
1.80-4.00
24
0.33-2.35
5
3.39-3.67
21
1.26-3.06
10
0.47-1.38
averageof many
averageof many
24
2.34
1.84
1.49-2.25
2
1.67-2.09
13
0.25-1.95
8
0.18-1.42
9
0.08-1.21
8
0.10-0.82
144 (total)
1.66 (average)
Basalt
9a
Chloritic Golden Mile basalt,0% saturation[Sass, 1964]
AmphiboliticGoldenMile basalt,0% saturation[Sass,1964]
Nomeman basalt, 0% saturation[Sass, 1964]
10a
b
11
12a
b
PortageLake lava (amygdaloidaltops),0% saturation[Birch, 1950]
PortageLake lava (denseflows),0% saturation[Birch, 1950]
Ventersdorplava, 0% saturation[Bullard, 1939]
Vesicular Hawaiian basalt, 100% saturation[Robertsonand Peck, 1974]
Vesicular Hawaiian basalt,0% saturation[Robertsonand Peck, 1974]
13
Columbia River Plateau basalt, 0% saturation [Sass and Munroe, 1974]
14
Knippabasalt,0% saturation[Horai and Baldridge, 1972]
Deep-SeaDrilling Projectleg 37 basalts,100% saturation[Hyndmanand Drury, 1976]
15
28
3.85-5.40
11
3.22-4.98
7
2.47-2.93
10
2.30-3.77
27
1.72-2.76
9
2.64-3.60
57
0.84-2.41
60
0.09-1.80
72
1.12-2.38
1
19
301 (total)
2.30
1.66
2.06 (average)
10,978
CLIFFORD:HYDROLOGICAND CLIMATIC BEHAVIOROF WATER ON MARS
near the surface,where fine-grainedmaterialsmay be present
in abundance,and higher values occurringat depth, where the
lithologyof the crustis likely to be characterizedalmostexclusivelyby fracturedigneousrock [Clifford and Fanale, 1985]. In
contrast,previousestimateswere often based on the thermal
propertiesof a specificterrestrialanalog.For example,Fanale
[1976] assumedthat the propertiesof the megaregolithwere
data) are 82 mW m-2 [Sclateret al., 1980] and 16mW m-2
[KeihmandLangseth,1977],respectively.
Given the broad range of Martian heat flux estimates,a
globally
averaged
valueof 30mWm-2appears
tobea reasonable
choicefor the presentday heat flow. Substitutingthis estimate,
and the currentbest estimatesof crustalthermalconductivity
(2.0 W m-• K-1) andground
icemeltingtemperature
(252K)
well-represented
by a hard-frozen
limoniticsoil(•: -- 0.8 W m-• into equation(2), we find that the depth to the base of the
K-l), whileCrescenti
[1984]assumed
a purelybasaltic
composi-cryosphereshouldvary from about2.3 km at the equatorto
tion(•:- 2.09-2.5W m-• K-l).
approximately6.5 km at the poles,an increasethat reflectsthe
2.2.2. Melting temperature.The melting temperatureof corresponding
polewarddeclinein mean annual surfacetemgroundice can be depressedbelow 273 K by both pressureand perature (Table 4 and Figure 5). For completeness,maximum
solute effects; however, the effect of pressure is minimal and minimum cryospheredepthshave also been calculatedby
(-7.43 x 10-8 K Pa-• [Hobbs,1974]),whiletheeffectof saltcan combiningthe appropriatelimiting values of geothermalheat
be quite large. The existenceof varioussalts in the regolith is flow, thermalconductivity,and melting temperature.Although,
supportedby the discoveryof a duricrustlayer at both Viking the local thermalpropertiesof the crust are likely to display a
Lander sitesand by the elementalcompositionof the soil as de- high degreeof variability,on a globallyaveragedbasisit appears
termined by the inorganic chemical analysis experimentson unlikely that any geologicallyreasonablecombinationwill result
boardeach spacecraft[Toulminet al., 1977; Clark, 1978; Clark in cryospheredepths that differ by more than 50% from the
and Van Hart, 1981]. Among the most commonlycited candi- valuespredictedby the nominalmodel.
datesareNaC1,MgC12,
andCaC12,
whichhavefreezing
pointsat
By integratingthe crustal porosityprofile given by equatheir eutecticsof 252 K, 238 K, and 218 K, respectively[Clark tion (1) from the surfacedown to the melting isothermdepths
and Van Hart, 1981]. Indeed, some multicomponentsalt solu- presentedin Table 4, the potentialpore volume of the cryostionshave freezingtemperaturesas low as 210 K [Brass,1980]. phere is readily determined(Table 5). For the given range of
It shouldbe noted, however, that seriousquestionshave been porositiesand the likely thermal propertiesof the crust (i.e.,
raised
concerning
thechemical
andthermodynamic
stability
of those
represented
bythenominal
model),
thisamounts
toa pore
CaC12
andMgC12underambientMartianconditions,
particularlyvolume sufficient to store a global layer of water some 370in the presenceof abundantsulfates[Clark and Van Hart, 1981].
Given these arguments,brines based on NaC1 appearto be the
mostlikely candidatesto be foundwithin the crust.
2.2.3. Geothermal heat flux. Like the other variables in
equation(2), estimatesof the Martian geothermalheat flux have
varied over a wide range (Table 3). Solomonand Head [1990]
have notedthat if Mars losesheat at the samerate per unit mass
940m deep. For the extreme conditionsrepresentedby the
minimum and maximumthermal models,the range in potential
storagecapacityvaries from a global ocean as small as 40 m
deep, to one as large as 1400 m. Note that for the thermal conditions defined by the maximum case,the megaregolithshould
be frozenthroughout,a conditionthat appearsincompatiblewith
the geomorphicevidence for abundantgroundwater(i.e., the
astheEarth,thenit should
havea meanglobal
heatfluxof outflow
channels)
throughout
much
of Martian
geologic
history
-31mWm-2,a figure
thatagrees
reasonably
wellwiththein- [Baker,
1982;Tanaka,
1986;Tanaka
andScott,
1986;Carr,
dependentlyderived estimatesof Fanale [1976], Toks6z and
1986, 1987; Mouginis-Mark, 1990; Baker et al., 1992].
Hsui [1978], Turcotte et al. [1979], and Stevensonet al. [1983].
However,other publishedestimateshave beenboth significantly 2.3. The Distribution of Groundwater
higher and lower. For example, thermal modelingby Toks6zet
Thermodynamically,
theprimarysinkfor subsurface
H20 on
al. [1978], Davies and Arvidson [1981], and Schubertand Spohn
however,oncethe pore volumeof the
[1990] suggestsa present-dayheat flux as high as 40-45 mW Mars is the cryosphere;
m-2;whereas
workbySolomon
andHead[1990],based
onrheo- cryospherehasbeensaturatedwith ice, any remainingwater will
logicestimatesof lithosphericthicknessand mantleheat produc- drain to saturatethe lowermostporousregionsof the crust.But
tion (inferred from the compositionof the SNC meteorites), how deepand areallyextensivewill the resultingzoneof saturasuggests
values
aslowas 15-25mWm-2. Forcomparison
pur- tion be?As a first approximation,Mars can be considereda perposes,the currentbest estimatesof the averageheat flux of the fect spherewhose porosity profile is everywheredescribedby
Earth and Moon (the only bodiesfor which there is any actual equation(1). The quantityof water requiredto producean aquifer of any given thicknesscan then be calculatedby integrating
theporevolumeof themegaregolith
betweenthe self-compaction
TABLE 3. EstimatedGloballyAveragedGeothermalHeatFlux
depth and any shallower region of the crust. For example, a
Heat Flux
quantityof water equivalentto a globallayer 10 m deepis suffiPlanet
Source
mW m -2
cientto saturatethe lowermost0.85 km of the megaregolith(Figure 6), while a quantity of water equivalentto a 100-m layer
Mars
Fanale [ 1976]
30
would createa globalaquifernearly4.3 km deep [Clifford, 1984,
Toks& and Hsui [1978]
35
Toksb'zet al. [1978]
Turcotte et al. [1979]
Davies and Amidson [ 1981]
Stevensonet al. [1983]
Schubertand Spohn[1990]
Solomonand Head [1990]
Earth
Sclater et al. [1980]
Moon
Keihm and Langseth[1977]
,
45
33.5
40
28-32.4
40
15-25
82.3
14-18
1987a].
However,Mars is not a perfectsphere.Its crusthas been affectedby a varietyof geologicprocesses
that have createda surface of considerableheterogeneityand topographicrelief. This
diversityis undoubtedlyreflectedin the variabilityof a number
of importanthydrologiccharacteristics,
includingboth the local
porosityprofile and the depth of self-compaction.
Unfortunately
withoutfurtherdata, the magnitudeof this variationis impossi-
CLIFFORD:HYDROLOGICAND •TIC
BEHAVIOROFWATER ON MARS
10,979
TABLE 4. LatitudinalVariationof Cryosphere
Thickness
MeanAnnual
Latitude
Depth,km
Temperature,
K
90
Minimum
Nominal
Maximum
80
154
157
1.24
1.18
6.53
6.33
23.8
23.2
70
167
0.96
5.67
21.2
60
179
0.69
4.87
18.8
50
40
193
206
0.38
0.09
3.93
3.07
16.0
13.4
30
211
--
2.73
12.4
20
215
--
2.47
11.6
10
216.5
--
2.37
11.3
218
--
2.27
11.0
0
-10
216.5
•
2.37
11.3
-20
215
•
2.47
11.6
-30
211
2.73
12.4
-40
206
0.09
•
3.07
13.4
-50
193
0.38
3.93
16.0
-60
179
0.69
4.87
18.8
-70
167
0.96
5.67
21.2
-80
157
1.18
6.33
23.2
-90
154
1.24
6.53
23.8
Thermal
model
properties:
Minimum:
Qg= 45mWm-2,k = 1.0W m-1K-1,Trap
= 210K; Nominal:
Qg-- 30
mWm-2,k = 2.0W m-1K-1,Trap
= 252K; andMaximum:
Qg= 15mWm-2,k = 3.0W m-1K-1,Trap
= 273K.
LATITUDE
-90
-60
-30
0
30
60
-90
0
Minimum
Nominal
-10
Maximum
-15
-2O
-25
Fig. 5. Extentof theMartiancryosphere
for thethreethermophysical
modelsdefinedin thetextandin Table4.
TABLE 5. StoragePotentialof MartianCryosphere
PoreVolume, x107 km3
EquivalentGlobalOceanof H20, m
Extent of
Cryosphere
(I)(0) = 20%
(I)(0) = 50%
(I)(0) = 20%
(I)(0) = 50%
99
936
Minimum
0.57
Nominal
5.42
1.43
13.6
39
37 4
Maximum
7.76
20.0
536
1382
Thermal
model
properties:
Minimum:
Qg= 45 mWm-2,k = 1.0W m-1 K-1, Trap
= 210K; Nominal:
Qg-30mWm-2,k = 2.0W m-1K-1,Trap
= 252K;andMaximum:
Qg= 15mWm-2,k = 3.0W m-1K-1,Trap
= 273K.
ble to quantify.Thus, althoughit is clearthat the local characterThe one improvementthat can be made in attemptingto
isticsof the crustare poorlydescribedby a singleset of globally model the potential distributionof groundwateron Mars is to
averagedvalues,they are the best approximationof theseprop- considerthe effect of topography.If we assumethat the local
porosityprofile of the crust is describedeverywhereby equaertiesthatwe canpresentlymake.
10,980
GLIb-WORD:
HYDROLOGICAND CLIMATIC BEHAVIOROF WATER ON MARS
POROSITY
0
10
eral
(PERCENT)
20
30
40
50
I
kilometers
or more
beneath
the surface.
As illustrated
in
Figure7, the differencesbetween these controlling influences
(porosity, gravity, and thermal structure) are of considerable
importancein determiningthe state and vertical stratificationof
H20 withinthe crust.For example,beneathtopographic
highs,
the absoluteelevation of the local self-compactiondepth may
exceedthe elevationof the global water table; thus, only nearsurfaceground ice may be present in a vertical sectionof the
crust.Beneathareasof slightly lower elevation,both groundice
and groundwatermay be present;however, the vertical distances
separatingtheseregionsmay be substantial,leaving an intervening unsaturatedzone that couldbe manykilometersthick. In still
lower regions,the entire crustal column may be saturatedwith
-10
groundice and groundwater.Indeed, in the very lowest regions,
suchasthe interior of Hellas, the absoluteelevationof the global
water table may exceed that of the local topography.In suchinFig. 6. Resultingsaturated
thicknesses
of groundwater
for inventories
equivstancesthe groundice layer will be under a substantialhydraulic
alentto a globalocean10 and100 rn deep.In thismodelMars is considered
head.
As discussedby Carr [1979], a ruptureof this barriercould
a perfectspherewhoseporosityprofile is described
everywhereby equalead to a significantdischargeof groundwater.However, sucha
tion (1) [Clifford, 1984, 1987a].
rupture is eventually self-sealing,becauseas the groundwater
tion (1), then the depthof self-compaction
will mirror the gross erupts onto the surface,it will lower the local hydraulic head
___
variation of surfacetopography,defining an irregular, imper-
until it falls even with
the elevation
of the basin floor.
At that
meable lower bound for the occurrenceof groundwaterat a con- time, the reduceddischargewill permit the water-saturatedregolith to refreezeat the point of breakout,until the original ground
stantdepthapproximately
10 km beneaththesurface.
Figure7 is
ice thicknessis eventuallyreestablished.
a pole-to-polecrosssectionof this crustalmodel,wherethe surFigure 8a illustrateshow the areal coverageof groundwaterin
face elevationsand self-compaction
depthshave been averaged
the crustal model describedabove should vary as a function of
as a function of latitude. This cross section illustrates the po-
inventory
of groundwater
(i.e., in excess
of theH20
tential stratigraphicrelationships
betweensurfacetopography, theavailable
already storedas groundice in the cryosphere).This relationgroundice, andgroundwater,
for groundwater
inventories
rangship is seen more clearly in Plate 1, where the areal coverage
ing from 10 to 250 m. Note that for a groundwater
systemin
of groundwatersystemsbased on available inventoriesof 10 m,
hydrostatic
equilibrium,the watertableconforms
to a surfaceof
100 m, and 250 m of water are superimposed
on a topographconstantgeopotential.
In contrast,the distributionof groundice
ic map of Mars. For the assumedcrustal characteristics,the
is controlledby the localsurfacetemperature
andthe magnitude
resultingaquifersunderlie 34%, 91%, and 98% of the planet's
of the geothermalgradient.As a result,the positionof the melting isothermat the base of the cryosphere
will mirror the surface(Figure 8a), and possesslocal saturatedthicknessesthat
first-ordervariationsin surfacetopography,but at a depth sev- rangefrom zero to a maximumof 5 km, 10 km, and 13 km, respectively(Figure8b).
To summarize,this analysissuggeststhat oncethe pore volumeof the cryosphere
hasbeensaturatedwith ice, very little additional water (-10 m) is required to producea groundwater
systemof substantialextent. Indeed, given an unlikely combination of low crustalthermal conductivity,high heat flow, and
large freezingpoint depression,a global-scalegroundwatersystem couldconceivablyresult from an outgassedglobalinventory
10
ofH20 assmallas50 m;however,
formoreplausible
conditions,
suchasthosedescribedby the nominalmodel,a planetaryinventory in excessof 400 m appearsnecessary.
>-
3. TERRESTRIAL ANALOGS: THE OCCURRENCE OF
---J q0
GROUNDWATER AND THE PERMEABILITY
OF THE EARTH'S CRUST
-90
-60
-30
0
30
60
90
While the calculationspresentedin the previoussectionindicatethat a planetary-scale
groundwatersystemon Mars is physiFig. 7. A pole-to-pole
crosssection
of theMartiancrustillustrating
thepo- cally possible,is it geologicallyreasonable?Unfortunately,a
tentialrelationship
betweentopography,
groundice, and groundwater,
for clear answerto this questionis cloudedby the fact that subsurhypothetical
groundwater
inventories
equivalent
to a globallayer 10, 100,
and250 rn deep.Surfaceelevations
are averaged
as a functionof latitude face hydrologyremainsan inexact scienceeven here on Earth.
basedon the USGS MarsDigital TerrainModel,whilethe latitudinalvari- Much of this uncertaintyis attributableto our limited knowledge
LATITUDE
ationin groundicethickness
is basedonthenominalmodelresultslistedin of the detailed three-dimensional structure of the Earth's crust. It
Table 4. The calculated
groundwater
depthsassume
thatthe groundwater
is is alsodue to the subjectiveand often erroneousway in which
in hydrostatic
equilibrium,
thatthelocalporosity
proœfie
of thecrustis given
thisknowledgehashistoricallybeeninterpreted.
everywhere
by equation(1), andthatthe self-compaction
depthmirrorsthe
Until recently, terrestrial groundwaterinvestigationswere
grossvariationof surfacetopography
at a constant
depthof 10 km beneath
the surface.
driven almostexclusivelyby a desire to locate easily tapped
CLIFFORD:
HYDROLOGIC
ANDCI•MATICBEHAVIOR
OFWATERONMARS
3.1. The Occurrenceof Groundwater
"g'
o 100
Deepwell observations
indicatethatgroundwater
is present,
at somedepth,virtuallyeverywhere
beneaththe Earth'ssurface
z
<
80
o
60
LU
40
[Waltz,1969;deMarsilyet al., 1977;Fetter, 1980].According
to
Brace[ 1971], thiszoneof saturation
generallyextendsto a depth
that is at least4-5 km belowthe regionalwatertable.However,
thereis considerable
evidencethat groundwater
persiststo even
greater
depths.
Someof thisevidence
comes
fromstudies
of the
electricalconductivity
of the top 20 km of the Earth'scrust,a
conductivity
thatis severalordersof magnitude
higherthanthat
0
n-
O
<
of dryrockstudied
undersimilarconditions
of temperature
and
pressure
[Hyndman
and Hyndman,1968;Brace,1971;Nekut
20
0
10,981
•
o
1oo
•
200
et al., 1977; Thompsonet al., 1983; Shankland and Ander,
I
3OO
400 1983].Although
a widevarietyof explanations
havebeenpro-
EQUIVALENT GROUNDWATER INVENTORY (m)
(b)
posedto accountfor these observations,laboratorystudiesand
theoreticalargumentsboth stronglysuggestthat the high electrical conductivityof the crustowesits origin to the existenceof
water-saturatedpermeablerock at depth [Hyndmanand Hyndman, 1968; Brace, 1971; Shanklandand Ander, 1983; Gough,
1992].
More direct evidence for the existence of groundwaterat
depth comes from deep borehole studies, such as the Russian
"superdeep"researchwell locatedin the Kola Peninsula[Kozlovsky,1982, 1984]. The Kola well, which is part of an extensive
Russianprogramto studythe deepstructureand evolutionof the
m
-10
<C
continentalcrust, has penetratedto a depth of over 12 km.
Throughoutthe interval of 4.5-9 km, the well encountered
uJ -12
numerouszones of intensely fractured crystalline rock from
<C
•
-•4
which largeflows of hot, highly mineralizedwaterwere released.
These
flows occurreddespite confining pressuresin excess of
-16
•
•
•
0
100
200
300
4oo 3 kbar [Kozlovsky,1982]. Flow undertheseconditionsis thought
to be possibleonly when the permeabilityof the hostrock is low
EQUIVALENT GROUNDWATER INVENTORY (m)
enoughfor pore fluid pressuresto reachlithostaticvalues;transFig. 8. (a) The percentof Mars underlainby groundwater
and (b) the abso- port may then occurby the propagationof fluid-filled microfraclute elevationof the globalgroundwater
tableas a functionof the planetary tures in responseto tectonic stress[Thompsonand Connolly,
inventoryof groundwater
(expressed
as an equivalentglobaloceanof H20 ). 1992]. Such an argumenthas been proposedto explain the isoThis modelis basedon thesamedatasetandassumptions
asFigure7.
topic(fid and5180)composition
of groundwater
foundin deep
sourcesof water for human, industrial, and agriculturalcon-
fault zones, which indicates that surface-derived water has circulated to depths as great as 10-15 km [Kerrich et al., 1984;
McCaig, 1988].
sumption.
As a result,little effortwasspentto characterize
the
natureand extent of groundwatersystemswhosedevelopment 3.2. The Large-Scale Permeabilityof the Earth's Crust
wasperceivedas economically
prohibitiveor whosewater qualNumerous borehole and seismic investigationshave estabity was poor. This limited perspectivehas contributedto a
numberof misconceptions
aboutthe nature of the subsurface lished that the Earth's crust consistslargely of fractured rock
hydrologic
environment,
a problemthathasbeenfurtheraggra- [LeGrand, 1979; Brace, 1980, 1984; Mair and Green, 1981; Seevatedby the frequentand often uncriticaluse of terms like burger and Zoback, 1982]. While someearly studiessuggested
"aquifer"and "aquiclude",
that lack precisedefinitions.For ex- thatthe densityof fracturesdeclinesappreciablywith depth [e.g.,
ample,a water-bearing
formationthat may be consideredan Snow, 1968], more recent investigationsindicate that this coraquiferin oneregion(suchasa desert),mightwell be considered relationis limited to the weathered,near-surfacelayer. Indeed,in
an aquiclude(i.e., essentiallyimpervious)in a region where numerouswells drilled in variousparts of the world, fractures
othersignificantly
higher-yielding
formationsare present[Davis are invariablyfound down to the limit of exploration,with little
and De Wiest, 1966]. The evaluationof groundwatersystemsby
suchsubjectivestandards
has led to the widespreadperception
that groundwater
flow on Earth is restrictedto shallow,local
aquiferswith well-definedimpermeableboundaries.However,
overthe past30 years,numerous
detailedsubsurface
hydrologic
investigations
haveclearlydemonstrated
the inaccuracy
of this
picture.In this section,someof the key findingsof theseinvestigations
will be summarized,
providingthe necessary
terrestrial
background
for evaluatingthe likelihood,potentialextent,and
subsequent
evolution,of a globalgroundwater
systemon Mars.
or no evidenceof a significantdecline in fracturedensity [Seeburger and Zoback, 1982; Haimson and Doe, 1983; Kozlovsky,
1982, 1984].
Although independentof depth, the variability of fracture
densitywithin a given borehole,or betweenboreholes,is often
considerable.
For example,onehole may exhibit a fairly uniform
distributionof fracturesthroughoutits length,while another,just
a few kilometersaway,may displayconcentrations
of fracturesin
denselyfracturedintervals[Seeburgerand Zoback, 1982; Haimson and Doe, 1983]. As a result, neighboringwells may some-
10,982
CLIFFORD:HYDROLOGICAND CLIMATICBEHAVIOROFWATERON MARS
E
pz
•J
•
E
z
z
z
z
o
E
pz
•J
z
z
CLIFFORD:HYDROLOGICAND CI•MATIC BEHAVIOROFWATER ON MARS
timesshowas muchas a four-order-of-magnitude
differencein
permeability
overthesamedepthinterval[Brace,1980].
Becauseof the spatialvariabilityof fractures,the effective
permeabilityof crustalrocksis criticallydependenton the scale
of thesampleunderconsideration
(Figure9). For example,laboratorymeasurements
of samplesseveralcentimeters
in sizegenerally indicateonly the minimumpermeabilityof a rock mass
[Brace,1984]. However,at the scaleof interestfor mosthydro-
10,983
is calleda groundwater
divide. The extentto which infiltration
fromthe surfacecontributes
to groundwater
flow in neighboring
basinsis basedsolelyon which sideof the dividethe infiltration
occurs.The resultingvariationin hydraulicheadthen drivesthe
flow of groundwaterto the basin interior, where it evaporates
from the water table or is dischargedto the surfaceas a lake or
spring-fedstream.
Althoughmostbasinaquifersare modeledas if theywerehygeologic
studies
(generally
102-103
m),virtually
allcrustal
rocks draulicallyindependent,virtuallyall are part of largerintermedihaveundergone
a considerable
degreeof fracturing,dramatically ate and regional groundwaterflow systems(Figure 11) [Toth,
increasingtheir effective permeabilities[Streltsova,1976; Le- 1963, 1978; Ambroggi, 1966; Freeze and Witherspoon,1967;
Mifflin and Hess, 1979; Habermehl,1980; Castany,1981; Issar,
Grand, 1979; Seeburgerand Zoback, 1982; Brace, 1980, 1984].
Despitethe low porosityof fracturedrock (-1%), its perme- 1985]. In such systems,neighboringbasinsare linked by net-
abilityis oftenquitehigh[LeGrand,
1979;Brace,1980;Fetter, works
of intersecting
faultsandfractures.
In practice,
theextent
1980].Thisis because
theporegeometry
of a fracture
is inher- of thisinterconnection
is notoftenrecognized
because
thevolentlymoreefficient
at conducting
a fluidperunitporosity
than umeof waterthatparticipates
in interbasin
flowusually
reprethegeometry
of anintergranular
porenetwork;
thus,a rockwith sents
onlya smallfraction
of a basin's
totalhydrologic
budget.
a fracture
porosity
ofonly0.011%canhavethesamepermeabil-Exceptions
arenotedwhentherearesizable
differences
in preityasa siltwitha porosity
of50%[Snow,
1968].
cipitation
between
neighboring
basins
and/or
thefracture
permeThepervasive
natureof crustal
fractures
means
thatfew, if abilityof theintervening
formation
ishigh.
any,large-scalegeologicformationscanbe consideredimpermeable [de Marsily et al., 1977; Fetter 1980; Brace, 1980, 1984]. 3.4. Examplesof Large-ScaleTerrestrial
Indeed, Brace [ 1980, 1984] has summarizedthe results of in situ
GroundwaterFlow Systems
boreholepermeabilitymeasurements,
as well as permeabilities
In areasthatexperiencefrequentprecipitation,boththe shape
inferredfrom large-scalegeologicphenomena(such as earth- of the water table and the direction of groundwaterflow are
quakestriggeredby fluid injectionfrom nearbywells), and has stronglyinfluencedby the localtopography,makingany evidence
concluded
that,on a sizescaleof 1 km, the averagepermeability of regionalor interbasinflow difficult to recognize.However,in
of the top 10 km of the Earth'scrustis roughly10-2 darcies arid regions,the long intervals between atmosphericrecharge
(where1 darcyis the permeabilitynecessary
to permit a specific oftenprovidesufficienttime for the topographicinfluenceon the
discharge
of 1 cms-1 fora fluidwitha viscosity
of 1 centipoiseshapeof the water table to decay,makingevidenceof large-scale
undera hydraulicpressure
gradientof 1 bar cm-l; 1darcy-- hydrauliccontinuityconsiderablyeasierto identify. For this rea10-•2m2).Thus,at thissizescale,
virtually
all groundwater
sys- son,the best recognizedexamplesof regionalgroundwaterflow
tems on Earth may be consideredhydraulicallyinterconnected. on Earth are all found in arid environments.
The extentof this interconnection
has becomeincreasinglyap3.4.1. The Great Basin Carbonate Aquifer System, USA.
parent as detailed hydrogeologicstudieshave demonstratedthe Some of the very first evidencefor interbasingroundwaterflow
potentialfor contamination
of groundwater
suppliesby migrating camefrom Death Valley, California, where it was observedthat
chemical and radioactive wastes [de Marsily et al., 1977;
the dischargeof certainspringsfar exceededthat which couldbe
Anderson, 1987].
explained by local recharge[Hunt and Robinson, 1960]. This
discoverysuggestedthat groundwaterderived from the higher
3.3. Local and RegionalGroundwaterFlow
intermontanebasinsto the eastwas reachingDeath Valley via an
On Earth,the smallestandmostdynamicelementof a ground- extensive network of interconnectedfractures through a thick
water flow systemis typically a shallow unconfinedaquifer interveningformationof carbonaterock. Convincingsupportfor
locatedwithin a smalltopographic
basin.Becausethe aquiferis this hypothesiscamefrom the near identicalchemicalcomposirechargedby atmosphericprecipitation,the water table general- tion of springwater in Death Valley and that found -70 km to
ly conformsto the shapeof the local terrain (Figure 10). The the eastin the intermontanevalley of Ash Meadows,Nevada.
The discoveryof interbasinflow betweenAsh Meadows and
elevatedwater table that occursat the boundarybetweenbasins
Death Valley raisedconcernaboutthe possibilityof groundwater
contaminationfrom undergroundnuclear tests conductedat the
PERMEABILITY:
THE EFFECT OF SCALE
nearbyNevadaTest Site [Winograd, 1962]. Althoughthe three
large basinsencompassed
by the Test Site are topographically
isolated,the well water levels in all three are essentiallyidentical, a result that arguesstronglyfor hydraulic interconnection.
Shortlyafter this discovery,anotherregionalgroundwatersystem
was discovered
CENTIMETER
10 - 100 METER
KILOMETER
Fig. 9. The effectof scaleoncrustalpermeability
measurements
(afterBrace
[1984]). Laboratorystudiesof rock samplesonly a few centimeters
in size
generallyyieldonlytheminumumpermeabilityof a rockmass.However,on
a sizescaleof kilometers,thepervasivenatureof crustalfaultsand fractures
yieldsa meanpermeability
of -10 -2darcies
for thetop 10 km of theEarth's
crust.
to the east of the Test Site that linked
13 inter-
montanevalleysinto a regionalflow systemmeasuringroughly
385 by 115 km [Eakin, 1966]. Indeed,as investigations
continue,
it is now believed that most of western Utah, eastern and southern Nevada, and the southeasterncomer of California are under-
lain by oneor moredeepregionalflow systemsthat extendfrom
Great Salt Lake to Death Valley. The host rock is a thick (69 km) accumulation of Paleozoic limestone and dolomite that
underlies
-1.6 x 105km2 of theGreatBasinprovince
[Mifflin
10,984
CLI•ORD: HYDROLOGIC
ANDCLIMATICBEHAVIOROFWATERONMARS
groundwater
divide
water•'....
topographygroundwater
•
',,,,C,,__,.__,..._,•
,,;:';,';,'Z,;,"/;';'
_table
_•,,,-•/{
•'"'•,/
_•-"/
.
...•de
/
Fig. 10. A sketchof a localgroundwater
flow system,illustratingtherelationship
betweentopography,
the shapeof thewatertable,andthe directionof subsurface flow.
local flow
a total east-westtransittime in excessof 1 million years[Bentley
systems
et al., 1986; Cathies, 1990].
•ntermed•ate
Unlike the Great Basin Carbonate Aquifer System in the
United States,the geologicsimplicityof the Gmat ArtesianBasin
Aquifer led to early recognitionof both its physicaldimensions
and the extentof groundwaterflow [e.g., Pittman, 1914]. To this
day, it remainsthe largestrecognizedsingle-basingroundwater
systemon Earth.
3.4.3. The Nubian Aquifer Systemof the Eastern Sahara.
The groundwater
resourcesof the SaharaDesertin North Africa
are divided amongeight major sedimentarybasins [Ambroggi,
1966;Burdon, 1977; Margat and Saad, 1984]. Two of these,the
Dakhla Basinof Egypt and the Kufra Basin of Libya, form the
NubianAquifer Systemof the EasternSahara,a regionalaquifer
flow
system
regional flow
system
,
xx
x.x.x
with an areaof-2 x 106 km2 [Schneider,
1986;Hesseet al.,
,/
/..1\/.•,\/•\/--\/-...\/•\/.-.•/.-\/--\/-...\/._/• /"t/•l/"'l/"'-i
•1/'-i/•1/"'1/'"-i
-
x......xxxx...x,
/x......xx...x...x,
,-,,-,,-,<-:.,,..--'•,-,,-,,-,<-:,,.--'•,
•1/•1/•1/\1/\'1/•1/•1/•1/\1/\'1/•1/•1/•1/•
/
/- ,.. /....\/..•/..•/..\/•\/....\/•\/..\/•\/..\
[•c•,rw•,r•{
"-I
•1/"1/•1/"'1/'"-I
•1/"1/•1/"'1/
•,o•111•11•
,
,
,
x. /x...xxxxxxx,
/x...xxxxxx
,.'--'•,-,,-,,-,,-,,--'•,-,,-,,-,,-,
/•'1/•1/•1/•1/"1/•'1/•1/•1/•1/"1
/
1987]. The aquifer'sprincipal water-bearingformation is the
Nubian Sandstone, which varies in thickness from less than
Fig. 11. An illustration
of thenested
nature,lateralextent,andrelativedepth 500m to more than 3000 m [Sham, 1982]. In the northern
of flow of local,intermediate,
andregionalgroundwater
flow systems.
portionof the system(i.e., between-25øN and the southern
shore of the Mediterranean Sea) the sandstoneis intercalated
and Hess, 1979; Harrill, 1984; Thomas and Mason, 1986]. Bewith shalesand clays and overlainby fracturedcarbonaterock,
causelittle datahasbeencollectedbelow the upperzoneof saturation, the full extent of hydrauliccontinuitywithin the system
has yet to be established.However, at depth, the limited evidence that does exist suggeststhat solution-widenedfractures
and cavernshave created widespreadregions of high permeability, a characteristic
that has made carbonateaquifersamong
the most extensiveand productivein the world [LeGrand and
Stringfield, 1973;Mifflin and Hess, 1979].
creatinga confinedmultilayeredsystemof considerablecomplexity[Sham,1982;Hesseet al., 1987].
From a human and agricultural resource perspective,the
Nubian Aquifer is generallyconsideredhydraulicallyisolated;
however,them is considerableevidenceof hydraulic continuity
far beyondthe system's
recognizedboundaries.For example,the
northernlimit of the aquiferis usuallydefinedby the locationof
the saline-freshwater interfacethat occursup to severalhundred
3.4.2 The Great Artesian Basin, Australia. The Great Artesian Basin underlies -1.7 x 106 km2 of the eastern half of
kilometers inland from the Mediterranean Sea [Sham, 1982;
Thorweihe,1986]. Althoughthe locationof this chemicaltransition is importantin the contextof water quality, it hasno beating
fifth the land area of the entire continent [Habermehl, 1980]. on theextentof hydrauliccontinuity.Indeed,explorationwells in
perStructurally,the basin is a bowl-shapeddepressionthat contains northernEgypthave establishedthat the Nubian sandstone
up to 3 km of sedimentarydeposits.These depositsform a sistsanddeepensas it extendsnorthwardbeneaththe Mediterramultilayerconfinedaquifer systemconsistingof sandstoneaqui- nean'ssouthernshore[Shata, 1982; Thorweihe, 1986].
The remainingboundariesof the NubianAquifer are similarly
fers sandwichedbetweenless permeablelayersof siltstoneand
vague.For example,alongmostof its easternmargin,the Nubian
mudstone[Habermehl, 1980; Cathles, 1990].
The basinis rechargedalongits easternmarginby precipita- Aquiferis boundedby an outcropof basementbetweenthe Nile
tion on the elevatedslopesof the Great Dividing Range.Dis- Valley and Red Sea. However,further north, where the outcrop
thereis evidenceof a connection
to a majoraquifer
chargeby naturalspringsoccursprimarilyin a region900 km to disappears,
the southwest,in the vicinity of Lake Eyre [Habermehl,1980]. in the Sinai peninsula[Sham, 1982; Issar, 1985]. To the south,
Numericalmodelsand isotopicdatasuggestthat the naturalflow water table contourssuggesthydrauliccontinuitywith the Blue
velocity
through
thebasin's
principal
aquifer
is -1.0 m yr-•, with Nile-Main Nile Basin [Hesseet al., 1987] as well as groundwater
Australia, an arid to semi-aridregion that representsover one-
CLIFFORD:HYDROLOGIC
ANDCLIMATICBEHAVIOROFWATERONMARS
inflow from northeastern
Chad [Ambroggi,1966; Edmundsand
Wright, 1979]. Finally, in the west,there is evidenceof a hydrauliclink betweenthe NubianAquiferand the Sirte Basinin
10,985
Schaber, 1977; Allen, 1979a; Rossbacherand Judson, 1981;
Lucchitta, 1981, 1985; Squyresand Carr, 1986; Carr, 1986;
Squyres, 1989; and others];their common conclusionhas been
Libya[Edmunds
andWright,1979].Because
detailedhydrologic that of the possiblemechanisms
that mightexplainthe presence
information
is scarcethroughout
the EasternSahara,the degree of thesefeatures,thoseinvolvinggroundice appearthe mostreaof the hydraulicinterconnection
betweentheseneighboring
sys- sonable.Additionalevidence(foundat all latitudes)for the prestems is difficult to assess.It is clear, however, that as the area of enceof subsurface
H20, isprovided
bytheoccurrence
of rampart
recognizedhydrauliccontinuityexpands,the likelihoodof addi- craters,whosedistinctivelobateejectamorphology
is thoughtby
tionallinks with neighboringbasinsincreasesaswell.
manyinvestigators
to originatefrom the fluidizationof ejecta
In summary,the distributionand flow of groundwateron materialduringan impactinto a water- or ice-richcrust[Carr et
Earth exhibitsseveralcharacteristics
that are of potentialimpor- al., 1977;Johansen,1978;Allen, 1979b;Mouginis-Mark, 1979,
tancein understanding
the subsurface
hydrologyof Mars. First, 1987; Blasius and Cutts, 1981; Kuzmin, 1983; Kuzrnin et al.,
givena globalinventory
of H20 thatexceeds
theporevolumeof 1988; Costard, 1989; Barlow and Bradley, 1990]. Finally, the
thecryosphere
by as little as a few percent,groundwater
is likely survival of a significantreservoirof subsurfacewater in the
to be found virtually everywherebeneaththe Martian surface. equatorialregionis alsosupported
by the presenceof the outflow
Second,as on Earth, it is likely that suchgroundwaterwill per- channels,whoseepisodicdevelopment
appearsto have spanned
sist and circulateto depthsfar in excessof the 10 km self- much of Martian geologichistory [Carr, 1981; Baker, 1982;
compaction
depthassumedin this study.Third, in the absenceof Tanaka, 1986].
The aboveevidencepresentsa problem,for it is difficult to
atmospheric
precipitation,the hydraulicboundariesof a groundwater systemon Mars will be determined,not by the local to- account
forboththeinitialoriginandcontinued
survival
of H20
pographyor the presenceof groundwaterdivides, but by the in a regionwherethe presentmeanannualsurfacetemperature
continuityof pore spacebeneaththe water table. Fourth,givena exceedsthe frostpointby morethan 20 K. Indeed,undercurrent
km-scalepermeabilityof the Martiancrustno greaterthanthat of climaticconditions,
anysubsurface
H20 should
experience
a net
theEarth(-10-2 darcies),
theextentof hydraulic
continuity,
and annualdepletion,resultingin its preferentialtransferfrom the
thusthe potentialarealextentof a Martian groundwatersystem, '•ot" equatorialregionto the colderlatitudespolewardof +400
[Flasar and Goody, 1976;Toon et al., 1980; Clifford and Hillel,
is essentiallyglobal.
1983; Fanale et al., 1986].
4. THESTABILITY
ANDREPLENISHMENT
OFEQUATORIAL
H20
Currently,the mostwidely acceptedexplanationfor the exis-
tenceof a subsurface
reservoir
of equatorial
H20 is thatit is a
Theoretical considerationsand various lines of morphologic relic,emplacedveryearlyin Martiangeologichistory(> 3.5 b.y.)
differentclimaticconditions.This explaevidencesuggestthat, in additionto the normal seasonaland and undersubstantially
nation
is
based
in
part
on
the work of Smoluchowski[ 1968], who
climaticexchange
of H20 thatoccurs
betweentheMartianpolar
showed
that
under
certain
restrictedconditionsof porosity,pore
caps, atmosphere,and mid- to high-latituderegolith [e.g.,
kosky,1985;Zent et al., 1986], largevolumesof water havebeen size, temperature,and depth of burial, the diffusion-limiting
introducedinto the atmosphericleg of the planer'slong-term propertiesof a fine-grainedregolith could preserveequatorial
hydrologiccycleby the sublimationof equatorialgroundice, im- groundice for billionsof years.
The stabilityof groundice is governedby the rate at which
pacts,catastrophic
flooding,and volcanism.In this sectionboth
candiffusethroughthe regolithandintothe atendpointsof the proposed
cyclearediscussed,
beginningwith the H20 molecules
lossof water from crustalreservoirsat equatorialand temperate mosphere.This processis complicatedby the fact that the colin the Martian
latitudesand concludingwith its possiblereplenishmentby sub- lisionalmeanfree pathof an H20 molecule
atmosphere
is
-10
gm.
When
the
ratio
of
the
pore
radius to the
surface
sources
of H20. The intermediate
stepsof the proposed
cycle, includingpolar deposition,basal melting, and pole-to- mean free path of the diffusingmoleculesis large (r/)• >10),
bulk moleculardiffusionis the dominantmodeof transport(i.e.,
equatorgroundwater
flow, arediscussed
at lengthin section5.
wherediffusionoccursin responseto the repeatedcollisionsthat
happenwith othermoleculespresentin the soil pores).However,
4.1. The Stability of Equatorial GroundIce
for verysmallpores(r/• < 0.1), collisionsbetweenthe diffusing
Althoughmean annual surfacetemperaturesare below freez- moleculesand the pore walls greatlyoutnumberthosethat occur
ing everywhereon Mars, observations
madeby the Viking Or- with other molecules,a processknown as Knudsendiffusion.
biter Mars AtmosphericWater Detectors(MAWD) indicate a Becausethe frequencyof porewall collisionsincreaseswith degloballyaveragedfrost point temperatureof-198 K. Therefore, creasingpore size, small porescan substantiallyreducethe effigiven the presentlatitudinalrangeof mean annualsurfacetem- ciencyof the transportprocess.For poresof intermediatesize
peratures
(-154-218 K), any subsurface
reservoirof H20 is (0.1 < r/ )• <10), the contributionsof both diffusive processes
unstablewith respectto the water vaporcontentof the atmos- mustbe takeninto account[Younquist,1970; Clifford and Hillel,
phereat latitudesequatorwardof +40ø (Figure 3) [Farmer and
Doms, 1979].
1983, 1986].
Theeffectof a 10gmmeanfreepathonthediffusion
of H20
Despitethis fact, thereis a considerable
bodyof morphologic throughthe regolithis clearly seenin Figure 12, where the efdiffusion
coefficient
ofwater
vapor
Deft
hasbeenplotted
evidencethat suggeststhat both ground ice and groundwater fective
ofpore
size.
Deftis
given
by
have survived at some depth within the equatorial regolith asafunction
throughoutmuch of Martian geologichistory.At latitudespoleward of 30ø, this evidence is based on the identification of
Martian analogsto cold-climatefeaturesfoundon Earth, suchas
debris flows, table mountains, and thermokarst. These features
have been reviewed by a number of investigators[Carr and
Deft =
DAB DKA
DKA + DAB
(3)
10,986
•ORD:
HYDROLOGIC
ANDCLIMATIC
BEHAVIOR
OFWATERONMARS
1/2
(5)
DKA = -- r
3
ToMA
•
whereR is the universal
gasconstant
andMA is the molecular
weightof H20. Of course,mostsoilsgenerallyexhibita broad
o
spectrumof poresizes.The impactof this characteristic
on vapor
transportis illustrated in Figure 13, where the differential and
E
cumulative
flux of H20 is plottedforthreehypothetical
poresize
distributions.
¸
The survivalof equatorialgroundice was consideredin detail
by bothCliffordandHillel [ 1983]andFanale et al. [ 1986].They
foundthat, for reasonablevaluesof porosityand pore size, the
near-equatorialcrusthas probablybeen desiccatedto a depth of
300-500 m over the past3.5 billion years.However,becausethe
-2
4
-10
•
I
I
i
I
1
-9
-8
-7
-6
-5
-4
sublimation
of H20 is sensitively
dependent
on temperature,
the
-3
quantityof ice lost from the regolithis expectedto decline with
increasinglatitude, falling to perhapsa few tens of metersat a
latitudeof 35ø (Figure 14) [Clifford and Hillel, 1983; Fanale et
LOG OF PORE RADIUS (m)
Fig. 12. The effectivediffusioncoefficientof water vapor in the Martian
regolithplottedasa functionof poresize[CliffordandHillel, 1983].
al., 1986].
Of course,a variety of factorsare likely to complicatethis
simplepictureof equatorialdesiccation.For example,if the efwhereDABandDKAarethebulkandKnudsen
diffusioncoeffi- fective pore size of the regolith is larger than 10 gm, or if the
cients respectively[Scott and Dullien, 1962; Rothfield, 1963]. regolith
hasa specific
surface
area->103m2 g-• (a condition
that
After Wallace and Sagan[1979], the bulk diffusioncoefficientof wouldgive rise to a diffusivesurfaceflux greaterthanany likely
pore gas flux [Clifford and Hillel, 1983]), the actual depth of
H20through
anatmosphere
ofCO2(incm2s-1)isgiven
by
desiccationcouldwell exceedthe valuescalculatedby Clifford
DAB
= 0.1654
(T/273.15)
3/2(1.013
x 106/p)
(4) and Hillel [1983] and Fanale et al. [1986]. Altematively, shalwhere T is the temperatureand P is the total pressure(in dynes lowerdepthsof desiccation
will resultif the goundice is replencm-2).However,asdiscussed
by CliffordandHillel [1986],the ished(section4.5), the effectiveregolithpore size is less than
expression
forcalculating
DgAis dependent
onthespecificshape 1 gm, or if its porosityis less than the 50% value assumedin
of the soil pores.For the simplecaseof a straightcylindricalpore thesetwo studies.Considerations
that arguein favor of a spaof radius r, we have
tially variable(and generallylower) porosityinclude:igneousrePORE SIZE DISTRIBUTIONS
12 ! ! I
•';a
•o
I I
I I I
I
I
I
I
[•-'''""-'-1 b
I
I I
I
,//"--
.
I
I
I I
I I
c /•'--
,ooo
/
8o
//
c
---.-' O
•:
40
u.
/
20
I
I
I
MOLECULAR
I
I
I
I
I
I
I
!
I
100
-
80
-
60
10-
-
40
5--
-
20
z•)
15-
/"/
I
QX
v
0
-
20-
u.•
I
FLUX DISTRIBUTION
I
b'
!
u-
o
-'0
33
0
I
-6
-4
-2
o
I
I
1
-8
-6
-4
i
-2
-10
-4
0
-2
LOG OF PORE RADIUS (m)
Fig. 13. (a-c) Thedifferential
andcumulative
porosities
of threehypothetical
soilsand(a'-c9 thecorresponding
diffusive
flux of H20 thatresults
fromthese
poresizedistributions
[CliffordandHillel, 1986].
CLI•ORD: HYDROLOGIC
ANDCLIMATICBEHAVIOROFWATERON MARS
10,987
b
0.9
0.0
•_,• 0.0
1.8
40
2.7
E
•
3.6
80
I•.
'
4.5
c• 120-
160
40
0.9
E
•
80
1.8
c3 120
--
1602.7
.
200
200 -
90
80
70
60
50
40
30
20
10
36
90
0
80
70
60
LATITUDE, ø
50
40
30
20
10
0
LATITUDE, ø
Fig.14.Therecession
ofequatorial
ground
iceonMarsasa function
oflatitude
andtime(b.y.).Theregolith
models
adopted
forthese
calculations
differonly
in assumed
poresize:(a) r-- 1 }xm,and(b) r-- 10 grn(fromFanaleet al. [1986]).
consolidation,
dudcrust
formation,
andtheself-compaction
of the
regolithwith depth.Perhapsmoreimportantly,variationsin the
localthermophysical
properties
of the surface(versusthe globally averagedvaluesassumedin Figure14) can affect meanannual temperatures,causingsignificantdifferencesin both the
geographicstabilityof groundice and its predicteddepth of
desiccation[Paige, 1992; Mellon and Jakosky,1993]. A final
caveatregardsthe potentialeffectof quasi-periodic
changes
in
Martianobliquityand orbitalelements,the primarydriversof
climatechange.
Recentstudies
suggest
thattheobliquityof Mars
is chaoticandmayvaryfroma minimumof 0ø to a maximumof
50ø or higher [Bills, 1990; Toumaand Wisdom, 1993; Laskar
and Robutel,1993]. Althoughtheseextremesexceedthe 10.8ø38ø obliquityrangeconsidered
by Fanale et al. [1986], their
shortduration
andlimitedeffectonequatorial
temperatures
suggeststhattheirpotentialimpacton the lossof equatorial
ground
ice will be minimal.More pronounced
effectsare likelyat the
poles,wheretheincreased
insolation
associated
withhighobliquitiescouldhavea considerable
effecton the stabilityof the ice
caps.(A moredetaileddiscussion
of the polar massbalanceand
highobliquitiesis containedin section7.2.)
By integratingthe total porevolumebetweenthe Martian surfaceandthe desiccation
depthspresentedin Figure 14, Fanale et
al. [ 1986]haveestimatedthat overthe courseof geologichistory
asmuch
as2.7-5.6x 106km3 of H20(equivalent
to a global
4.2. Other Crustal Sourcesof AtmosphericWater
Perhapsthe clearestevidencethat the crusthas been a major
sourceof atmosphericwaterare the outflowchannels.The abrupt
emergenceof thesefeaturesfrom regionsof collapsedand disruptedterrain, suggeststhat they were formedby a massiveand
catastrophicrelease of groundwater[Sharp and Malin, 1975;
Carr, 1979; Baker, 1982; Baker et al., 1992]. Channel ages,inferred from the densityof superposedcraters,indicate at least
severalepisodesof flooding,the oldestdatingback as far as the
Late Hesparian(-3 billion yearsago), while the youngestmay
have formed as recently as the Mid-to-Late Amazonian (i.e.,
within the last 1 billion years)[Tanaka, 1986; Tanakaand Scott,
1986; Parker et al., 1989; Mouginis-Mark, 1990; Rotto and
Tanaka, 1991; Baker et al., 1992]. Based on a conservativeestimate of how much material
was eroded to form the channels in
Chryse
Planitia(-5 x 106km3) andthemaximum
sediment
load
that the flood waters couldhave carried (-40% by volume), Carr
[1987] has estimateda minimum cumulativechanneldischarge
of 7.5x 106km3 of H20(equivalent
to a global
ocean
-50 m
deep). However, if the channelswere formed by multiple episodesof outbreakand erosion,then the flood waters may have
been less turbulentand carriedless sedimentthan generallyassumed [Baker et al., 1992]. If so, the total volume of water re-
quired to erode the channelsmay have been many times the
estimateof Carr [ 1987]. Indeed,Baker et al. [1991] suggestthat
the totaldischargemay havebeensufficientto flood the northern
ocean-20-40 m deep) may have been sublimedfrom the equawithasmuchas6.5x 107km3of water(equaltoa global
torial regolithand cold-trappedat the poles.As seenin Table 6, plains
however,the sublimationof equatorialgroundice is just one of layer 450 m deep).
Impactsinto the Martian crustare anotherpotentialsourceof
severalpotentialprocesses
that may haveepisodicallyintroduced
atmosphericwater [Carr, 1984]. Assuminga representativecrylargevolumesof waterinto the atmosphere.
TABLE 6. CmstalSourcesandPotentialContributedVolumesof Atmospheric
Water
CrustalSource
Sublimation
of groundice [Fanaleet al., 1986]
Catastrophic
floods[Carr, 1987; Baker et al., 1991]
Volcanism[Greeleyand Schneid,1991]
Impacts[thiswork]
Excavation/volatization*
HydrothermalcirculationS'
Totals
Volume,km3
Equivalent
Layer,m H20
2.7-5.6 x 106
0.75-6.5 x 107
2.3 x 106
20-40
50-450
15
1.5-3.0 x 107
1.9 x 107
100-200
130
0.47-1.2
x 108 km3
315-830
m
*Calculationassumes
a crustalinventoryof 500-1000 m of waterwithinthetop 10 km of the crustanda global
craterdensityequivalentto thatfoundin thecrateredhighlands.
•'Figure represents
the potentialquantity of water brought to the surfaceby impact-generated
hydrothermal
systemsalone(section4.4.3).
10,988
CLIFFORD:HYDROLOGIC
ANDCLIMATICBEHAVIOROFWATERONMARS
ospherethicknessof 2.5 km, an ice contentof 20%, and a trans- 1986]. Yet, regardlessof the actualprocessby which it may have
ient crater diametergiven by equation(11) (see section4.4.2), occurred,considerationof the valley networks,outflow channels
the volumeof water excavatedand/orvolatilizedby individual andthe crustalmassbalance
of H20 arguesstrongly
for some
impacts
will rangefrom-34 km3 fora crater10km in diameter type of crustal resupply [Clifford, 1980b, 1984; Carr, 1984;
toinexcess
of 2.8x 105km3fora majorimpact
basinlikeHellas Jakoskyand Carr, 1985; Baker et al., 1991]. This conclusionis
by geomorphicevidencewhichsuggests
that, at
(D -2000 km). Note that becausecraterswith diameters ->40 km furthersupported
have excavationdepthsthat exceedthe predicted10 km self- leastin somelocationswithin the latitudebandof +30ø, ground
compaction
depthof the megaregolith,the volumeof water exca- ice hasindeedbeenreplenished.
Considerfirst the consequences
of a major impact at equavatedby largeimpactsdependson neitherthe statenor the depth
of thesubsurface
reservoir
of H20, butsolelyonthequantityof torial latitudes. As noted by Allen [1979a] and Clifford and
water storedper unit area in the crust.Therefore,given a global Johansen[1982], the productionof a crater many tens of kilocratersize-frequency
distributionequivalentto that preservedin metersin diametershouldresultin the excavationof any ground
the crateredhighlands[e.g., Barlow, 1990] and a crustalwater ice that existed,prior to the impact,within the regioninterior to
inventoryof 500-1000 m [Carr, 1987], we find that the cumu- the crater walls (Figure 15). While backfillingand melting of
lative volumeof water injectedinto the atmosphere
by impacts nearby
ground
ice maypartiallyreplenish
someof theH20 lost
overgeologic
time is -1.5-3.0 x 107km3 (or roughly100- near the crater periphery, it appearsunlikely that its lifetime
200 m). However,this figure representsonly the water that was would be very long given the high temperatureand porosityof
physically excavated by the impacts. As discussedin sec- the post-impactenvironment.
It is interestingto note, therefore,that within many large
tion 4.4.3, the subsequentdevelopmentof impact melt-driven
hydrothermalsystemscould have broughtas much as an addi- equatorialimpactcratersthereexist clearlydefinedrampartcrational 130 m of waterto the surface.This possibilityis supported ters[Allen, 1979a; Clifford and Johansen,1982]. If the morpholby both the evidencefor hydrothermalactivity associatedwith ogy of thistype of craterdoesindeedarisefrom an impactinto an
terrestrialimpact cratersand the observedassociation
of many ice-richcrust,then the occurrenceof rampartcraterswithin the
valley networkswith the outsiderims of cratersthroughoutthe interiorsof numerousolder impactspresentsa problem,for it is
Martian crateredhighlands[Newsom,1980; Brakenridgeet al., difficult to conceiveof a scenarioby which any groundice that
existedprior to the original crateringevent could have survived
1985].
Finally, as discussedby Greeley[1987] and Plesciaand Crisp to producethe well-definedfluidizedejectapatternoftenseenas
[1991], it is likely that volcanismalso injectedlarge volumes the result of a second and sometimes third consecutive and conof water into the atmosphere.For example, Plescia and Crisp centricimpact(Figure 16).
There are at leasttwo explanationsthatmay accountfor these
[1991] estimate that during the emplacementof the volcanic
plainsin southeastern
Elysium(5ø N, 195ø W), lavasmay have observations.First, contraryto popular belief, rampart craters
exsolved
between
103-104
km3ofH20,assuming
awater
contentmay not be specific indicatorsof groundice. Experimentsby
Schultz [1992] and Schultz and Gault [ 1979, 1984] have demcomparableto that of terrestrialmafic to ultramaficlavas (-1%
by weight).Greeley[1987] has takena moreglobalperspective, onstratedthat when an impact occursin the presenceof an
the effectsof drag and turbulencecan modify the
calculatingthe total volumeof juvenile water releasedfrom the atmosphere,
planet'sinteriorby estimatingthe extentand thicknessof all vol- emplacementof ejecta, reproducingmany of the featuresgencanic units visible on the planet'ssurface.However, Greeley's erally associatedwith Martian rampart craters.This effect is
[ 1987]estimateof extrusivemagmaproductionhasrecentlybeen clearlyseenin therecentMagellanradarimagesof Venus,where
are abunreviseddownwardby Greeleyand Schneid[1991]. Substituting craterswith multilobate,fluidizedejectamorphologies
this revisedfigure for that in Greeley's[1987] originalanalysis dantdespitethe absenceof water[Phillipset al., 1991].
Although laboratoryimpact experimentsand the Magellan
suggeststhat volcanicprocesseshave releaseda total of 2.3 x
106km3(-15m)ofH20intotheatmosphere.
It should
benoted,radar imagesboth suggestthat the presenceof an atmosphere
however,that in light of our inability to accuratelyassessboth mayplay a role in rampartcraterformation,they do not exclude
the extent of plutonic activity and the magnitudeof ancient the possibilitythat, on Mars, water andice mayhavecontributed
(->4 billion yearold) v,olcanism,this estimateis likely a mini- to the processas well. Indeed,three lines of evidencelend cremum. Note also that, unlike water derived from other crustal denceto the originalproposalof a link betweenrampartcraters
sources(which simplyundergoesan exchangefrom one volatile and subsurface volatiles. The first is the observed latitudinal
of severalMartian rampartcraterejectamorpholoreservoirto another),water releasedby volcanismrepresentsan dependence
single-rampart
actual addition to the planet'soutgassedinventory. However, gies,whichvary from an apparenthigh-viscosity
near
oncethis waterhas beenintroducedinto the atmosphere,
its fate styleat polarlatitudesto a highlyfluidizedmultilobate-style
is governedby the sameprocesses
that affectwaterderivedfrom the equator[Johansen,1978; Mouginis-Mark,1979; Saunders
anyothercrustalsource,leadingto a slowbut inexorabletransfer
from equatorialandtemperatelatitudesto thepoles[Cliffordand
-2-3 km
Hillel, 1983; Fanale et al., 1986].
4.3. Evidenceof GroundIce Replenishment
dry
interior
. '".....•....•
'-'....
ß
...
.....
Under the climatic conditionsthat have apparentlyprevailed
on Mars throughoutmost of its history,the loss of equatorial
ground
iceappears
irreversible;
thus,
once
icehassublimated,
or Fig.15.The
probable
ground
icedistribution
resulting
from
amajor
impact
been
removed
bysome
other
process
(e.g.,
impact
cratering),
itis in
the
equatorial
region
ofMars.
The
ofacrater
many
tens
of
kilometers
in diameter
should
result
inproduction
the excavation
of any
ground
ice
difficultto seehowthedepleted
crustcouldbe replenished
by which
existed,
within
theregion
interior
tothecrater
walls,
priortotheimany atmosphericmeans[Clifford and Hillel, 1983;Fanale et al.,
pact[Clifford
andJohansen,
1982].
•ORD:
HYDROLOGIC
ANDCI•MATICBEHAVIOR
OFWATERONMARS
;•
km
10,989
'
Fig. 16. A rampartcraterwithin two earlierand concentricimpacts(20ø S, 203ø W) [Clifford and Johansen,1982]. The oldestcraterin the sequence
(Hadley)is approximately
110km in diameter,whilethe innermostcrater(arrow)hasa diameterof roughly13 km.
and Johansen, 1980; Blasius et al., 1981; Kuzmin et al., 1988;
Costard, 1989; Barlow and Bradley, 1990]. Advocatesof the
groundice hypothesissuggestthat this latitudinaldependenceis
consistentwith the pole-to-equatorthinning of frozen ground
predictedby thermalmodelsof the crust(e.g., Figure3). A second, but complementary,observationhas been reported by
Kuzmin et al. [1988], who have found that rampart crater onset
diametersincreasewith decreasinglatitude, a relationshipthat
may reflectthe greaterdepthof crustaldesiccation
expectedfrom
the instabilityof groundice at theselatitudes(e.g., Figure 14).
The third and final line of evidence is the tentative identification
of single-rampart("pedestal")craterson Ganymede[Horner and
Greeley, 1982], an observationthat is difficult to reconcilewith
an atmosphericorigin, but one that is fully compatiblewith an
origin basedon an impactinto an ice-richcrust.
If rampartcraterejectamorphologydoesindeedarisefrom an
impactinto a volatile-richtarget,then perhapsthe most reasonable explanationfor the occurrenceof rampartcraterswithin the
theoreticallyice-free interiorsof numerousolder cratersis that,
at sometime followingthe originallossof groundice, it was replenished.Given our presentunderstanding
of Martian geology
and climate history, it appearsthat such replenishmentcould
have only occurredfrom sourcesof water residingdeep within
from a subpermafrostaquifer [Clifford, 1980a, 1984]. However,
as illustrated in Figure 7, the vertical distance separatingthe
groundwatertable from the base of the cryospheremay in some
regions be many kilometers;thus, for replenishmentto occur,
someprocess
for the verticaltransport
of H20 betweena deeplying sourceregionand the baseof the cryospheremust exist. In
this section,three possiblemechanismsfor this type of transport
are considered.
4.4.1. Thermal vapor diffusion. Although less dramatic and
energeticthan the othertwo processes
discussedin this section,
perhapsthe mostimportantmechanismfor the vertical transport
of H20 in the Martiancrusthasbeenthe process
of thermal
vapordiffusion[Clifford, 1980a; 1983]. Clearly, given the existenceof a water-richcrust,the presenceof a geothermaltemperature gradient will give rise to a correspondingvapor pressure
gradient.As a resultof this pressuredifference,water vaporwill
diffuse from the higher temperature(high vaporpressure)depths
to the colder(lower vaporpressure)near-surfaceregolith.
It has been known for over 75 years that vapor transportin
excess of that predicted by Fick's law will occur in a moist
porousmedium under the influenceof a temperaturegradient
[Bouyoucos,1915]. More recently,Philip and deVries[1957] and
Cary [1963] haveproposedtwo differentbut widely usedmodels
the crust.
for calculatingthe magnitudeof this type of thermallydriven vapor transfer.The Philip and deVries[1957] approachis basedon
4.4. Processesof Replenishment
a mechanisticdescriptionof the transportprocess.They suggest
It has been proposedthat equatorialgroundice on Mars may that the exchangeof water vapor in an unsaturatedsoil occurs
be episodicallyor continuouslyreplenishedby water derived betweennumeroussmall "islands"of liquid that exist at the con-
10,990
•ORD:
HYDROLOGIC
ANDCLIniC
tact pointsof neighboringparticles.The existenceof a temperature gradientcauseswater from the warmer liquid islandsto
evaporate,diffuse acrossthe interveningpore space,and condenseon the coolerliquid islandsat the oppositeend of the pore.
In this fashion
both moisture
and latent
heat are transferred
BEHAVIOROFWATERONMARS
270
1.33
•
275
' barometric
1.00
throughthe soil.
The Cary [1963]modelof H20 transport
differsfrom the
Philip and deVriesapproachin that it makesno assumptions
regardingthe actualmechanismof vaportransportbut merely attemptsto providea phenomenological
description
of the process
basedon the thermodynamics
of irreversibleprocesses.
Despite
280
-
this difference, it has been shown that the final form of the flux
equations
for bothmodelsare identical[Taylorand Cary, 1964;
Jury and Letey, 1979]. After Cary [1966], the thermallydriven
0.67
saturated \
285
-
vapor
pressure
•
0.33
I
vaporflux is givenby
qv =
-
[3Def
t P820Lv dT
pry2 T3
•
dZ
0.00
29O
(6)
1.0E+02
1.0E+03
1.0E+04
VAPOR PRESSURE (Pa)
where
Def
f istheeffective
diffusion
coefficient
ofH20in CO2,
PH20is thesaturated
vaporpressure
of H20 at a temperature
T,
L,,islatent
heatofvaporization
(--2.3x 106Jkg-l),Rvisthegas
constant
forwatervapor(-- 461.9J kg-1 K-I), Ois thedensity
of
Fig. 17. The saturatedvaporpressureof waterPH20(T) as a functionof
crustaltemperature
T compared
with the barometric
profileof vaporin an
isothermal
crust,PH20(z),where,for illustrative
purposes,
thetemperature
at
the surface of the water table has an assumed value of 290 K.
liquidwater,and[3is an empiricaldimensionless
factorthathas
been found to have a mean value of 1.83 _+0.79 when measured
overgeologically
reasonable
rangesof temperature
(276-314 K),
porosity(0.3-0.5), saturation
(0-100%), andsoil type[Juryand
Letey,1979].
area)reachingthe freezingfront at the baseof the cryosphere
is
-8.3 x 10-5-2.8
x 10-4 m H20yr-l. Thisfluxisequivalent
to
theverticaltransport
of 1 km of waterevery106-107years,or
roughly
102-103
kmofwateroverthecourse
ofMartiangeologic
The physicalbasisfor the verticaltransportof water vaporin history.However,there is reasonto believe that this thermally
responseto the geothermalgradientis perhapsbest understood inducedvapor flux was even greaterin the past. Recall that
by considering
first the equilibriumdistributionof vaporin an modelsof the thermalhistoryof Mars suggestthat 4 billion years
isothermal
crust.Underthiscondition,
thevaporpressure
of H20
at anyheightz abovethe watertableis givenby the barometric
relation
PH20(Z)
-- PH20(0)
exp(-z/H)
(7)
agotheplanet'sinternalheatflow was-3-5 timeslargerthanit
is today[e.g.,Daviesand Arvidson,1981,Schubertand Spohn,
1990]. Sincethe flux rate predictedby equation(6) is directly
proportional
to the temperature
gradient,this impliesa similar
increasein the volumeof water cycledthroughthe early crust.
wherePH2o(0)
is thesaturated
vaporpressure
of waterat z -- 0, (Note:Thefluxratesreported
hereare-103 timesgreater
than
andH is the watervaporscale-height
(= kT/mH20
g _=36 km, thosepreviouslypublishedby Clifford [1983, 1984]. Theseearwhere T = 290 K and k is the Boltzmann constant). Thus, at a
heightof 1 km abovethe water table, the resultinghydrostatic
reductionin vaporpressureis .--3%(Figure 17). However,over
thissameinterval,a geothermal
gradient
of 15K km-1 reduces
the equilibriumsaturatedvaporpressureby 68%. Becausethe
thermallyinducedgradientin saturatedvaporpressuregreatly
exceedsthe isothermal/gravitationally
inducedgradient, water
vaporwill diffuseupwardin an effort to achievean equilibrium
barometricprofile. However,as the risingvaporencounters
the
colderregionsof the crust,the associated
reductionin saturated
vapor pressureforcessomeof the rising vapor to condense,
ultimatelydrainingbackto the water table as a liquid. As a result, the flux of vaporthat leavesthe groundwatertable greatly
exceedsthat which finally reachesthe freezingfront at the base
of the cryosphere.As shownby Jacksonet al. [1965], oncea
closedsystemhas beenestablished
(i.e., the porevolumeof the
cryosphere
has beensaturatedwith ice), a dynamicbalanceof
opposing
fluxesis achieved,creatinga circulationsystemof rising vaporanddescending
liquidcondensate
(Figure18).
In Figure 19, the vapor flux resultingfrom a geothermal
vapor condensation
upward
vapor
I I I ,$ returning
liquid
flux
flux
gradient
of 15K km-l hasbeencalculated
fromequation
(6) and
plottedas a functionof crustaltemperaturefor pore sizesof 1
and 10 lam.Under theseconditions,the flux of vapor(per unit
Fig. 18. An exampleof low-temperature
hydrothermal
circulationdrivenby
theMartiangeothermal
gradient.
CLIFFORD:HYDROLOGICANDCLIMATICBEHAVIOROFWATERON MARS
270
1.33
10,991
Cintala [1992]. Their expressionfor the maximumdiameterof
•
thetransient
cavity
(i.e.,before
gravitational
slumping
ofthe
•
cavity
walls)written
asa function
of projectile
diameter
De is
u.{ given
by
275
1.00•
1/3
10gm .•.
Dtc
= 2.89 . r•ø.78
Ug
(9)
280
'0.675
285
.•' surface
(allinSIunits).
Intheir
analysis,
Grieve
andCintala
0.33¸m [1992]
assume
achondritic
projectile
density
of3.58
x 103
kg
290
0.00
1.0E-05
¸C9
m where
15/o
and
Pt
are
the
projectile
and
target
densities,
Uisthe
impact
velocity
andgistheacceleration
ofgravity
attheplanet's
1.0E-04
•
•
•
1.0E-03
m-3and
target
density
of2.73x 103kgm-3.Adopting
these
same
values,
and
making
theappropriate
substitution
forDe(=2
(3rn•/4n15p)
1/3,
where
m?-2E•/U2),
equation
(9)can
berewritten
to yieldthe relationship
betweentransientcraterdiameterand
projectilekineticenergywhere
g -0.22
Dtc= 0.219
Ek0'26
U'0'09
UPWARDVAPORFLUX,DOWNWARDLIQUIDFLUX(m H20yr-•)
Fig. 19. Therma]vaporfluxescalculatedfromequation(6) for poresizesof
1 jzrnand 10 jzrn,and a geothermalgradientof 15 K km-1. Note that in a
dosedsystem(suchas thatillustratedin Figure 18) the risingvaporflux at
any level is counteredby an equal and oppositedownwardflux of liquid
condensate.
(10)
Thecorresponding
finalcrater
diameter
Df canthenbefound
throughthe empiricalscalingrelationof Croft [1985], which is
givenby
Dtc_=
Dcø'15-+ø'ø4
Df0'85-+0'04
(11)
lier calculations are incorrect, the result of a unit conversion
error.)
whereDc is thetransition
diameter
betweensimpleandcomplex
4.4.2. Seismicpumping.In lightof the densityof impactcra- cratermorphology,whichon Mars occursat a diameterof ~6 km
terspreserved
in the crateredhighlands,
perhapsthe mostobvi- [Pike, 1980].
The foregoinganalysissuggests
that a projectilewith a kineousmechanism
for theverticaltransport
of H20 in thecrustis
of 2.2 x 1021J will produce
a finalcraterroughly
seismicpumping.Shockwavesgenerated
by earthquakes,
im- tic energy
pacts,andexplosivevolcaniceruptions
canproducea transient 33 km in diameter,assuminga characteristicMars impactveloc1977].Therefore,
if thecratersizedilatationandcompression
of water-bearing
formationsthat can ity of 10km s-• [Hartmann,
force water to the surfacethroughcrustalfracturesand pores. frequencydistribution preservedin the cratered highlands is
DuringthegreatAlaskaearthquake
of 1964,thisprocess
resulted representativeof the crateringflux experiencedover the entire
in water and sedimentejectionfrom shallowaquifersas far as planet(Table 7), then a minimumof-10,000 impacteventswith
400 km from the earthquake's
epicenter,with someeruptions seismicenergiesgreaterthanor equal to that of the 1964 Alaska
risingover30 m intotheair [Grantzet al., 1964;Waller,1968]. earthquakehave occurredthroughoutMartian geologichistory.
In addition,seismicallyinducedwaterlevelfluctuations
wereob- At the lower end of this size range,the forcefulclosureof waterserved in over 700 wells worldwide, the most notable being a filled fracturesby impact generatedshock waves may have re2.3-m variation recordedin an artesianwell in Perry, Florida, sultedin surfaceeruptionsof water and sedimentat distancesof
locatedsome 5500 km from the quake [Cooperet al., 1968; up to severalcrater radii from the impact.However, at the high
Gabert, 1968]. The Martian crateringrecordprovidesabundant end,the seismicenergiesassociated
with the impactsthat formed
evidence that Mars has witnessed numerous events of a similar,
Hellas (-2000 km), Isidis (-1900 km), and Argyre (-1200 km),
are as much as four to six ordersof magnitudegreater [O'Keefe
andoftenmuchgreater,magnitude.
After Bath [1966],the seismicenergyEs.associated
with and Ahrens, 1975; Gault et al., 1975]. Seismic energies this
aquifers
an earthquakeof magnitudeM can be calculatedfrom the largemay have been sufficientto disruptsubpermafrost
andvent groundwateron a globalscale.
Gutenberg-Richter
relation,where
4.4.3. Hydrothermal convection.Given the widespreadevi(8)
1Oglo
Es= 1.44M + 5.24
dence of volcanism [Greeley and Spudis, 1981; Greeley and
For the 8.4 magnitude1964 Alaskaearthquake,equation(8) Schneid,1991] and large impacts[Schultzet al., 1982] on Mars,
yields
acorresponding
seismic
energy
of-2.2 x 10]7J.However,hydrothermalactivity has long been recognizedas a potentially
according
toSchultz
andGault[1975a,b],
onlyabout10-4 of a importantprocessin the mineralogicand geomorphicevolution
projectile's
initial kineticenergyis converted
intoseismicenergy of the planer'ssurface[Allen, 1979b; Schultzand Glicken, 1979;
uponimpact.Thus,to matchthe seismicoutputof the Alaska Pieri, 1980; Newsom, 1980; Morris, 1980; Clifford, 1982]. For
earthquake,
an impacting
projectilemusthavean initial kinetic example,hydrothermalcirculationhasbeendiscussedin connection with the developmentof the small valleys found on the
energy
inexcess
of 102]J.
The sizeof the craterproduced
by a projectileof kineticen- flanksof Alba Pateraand five othermajor volcanoes[Gulick and
ergyEkcanbecalculated
fromthecrater
volume-scaling
relation- Baker, 1990], while Allen [1979a], Hodges and Moore [1979],
shipof Schmidtand Housen[1987],as revisedby Grieveand Schultzand Glicken [1979], Squyreset al. [1987] and Wilhelms
10,992
CLIFFORD:
HYDROLOGIC
ANDCLIMATICBEHAVIOR
OFWATERONMARS
TABLE 7. CraterStatistics,
ImpactEnergies,andMelt Volumesfor theCrater-SizeFrequencyDistributionof theMartianHighlands
amax,
Ornea
n,
km
km
O to
Ek,
km
J
grn,
N
logR
Ng
Equivalent
Vt (= N•½
* Vm), GlobalMelt
km3
km3
Layer,
m
8.00
11.31
9.51
8.88
2.72E + 19
946
-1.55
15705
1.07E + 00
1.01E + 03
11.31
16.00
13.45
11.92
8.44E + 19
777
-1.34
12735
3.31E
+ 00
2.57E + 00
0.02
16.00
22.63
19.03
16.00
2.62E + 20
582
-1.16
9638
1.02E + 01
5.96E + 03
0.04
22.63
32.00
26.91
21.48
8.14E
+ 20
499
-0.93
8184
3.16E + 01
1.58E + 04
0.11
32.00
45.25
38.05
28.84
2.53E + 21
417
-0.71
6791
9.77E + 01
4.08E + 04
0.28
45.25
64.00
53.82
38.73
7.84E
+ 21
227
-0.67
3723
3.02E
+ 02
6.86E + 04
0.47
64.00
90.51
7 6.11
51.99
2.44E + 22
119
-0.65
1949
9.33E + 02
1.11E + 05
0.77
90.51
128.00
107.63
69.80
7.56E
+ 22
51
-0.72
830
2.88E + 03
1.47E + 05
1.01
128.00
181.02
152.22
93.72
2.35E
+ 23
14
-0.98
228
8.91E + 03
1.25E + 05
0.86
181.02
256.00
256.00
362.04
215.27
304.44
125.82
168.93
7.29E + 23
2.26E + 24
11
8
-1.74
-1.57
20
15
2.75E + 04
8.51E + 04
3.03E + 05
6.81E + 05
2.09
4.70
362.04
512.00
724.08
512.00
724.08
1024.00
430.54
608.87
861.08
226.79
304.49
408.80
7.03E + 24
2.18E + 25
6.78E + 25
9
4
2
-1.22
-1.27
-1.27
16
7
4
2.63E + 05
8.13E + 05
2.51E + 06
2.37E + 06
3.25E + 05
5.02E + 06
16.33
22.42
34.65
1024.00
1448.15
1217.75
548.84
2.10E
+ 26
2
-0.97
4
7.76E
+ 06
1.55E + 07
107.07
1448.15
2048.00
1722.16
736.86
6.53E + 26
2
-0.67
4
2.40E + 07
4.80E + 07
330.89
7.56E + 07
521.72
Global Totals
0.01
Read 2.72E + 19 as 2.72 x 1019,for instance.
The statistical
dataon thecratersize-frequency
distribution
of themartianhighlandsis takenfromBarlow [ 1990]. The datahavebeenbinnedandanalyzed
usingtherelative(R plot)procedure
recommended
by the Crater AnalysisTechniques
WorkingGroup [1978]. The R plottechnique
highlightsanydeviation
from a powerlaw distribution
functionby presenting
the cratersize-frequency
datain differentialform (wherelog R is plottedagainstlog Dmean).
R --
(Dmean)3N/A(Dmax
- Drain)
where
N isthenumber
ofcraters
within
thediameter
range
Drain
toDmax
(Dmax
= Drain
•f•'),Dmean
isthegeometric
mean
diameter
of thebin(--,/D.minDmax
andA isthesurface
areaoverwhichthecraters
arecounted
(A= 8.8x 106km2forDmax
< 181kmandA = 8.0 x 107km2forDma
x>
181 km). Assumingthat the differentialcratersize-frequency
distributionpreserved
in the crateredhighlands(i.e., R) is representative
of the crateringflux
experienced
overthe entireplanet,the globalnumberof impactsthathaveoccurredwithin a particularsizerangecan be calculatedby settingA equalto the
surface
areaofMars(= 1.45x 108km2)andsolving
forN (listed
under
Nginthetable).
Ekistheprojectile
kinetic
energy,
Vmisthemeltvolume
produced
per
impact,andVt is thetotalvolumeof impactmeltproduced
by the impactswithina givenbin size.
and Baldwin [ 1989], have consideredhow volcaniceruptionsand by the vertical impactof a chondriticprojectile(gravitationally
igneoussills may have interactedwith groundice to form the scaledfor Mars) is
outflow channelsand the small valleys that dissectthe ancient
Vm=7.55x 10-7Dtc
TM
(12)
heavilycrateredterrain.
which, as before, assumesa characteristicimpact velocity of
An alternativemechanismfor the origin of the small valleys 10 km s-•.
invokesan impact-generated
heat source.As discussed
by NewGiven a globalcratersize-frequency
distributionequivalentto
som [1980], a major impactwill result in the productionof a that preservedin the crateredhighlands(e.g., Barlow [1990] ),
large quantityof impact melt. The interactionof groundwater and melt volumescalculatedfrom equation(12), the cumulative
withsucha long-lived
(upto 104years)
heatsource
will resultin volume of impact melt generatedover the courseof Martian
the development
of a large-scalehydrothermal
circulationsystem geologichistoryis readilyestimated.The resultsof thesecalcucenteredon the impact.Cool waterwill enterthe systemfrom the lations,for cratersin the 8-2048 km size-range,are summarized
base
oftheaquifer,
riseasitsheated,
andthenflowradiallyinTable
7.They
indicate
thatthecumulative
fluxofimpacts
on
away
asit reaches
thetop.Directly
beneath
theimpact,
the Mars
has
produced
avolume
ofmelt
equivalent
toaglobal
layer
groundwater
mayboil,carrying
away
heatthrough
theconvection
over0.5kmthick,
more
than85%ofwhich
hasbeen
contributed
ofsuper-heated
water
andsteam.
Fractures
around
theimpactbyimpacts
withfinaldiameters
greater
than
103
km.
may
then
serve
asconduits
tothesurface,
allowing
thesteam
and Thetotal
heat,
AQmelt,
released
perunit
area
bythecooling
of
boiling
water
todischarge
ashot-springs
and
geysers
around
the animpact
meltsheet
from
aninitial
temperature
Ti toa final
periphery
ofthecrater.
Such
ascenario
may
well
explain
theas-temperature
Tfcan
becalculated
from
sociationof valleynetworkswith theoutsiderimsof largecraters
throughout
thecratered
highlands
[Pieri,1980;
Schultz
and'
AQrnelt
= pCp(Ti - Tf)AZ
(13)
Glicken,
1979;
Newsom,
1980;
Clifford,
1982;
Brakenridge
etal., where
pCpisthevolumetric
heatcapacity
ofthemelt,andAzis
1985;Brakenridge,1990].
its thickness.From this relationship,the quantityof heat repre-
AfterNewsom
[1980]andBrakenridge
et al. [1985],thevol- sentedby a 520-mthickgloballayerof impactmelt (cooling
umeof waterthatisvertically
discharged
byanimpact-generated
fromaninitialtemperature
of 1473K to a finaltemperature
of
hydrothermal
system
canbeestimated
fromthequantity
ofmelt 473K)isfound
tobe-2.2x 1012
Jm-2.Ofthisenergy,
onlya
produced
by theimpact.However,
because
largediscrepancies
smallfraction
(-20%) will gointodrivinghydrothermal
convecexistbetween
theobserved
andtheoretically
predicted
meltvol- tion,theremainder
will be lostto the surface
by radiation
and
umesof manyterrestrial
impactcraters,
reliableestimates
of im- conduction,
andbyheating
muchofthesurrounding
medium
to a
pactmeltproduction
havebeendifficulttomake.To address
this temperature
thatfallsshortof theboilingpoint[Onorato
et al.,
problemGrieveand Cintala[1992]haverecentlypresented
a 1978;Newsom,
1980;Brakenridge
etal., 1985].
revisedscalingrelationship
that providesa betterfit to the obNewsom[1980]andBrakenridge
et a1.[1985]assume
thatany
serveddata.Their expression
for the volumeof melt produced steamgenerated
by the interaction
of groundwater
with the im-
CIZFFORD:HYDROLOGIC
AND CLIMATICBEHAVIOROFWATERON MARS
pactmelt mustbe superheated
by at least300 K to reachthe surface.Thus,if the initial temperature
of thegroundwater
is 273 K,
theheatfrom the melt mustprovideenoughenergyto elevatethe
temperature
a total of 400 K and drive a phasechangefrom liquid to steam.Based on these assumptions,the mass of steam
reachingthesurfaceis givenby
0.2 AQmel
t
l•nstearn
=
(14)
CpwATwater
+ Lv + CpsATsteam
10,993
umesof H20 between
thelocalwatertableandthebaseof the
cryosphere,it seemsreasonableto expect that the subsequent
freezingof this waterwill createa barrierthat precludesany further rise of waterbeyondthe baseof the frozencrust.However,
as discussed
in section4.4.1, the presenceof a geothermalgradient can havea profoundinfluenceon both the stateand redistri-
butionof crustalH20, a fact that is equallytruewhetherthe
temperature
is aboveor belowthe freezingpoint.Indeed,there
areat leastthreedifferentprocesses,
involvingall threephasesof
water, that will contributeto the thermallyinducedtransportof
where
Ct,
wandCt,
saretheheatcapacities
ofwaterandsteam;
H20through
thecryosphere.
In the gasphase,the transport
of H20 through
unsaturated
porization(adoptedvaluesfor all variablesare listedin Table 8).
This modelsuggests
thatthe totalmassof waterthat was brought
to the surfaceby impact-generated
hydrothermalsystemswas
equivalentto a globalocean-130 m deep.For severalreasons,
however,this is likely a conservative
estimate.For example,the
crater statisticsof Barlow [1990] do not include any correction
for erosionor obliteration;therefore,they likely underestimate
the cumulativenumber of impactsthe highlandshave experi-
ent createsa corresponding
vaporpressuregradientthat drives
thediffusionof vaporfromthe warmerdepthsto thecoldernearsurfacecrust.However,subfreezing
temperatures
affectthis processin two importantways.First, becausethe vaporflux at any
depthis proportionalto the local saturatedvaporpressure,the
magnitude
of vaportransport
necessarily
declines
asthediffusing
vaporriseshigherin the frozencrust.Second,as a consequence
ATwate
r andATstearn
arethecorresponding
temperature
intervals frozengroundoccursby the familiar processof thermalvapor
overwhicheachphaseis heated;
andLvis thelatentheatof va- diffusionwhere,as before,the presenceof a temperaturegradi-
enced. Nor do Barlow's [1990] statisticsinclude any of the six
of this decline in temperatureand saturatedvapor pressure,a
portionof the ascending
vaporflux will condense
and freeze,
"megabasins"
(i.e., D> Hellas) that haverecentlybeen reported
preferentiallyblockingthe smallestporespresentin the pore
in the literature [Schultzet al., 1982; McGill, 1989; Schultz and
system.
Thiscondensation
canbothsubstantially
retarddiffusion
Frey, 1990]. The omissionof thesebasinsreflectsboth the tentative natureof their identification,and the clear geometricand
scalingdifficultiesassociated
with estimatingthe amountof impact melt producedby basinswhosediametersapproachor exceed the radius of Mars. It appearslikely, however, that their
inclusionwouldincreaseboththe estimatedproductionof impact
melt and the resultingcumulativeflux of water by as muchas an
orderof magnitude.
Finally, no attempthasbeenmadeto quantifythe contribution
of igneousintrusionsor volcaniceruptionsto hydrothermalactivity. Althougha large quantityof volcanicmaterialhas beenextruded onto the Martian surface (estimated by Greeley and
Schneid[1991] to be equivalentto a globallayer -0.5 km thick),
its eraplacement
overthepreexistingtopographyis not conducive
to the hydrothermalconvectionof water from deep within the
crust. However, around volcanicvents and igneousintrusions,
the potential for the developmentof deeply circulating hydrothermalsystemsis greatlyincreased.To date,the bestquantitative analysesof the interactionof dikes, sills, and lava flows
with groundice are thoseof Squyreset al. [1987] and Gulick
[1991]. Unfortunately,the lack of a reasonable
basisfor estimating the number,extent, and eraplacementgeometry,of deeply
penetratingmagmabodieson Mars precludesany global assessmentof thequantityof watercirculatedby suchactivity.
and chokeoff muchof the pore networklong beforethe larger
poresare filled with ice. With time, however,theseblockages
succumb
to the samethermalprocessthatled to their formation.
Thus, vapor will sublimefrom the ice plugs formed in the
warmer,deeperregionsof the cryosphere
andredistribute
itself
(througha repeatedprocessof condensation,
sublimation,and
diffusion) to the colder near-surfacecrust.In this way, the pro-
cessof thermalvapordiffusionwill continueuntil the cryosphere
is ultimatelysaturatedwith ice.
The possibility
of liquid phasetransport
arisesfrom the fact
that both adsorbedwater and water in small capillariescan survive in frozen soil down to very low temperatures(see section 2.2). Under conditionswhere the unfrozenwater contentis
highenoughto providethin film continuity,the presenceof a
temperature
gradientcreatesa corresponding
gradientin soil
waterpotentialA•, a quantitythatreflectsthe differencein effectivepressurebetweenthe phasesof ice and unfrozenwater
presentin the soil.Underatmospheric
conditions
(i.e., in the absenceof a confining
pressure),
themagnitude
of thispressure
differencecan be calculatedfrom a form of the Clausius-Clapeyron
equation[Edlefsenand Anderson,1943; Williamsand Smith,
1989], given by
dpw
4.5. TransportThroughthe Cryosphere
dT
Althoughthermalvapordiffusion,seismicpumping,and hydrothermalconvectionare all capableof transportinglarge volTABLE 8. AdoptedValuesforHydrothermal
Calculations
Vahable
p C•,
C•
Cps
Description
volumetric
heatcapacity
ofmelt
heatcapacity
ofwater
heatcapacity
of steam
•STwater 373 K-273 K
•5Twater 673 K-373 K
Lv
latentheatofvaporization
Value
4.2x 106J m-3K-1
4188J kg-1K-1
2092J kg-1K-1
100 K
300 K
2.3 x 106J Kg-•
Lf
(15)
T Vw
where
Pwisthepressure
(orhydraulic
head)
ofsoilwater,Lf is
thelatent
heatoffusion
(--3.35x 105Jkg-l),andVwisthespecific volumeof water (-- l/p) at the crustaltemperatureT. Equation (15) indicatesthat the pressuredifferencebetweenice and
waterin the soilincreases
by -1.2 x 106Pa K-l for crustal
temperatures
below273 K. After Smithand Burn [1987] and
Williamsand Smith[1989], the liquid flow (per unit area) that
occursin responseto this temperature-induced
pressuredifferenceis given by
10,994
CLIFFORD:
HYDROLOGIC
ANDCLIMATIC
BEHAVIOR
OFWATERONM•S
ql
=
kf g d•t dT
v
dT
(16)
dz
wherekf is thepermeability
of thefrozen
soil,g is theacceleration of gravity, v is the kinematic viscosity,and d•t/dT
by lavas,sediments,or someothertype of deposit,the resulting
increasein insulationprovidedby the depositionallayer will
causelocal crustaltemperaturesto rise, permittingthe buried
groundice to be thermallyredistributedinto the overlyingmantle.
The abilityof H20 to thermallymigratethroughthe cryos(=_dPw/dT)is the temperature-dependent
gradient
in soilwater phere also has implicationsfor the sublimationof equatorial
potential.
Assuming
a geothermal
gradient
of 15K km-1, a value
groundice. As the sublimationfront propagates
deeperinto the
of d•/dT-- 1.2x 106 PaK-1 (fromequation
(15)),anda frozen
crust(e.g., Figure 14), it may ultimatelyreacha depthwherethe
permeability
of-2 x 10-7 darcies
(a valueappropriate
to a silty
clay soil at a temperaturejust below freezing [Smith, 1985;
Williams and Smith, 1989]), the resultingvertical flux of liquid
water throughthe base of the cryosphereis found to be -4.3 x
diffusivelossof groundice is exactlybalancedby the upward
thermalmigrationof H20 throughthe cryosphere,
a condition
that couldsignificantlylimit the depthof equatorialdesiccation
predictedby currentmodels[Clifford and Hillel, 1983; Fanale et
10-5 m yr-•, orroughly
0.4kmevery107years.
It should
becaual., 1986]. Unfortunately,the processes
governingthe transport
tioned,however,that this flux is highly sensitiveto boththe local
of
H20,
both
to
and
from
the
sublimation
front,are sufficiently
lithologyand effectiveconfiningpressureof the crust;therefore,
complexthat calculatinga specificdepthat which this equilibbecausetheseconditionsare so poorlyconstrained
at the baseof
rium conditionis reachedis virtually impossiblewithout a more
the cryosphere,this estimatehas an inherentuncertaintyof as
detailedknowledgeof a numberof crustalparameters(e.g., limuch as two orders of magnitude.Note also, that becausethe
thology,porosity,pore size, specificsurfacearea,heat flow, and
permeabilityof frozensoil declineswith decreasingtemperature,
salt content).
the magnitudeof liquid transportwill necessarilydeclineas the
In summary,variouslines of evidencesuggestthat, over the
waterreachesthe colderand shallowerregionsof the crust.
courseof Martian geologichistory,at least four processes
have
Finally,in additionto themovement
of H20 vaporandliquid introducedsubstantialamountsof water into the atmosphere,
throughthe cryosphere,transportin the solidphasecan occurby
these include:the sublimationof equatorialground ice, catathe processof thermalregelation;where,as before,the direction
strophicfloods,impacts,and volcanism.Under the climatic conof transfer is from warm to cold [Miller et al., 1975; Miller,
ditions that have apparentlyprevailed on Mars throughoutits
1980]. As discussed
by Williamsand Smith[1989], theprocessof
history,the atmospheric
lossof this H20 fromequatorialand
regelationinvolvesthe movementof both ice and unfrozenwater
temperatelatitudes appears irreversible. However, if Mars is
througha saturated(or nearly saturated)frozen soil. Fundamenwater-rich,thenthesedepletedcrustalreservoirsmay have been
tal to this processis the thermodynamicrelationshipbetween
replenishedby sourcesof groundwaterresidingdeep within the
freezing point depressionand the effective pressuredifference
crust.At least three processes(thermal vapor diffusion, seismic
betweenthe ice and water phasespresentin the pores.As the
pumping,andhydrothermalconvection)appearviable for driving
geothermalgradientdrives the flow of water throughthe unfrothe verticaltransportof H20 from the local water table to
zen films that permeatethe cryosphere,the entry of liquid water
the baseof the cryosphere.While the calculationspresentedin
at the warm end of the pores causesa local increasein water
section4.4 indicatethatall threeprocesses
are potentiallyimporpressurethat decreases
the effectivepressuredifferencebetween
tant, the flux arisingfrom thermalvapordiffusionaloneis suffithe ice and water phases.This reductionin effectivepressureincient to supplythe equivalentof-1 km of water to the baseof
creasesthe local freezingpointby an amountsufficientto causea
thecryosphere
every106-107years.Thermalvapordiffusion,
small quantityof water to freeze at the warm end of the pore.
aidedby thermalliquid transportand regelation,may then redisThe addition of this ice also increasesthe effective pressureat
tributethisH20 throughout
muchof thefrozencrust.Notethat
the pore'scold end, where it lowers the local freezing point.
these thermal processeswill occur on a global basis, wherever
Water releasedby the subsequentmelting of ice from the cold
thereexistsa crustaltemperaturegradient,a subsurface
reservoir
end of the porethen becomespart of the thin-filmflow that enof
H20,
and
the
continuity
of
pore
space
between
the
source
retersthe colderice-filled poreslocatedhigherin the crust,followgion and the near-surfacecrust.In this way, groundice that was
ing which the whole processis repeatedagain.
removedby impactsor sublimationto the atmosphere
may have
Note that becauseeach of the three thermal processesdisbeenreplenishedon a global scale(e.g., Figure20), withoutthe
cussedhere operate by driving the movementof water from
needto invokeexoticscenariosof climatechange.
warmerto colderregionsof the crust,the transport
of H20
throughthe cryosphereis necessarilya one-waystreet.That is,
if one attemptsto introducewater into the cryospherevia the
atmosphere,the maximum depth of penetrationis necessarily
limited to the maximumdepth at which surfacetemperaturevariationsare sufficientto overwhelmthe influenceof the local geothermalgradient.For the surfacetemperature
variationsexpected
at equatoriallatitudes from the periodic changesin Martian
obliquityand orbital elements[e.g., Toonet al., 1980; Fanale et
al., 1986], this depth is not likely to exceedmore than ten me-
interior
•i..?:..!.'.:.?::::'::.:i.-.'•:
•..i.:!
i-).¾
•.7•
i::•i-.'•:•11::•':•..'•::??.:.i:
•"'""'':'":":''"'
....
ß
:.•:.:•....:i.:!::•......•.•;•.•...:...:•:.!:.:.:•:::.:.i•.:.:.::.::.):!::??..•:!i:!!;•!..?.•i::5•::•.•i•..•:•.::•:.•..•?
' ...........
(•
•
•
ofH20
ters.
In contrast,when water is suppliedto the cryospherefrom
below, the processesof thermal vapordiffusion,thermal liquid
transport,and regelation,will permit its eventualredistribution
throughoutthe frozencrust.This fact has a numberof important
consequences.
For example, shouldan ice-richregionbe buried
Fig. 20. A geothermal
gradientas smallas 15 K km-I couldsupplythe
equivalentof 1 km of waterto the freezingfrontat thebaseof the cryosphere
every106-107years,a process
thatmayexplainhowtheinteriorsof equatorialcraterswererechargedwith groundice.
CLIFFORD:
HYDROLOGIC
ANDCLIMATIC
BEHAVIOR
OFWATERONMARS
10,995
5. POLARDEPOSITION,BASALMELTING, ANDTHE
PHYSICALREQUIREMENTSFORPOLE-TO-EQUATOR
will not occurat the actualbaseof the polar deposits,it will occur at the baseof the cryosphere
in responseto any increasein
GROUNDWATER FLOW
polardepositthickness.Shoulddepositionpersist,the polar depositsmay eventuallyreachthe thicknessnecessaryfor melting
With meanannualtemperaturesthat are -40 K below the atto occur at their physicalbase (Figure 21c) [Clifford, 1980b,
mosphericfrost point of water vapor,the Martian polar regions
1987b]. Under suchconditions,the depositsmay then reach a
represent
the dominantthermodynamic
sink for H20 on the stateof equilibrium,wherebythe depositionof any additionalice
planet. As a result, any water that is introducedinto the atmosat the surfaceis offsetby the meltingof an equivalentlayerat the
phere, above its normal saturationlevel, is eventually coldbaseof thecap.Sincethislaststageis merelytheendpointin the
trappedat the poles.Pollack et al. [1979] have suggestedthat
evolutionof a single continuousprocess,the use of the term
this processof polar depositionis intimatelytied to the fate of
"basalmelting"is broadened
hereto includeanysituationwhere
atmospheric
dust and the formationof the seasonalpolar caps.
poreor glacialice is meltedas the resultof a rise in the position
They proposethat airbornedust particles,raised by local and
of the meltingisotherm,regardless
of whethersuchmeltingocglobaldust storms,may serveas nucleationcentersfor the condensationof water ice. As either hemisphereentersthe fall season,the suspended
dustparticlesreceivean additionalcoatingof
CO2 thatmakesthemheavyenough
to precipitate
fromthe at-
a
mosphere,contributingto the formationof the seasonalcaps.In
thespringtheCO2 sublimes
away;however,
at highlatitudesit
leavesbehinda residual
deposit
of H20 iceanddustthataddsto
the perennialcaps[Cutts,1973; Pollack et al., 1979]. Insolation
changesdue to axial precessionand periodicvariationsin obliquity and orbitaleccentricity[e.g., Ward, 1974, 1979; Bills, 1990]
may alter the erostonaland deposittonalbalanceat the poles, as
well as the mixing ratio of ice to dustin the annualdeposittonal
layer [Murray et al., 1973; Toon et al., 1980; Cutts and Lewis,
1982]. Sucha scenariomay well explainthe origin of the numeroushorizontallayersthat comprisethe stratigraphyof both polar
caps [Murray et al., 1972; Soderblomet al., 1973; Squyres,
unsaturated
• melting
isotherm
I
zone
'
ß'
_
1979b; Howard et al., 1982].
In this section,the effect of polar depositionon the thermal
evolutionof the cryosphereand polar capsis considered.Given
an initially ice-saturatedcondition,the depositionof ice and dust
at polar latitudeswill result in a situationwhere the equilibrium
depthto the melting isothermhas been exceeded,melting ice at
the base of the cryosphereuntil thermodynamicequilibrium is
once again established.The drainageof the resultingmeltwater
into the underlyingglobalaquiferwill then causethe local water
table to rise in response,creatinga gradientin hydraulic head
that will drive the flow of groundwateraway from the poles.In
the discussionwhich follows, the processof basal melting, the
rise of the polar water table, and the physicalrequirementsfor
pole-to-equatorgroundwaterflow are analyzedin detail.
b
• depøsitiøn
of
dust
basal
melting
initiated
•.5
2%'.':?.'•
:•//,:'•'.•k'/•
:•?-;,'•.-;
:C.'•'•"::
5.1. Polar Basal Melting
In studiesof terrestrialglaciers,the term "basalmelting" is
usedto describeany situationwhere the local geothermalheat
flux, as well as anyfrictionalheatproducedby glacialsliding,is
sufficientto raisethe temperatureat the baseof an ice sheetto
its meltingpoint. In this regard,the processis alwaysdiscussed
c
deposition
of dust
+
with reference to the interface between an ice sheet and the bed
on which it rests. However, as discussedby Clifford [1980b,
1987b] and as illustratedin Figure 21, it appearsappropriateto
broadenthe useof thisterm as it appliesto Mars.
Figure21a is an idealizedcrosssectionof the Martian polar
crustprior to the depositionof any dust or ice. Given a cryospherethat is initially saturatedwith ice, the depositionof any
material at the surfacewill result in a situationwhere the equilibrium depthto the meltingisothermhas been exceeded(Figure 2lb). In responseto this added layer of insulation, the
positionof the meltingisothermwill rise in the crustuntil thermal equilibriumis onceagainestablished.
Thus, while melting
Fig. 21. An idealizedcrosssection
of thepolarcrustillustrating
thepossible
timeevolutionof basalmelting[Clifford,1987b].The sequence
depicts(a) a
timepriorto the deposition
of any dustandice, (b) the onsetof deposition
andbasalmelting,and(c) meltingat theactualbaseof thedeposits.
10,996
CLIFFORD:
HYDROLOGIC
ANDCLIMATICBEHAVIOR
OFWATERONMARS
cursat the actualbaseof the deposits
or at thebaseof the cryospherewithin the underlyingterrain.
As with the cryospherecalculationsdiscussedin section2.2,
thepolardepositthickness
requiredfor basalmeltingcanbe calculatedby solvingthe one-dimensional
steadystateheatconduction equation.After Weertman[1961] and Clifford [1987b], this
thicknessis givenby
=
(17)
Qg + Qf
mixtureshavethermalconductivities
comparable
to that of ice
(i.e.,>2.25W m-l K-l), whiletheresthavevaluesasmuchas
60% lower.Sincetheconductivities
of mostclaymineralsequal
or exceedthatof ice [Clark, 1966;Horai and Simmons,1969], it
is difficultto explainhowanymixtureof thesetwocomponents
couldhave a lower value. As discussedin section2.2.1, this dis-
crepancy
maybe explainedby the presence
of low-conductivity
adsorbed
wateron highspecificareaclay.
In Table 9, basal melting thicknesseshave been calculated
basedon a meanpolar surfacetemperatureof 154 K, thermal
conductivities
of 1.0-3.0W m-l K-l, andmeltingtemperatures
of 252 and 273 K. In addition,to assessthe potentialfor basal
where•cis the effectivethermalconductivity
of the polardepos- meltingat earlier epochs,calculationshave alsobeencarriedout
andHsui,
its,Trn
p is themelting
temperature
of theice,Tins
is themean forheatflowsof 90 and150mW m-2 [e.g.,ToksOz
1978; Davies and Arvidson, 1981; Schubertand Spohn, 1990].
polar
surface
temperature,
Qgisthegeothermal
heatflux,andQf
is the frictionalheatdueto glacialsliding.With theexceptionof
the frictional heat term, all of these variables are discussedat
lengthin section2.2. However, becauseof differencesin the degree of homogeneity,
particle size, and ice content,the thermal
conductivityof the polar depositsis likely to differ from that
which characterizesthe regolith or crust as a whole. For this
reason,both the thermal conductivityof the polar ice and the
For these calculations,no pressure-induced
freezing point depressionor frictionalheat input due to glacial sliding was assumed.
Based on an analysis of Mariner 9 radio occultationdata,
Dzursin and Blasius [1975] have determined that the Martian
polarcapsreacha maximumthicknessof 4-6 km in the northern
hemisphereand 1-2 km in the southern.Therefore,only in the
potentialrole of glacial sliding are discussed
here in greater north does the total thicknessof the cap overlap the potential
range
ofpresent-day
(i.e.,Qg--30mWm-2)basal
melting
thick-
detail.
The thermalconductivity
of the Martianpolardepositsis determinedby suchfactorsas the volumetricmixingratiosof ice
anddust,their spatialvariability,temperature-dependent
thermal
properties,and the presenceof othercontaminants,
suchas salts.
While a comprehensive
analysisof thesefactorsis beyondthe
scopeof this paper,a reasonablerangeof valuescan be inferred
fromthe availabledata.For example,the light-scattering
properties of the dust suspended
in the Martian atmosphere
indicate
grain diametersin the rangeof 0.2-2.5 gm [Panget al., 1976;
Pollacket al., 1979;Chylekand Grams,1978].If thissizerange
is representative
of the dustentrainedin the polarice, then the
thermalpropertiesof the polar depositsshouldbe closelyapproximatedby laboratorymixturesof ice andclay.
In Figure 22 the thermal conductivities
of variousclay-ice
nesseslistedin Table 9. In the south,the depositsappearsufficientlythin that any melting is likely to be relegatedto a depth
that lies well below the regolith-polarcap interface.Of course,
given the highergeothermalheat flow that likely characterized
the planet'searly history, the conditionsfor basal melting (at
both poles) were almost certainly more favorable in the past.
However,even under currentconditions,given an initially icesaturatedregolith,melting at the base of the cryosphere(Figure 21b) appearsto be an inevitableconsequence
of polar deposition.
For basalice at the meltingpoint,the thicknessof the layerAz
thatcanbemelted
perunitareabya geothermal
heatfluxQgis
givenby
mixturesare plottedas a functionof their volumetricice content.
Az =
Additionalinformationaboutthesemixturesis presentedunder
the "frozensoil" headingof Table 2. Note that roughlyhalf the
3.5
i
I
I
i
I
Qg
At
(18)
pLf
where
Lfisthelatent
heatoffusion
andAtis theelapsed
time.
I
Thus,a geothermal
heatfluxof 30mWm-2 hasthepotential
for
melting
asmuchas3 x 10-3 mof icefrombeneath
thepolarcaps
TABLE 9. CalculatedBasalMeltingThicknesses
2.5Geothermal
Heat Flux,
mW m -2
2.0-
1.5-
1.0-
ß
ß
o
[]
/x
Sanger (1963)
Penner (1970)
Lachenbruch (1970)
Kersten (1963)
Higashi (1953)
30
90
0.535
I
I
I
I
40
45
50
55
VOLUMETRIC
ICE CONTENT,
I
60
65
PolarDeposit
ThermalConductivity
Wm-I
k-1
Thickness,km
252 K
273 K
1.0
3.27
3.97
2.0
3.0
6.53
9.80
7.93
11.90
1.0
1.09
1.32
2.0
2.18
2.64
3.0
3.27
3.97
1.0
0.65
0.79
2.0
3.0
1.31
1.96
1.59
2.38
70
%
Fig. 22. The thermalconductivities
of variousterrestrialclay-icemixtures
plottedasa functionof their ice content[Clifford, 1987b]. Additionalinformarionis presented
in Table2.
150
Theseresultsassume
a meanpolarsurfacetemperature
of 154 K.
CLIFFORD:
HYDROLOGIC
ANDCLIMATICBEHAVIOROFWATERONMARS
eachyear. Of course,if glacial sliding shouldoccur,the resulting
frictionalheat couldboth substantiallyreducethe requiredthicknessfor basalmelting and increasethe productionof meltwater.
Fora given
basalsliding
velocity
Vbthefrictional
heatfluxQf
can be calculated from
Qf = VbZb
dh
10,997
gradientin hydraulichead createdby the presenceof the mound
will then drive the flow of groundwateraway from the poles.The
two principlefactorsthat will governthe magnitudeof this transø
port are the size of the groundwatermound and the effective
permeabilityof the crust.In the following discussion,the relative
importanceof these factorsis assessedthroughthe use of well
establishedterrestrialhydrogeologicmodels.
(19)
= VbPigh•
5.2. Growth of a Polar GroundwaterMound
dx
The developmentof a groundwatermound in responseto
polar basalmeltingis analogousto a problemfrequentlystudied
(includingany componentof entraineddust),g is the acceleration on Earth: the artificial rechargeof an aquifer beneatha circular
of gravity,h is the local thicknessof the cap, and dh/dx is the lo- spreadingbasin[Hantush,1967;Marino, 1975;Schmidtkeet al.,
cal slopeat the polar cap'ssurface[Weertman,1961; Clifford, 1982]. To obtain an analytical expressionfor the growth of a
1987b].As seenin Figure23, a slidingvelocityof 10 m yr-1, groundwatermoundbeneatha rechargingsource,a number of
simplifyingassumptions
must be made, i.e., (1) the aquifer is
driven by a basal shearstressof 100 kPa (a value typical of terisotropic,infinite in areal extent, and rests upon
restrial glaciersand ice sheets[Paterson,1981]), generatessuf- homogeneous,
ficientheat(-30 mWm-2) tohalvethethicknesses
necessary
for an impermeablehorizontalbase;(2) the hydraulicpropertiesof
the aquiferare invariantin bothspaceandtime; and (3) the conbasalmeltingduringthe presentepoch.
Possibleevidenceof pastbasalmeltinghas beendiscussedby stantdownwardpercolationof water proceedsat a rate which is
severalinvestigators.For example, Carr et al. [1980], Howard sufficientlysmall (comparedto the aquiferpermeability)that the
[ 1981], andKargel and Strom[ 1992] have notedthe resemblance influx is almostcompletelyrefractedin the directionof the local
slopeof the water table when it reachesthe mound[Hantush,
of the braidedridgesof theDorsaArgentearegion(78ø S, 40ø W,
Figure24) to terrestrialeskers,landformscreatedby the deposi- 1967; Marino, 1975; Schmidtkeet al., 1982].
After Hantush [1967], the governingequationfor the develtion of fluvial sedimentsbeneathglaciersand ice sheetsthat have
opment
of a groundwatermoundbeneatha circularrecharging
undergonebasal melting. In addition, Clifford [1987b] has cited
source is
the geomorphicsimilarities betweenthe major polar reentrant
Chasma Boreale (85ø N, 0ø W) and the outflow channel Ravi
Vallis (1ø S, 43ø W), suggesting
that ChasmaBoreale,and simi32Z 1 •Z
2 w¾
œ¾ •Z
+
+
(20)
lar featuresfound elsewherein the polar regions,may have
•r
2
r
•r
k
g
•'k
g
•t
formedas the resultof a j6kulhlaup,the catastrophic
drainageof
a large subglacialreservoirof basal meltwater. A terrestrial example of this processis the recurrentcatastrophicdrainageof
Grimsv6tn, a large subglaciallake in the center of the Vatnawhere
Z = h2-hi
2,h is theheight
of thewatertableabove
the
baseof the aquiferafteranelapsed
timet, hi is the initial satuj6kull ice cap in Iceland[Nye, 1976].
Given the presenceof a subpermafrost
aquifer and geologi- rated thicknessof the aquifer,h is a constantof linearization
cally reasonablevaluesof crustalpermeability,the deep infiltra(= 0.5(h+ hi)) whichrepresents
theweighted
meandepthof
tion of basal meltwater will result in the rise of the local water
saturation [Hantush, 1964], r is the radial distance from the
centerof the mound,w is the rechargerate per unit area,k is the
table in the form of a groundwatermound (Figure 21c). The
where•, isthebasalshearstress,
Piisthedensity
of thepolarice
aquiferpermeability,g is the acceleration
of gravity,¾ is the
kinematicviscosity,andœis theeffectiveporosity.
The boundaryand initial conditionsthat apply to equation (20) are
•[
/150
kPa/_
_
Z(r, O) -- 0
•Z(O, t)/•r-- 0
w--w
x
6
--0
(O<r<a)
(r>a)
Z(oo, t) = 0
These conditionscorrespondto four basic assumptions:(1) the
water table is initially horizontal,(2) the groundwatermound is
symmetricaboutits verticalaxis, (3) the rechargeis limited to a
circular region of radius a, and (4) the effect of the recharge on
the shapeof the water table is negligibleat largeradial distances
[Hantush, 1967; Marino, 1975' Schrnidtkeet al., 1982].
0
0
10
20
30
40
50
BASAL SLIDING VELOCITY (m yr 'l)
After Hahtush [1967], equation(20) can be solvedusing Laplaceand zero-orderedHankel transformsto obtainthe following
Fig. 23. Thefrictionalheatproduced
by basalslidingunderan appliedbasal
expression
for the maximumheighthm of the water table
shearstressof 50, 100, and 150 kPa [Clifford, 1987b].
(evaluatedat r -- 0) at any time t
10,998
CLIFFORD:HYDROLOGIC
ANDCLIMATICBEHAVIOROFWATERONMARS
Fig.24. Braided
ridges,
in theDorsaArgentea
region(77øS,44øW),thathavebeeninterpreted
aspossible
analogs
of terrestrial
eskers
(VikingOrbiterframe
421B14).
hm
2- h/ = Qr¾W(tto)
+
2nkg
Note that the solutiongivenby equation(21) is valid for ground-
1-e-Uo
I
(21) watermoundheights(bin-hi)up to 50% of the initialdepthof
uo
saturation
(hi) [Hahtush,
1967].
where
therecharge
volume
Qr-- lrzl2
w,uo -- a2ve/4
kght, and
whereW(uo)is thewellfunction
fora nonleaky
aquifergivenby
from0.01-2.2km3 H20yr-1,andarebased
onhydraulic
prop-
-u o
W(uo) =
erties that might reasonablycharacterizethe Martian crust.The
calculationsassumesaturatedaquifer thicknessesof 1 km and
5 km, an effectiveporosityof 0.1, and a permeabilityof 1 darcy.
For comparisonpurposes,a secondset of developmenttimes
duo
o
Developmenttimes for groundwatermoundsfrom 100 m to
2500 m in heightare presentedin Table 10 and Figure25. These
times were calculatedfor four rechargevolumes,rangingin size
glo
(22)
(-1)
l+n
Uo
n
= -0.5772 - logeUo +
n-n!
i=l
werecalculated
fora recharge
volume
of0.01km3H20yr-1 and
TABLE 10. Groundwater
MoundHeightsasa Functionof Time
Time t, years
Initial Aquifer
Thickness
hi, m
1000
50OO
Groundwater
Mound
Height
hm- hi, m
O -- 2.2 km3yr-1
O -- 1 km3yr-•
O -- 0.1 km3yr-•
O -- 0.01 km3yr-•
k = 1 darcy
k = 10 mdarcies
100
3.54E3
7.84E3
9.95E4
1.47E9
200
7.08E3
1.57E4
3.75E5
--
7.85E5
1.57E6
300
1.06E4
2.38E4
1.31E6
--
2.38E6
400
1.42E4
3.25E4
4.78E6
--
3.25E6
500
1.78E4
4.22E4
1.91E7
--
4.22E6
100
3.54E3
8.18E3
1.46E6
--
8.18E5
500
1000
2.39E4
1.00E5
1.23E5
2.08E6
•
•
•
•
2.08E8
2500
8.33E6
....
1.23E7
Unlessotherwise
noted,development
timesarebasedon an effectiveporosityof 0.1 anda crustalpermeability
of 1 darcy(=10-12m2).
Read3.54E3 as
3.54 x 103,for instance.No entryindicates
a development
timegreaterthantheageof thesolarsystem.
•ORD:
HYDROLOGIC
ANDCLIMATICBEHAVIOROFWATERONMARS
10,999
600
_(a)
550
500
Aquifer Thickness: 1000 m
- O=2.2km
3yr-1
450
-
400
-
350
-
300
-
250
-
200
-
150
-
100
-
O= 1.0km3
yr-1
O= 0.1km3yr-•
= 0.01km3yr-1
•k=
10md)
I
50
I I IllIll
103
I
I I IllIll
104
I
I I IllIll
105
I
II
IIIIII
106
I
I I Illll
107
10•
TIME, t (yrs)
!-
3000
-1-
(b)
iii
2500
z
• •
OE
n'
Aquifer Thickness- 5000 rn
2.2
2000
,
•:
1500
•Q=0.01
km
3yr-l•,•/
1000
Z
•
o
500
!
103
! I IllIll
10'•
I
I I IlIIII
I
I I IIIIII
105
J
106
I
I I IIIIII
I
107
I I IIIIII
Q:0'1
km3
yr-1
I
108
I I IIIIII
I
109
I I Illl'
10•ø
TIME, t (yrs)
Fig.25. Groundwater
mounddevelopment
timesforrecharge
volumes
between
0.01 and2.2 km3 H20 yr-I andaquiferthicknesses
of (a) 1000m and
(b)5000m. Unless
otherwise
noted,
thecalculations
assume
a crustal
permeability
of 1 darcyanda basalmelting
radius
equaltothatofthepermanent
north
polarcap(a = 5 x l0 s m).
a permeability
of 10-2 darcies.
In allcases,
theradius
of thebasal Groundwatermounddevelopmenttimes also lengthenif the
meltingareawastakento beequalto thatof thepermanent
north rechargevolumeis reduced.For example,cuttingthe recharge
polarcap(a = 5 x 105m).
volume
from2.2km3to0.01km3H20yr-1increases
thegrowth
For an aquiferwith an initial saturatedthicknessof 1 km and timefor a 100m moundin a 1-km-thick
aquiferto over109
a recharge
volume
of2.2km3 H20yr-l (equal
tothemaximumyears.In contrast,a reductionin crustalpermeabilityshortens
volumeof ice that couldbe meltedper year from beneaththe development
times.Thisis illustrated
by reducingthepermeabilnorthpolarcapbya geothermal
heatfluxof 30 mWm-2),there- ity in thepreceding
example
from1 to 10-2 darcies,
thereby
sultssummarized
in Table10 indicate
thata groundwater
mound shortening
the development
time for a 100 m moundto lessthan
will growto a height
of 100m in lessthan4 x 103years_and106years.
reach
a height
of500m in a littleover104years.
Although
these
growthtimeslengthenconsiderably
asthe initial saturatedthick-
Thedifference
in development
timethatresultsfroma change
in aquiferthickness,
permeability,
or rechargevolume,simply
nessof theaquiferis increased,
evenin a 5-krn-thickaquifer,a
reflectsa changein the relative massbalanceof water between
groundwater
mound2500m highwill develop
in lessthan107 verticalrecharge
Qr,storage
(i.e.,thevolumeof watercontained
years[Figure25b].
in themound),
andradialdischarge
Qd,whichisgivenby
11,000
CL•'FORD: HYDROLOGICAND CLIMATIC BEHAVIOROFWATER ON MARS
Qa-- 2reah v
(23)
whereh is the saturatedthicknessof the aquiferat r = a, and v is
the specificdischarge(the dischargeper unit area) given by
Darcy'slaw
v =
kg •)h
-
v
(24)
•)r
I AQUIFER I
Of course,whenthe radial dischargeof the moundfinally balancesthe vertical recharge,a steadystate conditionis reached.
The permeabilityrequirementsnecessaryto supportsuchsteady
stateflow are discussedin the following section.
z',-',-,,-,•'-,•-,7-,•'-,"2,'-2,'l \ / I x`/ I x` ix` i x` x` x` \
-'.-\.
,' \' ,",'•\.'_,'-
Flow
!
'•
',
\ - \ -. \•\<. -I•'..'\'..'\",./
./\. .... \./,\./,•./:./.,,
'.. • '..\
.... \-/x-/x-Ix`-/
' ,. ,. ,,\,,x` -I,; -/ BASEMENT .....
"\ "
x`
i•,
f .•, '.' ,;4\'4, -.'•-.,•-,•.
,•.,•
-. ,E/x-,x-/x-/,_
.... .'-_.,.'-_,--
5.3. The Effect of Crustal Permeabilityon Pole-to-Equator
Groundwater
Q
.--,...,
..x ..\ ..\
Fig. 27. A schematic
diagramof confinedsteadystatewell flow.
Given the presenceof a global interconnectedgroundwater
systemon Mars, the developmentof a groundwatermound in
responseto polarbasalmelting will createa gradientin hydraulic
rck g
headthat will drive the flow of groundwateraway from the pole.
The effect of crustalpermeabilityon the magnitudeof this flow
Evaluatedat r -- a, equation(26) yields an expressionfor the
can be readily assessedon the basis of establishedmodels of
maximumhydraulichead which can then be solvedfor k to find
unconfinedand confinedsteadystatewell flow. In this analysis,
the permeabilitynecessaryto sustainunconfinedsteady state
the well radius,a, is equivalentto the radiusof the recharge(or flow
basalmelting) area discussedin the previousanalysis;while, as
before, the groundwatermound height is taken to be the differencebetweenthe maximum and minimum hydraulicheads
QrV In (R / a )
=
(27)
h2= hi
2 + QrV In(R/r)
2
(hm-hi).The distance
R to the regionof lowesthydraulic
head
(26)
2
rcg(hm - hi)
representsthe separationbetween the regions of net vertical
recharge(the poles) and discharge(the equator), and is taken
Of course,the possibilityexiststhat,in an initially unconfined
here to be of the order of the planetary radius of Mars. These
aquifer,a polar groundwatermoundcouldgrow to the point of
relationshipsare illustratedin Figures26 and 27.
contactwith the baseof the caps;in this event, the aquifer will
The governingequationand appropriateboundaryconditions
undergoa transitionbetweenconfinedconditionsat the polesto
for steadyunconfinedwell flow are [after Todd, 1959]
unconfinedconditionscloserto the equator.It is also possible
that the polaraquiferhas been confinedfrom the very outsetof
basal
melting(i.e., see Figure 7). Given either case,the solution
(25)
presentedin equation(27) is no longervalid.
3r
3r
The possibilityof confinedflow can be analyzedby solving
the steadyconfinedwell equation,which, after Todd [1959], is
h2--hi2
(r = R)
givenby
Qr= 2rcrhv
(i.e.,Qr-- Qd)
where as before, v is the specificdischarge(the dischargeper
unit area)givenby equation(24). Solvingequation(25) in light
of the aboveboundaryconditions,we obtain
r-3r
= 0
(28)
3r
and whichis subjectto the followingboundaryconditions
h--hi(r=R )
Qr-- 2rer hi v
Q
•i•.•...•:(.:.;:.!.:
!:).i.::•i:!....:.:.!:•:i:.!}•..i.
:.......!.!?•::.i.:i!•:i.•.•:•.•.:.::.•(;•.:!.5:
•:y...::.:::;..!:..:•.....:!:;i::)!.....T...•..:i:.....?:.:..::•:.•.....:)i.....:.•.•:•.:?....!..)...:
'
Solvingfor the permeabilityof
v
.............
?:"'
', I
I
;
!
ß --
'
'1'
I
I
--
AQUIFER
I
I
',
I
,
•
I
I
the crustin the samemanneras
before,yields
v
! -
k=
;
Qrv
In(R/a)
(29)
2 rcghi(hm - hi)
v
)
I
I
I
I
,(---.
-/?\ -.-/•.....- \-.
• ,/•../.•,/•.
,/.•\ ..,/.•\• ,/•\ •,/?,/•
\ .. \ .• \.•,/•.,/•../•.,/•
\ .. \ .• \.. \ .../-•,/.•./•,/.•,/•,/-•
\../\ \l/\l/\l/xl/xl/xl
•, \ .. \ .. \ ... \.. -/•,/•
\7./\...
\ • \
\l/\l/\l/\l/\l/\l/\l/\l/\l/\l/x`l/\l
x.I/\l/x.I/x.I/x.I/\
\7'/\"'
\"
\1
.xlz\l/\l
\•'/\"\l/\l/\l/\l/\l/\l/\,t/\l
\'• \'• \"
\"
\'•
\'•
\,"/x"
\" \"\
.xl/\l/.xl/\l
D/'•.•.IVI•.111
\
x •. x`
'"- \"
\"
Fig. 26. A schematic
diagramof unconfmed
steadystatewellflow.
\
In Table 11 and Figure 28, crustalpermeabilitiesnecessary
for steadystateflow (calculatedfrom equations(27) and (29))
are presentedfor a reasonablerangeof polar rechargevolumes
and net hydraulicheads.The resultsindicate that a recharge
volume
of I km3H20yr-l, introduced
intoa 1-km-thick
aquifer
•ORD:
HYDROLOGIC
AND•TIC
BEHAVIOROFWATERONMARS
11,001
TABLE 11. Permeability
Requiredfor SteadyStateFlow
Permeabilityk, darcies
Groundwater Mound
InitialAquifer
Height
Thickness
hf•n
Q- 2.2km
3yr-I
hm-h•,m
1000
100
5000
103
Q- 1km
3yr-I
Unconf'med
Confined
102.0
107.0
200
300
400
48.69
31.05
22.32
53.56
35.71
26.78
500
17.14
21.42
100
21.21
21.42
500
4.08
4.28
1000
2500
1.95
0.69
2.14
0.86
Q=0.1km
3yr-I
Unconf'med
Confined
Q- 0.01
km
3yr-I
Unconf'med
Confined
Unconfmed
Confined
45.96
21.93
13.99
10.05
7.72
48.25
24.13
16.08
12.06
9.65
4.60
2.19
1.40
1.01
0.77
4.83
2.41
1.61
1.21
0.97
0.46
0.22
0.14
0.10
0.08
0.48
0.24
0.16
0.12
0.10
9.56
1.84
0.88
0.31
9.65
1.93
0.97
0.39
0.96
0.18
0.09
0.03
0.97
0.!9
0.10
0.04
0.10
0.02
0.01
0.003
0.10
0.02
0.01
0.004
than5 x 10-3 darcies,a valuethatlieswithinthelowerextreme
"=(a)
AquiferThickness-1000 rn
.
of measuredpermeabilitiesfor fracturedigneousand metamorphic rock (Figure 29). Note that even this low value of crustal
permeabilitypermitsthe pole-to-equator
transportof as much as
102::
4.5x 107km3of groundwater
(fromeachpole)overthecourse
of
10
h.,- h,= 100rn
Martian
geologic
history,
or-108km3H20(equivalent
toa global ocean-600 m deep) when the potentialcontributionof both
polesis takeninto account.
1
mQ
h.,- h, = 500 rn
5.4. The Large-ScalePermeabilityof the Martian Crust
10'•
10-2
, , , ,,,
, , , , ,,,,,
, , , ,,,,,,
, , , , ,,,,
RECHARGEVOLUMEQ (km3yr-:)
102
(b)
The significanceof the steadystatepermeabilitiespresented
in Table 11 can be placedin perspectiveby comparingthem with
the crustal values assumedby Carr [1979] in his discussionof
the origin of the outflowchannels.Basedon both the size of the
channelsand the assumptionthat each was formed by a single
catastrophicevent, Carr [1979] calculatedthat dischargesof
-107 to 5 x 108m3 s-! werenecessary
to produce
theobserved
AquiferThickness:5000 rn
erosion.To achieverates this high requires large-scaleperme-
abilitieson the orderof 103darcies,permeabilities
that Carr
lO
_
[1979] arguedwere only reasonableif the Martian crustwas intenselyfracturedand/or possessed
numerousunobstructedlava
_-
tubes, characteristicssimilar to thoseof certain Hawaiian basalts
[Davis, 1969].
1
Arguments
forcrustal
permeabilities
of 103darcies
or higher
have also been advancedby MacKinnon and Tanaka [1989].
•
lO-2
1o-3
i
o.ool
I
i
i
i
iiii
hi,,
-h,
=2500
i
O.Ol
i
I
i
iiiii
i
o.1
i
i
i
illit
i
i
1
i
i
i
REL A TI VE PERMEA
•permeable
basalt
iii
lO
fractqredigneousa
RECHARGEVOLUMEQ (km3yr'•)
Fig. 28. Permeabilityrequiredfor pole-to-equator
steadystate flow for
various rechargevolumesand groundwatermound heightsin aquifers
(a) 1000 m and (b) 5000 m thick. Unlessotherwisenoted,the calculations
assumea crustalpermeability
of 1 darcyanda basalmeltingradiusequalto
thatof thepermanent
northpolarcap(a = 5 x 105m).
BILI T Y
meta{morphic
rock
Mars'
'fractured
MacKinnon
and
zone'
Tanaka
unfractured
igneous
& *-Ave.,
Earth's
'•"•':•;'•':•'::•='='•=":':•?":•
......... silIt, Ioess
Brace
(1980,
1984)
metamorphic
rock
crust
(1989)
Megaregolith
value
required for inferred
outflow
channel
discharge
rates
Carr (1979)
at the poles,coulddrive the flow of a similar volumeof water to
the equator,givena crustalpermeabilityof-100 darciesand a
groundwater
moundheightof 100 m. If the rechargevolumeis
lowered
to0.01km3H20yr-1,andif wepermit
a nethydraulic
grav{,•l
-8
-7
-6
-5
-4
-3
-2
-1
0
1
LOG k (darcies)
2
3
4
5
headof 2500 m (equivalentto the lithostaticpressureexertedby
a 1.5-km thicknessof ice-rich permafrost),then the minimum Fig. 29. Relative permeabilityof typical terrestrialgeologic formations
permeabilityrequiredto supportsteadystateflow falls to less (afterFreeze and Cherry [1979]).
11,002
CIJFFORD:HYDROLOGIC
ANDCLIMATICBEHAVIOROFWATERONMARS
Basedon gravity studiesof terrestrialand lunar impactcraters,
andboreholeobservations
of terrestrialimpactandexplosioncraters,they suggestthat porositiesashigh as 20% may characterize
the Martian fracturedbasement.They further suggestthat much
of this impact-generated
porositymay occuras openplanar fractureshavingwidths of 1-5 mm and associatedpermeabilitiesas
levels far in excessof their respectivesaturationpoints. The
resultingprecipitationof thesemineralsbeneaththe water table
shouldleadto widespread
diagenesis
andto thedevelopmentof a
distinct geochemicalhorizon within the crust [Soderblomand
Wenner, 1978]. Where exposedby subsequentfaulting or erosion, this horizonshouldappearas a relativelycompetentlayer
greatas104darcies.
whoseupperboundaryconformsto a surfaceof constantgeopoAlthough
localpermeabilities
ashighas103 darcies
undoubt-tential. Althoughnot diagnosticallyunique,suchan observation
edly occur on Mars, on a globally averagedbasis, an effective is consistent
with mineraldepositionin an unconfinedaquiferin
permeabilitythis large seemsdifficult to reconcilewith the five hydrostaticequilibrium.
order-of-magnitude
smallervalue inferredfor the near surfaceof
In summary,althoughpreviousestimatesof the large-scale
the Earth [Brace, 1980, 1984]. Therefore,given the generalim- permeability
of theMartiancrusthaverunashighas103darcies,
portanceof this parameterto understanding
the subsurfacehy- considerationof the mean permeability of the Earth's crust
drologyof Mars,just how reliableare thesehigherestimates?
[Brace, 1980, 1984], and the potentialfor extensivediagenesis,
As noted by Carr [1979], much of the need to invoke high suggeststhat a more reasonablevalue may be 3-5 orders of
dischargerates (and thushigh permeabilities)to accountfor the magnitudesmaller. As discussedin section5.3, even permeorigin of the outflow channelsis basedon the assumptionthat abilities this low will permit the pole-to-equatortransportof a
each channel was carved by a single catastrophicevent. How- significant
volume
of groundwater
(• 108km3) overtheplanet's
ever, if the channelswere createdby multiple episodesof out- history.It shouldbe noted,however,that evenif only a few perbreak and erosion,or by continuousshallowflows actingover a cent of the Martian crust possesses
permeabilitiesas high as
prolongedperiodof time, then the need for high crustalperme- those estimatedby Carr [1979] and MacKinnon and Tanaka
abilitiesis significantlyreduced.
[1989], the potentialfor pole-to-equatorgroundwaterflow will
Similarqualificationsapplyto thehighpermeabilities
inferred be vastlyincreased.
by MacKinnonand Tanaka [1989]. The validityof their analysis
6. TH• EARLY EVOLUTION OF THE MARTIAN
restson two key assumptions:
(1) that the gravityanomaliesasHYDROSPHERE AND CLIMATE
sociatedwith terrestrialand lunar cratersare almostexclusively
due to an increasein the fracture porosityof the surrounding
The way in whichthe Martian crustwas initially chargedwith
basement,and (2) that the geometryof these fracturesis both
H20
is criticallydependent
on the natureof theplanet's
early
open and planar. As discussedbelow, there are goodreasonsto
climate.Was Mars was warm and wet, as suggested
by the valley
questionboth assumptions.
networks?Or has it always resembledthe frozen state we obFirst, contraryto the assertionby MacKinnon and Tanaka
servetoday?And, finally, if the climatedid startwarm, how was
[1989], the largestcontributorto the gravity anomaliesrecorded
the planet'shydrologiccycleaffectedby the onsetof coldertemover terrestrialand lunarcratersis not the fractureporosityof the
peratures?These,and severalrelatedquestionsaboutthe develsurroundingbasement,but the increasein porosityassociated
opmentof the early hydrosphereand climate, are addressedin
with the breccia lens at the bottom of the crater [Dvorak and
the followingdiscussion.
Phillips, 1978]. As discussed
by Shoemaker[ 1963], Short[ 1970],
and Grieve and Garyin [1984], the breccia lens consistsof coun6.1. TheEvolutionof the Early Martian Climateand the
try rock that is pulverizedalongthe wall of the transientcavity
InitialEmplacement
of Crustalt120
and then slumpsto the bottomlater in the crateringevent. As
such,its lithologyconsistsof boulder-sizedfragmentsimbedded
Giventhe geomorphic
evidencefor the widespreadoccurrence
in a substantialmatrix of more finely divided debris.The hydro- of water and ice in the early crust,and the difficulty involvedin
logic propertiesof sucha mix are morecloselyrelatedto thoseof accountingfor this distributiongiven the presentclimate,it has
a low-permeabilityglacialtill than to a regularnetworkof open been suggestedthat the Martian climate was originally more
planar fractures.Second,shockwavesgeneratedby subsequent Earth-like,
permitting
theglobalemplacement
of crustalH20 by
impactswill help to eliminateany sizableopeningsin the frac- directprecipitationas snowor rain [e.g., Masurskyet al., 1977;
of the valley networksto
tured basementby both shifting and compactingthe overlying Pollacket al., 1987]. The resemblance
debris(i.e., seeFigure 1) andby rupturingadditionalmaterialoff terrestrial runoff channels, and their almost exclusive occurrence
the fracture walls as the shock waves are reflected along the in the planet'sancient(-4 billion year old) heavilycrateredterfracture boundaries[Short, 1970].
rain, is oftencitedas evidenceof just sucha period.
Clearly,if the valleynetworksdid originatefrom an earlyepiFinally, as notedin section2.1, the presenceof groundwater
can also contributeto a significantreductionin crustalporosity sodeof precipitationand surfacerunoff, it requiredatmospheric
andpermeability.On Earth, groundwaterthat residesin the crust pressuresand surfacetemperaturesfar higher than those obfor millions of yearsgenerallyevolvesinto a highly mineralized servedtoday. For this reason,it has been suggestedthat early
a greenhouseclimate, a conditionthat would
brine consistingof a saturatedmixture of chlorides,carbonates, Mars possessed
sulfates,silica, and a variety of other dissolvedspecies[White, haverequiredin excess
of 5 barsof CO2 andthe presence
of
gasses,suchas methaneand ammonia,
1957]. On Mars, this geochemicalevolutionwill likely be accel- otherpotentgreenhouse
erated by the influx of mineralsleachedfrom the crustby low- to maintainsurfacetemperaturesabove freezing [Postawkoand
temperaturehydrothermalcirculation(see section4.4.1 and Fig- Kuhn, 1986; Pollack et al., 1987; Kasting, 1987, 1991]. Al-
ure18).Theconvective
cycling
of 102-103
kmof water(perunit though
thisamount
ofCO2is---102-103
times
more
thancontainarea) betweenthe water table and the baseof the cryospherewill ed in the presentatmosphere,
it is well within currentestimates
depletethe interveningcrustof any easily dissolvedsubstances, of the planet'stotal volatile budget[Pepin, 1987]. The surface
may also
concentrating
many of them in the underlyinggroundwaterto erosionexpectedfrom sucha massiveearly atmosphere
CLI•ORD: HYDROLOGIC
ANDCI.•MATICBEHAVIOROFWATERON MARS
11,003
explainthe early episodeof craterobliterationinferredfrom
Althoughit is possiblethat evidenceof an ancientperiodof
craterdiameter-frequency
plotsof the ancientcrateredhighlands globalprecipitation
hasbeenlostby erosionand resurfacing,
it
[Mutch et al., 1976; Arvidson et al., 1980; Carr, 1981].
seemsequally reasonable.to take this lack of evidenceat face
However,if Mars did possessan early greenhouse,
then what valueandconsidertheposs!bility
thatsuchan episodemaynever
caused
theatmospheric
inventory
of CO2 to fall froman initial hav.e occurred. In this regard, $oderblom and Wenner [1978]
value of 5 bars to its presentlevel of 6.1 mbar?At least four suggest
thattheemplacement
of crustal
H20 wastheresultof the
processesappear likely. Calculationsby Watkins and Lewis directinjectionand migrationof juvenile water derivedfrom the
[1985] suggestthat shockwavesfrom large impactsmay have planet'sinterior.There are at leasttwo ways in which this emblown off a significantportionof the early atmosphere.This placementmay have occurred.First, by the processof thermal
processwas probablymosteffectiveduringthe heavybombard- vapordiffusion,water exsolvedfrom coolingmagmaswill mimentperiod,whenlargeimpactingbodieswere still prevalentin gratefrom warmerto colderregionsof the crust.As a result,any
the solar system.The depletionof the atmospherewas likely part of the cryospherethat overlies or surroundsan area of
further enhancedby the interactionof the solar wind with the magmaticactivity, will quickly becomesaturatedwith ice. The
ionosphere.
Particlevelocitieswithin the resultingplasmaflow introductionof any additionalwater will then result in its accucouldhaveeasilyexceeded
theplanet's
5 kms-I escape
velocity. mulationas a liquid beneaththe cryosphere,where, under the
Calculationsindicatethat this processalone couldhave reduced influenceof the growinglocalhydraulichead,it will spreadlata denseearly atmosphere
to its presentstatein lessthan a billion erally in an effort to reachhydrostaticequilibrium.
years[Perez-de-Tejada,
1987].Finally,atmospheric
CO2 may
However, the fate of water released to the cold Martian at-
havebeen lost to the regolithby both adsorption[Fanale et al.,
1986] andby reactionwith surfaceandsubsurface
liquid water to
form carbonaterocks [Booth and Kieffer, 1978; Kahn, 1985;
Pollack et al., 1987]. Ultimately, all four processes
may have
contributedto reducingthe atmosphericpressureand temperature to the point whereliquid water was no longerstableat the
surface.Proponentsof this idea suggestthat this transitionoccurredsome4 billion yearsago;thus,endingthe periodof valley
mosphereis significantlydifferent.The rapid injectionof a large
quantityof vapor into the atmosphere(e.g., by volcanism)will
lead to its condensation
as ice on, or within, the surrounding
near-surfaceregolith.As the availablepore spacein the upper
few metersof the regolithis saturatedwith ice, it will effectively
sealoff andeliminateany deeperregionof the crustas an area of
potentialstorage.From thatpointon, any excesswater vaporthat
is introducedinto the atmospherewill be restrictedto condensa-
network formation.
tion and insolation-driven
An alternativeschoolof thoughtsuggeststhat the early Martian climatedid not differ substantiallyfrom that of today.Advocatesof this view [e.g., Pieri, 1979, 1980; Carr, 1983] find no
compellingreasonto invokea warmer,wetter periodto explain
the origin of the valley networks.Rather,they cite evidencethat
the primary mechanismof valley formation was groundwater
sapping[Sharp and Malin, 1975; Pieri, 1980; Baker, 1982; Carr,
1983; Brakenridge et al., 1985; Baker and Partridge, 1986], a
processthat doesnot requirethat surfacewater exist in equilibrium with the atmosphere.Accordingto this scenario,as groundwater seepedonto the surface,the heat removed by its rapid
vaporizationled to the formation of a protective and thickening coverof ice, beneathwhich water may have continuedto
eventuallycold-trappedat the poles.
Shouldthe depositionof ice at the polescontinue,it will ultimately lead to basalmelting,recyclingwater back into the crust
beneaththe caps.As the meltwateraccumulatesbeneaththe polar cryosphere,it will create a gradientin hydraulichead that
will drive the flow of groundwateraway from the poles. As the
flow expands radially outwards,it will pass beneath regions
where, as a result of vapor condensationfrom the atmosphere,
only the top few meters of the cryospherehave been saturated
with ice. As before,the presenceof a geothermalgradientwill
flow for considerable
distances even under current climatic
con-
ditions [Wallace and Sagan, 1979; Carr, 1983; Brakenridge et
al., 1985].
Of course,if the early climatewas similar to the presentone,
why are the valley networks found almost exclusively in the
ancientcrateredhighlands?As discussedin section4.4, the associationof most small valleys with the rims of large craters
suggestsa geneticrelationship,wherebythe melt generatedby
largeimpactsresultedin the formationof localhydrothermalsystems whose dischargethen formed the valleys [Newsom,1980;
Brakenridgeet al., 1985]. Becauseonly large impactsmay have
producedsufficientmelt to establishthe necessaryhydrothermal
activity,the decline in valley networkformationmight then simply reflectthe earlydeclinein thenumberof largeimpactors.
However, while groundwatersappingmay successfullyexplain the origin of the small valleys,it fails to addresshow the
redistribution
on the surface until it is
thenleadto theverticalredistribution
of H20 fromtheunderlying groundwaterto the cryosphereuntil its pore volume is saturated throughout(see section 4.5). In this way, and by these
processes,the early crust may have been globally chargedwith
water and ice without the need to invoke an early period of atmosphericprecipitation.
6.2. The HydrologicResponseof Mars to the Thermal
Evolution of lts Early Crust
Althoughunambiguousevidencethat Mars once possesseda
warmer, wetter climate is lacking, a studyof the transitionfrom
such conditionsto the present climate can benefit our understandingof both the early developmentof the cryosphereand the
variouswaysin whichthe currentsubsurface
hydrologyof Mars
is likely to differ from that of the Earth. Viewed from this perspective,the early hydrologicevolution of Mars is essentially
identical to consideringthe hydrologicresponseof the Earth to
the onsetof a globalsubfreezingclimate.
If the valley networksdid result from an early period of atcrustwasinitiallycharged
withH20. Indeed,evenadvocates
of
the sappinghypothesissometimessidestepthis issue by sug- mosphericprecipitation,then Mars must have once possessed
gestingthat the groundwaterinvolved in the formation of the near-surfacegroundwaterflow systemssimilar to thosecurrently
networkswas eraplacedduringa periodof precipitationthat oc- found on Earth, where, as a consequenceof atmosphericrecurred so early that no physicalrecordof that period remains charge,the water table conformedto the shapeof the local ter[Pieri, 1979, 1980].
rain (Figure 30a). However,with both the transitionto a colder
11,004
CLIFFORD:HYDROLOGIC
ANDCLIMATICBEHAVIOROFWATERONMARS
(a)
prec•p•tabon
•nfiltrabon
water
table :111
W
:: :i
•'
groundwater
:::i:::::
d,v,de•
:: ;:
r,½
:•groOn:dwate:;•
i:::1111
i:: d•wde
(b)
water
table
W
(c)
Fig.30. Thehydrologic
response
of Marsto theonset
of a colderclimate.
(a) If Marsoncehada warmer,
wetterclimate,
it mayhavehadnear-surface
groundwater
flowsystems
similar
tothose
foundonEarthwhich,asa resultof atmospheric
precipitation,
hadwatertables
thatfollowed
thelocaltopography.
(b) Asthetemperature
fellbelowfreezing,
thecondensation
of icein thenear-surface
crusteliminated
anyfurtherreplenishment
of theunderlying
groundwater,leading
to thedecayof theprecipitation
andtopographically
induced
groundwater
divides.
(c) Ultimately,
asthegroundwater
reached
hydrostatic
equilibrium,
it saturated
thelowermost
porous
regions
ofthecrust,
resulting
in a groundwater
tablethatconformed
toasurface
ofconstant
geopotential.
fromanyfurtheratmospheric
supply.Fromthatpointon,theonly
fronteventuallydevelopedin the regoliththatpropagated
down- sourceof water for the thickeningcryospheremust have been
ward with time, creatinga thermodynamic
sink for any H20 thethermallydrivenupwardflux of vaporfrom the underlying
(Figure30b).
within the crust.Initially,watermayhaveenteredthis develop- groundwater
With the eliminationof atmosphericrecharge,the elevated
ing regionof frozengroundfrom boththe atmosphere
and underlyinggroundwater.
However,as ice condensed
within the water tablesthat once followed the local topographyeventually
near-surface
pores,the deeperregolithwasultimatelysealedoff decayed.The continuityof pore spaceprovidedby sediments,
climate and the decline in Mars' internal heat flow, a freezing
CLIFFORD:
HYDROLOGIC
ANDCI•MATICBEHAVIOROFWATERONMARS
breccia, and interbasin faults and fractures should have then al-
lowedthewatertableto hydrostatically
readjuston a globalscale
untilit ultimatelyconformedto a surfaceof constantgeopotential
(Figure30c). This conclusionis supportedby investigations
of
areallyextensivegroundwater
systemson Earth that experience
little or no precipitation[e.g.,Mifflin and Hess, 1979; Cathles,
11,005
For the conditionsdescribedabove,equation(30) was solved
numericallyusing the method of finite-differences.The results
indicatethat,given a present-daygeothermalheatflux of 30 mW
m-2,thefreezing
frontatthebaseof thecryosphere
will reachits
equilibrium
depthattheequator
in-4.6 x 105years,
whileat the
polesit will takeroughly1.5x 106years(Figure31). Giventhe
elevated geothermal conditions that likely characterizedthe
The time requiredfor the development
of the cryosphere
can planet
4 billion
years
ago(i.e.,Qg- 150mWm-2),
thecorredevelopment
timesare2 x 104yearsand1.3 x 105
be calculatedby solvingthe transientone-dimensional
heat con- sponding
ductionequationfor the caseof a semi-infinitehalf-spacewith years,respectively.These calculationsare basedon a thermal
1990].
conductivity
of 2.0 W m-• K-z, a freezing
temperature
of 273K,
internalheatgeneration,where
and a maximum latent heat release (due to the condensationof
32T
S
1 •}T
H20vapor
asicein thepores)
thatdoes
notexceed
Qg,a limit
(3O)
that is imposedby the geothermaloriginof the vaporflux reaching the base of the cryosphere(e.g., Figure 30b; see also section 4.4.1). Note that althoughthese developmenttimes assume
andwhereT is the crustaltemperature,z is the depth,t is time, K an initially dry crust, they would not be significantlydifferent
is the crustal thermal conductivity,ct is the thermal diffusiv- evenif the crustwere initially saturatedthroughout.Althoughthe
ity (= Wpc), and S is the heat generationrate per unit volume early growth of the cryospherewould be slowed by the ready
(--3Qg/R,
where
Qgisthegeothermal
heat
fluxanRistheradiussupplyof latent heat, this periodrepresentsonly a small fraction
of Mars) [Fanale et al., 1986]. An upperlimit can be placedon of the total time requiredfor the cryosphereto reachequilibrium.
howrapidlythe cryosphere
evolvedif we assumethat the surface In the later stagesof growth, which are controlledalmostexclutemperature
of Mars underwentan instantaneous
transitionfrom sively by conductionthroughthe frozen crust, the rate of heat
a meanglobalvalueof 273 K to its currentlatitudinalrangeof lossis sufficientlysmall that the effect of latent heat releasecan
154-218 K. Given this assumption,the boundaryand initial be virtually ignored.
conditionsthat applyto equation(30) are
Althoughthe assumptionthat Mars underwentan instantaneoustransitionfrom a warm to cold early climate is clearly incorT(0, 0) -- 273 K
rect,thisextremeexampleservesto illustratean importantpoint,
T(0, t) -- 218 K (at the equator)
8z2
K
c• 8t
thatis:ona timescalegreaterthan-106 years,thebaseof the
-- 154 K (at the poles)
•T
cryosphereis essentiallyin thermalequilibriumwith meantemperatureenvironmentat the surface.As a result, for any reasonable model of climate evolution, the growth of the cryosphereis
not controlledby the rate of conductionthroughthe crust,but by
Qg
•z
-"--"==•==%••
150
mW
rn
-2
N
Ill
Ill
rn
-4
rr
-5
O
-•
•
-7
',,(Present
Mars)
LAT= 0 ø
LAT=
I IIIIII
r'h -13
10
I
10 2
I
I
III
1 03
I
I
90
IIIIIII
I
I
!
I IIIII
10 4
10 5
I I IIIIII
% !
10 6
I I IIII
10 7
TI ME, t (yrs)
Fig.31. Development
timesfortheMartiancryosphere
attheequator
(Ts-- 218K) andpoles(Ts= 154K), assuming
aninstantaneous
transition
froma previouswarmearlyclimate
(Ts-- 273K). Thecalculations
arebased
ona crustal
thermal
conductivity
of2.0W m-1K-1,a basalfreezing
temperature
of 273K,
andgeothermal
heatfluxesof 30 and150mWm-2.Theresulting
equilibrium
depths
attheequator
andpolesforthetwovalues
of geothermal
heatfluxare,
respectively,
3670 m and7930 m, and730 m and 1590m.
11,006
C)_,IFFORD:
HYDROLOGICAND CLIMATIC BEHAVIOROFWATER ON MARS
how rapidly the mean surfacetemperatureenvironmentchanges by the limited hydrostaticpressurethat could develop in a
with time. Pollack et al. [1987] estimate that if the primary perchedaquifer, thus terminatingthe potentialcontributionof
mechanismdriving climatechangewas the removalof a massive low-temperaturehydrothermalconvectionto valley network for-
(1-5 bar) CO2 atmosphere
by carbonateformation,then the
transitionfrom a warm to cold early climate musthave taken be-
mation.
Finally, the postcryosphere
groundwaterhydrologyof Mars
tween1.5x 107to 6 x 107years.Fortransition
timesthisslow, will differ from its possible precryospherepredecessor(and
the downwardpropagationof the freezing front at the base of
the cryosphereproceedsat a rate that is sufficientlysmall (when
comparedwith the geothermally-induced
vaporflux arisingfrom
the groundwatertable) that the geothermalgradient shouldhave
no trouble supplyingenoughvapor to keep the cryospheresaturatedwith ice throughoutits development.
From a massbalanceperspective,the thermalevolutionof the
early crusteffectivelydivided the subsurfaceinventoryof water
into two reservoirs:(1) a slowly thickeningzone of near-surface
groundice and (2) a deeperregionof subpermafrost
groundwater
[Carr, 1979]. Regardlessof how rapid the transitionto a colder
climate actuallywas, the cryospherehas continuedto thicken as
the geothermaloutput from the planet'sinterior has gradually
declined.One possibleconsequence
of this evolutionis that, if
the planet'sinitial inventory of outgassedwater was small, the
cryospheremay have eventually grown to the point where all of
the availableH20 wastakenup as groundice [Soderblom
and
Wenner,
1978].Alternatively,
if theinventory
of H20 exceeds
the
currentporevolumeof the cryosphere,then Mars hasalwayshad
extensivebodiesof subpermafrost
groundwater.
Becausethe pore volume of the cryospherewas likely saturated with ice throughoutits early development,the thermally
drivenvaporflux arisingfrom the reservoirof underlyinggroundwater could have led to the formation
and maintenance
of near-
thereforefrom present-dayterrestrialgroundwatersystems)in at
least one other importantway. In contrastto the local dynamic
cyclingof near-surfacegroundwaterthat may have characterized
the first half-billion yearsof Martian climate history(e.g., Figures 11 and 30a), the postcryosphere
periodwill necessarilybe
dominatedby deeper, slower interbasinflow (e.g., Figure 30c).
Aside from polar basal melting, there are at least three other
processesthat are likely to drive flow under these conditions,
they are (1) tectonicuplift (essentiallythe samemechanismproposedby Carr [1979] to explainthe origin of the outflowchannels eastof Tharsis),(2) gravitationalcompactionof aquifer pore
space(perhapsaided by the accumulationof thick layers of
sedimentand basalt on the surface),and (3) regional-scalehydrothermalconvection(e.g., associatedwith major volcaniccenters suchas Tharsisand Elysium). Note that, with the exception
of active geothermalareas, the flow velocitiesassociatedwith
theseprocesses
are likely to be ordersof magnitudesmallerthan
thosethatcharacterizeprecipitation-driven
systemson Earth.
7. FURTHER CONSIDERATIONS
A unique feature of the hydrologicmodel presentedin this
paperisthat,withregardto thetransfer
of H20 between
its long-
term sourcesand sinks,it is essentiallya closedloop (Figure 33).
That is, given an inventoryof outgassed
water thatis sufficientto
both saturatethe pore volumeof the cryosphereand form a subpermafrostgroundwater
systemof globalextent,the lossof crustal water from any regionon the planetis ultimatelybalancedby
surfacedeposition,basalmelting,and subsurface
replenishment.
Further,givena geologicallyreasonabledescriptionof the crust,
this cycleappearsto be an inevitableconsequence
of both basic
physicsand the climatic conditionsthat have apparentlyprevailedon Mars throughoutthe past3.5-4.0 billion years.For this
reason,the model has importantimplicationsfor a variety of
problemsassociatedwith the planet'shydrologicand climatic
1980; Carr, 1983]. However, as the internal heat flow of the
history.In this sectiontwo examplesthat illustratethe relevance
planetcontinuedto decline,the thicknessof the cryosphere
may andpotentialimportanceof thismodelare considered:
(1) the rehave grownto the point where it could no longerbe disrupted chargeof the valley networksand outflowchannels,and (2) the
surfaceperchedaquifers,fed by the downwardpercolationof
condensedvaporfrom the higher and coolerregionsof the crust
(Figure 32). Eventually the hydrostaticpressureexerted by the
accumulatedwater may have been sufficientto disruptthe overlying groundice, allowing the storedvolume to dischargeonto
the surface.Sucha scenariomay havebeenrepeatedhundredsof
times during the planet's first half-billion years of geologic
history,possiblyexplaining(in combinationwith local hydrothermal systemsdriven by impact melt [Newsom,1980] and
volcanism[Gulick, 1991]) how somevalley networksmay have
evolvedin the absenceof atmosphericprecipitation[Pieri, 1979,
polarmassbalance
of H20.
developing
••'......
i:'i:
:':'i.
:':.
:i•:);:
'.'::.
7
:.._....:
:...•h
'.'•:..:-...:...
.__•..._-.•.•
...!•..•?•.:.¾.:.:
ere
i•?....,•?•:.•.,
-•,•/:•.,...•
...:
....
•
condensation
I - •'""•
"'-.•
"'" •"""
•:'3','
Seasonal
•
North
Polar
Cap
/ / tt•a:P:•i:,
n
•'"
aq
u'
tarO"•
:'•;"!•:!':'•.'•'•
•••
li•'•
-I••ii•• •'
Fig. 32. An illustration
of howtheprocess
of thermalvapordiffusionmay
haveled to the development
and maintenance
of near-surface
perchedaquifersin the absence
of atmospheric
precipitation.
and Climatic
Exchange
ofH20
•
I
/
South
Polar
Cap
I Thermal
H20
Transport
Groun•er
Fig. 33. A modelof theclimaticbehaviorof wateronMars.
CLIFFORD:HYDROLOGICAND •_,IMATIC BEHAVIOR OF WATER ON MARS
11,007
7.1. Rechargeof the ValleyNetworksand OutflowChannels
the episodicrechargeof the Chryseoutflow channelsand the
development
of recent(Amazonianage) valleynetworkson the
A recurrentissueregardingthe originof the valleynetworks
flanksof severallargevolcanoes.
Bakeret al. [1991] haveproand outflowchannelsis that the amountof water requiredto
posedthat an episodeof intensevolcanicactivity,centeredon
erodethesefeaturesis so large,compared
with the storagecaTharsis,mayhavetriggered
a massive
regionalmeltingof ground
pacityof theirlikelysource
regions,
thatsometypeof recycling
ice thatultimatelyresultedin the catastrophic
releaseof asmuch
process
appearsnecessary.
In an effortto addressthis problem,a
as
6.5
x
107
km
3
of
groundwater
onto
the
surface.
Theyargue
varietyof potentialrecyclingmechanisms
havebeenproposed
thatthismassivedischarge
inundated
thenorthernplains,cover[e.g., Masurskyet al., 1977; Carr, 1984; Jakoskyand Carr,
10-30%of theplanetwith a standing
bodyof
1985; Clow, 1987; Gulick and Baker, 1990; Baker et al., 1991; ingapproximately
water
102-103
m
deep.
In
support
of
this
conclusion,
Baker
etal.
Plesciaand Crisp, 1991;Mooreet al., 1991]. Althoughseveral
[1991] cite the enormousdischargerates inferredfrom the diof theseschemes
appearviable,virtuallyall requireeither a
of the Chryseoutflowchannels,
aswell asgeomorphic
coincidenceof environmentalconditions,or a combinationof mensions
evidenceof ancientshorelines
discovered
by Parkeret al. [1989]
physicalproperties,
that is needlessly
complexor whoseoccurthroughout
the northernplains.
renceis poorlyconstrained.
An assumption
commonto eachof the abovescenarios,is that
Perhaps the most controversialelement of the Baker et al.
climate
thereservoirs
of groundwater
thatweretappedin the formation [ 1991]modelis the needfor a late, transientgreenhouse
to
thaw
the
cryosphere
at
the
time
of
the
Chryse
flooding.
Baker
of the valley networksand outflow channelswere limited in
et
al.
[1991]
require
this
geologically
short
but
extreme
change
capacity
andisolatedwithrespect
to otherreservoirs
of groundwater present on the planet. However, as discussedin sec- in climate becausethey believe it to be the only way that the
tion3.2, investigations
of thekilometer-scale
permeability
of the large volumesof water dischargedby the outflow channelsand
Earth'scrustsuggestthat virtuallyall terrestrialgroundwater youngervalley networkscouldhave been reassimilatedinto the
systems
sharesomedegreeof hydraulicinterconnection.
Clearly, crust.This problemis viewedas critical not only becauseof the
if thisis trueof the Earth,with an inferredmeancrustalpermeability
of 10-2 darcies
[Brace,1980,1984],thenthecasefor
hydraulic
continuity
onMars,wheresomehavearguedfor largescalepermeabilities
asmuchas 105timeshigher[Carr, 1979;
present absenceof this water on the surface, but becausethe
networksandoutflowchannels
is that,ratherthandrawingon
small,isolated,and rapidlydepletedlocal sources
of groundwater,thesefeaturesmayhavetappedan enormously
largerand
self-replenishing
globalreservoir,wherebyany water that was
discharged
to the surfacewaseventually
balanced
by the introduction
of anequivalent
amount
backintotheaquiferthrough
the
warming.
magnitudeof erosionassociated
with the channelsimpliesa sustainedor episodicdischargethat Baker et al. [1991] believe can
only be explainedif the sourceregionswheresomehowreplenMacKinnon
andTanaka,1989],shouldbe significantly
stronger. ished.As notedby Carr [ 1991], however,thereis little geologic
The importance
of this argument
to the recharge
of the valley evidenceto supportsucha dramaticandrecentepisodeof global
In lightof theabove,is thereanycompelling
needto invokea
differentclimateto account
for the originof the valleynetworks
(eitherold or new) or the repeatedoccurrence
of catastrophic
floods?As discussed
in section4.4.3, impact-generated
hydrothermalsystems,suchas thoseproposed
by Newsom[1980] and
Brakenridge
et al. [1985],appearperfectlycapableof generating
processbasalmelting.
Yet, because
neitherthe likely extentof hydrauliccontinuity the valleynetworksfoundin the crateredhighlandseven under
withinthecrustnorthepotential
roleof basalmeltingarewidely current climatic conditions. The small number of more recent
recognized,most investigatorshave attemptedto addressthe networks, found on the flanks of Alba Patera and several other
canbe similarlyexplainedas the resultof local
problemof localgroundwater
depletion
by invokinglocalmech- largevolcanoes,
anismsof resupply.The commonproblemwith suchmechanisms hydrothermalactivity [Gulick and Baker, 1990]. In neither into invokea changein climatenor,givena
is thatoncegroundwater
hasbeendischarged
to the surface,it is stanceis it necessary
unableto infiltratebackthroughthefrozencrustto replenishthe hydrauliclink to a globalaquifer,any additionalmechanismof
systemfrom whichit was initially withdrawn.In supportof local resupply.
thisconclusionrecall that under currentclimaticconditions,the
A similarconclusion
is reachedregardingthe repeatedoccurthickness
of the cryosphere,
evenat the equator,is likely to renceof catastrophicfloods.As discussedby Carr [1979], one
exceed2 km (section2.2). Further,a necessary
prerequisite
for consequence
of the tectonicuplift of Tharsisis that it may have
the widespreadoccurrence
of groundwater
is that the thermo- placedthe frozencrustin the lower elevationsaroundChryse
dynamicsink represented
by the cryosphere
mustalreadybe Planitiaundera substantial
hydraulichead,leadingto its evensaturated
with ice. Thus,the cryosphere
actsas an impermeable tual failure and the catastrophic
releaseof groundwateronto the
self-sealing
barrierthateffectively
precludes
the localresupply surface.However,as the dischargecontinued,the localhydraulic
of subpermafrost
groundwater
eitherby the infiltrationof water head eventuallydeclinedto the point where the water-saturated
discharged
by catastrophic
floods,or by atmospheric
precipita- crustwas able to refreezeat the point of breakout,ultimately
tionon somehighlandsourceregion.Note thatthe problemof reestablishingthe original groundice thickness.The water relocal infiltrationand subsurface
replenishment
is not signifi- leasedby sucheventsmay haveformedtemporarylakes or seas
cantlyimprovedevenif the cryosphere
is initiallydry, for as thateventuallyfrozeandsublimedaway,with the resultingvapor
waterattemptsto infiltratethe cold, dry crust,it will quickly ultimatelycold-trappedat the poles.Such a processmay well
freeze,creatinga sealthatpreventsanyfurtherinfiltrationfrom explainthe originof the largepolarice sheetsinferredby both
the pondedwater above.
Allen [ 1979a] andBakeret al. [ 1991]. The identificationof posIndeed,virtuallythe only way a subpermafrost
groundwater sibleeskersnearthe southpolarcap[Carr et al., 1980;Howard,
systemcanbe directlyreplenished,
is if the interveningcryos- 1981; Kargel and Strom, 1992] is also consistentwith this interphereis somehow
thawedthroughout.
This is essentiallythe pretationand with the subsequentreassimilationof the water
explanation
advocated
by Bakeret al. [ 1991]to accountfor both intothecrustthroughtheprocess
of basalmelting.
11,008
•ORD:
HYDROLOGICANDCLIMATICBEHAVIOROFWATERON MARS
However,basalmeltingis not necessarilyrestrictedto just the
poles.As discussed
by Clifford [1987b], whereverthe deposition
and long-term retention of material occursat the surface, the
addedinsulationwill result in the upward displacementof the
melting isotherm at the base of the cryosphereuntil thermal
equilibriumis reestablished.
Thus, if the frozen lakesor seasthat
were formedby the dischargeof the outflow channelspersisted
formorethan105-106years,thelocalgroundwater
system
may
have been indirectly replenishedby the onset of melting at the
baseof the cryosphem.It is likely, however,that this replenishment was only temporary.For with the eventual sublimationof
the frozen lakes or seas on the surface, the melting isotherm
shouldhave returnedto its original location,creatinga cold-trap
at the baseof the cryosphemfor any vaporor liquid suppliedby
the groundwaterbelow (section 4.4.1). In this way, any water
that was temporarily liberated from the cryosphemby basal
melting,waseventuallyreassimilated
into the frozencrust.
Note that nothingin this proposedcycle is precludedby the
current climate. Indeed, given the continueduplift of Tharsis
and the probableoccurrenceof other crustal disturbances(such
as earthquakes,impacts,and volcaniceruptions),failures of the
cryosphem's
hydraulicseal were undoubtedlycommon.This suggeststhat the cycling of water by catastrophicfloods, surface
deposition,basal melting, and groundwaterrecharge,may have
been repeatedmany times throughoutgeologichistory, without
the need to invoke any special conditionsregardingeither the
geologyor climateof Mars.
ation,andthe fact that the polarregionsam the planet'sdominant
sinkforH20, howdoesoneaccount
forboththeyouthfulness
of
the presentdepositsand the apparentdeficit of older material at
the poles?
Clearly one possibilityis that the estimatedvolumeof water
suppliedto the polesby variouscrustalsourcesis wrong, and
that all of the water ever releasedto the atmosphereis now
storedin thepolarice. In that event,the apparentyouthfulness
of
the currentdepositsmight be explainedby the simpleracycling
of old polarlaminaeinto new [Toonet al., 1980]. This possibility is raised by current models of the evolutionof the polar
troughs[Howard, 1978; Howard et al., 1982]. These features,
whichform the conspicuous
spiralpatternsvisiblein the remnant
caps,are thoughtto originatenear the edgeof the depositsand
then migrate, throughthe preferentialsublimationof ice from
their equatorwardfacing slopes,towardthe pole. Dust, liberated
from the ice, may then be scavengedby the polar winds and
redistributedover the planet,while the sublimedice may simply
be recycledby cold trappingon the polewardfacing slopesand
on the flats that separatethe troughs.By theseprocesses,
Toonet
al. [1980] suggestthat the polar depositshave reacheda stateof
equilibrium
wherebyancient(•109 yearold) polarmaterialis
continuallymworked,maintaininga comparativelyyouthfulsurficial appearancein spiteof its greatage.
Althoughit is possiblethat the volumeof water suppliedto
the poles by various crustal sourcesis significantlyless than
current estimates, such a conclusion is inconsistent with both our
present understandingof the processesthat have affected the
7.2. The Polar Mass Balance and High Obliquities
evolution of the surface (sections 4.1 and 4.2) and with the
growingevidencethat Mars is waterrich [e.g., Carr, 1986, 1987;
It is generallyacceptedthat the Martian polar layereddeposits Squyres,1989]. The case for the local racyclingof old polar
owe their origin and apparentyouthfulnessto the annualdeposi- laminae is also at odds with the observations of Howard et al.
tionof dustandH20 andthatthe magnitude
of thisdeposition [1982], whosedetailedexaminationof the polar stratigraphyhas
has beenmodulatedby quasiperiodicvariationsin insolationdue revealedthat the erosionof equatorwardfacing scarpshas not
to changesin the planet'sorbital elementsand obliquity [Cuttset kept pace with layer deposition,an observationthat requiresa
al., 1979; Pollack et al., 1979; Toon et al., 1980]. On the basis of net long-termaccumulationof materialin the polar terrains.
Anotherpotentialsolutionto the massbalanceproblemis sugtheir evident thicknessand the scarcityof craterswith diameters
larger than 300 m, Plaut et al. [1988] estimatethat the present gestedby recenttheoreticalstudieswhich indicatethat the obliqdepositsaccumulatedat the rate of--10 km/b.y. over a time span uity of Mars is chaoticand may reachpeak valuesin excessof
of--108years.However,studies
by Fanaleet al. [1982,1986] 50ø [Bills, 1990; Ward and Rudy, 1991; Touma and Wisdom,
suggestthat conditionsconduciveto polar depositionare not 1993;Laskarand Robutel,1993].Undersuchconditions,periods
unique to the presentclimate but are characteristicof the planet of intensepolar erosionmay alternatewith periodsof accumulaover a broad range of likely obliquities and orbital variations. tion,redistributing
the polardustandH20 overmuchof the
Therefore,becausethe polar regionsrepresentthe planet'sdomi- planet.This possibilitywas first consideredby Jakoskyand Carr
nantthermodynamic
sinkfor H20, anycrustalwaterreleased
to [ 1985] in connectionwith the originof the valley networks.Their
the atmosphereshouldultimately be cold trappedat the poles.
work was based on the then acceptedbelief that, prior to the
Consideringonly those sourcesof water for which there is formationof Tharsis,Mars had experiencedobliquitiesas high
both unambiguous
evidenceand a reliable estimateof their min- as 45ø [Ward et al., 1979], valuesthat significantlyexceeded
imum volumetriccontribution(i.e., volcanismand catastrophic thosethat were thoughtto characterizethe planet after the defloods),we findthattheminimuminventory
of H20 thatshould velopmentof Tharsis( --11ø - 38ø [Ward, 1979]).
haveaccumulated
at the polesovergeologictime is equivalentto
Althoughthe length of time Mars spendsnear its maximum
a globallayer-*65
m deep(Table6), a volume
roughly
2-5 times. obliquity
duringa givencycleis brief(,--10
4 years),theresultgreaterthan that observedin the residualcaps.Given morereasonableestimatesof channeldischarge,as well as the volumes
of water contributedby the valley networks,impacts,and the
sublimationof equatorialgroundice, the disparitybetweenthe
expected and observedpolar inventories increasesby over an
orderof magnitude.Althoughthe water lost by atmospheric
escape (,*60 m, Jakosky [1990]) and oxidation of the regolith
(-*27 m, Owen et al. [1988]) may explain someof this discrepancy,theselossmechanismsfall considerablyshortof resolving
the imbalancefor any reasonableestimate of total crustal dischargeand expectedpolar inventory(Table 6). Given this situ-
ing increasein peak and mean annualinsolationat polar latitudescould affect the polar massbalancein severalimportant
ways.For example,Jakoskyand Carr [ 1985] havearguedthat, at
an obliquityof 45ø, summerpolar temperatures
may rise high
enoughto resultin the sublimationof 20 cm of ice from the per-
ennialcaps.Therefore,
overthe104 yearsthatsuchobliquities
persist,a total of as much as 2 km of ice might be removed
from the caps.Jakoskyand Carr [1985] suggestthat both dynamicalconsiderations
andcoldnighttimetemperatures
may conspire to limit the maximumdistancethat the resultingvaporis
transportedfrom the cap. This, they argue, could lead to the
•ORD:
HYDROLOGIC
ANDCliMATICBEHAVIOR
OFWATERONMARS
11,009
precipitation
of iceat low-andmid-latitudes,
withsurface
accu- 1988], and (4) satisfyall of the previousconditionswithin the
mulations
of up to several
tensof metersovertheduration
of the constraintimposedby the apparentdeficitof oldermaterialthat
highobliquity
portion
of thecycle.Theabsorption
of sunlight
in currentlyexistsat the poles.
by Clifford [1987b],the processof basalmelting
theresulting
snowpack,
couldthenleadto transient
summertime As discussed
Oncethe polardemeltingwhichtheysuggest
mayhavecontributed
to the forma- appearsto satisfyeachof theserequirements.
posits
have
reached
the
required
thickness
for
basal
melting,they
tionof the valleynetworksandthe replenishment
of equatorial
will
have
achieved
a
condition
of
relative
equilibrium,
whereby
reservoirs
of H20.
of anyH20 at theicecap'ssurface
will evenWhile the calculationsof Jakoskyand Cart [1985] clearly theaccumulation
demonstrate
the potentialfor significant
masslossat timesof tually be offsetby meltingat its base.Indeed,a geothermalheat
easily
keeppacewithan}t20depohighobliquity,thereareat leasttwoobservations
thatappearto fluxof30mWm-2K-1could
sition
rate
as
high
as
-*3
x
10
-3
m
yr
-l. Therefore
theoccurrence
significantly
constrain
boththemagnitude
of polarerosionand
the extentof equatorial
deposition.
Consider
first the casefor of basalmeltingis consistentwith boththe predictionof climate
equatorial
deposition
andmelting.A principleassetof theJako- models [Fanale et al., 1982, 1986] and the observationaleviskyandCart [1985]model,in thecontextit wasoriginallypro- dence[Howardet al., 1982], indicatingthat a long-termnet depposed,
wasthatit provided
a self-consistent
explanation
forboth ositionalenvironmenthasexistedat the poles.
the geographic
distribution
of valleynetworks(whichare concentrated
at equatorialandtemperate
latitudes[Cart and Clow,
8. QUALIFICATIONS
ANDPOTENTIAL
TESTS
1981])andtheir almostexclusiveoccurrence
in terrainsthat predatethedevelopment
of Tharsis[Cart and Clow,1981;Tanaka,
1986]. This self-consistency
breaksdown, however,with the
recognition
that Mars has likely experienced
high obliquities
throughout
its history,includingthe recentpast [Bills, 1990;
Wardand Rudy, 1991;Toumaand Wisdom,1993;Laskarand
Robutel,1993].Althougha few "young"
valleyshavebeenfound
A model of any natural processis necessarilya compromise
between the desire to consider all first-order effects, and the
practical reality that it must be simple enough to be readily
communicatedand understood.Unfortunately,the inherentcomplexity of real world systemsis often poorly representedwhen
describedin such general terms. With regard to the hydrologic and climatic behavior of water on Mars, the transport of
on Alba Pateraand severalother large volcanoes[Gulick and
the atmosphere,
overthe surface,andbeneaththe
Baker,1990],theirabsence
fromanyotherterrainsthatpost-date H20 through
Tharsisstrongly
suggests
anendogenic,
ratherthanexogenic,
ori- ground,involvesnumerousindividual processes,each of which
may be significantlyaffectedby naturalvariationsin the local or
globalenvironment.Spatialvariations,like local changesin the
thermophysical
propertiesof the crust,are perhapsthe best understoodand easiestto model. While characteristicslike poroslater than the formationof Tharsis (-3.5-4 b.y.a. [Wise et al., ity, permeabilityandheatflow, may changeappreciablyfrom one
locationto another,this variationis likely to occurwithin a fairly
1979]).
With regardto themagnitude
of polarerosion,boththe infer- well-definedrangeof limits basedon our knowledgeof the geolred108-year
ageof thepolardeposits
[Plautet al., 1988]andthe ogy of the Earth and Moon, and what we have deducedabout
apparentfrequency
of high obliquityexcursions
[Bills, 1990; Mars from spacecraftinvestigationsof its surface.Temporal
Wardand Rudy,1991;Toumaand Wisdom,1993;Laskarand changesare anothermatter.Some,like the declinein the planet's
Robutel,1993] appearto placea severeconstraint
on the mag- internalheatflow or the rise in solarluminosity,are evolutionary
nitudeof masslossthat the polestypicallyexperienceduring and, therefore,at least somewhatpredictable.The occurrenceof
such
periods.
Forexample,
if thelossamounted
to the---102-others,suchas a major impact,the catastrophicdischargeof an
103mperhighobliquity
cycleoriginally
suggested
by Jakosky outflow channel,or the long-termchaoticevolutionof the Marand Carr [1985],thenthe maximum"life cycle"of the deposits, tian obliquityand orbital elements,completelydefy prediction,
frombuild-upto erosion,
wouldnecessarily
be limitedto just a yet theirimpacton the localor globalenvironmentmay, at times,
few millionyears.Yet, if the inferred108-year
ageof the completelyoverwhelmall othereffects.It is the synergisticinterdeposits
is correct,
thentheyhavenotonlysurvived
a minimum actionof thesevariouselementsthat hasgovernedthe hydrologic
gin.Thus,if meltingandsurface
runoffhaseveroccurred
in association
with the development
of equatorialsnowpacks
at high
obliquity,
itscontribution
to theformation
of thevalleynetworks
andthereplenishment
of equatorial
H20 apparently
ceasedno
of 103obliquity
cycles(manyof whichshould
haveexceededand
climatic behavior of water on Mars.
with the absence of observationalevidence indicative of any
Clearly, giventhis manyfree parameters,the numberof possible permutations
of eventsand conditionsthat may have affected the Martian climate is virtually endless.One example is
the evidencefor polarwanderingpresented
by Schultzand Lutz
[1988]. As hasbeenstatedmanytimesin this analysis,givenour
massive,
widespread
erosion
of thepolarlaminae[Howardet al.,
presentunderstanding
of Martian climatichistory,a net long-
1982].
termlossof H20 fromtheequatorial
crustto theatmosphere
45ø),but have actuallyaccumulated
at the rate of--10 km/b.y.
[Plaut et al., 1988]. This fact is consistent
with previoustheoreticalstudiesindicatingthe existenceof a long-termnet depositionalenvironment
at thepoles[Fanaleet al., 1982, 1986]and
irreversible.
Thisconclusion
assumes,
however,thatthe
To summarize,
it appearsthat any solutionto the massbal- appears
locationof the p!anet's
spinaxishasremainedfixed
anceproblem
should
(1) beconsistent
withtheoretical
modelsof geographic
that Schultzand Lutz [1988] have
the Martian climate,whichindicatethat a net depositionalenvi- with time, an assumption
challenged.
Perhapsthe mostpersuasive
evidencefor
ronmenthasexistedat the polesthroughout
mostof the planet's vigorously
comesfromthe identification
of severalextenhistory[Fanaleet al., 1982,1986],(2) be ableto account
for the polarwandering
a
observational
evidencethatthe evolutionof the polar terrainshas sive antipodallayereddepositsnear the equatorthat possess
similaritiesto the polarlayered
indeedbeendominated
by depositional
processes
[Howardet al., numberof strikingmorphologic
1982],(3) be ableto accommodate
a rate of deposition,implied terrains. To account for these features, Schultz and Lutz [1988]
thatovera time scaleof severalbillionyears,the
bythepaucity
of craters
withinthedeposits,
of from10-5to haveproposed
in relationto
10-4myr-1[Cuttset al., 1976;Pollacket al., 1979;Plautet al., crustof Mars hasundergonea majorreorientation
11,010
•ORD:
HYDROLOGIC
ANDCI•MATICBEHAVIOR
OFWATERONMARS
its spin axis. They attribute this movementto changesin the
planet'smomentof inertia causedby the formationof Tharsis.
While the actual dynamicsnecessaryto producethis shift are
presentlyunclear,the slow migrationof the geographiclocation
of the poles providesa mechanismfor movingthe planet'scold
other active geothermalregions, would establishthat Mars is
bothwater-rich
andthatit possesses
an inventory
of H20 that
significantly
exceedsthe porevolumeof the cryosphere.
Second,
should it be found that the absolute elevation of the water table is
the sameat widely separatedlocations(disregardinglocal diftrapandatmospherically
replenishing
subsurface
H20 ona glob- ferencescausedby recenttectonicactivity,anomalousgeotheral scale.
mal heating,or prolongeddepositionat the surface),it would
It is important to note, however, that while polar wandering stronglyindicatethat groundwateron Mars has hydrostatically
[Schultzand Lutz, 1988], massivepolar erosionat high obliq- adjustedon a globalbasis,a conditionthat canonlybe reachedif
uities [Jakoskyand Carr, 1985], and recent transient global the systemis interconnected.
If this last conditionis actually
warming [Baker et al., 1991], may all have occurred,none of observed,it will essentiallyconfirmthe singlemostimportant
these scenariosis required to explain any aspectof the hydro- elementof the model presentedhere, that Mars possesses
an
groundwater
systemof globalextent.Sinceall the
logicevolutionof a water-richMars that cannotalreadybe satis- interconnected
factorilyexplainedunder the physicaland climaticconditionswe
observeon the planettoday.This conclusionis basedon only two
assumptions:
(1) that the physicalpropertiesof the Martian crust,
includingporosity,permeability,and crustalthermal conductivity, are no different then those which characterizethe Earth and
Moon, and (2) that Mars possesses
an inventoryof water that
exceedsthe pore volume of the cryosphereby as little as a few
percent. Given these conditions,basic physicsdictatesthat the
processes
of surfacedeposition,basalmelting,groundwaterflow,
andthe thermaltransport
of H20, will thermodynamically
and
hydraulicallylink the atmospheric,surface,and subsurfacereservoirsof wateron Mars into a singleself-compensating
system.
Althoughunequivocalevidenceof a planetary-scalegroundwater systemis currentlylacking,its existenceis consistentwith
the calculationspresentedin section2 and with the geomorphic
evidencethat Mars possesses
an inventoryof water equivalentto
a global ocean0.5-1 km deep [Carr, 1987]. More direct evidencethat sucha systemhasexistedthroughoutmuchof Martian
geologichistory is providedby the timing and thermodynamic
implicationsof the outflow channels.As discussedin section2.3,
a prior conditionfor the existenceof any largevolumeof groundwater is that the pore volumeof the cold-traprepresented
by the
cryospheremust first be saturatedwith ice. This conclusion
followsfrom the fact that,givenan availablereservoirof waterat
remainingelementsof the model follow from this foundation,
and from basicphysics,the greatestremaininguncertaintywill
be the extentto which basalmelting,groundwaterflow, and the
thermaltransport
of H20 in the crust,havecompeted
with, or
complemented,
other processes
in the transportof water above,
across, or beneath the Martian surface.
9. CONCLUSIONS
The analysispresentedhere leads to the following conclusions:
1. If theinventory
of H20 on Marsexceeds
by morethana
few percentthe quantityrequiredto saturatethe porevolumeof
the cryosphere,then a subpermafrostgroundwatersystemof
globalextentwill necessarilyresult.
2. Under the climaticconditionsthat have prevailedthroughout mostof Martian geologichistory,the inherentinstabilityof
equatorialgroundice has lead to a net atmospherictransportof
H20 fromthehotequatorial
regionto thecolderpoles.Theoretical arguments
andvariouslines of morphologic
evidencesuggest
thatthispoleward
fluxof H20 hasbeenaugmented
byadditional
releasesof waterresultingfrom impacts,catastrophic
floods,and
volcanism.
3. Based on the conditionspostulatedin conclusion1, the
depth,thermalprocesses
will supplyenough
H20 to saturate
the depositionand retentionof materialat the poles(or any other
cryosphere
in lessthan107years(sections
4.4.1and4.5).Since location)will eventuallyresultin basalmelting.The downward
the youngestoutflow channelsmay be less than 1 billion years percolationof meltwaterinto the underlyingglobal aquifer will
old[Tanaka,
1986;Tanaka
hfidScott,1986;Parker
etal., 1989;
then result in the rise of the local water table in the form of a
Mouginis-Mark, 1990; Rotto and Tanaka, 1991; Baker et al.,
1992], this suggests
that an inventoryof water in excessof that
storedin the cryosphere
has persistedon Mars until very recent
times,andmay continueto persistto the presentday.
While theoreticalarguments
for a planetary-scale
groundwater
systembasedon the thermodynamic
significanceof the outflow
channelsare interesting,theyfall shortof an actualproof.Unfortunately, at present,the channelsare the best evidencethat we
have. However, as the explorationof Mars continues,there will
be opportunities
for moredirectinvestigations
of the subsurface
that shouldresolvethis issueconclusively.While prospectsfor
a Mars Deep Drilling Project are likely to remain dim for the
foreseeablefuture, at least two other geophysicalmethods,active seismicexploration[Tittmann,1979;Zykovet al., 1988] and
electromagnetic
sounding[Rossiteret al., 1978;Ehrenbardet al.,
1983], couldbe usedto deteci xndmapthe distributionof ground
ice andgroundwaterbeneatt,theplanet'ssurface.
Assumingthat such investigationsare actually conducted,
what observations
would provideconclusiveevidencethat Mars
possesses
an interconnected
groundwatersystemof globalscale?
First, the detectionof groundwaterat locationsfar removedfrom
any obvioussourceof transientproduction,suchas volcanoesor
groundwatermound.
4. Given a geologicallyreasonablevalue of large-scaleper-
meability
(i.e., •>10-2 darcies),
thegradient
in hydraulic
head
createdby the developmentof groundwater
moundsat bothpoles
could drive the equatorwardflow of a significantvolume of
groundwater
(->108km3 H20) overthecourse
of theplanet's
history.
5. At equatorialand temperatelatitudes,the presenceof a
geothermalgradientwill resultin a net dischargeof the groundwater systemas vapor is thermally pumpedfrom the warmer
(highervapor pressure)depthsto the colder(lower vaporpressure) near-surfacecrust. By this processa gradientas small as
15K km-I coulddrivethe verticaltransport
of 1 km of water
tothefreezingfrontat thebaseof the cryosphere
every106107years,or theequivalent
of a 102-103
km of wateroverthe
4.5 billion yearhistoryof the planet.In this manner,muchof the
groundice that has been lost from the crustmay ultimatelybe
replenished.
While particularaspectsof the modelpresentedin this paper
may be debated(e.g., the actualporosityand permeabilityof the
crust,the magnitudeof polar deposition,etc.), the occurrence
of
subsurface
transporton Mars is essentiallycontingenton a single
•ORD:
HYDROLOGIC
ANDCI•MATICBEHAVIOR
OFWATERONMARS
factor:doesthe presentplanetary
inventory
of H20 exceed,by •rtI stearn
morethana few percent,the quantityof water requiredto saturate the pore volumeof the cryosphere?
If so, then basicphysics
suggests
that the hydrologicmodeldescribedhere will naturally
evolve.Given a geologicallyreasonabledescriptionof the crust,
thequantity
of H20 transported
through
thesubsurface
maythen
play an importantrole in the geomorphicevolutionof the Mar-
tiansurface
andthelong-term
cycling
of H20 between
theatmosphere,polarcaps,and near-surfacecrust.
Acknowledgements.
The fast draft of this paper was written in 1980.
Sincethattime,boththepaperandtheideaspresented
in it, havehada long
andtortuous
evolution.Bothhavebenefitedfrom theinputI•te receivedfrom
manyfriendsandcolleagues.
I wouldespeciallylike to thankBruceJakosky,
FraserFanale,MichaelCarr,DanielHillel, Geo•e McGill, Bill Irvine, Peter
Schloerb,Bruce Bills, Mark Cintala,DeborahDomingue,Jim Zimbelman,
ScottMurchie, Karen Miller and JoseValdez, for havingreviewedearlier
drafts of this paper and providedmany helpfid suggestions
for its improvement.I would alsolike to thankPeteSchultz,Matt Golembek,Lisa
Rossbacher,
StevenSquyres,Mike Malin, RuslanKuzmin, Alan Howard,
Laurie Johansen,Peter Mouginis-Mark,Nadine Barlow, Bob Miller, and
Ken Tanaka,for havingindulgedme in many extendeddiscussions
about
water on Mars. My thanksalsoto AmandaKubala and Brian Fessler,who
throughthe yearshaveprovidedinvaluableprogrammingand technicalassistance,
and to Fran Waraniusand StephenTellier, who locatedcopiesof
countless,
butmuchneeded,references.
I am especiallygratefulandindebted
to the followingpeople:to Bob Huguenin,who providedmuchof the initial
encouragement,
freedom,andfinancialsupportthatallowedme to beginthis
research;
to Kevin BurkeandDavid Black, who havegenerouslycontinued
that supportwhile I•te beenat LPI; to my friend JonathanEberhart,who
helpeda very frightenedgraduatestudentmake it throughhis fast professionaltalk; and, most of all, to my wife Julie and daughterMiranda,
withoutwhoselove andsupport
I wouldhavegiventhisup longago.This researchwassupported
by theLunarandPlanetaryInstitute,whichis operated
by the UniversitySpaceResearchAssociationunder contractNo. NASW4574 with the National Aeronauticsand SpaceAdministration,and by a
grantfrom NASA's PlanetaryGeologyand Geophysics
Program.LPI Con-
radius, m.
time, s.
temperature,K.
initial impactmelt temperature,1473 K.
final impactmelt temperature,K.
meltingpointtemperature,K.
mean annualsurfacetemperature,K.
temperatureintervalover which steamis heated,K.
temperatureintervalover which water is heated,K.
= a2ved4kgh t.
projectileimpactvelocity,m s4.
aquiferspecificdischarge,m s-1.
basalslidingvelocity,m s-1.
impactmelt volume,km3.
maximumvolumeof transientcratercavity, m3.
aquiferrechargerate, m
well functionfor a nonleakyaquifer.
depth,m.
NOTATION
radiusof basalmelting/rechargearea, m.
heatcapacityof water,2092 J kg-1K -I.
heatcapacityof steam,4186 J kg4 K-l.
volumetricheatcapacityof impactmelt, 4.2 x 106J
m-3 K4.
DAB
bulk moleculardiffusioncoefficientof H20 in CO2,
cm 2 s-l.
Dc
D•.•
transitiondiameterbetweensimpleandcomplex
cratermorphology,-6 km on Mars.
effectivediffusioncoefficientof H20 in CO2, cm2 s4.
final crater diameter, m.
Dtc
g
h
hm
Knudsendiffusioncoefficientof H20, cm2 s-l.
diameterof transientcratercavity, m.
projectilekineticenergy,J.
seismicenergy,J.
meanMartian accelerationof gravity,3.71 m s-2.
heightabovelocal datum,m.
initial heightof watertable abovelocal datum, m.
centralheightof groundwatermoundabovelocal
datum, m.
h
H
k
gMars
steammasstransportedby hydrothermalconvection,
kg m-2.
Gutenberg-Richter
magnitudeof seismicevent.
molecularweightof H20, 0.018 kg mo14.
total gaspressure,dynescm-2.
vaporpressureof H20, dynescm-2.
thermallyinducedliquid flux, m s-1(per unit area).
thermallyinducedvaporflux, m s-I (perunitarea).
= 2hah v, radial dischargethroughaquifer,m3 s-l.
frictionalheat due to glacial sliding,W m-2.
geothermalheatflux, W m-2.
= • a2 w, aquiferrechargevolume, m3 s4.
heat contentof impactmelt, J m-2.
universalgasconstant,8.314 J mol-I K-l.
watervaporgasconstant,461.9 J kg-I K -l.
heatgenerationper unit volumeof planet,W m-3.
tribution No. 807.
a
11,011
= .5 (h + hi), weightedmeandepthof saturation,m.
polardepositthicknessrequiredfor basalmelting,m.
crustalpermeability,m:.
frozenpermeability,m2.
porositydecayconstant,2820 m.
latentheat of fusionof H2¸, 3.35 x 105J kg-•.
latentheatof vaporizationof H20, 2.3 x 106J kg-•.
thickness, m.
= h2 _ hi2, m2.
(= •pc), thermaldiffusivity,m2 s4.
empiricaldimensionless
factor [Cary, 1966], 1.83 +
œ
0.79.
effective
porosity.
thermal
conductivity,
•h :!•1.00-- 100%.
crustal
porosity
atadeptf
collisionalmeanfree path of an H20 moleculein the
Martian atmosphere,- 10 gm.
kinematicviscosity,m2 s-•.
density,kg m-3.
basal shear stress, Pa.
soil water potential,Pa.
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