A Model for the Hydrologic and Climatic Behavior of Water on Mars

Home , Aeolis quadrangle, Aquifer, Bouguer (Martian crater), Clausius (crater), Climate of Mars, Deuteronilus Mensae

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 98, NO. E6, PAGES 10,973-11,016, JUNE 25, 1993

A Model for the Hydrologicand Climatic Behavior of Water on Mars

STEPHEN M. CLIFFORD

Lunar and Planetary Institute,Houston, Texas

Paststudies of the climaticbehavior of wateron Mars haveuniversally assumed that the atmosphereis the sole pathwayavailable for volatileexchange between the planet'scrustal and polar reservoirs of H20. However,if the planetaryinventory of outgassedH20 exceedsthe pore volume of thecryosphere by morethan a few percent,then a subpermafrostgroundwater system of globalextent will necessarilyresult. The existenceof sucha systemraises the possibilitythat subsurface transport may complementlong-term atmospheric exchange. In thispaper, the hydrologic responseof a water-richMars to climatechange and to the physicaland thermal evolution of its crustis considered. The analysisassumes that the atmosphericleg of the planet'slong-term hydrologic cycle is reasonablydescribed by current models of insolation-drivenexchange. Under the climatic conditionsthat have apparentlyprevailed throughoutmost of Martiangeologic history, the thermalinstability of groundice at low- to mid-latitudeshas led to a netatmospheric transport of H20 fromthe "hot"equatorial region to the colderpoles. Theoretical arguments and variouslines of morphologicevidence suggest that thispoleward flux of H20 hasbeen episodically augmented by additionalreleases of water resultingfrom impacts,catastrophic floods, and volcanism.Given an initially ice- saturatedcryosphere, the deposition of materialat thepoles (or any otherlocation on the planet'ssurface) will result in a situationwhere the local equilibrium depth to the meltingisotherm has been exceeded, melting ice at thebase of the cryosphereuntil thermodynamicequilibrium is once again established.The downwardpercolation of basal meltwaterinto the globalaquifer will resultin the riseof the local watertable in the form of a groundwatermound. Given geologicallyreasonable values of large-scalecrustal permeability (i.e., >•10 -2 darcies),the gradientin hydraulichead created by the presenceof the moundcould then drive the equatorwardflow of a significantvolume of groundwater(>• 108 km 3) overthe courseof Martiangeologic history. At temperateand equatorial latitudes, the presenceof a geothermalgradient will then result in a net dischargeof the systemas water vapor is thermally pumpedfrom the highertemperature (higher vapor pressure)depths to the colder (lower vapor pressure)near- surfacecrust. By thisprocess, a gradientas smallas 15 K km-1 coulddrive the verticaltransport of 1 km of water to thefreezing front at thebase of the cryosphereevery 106-10 7 years,or theequivalent of -102-103 km of water overthe courseof Martian geologichistory. In thismanner, much of the H20 that hasbeen lost from the crustby the sublimationof equatorialground ice, impacts,and catastrophicfloods may ultimately be replenished.The validity of this analysisis supportedby a detailedreview of relevantspacecraft data, discussionsof lunar and terrestrialanalogs, and the use of well-establishedhydrologic models. Among the additionaltopics discussed are the thermaland hydrologic properties of the crust,the potentialdistribution of groundice and groundwater,the thermal evolutionof theearly cryosphere, the rechargeof thevalley networksand outflowchannels, the polarmass balance, and a reviewof severalimportant processes that are likely to drive the large-scalevertical and horizontaltransport of H20 beneaththe Martian surface.Given a geologicallyreasonable description of the crust,and an outgassed inventoryof waterthat exceeds the porevolume of the cryosphereby just a few percent,basic physics suggests that thehydrologic model described here will naturallyevolve. If so, subsurfacetransport has likely playedan important rolein the geomorphicevolution of theMartian surface and the long-term cycling of H20 betweenthe atmosphere, polarcaps, and near-surface crust.

CONTENTS The Stability and Replenishment of Equatorial H20 ...... 10,985 The Stability of Equatorial Ground Ice ...... 10,985 Introduction ...... 10,974 Other Crustal Sources of Atmospheric Water ...... 10,987 The Geophysical Basis for a Global Groundwater Evidence of Ground Ice Replenishment ...... 10,988 System on Mars ...... 10,974 Processes of Replenishment ...... 10,989 Porosity Versus Depth ...... 10,975 Transport Through the Cryosphere ...... 10,993 Thermal Structure ...... 10,976 Polar Deposition, Basal Melting, and the Physical The Distribution of Groundwater ...... 10,978 Requirementsfor Pole-to-Equator Groundwater Flow ...... 10,995 Terrestrial Analogs: The Occurrence of Groundwater Polar Basal Melting ...... 10,995 and the Permeability of the Earth's Crust ...... 10,980 Growth of a Polar Groundwater Mound ...... 10,997 The Occurrence of Groundwater ...... 10,981 The Effect of Crustal Permeability on Pole-to-Equator The Large-Scale Permeability of the Earth's Crust ...... 10,981 Groundwater Flow ...... 11,000 Local and Regional Groundwater Flow ...... 10,983 Examples of Large-Scale Terrestrial Groundwater The Large-Scale Permeability of the Martian Crust ...... 11,001 Flow Systems ...... 10,983 The Early Evolution of the Martian Hydrosphere and Climate ...... 11,002 The Evolution of the Early Martian Climate and the Copyright1993 by the AmericanGeophysical Union Initial Emplacementof Crustal H20 ...... 11,002 Papernumber 93JE00225. The Hydrologic Response of Mars to the Thermal 0148-0227/93/93JE-00225505.00 Evolution of Its Early Crust ...... 11,003

10,973 10,974 CLIFFORD:HYDROLOGIC AND CI_IMATIC BEHAVIOR OF WATER ON MARS

Further Considerations ...... 11,006 meltwaterbeneath the polar capswill then result in the rise of Recharge of the Valley Networks and the localwater table in the form of a groundwatermound. Given Outflow Channels ...... 11,007 geologicallyreasonable values of crustalpermeability, the gra- The Polar Mass Balance and High Obliquities ...... 11,008 dientin hydraulichead created by the presence of themound will Qualifications and Potential Tests ...... 11,009 then drive the flow of groundwateraway from the poles and Conclusions ...... 11,010 towardsthe equator.At equatorialand temperatelatitudes, the Notation ...... 11,011 presenceof a geothermalgradient will result in the local dischargeof the systemas water vapor is thermally pumpedfrom the higher temperature(higher vapor pressure)depths to the 1. INTRODUCTION colder(lower vaporpressure) near-surface crust. In this fashion, Virtually all past studiesof the climatic behaviorof water on much of the groundice and groundwaterthat has been removed Mars have focused on the potential for insolation-drivenex- from the crust by impacts, catastrophicfloods, and long-term changebetween the regolith, atmosphere,and polar caps [e.g., sublimation,may ultimatelybe replenished. Leighton and Murray, 1966; Toon et al., 1980; Fanale et al., Variousaspects of this model, includingthe inherentinstabil- 1982, 1986]. Implicit in this work has been the assumptionthat ity of equatorialground ice [Clifford and Hillel, 1983], and polar the atmosphereis the sole pathway available for volatile ex- basal melting [Clifford, 1987b], have been discussedin detail change.However, if the planetaryinventory of outgassedH20 elsewhere.The focusof this paperwill thereforebe on thoseas- exceedsby morethan a few percentthe quantityrequired to satu- pectsof the hydrologicresponse of Mars to climate changethat rate the pore volumeof the cryosphere(that regionof the crust have so far receivedlittle or no attention,with particularempha- where the temperatureremains continuously below the freezing sis on the potentialrole of subsurfacetransport. Among the top- point of water), then a subpermafrostgroundwater system of ics discussedare the thermal and hydrologicproperties of the global extent will necessarilyresult. As discussedby Clifford crust, the potentialdistribution of groundice and groundwater, [198lb, 1984], the existenceof sucha systemmay have playeda the stability and replenishmentof equatorialground ice, basal criticalrole in the long-termclimatic cycling of wateron Mars. meltingand the polar massbalance, the thermalevolution of the This paper examinesthe potentialhydrologic response of a early cryosphere,the rechargeof the valley networksand outflow water-richMars to both climate changeand to the physicaland channels,and a review of several processesthat are likely to thermalevolution of its crust.It is basedon the ad hoc assump- drivethe large-scalevertical and horizontaltransport of H20 tion that Mars possessesa global inventoryof water sufficientto within the crust. Throughoutthis discussionit is assumedthat both saturatethe pore volume of the cryosphereand create a the atmosphericleg of the long-termhydrologic cycle is reason- groundwatersystem of global extent. Evidencefor sucha large ably describedby currentmodels of insolation-drivenexchange inventoryis providedby a long list of Martian landformswhose [Toon et al. 1980; Fanale et al. 1982, 1986]. Therefore,this pa- morphologyhas been attributed to the existenceof subsurface per will emphasizethe geologicrequirements and actualphysics volatiles [Rossbacher and Judson, 1981; Carr, 1986, 1987; of subsurface flow. Squyres,1989]. In particular,it is supportedby the existenceof Finally, it shouldbe stressedagain that this is a theoretical the outflow channels,whose distribution, size, and rangeof ages, analysis,one whose scope is purposelyrestricted to consideration suggeststhat a significantbody of groundwaterhas been pres- of the hydrologicevolution of a water-richMars. For this reason, ent on Mars throughoutmuch of its geologichistory [Baker, no attempthas been made to conclusivelydemonstrate that Mars 1982; Tanaka, 1986; Tanaka and Scott, 1986; Carr, 1986, 1987; is indeedwater-rich, or that it possessesan inventoryof water Mouginis-Mark, 1990; Baker et al., 1992]. Based on a conserva- sufficientlylarge to form a groundwatersystem of global extent. tive estimateof the dischargerequired to erodethe channels,and Rather, the volumeof water requiredto satisfythis conditionis the likely extent of their original sourceregion, Carr [1986, estimatedand its potential hydrologicconsequences explored. 1987] estimatesthat Mars may possessa crustal inventory of The resultsof this analysissuggest that, given a geologically waterequivalent to a globalocean 0.5-1 km deep. reasonabledescription of the physicalproperties of the planet's Under the climatic conditionsthat have apparentlyprevailed crustand an inventoryof water that exceedsthe pore volumeof on Mars throughoutmost of its geologichistory, ground ice is un- the cryosphereby as little as a few percent,the hydrologicmodel stablewith respectto the water vaporcontent of the atmosphere describedhere will naturallyevolve. If so, subsurfacetransport at latitudesequatorward of +40ø [Toon et al., 1980; Clifford and has likely playedan importantrole in the geomorphicevolution Hillel, 1983; Fanale et al., 1986]. As a result, the inventoryof of theMartian surface and the long-term cycling of H20 between equatorialground ice is thoughtto haveexperienced a steadyde- the atmosphere,polar caps, and near-surface crust. cline. Becausethe cold polar regionsare the dominantthermo- dynamicsink for anyH20 releasedto theatmosphere, there is a 2. THE GEOPHYSICAL BASIS FOR A GLOBAL preferentialtransfer of H20 fromthe comparatively 'Not" equa- GROUNDWATER SYSTEM ON MARS torial regionto the colderpoles. Theoretical arguments and variouslines of morphologicevidence suggest that this polewardflux The existenceof a globalgroundwater system on Mars is nec- of H20 hasbeen augmented throughout the planet'shistory by essarilysubject to certaingeologic constraints; the mostobvious additionalreleases of water resultingfrom impacts,catastrophic of whichis that theremust exist a suitablyporous and permeable floods, and volcanism.The subsequentdeposition of dust and layer in which the groundwatercan reside. In this sectionthe H20 at the poleswill ultimatelyresult in a situationwhere the evidencesupporting the existenceof sucha layer is summarized. thermalequilibrium depth to the meltingisotherm has been ex- In addition,several relevant parameters are discussed,including: ceeded.In responseto this deposition,melting will begin and the variationof porositywith depth,the thermal structureof the continueat the base of the polar cryosphereuntil thermal equi- crust, and how these two factors interact to influence the state librium is once again established.The downwardpercolation of anddistribution of waterwithin the crust. •ORD: HYDROLOGICAND CLIniC BEHAVIOROF WATER ON MARS 10,975

2.1. Porosity VersusDepth Toddet al., 1973; Siegfriedet al., 1977]. Still greaterpressures (>>10 kbar) are often necessaryto eliminateprimary porosity, Impact processeshave played a major role in the structural evolution of the Martian crust [Soderblom et al., 1974; Gurnis, suchas vesiclesin basaltor the intergranularpore space of sedi- mentaryrock [Birch, 1961; Gold et al., 1971; Todd et al., 1973; 1981]. Field studiesof terrestrial impact craters [Shoemaker, 1963; Short, 1970; Dence et al., 1977] and theoretical models of Siegfriedet al., 1977]. Thus, any estimateof crustalporosity, the crateringprocess [Melosh, 1980, 1989; O'Keefeand Ahrens, basedon the assumptionof a 1 kbar closurepressure, is nec- 1981] have shownthat impactsmodify the structureof a plane- essarilyconservative. tary surfacein at leasttwo importantways: (1) by the production Binderand Lange [1980] suggest that the seismicproperties and dispersalof large quantitiesof ejecta, and (2) throughthe of thelunar crust are best described by an exponentialdecline in intensefracturing of the surroundingand underlyingbasement. porositywith depth, a relationshipthat is consistentwith that Fanale [1976] has estimated that over the course of Martian observedin manygeologic environments on Earth [e.g., Athy, geologichistory, the volumeof ejecta producedby impactswas 1930;Schmoker and Gautier,1988]. According to thismodel, the sufficientto createa global blanketof debris up to 2 km thick. porosityat a depthz is givenby As notedby Carr [1979], it is likely that this ejecta layer is in- ß (z) -- cI)(O)exp(-z/K) (1) terbeddedwith volcanicflows, weatheringproducts, and sedimentarydeposits, all overlyingan intenselyfractured basement where•(0) is the porosityat the surfaceand K is the porosity (Figure 1). This descriptionof the Martian crust is essentially decayconstant. identical to that proposedby Hartmann [1973, 1980] for the Assumingthat the densityof the Martiancrust is comparable near-surfaceof the Moon, where the early period of intense to its lunarcounterpart, the inferredvalue of the lunarporosity bombardmentis believed to have resultedin the productionof decayconstant (-6.5 km) canbe gravitationallyscaled to find the a blocky, porous "megaregolith"that extends to considerable appropriatevalue for Mars, i.e., depth,a view that is supportedby the seismicpropagation char- acteristicsof the lunar crust [Toks6z et al., 1972, 1974; Toks6z, K Mars- 6.5 km (g Moon/ g Mars) 1979]. = 2.82 km. For the near-surface of the moon, P wave velocities increase with depthuntil they reacha local maximumat about20-25 km wheregMoon (=1.62 m s -2) and gMars (=3.71 m s -2) are the gravi- [Toks6zet al., 1972, 1974; Simmonset al., 1973; Toks6z, 1979]. tational accelerationsat the surfaceof the Moon and Mars, re- This behavior is consistentwith a reduction in crustal poros- spectively. ity with increasinglithostatic pressure. The transitionbetween Two potentialporosity profiles of the Martian crust are illus- fractured and coherent lunar basement is believed to coincide trated in Figure 2. The first is basedon a surfaceporosity of with the beginningof the constantvelocity zone at a depth of 20%, thesame value assumed for theMoon by Binderand Lange -20 km, where the lithostaticpressure is thoughtto be sufficient [1980], and one that agreesreasonably well with the measured (>1 kbar-- 108Pa) to closevirtually all impact-generatedpore porosityof lunar breccias[Warren and Rasmussen,1987]. This space[Toksb'z et al., 1972, 1974; Toks6z,1979]. modelyields a self-compactiondepth (the depthat which crustal A closurepressure of 1 kbar is consistentwith mostlaboratory porosityfalls below 1%) of approximately8.5 km. By integrating studiesof fracturedigneous rock [Birch, 1961; Siegfriedet al., theporosity of the crustdown to thisdepth, the totalpore volume 1981], but pressuresin excessof 5 kbar are sometimesrequired is foundto be sufficientto storea globallayer of waterapproxi- mately 540 m deep [Clifford, 198l a]. to ensurethe closureof all fractureopenings [Gold et al., 1971; In the secondprofile, a surfaceporosity of 50% is assumed,a value consistentwith estimatesof the bulk porosityof Martian

POROSITY (PERCENT) Crater ejecta 00 10 20 30 40 50 Volcanic flows

= 20% Increasing Weathering products '.:.'..L..-.'.1....ß.• ...... :.:•...:• : C5 depth .• ...... 3!57:..r•'. Sedimentary deposits ß.:. .. •,(o) = 50%

Basement fractured in situ. -10

Fig. 2. Theoreticalporosity profiles of theMartian crust based on the lunar modelof Binder and Lange [1980]. The curvebased on a surfaceporosity I I I I I Self-compactiondepth of 20% is simplythe lunar model of Binderand Lange [1980] gravitationally scaledto Mars.The curvecorresponding to a surfaceporosity of 50% is includedto accountfor the possibilitythat various processes of physicaland Fig. 1. An idealized stratigraphiccolumn of the Martian crust Clifford chemicalweathering and large-scale ice segregationmay havesubstantially [1981a, 1984]. increasedthe availablepore space in theouter crust [Clifford, 1984, 1987a]. 10,976 CLI•ORD: HYDROLOGICAND CLIMATICBEHAVIOR OF WATER ON MARS soil as analyzedby the Viking Landers[Clark et al., 1976]. A formationof extensivebodies of subpermafrostgroundwater surfaceporosity this largemay be appropriateif the regolithhas [Clifford,1981 b, 1984].The fate andduration of groundwateron undergonea significantdegree of weathering[e.g., Malin, 1974; Mars is thereforecritically dependent on both the size of the Huguenin,1976; Gooding,1978] or if it containslarge segre- planetaryinventory of H20 andtotal pore volume of the frozen gatedbodies of groundice. The self-compactiondepth predicted crust. by this modelis roughly11 km, while its total pore volumeis equivalentto a globalocean some 1.4 km deep[Clifford, ! 984]. 2.2. Thermal Structure This pore volumeis likely an upperlimit, for it seemsdoubtful that weatheringor large-scaleice-segregation will affect more The Martiancryosphere is definedas that regionof the crust thanthe upperfew kilometersof the crust.Below this depth, the wherethe temperatureremains continuously below the freezing point of water (Figure3) [Fanale, 1976;Rossbacher and Judson, porosityprofile will most likely resemblethe gravitationally scaledlunar curve. The physicalcharacteristics of both models 1981;Kuzmin, 1983]. If we assumea solute-freefreezing point of are summarized in Table 1. 273 K, thenat the surfacethis condition is satisfiedat everylati- The presenceof groundwatercould affect estimatesof the tudebelow the diurnalskin depth, thus defining the cryosphere's self-compactiondepth and total pore volumein severalways. upper bound.However, because neither the magnitudeof the As discussedby Hubert and Rubey[1959] and others[Byeflee Martiangeothermal heat flux nor the thermalconductivity of the:' and Brace, 1968; Brace and Kohlstedt,1980; Thompsonand crustare known,the depthto the lowerbound of the cryosphere is considerablyless certain. Cormoily,1992], the hydrostaticpressure of waterwithin a pore The depthto the baseof the cryospherecan be calculatedfrom can partially offset the lithostaticpressure acting to close it. the steadystate one-dimensional heat conduction equation, where Thus,for a "wet"Mars, crustalporosity may persistto depths roughlya third greaterthan those indicated by the "dry"models in Figure2. However,groundwater can also reduce crustal porosity by solution,compaction, and cementation[Maxwell, 1964; z = • (2) Rittenhouse,1971]. Suchprocesses are of greatestsignificance Qg under conditionsof high temperatureand pressure[Maxwell, 1964; Petrijohn, 1975]. Currently, these conditionsare likely to andwhere •cis the thermal conductivity ofthe crust, Trap is the exist only at great depth on Mars, where their impact on the meltingtemperature of the ground ice, Tins is themean annual overall porosityof the megaregolithis expected to be small. surfacetemperature, andQg is the value of the geothermal heat However, conditionswere almostcertainly different in the past. flux [Fanale,1976]. At present,only the current latitudinal range For example,models of the thermalhistory of Mars suggestthat of mean annualsurface temperature is known to any accuracy 4 billion years ago the planet'sinternal heat flow was some3- (-154-218 K +5 K), while the remainingvariables have asso- 5 times greaterthan it is today [Toksrz and Hsui, 1978; Davies ciated uncertaintiesof 20-50%. Plausible rangesfor each of these variables are discussed below. and Arvidson, 1981; Schubertand $pohn, 1990]. In addition,the existenceof an early atmosphericgreenhouse may have permit- 2.2.1. Thermalconductivity. Four principalfactors influence ted liquid water to exist at or near the surface,where it may have the thermalconductivity of terrestrialpermafrost, they are: bulk reactedwith atmosphericCO 2 to formextensive carbonate de- density,degree of pore saturation,particle size, and temperature positswithin the crust [Kahn, 1985; Postawkoand Kuhn, 1986; [Clifford and Fanale, 1985]. The effect of an increasein bulk Kasting, 1987; Pollack et al., 1987]. The extent to which such density(and/or pore saturation)on the thermalconductivity of processesmay have affectedthe porosityand depthof the mega- permafrostis readily understoodbecause the conductivitiesof regolithis unknown. rockand ice are significantlyhigher than the conductivityof the Whether Mars oncepossessed a warmer, wetter climate [Ma- air they displace.However, the effectsof particlesize and tem- surskyet al., 1977; Pollack et al., 1987], or a climate that has al- peratureare a bit morecomplicated. ways resembledthe conditionswe observetoday [Soderblom and Experiments have shown that thin films of adsorbedwater Wennet, 1978], as the interior of the planet graduallycooled, a remainunfrozen on mineralsurfaces down to very low tempera- fleezing-frontdeveloped within the crust that propagateddown- tures[Anderson et al., 1967;Anderson and Tice, 1973], particu- ward with time [Cart, 1979] (see also section6.2). If the total larly in the presenceof potentfleezing point depressorssuch as pore volume of this frozen region grew to exceedthe planetary inventory of water, then eventually all of the water on Mars NorthPolar Cap SouthPolar Cap should have been cold-trappedwithin the frozen near-surface crust [Soderblomand Wennet, 1978]. Alternatively, if the pore _...... ,...... ;...... _ ...... volume of this regionis less than the planetaryinventory of outgassedwater (defined here as the sum total of chemicallyun- ...... :.:;!::::;:t;i.?;?;'• ?'?'•"•'.::;?i!?.;.:);.{'::;i':i:•':i'i}• MeltingCyosphe Isotherm e• •'•"":•:';'?'•?.ii•.';;?:'.::.; boundwater presentin the planet'satmosphere, on its surface,or withinits crust),then the excess H20 shouldhave resulted in the

Fig. 3. A pole-to-polecross section of the Martian crust illustratingthe TABLE 1. CalculatedMegaregolith Characteristics theoreticallatitudinal variation in depthof the freezingfront at the baseof thecryosphere. Note that groundice canexist in equilibriumwith the atmos- SurfacePorosity Self-Compaction StorageCapacity phereonly at thoselatitudes and depths where crustal temperatures are below the frost point of atmosphericwater vapor [-198 K, Farmer and Doms, (I)(0),% Depth,km x107 km 3 mH20 1979].Outside these locations, ground ice canonly surviveif it is diffusively 20 8.5 7.8 540 isolatedfrom the atmosphereby a regolithof low gaseouspermeability [e.g., 5O 11.0 20 1400 Smoluchowski,1968; Clifford and Hillel, 1983; Fanale et al., 1986]. Figureadapted from Fanate [ 1976]and Rossbacher and Judson[ 1981]. •ORD: HYDROLOGICAND CLIMATIC BEHAVIOR OF WATER ON MARS 10,977

NaC1and CaCI 2 [Baninand Anderson, 1974]. Because the thermalconductivity of unfrozen water (-0.54 W m-I K-I [Penner, /2

1970])is significantlylower than that of ice(2.25 W m-l K-I at 3b 273 K), its presencewill necessarilydecrease the effectivether- 14a mal conductivityof silicate-icemixtures. Since the quantity of •5 16 H20 adsorbedper unit surfacearea is roughlyconstant for all 7 8a mineral soils [Puri and Murari, 1963], it follows that the con- 8b Frozen Soil ductivity of a frozen soil will be proportionalto its contentof high specificsurface area clay. However,as the temperatureof a

frozen soil declines, so too does its content of adsorbed water 19c 10a [Andersonet al., 1967; Anderson and Tice, 1973]. This results in lob 11 an increasein the soil'seffective conductivity, an increasethat is 12a compoundedby the strongtemperature dependence of the ther- 12b mal conductivityof ice, whichrises from 2.25 W m-1 K-I at 114 Basalt 115 273K, to 4.42W m-1 K-1 at 160K [Ratcliffe,1962]. I I I I I Althougha directmeasurement of the bulk thermalconductiv- o 1 2 3 4 5 6 ity of the Martian megaregolithis lacking,a likely rangeof values can be inferred by consideringterrestrial analogs. Images of Thermal Conductivity(W m K the surfacetaken by the Viking spacecraftsuggest that the li- Fig. 4. Thermalconductivities of frozensoil and basalt[Clifford and thologyof theupper few kilometersof thecrust varies from a Fanale,1985]. loosefine-grained regolith to meter-sizedblocks of ejecta, all in- tercalatedwith a significantquantity of volcanics[Greeley and Spudis,1981; Greeley, 1987; Arvidsonet al., 1989]. If so, then samplesrange from 0.08-4.0 W m-1 K-1, withan average value thermalproperties of the megaregolithshould be closelyapproxi- of-1.66 W m-1 K-i; while the basaltconductivities exhibit a matedby thoseof terrestrialfrozen soil and basalt. greaterspread, 0.09-5.40 W m-1 K-1, withan averagevalue of Laboratorymeasurements of the thermal conductivityof 144 -2.06 W m-1 K -1. samplesof frozen soil and 301 samplesof basalt are summarized If our assumptionsabout the structureand lithology of the in Table 2 and Figure 4. The samplesvary in composition,lithol- outercrust are correct(i.e., Figure 1), then the thermalproperties ogy, porosity, and degree of pore saturation,but all represent of the megaregolithwill be moststrongly influenced by basalt.If conditionsthat are likely to exist somewherewithin the top so, the data in Table 2 suggest a column-averagedthermal 10 km of the Martian crust. The thermal conductivities of the soil conductivityof-2.0 (_1.0)W m-l K-1, withlower values likely

TABLE 2. ThermalConductivity of MegaregolithAnalogs

Number of ConductivityRange, Group Description Samples W m -1 K -1

Frozen Soil

la Sandysoils, 50-100% saturation[Sanger, 1963] 18 1.80-4.00 b Sandysoils, 3-45% saturation[Sanger, 1963] 24 0.33-2.35 2 Poorlygraded clean sand, 100% saturation[Lachenbruch et al., 1982] 5 3.39-3.67 3a Clay soils,50-100% saturation,T= 263 K [Sanger, 1963] 21 1.26-3.06 b Clay soils,15-45% saturation,T= 263 K [Sanger, 1963] 10 0.47-1.38 4a Generic silt soil, 100% saturation[ Lachenbruch, 1970] averageof many 2.34 b Genericclay soil, 100% saturation[Lachenbruch, 1970] averageof many 1.84 5 Clay soil,nearly saturated [Slusarchuk and Watson, 1975] 24 1.49-2.25 6 Leda clay andSudbury silty clay soils,100% saturation,T = 253 K [Penner,1970] 2 1.67-2.09 7 Fairbankssilty clay loam, 5-100% saturation,T = 269 K [Kersten,1963] 13 0.25-1.95 8a Black cultivatedsoil, 0-100% saturation,T = 268 K [Higashi, 1953] 8 0.18-1.42 b Brownsubsoil, 0-100% saturation,T = 268 K [Higashi, 1953] 9 0.08-1.21 c Yellow brownsubsoil, 0-100% saturation,T = 268 K [Higashi, 1953] 8 0.10-0.82 144 (total) 1.66 (average) Basalt

9a Chloritic Golden Mile basalt,0% saturation[Sass, 1964] 28 3.85-5.40 AmphiboliticGolden Mile basalt,0% saturation[Sass, 1964] 11 3.22-4.98 Nomeman basalt, 0% saturation[Sass, 1964] 7 2.47-2.93 10a PortageLake lava (amygdaloidaltops), 0% saturation[Birch, 1950] 10 2.30-3.77 b PortageLake lava (denseflows), 0% saturation[Birch, 1950] 27 1.72-2.76 11 Ventersdorplava, 0% saturation[Bullard, 1939] 9 2.64-3.60 12a Vesicular Hawaiian basalt, 100% saturation[Robertson and Peck, 1974] 57 0.84-2.41 b Vesicular Hawaiian basalt, 0% saturation[Robertson and Peck, 1974] 60 0.09-1.80 13 Columbia River Plateau basalt, 0% saturation [Sass and Munroe, 1974] 72 1.12-2.38 14 Knippabasalt, 0% saturation[Horai and Baldridge, 1972] 1 2.30 15 Deep-SeaDrilling Projectleg 37 basalts,100% saturation[Hyndman and Drury, 1976] 19 1.66 301 (total) 2.06 (average) 10,978 CLIFFORD:HYDROLOGIC AND CLIMATIC BEHAVIOROF WATER ON MARS near the surface,where fine-grainedmaterials may be present data) are 82 mW m-2 [Sclateret al., 1980] and 16mW m-2 in abundance,and higher values occurringat depth, where the [Keihmand Langseth, 1977], respectively. lithologyof the crust is likely to be characterizedalmost exclu- Given the broad range of Martian heat flux estimates,a sively by fracturedigneous rock [Clifford and Fanale, 1985]. In globallyaveraged value of 30 mWm -2 appearsto bea reasonable contrast,previous estimates were often based on the thermal choicefor the presentday heat flow. Substitutingthis estimate, propertiesof a specificterrestrial analog.For example,Fanale and the currentbest estimatesof crustalthermal conductivity [1976] assumedthat the propertiesof the megaregolithwere (2.0 W m-• K-1) andground ice meltingtemperature (252 K) well-representedby a hard-frozenlimonitic soil (•: -- 0.8 W m-• into equation(2), we find that the depth to the base of the K-l), whileCrescenti [1984] assumed a purely basaltic composi- cryosphere should vary from about 2.3 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 correspondingpoleward decline in mean annual surfacetem- groundice 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 cryospheredepths have also been calculatedby (-7.43 x 10-8 K Pa-• [Hobbs,1974]), while the effect of saltcan combiningthe appropriatelimiting values of geothermalheat be quite large. The existenceof various salts in the regolith is flow, thermal conductivity,and melting temperature.Although, supportedby the discoveryof a duricrustlayer at both Viking the local thermal propertiesof the crust are likely to display a Lander sitesand by the elementalcomposition of the soil as de- high degreeof variability,on a globallyaveraged basis it appears termined by the inorganic chemical analysis experiments on unlikely that any geologicallyreasonable combination will result board each spacecraft[Toulmin et al., 1977; Clark, 1978; Clark in cryospheredepths that differ by more than 50% from the and Van Hart, 1981]. Among the most commonlycited candi- valuespredicted by the nominalmodel. datesare NaC1, MgC12, and CaC12, which have freezing points at By integratingthe crustal porosity profile given by equa- their 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 potential pore volume of the cryos- tionshave freezingtemperatures as low as 210 K [Brass, 1980]. phere is readily determined(Table 5). For the given range of It shouldbe noted, however, that seriousquestions have been porositiesand the likely thermal propertiesof the crust (i.e., raisedconcerning the chemical and thermodynamic stability of thoserepresented bythe nominal model), this amounts to a pore CaC12and MgC12 under ambient Martian conditions, particularly volume sufficient to store a global layer of water some 370- in the presenceof abundantsulfates [Clark and Van Hart, 1981]. 940m deep. For the extreme conditionsrepresented by the Given these arguments,brines based on NaC1 appear to be the minimum and maximumthermal models,the range in potential mostlikely candidatesto be found within the crust. storagecapacity varies from a global ocean as small as 40 m 2.2.3. Geothermal heat flux. Like the other variables in deep, to one as large as 1400 m. Note that for the thermal con- equation(2), estimatesof the Martian geothermalheat flux have ditions defined by the maximum case, the megaregolithshould varied over a wide range (Table 3). Solomonand Head [1990] be frozenthroughout, a conditionthat appearsincompatible with have notedthat if Mars losesheat at the samerate per unit mass the geomorphicevidence for abundantgroundwater (i.e., the asthe Earth, then it shouldhave a meanglobal heat flux of outflowchannels) throughout much of Martiangeologic history -31mW m -2, a figurethat agrees reasonably wellwith the in- [Baker,1982; Tanaka, 1986; Tanaka and Scott, 1986; Carr, dependentlyderived estimates of 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 publishedestimates have been both significantly 2.3. The Distribution of Groundwater higher and lower. For example, thermal modelingby Toks6zet al. [1978], Davies and Arvidson [1981], and Schubertand Spohn Thermodynamically,theprimary sink for subsurfaceH20 on [1990] suggestsa present-dayheat flux as high as 40-45 mW Mars is the cryosphere;however, once the pore volume of the m-2;whereas work by Solomon and Head [ 1990], based on rheo- cryospherehas been saturatedwith ice, any remainingwater will logic estimatesof lithosphericthickness and mantleheat produc- drain to saturatethe lowermostporous regions of the crust.But tion (inferred from the compositionof the SNC meteorites), how deepand areallyextensive will the resultingzone of satura- suggestsvalues as low as 15-25mW m-2. Forcomparison pur- tion be? As a first approximation,Mars can be considereda per- poses,the currentbest estimatesof the averageheat flux of the fect sphere whose porosity profile is everywhere describedby 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 the porevolume of the megaregolithbetween the self-compaction TABLE 3. EstimatedGlobally Averaged Geothermal Heat Flux depth and any shallower region of the crust. For example, a Heat Flux quantityof water equivalentto a globallayer 10 m deepis suffi- Planet Source mW m -2 cient to saturatethe lowermost0.85 km of the megaregolith(Fig- ure 6), while a quantity of water equivalentto a 100-m layer Mars Fanale [ 1976] 30 Toks& and Hsui [1978] 35 would createa global aquifernearly 4.3 km deep [Clifford, 1984, Toksb'zet al. [1978] 45 1987a]. Turcotte et al. [1979] 33.5 However,Mars is not a perfectsphere. Its crusthas been af- Davies and Amidson [ 1981] 40 fectedby a varietyof geologicprocesses that have createda sur- Stevensonet al. [1983] 28-32.4 face of considerableheterogeneity and topographicrelief. This Schubertand Spohn[1990] 40 Solomon and Head [1990] 15-25 diversityis undoubtedlyreflected in the variability of a number Earth Sclater et al. [1980] 82.3 of importanthydrologic characteristics, including both the local porosityprofile and the depth of self-compaction.Unfortunately Moon Keihm and Langseth[1977] 14-18 , without further data, the magnitudeof this variationis impossi- CLIFFORD:HYDROLOGIC AND •TIC BEHAVIOROF WATER ON MARS 10,979

TABLE 4. LatitudinalVariation of CryosphereThickness

MeanAnnual Depth,km Latitude Temperature,K Minimum Nominal Maximum

90 154 1.24 6.53 23.8 80 157 1.18 6.33 23.2 70 167 0.96 5.67 21.2 60 179 0.69 4.87 18.8 50 193 0.38 3.93 16.0 40 206 0.09 3.07 13.4 30 211 -- 2.73 12.4 20 215 -- 2.47 11.6 10 216.5 -- 2.37 11.3 0 218 -- 2.27 11.0 -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

Thermalmodel properties: Minimum: Qg = 45 mWm -2, k = 1.0W m-1 K-1, Trap = 210K; Nominal:Qg -- 30 mWm -2, k = 2.0W m-1K -1, Trap = 252 K; andMaximum: Qg = 15mW m -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 theMartian cryosphere for thethree thermophysical models defined in thetext andin Table4.

TABLE 5. StoragePotential of MartianCryosphere

Pore Volume, x107 km3 EquivalentGlobal Ocean of H20, m Extent of Cryosphere (I)(0) = 20% (I)(0) = 50% (I)(0) = 20% (I)(0) = 50%

Minimum 0.57 1.43 39 99 Nominal 5.42 13.6 37 4 936 Maximum 7.76 20.0 536 1382

Thermalmodel properties: Minimum: Qg = 45 mWm -2, k = 1.0W m-1 K-1, Trap= 210K; Nominal:Qg -- 30mW m -2, k = 2.0W m-1K -1, Trap = 252 K; andMaximum: Qg = 15mW m -2, k = 3.0W m-1K -1, Trap = 273K. ble to quantify.Thus, althoughit is clear that the local character- The one improvementthat can be made in attemptingto isticsof the crust are poorlydescribed by a single set 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 ertiesthat we can presentlymake. porosityprofile of the crust is describedeverywhere by equa- 10,980 GLIb-WORD:HYDROLOGIC AND CLIMATIC BEHAVIOROF WATER ON MARS

POROSITY (PERCENT) eral kilometers or more beneath the surface. As illustrated in 0 10 20 30 40 50 Figure 7, the differences between these controlling influences I (porosity, gravity, and thermal structure) are of considerable importancein determiningthe state and vertical stratificationof H20 withinthe crust.For example,beneath topographic highs, the absoluteelevation of the local self-compactiondepth may exceedthe elevation of the global water table; thus, only near- surfaceground ice may be present in a vertical sectionof the crust. Beneathareas of slightly lower elevation, both groundice ___ and groundwatermay be present;however, the vertical distances separatingthese regions may be substantial,leaving an interven- ing unsaturatedzone that couldbe many kilometersthick. In still

-10 lower regions,the entire crustal column may be saturatedwith groundice and groundwater.Indeed, in the very lowest regions, suchas the interior of Hellas, the absoluteelevation of the global water table may exceed that of the local topography.In such in- Fig. 6. Resultingsaturated thicknesses of groundwater for inventoriesequiv- stancesthe groundice layer will be under a substantialhydraulic alentto a globalocean 10 and 100 rn deep.In thismodel Mars is considered a perfectsphere whose porosity profile is describedeverywhere by equa- head.As discussedby Carr [1979], a ruptureof this barrier could tion (1) [Clifford, 1984, 1987a]. lead to a significantdischarge of groundwater.However, such a rupture is eventually self-sealing,because as the groundwater tion (1), then the depthof self-compactionwill mirror the gross erupts onto the surface, it will lower the local hydraulic head until it falls even with the elevation of the basin floor. At that variation of surfacetopography, defining an irregular, impermeable lower bound for the occurrenceof groundwaterat a con- time, the reduceddischarge will permit the water-saturatedreg- stantdepth approximately 10 km beneaththe surface. Figure 7 is olith to refreezeat the point of breakout,until the original ground ice thicknessis eventuallyreestablished. a pole-to-polecross section of this crustalmodel, where the surface elevationsand self-compactiondepths have been averaged Figure 8a illustrateshow the areal coverageof groundwaterin the crustal model describedabove should vary as a function of as a function of latitude. This cross section illustrates the potential stratigraphicrelationships between surface topography, theavailable inventory of groundwater(i.e., in excessof theH20 already storedas groundice in the cryosphere).This relation- groundice, and groundwater,for groundwaterinventories rang- ship is seen more clearly in Plate 1, where the areal coverage ing from 10 to 250 m. Note that for a groundwatersystem in of groundwatersystems based on available inventoriesof 10 m, hydrostaticequilibrium, the watertable conforms to a surfaceof constantgeopotential. In contrast,the distributionof groundice 100 m, and 250 m of water are superimposedon a topograph- is controlledby the localsurface temperature and the magnitude ic map of Mars. For the assumedcrustal characteristics,the of the geothermalgradient. As a result,the positionof the mel- resultingaquifers underlie 34%, 91%, and 98% of the planet's ting isothermat the base of the cryospherewill mirror the surface(Figure 8a), and possesslocal saturatedthicknesses that first-ordervariations in surfacetopography, but at a depth sev- rangefrom zero to a maximumof 5 km, 10 km, and 13 km, respectively(Figure 8b). To summarize,this analysissuggests that once the pore vol-

10 ume of the cryospherehas beensaturated with 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-scalegroundwater system couldconceivably result from an outgassedglobal inventory ofH20 assmall as 50 m;however, for moreplausible conditions, suchas thosedescribed by the nominalmodel, a planetaryinventory in excessof 400 m appearsnecessary.

>- ---J q0 3. TERRESTRIAL ANALOGS: THE OCCURRENCE OF GROUNDWATER AND THE PERMEABILITY OF THE EARTH'S CRUST

-90 -60 -30 0 30 60 90 While the calculationspresented in the previoussection indi- LATITUDE catethat a planetary-scalegroundwater system on Mars is physi- Fig. 7. A pole-to-polecross section of theMartian crust illustrating the po- cally possible,is it geologicallyreasonable? Unfortunately, a tentialrelationship between topography, ground ice, and groundwater,for clear answerto this questionis cloudedby the fact that subsur- hypotheticalgroundwater inventories equivalent to a globallayer 10, 100, and250 rn deep.Surface elevations are averagedas a functionof latitude face hydrologyremains an inexact scienceeven here on Earth. basedon the USGS Mars Digital TerrainModel, while the latitudinalvari- Much of this uncertaintyis attributableto our limited knowledge ationin groundice thicknessis basedon the nominal model results listed in of the detailed three-dimensional structure of the Earth's crust. It Table 4. The calculatedgroundwater depths assume that the groundwateris is also due to the subjectiveand often erroneousway in which in hydrostaticequilibrium, that the local porosity proœfie of thecrust is given thisknowledge has historically been interpreted. everywhereby equation(1), andthat the self-compactiondepth mirrors the grossvariation of surfacetopography at a constantdepth of 10 km beneath Until recently, terrestrial groundwaterinvestigations were the surface. driven almostexclusively by a desire to locate easily tapped CLIFFORD:HYDROLOGIC AND CI•MATIC BEHAVIOR OF WATER ON MARS 10,981

"g'o 100 3.1. The Occurrenceof Groundwater Deepwell observationsindicate that groundwateris present, z < 80 at somedepth, virtually everywhere beneath the Earth'ssurface [Waltz,1969; de Marsily et al., 1977;Fetter, 1980].According to Brace[ 1971], thiszone of saturationgenerally extends to a depth o 60 that is at least4-5 km belowthe regionalwater table. However, thereis considerableevidence that groundwaterpersists to even

LU 40 greaterdepths. Some of thisevidence comes from studies of the electricalconductivity of the top 20 km of the Earth'scrust, a 0 conductivitythat is severalorders of magnitudehigher than that n- 20 of dry rockstudied under similar conditions of temperatureand pressure[Hyndman and Hyndman,1968; Brace, 1971;Nekut O 0 • • I et al., 1977; Thompsonet al., 1983; Shankland and Ander, < o 1oo 200 3OO 400 1983].Although a widevariety of explanationshave been pro- EQUIVALENT GROUNDWATER INVENTORY (m) posed to accountfor these observations,laboratory studies and theoreticalarguments both stronglysuggest that the high electrical conductivityof the crustowes its origin to the existenceof

(b) water-saturatedpermeable rock at depth [Hyndmanand Hynd- man, 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"research well locatedin the Kola Peninsula [Koz- lovsky,1982, 1984]. The Kola well, which is part of an extensive Russianprogram to studythe deep structureand evolutionof the m -10

uJ -12 Throughoutthe interval of 4.5-9 km, the well encountered

-16 • • • These flows occurreddespite confining pressuresin excess of 0 100 200 300 4oo 3 kbar [Kozlovsky,1982]. Flow underthese conditions is thought to be possibleonly when the permeabilityof the host rock is low EQUIVALENT GROUNDWATER INVENTORY (m) enoughfor pore fluid pressuresto reachlithostatic values; trans- Fig. 8. (a) The percentof Mars underlainby groundwaterand (b) the abso- port may then occurby the propagationof fluid-filled microfrac- lute elevationof the globalgroundwater table as a functionof the planetary tures in responseto tectonic stress [Thompsonand Connolly, inventoryof groundwater(expressed as an equivalentglobal ocean of H20 ). 1992]. Such an argumenthas been proposedto explain the iso- This modelis basedon the samedata set and assumptions as Figure7. topic(fid and5180) composition of groundwater found in deep fault zones, which indicates that surface-derived water has cir- culated to depths as great as 10-15 km [Kerrich et al., 1984; sourcesof water for human, industrial, and agricultural con- McCaig, 1988]. sumption.As a result,little effortwas spentto characterizethe nature and extent of groundwatersystems whose development 3.2. The Large-Scale Permeability of the Earth's Crust wasperceived as economicallyprohibitive or whosewater quality was poor. This limited perspectivehas contributedto a Numerous borehole and seismic investigationshave estab- numberof misconceptionsabout the nature of the subsurface lished that the Earth's crust consistslargely of fractured rock hydrologicenvironment, a problemthat has beenfurther aggra- [LeGrand, 1979; Brace, 1980, 1984; Mair and Green, 1981; See- vated by the frequentand often uncriticaluse of terms like burger and Zoback, 1982]. While someearly studiessuggested "aquifer"and "aquiclude",that lack precisedefinitions. For ex- that the densityof fracturesdeclines appreciably with depth [e.g., ample, a water-bearingformation that may be consideredan Snow, 1968], more recent investigationsindicate that this cor- aquiferin oneregion (such as a desert),might well be considered relationis limited to the weathered,near-surface layer. Indeed, in an aquiclude(i.e., essentiallyimpervious) in a region where numerouswells drilled in variousparts of the world, fractures othersignificantly higher-yielding formations are present[Davis are invariablyfound down to the limit of exploration,with little and De Wiest, 1966]. The evaluationof groundwatersystems by or no evidenceof a significantdecline in fracture density [See- suchsubjective standards has led to the widespreadperception burger and Zoback, 1982; Haimson and Doe, 1983; Kozlovsky, that groundwaterflow on Earth is restrictedto shallow,local 1982, 1984]. aquiferswith well-definedimpermeable boundaries. However, Although independentof depth, the variability of fracture overthe past30 years,numerous detailed subsurface hydrologic densitywithin a given borehole,or betweenboreholes, is often investigationshave clearly demonstrated the inaccuracyof this considerable.For example,one hole may exhibit a fairly uniform picture.In this section,some of the key findingsof theseinves- distributionof fracturesthroughout its length,while another,just tigationswill be summarized,providing the necessaryterrestrial a few kilometersaway, may displayconcentrations of fracturesin backgroundfor evaluatingthe likelihood,potential extent, and denselyfractured intervals [Seeburger and Zoback, 1982; Haim- subsequentevolution, of a globalgroundwater system on Mars. son and Doe, 1983]. As a result, neighboringwells may some- 10,982 CLIFFORD:HYDROLOGIC AND CLIMATICBEHAVIOR OF WATER ON MARS

p- z •J • E

z o

p- z •J

z CLIFFORD:HYDROLOGIC AND CI•MATIC BEHAVIOROF WATER ON MARS 10,983 timesshow as muchas a four-order-of-magnitudedifference in is calleda groundwaterdivide. The extentto which infiltration permeabilityover the same depth interval [Brace, 1980]. fromthe surfacecontributes to groundwaterflow in neighboring Becauseof the spatial variability of fractures,the effective basinsis basedsolely on which sideof the divide the infiltration permeabilityof crustalrocks is criticallydependent on the scale occurs.The resultingvariation in hydraulichead then drivesthe of the sampleunder consideration (Figure 9). For example,labo- flow of groundwaterto the basin interior, where it evaporates ratorymeasurements of samplesseveral centimeters in size gen- from the water table or is dischargedto the surfaceas a lake or erally indicateonly the minimumpermeability of a rock mass spring-fedstream. [Brace,1984]. However,at the scaleof interestfor mosthydro- Althoughmost basin aquifers are modeledas if they were hy- geologicstudies (generally 102-103 m), virtually all crustalrocks draulicallyindependent, virtually all are part of largerintermedi- haveundergone a considerabledegree of fracturing,dramatically ate and regional groundwaterflow systems(Figure 11) [Toth, increasingtheir effective permeabilities[Streltsova, 1976; Le- 1963, 1978; Ambroggi, 1966; Freeze and Witherspoon,1967; Grand, 1979; Seeburgerand Zoback, 1982; Brace, 1980, 1984]. Mifflin and Hess, 1979; Habermehl, 1980; Castany,1981; Issar, Despitethe low porosityof fracturedrock (-1%), its perme- 1985]. In such systems,neighboring basins are linked by net- abilityis oftenquite high [LeGrand, 1979; Brace, 1980; Fetter, worksof intersectingfaults and fractures. In practice, the extent 1980].This is becausethe pore geometry of a fractureis inher- of thisinterconnection is not often recognized because the vol- entlymore efficient at conductinga fluid per unit porosity than umeof waterthat participates in interbasin flow usually repre- thegeometry of anintergranular pore network; thus, a rockwith sentsonly a smallfraction of a basin'stotal hydrologic budget. a fractureporosity of only0.011% can have the same permeabil- Exceptions are noted when there are sizable differences in pre- ityas a siltwith a porosityof 50%[Snow, 1968]. cipitationbetween neighboring basins and/or the fracture perme- Thepervasive nature of crustalfractures means that few, if abilityof theintervening formation ishigh. any, large-scalegeologic formations can be consideredimperme- able [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 boreholepermeability measurements, as well as permeabilities In areasthat experiencefrequent precipitation, both the shape inferredfrom large-scalegeologic phenomena (such as earth- of the water table and the direction of groundwaterflow are quakestriggered by fluid injectionfrom nearbywells), and has stronglyinfluenced by the local topography,making any evidence concludedthat, on a size scaleof 1 km, the averagepermeability of regionalor interbasinflow difficult to recognize.However, in of the top 10 km of the Earth'scrust is roughly10 -2 darcies arid regions, the long intervals between atmosphericrecharge (where 1 darcyis the permeabilitynecessary to permit a specific often providesufficient time for the topographicinfluence on the dischargeof 1 cms -1 for a fluidwith a viscosityof 1 centipoiseshape of the water table to decay,making evidence of large-scale undera hydraulicpressure gradient of 1 bar cm-l; 1 darcy-- hydrauliccontinuity considerably easier to identify. For this rea- 10-•2 m2).Thus, at thissize scale, virtually all groundwatersys- son, the best recognizedexamples of regionalgroundwater flow tems on Earth may be consideredhydraulically interconnected. on Earth are all found in arid environments. The extentof this interconnectionhas becomeincreasingly ap- 3.4.1. The Great Basin Carbonate Aquifer System, USA. parent as detailed hydrogeologicstudies have demonstratedthe Some of the very first evidencefor interbasingroundwater flow potentialfor contaminationof groundwatersupplies by migrating camefrom Death Valley, California, where it was observedthat chemical and radioactive wastes [de Marsily et al., 1977; the dischargeof certainsprings far exceededthat which couldbe Anderson, 1987]. explained by local recharge[Hunt and Robinson, 1960]. This discoverysuggested that groundwaterderived from the higher 3.3. Local and Regional GroundwaterFlow intermontanebasins to the eastwas reachingDeath Valley via an On Earth,the smallestand mostdynamic element of a ground- extensive network of interconnectedfractures through a thick water flow system is typically a shallow unconfinedaquifer interveningformation of carbonaterock. Convincingsupport for locatedwithin a small topographicbasin. Because the aquiferis this hypothesiscame from the near identicalchemical composi- rechargedby 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. elevatedwater table that occursat the boundarybetween basins The discoveryof interbasinflow betweenAsh Meadows and Death Valley raisedconcern about the possibilityof groundwater contaminationfrom undergroundnuclear tests conductedat the PERMEABILITY: THE EFFECT OF SCALE nearby Nevada Test Site [Winograd, 1962]. Althoughthe three large basinsencompassed by the Test Site are topographically isolated,the well water levels in all three are essentiallyidenti- cal, a result that arguesstrongly for hydraulic interconnection. Shortlyafter this discovery,another regional groundwater system was discovered to the east of the Test Site that linked 13 inter- montanevalleys into a regionalflow systemmeasuring roughly 385 by 115 km [Eakin, 1966]. Indeed,as investigationscontinue, CENTIMETER 10 - 100 METER KILOMETER it is now believed that most of western Utah, eastern and south- Fig. 9. The effectof scaleon crustalpermeability measurements (after Brace ern Nevada, and the southeasterncomer of California are under- [1984]). Laboratorystudies of rock samplesonly a few centimetersin size lain by one or moredeep regional flow systemsthat extendfrom generallyyield only theminumum permeability of a rock mass.However, on a sizescale of kilometers,the pervasivenature of crustalfaults and fractures Great Salt Lake to Death Valley. The host rock is a thick (6- yieldsa meanpermeability of -10 -2darcies for thetop 10 km of the Earth's 9 km) accumulation of Paleozoic limestone and dolomite that crust. underlies-1.6 x 105km 2 of the GreatBasin province [Mifflin 10,984 CLI•ORD: HYDROLOGICAND CLIMATIC BEHAVIOR OF WATER ON MARS

groundwater • topographygroundwater divide ',,,,C,,__,.__,..._,• water•'.... ,,;:';,';,'Z,;,"/;';' . ...•de _table_•,,,-•/{ •'"'•,/ _•-"/ /

Fig. 10. A sketchof a local groundwaterflow system,illustrating the relationshipbetween topography, the shapeof the watertable, and the directionof subsurface flow.

local flow a total east-westtransit time in excessof 1 million years[Bentley systems et al., 1986; Cathies, 1990]. Unlike the Great Basin Carbonate Aquifer System in the United States,the geologicsimplicity of the Gmat ArtesianBasin Aquifer led to early recognitionof both its physicaldimensions and the extentof groundwaterflow [e.g., Pittman, 1914]. To this day, it remainsthe largestrecognized single-basin groundwater systemon Earth. •ntermed•ate flow system 3.4.3. The Nubian Aquifer System of the Eastern Sahara. The groundwaterresources of the SaharaDesert in North Africa are divided among eight major sedimentarybasins [Ambroggi, 1966; Burdon, 1977; Margat and Saad, 1984]. Two of these,the regional flow Dakhla Basin of Egypt and the Kufra Basin of Libya, form the system xx x.x.x Nubian Aquifer Systemof the EasternSahara, a regionalaquifer , ,/ with an areaof-2 x 106 km2 [Schneider,1986; Hesse et al., /..1\/.•,\/•\/--\/-...\/•\/.-.•/.-\/--\/-...\/._/-• /"t/•l/"'l/"'-i •1/'-i/•1/"'1/'"-i - [•c•,rw•,r•{/- ,.. /....\/..•/..•/..\/•\/....\/•\/..\/•\/..\"-I •1/"1/•1/"'1/'"-I •1/"1/•1/"'1/ x...... xxxx...x, /x...... xx...x...x, / •,o•111•11• x. /x...xxxxxxx, /x...xxxxxx 1987]. The aquifer'sprincipal water-bearingformation is the ,-,,-,,-,<-:.,,..--'•,-,,-,,-,<-:,,.--'•,•1/•1/•1/\1/\'1/•1/•1/•1/\1/\'1/•1/•1/•1/• , , , ,.'--'•,-,,-,,-,,-,,--'•,-,,-,,-,,-,/•'1/•1/•1/•1/"1/•'1/•1/•1/•1/"1 / Nubian Sandstone, which varies in thickness from less than Fig. 11. An illustrationof thenested nature, lateral extent, and relative depth 500m to more than 3000 m [Sham, 1982]. In the northern of flow of local,intermediate, and regional groundwater 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]. Be- with shalesand clays and overlain by fracturedcarbonate rock, causelittle datahas been collected below the upperzone of satur- creatinga confinedmultilayered system of considerablecom- ation, the full extent of hydraulic continuitywithin the system plexity [Sham,1982; Hesse et al., 1987]. has yet to be established.However, at depth, the limited evi- From a human and agricultural resource perspective,the dence that does exist suggeststhat solution-widenedfractures Nubian Aquifer is generallyconsidered hydraulically isolated; and caverns have created widespreadregions of high perme- however, them is considerableevidence of hydraulic continuity ability, a characteristicthat has made carbonateaquifers among far beyondthe system'srecognized boundaries. For example,the the most extensiveand productivein the world [LeGrand and northernlimit of the aquiferis usuallydefined by the locationof Stringfield, 1973; Mifflin and Hess, 1979]. the saline-freshwater interfacethat occursup to severalhundred 3.4.2 The Great Artesian Basin, Australia. The Great Arte- kilometers inland from the Mediterranean Sea [Sham, 1982; sian Basin underlies -1.7 x 106 km2 of the eastern half of Thorweihe,1986]. Althoughthe locationof this chemicaltransi- Australia, an arid to semi-aridregion that representsover one- tion is importantin the contextof water quality, it hasno beating fifth the land area of the entire continent [Habermehl, 1980]. on the extentof hydrauliccontinuity. Indeed, exploration wells in Structurally,the basin is a bowl-shapeddepression that contains northernEgypt have establishedthat the Nubian sandstoneper- up to 3 km of sedimentarydeposits. These depositsform a sistsand deepensas it extendsnorthward beneath the Mediterra- multilayerconfined aquifer systemconsisting of sandstoneaqui- nean'ssouthern shore [Shata, 1982; Thorweihe, 1986]. fers sandwichedbetween less permeablelayers of siltstoneand The remainingboundaries of the Nubian Aquifer are similarly mudstone[Habermehl, 1980; Cathles, 1990]. vague.For example,along most of its easternmargin, the Nubian The basinis rechargedalong its easternmargin by precipita- Aquiferis boundedby an outcropof basementbetween the Nile tion on the elevatedslopes of the Great Dividing Range.Dis- Valley and Red Sea. However, further north, where the outcrop chargeby naturalsprings occurs primarily in a region900 km to disappears,there is evidenceof a connectionto a major aquifer the southwest,in the vicinity of Lake Eyre [Habermehl,1980]. in the Sinai peninsula[Sham, 1982; Issar, 1985]. To the south, Numericalmodels and isotopicdata suggestthat the naturalflow water table contourssuggest hydraulic continuity with the Blue velocitythrough the basin's principal aquifer is -1.0 m yr-•, with Nile-Main Nile Basin [Hesseet al., 1987] as well as groundwater CLIFFORD:HYDROLOGIC AND CLIMATICBEHAVIOR OF WATER ON MARS 10,985 inflow from northeasternChad [Ambroggi,1966; Edmundsand Schaber, 1977; Allen, 1979a; Rossbacherand Judson, 1981; Wright, 1979]. Finally, in the west,there is evidenceof a hy- Lucchitta, 1981, 1985; Squyresand Carr, 1986; Carr, 1986; drauliclink betweenthe Nubian Aquifer and the Sirte Basinin Squyres, 1989; and others]; their common conclusionhas been Libya[Edmunds and Wright,1979]. Because detailed hydrologic that of the possiblemechanisms that mightexplain the presence informationis scarcethroughout the EasternSahara, the degree of thesefeatures, those involving ground ice appearthe mostrea- of the hydraulicinterconnection between these neighboring sys- sonable.Additional evidence (found at all latitudes)for the pres- tems is difficult to assess.It is clear, however, that as the area of enceof subsurfaceH20, isprovided by the occurrence of rampart recognizedhydraulic continuity expands, the likelihoodof addi- craters,whose distinctive lobate ejecta morphology is thoughtby tional links with neighboringbasins increases as well. many investigatorsto originatefrom the fluidizationof ejecta In summary,the distribution and flow of groundwateron materialduring an impactinto a water- or ice-richcrust [Carr et Earth exhibits severalcharacteristics that are of potentialimpor- al., 1977;Johansen, 1978; Allen, 1979b;Mouginis-Mark, 1979, tancein understandingthe subsurfacehydrology of Mars. First, 1987; Blasius and Cutts, 1981; Kuzmin, 1983; Kuzrnin et al., givena globalinventory of H20 thatexceeds the pore volume of 1988; Costard, 1989; Barlow and Bradley, 1990]. Finally, the thecryosphere by as little as a few percent,groundwater is likely survival of a significantreservoir of subsurfacewater in the to be found virtually everywherebeneath the Martian surface. equatorialregion is alsosupported by the presenceof the outflow Second,as on Earth, it is likely that suchgroundwater will per- channels,whose episodic development appears to have spanned sist and circulateto depthsfar in excessof the 10 km self- much of Martian geologichistory [Carr, 1981; Baker, 1982; compactiondepth assumed in this study.Third, in the absenceof Tanaka, 1986]. atmosphericprecipitation, the hydraulicboundaries of a ground- The aboveevidence presents a problem,for it is difficult to water systemon Mars will be determined,not by the local to- accountfor both the initial origin and continued survival of H20 pographyor the presenceof groundwaterdivides, but by the in a regionwhere the presentmean annualsurface temperature continuityof pore spacebeneath the water table. Fourth,given a exceedsthe frost point by morethan 20 K. Indeed, undercurrent km-scalepermeability of the Martiancrust no greaterthan that of climaticconditions, any subsurface H20 shouldexperience a net theEarth (-10 -2 darcies),the extent of hydrauliccontinuity, and annual depletion,resulting in its preferentialtransfer from the thusthe potentialareal extentof a Martian groundwatersystem, '•ot" equatorialregion to the colderlatitudes poleward of +400 is essentiallyglobal. [Flasar and Goody, 1976; Toon et al., 1980; Clifford and Hillel, 1983; Fanale et al., 1986]. Currently, the most widely acceptedexplanation for the exis- 4. THESTABILITY AND REPLENISHMENT OFEQUATORIAL H20 tenceof a subsurfacereservoir of equatorialH20 is thatit is a Theoretical considerationsand various lines of morphologic relic,emplaced very earlyin Martiangeologic history (> 3.5 b.y.) evidencesuggest that, in addition to the normal seasonaland and undersubstantially different climatic conditions. This expla- climaticexchange of H20 thatoccurs between the Martian polar nation is basedin part on the work of Smoluchowski[ 1968], who caps, atmosphere,and mid- to high-latituderegolith [e.g., showedthat undercertain restricted conditions of porosity,pore kosky,1985; Zent et al., 1986], large volumesof water have been size, temperature,and depth of burial, the diffusion-limiting introducedinto the atmosphericleg of the planer's long-term propertiesof a fine-grainedregolith could preserveequatorial hydrologiccycle by the sublimationof equatorialground ice, im- groundice for billionsof years. pacts,catastrophic flooding, and volcanism.In this sectionboth The stability of groundice is governedby the rate at which endpointsof the proposedcycle are discussed,beginning with the H20 moleculescan diffuse through the regolithand into the at- lossof water from crustalreservoirs at equatorialand temperate mosphere.This processis complicatedby the fact that the col- latitudesand concludingwith its possiblereplenishment by sub- lisionalmean free pathof an H20 moleculein the Martian surfacesources of H20. The intermediatesteps of the proposedatmosphere is -10 gm. When the ratio of the pore radius to the cycle, including polar deposition,basal melting, and pole-to- mean free path of the diffusing moleculesis large (r/)• >10), equatorgroundwater flow, arediscussed at lengthin section5. bulk moleculardiffusion is the dominantmode of transport(i.e., wherediffusion occurs in responseto the repeatedcollisions that happenwith othermolecules present in the soil pores).However, 4.1. The Stability of Equatorial Ground Ice for very smallpores (r/• < 0.1), collisionsbetween the diffusing Althoughmean annual surfacetemperatures are below freez- moleculesand the pore walls greatlyoutnumber those that occur ing everywhereon Mars, observationsmade by the Viking Or- with other molecules,a processknown as Knudsen diffusion. biter Mars AtmosphericWater Detectors(MAWD) indicate a Becausethe frequencyof pore wall collisionsincreases with de- globallyaveraged frost point temperatureof-198 K. Therefore, creasingpore size, small porescan substantiallyreduce the effi- given the presentlatitudinal rangeof mean annual surfacetem- ciencyof the transportprocess. For poresof intermediatesize peratures(-154-218 K), any subsurfacereservoir of H20 is (0.1 < r/ )• <10), the contributionsof both diffusive processes unstablewith respectto the water vaporcontent of the atmos- mustbe takeninto account[Younquist, 1970; Clifford and Hillel, phere at latitudesequatorward of +40ø (Figure 3) [Farmer and 1983, 1986]. Doms, 1979]. Theeffect of a 10 gmmean free path on the diffusion of H20 Despitethis fact, thereis a considerablebody of morphologic throughthe regolith is clearly seen in Figure 12, where the ef- evidence that suggeststhat both ground ice and groundwater fectivediffusion coefficient ofwater vapor Deft has been plotted have survived at some depth within the equatorial regolith asa function ofpore size. Deftis given by throughoutmuch of Martian geologichistory. At latitudespole- ward of 30ø , this evidence is based on the identification of Martian analogsto cold-climatefeatures found on Earth, suchas DAB DKA debris flows, table mountains, and thermokarst. These features Deft = (3) have been reviewed by a number of investigators[Carr and DKA + DAB 10,986 •ORD: HYDROLOGICAND CLIMATIC BEHAVIOR OF WATER ON MARS

1/2

DKA = -- r (5) 3 ToMA

whereR is the universalgas constant and M A is the molecular weightof H20. Of course,most soils generally exhibit a broad • o spectrumof pore sizes.The impactof this characteristicon vapor E transportis illustrated in Figure 13, where the differential and cumulativeflux of H20 is plottedfor threehypothetical pore size distributions. ¸ -2 The survival of equatorialground ice was consideredin detail by bothClifford and Hillel [ 1983] andFanale et al. [ 1986]. They found that, for reasonablevalues of porosityand pore size, the near-equatorialcrust has probablybeen desiccatedto a depth of 300-500 m over the past3.5 billion years.However, because the 4 • I I i I 1 sublimationof H20 is sensitivelydependent on temperature,the -10 -9 -8 -7 -6 -5 -4 -3 quantityof ice lost from the regolithis expectedto decline with LOG OF PORE RADIUS (m) increasinglatitude, falling to perhapsa few tens of metersat a latitude of 35ø (Figure 14) [Clifford and Hillel, 1983; Fanale et Fig. 12. The effectivediffusion coefficient of water vapor in the Martian al., 1986]. regolithplotted as a functionof poresize [Clifford andHillel, 1983]. Of course,a variety of factorsare likely to complicatethis simplepicture of equatorialdesiccation. For example,if the ef- whereDAB and DKA are the bulk andKnudsen diffusion coeffi- fective pore size of the regolith is larger than 10 gm, or if the cients respectively[Scott and Dullien, 1962; Rothfield, 1963]. regolithhas a specificsurface area -> 103 m 2 g-• (a conditionthat After Wallace and Sagan [1979], the bulk diffusion coefficientof wouldgive rise to a diffusivesurface flux greaterthan any likely H20through anatmosphere ofCO 2 (in cm 2 s -1) is given by pore gas flux [Clifford and Hillel, 1983]), the actual depth of DAB= 0.1654(T/273.15) 3/2(1.013 x 106/p) (4) desiccationcould well exceedthe valuescalculated by Clifford and Hillel [1983] and Fanale et al. [1986]. Altematively, shal- where T is the temperatureand P is the total pressure(in dynes lowerdepths of desiccationwill resultif the goundice is replen- cm-2).However, as discussed by Cliffordand Hillel [1986],the ished (section4.5), the effectiveregolith pore size is less than expressionfor calculatingDg A is dependenton the specific shape 1 gm, or if its porosityis less than the 50% value assumedin of the soil pores.For the simplecase of a straightcylindrical pore thesetwo studies.Considerations that arguein favor of a spa- of radius r, we have tially variable(and generallylower) porosityinclude: igneous re-

PORE SIZE DISTRIBUTIONS 12 ! ! I I I I I I I I I I I I I I I I I I I I

•';a•o [•-'''""-'-1. b ,//"-- c / /•'-- ,ooo8o c // - ---.-' O •: 40 033 u. / 20 I I I I I I I I 0

MOLECULAR FLUX DISTRIBUTION

I I I I ! I

- 100 b' /"- ! u- 20- - 80

- 60 z•) 15- / I u.• 10- - 40 QX v 5-- - 20

o I I I 1 i 0 -'0 -6 -4 -2 o -8 -6 -4 -2 -10 -4 -2

LOG OF PORE RADIUS (m)

Fig. 13. (a-c) Thedifferential and cumulative porosities of threehypothetical soils and (a'-c9 thecorresponding diffusive flux of H20 thatresults from these poresize distributions [Clifford and Hillel, 1986]. CLI•ORD: HYDROLOGICAND CLIMATICBEHAVIOR OF WATER ON MARS 10,987

b 0.9 0.0 1.8 40 40 2.7 E •_,• 0.0E 0.9 • 80 3.6 • 80 I•. ' 4.5 c• 120- c3 120 1.8

- 160 -- 160-

. 2.7 200 200 - 36

90 80 70 60 50 40 30 20 10 0 90 80 70 60 50 40 30 20 10 0 LATITUDE, ø LATITUDE, ø

Fig.14. Therecession ofequatorial ground ice on Mars as a functionoflatitude and time (b.y.). The regolith models adopted for these calculations differ only in assumedpore size: (a) r-- 1 }xm,and (b) r-- 10 grn(fromFanale et al. [1986]). consolidation,dudcrust formation, and the self-compactionof the 4.2. Other Crustal Sourcesof AtmosphericWater regolithwith depth.Perhaps more importantly, variations in the Perhapsthe clearestevidence that the crusthas been a major local thermophysicalproperties of the surface(versus the glob- sourceof atmosphericwater are the outflow channels.The abrupt ally averagedvalues assumed in Figure 14) can affect mean an- emergenceof thesefeatures from regionsof collapsedand dis- nual temperatures,causing significant differences in both the rupted terrain, suggeststhat they were formed by a massiveand geographicstability of groundice and its predicteddepth of catastrophicrelease of groundwater [Sharp and Malin, 1975; desiccation[Paige, 1992; Mellon and Jakosky,1993]. A final Carr, 1979; Baker, 1982; Baker et al., 1992]. Channel ages, in- caveatregards the potentialeffect of quasi-periodicchanges in ferred from the densityof superposedcraters, indicate at least Martianobliquity and orbitalelements, the primarydrivers of severalepisodes of flooding,the oldestdating back as far as the climatechange. Recent studies suggest that the obliquityof Mars Late Hesparian(-3 billion years ago), while the youngestmay is chaoticand may vary from a minimumof 0ø to a maximumof have formed as recently as the Mid-to-Late Amazonian (i.e., 50ø or higher [Bills, 1990; Touma and Wisdom, 1993; Laskar within the last 1 billion years)[Tanaka, 1986; Tanaka and Scott, and Robutel,1993]. Althoughthese extremes exceed the 10.8ø- 1986; Parker et al., 1989; Mouginis-Mark, 1990; Rotto and 38ø obliquityrange considered by Fanale et al. [1986], their Tanaka, 1991; Baker et al., 1992]. Based on a conservative esti- shortduration and limited effect on equatorial temperatures sug- mate of how much material was eroded to form the channels in geststhat their potential impact on the lossof equatorialground ChrysePlanitia (-5 x 106km 3) andthe maximum sediment load ice will be minimal.More pronouncedeffects are likely at the that the flood waters could have carried (-40% by volume), Carr poles,where the increased insolation associated with high obliq- [1987] has estimateda minimum cumulativechannel discharge uitiescould have a considerableeffect on the stabilityof the ice of 7.5x 106km 3 of H20(equivalent to a globalocean -50 m caps.(A moredetailed discussion of the polar massbalance and deep). However, if the channelswere formed by multiple epi- highobliquities is containedin section7.2.) sodesof outbreakand erosion,then the flood waters may have By integratingthe total porevolume between the Martian sur- been less turbulentand carried less sedimentthan generallyas- face and the desiccationdepths presented in Figure 14, Fanale et sumed [Baker et al., 1992]. If so, the total volume of water real. [ 1986] haveestimated that over the courseof geologichistory quired to erode the channelsmay have been many times the asmuch as 2.7-5.6 x 106km 3 of H20(equivalent to a global estimateof Carr [ 1987]. Indeed,Baker et al. [1991] suggestthat ocean-20-40 m deep) may have been sublimedfrom the equa- the total dischargemay have beensufficient to flood the northern torial regolithand cold-trappedat the poles.As seenin Table 6, plainswith as much as 6.5 x 107km 3 of water(equal to a global however,the sublimationof equatorialground ice is just one of layer 450 m deep). severalpotential processes that may have episodicallyintroduced Impactsinto the Martian crustare anotherpotential source of largevolumes of waterinto the atmosphere. atmosphericwater [Carr, 1984]. Assuminga representativecry-

TABLE 6. CmstalSources and Potential Contributed Volumes of AtmosphericWater

CrustalSource Volume,km 3 EquivalentLayer, m H20

Sublimationof groundice [Fanaleet al., 1986] 2.7-5.6 x 106 20-40 Catastrophicfloods [Carr, 1987; Baker et al., 1991] 0.75-6.5 x 107 50-450 Volcanism[Greeley and Schneid,1991 ] 2.3 x 106 15 Impacts[this work] Excavation/volatization* 1.5-3.0 x 107 100-200 HydrothermalcirculationS' 1.9 x 107 130 Totals 0.47-1.2 x 108 km3 315-830 m

*Calculationassumes a crustalinventory of 500-1000 m of waterwithin the top 10 km of the crustand a global craterdensity equivalent to thatfound in the crateredhighlands. •'Figure representsthe potentialquantity of water brought to the surfaceby impact-generatedhydrothermal systemsalone (section 4.4.3). 10,988 CLIFFORD:HYDROLOGIC AND CLIMATICBEHAVIOR OF WATER ON MARS ospherethickness of 2.5 km, an ice contentof 20%, and a trans- 1986]. Yet, regardlessof the actualprocess by which it may have ient crater diametergiven by equation(11) (see section4.4.2), occurred,consideration of the valley networks,outflow channels the volumeof water excavatedand/or volatilized by individual andthe crustalmass balance of H20 arguesstrongly for some impactswill rangefrom -34 km3 for a crater10 km in diameter type of crustal resupply [Clifford, 1980b, 1984; Carr, 1984; toin excess of 2.8x 105km 3 for a majorimpact basin like Hellas Jakoskyand Carr, 1985; Baker et al., 1991]. This conclusionis (D -2000 km). Note that becausecraters with diameters ->40 km furthersupported by geomorphicevidence which suggests that, at have excavationdepths that exceed the predicted 10 km self- least in somelocations within the latitudeband of +30ø , ground compactiondepth of the megaregolith,the volumeof water exca- ice hasindeed been replenished. vatedby largeimpacts depends on neitherthe statenor the depth Considerfirst the consequencesof a major impact at equa- of the subsurfacereservoir of H20, but solelyon thequantity of 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 kilo- cratersize-frequency distribution equivalent to that preservedin metersin diametershould result in 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 atmosphereby impacts nearbyground ice maypartially replenish some of theH20 lost overgeologic time is -1.5-3.0 x 107km 3 (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. tion 4.4.3, the subsequentdevelopment of impact melt-driven It is interestingto note, therefore,that within many large hydrothermalsystems could have brought as much as an addi- equatorialimpact craters there exist clearlydefined rampart cra- tional 130 m of waterto the surface.This possibilityis supported ters [Allen, 1979a; Clifford and Johansen,1982]. If the morphol- by both the evidencefor hydrothermalactivity associatedwith ogy of this type of craterdoes indeed arise from an impactinto an terrestrialimpact cratersand the observedassociation of many ice-richcrust, then the occurrenceof rampartcraters within the valley networkswith the outsiderims of cratersthroughout the interiorsof numerousolder impactspresents a problem, for it is Martian crateredhighlands [Newsom, 1980; Brakenridgeet al., difficult to conceiveof a scenarioby which any groundice that 1985]. existedprior to the original crateringevent could have survived Finally, as discussedby Greeley[1987] and Plesciaand Crisp to producethe well-definedfluidized ejecta pattern often seen as [1991], it is likely that volcanismalso injected large volumes the result of a second and sometimes third consecutive and con- of water into the atmosphere.For example, Plescia and Crisp centricimpact (Figure 16). [1991] estimate that during the emplacementof the volcanic There are at leasttwo explanationsthat may accountfor these plainsin southeasternElysium (5 ø N, 195ø W), lavasmay have observations.First, contrary to popular belief, rampart craters exsolvedbetween 103-104 km 3 of H20, assuming awater content may not be specific indicatorsof ground ice. Experimentsby comparableto that of terrestrialmafic to ultramaficlavas (-1% Schultz [1992] and Schultz and Gault [ 1979, 1984] have dem- by weight).Greeley [1987] has takena moreglobal perspective, onstratedthat when an impact occursin the presenceof an calculatingthe total volume of juvenile water releasedfrom the atmosphere,the effectsof drag and turbulencecan modify the planet'sinterior by estimatingthe extent and thicknessof all vol- emplacementof ejecta, reproducingmany of the featuresgen- canic units visible on the planet'ssurface. However, Greeley's erally associatedwith Martian rampart craters.This effect is [ 1987] estimateof extrusivemagma production has recently been clearlyseen in the recentMagellan radar images of Venus,where reviseddownward by Greeleyand Schneid[1991]. Substituting craterswith multilobate,fluidized ejecta morphologies are abun- this revisedfigure for that in Greeley's[1987] original analysis dantdespite the absenceof water[Phillips et al., 1991]. suggeststhat volcanicprocesses have releaseda total of 2.3 x Although laboratoryimpact experimentsand the Magellan 106km 3 (-15 m) of H20 into the atmosphere. It should be noted, radar imagesboth suggestthat the presenceof an atmosphere however,that in light of our inability to accuratelyassess both may play a role in rampartcrater formation, they do not exclude the extent of plutonic activity and the magnitudeof ancient the possibilitythat, on Mars, water and ice may havecontributed (->4 billion year old) v,olcanism, this estimateis likely a mini- to the processas well. Indeed,three lines of evidencelend cre- mum. Note also that, unlike water derived from other crustal denceto the original proposalof a link betweenrampart craters sources(which simply undergoesan exchangefrom one volatile and subsurface volatiles. The first is the observed latitudinal reservoirto another),water releasedby volcanismrepresents an dependenceof severalMartian rampartcrater ejecta morpholo- actual addition to the planet's outgassedinventory. However, gies,which vary from an apparenthigh-viscosity single-rampart oncethis water has beenintroduced into the atmosphere,its fate styleat polarlatitudes to a highlyfluidized multilobate-style near is governedby the sameprocesses that affectwater derivedfrom the equator[Johansen, 1978; Mouginis-Mark, 1979; Saunders anyother crustal source, leading to a slowbut inexorabletransfer from equatorialand temperate latitudes to the poles[Clifford and -2-3 km Hillel, 1983; Fanale et al., 1986].

4.3. Evidenceof GroundIce Replenishment dryinterior . '".....•....•'-'....ß...... Under the climatic conditionsthat have apparentlyprevailed on Mars throughoutmost of its history,the loss of equatorial groundice appears irreversible; thus, once ice has sublimated, or Fig. 15. The probable ground icedistribution resulting froma major impact beenremoved bysome other process (e.g.,impact cratering), itis inkilometers the equatorial in diameterregionshould of Mars. result The in production the excavationofa crater of any many ground tensice of difficultto seehow the depletedcrust could be replenishedby whichexisted, within the region interior to the crater walls, prior to the im- any atmosphericmeans [Clifford and Hillel, 1983; Fanale et al., pact[Clifford andJohansen, 1982]. •ORD: HYDROLOGICAND CI•MATIC BEHAVIOR OF WATER ON MARS 10,989

;• km '

Fig. 16. A rampartcrater within two earlierand concentricimpacts (20 ø S, 203ø W) [Clifford and Johansen,1982]. The oldestcrater in the sequence (Hadley)is approximately110 km in diameter,while the innermostcrater (arrow) has a diameterof roughly13 km.

and Johansen, 1980; Blasius et al., 1981; Kuzmin et al., 1988; from a subpermafrostaquifer [Clifford, 1980a, 1984]. However, Costard, 1989; Barlow and Bradley, 1990]. Advocatesof the as illustrated in Figure 7, the vertical distance separating the groundice hypothesissuggest that this latitudinaldependence is groundwatertable from the base of the cryospheremay in some consistentwith the pole-to-equatorthinning of frozen ground regions be many kilometers;thus, for replenishmentto occur, predictedby thermalmodels of the crust(e.g., Figure3). A sec- someprocess for the verticaltransport of H20 betweena deep- ond, but complementary,observation has been reported by lying sourceregion and the baseof the cryospheremust exist. In Kuzmin et al. [1988], who have found that rampart crater onset this section,three possiblemechanisms for this type of transport diametersincrease with decreasinglatitude, a relationshipthat are considered. may reflectthe greaterdepth of crustaldesiccation expected from 4.4.1. Thermal vapor diffusion. Although less dramatic and the instabilityof groundice at theselatitudes (e.g., Figure 14). energeticthan the othertwo processesdiscussed in this section, The third and final line of evidence is the tentative identification perhapsthe most importantmechanism for the vertical transport of single-rampart("pedestal") craters on Ganymede[Horner and of H20 in the Martiancrust has been the processof thermal Greeley, 1982], an observationthat is difficult to reconcilewith vapordiffusion [Clifford, 1980a; 1983]. Clearly, given the exis- an atmosphericorigin, but one that is fully compatiblewith an tenceof a water-richcrust, the presenceof a geothermaltempera- origin basedon an impactinto an ice-richcrust. ture gradient will give rise to a correspondingvapor pressure If rampartcrater ejecta morphology does indeed arise from an gradient.As a resultof this pressuredifference, water vaporwill impact into a volatile-richtarget, then perhapsthe most reason- diffuse from the higher temperature(high vaporpressure) depths able explanationfor the occurrenceof rampartcraters within the to the colder (lower vaporpressure) near-surface regolith. theoreticallyice-free interiorsof numerousolder cratersis that, It has been known for over 75 years that vapor transportin at sometime following the original lossof groundice, it was re- excess of that predicted by Fick's law will occur in a moist plenished.Given our presentunderstanding of Martian geology porousmedium under the influenceof a temperaturegradient and climate history, it appearsthat such replenishmentcould [Bouyoucos,1915]. More recently,Philip and deVries [1957] and have only occurredfrom sourcesof water residing deep within Cary [1963] haveproposed two 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 mechanisticdescription of the transportprocess. They suggest It has been proposedthat equatorialground ice on Mars may that the exchangeof water vapor in an unsaturatedsoil occurs be episodicallyor continuouslyreplenished by water derived betweennumerous small "islands"of liquid that exist at the con- 10,990 •ORD: HYDROLOGICAND CLIniC BEHAVIOROF WATER ON MARS tact pointsof neighboringparticles. The existenceof a tempera- 270 1.33 ture gradient causeswater from the warmer liquid islands to evaporate,diffuse acrossthe interveningpore space,and con- denseon the coolerliquid islandsat the oppositeend of the pore. • ' barometric In this fashion both moisture and latent heat are transferred 275 1.00 throughthe soil. The Cary [1963]model of H20 transportdiffers from the Philip and deVriesapproach in that it makesno assumptionsre- gardingthe actualmechanism of vapor transportbut merely at- 280 - 0.67 temptsto providea phenomenologicaldescription of the process saturated \ basedon the thermodynamicsof irreversibleprocesses. Despite this difference, it has been shown that the final form of the flux vaporpressure• I equationsfor bothmodels are identical[Taylor and Cary, 1964; 285 - 0.33 Jury and Letey, 1979]. After Cary [1966], the thermallydriven vaporflux is givenby

[3Def t P820Lv dT 29O 0.00 qv = - • (6) 1.0E+02 1.0E+03 1.0E+04 pry2 T3 dZ VAPOR PRESSURE (Pa) whereDef f is theeffective diffusion coefficient of H20 in CO2, Fig. 17. The saturatedvapor pressureof waterPH20 (T) as a functionof PH20is thesaturated vapor pressure of H20 at a temperatureT, crustaltemperature T comparedwith the barometricprofile of vaporin an L,,is latent heat of vaporization (--2.3 x 106 J kg-l), R v is the gas isothermalcrust, PH20(z), where, for illustrativepurposes, the temperature at constantfor water vapor (-- 461.9J kg-1 K-I), Ois thedensity of the surface of the water table has an assumed value of 290 K. liquid water,and [3is an empiricaldimensionless factor that has been found to have a mean value of 1.83 _+0.79 when measured area) reachingthe freezingfront at the baseof the cryosphereis overgeologically reasonable ranges of temperature(276-314 K), -8.3 x 10-5-2.8x 10-4 m H20yr -l. Thisflux is equivalentto porosity(0.3-0.5), saturation(0-100%), andsoil type [Juryand thevertical transport of 1 km of waterevery 106-107 years, or Letey,1979]. roughly102-103 km of waterover the course of Martiangeologic The physicalbasis for the verticaltransport of water vaporin history.However, there is reasonto believe that this thermally responseto the geothermalgradient is perhapsbest understood inducedvapor flux was even greaterin the past. Recall that by consideringfirst the equilibriumdistribution of vapor in an modelsof the thermalhistory of Mars suggestthat 4 billion years isothermalcrust. Under this condition, the vapor pressure of H20 agothe planet's internal heat flow was-3-5 timeslarger than it at any heightz abovethe watertable is givenby the barometric is today[e.g., Davies and Arvidson,1981, Schubertand Spohn, relation 1990]. Sincethe flux rate predictedby equation(6) is directly PH20(Z)-- PH20(0)exp(-z/H) (7) proportionalto the temperaturegradient, this impliesa similar increasein the volumeof water cycledthrough the early crust. wherePH2o(0) is thesaturated vapor pressure of waterat z -- 0, (Note:The flux rates reported here are -103 timesgreater than andH is the watervapor scale-height (= kT/mH20g _=36 km, thosepreviously published by Clifford [1983, 1984]. Theseear- where T = 290 K and k is the Boltzmann constant). Thus, at a height of 1 km abovethe water table, the resultinghydrostatic reductionin vaporpressure is .--3%(Figure 17). However,over thissame interval, a geothermalgradient of 15 K km-1 reduces the equilibriumsaturated vapor pressure by 68%. Becausethe thermally inducedgradient in saturatedvapor pressuregreatly exceedsthe isothermal/gravitationallyinduced gradient, water vapor condensation vaporwill diffuseupward in an effort to achievean equilibrium barometricprofile. However,as the rising vaporencounters the colderregions of the crust,the associatedreduction in saturated vapor pressureforces some of the rising vapor to condense, flux flux ultimatelydraining back to the water table as a liquid. As a result, the flux of vapor that leavesthe groundwatertable greatly upwardvaporI I I ,$ returningliquid exceedsthat which finally reachesthe freezingfront at the base of the cryosphere.As shownby Jacksonet al. [1965], once a closedsystem has beenestablished (i.e., the porevolume of the cryospherehas been saturatedwith ice), a dynamicbalance of opposingfluxes is achieved,creating a circulationsystem of rising vaporand descending liquid condensate (Figure 18). In Figure 19, the vapor flux resultingfrom a geothermal gradientof 15K km-l hasbeen calculated from equation (6) and plottedas a functionof crustaltemperature for pore sizesof 1 Fig. 18. An exampleof low-temperaturehydrothermal circulation driven by and 10 lam. Under theseconditions, the flux of vapor(per unit the Martiangeothermal gradient. CLIFFORD:HYDROLOGIC AND CLIMATICBEHAVIOR OF WATER ON MARS 10,991

270 1.33 Cintala [1992]. Their expressionfor the maximumdiameter of • thetransient cavity (i.e., before gravitational slumping ofthe • cavitywalls) written as a functionof projectilediameter De is u.{ givenby 275 1.00• 1/3 10gm .•. Dtc= 2.89 . r•ø.78U g (9) 280 '0.675 ¸m where15/oandPt are theprojectile andtarget densities, Uis the C9 impactvelocity and g isthe acceleration ofgravity atthe planet's .•' surface(allin SI units). Intheir analysis, Grieve and Cintala 285 0.33¸m [1992]assume achondritic projectile density of3.58 x 103kg • m-3 and target density of2.73 x 103kg m -3. Adopting these • samevalues, andmaking theappropriate substitution forD e (= 2 • (3rn•/4n15p)1/3,where m?-- 2E•/U2), equation (9)can be rewritten 290 0.00 to yieldthe relationshipbetween transient crater diameter and 1.0E-05 1.0E-04 1.0E-03 projectilekinetic energy where

UPWARDVAPOR FLUX, DOWNWARD LIQUID FLUX (m H20 yr-•) Dtc= 0.219Ek 0'26 U'0'09 g -0.22 (10) Fig. 19. Therma]vapor fluxes calculated from equation (6) for poresizes of 1 jzrnand 10 jzrn,and a geothermalgradient of 15 K km-1. Note that in a Thecorresponding finalcrater diameter Df canthen be found dosedsystem (such as that illustratedin Figure 18) the risingvapor flux at throughthe empiricalscaling relation of Croft [1985], which is any level is counteredby an equal and oppositedownward flux of liquid condensate. givenby

Dtc_= Dcø'15-+ø'ø4 Df0'85-+0'04 (11) lier calculations are incorrect, the result of a unit conversion error.) whereD c is thetransition diameter between simple and complex 4.4.2. Seismicpumping. In light of the densityof impactcra- cratermorphology, which on Mars occursat a diameterof ~6 km terspreserved in the crateredhighlands, perhaps the mostobvi- [Pike, 1980]. ousmechanism for thevertical transport of H20 in the crustis The foregoinganalysis suggests that a projectilewith a kine- seismicpumping. Shock waves generated by earthquakes,im- tic energyof 2.2 x 1021J will producea final craterroughly pacts,and explosive volcanic eruptions can produce a transient 33 km in diameter,assuming a characteristicMars impactveloc- dilatationand compressionof water-bearingformations that can ity of 10km s-• [Hartmann,1977]. Therefore, if thecrater size- force water to the surfacethrough crustal fractures and pores. frequencydistribution preservedin the cratered highlands is Duringthe great Alaska earthquake of 1964,this process resulted representativeof the crateringflux experiencedover the entire in water and sedimentejection from shallowaquifers as far as planet(Table 7), then a minimumof-10,000 impactevents with 400 km from the earthquake'sepicenter, with some eruptions seismicenergies greater than or equal to that of the 1964 Alaska risingover 30 m intothe air [Grantzet al., 1964;Waller, 1968]. earthquakehave occurredthroughout Martian geologichistory. In addition,seismically induced water level fluctuationswere ob- At the lower end of this size range,the forcefulclosure of water- served in over 700 wells worldwide, the most notable being a filled fracturesby impact generatedshock waves may have re- 2.3-m variation recordedin an artesianwell in Perry, Florida, sultedin surfaceeruptions of water and sedimentat distancesof locatedsome 5500 km from the quake [Cooper et al., 1968; up to severalcrater radii from the impact. However, at the high Gabert, 1968]. The Martian crateringrecord provides abundant end, the seismicenergies associated with the impactsthat formed evidence that Mars has witnessed numerous events of a similar, Hellas (-2000 km), Isidis (-1900 km), and Argyre (-1200 km), andoften much greater, magnitude. are as much as four to six ordersof magnitudegreater [O'Keefe After Bath [1966], the seismicenergy E s. associated with and Ahrens, 1975; Gault et al., 1975]. Seismic energies this an earthquakeof magnitudeM can be calculatedfrom the large may have been sufficientto disruptsubpermafrost aquifers Gutenberg-Richterrelation, where andvent groundwateron a global scale. 4.4.3. Hydrothermal convection.Given the widespreadevi- (8) 1OgloEs = 1.44M + 5.24 dence of volcanism [Greeley and Spudis, 1981; Greeley and For the 8.4 magnitude1964 Alaska earthquake,equation (8) Schneid,1991] and large impacts[Schultz et al., 1982] on Mars, yieldsacorresponding seismic energy of-2.2 x 10]7 J. However, hydrothermal activity has long been recognizedas a potentially accordingto Schultz and Gault [1975a,b], only about 10 -4 of a importantprocess in the mineralogicand geomorphicevolution projectile'sinitial kineticenergy is convertedinto seismicenergy of the planer'ssurface [Allen, 1979b; Schultzand Glicken, 1979; uponimpact. Thus, to matchthe seismicoutput of the Alaska Pieri, 1980; Newsom, 1980; Morris, 1980; Clifford, 1982]. For earthquake,an impactingprojectile must have an initial kinetic example,hydrothermal circulation has been discussed in connec- energyin excess of 102]J. tion with the developmentof the small valleys found on the The size of the craterproduced by a projectileof kineticen- flanksof Alba Pateraand five othermajor volcanoes[Gulick and ergyE k can be calculated from the crater 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 AND CLIMATIC BEHAVIOR OF WATER ON MARS

TABLE 7. CraterStatistics, Impact Energies, and Melt Volumesfor theCrater-Size Frequency Distribution of the MartianHighlands

Equivalent amax, Ornean, O to Ek, grn, Vt (= N•½* Vm), GlobalMelt km km km J N logR Ng 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 0.01 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 0.86 181.02 256.00 215.27 125.82 7.29E + 23 11 -1.74 20 2.75E + 04 3.03E + 05 2.09 256.00 362.04 304.44 168.93 2.26E + 24 8 -1.57 15 8.51E + 04 6.81E + 05 4.70 362.04 512.00 430.54 226.79 7.03E + 24 9 -1.22 16 2.63E + 05 2.37E + 06 16.33 512.00 724.08 608.87 304.49 2.18E + 25 4 -1.27 7 8.13E + 05 3.25E + 05 22.42 724.08 1024.00 861.08 408.80 6.78E + 25 2 -1.27 4 2.51E + 06 5.02E + 06 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

Global Totals 7.56E + 07 521.72

Read 2.72E + 19 as 2.72 x 1019,for instance. The statisticaldata on the cratersize-frequency distribution of the martianhighlands is takenfrom Barlow [ 1990]. The datahave been binned and analyzed usingthe relative(R plot)procedure recommended by the Crater AnalysisTechniques Working Group [1978]. The R plot techniquehighlights any deviation from a powerlaw distributionfunction by presentingthe cratersize-frequency data in differentialform (wherelog R is plottedagainst log Dmean).R -- (Dmean)3N/A(Dmax- Drain) where N isthe number of craterswithin the diameter range Drain to Dmax (Dmax = Drain •f•'), Dmean isthe geometric mean diameter of thebin (-- ,/D.minDmax andA isthe surface area over which the craters are counted (A = 8.8 x 106km 2 for Dmax < 181km and A = 8.0 x 107km 2 for Dma x > 181 km). Assumingthat the differentialcrater size-frequency distribution preserved in the crateredhighlands (i.e., R) is representativeof the crateringflux experiencedover the entireplanet, the globalnumber of impactsthat have occurredwithin a particularsize rangecan be calculatedby settingA equalto the surfacearea of Mars (= 1.45x 108km 2) and solving for N (listedunder Ng in the table). Ek is the projectile kinetic energy, Vm is the melt volume produced per impact,and V t is thetotal volume of impactmelt produced by the impactswithin a givenbin size. and Baldwin [ 1989], have consideredhow volcaniceruptions and by the vertical impact of 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 10-7 Dtc TM (12) heavilycratered terrain. which, as before, assumesa characteristicimpact velocity of An alternativemechanism for the origin of the small valleys 10 km s-•. invokesan impact-generatedheat source.As discussedby New- Given a globalcrater size-frequency distribution equivalent to som [1980], a major impact will result in the productionof a that preservedin the crateredhighlands (e.g., Barlow [1990] ), large quantityof impact melt. The interactionof groundwater and melt volumescalculated from equation(12), the cumulative withsuch a long-lived(up to 104years) heat source will resultin volume of impact melt generatedover the courseof Martian the developmentof a large-scalehydrothermal circulation system geologichistory is readily estimated.The resultsof thesecalcu- centeredon the impact.Cool waterwill enterthe systemfrom the lations,for cratersin the 8-2048 km size-range,are summarized baseof the aquifer, rise as its heated, and then flow radially in Table 7. They indicate that the cumulative fluxof impacts on awayas it reachesthe top. Directly beneath the impact, the Marshas produced a volume ofmelt equivalent toa global layer groundwatermayboil, carrying away heat through the convection over 0.5 km thick, more than 85% of which has been contributed of super-heatedwaterand steam. Fractures around the impact by impacts with final diameters greater than 103 km. maythen serve asconduits tothe surface, allowing thesteam and Thetotal heat, AQmelt, released perunit area by the cooling of boilingwater to discharge ashot-springs andgeysers around the animpact melt sheet from an initial temperature Ti toa final peripheryofthe crater. Such ascenario maywell explain theas- temperature Tfcanbecalculated from sociationof valley networkswith the outsiderims of largecraters throughoutthecratered highlands [Pieri, 1980; Schultz and' AQrnelt= pCp (T i - Tf)AZ (13) Glicken,1979; Newsom, 1980; Clifford, 1982; Brakenridge etal., wherepCp is the volumetric heat capacity ofthe melt, and Az is 1985;Brakenridge, 1990]. its thickness.From this relationship,the quantityof heat repre- AfterNewsom [1980] and Brakenridge et al. [1985],the vol- sentedby a 520-mthick global layer of impactmelt (cooling umeof waterthat is verticallydischarged byan impact-generated from an initial temperature of 1473 K to a finaltemperature of hydrothermalsystem can be estimated from the quantity ofmelt 473K) isfound to be -2.2 x 1012J m -2. Of this energy, only a producedby the impact.However, because large discrepancies small fraction (-20%) will gointo driving hydrothermal convec- existbetween the observed and theoretically predicted melt vol- tion,the remainder will be lostto the surfaceby radiationand umesof manyterrestrial impact craters, reliable estimates of im- conduction,and by heating much of thesurrounding medium to a pactmelt production have been difficult to make.To addressthis temperaturethat falls short of theboiling point [Onorato et al., problemGrieve and Cintala [1992]have recently presented a 1978;Newsom, 1980; Brakenridge et al., 1985]. revisedscaling relationship that providesa betterfit to the ob- Newsom[1980] and Brakenridge et a1.[1985]assume that any serveddata. Their expressionfor the volumeof melt produced steamgenerated by the interactionof groundwaterwith the im- CIZFFORD:HYDROLOGIC AND CLIMATICBEHAVIOR OF WATER ON MARS 10,993 pactmelt mustbe superheatedby at least300 K to reachthe sur- umesof H20 betweenthe localwater table and the base of the face.Thus, if the initial temperatureof thegroundwater is 273 K, cryosphere,it seemsreasonable to expect that the subsequent theheat from the melt mustprovide enough energy to elevatethe freezingof this waterwill createa barrierthat precludesany fur- temperaturea total of 400 K and drive a phasechange from liq- ther rise of waterbeyond the baseof the frozencrust. However, uid to steam. Based on these assumptions,the mass of steam as discussedin section4.4.1, the presenceof a geothermalgradi- reachingthe surface is givenby ent can have a profoundinfluence on both the stateand redistri- butionof crustalH20, a fact that is equallytrue whetherthe 0.2 AQmelt temperatureis aboveor belowthe freezingpoint. Indeed, there l•nstearn= (14) areat leastthree different processes, involving all threephases of CpwATwater + Lv + CpsATsteam water, that will contributeto the thermallyinduced transport of H20 throughthe cryosphere. whereCt, w and Ct, s arethe heat capacities of water and steam; In the gasphase, the transportof H20 throughunsaturated ATwater and ATstearn are the corresponding temperature intervals frozenground occurs by the familiar processof thermalvapor overwhich each phase is heated;and L v is thelatent heat of va- diffusionwhere, as before,the presenceof a temperaturegradi- porization(adopted values for all variablesare listedin Table 8). ent createsa correspondingvapor pressure gradient that drives This modelsuggests that the totalmass of waterthat was brought thediffusion of vaporfrom the warmerdepths to the coldernear- to the surfaceby impact-generatedhydrothermal systems was surfacecrust. However, subfreezing temperatures affect this pro- equivalentto a global ocean-130 m deep.For severalreasons, cessin two importantways. First, becausethe vaporflux at any however,this is likely a conservativeestimate. For example,the depthis proportionalto the local saturatedvapor pressure, the crater statisticsof Barlow [1990] do not include any correction magnitudeof vaportransport necessarily declines as the diffusing for erosionor obliteration;therefore, they likely underestimate vaporrises higher in the frozencrust. Second, as a consequence the cumulativenumber of impactsthe highlandshave experi- of this decline in temperatureand saturatedvapor pressure,a enced. Nor do Barlow's [1990] statisticsinclude any of the six portionof the ascendingvapor flux will condenseand freeze, "megabasins"(i.e., D> Hellas) that have recentlybeen reported preferentiallyblocking the smallestpores present in the pore in the literature [Schultzet al., 1982; McGill, 1989; Schultz and system.This condensation can both substantially retard diffusion Frey, 1990]. The omissionof thesebasins reflects both the ten- and chokeoff much of the pore network long beforethe larger tative nature of their identification,and the clear geometricand poresare filled with ice. With time, however,these blockages scalingdifficulties associated with estimatingthe amountof im- succumbto the samethermal process that led to their formation. pact melt producedby basinswhose diameters approach or ex- Thus, vapor will sublimefrom the ice plugs formed in the ceed the radius of Mars. It appearslikely, however, that their warmer,deeper regions of the cryosphereand redistribute itself inclusionwould increaseboth the estimatedproduction of impact (througha repeatedprocess of condensation,sublimation, and melt and the resultingcumulative flux of water by as muchas an diffusion) to the colder near-surfacecrust. In this way, the pro- orderof magnitude. cessof thermalvapor diffusion will continueuntil the cryosphere Finally, no attempthas been made to quantifythe contribution is ultimatelysaturated with ice. of igneousintrusions or volcaniceruptions to hydrothermalactiv- The possibilityof liquid phasetransport arises from the fact ity. Althougha large quantityof volcanicmaterial has been ex- that both adsorbedwater and water in small capillariescan sur- truded onto the Martian surface (estimated by Greeley and vive in frozen soil down to very low temperatures(see sec- Schneid[1991] to be equivalentto a global layer -0.5 km thick), tion 2.2). Under conditionswhere the unfrozenwater contentis its eraplacementover the preexistingtopography is not conducive high enoughto providethin film continuity,the presenceof a to the hydrothermalconvection of water from deep within the temperaturegradient creates a correspondinggradient in soil crust. However, around volcanic vents and igneousintrusions, waterpotential A•, a quantitythat reflectsthe differencein ef- the potential for the developmentof deeply circulating hy- fectivepressure between the phasesof ice and unfrozenwater drothermalsystems is greatlyincreased. To date, the bestquanti- presentin the soil.Under atmospheric conditions (i.e., in the ab- tative analysesof the interactionof dikes, sills, and lava flows senceof a confiningpressure), the magnitude of thispressure dif- with groundice are thoseof Squyreset al. [1987] and Gulick ferencecan be calculatedfrom a form of the Clausius-Clapeyron [1991]. Unfortunately,the lack of a reasonablebasis for estimat- equation[Edlefsen and Anderson,1943; Williamsand Smith, ing the number,extent, and eraplacementgeometry, of deeply 1989], given by penetratingmagma bodies on Mars precludesany global assess- mentof thequantity of watercirculated by suchactivity.

4.5. TransportThrough the Cryosphere dpw Lf (15) dT T V Althoughthermal vapor diffusion, seismic pumping, and hy- w drothermalconvection are all capableof transportinglarge vol- wherePw is thepressure (or hydraulic head) of soilwater, Lf is TABLE 8. AdoptedValues for HydrothermalCalculations thelatent heat of fusion (-- 3.35 x 105J kg-l), and V w is the spe- Vahable Description Value cific volumeof water (-- l/p) at the crustaltemperature T. Equa- tion (15) indicatesthat the pressuredifference between ice and p C•, volumetricheat capacity of melt 4.2 x 106 J m-3 K-1 waterin the soilincreases by -1.2 x 106Pa K-l for crustal C• heatcapacity of water 4188J kg-1K -1 Cps heatcapacity of steam 2092J kg-1K -1 temperaturesbelow 273 K. After Smithand Burn [1987] and •STwater 373 K-273 K 100 K Williamsand Smith [1989], the liquid flow (per unit area) that •5Twater 673 K-373 K 300 K occursin responseto this temperature-inducedpressure dif- Lv latentheat of vaporization 2.3 x 106J Kg-• ferenceis given by 10,994 CLIFFORD:HYDROLOGIC AND CLIMATIC BEHAVIOR OF WATER ON M•S

kf g d•t dT by lavas, sediments,or someother type of deposit,the resulting ql = (16) increasein insulationprovided by the depositionallayer will v dT dz causelocal crustal temperaturesto rise, permitting the buried groundice to be thermallyredistributed into the overlyingman- wherekf is thepermeability of the frozen soil, g is theac- tle. celeration of gravity, v is the kinematic viscosity, and d•t/dT The abilityof H20 to thermallymigrate through the cryos- (=_dPw/dT) is the temperature-dependentgradient in soilwater potential.Assuming a geothermal gradient of 15K km-1, a value phere also has implicationsfor the sublimationof equatorial of d•/dT-- 1.2x 106 Pa K-1 (fromequation (15)), and a frozen groundice. As the sublimationfront propagatesdeeper into the permeabilityof-2 x 10-7 darcies(a valueappropriate to a silty crust(e.g., Figure 14), it may ultimatelyreach a depthwhere the diffusiveloss of groundice is exactlybalanced by the upward clay soil at a temperaturejust below freezing [Smith, 1985; Williams and Smith, 1989]), the resultingvertical flux of liquid thermalmigration of H20 throughthe cryosphere,a condition that could significantlylimit the depth of equatorialdesiccation water throughthe base of the cryosphereis found to be -4.3 x 10-5 m yr-•, orroughly 0.4 kmevery 107 years. It shouldbe cau- predictedby currentmodels [Clifford and Hillel, 1983; Fanale et al., 1986]. Unfortunately,the processesgoverning the transport tioned,however, that this flux is highly sensitiveto boththe local of H20, bothto andfrom the sublimationfront, are sufficiently lithologyand effectiveconfining pressure of the crust;therefore, complexthat calculatinga specificdepth at which this equilib- becausethese conditions are so poorlyconstrained at the baseof rium conditionis reachedis virtually impossiblewithout a more the cryosphere,this estimate has an inherentuncertainty of as detailedknowledge of a numberof crustalparameters (e.g., li- much as two orders of magnitude.Note also, that becausethe thology,porosity, pore size, specificsurface area, heat flow, and permeabilityof frozensoil declineswith decreasingtemperature, salt content). the magnitudeof liquid transportwill necessarilydecline as the In summary,various lines of evidencesuggest that, over the water reachesthe colderand shallowerregions of the crust. courseof Martian geologichistory, at least four processeshave Finally,in additionto themovement of H20 vaporand liquid introducedsubstantial amounts of water into the atmosphere, throughthe cryosphere,transport in the solidphase can occurby these include: the sublimationof equatorialground ice, cata- the processof thermalregelation; where, as before,the direction strophicfloods, impacts, and volcanism.Under the climatic con- of transfer is from warm to cold [Miller et al., 1975; Miller, ditions that have apparentlyprevailed on Mars throughoutits 1980]. As discussedby Williamsand Smith[1989], the processof history,the atmosphericloss of this H20 from equatorialand regelationinvolves the movementof both ice and unfrozenwater temperate latitudes appears irreversible. However, if Mars is througha saturated(or nearly saturated)frozen soil. Fundamen- water-rich,then thesedepleted crustal reservoirs may have been tal to this processis the thermodynamicrelationship between replenishedby sourcesof groundwaterresiding deep within the freezing point depressionand the effective pressuredifference crust. At least three processes(thermal vapor diffusion, seismic betweenthe ice and water phasespresent in the pores. As the pumping,and hydrothermal convection) appear viable for driving geothermalgradient drives the flow of water throughthe unfro- the verticaltransport of H20 from the local water table to zen films that permeatethe cryosphere,the entry of liquid water the base of the cryosphere.While the calculationspresented in at the warm end of the pores causesa local increasein water section4.4 indicatethat all threeprocesses are potentiallyimpor- pressurethat decreasesthe effectivepressure difference between tant, the flux arisingfrom thermalvapor diffusion alone is suffi- the ice and water phases.This reductionin effectivepressure in- cient to supplythe equivalentof-1 km of water to the base of creasesthe local freezingpoint by an amountsufficient to causea the cryosphereevery 106-107 years. Thermal vapor diffusion, small quantityof water to freeze at the warm end of the pore. aidedby thermalliquid transportand regelation,may then redis- The addition of this ice also increasesthe effective pressureat tributethis H20 throughoutmuch of thefrozen crust. Note that the pore's cold 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 thereexists a crustaltemperature gradient, a subsurfacereservoir end of the pore then becomespart of the thin-film flow that en- of H20, andthe continuity of porespace between the sourcere- tersthe colderice-filled poreslocated higher in the crust,follow- gion and the near-surfacecrust. In this way, groundice that was ing which the whole processis repeatedagain. removedby impactsor sublimationto the atmospheremay have Note that becauseeach of the three thermal processesdis- beenreplenished on a global scale(e.g., Figure 20), withoutthe cussedhere operate by driving the movementof water from needto invokeexotic scenarios of climatechange. warmerto colderregions of the crust,the transportof H20 throughthe cryosphereis necessarilya one-waystreet. That is, if one attemptsto introducewater into the cryospherevia the interior atmosphere,the maximum depth of penetrationis necessarily •i..?:..!.'.:.?::::'::.:i.-.'•:•..i.:!i-).¾•.7•i::•i-.'•:•11::•':•..'•::??.:.i::.:.:';.'..':.:.7:.?:;!.'::•i.•:: ....•"'""'':'":":''"'"• limited to the maximum depth at which surfacetemperature var- ß :.•:.:•....:i.:!::•...... •.•;•.•...:...:•:.!:.:.:•:::.:.i•.:.:.::.::.):!::??..•:!i:!!;•!..?.•i::5•::•.•i•..•:•.::•:.•..•?i...)i5.:.:.?.:.:.•:' ...... iationsare sufficientto overwhelmthe influenceof the local geothermalgradient. For the surfacetemperature variations expected at equatoriallatitudes from the periodic changesin Martian (• • • ofH20 obliquity and orbital elements[e.g., Toon et al., 1980; Fanale et al., 1986], this depth is not likely to exceedmore than ten meters. In contrast,when water is suppliedto the cryospherefrom below, the processesof thermal vapor diffusion,thermal liquid transport,and regelation,will permit its eventualredistribution Fig. 20. A geothermalgradient as smallas 15 K km-I couldsupply the equivalentof 1 km of waterto the freezingfront at the baseof the cryosphere throughoutthe frozencrust. This fact has a numberof important every106-107 years, a processthat may explain how the interiorsof equa- consequences.For example, shouldan ice-rich region be buried torialcraters were recharged with groundice. CLIFFORD:HYDROLOGIC AND CLIMATIC BEHAVIOR OF WATER ON MARS 10,995

5. POLARDEPOSITION, BASAL MELTING, ANDTHE will not occurat the actualbase of the polar deposits,it will oc- PHYSICALREQUIREMENTS FOR POLE-TO-EQUATOR cur at the baseof the cryospherein responseto any increasein GROUNDWATER FLOW polar depositthickness. Should deposition persist, the polar depositsmay eventuallyreach the thicknessnecessary for melting With meanannual temperatures that are -40 K below the at- to 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 representthe dominantthermodynamic sink for H20 on the stateof equilibrium,whereby the depositionof any additionalice planet. As a result, any water that is introducedinto the atmos- at the surfaceis offsetby the meltingof an equivalentlayer at the phere, above its normal saturationlevel, is eventually cold- baseof the cap.Since this last stage is merelythe endpointin 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 broadenedhere to includeany situationwhere atmosphericdust 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 whethersuch melting oc- global dust storms,may serveas nucleationcenters for the condensationof water ice. As either hemisphereenters the fall sea- son,the suspendeddust particles receive an additionalcoating of CO2 thatmakes them heavy enough to precipitatefrom the at- a mosphere,contributing to the formationof the seasonalcaps. In the springthe CO 2 sublimesaway; however, at highlatitudes it leavesbehind a residualdeposit of H20 iceand dust that adds to the perennialcaps [Cutts, 1973; Pollack et al., 1979]. Insolation changesdue to axial precessionand periodicvariations in obliquity and orbitaleccentricity [e.g., Ward, 1974, 1979; Bills, 1990] may alter the erostonaland deposittonalbalance at the poles, as well as the mixing ratio of ice to dust in the annual deposittonal layer [Murray et al., 1973; Toon et al., 1980; Cutts and Lewis, unsaturated zone ' 1982]. Sucha scenariomay well explain the origin of the numer- • meltingisothermß ' _ I oushorizontal layers that comprisethe stratigraphyof both polar caps [Murray et al., 1972; Soderblomet al., 1973; Squyres, 1979b; Howard et al., 1982]. In this section,the effect of polar depositionon the thermal evolutionof the cryosphereand polar capsis considered.Given b an initially ice-saturatedcondition, the depositionof ice and dust • depøsitiønof at polar latitudeswill result in a situationwhere the equilibrium dust depth to the melting isothermhas been exceeded,melting ice at the base of the cryosphereuntil thermodynamicequilibrium is once again established.The drainageof the resulting meltwater into the underlyingglobal aquifer will then causethe local water table to rise in response,creating a gradient in hydraulic head that will drive the flow of groundwateraway from the poles. In basalmelting initiated the discussionwhich follows, the processof basal melting, the rise of the polar water table, and the physicalrequirements for pole-to-equatorgroundwater flow are analyzedin detail.

•.52%'.':?.'• :•//,:'•'.•k'/• :•?-;,'•.-; :C.'•'•":: 5.1. Polar Basal Melting c In studiesof terrestrialglaciers, the term "basalmelting" is depositionof dust + usedto describeany situationwhere the local geothermalheat flux, as well as anyfrictional heat producedby glacial sliding,is sufficientto raise the temperatureat the base of an ice sheetto its meltingpoint. In this regard,the processis alwaysdiscussed 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 appearsappropriate to broadenthe use of this term as it appliesto Mars. Figure21a is an idealizedcross section of 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 meltingisotherm has been exceeded(Fig- Fig. 21. An idealizedcross section of thepolar crust illustrating the possible ure 2lb). In responseto this added layer of insulation, the timeevolution of basalmelting [Clifford, 1987b].The sequencedepicts (a) a positionof the meltingisotherm will rise in the crustuntil ther- time priorto the depositionof any dustand ice, (b) the onsetof deposition mal equilibriumis onceagain established. Thus, while melting andbasal melting, and (c) meltingat theactual base of thedeposits. 10,996 CLIFFORD:HYDROLOGIC AND CLIMATIC BEHAVIOR OF WATER ON MARS cursat the actualbase of the depositsor at the baseof the cryos- mixtureshave thermal conductivities comparable to that of ice pherewithin the underlyingterrain. (i.e., >2.25W m-l K-l), whilethe rest have values as muchas As with the cryospherecalculations discussed in section2.2, 60% lower.Since the conductivities of mostclay minerals equal the polardeposit thickness required for basalmelting can be cal- or exceedthat of ice [Clark, 1966;Horai and Simmons,1969], it culatedby solvingthe one-dimensionalsteady state heat conduc- is difficultto explainhow any mixture of thesetwo components tion equation.After Weertman[1961] and Clifford [1987b], this couldhave a lower value. As discussedin section2.2.1, this dis- thicknessis given by crepancymay be explainedby the presenceof low-conductivity adsorbedwater on highspecific area clay. In Table 9, basal melting thicknesseshave been calculated = (17) basedon a meanpolar surfacetemperature of 154 K, thermal Qg + Qf conductivitiesof 1.0-3.0 W m-l K-l, andmelting temperatures of 252 and 273 K. In addition,to assessthe potentialfor basal where•c is the effectivethermal conductivity of the polardepos- meltingat earlier epochs,calculations have also been carriedout its,Trn p is themelting temperature of the ice, Tins is themean for heatflows of 90 and150 mW m-2 [e.g.,ToksOz and Hsui, polarsurface temperature, Qgis the geothermal heatflux, and Qf 1978; Davies and Arvidson, 1981; Schubertand Spohn, 1990]. is the frictionalheat due to glacialsliding. With the exceptionof For these calculations,no pressure-inducedfreezing point de- the frictional heat term, all of these variables are discussedat pressionor frictional heat input due to glacial sliding was as- lengthin section2.2. However, becauseof differencesin the de- sumed. gree of homogeneity,particle size, and ice content,the thermal Based on an analysis of Mariner 9 radio occultation data, conductivityof the polar depositsis likely to differ from that Dzursin and Blasius [1975] have determined that the Martian which characterizesthe regolith or crust as a whole. For this polarcaps reach a maximumthickness of 4-6 km in the northern reason,both the thermal conductivityof the polar ice and the hemisphereand 1-2 km in the southern.Therefore, only in the potentialrole of glacial sliding are discussedhere in greater north does the total thicknessof the cap overlap the potential detail. rangeofpresent-day (i.e.,Qg -- 30 mW m -2) basal melting thick- The thermalconductivity of the Martian polardeposits is de- nesseslisted in Table 9. In the south,the depositsappear suffi- terminedby suchfactors as the volumetricmixing ratios of ice cientlythin that any melting is likely to be relegatedto a depth anddust, their spatialvariability, temperature-dependent thermal that lies well below the regolith-polarcap interface.Of course, properties,and the presenceof othercontaminants, such as salts. given the higher geothermalheat flow that likely characterized While a comprehensiveanalysis of thesefactors is beyondthe the planet'searly history, the conditionsfor basal melting (at scopeof this paper,a reasonablerange of valuescan be inferred both poles) were almost certainly more favorable in the past. fromthe availabledata. For example,the light-scatteringproper- However,even under currentconditions, given an initially ice- ties of the dust suspendedin the Martian atmosphereindicate saturatedregolith, melting at the base of the cryosphere(Fig- grain diametersin the rangeof 0.2-2.5 gm [Panget al., 1976; ure 21b) appearsto be an inevitableconsequence of polar depo- Pollacket al., 1979;Chylek and Grams,1978]. If this sizerange sition. is representativeof the dust entrainedin the polar ice, then the For basalice at the meltingpoint, the thicknessof the layer Az thermalproperties of the polar depositsshould be closelyap- thatcan be melted per unit area by a geothermalheat flux Qg is proximatedby laboratorymixtures of ice andclay. givenby In Figure 22 the thermal conductivitiesof variousclay-ice mixturesare plottedas a functionof their volumetricice content. Qg Additionalinformation about these mixtures is presentedunder Az = At (18) the "frozensoil" headingof Table 2. Note that roughlyhalf the pLf

3.5 whereLfis the latent heat of fusionand At is theelapsed time. i I I i I I Thus,a geothermalheat flux of 30 mWm -2 hasthe potential for meltingas much as 3 x 10-3 m of icefrom beneath the polar caps

TABLE 9. CalculatedBasal Melting Thicknesses 2.5- Geothermal PolarDeposit Heat Flux, ThermalConductivity Thickness,km 2.0- mW m -2 Wm-I k-1 252 K 273 K

ß Sanger (1963) 30 1.0 3.27 3.97 1.5- ß Penner (1970) o Lachenbruch (1970) 2.0 6.53 7.93 [] Kersten (1963) 3.0 9.80 11.90 /x Higashi (1953) 1.0- 90 1.0 1.09 1.32 2.0 2.18 2.64 0.5- I I I I I 3.0 3.27 3.97 35 40 45 50 55 60 65 70

VOLUMETRIC ICE CONTENT, % 150 1.0 0.65 0.79 2.0 1.31 1.59 Fig. 22. The thermalconductivities of variousterrestrial clay-ice mixtures 3.0 1.96 2.38 plottedas a functionof their ice content[Clifford, 1987b]. Additionalinfor- marionis presentedin Table2. Theseresults assume a meanpolar surface temperature of 154 K. CLIFFORD:HYDROLOGIC AND CLIMATIC BEHAVIOR OF WATER ON MARS 10,997

eachyear. Of course,if glacial sliding shouldoccur, the resulting gradientin hydraulichead createdby the presenceof the mound frictionalheat couldboth substantiallyreduce the requiredthick- will then drive the flow of groundwateraway from the poles.The nessfor basalmelting and increasethe productionof meltwater. two principlefactors that will governthe magnitudeof this transø Fora givenbasal sliding velocity Vb thefrictional heat flux Qf port are the size of the groundwatermound and the effective can be calculated from permeabilityof the crust.In the following discussion,the relative importanceof these factors is assessedthrough the use of well establishedterrestrial hydrogeologic models. Qf = VbZb dh (19) = VbPigh• dx 5.2. Growth of a Polar GroundwaterMound The development of a groundwatermound in response to where•, is thebasal shear stress, Pi is thedensity of thepolar ice polar basal melting is analogousto a problemfrequently studied (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 slope at the polar cap'ssurface [Weertman, 1961; Clifford, 1982]. To obtain an analytical expressionfor the growth of a 1987b].As seenin Figure23, a slidingvelocity of 10 m yr-1, groundwatermound beneath a rechargingsource, a number of driven by a basal shearstress of 100 kPa (a value typical of ter- simplifyingassumptions must be made, i.e., (1) the aquifer is restrial glaciersand ice sheets[Paterson, 1981 ]), generatessuf- homogeneous,isotropic, infinite in areal extent, and rests upon ficientheat (-30 mWm -2) to halvethe thicknesses necessary for an impermeablehorizontal base; (2) the hydraulicproperties of basalmelting during the presentepoch. the aquiferare invariantin both spaceand time; and (3) the con- Possibleevidence of pastbasal melting has been discussedby stantdownward percolation of 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 almostcompletely refracted in the directionof the local of the braidedridges of the DorsaArgentea region (78 ø S, 40ø W, slopeof the water table when it reachesthe mound [Hantush, Figure24) to terrestrialeskers, landforms created by the deposi- 1967; Marino, 1975; Schmidtkeet al., 1982]. tion of fluvial sedimentsbeneath glaciers and ice sheetsthat have After Hantush [1967], the governingequation for the devel- undergonebasal melting. In addition, Clifford [1987b] has cited opmentof a groundwatermound beneath a circular recharging the geomorphicsimilarities between the major polar reentrant source is Chasma Boreale (85ø N, 0ø W) and the outflow channel Ravi Vallis (1ø S, 43ø W), suggestingthat ChasmaBoreale, and simi- 32Z 1 •Z 2 w ¾ œ¾ •Z lar features found elsewherein the polar regions, may have + + (20) formedas the resultof a j6kulhlaup,the catastrophicdrainage of •r 2 r •r kg •'k g •t a large subglacialreservoir of basal meltwater. A terrestrial example of this processis the recurrentcatastrophic drainage of Grimsv6tn, a large subglaciallake in the center of the Vatna- whereZ = h2-hi2, h is theheight of thewater table above the j6kull ice cap in Iceland[Nye, 1976]. baseof the aquiferafter an elapsedtime t, hi is the initial satu- Given the presenceof a subpermafrostaquifer and geologi- rated thicknessof the aquifer, h is a constantof linearization cally reasonablevalues of crustalpermeability, the deep infiltra- (= 0.5(h+ hi)) whichrepresents the weightedmean depth of tion of basal meltwater will result in the rise of the local water saturation [Hantush, 1964], r is the radial distance from the table in the form of a groundwatermound (Figure 21c). The centerof the mound,w is the rechargerate per unit area, k is the aquiferpermeability, g is the accelerationof gravity,¾ is the kinematicviscosity, and œ is the effectiveporosity. The boundaryand initial conditionsthat apply to equation (20) are

Z(r, O) -- 0 • [ /150kPa/__ •Z(O, t)/•r-- 0 w--w (Oa) Z(oo, t) = 0

These conditionscorrespond to four basic assumptions:(1) the water table is initially horizontal,(2) the groundwatermound is symmetricabout its vertical axis, (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 large radial distances 0 [Hantush, 1967; Marino, 1975' Schrnidtkeet al., 1982]. 0 10 20 30 40 50 After Hahtush [1967], equation(20) can be solvedusing La- BASAL SLIDING VELOCITY (m yr 'l) placeand zero-orderedHankel transformsto obtainthe following Fig. 23. The frictionalheat produced by basalsliding under an appliedbasal expressionfor the maximumheight h m of the water table shearstress of 50, 100, and 150 kPa [Clifford, 1987b]. (evaluatedat r -- 0) at any time t 10,998 CLIFFORD:HYDROLOGIC AND CLIMATICBEHAVIOR OF WATER ON MARS

Fig.24. Braidedridges, in theDorsa Argentea region (77øS, 44øW), that have been interpreted as possible analogs of terrestrialeskers (Viking Orbiter frame 421B14).

Note that the solutiongiven by equation(21) is valid for ground- hm2- h/ = Qr¾W(tto) + (21) watermound heights (bin-hi) up to 50% of the initial depthof 2nkg 1-uoe-Uo I saturation(hi) [Hahtush,1967]. wherethe recharge volume Qr-- lrzl2w, u o -- a2ve/4kgh t, and Developmenttimes for groundwatermounds from 100 m to whereW(u o) is thewell function for a nonleakyaquifer given by 2500 m in heightare presentedin Table 10 and Figure25. These times were calculatedfor four rechargevolumes, ranging in size -u o from0.01-2.2 km 3 H20yr -1, andare based on hydraulic prop- W(uo) = duo erties that might reasonablycharacterize the Martian crust. The o glo calculationsassume saturated aquifer thicknessesof 1 km and (22) 5 km, an effectiveporosity of 0.1, and a permeabilityof 1 darcy. = -0.5772 - logeUo + For comparisonpurposes, a secondset of developmenttimes (-1)l+nn-n!Uo n i=l werecalculated fora rechargevolume of 0.01 km 3 H20 yr -1 and

TABLE 10. GroundwaterMound Heights as a Functionof Time

Time t, years

Initial Aquifer Groundwater Mound O -- 2.2 km3 yr-1 O -- 1 km3 yr-• O -- 0.1 km3 yr-• O -- 0.01 km3 yr-• Thickness Height hi, m hm - hi, m k = 1 darcy k = 10 mdarcies

1000 100 3.54E3 7.84E3 9.95E4 1.47E9 7.85E5 200 7.08E3 1.57E4 3.75E5 -- 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

50OO 100 3.54E3 8.18E3 1.46E6 -- 8.18E5 500 2.39E4 1.23E5 • • 1.23E7 1000 1.00E5 2.08E6 • • 2.08E8 2500 8.33E6 ....

Unlessotherwise noted, development times are based on an effectiveporosity of 0.1 anda crustalpermeability of 1 darcy(=10-12m2). Read 3.54E3 as 3.54 x 103,for instance.No entryindicates a development time greater than the age of thesolar system. •ORD: HYDROLOGICAND CLIMATIC BEHAVIOR OF WATER ON MARS 10,999

600

550 _(a) Aquifer Thickness: 1000 m

500 - O= 2.2 km 3yr -1 450 - O= 1.0km3 yr-1 400 -

350 -

300 -

250 - O= 0.1km 3 yr-•

200 - = 0.01km3 yr-1 150 - •k=10 md) 100 -

50 I I I IllIll I I I IllIll I I I IllIll I II IIIIII I I I Illll 103 104 105 106 107 10• TIME, t (yrs)

!- 3000 -1- (b) Aquifer Thickness- 5000 rn iii 2500 2.2

z • • 2000 OE n' , 1500 •Q= 0.01 km3yr-l• ,•/ •: 1000

Z • 500 o J Q:0'1 km3 yr-1 ! ! I IllIll I I I IlIIII I I I IIIIII I I I IIIIII I I I IIIIII I I I IIIIII I I I Illl' 103 10'• 105 106 107 108 109 10•ø

TIME, t (yrs)

Fig.25. Groundwatermound development times for rechargevolumes between 0.01 and2.2 km3 H20 yr-I andaquifer thicknesses of (a) 1000m and (b)5000 m. Unlessotherwise noted, the calculations assume a crustal permeability of 1 darcyand a basalmelting radius equal to that of thepermanent north polarcap (a = 5 x l0 s m). a permeabilityof 10 -2 darcies.In allcases, the radius of thebasal Groundwatermound development times also lengthenif the meltingarea was taken to beequal to thatof thepermanent north rechargevolume is reduced.For example,cutting the recharge polarcap (a = 5 x 105m). volumefrom 2.2 km 3 to 0.01 km 3 H20 yr -1 increasesthegrowth For an aquiferwith an initial saturatedthickness of 1 km and timefor a 100 m moundin a 1-km-thickaquifer to over 109 a rechargevolume of 2.2km 3 H20yr -l (equalto the maximum years. In contrast,a reductionin crustalpermeability shortens volumeof ice that couldbe meltedper year from beneaththe developmenttimes. This is illustratedby reducingthe permeabil- northpolar cap by a geothermalheat flux of 30 mWm-2), the re- ity in the precedingexample from 1 to 10-2 darcies,thereby sultssummarized in Table10 indicatethat a groundwatermound shorteningthe developmenttime for a 100 m moundto lessthan will growto a heightof 100m in lessthan 4 x 103years_and 106 years. reacha heightof 500 m in a littleover 104 years. Although these The differencein developmenttime thatresults from a change growthtimes lengthen considerably as the initial saturatedthick- in aquiferthickness, permeability, or rechargevolume, simply nessof the aquiferis increased,even in a 5-krn-thickaquifer, a reflectsa changein the relative massbalance of water between groundwatermound 2500 m highwill developin lessthan 107 verticalrecharge Qr, storage(i.e., thevolume of watercontained years[Figure 25b]. in themound), and radial discharge Qd, which is given by 11,000 CL•'FORD: HYDROLOGICAND CLIMATIC BEHAVIOROF WATER ON MARS

Qa-- 2reah v (23) whereh is the saturatedthickness of the aquifer at r = a, and v is Q the specific discharge(the dischargeper unit area) given by Darcy'slaw

kg •)h v = - (24) v •)r I AQUIFER I ! '• ',

Of course,when the radial dischargeof the moundfinally bal- ancesthe vertical recharge,a steady state conditionis reached. The permeabilityrequirements necessary to supportsuch steady stateflow are discussedin the following section. ',-',-,,-,•'-,•-,7-,•'-,"2,'-2,'- \ - \ -. \•\<. •'..'\'..'\",./ ./\. .... \./,\./,•./:./.,, z-'.-\. l \ / I x`/ I x`,' ix`\' i x`,",'•\.'_,'- x` x` \ x`.... \-/x-/x-Ix`-/' ,. ,. ,,\,,x`-I -I,; -/ BASEMENT .....'.. • '..\ " \ " i•,f .• , '.' ,;4\'4, -.'•-.,•-,•. ,•.,• 5.3. The Effect of Crustal Permeabilityon Pole-to-Equator -. ,E/x-,x-/x-/,_ .... .'-_.,.'-_,-- .--,..., ..x ..\ ..\ Groundwater Flow Fig. 27. A schematicdiagram of confinedsteady state well flow. Given the presenceof a global interconnectedgroundwater systemon Mars, the developmentof a groundwatermound in h2= hi2 + QrV In(R/r) (26) responseto polar basalmelting will createa gradientin hydraulic rck g headthat will drive the flow of groundwateraway from the pole. The effect of crustalpermeability on the magnitudeof this flow Evaluated at r -- a, equation (26) yields an expressionfor the can be readily assessedon the basis of establishedmodels of maximumhydraulic head which can then be solvedfor k to find unconfinedand confinedsteady state well flow. In this analysis, the permeabilitynecessary to sustain unconfinedsteady state the well radius,a, is equivalentto the radius of the recharge(or flow basalmelting) area discussedin the previousanalysis; while, as before, the groundwatermound height is taken to be the dif- ferencebetween the maximum and minimum hydraulicheads QrV = 2 2 In (R / a ) (27) (hm-hi).The distanceR to the regionof lowesthydraulic head rcg(hm - hi) representsthe separationbetween the regions of net vertical recharge(the poles) and discharge(the equator), and is taken Of course,the possibilityexists that, in an initially unconfined here to be of the order of the planetary radius of Mars. These aquifer,a polar groundwatermound could grow to the point of relationshipsare illustratedin Figures26 and 27. contactwith the baseof the caps;in this event, the aquifer will The governingequation and appropriateboundary conditions undergoa transitionbetween confined conditions at the polesto for steadyunconfined well flow are [after Todd, 1959] unconfinedconditions closer to the equator.It is also possible that the polar aquiferhas been confinedfrom the very outsetof (25) basalmelting (i.e., see Figure 7). Given either case,the solution 3r 3r presentedin equation(27) is no longervalid. The possibilityof confinedflow can be analyzedby solving the steadyconfined well equation,which, after Todd [1959], is h2 -- hi 2 (r = R) givenby Qr = 2rcrhv (i.e., Qr-- Qd)

where as before, v is the specific discharge(the dischargeper r-- = 0 (28) unit area) givenby equation(24). Solvingequation (25) in light 3r 3r of the aboveboundary conditions, we obtain and which is subjectto the followingboundary conditions

Q h--hi(r=R ) Qr-- 2rer hi v •i•.•...•:(.:.;:.!.:!:).i.::•i:!....:.:.!:•:i:.!}•..i. :...... !.!?•::.i.:i!•:i.•.•:•.•.:.::.•(;•.:!.5: •:y...::.:::;..!:..:•.....:!:;i::)!.....T...•..:i:.....?:.:..::•:.•.....:)i.....:.•.•:•.:?....!..)...: ' Solvingfor the permeability of the crustin the same manneras ...... before,yields v ?:"' ', I I v ß -- ' I I I I I -- ; AQUIFER , • ! ! - '1' I ', I ; k = Qrv In(R/a) (29) 2 rcghi(h m - hi)

v ) I I I I In Table 11 and Figure 28, crustalpermeabilities necessary ,(- -/? -/•.. - • ,/•../.•,/•. ,/•.,/•../•.,/• ./-•,/.•./•,/.•,/•,/-• -/•,/• ,/.• ,/.• ,/• ,/?,/• \l/\l/\l/\l/\l/\l/\l/\l/\l/\l/x`l/\l--. \ -. ... \-. \ .. \ .• \.• \ .. \ .• \.. \ .. \../\ \l/\l/\l/xl/xl/xl•, \ .. \ .. \ ... \.. \7./\...x.I/\l/x.I/x.I/x.I/\ \ .. \• \ • \ • \ for steadystate flow (calculatedfrom equations(27) and (29)) \1\7'/\"' .xlz\l/\l \" \•'/\"\l/\l/\l/\l/\l/\l/\,t/\l \'• \'• \" \" \'• \'• \,"/x".xl/\l/.xl/\l \" \"\ D/'•.•.IVI•.111\ x •. x` '"- \" \" \ are presentedfor a reasonablerange of polar rechargevolumes and net hydraulicheads. The resultsindicate that a recharge Fig. 26. A schematicdiagram of unconfmedsteady state well flow. volumeof I km3 H20yr -l, introducedinto a 1-km-thickaquifer •ORD: HYDROLOGICAND •TIC BEHAVIOROF WATER ON MARS 11,001

TABLE 11. PermeabilityRequired for SteadyState Flow

Permeabilityk, darcies

Initial Aquifer Groundwater Mound Thickness Height Q- 2.2km 3yr -I Q- 1km 3yr -I Q= 0.1 km 3yr -I Q- 0.01km 3yr-I hf•n hm-h•,m Unconf'medConfined Unconf'medConfined Unconf'medConfined UnconfmedConfined

1000 100 102.0 107.0 45.96 48.25 4.60 4.83 0.46 0.48 200 48.69 53.56 21.93 24.13 2.19 2.41 0.22 0.24 300 31.05 35.71 13.99 16.08 1.40 1.61 0.14 0.16 400 22.32 26.78 10.05 12.06 1.01 1.21 0.10 0.12 500 17.14 21.42 7.72 9.65 0.77 0.97 0.08 0.10

5000 100 21.21 21.42 9.56 9.65 0.96 0.97 0.10 0.10 500 4.08 4.28 1.84 1.93 0.18 0.!9 0.02 0.02 1000 1.95 2.14 0.88 0.97 0.09 0.10 0.01 0.01 2500 0.69 0.86 0.31 0.39 0.03 0.04 0.003 0.004

103 than5 x 10-3 darcies,a valuethat lies within the lower extreme "=(a) . AquiferThickness- 1000 rn of measuredpermeabilities for fracturedigneous and metamorphic rock (Figure 29). Note that even this low value of crustal 102:: permeabilitypermits the pole-to-equatortransport of as much as 4.5x 107km 3 of groundwater(from each pole) over the course of 10 h.,- h,= 100rn Martiangeologic history, or-108 km 3 H20 (equivalent toa global ocean-600 m deep) when the potentialcontribution of both polesis takeninto account. 1 h., - h, = 500 rn mQ 5.4. The Large-ScalePermeability of the Martian Crust 10'• The significanceof the steadystate permeabilitiespresented in Table 11 can be placedin perspectiveby comparingthem with 10-2 , , , ,,, , , , , ,,,,, , , , ,,,,,, , , , , ,,,, the crustal values assumedby Carr [1979] in his discussionof the origin of the outflowchannels. Based on both the size of the RECHARGEVOLUME Q (km3 yr-:) channelsand the assumptionthat each was formed by a single catastrophicevent, Carr [1979] calculatedthat dischargesof 102 -107 to 5 x 108m 3 s-! werenecessary to produce the observed (b) Aquifer Thickness:5000 rn erosion.To achieverates this high requires large-scaleperme- abilitieson the orderof 103darcies, permeabilities that Carr lO [1979] arguedwere only reasonableif the Martian crust was in- _ _- tenselyfractured and/or possessednumerous unobstructed lava 1 tubes, characteristicssimilar to those of certain Hawaiian basalts [Davis, 1969]. Argumentsfor crustal permeabilities of 103 darcies or higher have also been advancedby MacKinnon and Tanaka [1989]. lO-2 • hi,,-h, =2500 REL A TI VE PERMEA BILI T Y 1o -3 i I i i i iiii i i I i iiiii i i i i illit i i i i i iii o.ool O.Ol o.1 1 lO •permeable basalt fractqredigneous a RECHARGEVOLUME Q (km3 yr'•) meta{morphicrock

Fig. 28. Permeabilityrequired for pole-to-equatorsteady state flow for Mars' 'fractured zone' various rechargevolumes and groundwatermound heights in aquifers MacKinnon and Tanaka (a) 1000 m and (b) 5000 m thick. Unlessotherwise noted, the calculations unfracturedmetamorphicigneous rock & *-Ave.,Earth's crust (1989) assumea crustalpermeability of 1 darcyand a basalmelting radius equal to Megaregolith value thatof thepermanent north polar cap (a = 5 x 105m). required for inferred '•"•':•;'•':•'::•='='•=":':•?":•...... I Brace(1980,1984) outflow channel silt, Ioess discharge rates Carr (1979) at the poles,could drive the flow of a similar volumeof water to grav{,•l the equator,given a crustalpermeability of-100 darciesand a groundwatermound height of 100 m. If the rechargevolume is -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 loweredto0.01 km 3 H20yr -1, and if wepermit a nethydraulic LOG k (darcies) headof 2500 m (equivalentto the lithostaticpressure exerted by a 1.5-km thicknessof ice-rich permafrost),then the minimum Fig. 29. Relative permeabilityof typical terrestrialgeologic formations permeabilityrequired to supportsteady state flow falls to less (after Freeze and Cherry [1979]). 11,002 CIJFFORD:HYDROLOGIC AND CLIMATIC BEHAVIOR OF WATER ON MARS

Basedon gravity studiesof terrestrialand lunar impact craters, levels far in excessof their respectivesaturation points. The and boreholeobservations of terrestrialimpact and explosioncra- resultingprecipitation of theseminerals beneath the water table ters,they suggestthat porositiesas high as 20% may characterize shouldlead to widespreaddiagenesis and to thedevelopment of a the Martian fracturedbasement. They further suggestthat much distinct geochemicalhorizon within the crust [Soderblomand of this impact-generatedporosity may occuras open planar frac- Wenner, 1978]. Where exposedby subsequentfaulting or ero- tureshaving widths of 1-5 mm and associatedpermeabilities as sion, this horizonshould appear as a relativelycompetent layer greatas 104 darcies. whoseupper boundary conforms to a surfaceof constantgeopo- Althoughlocal permeabilities ashigh as 103 darciesundoubt- tential. Althoughnot diagnosticallyunique, suchan observation edly occur on Mars, on a globally averagedbasis, an effective is consistentwith mineraldeposition in an unconfinedaquifer in permeabilitythis large seemsdifficult to reconcilewith the five hydrostaticequilibrium. order-of-magnitudesmaller value inferredfor the near surfaceof In summary,although previous estimates of the large-scale the Earth [Brace, 1980, 1984]. Therefore,given the generalim- permeabilityof the Martian crust have run as high as 103 darcies, portanceof this parameterto understandingthe subsurfacehy- considerationof the mean permeability of the Earth's crust drologyof Mars, just how reliableare thesehigher estimates? [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 thus high permeabilities)to accountfor the magnitudesmaller. As discussedin section5.3, even perme- origin of the outflow channelsis basedon the assumptionthat abilities this low will permit the pole-to-equatortransport of a each channel was carved by a single catastrophicevent. How- significantvolume of groundwater(• 108 km 3) overthe planet's ever, if the channelswere createdby multiple episodesof out- history.It shouldbe noted,however, that even if only a few per- break and erosion,or by continuousshallow flows actingover a cent of the Martian crust possessespermeabilities as high as prolongedperiod of time, then the need for high crustalperme- those estimatedby Carr [1979] and MacKinnon and Tanaka abilitiesis significantlyreduced. [1989], the potential for pole-to-equatorgroundwater flow will Similarqualifications apply to the high permeabilitiesinferred be vastlyincreased. by MacKinnonand Tanaka [1989]. The validity of their analysis restson two key assumptions:(1) that the gravity anomaliesas- 6. TH• EARLY EVOLUTION OF THE MARTIAN sociatedwith terrestrialand lunar cratersare almostexclusively HYDROSPHERE AND CLIMATE 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 open and planar. As discussedbelow, there are good reasonsto H20 is criticallydependent on the natureof the planet'searly climate.Was Mars was warm and wet, as suggestedby the valley questionboth assumptions. networks?Or has it always resembledthe frozen state we ob- First, contrary to the assertionby MacKinnon and Tanaka servetoday? And, finally, if the climatedid startwarm, how was [1989], the largestcontributor to the gravity anomaliesrecorded the planet'shydrologic cycle affected by the onsetof coldertem- over terrestrialand lunar cratersis not the fractureporosity of the peratures?These, and severalrelated questions about the devel- surroundingbasement, but the increasein porosityassociated with the breccia lens at the bottom of the crater [Dvorak and opmentof the early hydrosphereand climate, are addressedin the followingdiscussion. Phillips, 1978]. As discussedby Shoemaker[ 1963], Short [ 1970], and Grieve and Garyin [1984], the breccia lens consistsof coun- 6.1. The Evolutionof the Early Martian Climateand the try rock that is pulverizedalong the wall of the transientcavity InitialEmplacement of Crustal t120 and then slumpsto the bottomlater in the crateringevent. As such,its lithologyconsists of boulder-sizedfragments imbedded Given the geomorphicevidence for 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 more closelyrelated to thoseof accountingfor this distributiongiven the presentclimate, it has a low-permeabilityglacial till than to a regularnetwork of open been suggestedthat the Martian climate was originally more planar fractures.Second, shock waves generated by subsequent Earth-like,permitting the global emplacement of crustal H20 by impactswill help to eliminateany sizableopenings in the frac- directprecipitation as snowor rain [e.g., Masurskyet al., 1977; tured basementby both shifting and compactingthe overlying Pollack et al., 1987]. The resemblanceof the valley networksto debris(i.e., seeFigure 1) and by rupturingadditional material off 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) heavily crateredter- fracture boundaries[Short, 1970]. rain, is often cited as evidenceof just sucha period. Finally, as noted in section2.1, the presenceof groundwater Clearly, if the valley networksdid originatefrom an early epi- can also contributeto a significantreduction in crustalporosity sodeof precipitationand surfacerunoff, it requiredatmospheric and permeability.On Earth, groundwaterthat residesin the crust pressuresand surfacetemperatures far higher than those ob- for millions of yearsgenerally evolves into a highly mineralized servedtoday. For this reason,it has been suggestedthat early brine consistingof a saturatedmixture of chlorides,carbonates, Mars possesseda greenhouseclimate, a conditionthat would sulfates,silica, and a variety of other dissolvedspecies [White, haverequired in excessof 5 barsof CO2 andthe presenceof 1957]. On Mars, this geochemicalevolution will likely be accel- other potentgreenhouse gasses, such as methaneand ammonia, erated by the influx of mineralsleached from the crust by low- to maintainsurface temperatures above freezing [Postawkoand temperaturehydrothermal circulation (see section4.4.1 and Fig- Kuhn, 1986; Pollack et al., 1987; Kasting, 1987, 1991]. Al- ure18). The convective cycling of 102-103km of water(per unit thoughthis amount ofCO 2 is---102-103 times more than contain- area) betweenthe water table and the baseof the cryospherewill ed in the presentatmosphere, it is well within currentestimates depletethe interveningcrust of any easily dissolvedsubstances, of the planet'stotal volatile budget [Pepin, 1987]. The surface concentratingmany of them in the underlyinggroundwater to erosionexpected from sucha massiveearly atmospheremay also CLI•ORD: HYDROLOGICAND CI.•MATICBEHAVIOR OF WATER ON MARS 11,003

explainthe early episodeof craterobliteration inferred from Althoughit is possiblethat evidenceof an ancientperiod of craterdiameter-frequency plots of the ancientcratered highlands globalprecipitation has been lost by erosionand resurfacing,it [Mutch et al., 1976; Arvidson et al., 1980; Carr, 1981]. seemsequally reasonable.to take this lack of evidence at face However,if Mars did possessan early greenhouse,then what valueand consider the poss!bility that such an episodemay never causedthe atmospheric 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 suggestthat the emplacement of crustal H20 wasthe result of the processesappear likely. Calculationsby Watkins and Lewis direct injectionand migrationof juvenile water derivedfrom the [1985] suggestthat shockwaves from large impactsmay have planet'sinterior. There are at least two ways in which this em- blown off a significantportion of the early atmosphere.This placementmay have occurred.First, by the processof thermal processwas probablymost effective during the heavybombard- vapordiffusion, water exsolvedfrom coolingmagmas will mi- mentperiod, when largeimpacting bodies were still prevalentin gratefrom warmerto colderregions of 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 becomesaturated with ice. The ionosphere.Particle velocities within the resultingplasma flow introductionof any additionalwater will then result in its accu- couldhave easily exceeded the planet's 5 km s-I escapevelocity. mulationas a liquid beneaththe cryosphere,where, under the Calculationsindicate that this processalone could have reduced influenceof the growinglocal hydraulichead, it will spreadlat- a denseearly atmosphereto its presentstate in lessthan a billion erally in an effort to reachhydrostatic equilibrium. years[Perez-de-Tejada, 1987]. Finally, atmospheric CO 2 may However, the fate of water released to the cold Martian at- have been lost to the regolithby both adsorption[Fanale et al., mosphereis significantlydifferent. The rapid injectionof a large 1986] and by reactionwith surfaceand subsurface liquid water to quantityof vapor into the atmosphere(e.g., by volcanism)will form carbonate rocks [Booth and Kieffer, 1978; Kahn, 1985; lead to its condensationas ice on, or within, the surrounding Pollack et al., 1987]. Ultimately, all four processesmay have near-surfaceregolith. As the availablepore spacein the upper contributedto reducingthe atmosphericpressure and tempera- few metersof the regolithis saturatedwith ice, it will effectively ture to the point where liquid water was no longerstable at the sealoff and eliminateany deeperregion of the crustas an area of surface.Proponents of this idea suggestthat this transition oc- potentialstorage. From that point on, any excesswater vaporthat curredsome 4 billion yearsago; thus, ending the periodof valley is introducedinto the atmospherewill be restrictedto condensa- network formation. tion and insolation-driven redistribution on the surface until it is An alternativeschool of thoughtsuggests that the early Mar- eventuallycold-trapped at the poles. tian climatedid not differ substantiallyfrom that of today. Advo- Shouldthe depositionof ice at the polescontinue, it will ulti- catesof this view [e.g., Pieri, 1979, 1980; Carr, 1983] find no mately lead to basalmelting, recyclingwater back into the crust compellingreason to invoke a warmer,wetter period to explain beneaththe caps.As the meltwater accumulatesbeneath the po- the origin of the valley networks.Rather, they cite evidencethat lar cryosphere,it will create a gradient in hydraulic head that the primary mechanismof valley formation was groundwater will drive the flow of groundwateraway from the poles. As the sapping[Sharp and Malin, 1975; Pieri, 1980; Baker, 1982; Carr, flow expands radially outwards, it will pass beneath regions 1983; Brakenridge et al., 1985; Baker and Partridge, 1986], a where, as a result of vapor condensationfrom the atmosphere, processthat doesnot requirethat surfacewater exist in equilib- only the top few meters of the cryospherehave been saturated rium with the atmosphere.According to this scenario,as ground- with ice. As before, the presenceof a geothermalgradient will water seepedonto the surface,the heat removed by its rapid thenlead to thevertical redistribution of H20 fromthe underly- vaporizationled to the formation of a protective and thick- ing groundwaterto the cryosphereuntil its pore volume is satu- ening cover of ice, beneathwhich water may have continuedto rated throughout(see section 4.5). In this way, and by these flow for considerable distances even under current climatic con- processes,the early crust may have been globally chargedwith ditions [Wallace and Sagan, 1979; Carr, 1983; Brakenridge et water and ice without the need to invoke an early period of at- al., 1985]. mosphericprecipitation. Of course,if the early climatewas similar to the presentone, why are the valley networks found almost exclusively in the 6.2. The HydrologicResponse of Mars to the Thermal ancientcratered highlands? As discussedin section4.4, the as- Evolution of lts Early Crust sociationof most small valleys with the rims of large craters suggestsa geneticrelationship, whereby the melt generatedby Although unambiguousevidence that Mars once possesseda largeimpacts resulted in the formationof local hydrothermalsys- warmer, wetter climate is lacking, a studyof the transitionfrom tems whose dischargethen formed the valleys [Newsom, 1980; such conditionsto the present climate can benefit our under- Brakenridgeet al., 1985]. Becauseonly large impactsmay have standingof both the early developmentof the cryosphereand the producedsufficient melt to establishthe necessaryhydrothermal variousways in which the currentsubsurface hydrology of Mars activity,the decline in valley networkformation might then sim- is likely to differ from that of the Earth. Viewed from this per- ply reflectthe early declinein the numberof largeimpactors. spective,the early hydrologicevolution of Mars is essentially However, while groundwatersapping may successfullyex- identical to consideringthe hydrologicresponse of the Earth to plain the origin of the small valleys,it fails to addresshow the the onsetof a globalsubfreezing climate. crustwas initially charged with H20. Indeed,even advocates of If the valley networksdid result from an early period of at- the sappinghypothesis sometimes sidestep this issue by sug- mosphericprecipitation, then Mars must have once possessed gestingthat the groundwaterinvolved in the formation of the near-surfacegroundwater flow systemssimilar to thosecurrently networkswas eraplacedduring a periodof precipitationthat oc- found on Earth, where, as a consequenceof atmosphericre- curred so early that no physicalrecord of 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 AND CLIMATICBEHAVIOR OF WATER ON MARS

(a) prec•p•tabon

•nfiltrabon •' r,½

waterWtable :111:: : i :::i::::: groundwaterd,v,de • :•groOn:dwate:;• :: ;: i:::1111i:: d•wde

(b)

water table W

(c)

Fig.30. Thehydrologic response of Marsto theonset of a colderclimate. (a) If Marsonce had a warmer,wetter climate, it mayhave had near-surface groundwaterflow systems similar to those found on Earth which, as a resultof atmosphericprecipitation, had water tables that followed the local topography. (b) Asthe temperature fell belowfreezing, the condensation of ice in thenear-surface crust eliminated any further replenishment of the underlying groundwater,leading to thedecay of theprecipitation and topographically induced groundwater divides. (c) Ultimately,as the groundwater reached hydrostatic equilibrium,it saturated the lowermost porous regions of thecrust, resulting in a groundwatertable that conformed to a surfaceof constantgeopotential.

climate and the decline in Mars' internal heat flow, a freezing fromany further atmospheric supply. From that point on, the only fronteventually developed in the regoliththat propagateddown- sourceof water for the thickeningcryosphere must have been ward with time, creatinga thermodynamicsink for any H20 thethermally driven upwardflux of vaporfrom the underlying within the crust.Initially, watermay haveentered this develop- groundwater(Figure 30b). ing regionof frozenground from both the atmosphereand un- With the eliminationof atmosphericrecharge, the elevated derlyinggroundwater. However, as ice condensedwithin the water tablesthat once followed the local topographyeventually near-surfacepores, the deeperregolith was ultimately sealed off decayed.The continuityof pore spaceprovided by sediments, CLIFFORD:HYDROLOGIC AND CI•MATIC BEHAVIOR OF WATER ON MARS 11,005 breccia, and interbasin faults and fractures should have then al- For the conditionsdescribed above, equation(30) was solved lowedthe watertable to hydrostaticallyreadjust on a globalscale numericallyusing the method of finite-differences.The results until it ultimatelyconformed to a surfaceof constantgeopotential indicatethat, given a present-daygeothermal heat flux of 30 mW (Figure30c). This conclusionis supportedby investigationsof m-2, the freezing front at thebase of thecryosphere will reachits areallyextensive groundwater systems on Earth that experience equilibriumdepth at theequator in -4.6 x 105years, while at the little or no precipitation[e.g., Mifflin and Hess, 1979; Cathles, polesit will takeroughly 1.5 x 106years (Figure 31). Giventhe 1990]. elevated geothermal conditions that likely characterizedthe The time requiredfor the developmentof the cryospherecan planet4 billion years ago (i.e., Qg - 150mW m-2), the corre- be calculatedby solvingthe transientone-dimensional heat con- spondingdevelopment times are 2 x 104years and 1.3 x 105 ductionequation for the caseof a semi-infinitehalf-space with years,respectively. These calculationsare based on a thermal internalheat generation, where conductivityof 2.0 W m-• K-z, a freezingtemperature of 273 K, and a maximum latent heat release (due to the condensationof 32T S 1 •}T H20vapor as ice in thepores) that does not exceed Qg, a limit (3O) that is imposedby the geothermalorigin of the vaporflux reach- 8z2 K c• 8t ing the base of the cryosphere(e.g., Figure 30b; see also section 4.4.1). Note that althoughthese developmenttimes assume andwhere T 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. Although the ity (= Wpc), and S is the heat generationrate per unit volume early growth of the cryospherewould be slowed by the ready (--3Qg/R, where Qg is the geothermal heatflux an R isthe radius supply of latent heat, this period representsonly a small fraction of Mars) [Fanale et al., 1986]. An upper limit can be placedon of the total time requiredfor the cryosphereto reachequilibrium. howrapidly the cryosphereevolved if we assumethat the surface In the later stagesof growth, which are controlledalmost exclu- temperatureof Mars underwentan instantaneoustransition from sively by conductionthrough the frozen crust, the rate of heat a meanglobal value of 273 K to its currentlatitudinal range of lossis sufficientlysmall that the effect of latent heat releasecan 154-218 K. Given this assumption,the boundaryand initial be virtually ignored. conditionsthat apply to equation(30) are Althoughthe assumptionthat Mars underwentan instantane- T(0, 0) -- 273 K oustransition from a warm to cold early climate is clearly incor- T(0, t) -- 218 K (at the equator) rect, this extremeexample serves to illustratean importantpoint, -- 154 K (at the poles) thatis: on a timescale greater than -106 years,the base of the cryosphereis essentiallyin thermalequilibrium with mean tem- •T Qg peratureenvironment at the surface.As a result, for any reasonable model of climate evolution, the growth of the cryosphereis •z not controlledby the rate of conductionthrough the crust,but by

-"--"==•==%•• 150mW rn

-2 rn N -4 Ill ',,(PresentMars) Ill LAT= 0 ø rr -5 LAT= 90 O -•

• -7

I IIIIII I I I III I I IIIIIII I I I IIIII ! I I IIIIII % ! I I IIII r'h -13 10 10 2 1 03 10 4 10 5 10 6 10 7

TI ME, t (yrs) Fig.31. Developmenttimes for the Martian cryosphere atthe equator (T s -- 218 K) andpoles (T s = 154K), assumingan instantaneous transition from a pre- viouswarm early climate (T s -- 273K). Thecalculations arebased on a crustalthermal conductivity of 2.0 W m-1 K -1, a basalfreezing temperature of 273 K, andgeothermal heat fluxes of 30 and150 mW m -2. The resulting equilibrium depths at theequator and poles for the two values of geothermalheat flux are, respectively,3670 m and7930 m, and730 m and 1590m. 11,006 C)_,IFFORD:HYDROLOGIC AND CLIMATIC BEHAVIOROF WATER ON MARS how rapidly the mean surfacetemperature environment changes by the limited hydrostaticpressure that could develop in a with time. Pollack et al. [1987] estimate that if the primary perchedaquifer, thus terminatingthe potentialcontribution of mechanismdriving climate changewas the removalof a massive low-temperaturehydrothermal convection to valley network for- (1-5 bar) CO2 atmosphereby carbonateformation, then the mation. transitionfrom a warm to cold early climate must have taken be- Finally, the postcryospheregroundwater hydrology of Mars tween1.5 x 107to 6 x 107years. For transition times this slow, will differ from its possible precryospherepredecessor (and the downwardpropagation of the freezing front at the base of thereforefrom present-dayterrestrial groundwater systems) in at the cryosphereproceeds at a rate that is sufficientlysmall (when least one other importantway. In contrastto the local dynamic comparedwith the geothermally-inducedvapor flux arisingfrom cyclingof near-surfacegroundwater that may have characterized the groundwatertable) that the geothermalgradient shouldhave the first half-billion yearsof Martian climate history(e.g., Fig- no trouble supplyingenough vapor to keep the cryospheresatu- ures 11 and 30a), the postcryosphereperiod will necessarilybe ratedwith ice throughoutits development. dominatedby deeper, slower interbasinflow (e.g., Figure 30c). From a massbalance perspective, the thermal evolutionof the Aside from polar basal melting, there are at least three other early crusteffectively divided the subsurfaceinventory of water processesthat are likely to drive flow under these conditions, into two reservoirs:(1) a slowly thickeningzone of near-surface they are (1) tectonicuplift (essentiallythe samemechanism pro- groundice and (2) a deeperregion of subpermafrostgroundwater posedby Carr [1979] to explainthe origin of the outflowchan- [Carr, 1979]. Regardlessof how rapid the transitionto a colder nels eastof Tharsis), (2) gravitationalcompaction of aquifer pore climate actually was, the cryospherehas continuedto thicken as space (perhapsaided by the accumulationof thick layers of the geothermaloutput from the planet's interior has gradually sedimentand basalt on the surface), and (3) regional-scalehy- declined.One possibleconsequence of this evolutionis that, if drothermalconvection (e.g., associatedwith major volcaniccen- the planet'sinitial inventory of outgassedwater was small, the ters suchas Tharsis and Elysium). Note that, with the exception cryospheremay have eventually grown to the point where all of of active geothermalareas, the flow velocitiesassociated with the availableH20 was takenup as groundice [Soderblomand theseprocesses are likely to be ordersof magnitudesmaller than Wenner,1978]. Alternatively, if theinventory of H20 exceedsthe thosethat characterizeprecipitation-driven systems on Earth. currentpore volume of the cryosphere,then Mars has alwayshad extensivebodies of subpermafrostgroundwater. Becausethe pore volume of the cryospherewas likely satur- 7. FURTHER CONSIDERATIONS ated with ice throughoutits early development,the thermally A unique feature of the hydrologicmodel presentedin this drivenvapor flux arisingfrom the reservoirof underlyingground- paperis that,with regard to thetransfer of H20 betweenits long- water could have led to the formation and maintenance of near- term sourcesand sinks,it is essentiallya closedloop (Figure 33). surfaceperched aquifers, fed by the downwardpercolation of That is, given an inventoryof outgassedwater that is sufficientto condensedvapor from the higher and coolerregions of the crust both saturatethe pore volumeof the cryosphereand form a sub- (Figure 32). Eventually the hydrostaticpressure exerted by the permafrostgroundwater system of globalextent, the lossof crus- accumulatedwater may have been sufficientto disruptthe over- tal water from any regionon the planet is ultimatelybalanced by lying groundice, allowing the storedvolume to dischargeonto surfacedeposition, basal melting,and subsurfacereplenishment. the surface.Such a scenariomay have beenrepeated hundreds of Further,given a geologicallyreasonable description of the crust, times during the planet's first half-billion years of geologic this cycleappears to be an inevitableconsequence of both basic history, possiblyexplaining (in combinationwith local hydro- physicsand the climatic conditionsthat have apparentlypre- thermal systemsdriven by impact melt [Newsom, 1980] and vailed on Mars throughoutthe past3.5-4.0 billion years.For this volcanism[Gulick, 1991]) how somevalley networksmay have reason,the model has importantimplications for a variety of evolvedin the absenceof atmosphericprecipitation [Pieri, 1979, problemsassociated with the planet'shydrologic and climatic 1980; Carr, 1983]. However, as the internal heat flow of the history.In this sectiontwo examplesthat illustratethe relevance planetcontinued to decline,the thicknessof the cryospheremay andpotential importance of this modelare considered:(1) the re- have grown to the point where it could no longerbe disrupted chargeof the valley networksand outflowchannels, and (2) the polarmass balance of H20.

developing

i•?....,•?•:.•.,••' ...... i:'i: :':'i. :':.:i•:);: '.'::.7 -•,•/:•.,...•:...•h:.._....:'.'•:..:-...:....__•..._-.•.• ... !•..•?•.:.¾.:.: ...: ....e re Seasonal and Climatic • condensationI - •'""•"'-.•"'" •"""•:'3',' • ExchangeofH20 NorthPolar Cap • SouthPolar Cap

/ / t t•a:P:•i:,n •'"aqu'tarO- "• :'•;"!•:!':'•.'•'• ••• li•'• I I ThermalH20 -I••ii•• •' / Transport

Fig. 32. An illustrationof how the processof thermalvapor diffusion may Groun•er haveled to the developmentand maintenanceof near-surfaceperched aquifers in the absenceof atmosphericprecipitation. Fig. 33. A modelof theclimatic behavior of wateron Mars. CLIFFORD:HYDROLOGIC AND •_,IMATIC BEHAVIOR OF WATER ON MARS 11,007

7.1. Rechargeof the ValleyNetworks and OutflowChannels the episodicrecharge of the Chryseoutflow channelsand the developmentof recent(Amazonian age) valleynetworks on the A recurrentissue regarding the originof the valleynetworks flanksof severallarge volcanoes. Baker et al. [1991] havepro- and outflowchannels is that the amountof water requiredto posedthat an episodeof intensevolcanic activity, centered on erodethese features is so large,compared with the storageca- Tharsis,may have triggered a massiveregional melting of ground pacityof theirlikely sourceregions, that sometype of recycling ice thatultimately resulted in the catastrophicrelease of as much processappears necessary. In an effortto addressthis problem,a as6.5 x 107km 3 of groundwateronto the surface. They argue varietyof potentialrecycling mechanisms have been proposed thatthis massive discharge inundated the northernplains, cover- [e.g., Masurskyet al., 1977; Carr, 1984; Jakoskyand Carr, 1985; Clow, 1987; Gulick and Baker, 1990; Baker et al., 1991; ing approximately10-30% of theplanet with a standingbody of Plesciaand Crisp, 1991;Moore et al., 1991]. Althoughseveral water102-103 m deep.In supportof thisconclusion, Baker et al. of theseschemes appear viable, virtually all requireeither a [1991] cite the enormousdischarge rates inferredfrom the di- coincidenceof environmentalconditions, or a combination of mensionsof the Chryseoutflow channels, as well as geomorphic evidenceof ancientshorelines discovered by Parkeret al. [1989] physicalproperties, that is needlesslycomplex or whoseoccur- throughoutthe northernplains. renceis poorlyconstrained. An assumptioncommon to eachof the abovescenarios, is that Perhaps the most controversialelement of the Baker et al. the reservoirsof groundwaterthat weretapped in the formation [ 1991] modelis the needfor a late, transientgreenhouse climate of the valley networksand outflow channelswere limited in to thaw the cryosphereat the time of the Chryseflooding. Baker capacityand isolated with respect to otherreservoirs of ground- et al. [1991] requirethis geologicallyshort but extremechange water present on the planet. However, as discussedin sec- in climate becausethey believe it to be the only way that the tion3.2, investigationsof the kilometer-scale permeability of the large volumesof water dischargedby the outflow channelsand Earth'scrust suggestthat virtually all terrestrialgroundwater youngervalley networkscould have been reassimilatedinto the systemsshare some degree of hydraulicinterconnection. Clearly, crust.This problemis viewed as critical not only becauseof the if this is true of the Earth,with an inferredmean crustal per- present absenceof this water on the surface, but becausethe meabilityof 10-2 darcies[Brace, 1980, 1984], then the case for magnitudeof erosionassociated with the channelsimplies a sus- hydrauliccontinuity on Mars, where some have argued for large- tained or episodicdischarge that Baker et al. [1991] believe can scalepermeabilities as much as 105times higher [Carr, 1979; only be explainedif the sourceregions where somehowreplen- MacKinnonand Tanaka,1989], should be significantlystronger. ished.As notedby Carr [ 1991], however,there is little geologic The importanceof this argumentto the rechargeof the valley evidenceto supportsuch a dramaticand recentepisode of global networksand outflowchannels is that, ratherthan drawingon warming. small,isolated, and rapidlydepleted local sourcesof ground- In lightof the above,is thereany compelling need to invokea water,these features may have tapped an enormouslylarger and differentclimate to accountfor the originof the valleynetworks self-replenishingglobal reservoir, whereby any water that was (eitherold or new) or the repeatedoccurrence of catastrophic dischargedto the surfacewas eventually balanced by the intro- floods?As discussedin section4.4.3, impact-generatedhydro- ductionof anequivalent amount back into the aquifer through the thermalsystems, such as thoseproposed by Newsom[1980] and processbasal melting. Brakenridgeet al. [1985],appear perfectly capable of generating Yet, becauseneither the likely extentof hydrauliccontinuity the valley networksfound in the crateredhighlands even under withinthe crust nor the potential role of basalmelting are widely 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 problemof localgroundwater depletion by invokinglocal mech- largevolcanoes, can be similarlyexplained as the resultof local anismsof resupply.The commonproblem with suchmechanisms hydrothermalactivity [Gulick and Baker, 1990]. In neither in- is thatonce groundwater has been discharged to the surface,it is stanceis it necessaryto invokea changein climatenor, givena unableto infiltrateback through the frozen crust to replenishthe hydrauliclink to a globalaquifer, any additionalmechanism of systemfrom which it was initially withdrawn.In supportof local resupply. thisconclusion recall that under currentclimatic conditions,the A similarconclusion is reachedregarding the repeatedoccur- thicknessof the cryosphere,even at the equator,is likely to renceof catastrophicfloods. As discussedby Carr [1979], one exceed2 km (section2.2). Further,a necessaryprerequisite for consequenceof the tectonicuplift of Tharsisis that it may have the widespreadoccurrence of groundwateris that the thermo- placedthe frozencrust in the lower elevationsaround Chryse dynamicsink representedby the cryospheremust already be Planitiaunder a substantialhydraulic head, leading to its even- saturatedwith ice. Thus,the cryosphereacts as an impermeable tual failure and the catastrophicrelease of groundwateronto the self-sealingbarrier that effectively precludes the localresupply surface.However, as the dischargecontinued, the local hydraulic of subpermafrostgroundwater either by the infiltrationof water head eventuallydeclined to the point where the water-saturated dischargedby catastrophicfloods, or by atmosphericprecipita- crust was able to refreezeat the point of breakout,ultimately tion on somehighland source region. Note that the problemof reestablishingthe original groundice thickness.The water re- local infiltrationand subsurfacereplenishment is not signifi- leasedby suchevents may have formedtemporary lakes or seas cantlyimproved even if the cryosphereis initiallydry, for as thateventually froze and sublimed away, with the resultingvapor water attemptsto infiltratethe cold, dry crust,it will quickly ultimatelycold-trapped at the poles. Such a processmay well freeze,creating a sealthat preventsany furtherinfiltration from explainthe origin of the large polar ice sheetsinferred by both the pondedwater above. Allen [ 1979a] andBaker et al. [ 1991]. The identificationof pos- Indeed,virtually the only way a subpermafrostgroundwater sibleeskers near the southpolar cap [Carr et al., 1980; Howard, systemcan be directlyreplenished, is if the interveningcryos- 1981; Kargel and Strom, 1992] is also consistentwith this inter- phereis somehowthawed throughout. This is essentiallythe pretation and with the subsequentreassimilation of the water explanationadvocated by Bakeret al. [ 1991]to accountfor both intothe crustthrough the process of basalmelting. 11,008 •ORD: HYDROLOGICAND CLIMATICBEHAVIOR OF WATER ON MARS

However,basal melting is not necessarilyrestricted to just the ation,and the fact that the polarregions am the planet'sdominant poles.As discussedby Clifford [1987b], whereverthe deposition sinkfor H20, howdoes one account for boththe youthfulness of and long-term retention of material occursat the surface, the the presentdeposits and the apparentdeficit of older material at added insulationwill result in the upward displacementof the the poles? melting isotherm at the base of the cryosphereuntil thermal Clearly one possibilityis that the estimatedvolume of water equilibriumis reestablished.Thus, if the frozen lakesor seasthat suppliedto the poles by variouscrustal sources is wrong, and were formed by the dischargeof the outflow channelspersisted that all of the water ever releasedto the atmosphereis now for morethan 105-106 years, the local groundwater system may storedin the polar ice. In that event,the apparentyouthfulness of have been indirectly replenishedby the onset of melting at the the currentdeposits might be explainedby the simple racycling baseof the cryosphem.It is likely, however,that this replenish- of old polar laminaeinto new [Toonet al., 1980]. This possibil- ment was only temporary.For with the eventual sublimationof ity is raised by current models of the evolutionof the polar the frozen lakes or seas on the surface, the melting isotherm troughs[Howard, 1978; Howard et al., 1982]. These features, shouldhave returnedto its original location,creating a cold-trap whichform the conspicuousspiral patterns visible in the remnant at the baseof the cryosphemfor any vapor or liquid suppliedby caps,are thoughtto originatenear the edgeof the depositsand the groundwaterbelow (section 4.4.1). In this way, any water then migrate, through the preferentialsublimation of ice from that was temporarily liberated from the cryosphemby basal their equatorwardfacing slopes,toward the pole. Dust, liberated melting,was eventuallyreassimilated into the frozencrust. from the ice, may then be scavengedby the polar winds and Note that nothing in this proposedcycle is precludedby the redistributedover the planet, while the sublimedice may simply current climate. Indeed, given the continueduplift of Tharsis be recycledby cold trappingon the polewardfacing slopesand and the probableoccurrence of other crustal disturbances(such on the flats that separatethe troughs.By theseprocesses, Toon et as earthquakes,impacts, and volcaniceruptions), failures of the al. [1980] suggestthat the polar depositshave reacheda stateof cryosphem'shydraulic seal were undoubtedlycommon. This sug- equilibriumwhereby ancient (•109 yearold) polarmaterial is gests that the cycling of water by catastrophicfloods, surface continuallymworked, maintaininga comparativelyyouthful sur- deposition,basal melting, and groundwaterrecharge, may have ficial appearancein spiteof its greatage. been repeatedmany times throughoutgeologic history, without Althoughit is possiblethat the volumeof water suppliedto the need to invoke any special conditionsregarding either the the poles by various crustal sourcesis significantlyless than geologyor climateof Mars. current estimates, such a conclusion is inconsistent with both our present understandingof the processesthat have affected the evolution of the surface (sections 4.1 and 4.2) and with the 7.2. The Polar Mass Balance and High Obliquities growingevidence that Mars is water rich [e.g., Carr, 1986, 1987; It is generallyaccepted that the Martian polar layereddeposits Squyres,1989]. The case for the local racyclingof old polar owe their origin and apparentyouthfulness to the annualdeposi- laminae is also at odds with the observations of Howard et al. tion of dustand H20 andthat the magnitudeof thisdeposition [1982], whosedetailed examination of the polar stratigraphyhas has beenmodulated by quasiperiodicvariations in 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-termaccumulation of materialin the polar terrains. their evident thicknessand the scarcityof craterswith diameters Anotherpotential solution to the massbalance problem is sug- larger than 300 m, Plaut et al. [1988] estimatethat the present gestedby recenttheoretical studies which indicatethat the obliq- depositsaccumulated at 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 conditionsconducive to polar depositionare not 1993;Laskar and Robutel,1993]. Under suchconditions, periods unique to the presentclimate but are characteristicof the planet of intensepolar erosionmay alternatewith periodsof accumula- over a broad range of likely obliquities and orbital variations. tion,redistributing the polardust and H20 overmuch of the Therefore,because the polar regionsrepresent the planet'sdomi- planet.This possibilitywas first consideredby Jakoskyand Carr nantthermodynamic sink for H20, anycrustal water released to [ 1985] in connectionwith the originof the valley networks.Their the atmosphereshould ultimately 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 experiencedobliquities as high both unambiguousevidence and 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 de- floods),we findthat the minimuminventory of H20 thatshould velopmentof Tharsis( --11ø - 38ø [Ward, 1979]). have accumulatedat the polesover geologictime is equivalentto Althoughthe length of time Mars spendsnear its maximum a globallayer-*65 m deep(Table 6), a volumeroughly 2-5 times . obliquityduring a givencycle is brief(,--10 4 years), the result- greaterthan that observedin the residualcaps. Given more rea- ing increasein peak and mean annualinsolation at polar lati- sonableestimates of channeldischarge, as well as the volumes tudes could affect the polar massbalance in severalimportant of water contributedby the valley networks, impacts, and the ways.For example,Jakosky and Carr [ 1985] haveargued that, at sublimationof equatorialground ice, the disparitybetween the an obliquityof 45ø, summerpolar temperaturesmay rise high expected and observedpolar inventories increasesby over an enoughto resultin the sublimationof 20 cm of ice from the per- orderof magnitude.Although the water lost by atmospherices- ennialcaps. Therefore, over the 104 yearsthat such obliquities cape (,*60 m, Jakosky [1990]) and oxidation of the regolith persist, a total of as much as 2 km of ice might be removed (-*27 m, Owen et al. [1988]) may explain someof this discrep- from the caps.Jakosky and Carr [1985] suggestthat both dy- ancy,these loss mechanisms fall considerablyshort of resolving namicalconsiderations and cold nighttimetemperatures may con- the imbalance for any reasonableestimate of total crustal dis- spire to limit the maximumdistance that the resultingvapor is chargeand expectedpolar inventory(Table 6). Given this situ- transportedfrom the cap. This, they argue, could lead to the •ORD: HYDROLOGICAND CliMATIC BEHAVIOR OF WATER ON MARS 11,009 precipitationof iceat low-and mid-latitudes, with surfaceaccu- 1988], and (4) satisfyall of the previousconditions within the mulationsof up to severaltens of metersover the duration of the constraintimposed by the apparentdeficit of older materialthat highobliquity portion of thecycle. The absorption of sunlightin currentlyexists at the poles. theresulting snowpack, could then lead to transientsummertime As discussedby Clifford [1987b],the processof basalmelting meltingwhich they suggest may have contributed to the forma- appearsto satisfyeach of theserequirements. Once the polarde- tion of the valleynetworks and the replenishmentof equatorial positshave reached the required thickness for basalmelting, they reservoirsof H20. will have achieveda conditionof relative equilibrium, whereby While the calculationsof Jakoskyand Cart [1985] clearly theaccumulation of any H20 at theice cap's surface will even- demonstratethe potentialfor significantmass loss at timesof tually be offsetby meltingat its base.Indeed, a geothermalheat highobliquity, there are at leasttwo observations that appear to fluxof 30 mW m -2 K -1 could easily keep pace with an }t20 depo- significantlyconstrain both the magnitudeof polarerosion and sitionrate as high as -*3 x 10-3 m yr-l. Thereforethe occurrence the extentof equatorialdeposition. Consider first the casefor of basalmelting is consistentwith both the predictionof climate equatorialdeposition and melting. A principleasset of theJako- models [Fanale et al., 1982, 1986] and the observationalevi- skyand Cart [1985]model, in thecontext it wasoriginally pro- dence[Howard et al., 1982], indicatingthat a long-termnet dep- posed,was that it provideda self-consistentexplanation for both ositionalenvironment has existed at the poles. the geographicdistribution of valleynetworks (which are con- centratedat equatorialand temperate latitudes [Cart and Clow, 8. QUALIFICATIONSAND POTENTIAL TESTS 1981])and their almostexclusive occurrence in terrainsthat pre- datethe developmentof Tharsis[Cart and Clow,1981; Tanaka, A model of any natural processis necessarilya compromise 1986]. This self-consistencybreaks down, however,with the between the desire to consider all first-order effects, and the recognitionthat Mars has likely experiencedhigh obliquities practical reality that it must be simple enough to be readily throughoutits history,including the recentpast [Bills, 1990; communicatedand understood.Unfortunately, the inherent com- Ward and Rudy, 1991; Toumaand Wisdom,1993; Laskar and plexity of real world systemsis often poorly representedwhen Robutel,1993]. Although a few "young"valleys have been found describedin such general terms. With regard to the hydrolog- on Alba Patera and severalother large volcanoes[Gulick and ic and climatic behavior of water on Mars, the transport of Baker,1990], their absence from anyother terrains that post-date H20 throughthe atmosphere,over the surface,and beneath the Tharsisstrongly suggests an endogenic, rather than exogenic, ori- ground,involves numerous individual processes,each of which gin.Thus, if meltingand surface runoff has ever occurred in as- may be significantlyaffected by natural variationsin the local or sociationwith the developmentof equatorialsnowpacks at high globalenvironment. Spatial variations,like local changesin the obliquity,its contributionto theformation of thevalley networks thermophysicalproperties of the crust, are perhapsthe best un- andthe replenishmentof equatorial H20 apparentlyceased no derstoodand easiestto model. While characteristicslike poros- later than the formationof Tharsis (-3.5-4 b.y.a. [Wise et al., ity, permeabilityand heat flow, may changeappreciably from one 1979]). locationto another,this variationis likely to occurwithin a fairly With regardto themagnitude of polarerosion, both the infer- well-definedrange of limits basedon our knowledgeof the geol- red108-year age of thepolar deposits [Plaut et al., 1988]and the ogy of the Earth and Moon, and what we have deducedabout apparentfrequency of high obliquityexcursions [Bills, 1990; Mars from spacecraftinvestigations of its surface. Temporal Wardand Rudy, 1991;Touma and Wisdom,1993; Laskar and changesare anothermatter. Some, like the declinein the planet's Robutel,1993] appearto placea severeconstraint on the mag- internalheat flow or the rise in solarluminosity, are evolutionary nitudeof massloss that the polestypically experience during and, therefore,at least somewhatpredictable. The occurrenceof suchperiods. For example, if the loss amounted to the ---102- others,such as a major impact, the catastrophicdischarge of an 103mper high obliquity cycle originally suggested by Jakosky outflow channel,or the long-termchaotic evolution of the Mar- and Carr [1985], thenthe maximum"life cycle"of the deposits, tian obliquityand orbital elements,completely defy prediction, frombuild-up to erosion,would necessarily be limitedto just a yet their impacton the localor globalenvironment may, at times, few millionyears. Yet, if the inferred108-year age of the completelyoverwhelm all othereffects. It is the synergisticinter- depositsis correct,then they have not only survived a minimum actionof thesevarious elements that has governedthe hydrologic of 103obliquity cycles (many of whichshould have exceeded and climatic behavior of water on Mars. 45ø),but have actuallyaccumulated at the rate of--10 km/b.y. Clearly, given this manyfree parameters,the numberof pos- [Plaut et al., 1988]. This fact is consistentwith previoustheo- sible permutationsof eventsand conditionsthat may have af- reticalstudies indicating the existenceof a long-termnet depo- fected the Martian climate is virtually endless.One example is sitionalenvironment at the poles[Fanale et al., 1982, 1986] and the evidencefor polarwandering presented by Schultzand Lutz with the absence of observationalevidence indicative of any [1988]. As hasbeen stated many times in this analysis,given our massive,widespread erosion of thepolar laminae [Howard et al., presentunderstanding of Martian climatichistory, a net long- 1982]. termloss of H20 fromthe equatorial crust to the atmosphere To summarize,it appearsthat any solutionto the massbal- appearsirreversible. This conclusionassumes, however, that the anceproblem should (1) be consistentwith theoreticalmodels of geographiclocation of the p!anet'sspin axis has remained fixed the Martian climate,which indicatethat a net depositionalenvi- with time, an assumptionthat Schultzand Lutz [1988] have ronmenthas existed at the polesthroughout most of the planet's vigorouslychallenged. Perhaps the mostpersuasive evidence for history[Fanale et al., 1982,1986], (2) be ableto accountfor the polarwandering comes from the identificationof severalexten- observationalevidence that the evolutionof the polar terrainshas sive antipodallayered deposits near the equatorthat possessa indeedbeen dominated by depositionalprocesses [Howard et al., numberof strikingmorphologic similarities to the polarlayered 1982],(3) be able to accommodatea rate of deposition,implied terrains. To account for these features, Schultz and Lutz [1988] bythe paucity of craterswithin the deposits, of from 10 -5 to haveproposed that over a time scaleof severalbillion years, the 10-4myr -1 [Cutts et al., 1976;Pollack et al., 1979;Plaut et al., crustof Mars hasundergone a majorreorientation in relationto 11,010 •ORD: HYDROLOGICAND CI•MATIC BEHAVIOR OF WATER ON MARS

its spin axis. They attribute this movementto changesin the other active geothermalregions, would establishthat Mars is planet'smoment of inertia causedby the formation of Tharsis. bothwater-rich and that it possessesan inventoryof H20 that While the actual dynamicsnecessary to producethis shift are significantlyexceeds the porevolume of the cryosphere.Second, presentlyunclear, the slow migrationof the geographiclocation should it be found that the absolute elevation of the water table is of the poles providesa mechanismfor movingthe planet'scold the sameat widely separatedlocations (disregarding local dif- trapand atmospherically replenishing subsurface H20 on a glob- ferencescaused by recenttectonic activity, anomalous geother- al scale. mal heating,or prolongeddeposition at the surface),it would It is important to note, however, that while polar wandering stronglyindicate that groundwateron Mars has hydrostatically [Schultzand Lutz, 1988], massivepolar erosionat high obliq- adjustedon a globalbasis, a conditionthat can onlybe 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 essentiallyconfirm the singlemost important these scenariosis required to explain any aspectof the hydro- elementof the model presentedhere, that Mars possessesan logic evolutionof a water-richMars that cannotalready be satis- interconnectedgroundwater system of globalextent. Since all the factorily explainedunder the physicaland climatic conditionswe remaining elements of the model follow from this foundation, observeon the planettoday. This conclusionis basedon only two and from basicphysics, the greatestremaining uncertainty will assumptions:(1) that the physicalproperties of the Martian crust, be the extentto which basal melting, groundwaterflow, and the includingporosity, permeability, and crustalthermal conductiv- thermaltransport of H20 in the crust,have competed with, or ity, are no different then those which characterizethe Earth and complemented,other processesin the transportof water above, Moon, and (2) that Mars possessesan inventoryof water that across, or beneath the Martian surface. exceedsthe pore volume of the cryosphereby as little as a few

percent. Given these conditions,basic physicsdictates that the 9. CONCLUSIONS processesof surfacedeposition, basal melting, groundwater flow, and the thermaltransport of H20, will thermodynamicallyand The analysispresented here leads to the following conclu- hydraulicallylink the atmospheric,surface, and subsurfaceres- sions: ervoirsof wateron Mars into a singleself-compensating system. 1. If the inventoryof H20 on Marsexceeds by morethan a Although unequivocalevidence of a planetary-scaleground- few percentthe quantityrequired to saturatethe pore volumeof water systemis currentlylacking, its existenceis consistentwith the cryosphere,then a subpermafrostgroundwater system of the calculationspresented in section2 and with the geomorphic globalextent will necessarilyresult. evidencethat Mars possessesan inventoryof water equivalentto 2. Under the climaticconditions that have prevailedthrough- a global ocean 0.5-1 km deep [Carr, 1987]. More direct evi- out mostof Martian geologichistory, the inherentinstability of dencethat sucha systemhas existedthroughout much of Martian equatorialground ice has lead to a net atmospherictransport of geologichistory is provided by the timing and thermodynamic H20 fromthe hot equatorial region to thecolder poles. Theoreti- implicationsof the outflow channels.As discussedin section2.3, cal argumentsand variouslines of morphologicevidence suggest a prior conditionfor the existenceof any largevolume of ground- thatthis poleward flux of H20 hasbeen augmented by additional water is that the pore volumeof the cold-traprepresented by the releasesof waterresulting from impacts,catastrophic floods, and cryospheremust first be saturatedwith ice. This conclusion volcanism. followsfrom the fact that, given an availablereservoir of waterat 3. Based on the conditionspostulated in conclusion1, the depth,thermal processes will supplyenough H20 to saturatethe depositionand retentionof materialat the poles(or any other cryospherein less than 107 years (sections 4.4.1 and 4.5). Since location)will eventuallyresult in basal melting.The downward the youngestoutflow channelsmay be less than 1 billion years percolationof meltwater into the underlyingglobal aquifer will old[Tanaka, 1986; Tanaka hfid Scott, 1986; Parker et al., 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., groundwatermound. 1992], this suggeststhat an inventoryof water in excessof that 4. Given a geologicallyreasonable value of large-scaleper- storedin the cryospherehas persistedon Mars until very recent meability(i.e., •>10 -2 darcies),the gradientin hydraulichead times,and may continueto persistto the presentday. createdby the developmentof groundwatermounds at bothpoles While theoreticalarguments for a planetary-scalegroundwater could drive the equatorwardflow of a significantvolume of systembased on the thermodynamicsignificance of the outflow groundwater(->108 km 3 H20) overthe course of theplanet's channelsare interesting,they fall shortof an actualproof. Unfor- history. tunately, at present,the channelsare the best evidencethat we 5. At equatorialand temperatelatitudes, the presenceof a have. However, as the explorationof Mars continues,there will geothermalgradient will resultin a net dischargeof the ground- be opportunitiesfor more direct investigationsof the subsurface water systemas vapor is thermally pumpedfrom the warmer that shouldresolve this issueconclusively. While prospectsfor (highervapor pressure)depths to the colder(lower vapor pres- a Mars Deep Drilling Project are likely to remain dim for the sure) near-surfacecrust. By this processa gradientas small as foreseeablefuture, at least two other geophysicalmethods, ac- 15K km-I coulddrive the verticaltransport of 1 km of water tive seismicexploration [Tittmann, 1979; Zykov et al., 1988] and tothe freezingfront at the baseof the cryosphereevery 106- electromagneticsounding [Rossiter et al., 1978;Ehrenbard et al., 107years, or theequivalent of a 102-103km of waterover the 1983], couldbe usedto deteci xndmap the distributionof ground 4.5 billion yearhistory of the planet.In this manner,much of the ice andgroundwater beneatt, the planet'ssurface. groundice that has been lost from the crustmay ultimatelybe Assumingthat such investigationsare actually conducted, replenished. what observationswould provideconclusive evidence that Mars While particularaspects of the modelpresented in this paper possessesan interconnectedgroundwater system of global scale? may be debated(e.g., the actualporosity and permeabilityof the First, the detectionof groundwaterat locationsfar removedfrom crust,the magnitudeof polar deposition,etc.), the occurrenceof any obvioussource of transientproduction, such as volcanoesor subsurfacetransport on Mars is essentiallycontingent on a single •ORD: HYDROLOGICAND CI•MATIC BEHAVIOR OF WATER ON MARS 11,011 factor:does the presentplanetary inventory of H20 exceed,by •rtI stea rn steammass transported by hydrothermalconvection, morethan a few percent,the quantityof water requiredto satur- kg m-2. ate the pore volume of the cryosphere?If so, then basic physics Gutenberg-Richtermagnitude of seismicevent. suggeststhat the hydrologicmodel described here will naturally molecularweight of H20, 0.018 kg mo14. evolve. Given a geologicallyreasonable description of the crust, total gaspressure, dynes cm -2. thequantity of H20 transportedthrough the subsurfacemay then vaporpressure of H20, dynescm -2. play an importantrole in the geomorphicevolution of the Mar- thermally inducedliquid flux, m s-1(per unit area). tiansurface and the long-term cycling of H20 betweenthe atmos- thermallyinduced vapor flux, m s-I (perunit area). phere,polar caps,and near-surfacecrust. = 2hah v, radial dischargethrough aquifer, m3 s-l. frictionalheat due to glacial sliding,W m-2. Acknowledgements.The fast draft of this paper was written in 1980. geothermalheat flux, W m-2. Sincethat time, both the paper and the ideas presented in it, havehad a long = • a2 w, aquiferrecharge volume, m3 s4. andtortuous evolution. Both have benefited from the inputI•te receivedfrom manyfriends and colleagues. I would especially like to thankBruce Jakosky, heat contentof impactmelt, J m-2. FraserFanale, Michael Carr, Daniel Hillel, Geo•e McGill, Bill Irvine, Peter radius, m. Schloerb,Bruce Bills, Mark Cintala,Deborah Domingue, Jim Zimbelman, universalgas constant, 8.314 J mol-I K-l. ScottMurchie, Karen Miller and JoseValdez, for havingreviewed earlier watervapor gas constant, 461.9 J kg-I K -l. drafts of this paper and providedmany helpfid suggestionsfor its im- heat generationper unit volumeof planet,W m-3. provement.I would alsolike to thankPete Schultz,Matt Golembek,Lisa Rossbacher,Steven Squyres, Mike Malin, RuslanKuzmin, Alan Howard, time, s. Laurie Johansen,Peter Mouginis-Mark,Nadine Barlow, Bob Miller, and temperature,K. Ken Tanaka, for havingindulged me in many extendeddiscussions about initial impactmelt temperature,1473 K. water on Mars. My thanksalso to AmandaKubala and Brian Fessler,who final impactmelt temperature,K. throughthe yearshave provided invaluable programming and technicalas- meltingpoint temperature,K. sistance,and to Fran Waraniusand StephenTellier, who locatedcopies of countless,but much needed, references. I am especiallygrateful and indebted mean annualsurface temperature, K. to the followingpeople: to Bob Huguenin,who providedmuch of the initial temperatureinterval over which steamis heated,K. encouragement,freedom, and financial support that allowedme to beginthis temperatureinterval over which water is heated,K. research;to Kevin Burke and David Black, who have generouslycontinued = a2ved4kgh t. that supportwhile I•te beenat LPI; to my friend JonathanEberhart, who helpeda very frightenedgraduate student make it throughhis fast pro- projectileimpact velocity, m s4. fessionaltalk; and, most of all, to my wife Julie and daughterMiranda, aquiferspecific discharge, m s-1. withoutwhose love andsupport I wouldhave given this up longago. This re- basalsliding velocity, m s-1. searchwas supported by the Lunarand Planetary Institute, which is operated impactmelt volume,km3. by the UniversitySpace Research Association under contractNo. NASW- 4574 with the National Aeronauticsand SpaceAdministration, and by a maximumvolume of transientcrater cavity, m3. grantfrom NASA's PlanetaryGeology and GeophysicsProgram. LPI Con- aquifer rechargerate, m tribution No. 807. well functionfor a nonleakyaquifer. depth,m. NOTATION thickness, m. = h2 _ hi2, m2. a radiusof basalmelting/recharge area, m. heatcapacity of water,2092 J kg-1 K -I. (= •pc), thermaldiffusivity, m 2 s4. heatcapacity of steam,4186 J kg4 K-l. empiricaldimensionless factor [Cary, 1966], 1.83 + volumetricheat capacity of impactmelt, 4.2 x 106J 0.79. œ m-3 K4. effectiveporosity. DAB bulk moleculardiffusion coefficient of H20 in CO2, thermalconductivity, •h cm 2 s-l. crustalporosity ata deptf :!• 1.00 -- 100%. collisionalmean free path of an H20 moleculein the Dc transitiondiameter between simple and complex Martian atmosphere,- 10 gm. cratermorphology,-6 km on Mars. kinematicviscosity, m 2 s-•. D•.• effectivediffusion coefficient of H20 in CO2, cm2 s4. density,kg m-3. final crater diameter, m. basal shear stress, Pa. Knudsendiffusion coefficient of H20, cm2 s-l. soil water potential,Pa. Dtc diameterof transientcrater cavity, m. projectilekinetic energy, J.

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