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The nature of the Martian polar capshas been a subject of speculation formany decades. They have been vari-ously conjectured to be composed offrozen water, carbon dioxide, or oxidesof nitrogen (1, p. 362; 2, 3). The weightof scientific opinion, based upon a vari-ety of evidence, currently favors waterice as the dominant substance compris-ing the polar caps. However, much ofthe relevant observational evidence hasundergone significant change and im-provement in recent years, so that itseems appropriate to reexamine thequestion in the light of the more com-plete and reliable measurements nowavailable.

The purpose of this article is toreport results of a new study of theproblem based on a consideration ofthe heat balance of the planet. Webelieve that this study points stronglytoward frozen CO2 as the dominantsubstance comprising the Martian polarcaps.

Further, we are led to suggestthat (i) the total amount of CO2 onMars may exceed the amount presentin the atmosphere by a considerablefactor, the excess being present assolid CO2 and CO2 permafrost in andunder the permanent north polar cap;(ii) the partial pressure of CO2 inMars's atmosphere may be regulatedby the north polar cap; and (iii) thetotal pressure of the Martian atmo-sphere may change semiannually by asignificant amount because of the freez-ing out of much of the atmosphericCO2 at either pole. Considerable quan-tities of water-ice permafrost may also

be present in the subsurface tf thepolar regions and perhaps of more tem-perate regions as well. Many organiccompounds of biological interest, how-ever, are more volatile than water atlow temperatures and might be easilyevaporated from permeable soil and be-come trapped as minor constituents ofthe permanent polar cap.We propose that selective trapping ofCO2 (and H20) in the solid phase mayhelp explain the anomalously high con-centration of CO2 (and probably H,O)on Mars relative to nitrogen.

Surface and Soil TemperaturesIn order to understand the behaviorof volatiles on Mars more fully, wehave investigated the expected diurnaland annual temperature variations atvarious latitudes, using a thermal modelof the Martian surface in which each

surface element is treated as a hori-zontal plane, at some instantaneoustemperature T1, which absorbs a frac-tion F of the incident solar radiation,emits blackbody radiation at tempera-ture T, with an emissivity E, exchangesheat with underlying layers by thermalconduction (with constant conductiv-ity), and absorbs or releases latent heatif a condensed volatile is present. Ra-diative thermal exchange with the at-mosphere is assumed negligible exceptinsofar as the atmosphere may affect Eby blocking certain wavelengths emit-ted by the surface. Horizontal heattransport by wind is also neglected, al-though some form of planetary circu-lation is presumed to replenish con-densed CO2 and H20.The latter two assumptions may con-stitute a significant oversimplification

of the actual situation on Mars. Inparticular, Sinton has suggested thepossibility of some horizontal heattransport, on the basis of temperaturemeasurements derived from infraredbrightness (3a). It is also possible thatcondensed H2O or CO2 particles in theatmosphere, particularly at the polesduring the autumn and winter, mayprovide a significant local blanketing ef-fect. We recognize that both effectsmay be important, but we have pur-posely confined our attention to asimple model in order to determinehow well such a model can account forthe observed properties of Mars. Wefind, in fact, surprisingly good agree-ment between the observed propertiesand .the properties predicted on thebasis of this model.

Typical values adopted for the vari-ous numerical parameters were as fol-lows: F = 0.85, corresponding to anaverage Bond albedo A -= 0.15; E -0.85, a value which allows for theblocking effect of 5000 centimeter-atmosphere of CO2 at pressure of 5millibars [based on the tables ofcalculated CO2 transparency of Stull,Wyatt, and Plass (4)] and an in-trinsic emissivity of 0.95 to 1.00(characteristic of powdered silicateminerals in the 10- to 50-micron wave-length range observed under naturalconditions); K - 2.5 X 10-4 wattcm-1 (?K)-; C = 3.3 j g-1 (?K)-1;p = 1.6 g cm-3. The above values forsoil conductivity (K), specific heat (C),and density (p) are similar to those de-rived by Leovy (5) from analysis ofthe infrared observations of Sintonand Strong (6).The thermal history of such a surfacewas followed for 2 to 5 Martian yearsat 19 latitudes from - 90? to + 90?,the equations of radiative and thermalexchange being evaluated (by a 7094computer) for each 1-hour period dur-ing every 5th day to a depth of 3meters, well below the thermal "skindepth" for annual temperature changes.The depth coordinate x was treated inthree parts: (i) the top surface, xl =O; (ii) nine equal layers 1.5 cm thick,centered at x. =- 0.75, . .. . x = 12.75cm; and (iii) ten equal layers 30 cmthick, centered at xll = 15, . . x20- 2.85 cm. The boundary conditionson the temperature at a given latitudewere as follows.

1) The surface temperature T1 wastaken as a linear extrapolation to thesurface of the values for the upper twolayers: T1 = (3T2/2) - (T3/2).

SCIENCE, VOL. 153

Behaviorof CarbonDioxide andOther Volatiles on Mars

A thermal model of the Martian surface suggeststhat Mars's polar caps are solid carbon dioxide.

Robert B. Leighton and Bruce C. Murray

Dr. Leighton is professor of physics at Cali-fornia Institute of Technology, Pasadena; Dr.Murray is associate professor of planetary sci-ence at California Institute of Technology.136

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2) The net heat gain or loss, Q2,for the top liayer was taken asQ2 = (- EJT14 Socos Z+- K(T - T2)/Ax) Atwhere So (= 0.06 W cm-2) is thesolar constant at Mars; u is the Stefan-Boltzmann constant; cos Z is the cosineof the zenith angle of the sun; At =3600 seconds, and Ax = 1.5 cm.

3) The quantity Q2 was used eitherto change the temperature of the toplayer or (as latent heat) to condense orevaporate CO2 or H20, as required bythe ambient conditions.

4) The layer x10 was assumed to ex-change heat with the upper layers inproportion to the temperature gradient(T0o - T9) /Ax, and with the lowerlayers in proportion to the gradient(T12 - T1l)/Ax', with Ax' = 30 cm.5) The temperature Tl1 was setequal to T1o, as described below.6) The layer x20 was assumed to ex-change heat only with overlying layers.The initial temperatures at eachlatitude were constant with depth andequal to the mean annual temperaturesfound in pilot calculations. In order tospeed the convergence to a steady state,the temperatures T, of all layers wereadjusted by amounts ATe at the endof each annual calculation accordingto the equation

AT- =- (Tav - T2o) (2xi/x0 - x 2/x2,,2)where Tav is the calculated yearly aver-age surface temperature at the cor-responding latitude.For each diurnal calculation, madeon an hourly basis, only the tempera-tures of the upper nine layers werechanged; at the end of this calculationfive successive iterations on the lowerten layers were made, T11 being heldconstant and equal to the final valueof T10.

Representative curves for the dailytemperature variations at the equatorare shown in Fig. 1 for three differentthermal conductivities; these are inadequate agreement with the measure-ments of Sinton and Strong (6). Atfirst, the possibility of condensation ofCO2 was ignored. The annual variationof daily minimum temperature foundfor this moonlike case are plotted inFig. 2, which shows that the minimumnight-time temperatures would remainabove 145?K at all seasons at the equa-tor and at low temperate latitudes,but would drop considerably below145?K in winter time at subpolar andpolar latitudes. Since the condensation8 JULY 1966

temperature of CO2 at the currently ac-cepted pressure of about 4 millibars is145?K, it is immediately clear fromFig. 2 that COs should precipitate outand accumulate at the higher latitudesduring local winter.

Carbon Dioxide RelationshipsA number of calculations which per-mitted the condensation of CO2 weremade. These were made progressivelymore complete and realistic until ul-timately even the effects of orbital

eccentricity and depletion of CO. byfreezing were included. Various albedosfor solid CO,, were used, ranging from0.60 to 0.75, and different initialamounts of atmospheric CO, were as-sumed. All these calculations are inagreement with respect to the followingmajor effects.1) Large amounts of COo were al-ways found to precipitate near eachpole during the Martian winter, asshown in Fig. 3. Typical maximumamounts were 100 to 150 g cm-2.

2) Carbon-dioxide precipitation oc-curred above latitude + 50? and below- 45?; this is about the range observedfor the actual Martian polar caps.3) At latitudes near the boundary ofa polar cap, the calculations indicated,CO., would precipitate at night andevaporate during the day; the "frost"would usually disappear before noon,unless the cap was growing rapidly.4) The amount of CO2 precipitatedin the polar regions was so great as toappreciably affect the total atmosphericpressure. In a typical case, the at-mospheric pressure varied semiannuallyby almost ? 1 millibar from the mean(Fig. 4).In addition, the calculated rate ofdisappearance of a CO., frost cap agreesrather well with the observed rate, asillustrated in Fig. 5.The total radio (thermal) emissionfrom Mars has been measured at vari-ous wavelengths (7-9) and constitutesan important constraint upon the soiltemperature derived from a model. Ofcourse, only the very surface of thesoil undergoes diurnal and annual tem-perature variations as great as thoseshown in Figs. I and 2. Within a fewcentimeters' depth the diurnal varia-tion is damped out, and within a depthof a few tens of centimeters the annualvariation is no longer significant. Theaverage temperature over the planetarydisk as seen from the direction of the

sun was calculated for each depth be-low the surface for a number ofmodels. Representative results for theCO2 model are shown in Fig. 6. Sincedry silicates are good insulators andtherefore somewhat transparent to ra-dio waves, radio brightness tempera-tures refer effectively to emission fromsome region within the soil at, perhaps,a depth of three to ten wavelengths. Thecurve of Fig. 6 for a depth of 15 centi-meters can therefore be taken as anapproximate guide to the radio emissionof 3- to 4-centimeter wavelength. InFig. 7, the temperature at this depthis compared with recent radio obser-vations (8) for two models.The calculations brought out anotherexpected consequence of CO2 solid-vapor equilibrium: if the total abun-dance of CO2 is greater than about 15g cm-2, the north polar cap will notdisappear during the summer, as is infact the case on Mars. The equilibriumpartial pressure of CO2 for this (or anygreater) abundance is 3 to 5 millibars.Thus, the observed partial pressure ofCO2 is itself strong evidence for theexistence of a permanent CO2 ice capand, probably, CO2-saturated perma-frost in the north polar region. Thisimportant point merits elaboration.Let us assume an initial amount ofatmospheric CO2 sufficient to allowsome COo to remain condensed in thenorth polar region throughout the sum-mer. In this case the permanent cap is,on the average, the coldest place onthe planet, and, furthermore, it is ofnearly constant temperature To through-out the year. Therefore, the rate R. atwhich heat is radiated throughout theyear is constant and is

Rr = EcrTo4where E is the infrared emissivity ofsolid C02, corrected for the effects ofatmospheric blanketing. On the otherhand, the yearly average insolation rateI,l at the north pole is fixed by thesize and eccentricity of Mars's orbitand the inclination of the rotation axis.Thus,

7r/21l,,av--- osin S0 os c5(1 - 2e cos 4) X27Jr -(1 3 d)sec d-7r/2where So is the mean intensity of solarradiation at Mars's orbit; o8 is the incli-nation of Mars's equator with respect toits orbital plane; c is the longitude ofthe sun, measured from the north sum-mer solstice; Eis the orbital eccentricity

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0

LIa:t--a-LJc,nDLLJ

0O)m

TIME (hours)

3 6 9 12

MARTIAN MONTHSFig. 1 (top left). Diurnal variation of surface temperature forthree values of thermal conductivity of the soil (time = 3mlonths). Experimental values found by Sinton and Strong (6)are also shown (vertical bars). The soil conductivity of themiddle curve was used throughout this study. Fig. 2 (topright). Annual variation of minimum diurnal temperature forvarious latitudes (numbers adjoining the curves) without CO,or H,O condensation. K _ 6 X 10-5 cal cm-' sec-1 (?K)-';E = 0.85. The condensation temperature of CO2 at pressureof 4 millibars is indicated by the dashed line. Fig. 3 (bottomleft). Amount of precipitated CO2 as a function of latitude(numbers adjoining the curves) and time. K as in Fig. 2. Con-ditions were such that a permanent north polar cap was present,so an arbitrary amount may be added to the indicated northpolar curve. Fig. 4 (bottom right). Variation in CO2 partialpressure, due to seasonal condensation and evaporation. TheMartian date for the measurement of CO pressure and totalpressure by Kaplan, Munch, and Spinrad (KMS) (12) andof total pressure by Mariner IV (M-IV) (18) are indicated.

5

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MARTIAN MONTHS FROM N. SUMMER SOLSTICE138

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(aphelion is assumed to coincide withthe north summer solstice); (1 - /)is the fraction of incident solar radia-tion which is assumed to reach the sur-face when the sun is at the zenith;and sec Z (= I/sin 80 cos la, (1 - A), the polarcap will gain CO2 at an average rate

M = (Rr -Iav.)/Lwhere L (- 450 j g-1) is the latentheat of vaporization of CO2 at tem-perature To. This removal of CO2 fromthe atmosphere will then reduce thepartial pressure of C02, thereby de-creasing the condensation temperatureTo and Rr. On the other hand, if Rr< la (1 - A), the polar cap will loseCO2 at an equivalent rate, a loss re-sulting in an increase in To and Rr.An equilibrium will therefore exist suchthat

Rr = I (I - A)This condition fixes To, which in turnfixes the mean CO2 partial pressure P0through the relation of vapor pressureto temperature. If A = 0.65 and E =0.85, we find

T,,= (av1 - A)/E)1/4 = 145 ?KAt this temperature, P0 = 4.0 milli-bars, in good agreement with currentexperimental values. If A and E differfrom the above values (or if we haveincorrectly estimated la,), PO will, ofcourse, differ also. The dependence ofP0 upon A and E is shown in Fig. 8.The rate at which the above-de-scribed equilibrium will be approachedmay be estimated. Let the minimumradius of the polar cap be r radiansof Martian latitude, and let P -Poe('T-TO) for T near To. Then, ifT = To + AT, a linear approximationto ARr and AP yields a time constant

r = ToPo L/r2Rrg- 0.6 X 1010ec (= 200 yr)In spite of its small radius of only3 degrees, the cap should thus be quiteeffective in maintaining a constant par-tial pressure of CO2.Several unsuccessful attempts weremade to simulate the very small re-sidual north polar cap in the modelbefore it was recognized that the ob-served behavior of the cap (it regu-

8 JULY 1966

o,-40

L.030- 'x

cr 20

10 x

-100 0 40DAYS FROMS. SUMMER SOLSTICEFig. 5. Observed radius of south polar cap as a function of time (21) compared withpredictions of models in which the caps are composed of C02 alone or H20 alone.(+) Observed radius; (0) model with cap of CO2 alone; (X) model with cap ofH0O alone. Local topographic irregularities are probably responsible for the slowrecession of the cap after summer solstice, since the remanent southern cap is situated6.5? from the pole. The recession of the cap in the H20 model is closely in step withthe solar declination because of the negligible mass of H20 precipitated.

larly shrinks to a diameter of a fewhundred kilometers but always resistscomplete evaporation) does not implythat the cap is on the verge of disap-pearing when it is at minimum size.In fact, a permanent polar cap will tendto become smaller in diameter and cor-respondingly thicker because of thevariation in insolation near the pole.Calculation shows that the insolationvaries approximately according to theformulaIav (X) =7 I,v (90?)[1 + (5 X 10-4) (90-X)2]At latitude 80?, for example, the meaninsolation is 5 percent greater than it isat the pole. However, all parts of thecap are at the same temperature, sincethe cap is in equilibrium with the CO2partial pressure, and thus radiatesequally everywhere (10). The differ-ential insolation therefore leads to adifferential rate of growth or loss ofCO, at the two latitudes in questionuntil the permanent COo all resides atthe pole. This transfer rate is relativelyrapid. In the example cited, the differ-ential rate of loss at latitude 80? wouldbe about 7 g cm-2 yr-1.The approximate annual "snowfall"of CO,, at the north pole mav alsobe estimated to be about half theamount that would be g?ined duringthe Martian year at the steady rateRr/L. This amounts to

M= l(l -A) t/2140 gcm-2

where ty (= 687 X 86,400) is thelength of the Martian year, in seconds.This is in good agreement with the re-sults of the more precise calculationsshown in Fig. 3.In summary, on a rather generalbasis, CO2 can be expected to be themajor constituent of the polar caps onMars, and this conclusion is consistentwith (i) the size and rate of disap-pearance of the observed caps, (ii)the observed permanence of the northpolar cap, (iii) the observed partialpressure of CO2 on the planet, and(iv) the disk brightness temperature atradio wavelengths.

Water RelationshipsWe have found, in the precedingsection, that the properties of a rather

simple thermal model of the Martiansurface are in good agreement withmany of the observed properties ofMars and suggest that the Martianpolar caps consist largely of frozenCO2. However, this result is in conflictwith observations which seem to indi-cate that water ice, and not CO,,, isthe substance comprising the polarcaps. We have sought to understandthe extent of this conflict and to findways of resolving it. We see three pos-sibilities.

1) The observations which indicatethe presence of water ice, or the con-clusions derived therefrom, may be inerror.2) Effects not taken into account in

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. ___ well shown in these curves. Fig. 7 (top right). Com-0 30 60 90LATITUDE (deg)Fig. 6 (top left). Annual variation of average temperature of.1 the disk as viewed from the sun for various depths, in centi-meters (numbers adjoining curves), for the CO2 model. Thedamping out of the diurnal and annual variations with depthc I are well shown in these curves. Fig. 7 (top right). Com-.3 4 .5 6 .7 .8 .9( parison of average disk temperature at depth of 15 centimeters

VISUAL REFLECTIVITY A for two thermal models with radio observations (vertical bars),at wavelength of 3 to 4 centimeters. The radio brightness temperatures have been multiplied by a factor 1.1 to correct ap-proximately for an observed reflectivity of about 0.10 (24). The two models are (curve 1) the CO0 model and (curve 2) amodel having lower (and variable) infrared emissivity adjusted so as to prevent the precipitation of C02 but permit the con-densation of H20. Fig. 8 (bottom left). Dependence of partial pressure P of CO0 in the Martian atmosphere upon visualreflectivity A and effective infrared emissivity E of CO0 frost. Fig. 9 (bottom right). Mean annual temperature as a func-tion of latitude (CO02 model). Saturation temperatures corresponding to three values for precipitable water vapor (in gramsper square centimeter) are indicated.

14 SCE.VLZ5

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the study discussed here may renderour conclusions invalid.3) A small amount of water ice maybe present together with a large amountof frozen CO2 and in some way affectthe observational results, giving a mag-nified estimate of the abundance of

water.Water in solid form on the frost capsof Mars has been reported by Kuiper

(1) and Dollfus (11), and water vaporhas been reported by Kaplan, Munch,and Spinrad (12) and by Dollfus (13).Kuiper compared the infrared spectralreflectivity of the polar cap with similarlaboratory spectra of ice and dry ice,while Dollfus made a study of thepolarization of the polar cap. Moroz(14) has recently confirmed the exist-ence of the near-infrared spectral fea-ture and, like Kuiper, attributes it tothe presence of water ice. However, weare not aware of a sufficiently thoroughpublished study of the reflection spec-trum of both solid H20 and CO2 de-posited under simulated Martian condi-tions to justify the identification.Dollfus' discussion of his polariza-tion measurements was restricted to aconsideration of the physical state ofthe condensed material and not itscomposition. He found difficulty in pro-ducing a form of water ice that wouldexhibit the very small amount of polar-ization that was observed, and he didnot study the properties of CO2 frost.There is at present no evidence, frompolarization studies of Mars, whichwould enable one to distinguish be-tween a frost cap of H20 and one ofCO2.There are also difficulties in reconcil-ing the optical properties and seasonalbehavior of supposed water ice polarcaps with the extremely minute quanti-ties of water that spectroscopic studieshave revealed. The Kaplan, Miinch,and Spinrad observation was sensitiveenough to permit an estimate of thetotal precipitable water above the Mar-tian surface: 14 ? 7 X 10-4 g cm-2.Comparable measurements of water va-por have also been obtained independ-ently by Spinrad over a number ofyears (15). Although Heyden et al.(16) have recently pointed out thatheretofore unrecognized weak H20 ab-sorption lines originating in the earth'satmosphere might complicate the inter-pretation of H20 absorption featuresof the Mars spectrum, it seems unlike-ly that all observations would be simi-larly affected because of the variableDoppler displacements of the Martianlines. A further consideration regarding8 JULY 1966

Martian water vapor has been raised byJohnson (17). He argues that very lowatmospheric temperatures are indicatedby the Mariner IV occultation experi-ment (18) and that these would be in-compatible with a water-vapor concen-tration of as much as 10-3 g cm-2,because ice-crystal cloud formationshould set in at a concentration lowerby perhaps an order of magnitude. Onthe other hand, Gross, McGovern, andRasool (19) believe that higher at-mospheric temperatures are more like-ly, in which case there is not necessarilya contradiction. Any such discrepancybetween theory and observation evi-dently will not be resolved until moreis known about the details of Martianmeteorology, so it seems reasonable toconclude for the present that there maywell be 10-3 g of water vapor persquare centimeter commonly presentin the Martian atmosphere but that anupper limit can perhaps be set around3 X 10-3 g cm-2. Thus we see thatwater constitutes at most 0.03 percent,by weight, of the Martian atmosphere,and probably less than 0.01 percent. Itis, therefore, a minor constituent, andits condensation and evaporation willdiffer markedly from that of the majorconstituent, C02, in several ways.First, the basic problem of the trans-fer of H20 in an evaporation-conden-sation cycle from a solid state at oneplace on the planet to a solid state atanother is vastly more difficult than thecorresponding problem for CO2, since,at the minimum, 104 times as muchCO2 as H20 must be transferred by thewind system. If all the HO2 is not re-moved during a single cycle (becauseof insufficient vertical mixing, for ex-ample) the ratio becomes correspond-ingly larger, and an unreasonablystrong wind system would be requiredfor the effective transport of water va-por. For example, one might assume,as an extreme upper limit, that duringthe disappearance of one cap and thegrowth of the other the entire 10-3 gof water vapor above each square centi-meter of the disappearing cap is trans-ported to the growing cap and de-posited there daily as frost. (Such aprocess would require net north-southwinds of about 500 kilometers per hourblowing steadily for perhaps 100 days,combined with complete vertical mixingdaily at each end.) Even in such anextreme case only about 0.1 g cm-2woud be transferred from one cap tothe other-a thickness of a few milli-meters at most. Since the Martian sur-face undoubtedly has some microrelief,

this tiny coating of frost would prob-ably accumulate only in the shadowedareas, such as on the colder, polewardslopes of topographic features and onthe poleward sides of individual rockfragments. A frost cap only a few milli-meters thick very probably would notbe observable at all from the directionof the sun, yet this is the direction fromwhich the planetary frost caps are ob-served from Earth at opposition.A second, and equally serious, diffi-culty with the hypothesis that water iceis the dominant constituent of the Mar-tian caps is the fact that, unlike thecase for CO2, the atmosphere near thesurface can become depleted in H20and the depletion causes the condensa-tion rate to become extremely smalland dependent upon the vagaries of thevertical and horizontal circulation sys-tem of the planet. Inasmuch as thatcirculation system is governed by theplanetary heating and reradiation, andperhaps by rotation, and, unlike thecase for Earth, is not significantly in-fluenced by the atmospheric content ofwater vapor, such redistribution of wa-ter as does take place is the result ofpurely accidental effects.These considerations make us doubtthat water could be the dominant con-stituent of the Martian polar caps. Toplace the analysis in more quantitativeform, however, we have investigatedtwo specific hypothetical cases whichhave also led us into some interestingconsiderations concerning the possibleoccurrence of permafrost on Mars.First, we have studied what is re-quired if the frost caps are in factH20 and if they always remain warmenough so that solid CO2 does not ac-cumulate on the surface at either poleat any time during the year. This isequivalent to requiring that the meandaily temperature not fall below about145?K anywhere on the planet. Sinceit appears, from terrestrial experience,that supplementary sources of heat (forexample, radioactivity) of adequatemagnitude are most unlikely, it is onlythrough introducing, in the model, adecrease in radiative heat loss from theplanet by atmospheric blanketing thatsuch a result may reasonably beachieved. In order to retard the radia-tive heat loss at low temperatures andyet avoid unduly high daytime tempera-tures, a far-infrared absorption was in-troduced such that, in addition to theexpected absorption of CO2 near 15microns, all wavelengths longer than 19microns were blocked. This led to aneffective emissivity relative to tempera-

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ture which ranged from 0.1 at 140?Kto 0.5 at 270?K. Although this proce-dure gave the desired result-a negli-gible quantity of CO2 was found tocondense-it led to other results thatare in serious conflict with observation.Not only would the assumed absorp-tion require the presence of substantialamounts of molecular species such asNH

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course of the 5 X 104-year precessionalcycle. We have not investigated thistransfer process in detail.

Although local irregularities in thesurface and subsurface conditions willintroduce corresponding fluctuationsin the depth to the top of the perma-frost, we do not expect to find grossdepartures from the results obtainedwith the model insofar as the distribu-tion and physical state of near-surfacewater are concerned. In particular, wewould not expect to find large amountsof water (or ice) at any depth in theequatorial regions unless the area wasextremely well isolated from the atmo-sphere.The possible occurrence of liquid wa-ter is a question of some concern. Anattractive idea is the possibility that soilmoisture sometimes exists in the Ely-sium region, where relatively strongradar reflections (24) and persistentmorning clouds (25) were observedduring the 1965 opposition period.However, nothing in our study pointstoward the occurrence of liquid waterat any place or time during the daily,annual, or precession cycle. The maxi-mum temperature attained in the per-mafrost layer was about 200?K-farbelow the melting temperature of ice,(273?K). Furthermore, even if the tem-perature were to rise above 273?K, itis not certain that the ice would meltrather than sublime, since the total at-mospheric pressure, 5 to 10 millibars,could be less than the 6.9-millibar vaporpressure of water at its triple point.Of course, we cannot exclude thepossibility that very small amounts ofliquid water might form for brief pe-riods in connection with the evapora-tion of the residual water ice of a polarcap after the CO2 has disappeared if,for example, the ice frost were partiallytrapped in the upper few millimetersof the surface under conditions wheresolar heating was intense but evapora-tion was retarded by the limited poros-ity of the soil. Again, strongly deli-quescent salts situated near the surfacemight, under some circumstances, leadto the presence of moisture in the soil.

Other VolatilesThere are no confirmed reports ofother volatiles on Mars. Kiess et al. (3)have reported nitrogen oxides; more re-cently that subject has been discussedby Sagan, Hanst, and Young (26) andby Heyden (27). Perhaps more surpris-ing than the possibility that nitrogen

8 JULY 1966

LL)nL 1000(:/

1-

200 0 30 60 90LATITUDE (deg)Fig. 10. Depth of top surface of H20permafrost, as a function of latitude. Thedifference in depth between the two hem-ispheres defines an amount of water thatshould be exchanged between the hemi-spheres or during the 5 X 104-year pre-cessional period.

oxides are present is the apparent dearthof nitrogen itself. An upper limit of afew millibars for the partial pressure ofnitrogen in the Martian atmosphere isimplied by the Mariner IV occultationresults. Such a low abundance wouldseem anomalous, on the basis of geo-chemical considerations, if the atmo-sphere of Mars was formed in a man-ner at all similar to the formation ofthe earth's atmosphere.Carbon dioxide can be expected tobe lost from Mars, by various dissocia-tion and ionization processes, at amuch higher rate than that at whichnitrogen is lost. Gravitational escapewill not be significant in either case ifthe exospheric temperatures are as lowas the 550 ?+ 150?K estimated byGross et al. (19) or the 85?K estimateof Johnson (17). Accordingly, it is dif-ficult to understand how an enormousCO, enrichment relative to nitrogencould take place if both gases werepresent either in a primordial atmo-sphere or in continuing volatile emis-sions from the interior of Mars. Onepossible clue to the apparent anomalyis the suggestion that CO2 might havebeen preferentially trapped upon andbeneath the surface in a solid statewhile the entire mass of nitrogen wasalways in the gas phase at the surfaceand thus able to escape much more ef-fectively. It is possible that on Mars,as on the moon (28), the presence ofa low-vapor-pressure solid phase of avolatile molecular or atomic speciesmay be of more significance in reten-tion of the volatile than is the species'resistance to escape from the vaporphase. Another fractionation mech-

anism for selective retention on Marsof a heavier, condensable gas relativeto a lighter, noncondensable one wasdiscussed by Stoney (2) prior to 1898.The other class of Martian volatilesabout which there has been much spec-ulation is that of organic compounds,particularly those related to possiblebiological activity. While our analysisis too restricted to form the basis ofany discussion of the a priori likelihoodof biogenic compounds being formednow, or having been formed in the past,on the surface of Mars, it may offersome insight into the probable redis-tribution of such compounds shouldthey be present on Mars. In particular,our analysis for the evaporation andredistribution of H20 should be rough-ly applicable to any volatile minorconstituent. If solid (or liquid) organiccompounds are present near the sur-face anywhere in the temperate or inthe equatorial regions of the planet,they should be evaporating also, andcondensing in the polar regions. If thecirculation is sufficiently rapid, the masstransferred would be roughly in pro-portion to the ratio of the evapora-tion rate of the substance to the evapo-ration rate of water in the temperaturerange around 170? to 200?K. Thusit would seem that organic substancessignificantly more volatile than H20in the low-temperature range should bedepleted from the soil over most of theplanet and transferred to the polar areaswell within a single 8000-year portionof the precessional cycle.

Summary and ConclusionsWe have found that a rather simplethermal model of the Martian surface,in combination with current observa-tions of the atmospheric composition,points strongly toward the conclusionthat the polar caps of Mars consist al-most entirely of frozen CO2. This studywas based upon the following principalassumptions.1) Carbon dioxide is a major con-stituent of the Martian atmosphere.2) The blanketing effect of the at-mosphere is small, and due principallyto the absorption band of CO2 near15 microns.3) Lateral and convective heat trans-fer by the atmosphere is negligible.4) The far-infrared emissivity of theMartian soil and of solid CO2 ,are near

unity.5) The reflectivities of the soil andof solid CO2 in the visible part of the

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spectrum are about 0.15 and 0.65, re-spectively.6) Values for soil conductivity, den-sity, and specific heat are those char-acteristic of powdered minerals at lowgas pressure.7) Water is a minor constituent ofthe Martian atmosphere, the maximumtotal amount in the atmosphere being10 to 30 X 10-4 g cm-2.In addition, several simplificationswere made, which might have signifi-cant effects but should not alter ourprincipal conclusions. Among these arethe following.1) Local blanketing or snowfall ef-fects due to clouds or polar haze wereignored.

2) Dark and light areas were not dif-ferentiated in this study, although Sin-ton and Strong (6) have observed tem-perature differences between such areas.

3) The effects of local topographyand microrelief were neglected. We be-lieve that these must have quite signif-icant effects at the higher latitudes,especially in connection with the evapo-ration of the remanent south polar cap.

4) Variation of reflectivity withangle of incidence of the sunlight wasneglected.

5) Temperature dependence of soilconductivity and specific heat was ig-nored.6) Effects of saturation of the soilby ice upon the thermal properties ofthe soil were neglected.Although in our main investigationwe used certain specific values for thevarious relevant parameters, we alsotested the effects of moderate changesin these quantities. Specifically, the soilconductivity was varied by a factor of

3, the albedo and emissivity of thesurface were changed by 15 to 20 per-cent, and the effects of a gross amountof atmospheric blanketing were studied,as described. Only the last of thesevariations had any significant effect on

the model, and other results of the at-mospheric blanketing were in disagree-ment with other physical observationsof the planet. Consequently, we find itdifficult to avoid the conclusion thatCO2 must condense in large amountsrelative to H20.The main conclusions indicated bythis study are the following.1) The atmosphere and frost capsof Mars represent a single system withCO2 as the only active phase.2) The appearance and disappear-ance of the polar caps are adequatelyexplained on the presumption that theyare composed almost entirely of solidCO2 with perhaps an occasional thincoating of water ice.

3) If the currently reported water-vapor observations are correct, water-ice permafrost probably exists underlarge regions of the planet at polar andtemperate latitudes.4) The geochemically anomalous en-richment of CO2 relative to N. inthe present Martian atmosphere may bea result of selective trapping of CO2 inthe solid phase at and under the sur-face.

5) If the basic evaporation and con-densation mechanisms for CO2 andH20 discussed in this article are cor-rect, the possible migration of volatileorganic compounds away from thewarm temperate regions of the planetand their possible accumulation in thepolar regions need to be carefully con-sidered.

References and Notes1. G. P. Kuiper, in The Atmospheres of theEarth and Planets, G. P. Kuiper, Ed. (Univ.of Chicago Press, Chicago, 1952).2. G. J. Stoney, Astrophys. J. 7, 25 (1898); thispaper refers to an even earlier suggestionby the same author.3. C. C. Kiess, S. Karrer, H. K. Kiess, Puibl.Astron. Soc. Pacific 72, 256 (1960).3a. W. M. Sinton, in Planets and Satellites, vol.3 of The Solar System, G. P. Kuiper, Ed.(Univ. of Chicago Press, Chicago, 1961), p.436.4. V. R. Stull, P. J. Wyatt, G. N. Plass, Appl.Opt. 3, 243 (1964).

5. C. Leovy, Icarus 5, 1 (1966).6. W. M. Sinton and J. Strong, Astrophys. J.131, 459 (1960).7. C. H. Mayer, T. P. McCullough, R. M.Sloanaker, Astrophys. J. 127, 11 (1958); E. E.Epstein, ibid. 143, 597 (1966); K. I.Kellerman, Nature 206, 1034 (1965); D. S.Heeschen, Astrophys. J. 68, 663 (1963).8. J. A. Giordmane, L. E. Alsop, C. H. Townes,C. H. Mayer, Astrophys. J. 64, 332 (1959);W. A. Dent, M. J. Klein, H. D. Allen, ibid.142, 1185 (1965).9. F. J. Low, private communication (1966).10. We neglect here the small but importantvariation of temperature with elevation dueto (i) decrease of barometric pressure withaltitude and (ii) adiabatic cooling of sur-face air as it flows from the edge to themiddle of the polar cap.11. A. Dollfus, in The Atmospheres of theEarth and Planets, G. P. Kuiper, Ed. (Univ.of Chicago Press, Chicago, 1952), p. 381.12. L. D. Kaplan, G. Munch, H. Spinrad, Astro-phys. J. 139, 1 (1964).13. A. Dollfus, in The Origin and Evolution ofAtmospheres and Oceans, Brancazio andCameron, Eds. (Wiley, New York, 1964).14. V. I. Moroz, Astron. Zh. 41, 350 (1964).15. M. Spinrad, unpublished results (privatecommunication, 1966).16. F. J. Heyden, C. C. Kiess, W. R. Willauer,Astrophys. J. 143, 595 (1966).17. F. S. Johnson, Science 150, 1445 (1965).18. A. Kliore, D. L. Cain, G. S. Levy, V. R.

Eshleman, G. Fjeldbo, F. D. Drake, ibid.149, 1243 (1965).19. S. H. Gross, W. E. McGovern, S. I. Rasool,ibid. 151, 1216 (1966).20. T. Dunham, Jr., in The Atmospheres of theEarth and Planets, G. P. Kuiper, Ed. (Univ.of Chicago Press, Chicago, 1952), p. 296.21. E. C. Slipher, in Mars, J. S. Hall, Ed. (SkyPublishing Corp., Cambridge, Mass.) p.20.22. G. Fjeldbo, W. Fjeldbo, V. R. Eshleman,Stanford Electronics Lab. Rep. SU-SEL-66-007(1966).23. The period for the precession of the peri-helion is about 72,000 years [see D. Brouwerand G. M. Clemence, Planets and Satellites(Univ. of Chicago Press, Chicago, 1961),p. 50] while that due to solar tidal pre-cession of the rotation axis may be estimatedas about 180,000 years, a value obtained bycorrecting the solar part of the total earth'sprecession, (7.5/2.4) by the appropriate fac-tors for distance and moment of inertia.We are indebted to Professor W. M. Kaulafor helpful discussion on this point.24. R. M. Goldstein, Science 150, 1715 (1965).25. C. Capen, private communication (1965).26. C. Sagan, P. L. Hanst, A. T. Young, Plan-etary Space Sci. 13, 73 (1965); ibid., p.1003.27. S. J. Heyden, ibid., p. 1003.28. K. Watson, B. C. Murray, H. Brown, J.Geophys. Res. 66, 3033 (1961).29. We are indebted to Drs. L. Davis, W. M.Kaula, Conway Leovy, R. S. Richardson,R. F. Scott, and R. P. Sharp for helpfuldiscussions. The thoughtful criticism of Dr.W. M. Sinton is also appreciated. This re-search was supported in part by NationalAeronautics and Space Administration grantsNsG-426 and NsG 56-60.

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