I(J.kI{US 33, 40--49 (1978)

Paleoatmospheric Temperature Structure

DEAN A. M()RSS, ~ aND WILLIAM 1{. KUHN Department of Atmospheric and Oceanic Science, The Uni~,ersity of Michigan, A ttn A rbor, Michigan .~8109 l~'eceived .hme 26, 1!)77; revised .hfly 2~, 1977

Radiative equilibrium and radiative (:onvective temperature profiles fiw the 's evolving have been cah.ulated. If the atmosphere evolved from one rich in dioxide, and deficient in , to its present composilion, the temperature structure showed consider- able change. The models of 3 to 4 billi(m years ago display steadily decreasing temperatures with altitude, being 185°K at pressures associated wilh the present-day upper stratosphere. A lapse rate feature similar to lhe presenl-day tropopause is n(,l indicated until about I billion years ago; but the slralospheric region is approximately 15°K colder lhan presently found at eompa- ra/)le pressures. Surface temperal ures approximately l ()°K warmer than at present existed unlil nearly l billion years ago. When the oxygen content exceeded roughly 0.1 times the present level, sm'face temperatures began to de(q'ease. If bi(~logical processes are important to --ozone w~riations, such "~s h~s been suggested during the Ice Ages, then estimales of surface temperature should inelu(te t he effe(qs of t)~)lh gases.

I NT RO1)UCTI()N the changes expected to tile present-day thermal structure, as might be brought No previous attempt has t)een made to about through changes in the vertical investigate the temperature structure of distribution of individual constituents, were the evolving atmosphere for atmospheric made by Berkner and Marshall 0964, models appropriate to particular geologic 1965, 1967), Abelson (1966), and WMker periods. Such a determination is important (1974). FinMly, in some studies (Holland, since the rt~te constants of reactions for 1962 ; Jastrow, 1964; Berkner and Marshall, many minor constituents are temperature 1966, 1967; Rutten, 1971; I(atner and dependent. Nearsurface temperatures are Walker, 1972) one finds a trend toward •dso important to clim'~tic variations :m(1 •tcceptanc, e of the present-day temperature the evolution of life forms. structure, and its :~ssociated thermody- l'revious studies related to the temper~- namic processes, throughout much of tures of the paleoatmosphere estimated geoh)gic time. exospheric temperatures or deduced varia- tions in planetary albedo, constituent This study presents calculated radiative- concentrations, etc., base(1 on variations convective, mean global, vertical tempera- from an assumed mean global tempen~ture ture profiles of the Earth's evolving atmo- (Holhmd, 1962, 19(i:~; Jastrow, 1964; sphere extending ba(',k to about 4.5 billion Rasool, 1966, 1967; Mc(lovern, 1969; years. We assume the atmosphere evoIve(t Sagan and Mullen, 1972). Estimates of from one rich in cart)on dioxide and ~Present attiliation: l)etachmenl 1, 2 Weather deficient in oxygen, and thus ozone. The Squadron, Wright-P.~tterson AFB, Ohio 45433. resultant temperature profiles are obviously

40

0019-1035/7g/0331-0040502.00/0 (!opyright ~) 1978 by Academic Pre,qs, Inc. All rights of reproduction in any form reserved. PALEOATMOSPHERIC TEMPERATURES 41 dependent upon the assumed concentra- model were obtained from the COESA tions and distributions of the radiatively preliminary report (Ellis et al., 1973). active gases. However, the thermal profiles The water vapor profile is one of fixed for other postulated carbon dioxide and specific humidity. ozone distributions can be at least qualita- The Ice Age model, Model 2, was in- tively inferred from the results presented. cluded to provide some insight as to the possibility that glacial periods may have ATMOSPHERIC MODELS been initiated by oscillations in the carbon Atmospheric oxygen concentrations form dioxide and oxygen concentrations. Such a the basis for correlation between the model dependence has been presented in the and geologic eras. The correla- literature by Berkner and Marshall (1964, tions are primarily derived from the 1965) and Cloud (1968). We have used a evolutionary descriptions as found in the carbon dioxide concentration of 0.65 PAL several articles of Berkner and Marshall (present atmospheric level) from their (1964-1967) but with a more liberal inter- study and Levine's (1975) ozone profile pretation of the times involved. We have corresponding to their oxygen abundance further based the evolutionary atmospheric of 2 PAL. models on the carbon dioxide/oxygen com- The , Algonkian, Cryptozoic, binations suggested by Rutten (1966, and models, Models 3 though 6, 1971). It must be emphasized that this respectively, are sequential in that they study does not attempt to delve into the reflect the proposed evolution of oxygen chemical reactions or geologic processes as based upon the works of Berkner and producing or destroying any particular Marshall (1964, 1965, 1967), and carbon constituent ; we only determine the thermal dioxide as proposed by Rutten (1966, 1971). environment that would have existed for The ozone profiles (Fig. 1) are from that postulated atmospheric composition. Levine (1975), who calculated ozone con- Seven models describe the evolving centrations from the assumed oxygen evolu- atmosphere (refer to Table I). Model 1 tionary model. We have introduced varia- represents the present-day atmosphere. tions in the water vapor distribution Concentrations for the constituents of this from that of the present-day mean annual

TABLE I ATMOSPHERIC ~IODELSa

Compound Model (years ago)

1 2 3 4 5 6 7 Present- Ice Age Cambrian Algonkian Cryptozoic Archean Pre-Arehean day 300-800 MY 800 MY-2.5 BY 2.5-3.5 BY 3.5-4.0 BY 4.0-4.5 BY

CO2 PAL 0.65 PAL 3.5 PAL 5 PAL 8 PAL 10 PAL 0.01 PAL

O~ PAL 2 PAL 0.1 PAL 0.01 PAL 0.001 PAL 0.0001 PAL 0.000001 PAL

H~O Curve 1, Fig. 2 Curve 4 Curve 5 Curve 6 Curve 7 Fig. 2 Fig. 2 Fig. 2 Fig. 2 PAL PAL PAL

CH4 PAL PAI, PAL PAL PAL PAL 20% by total number density

NHa Not included in calculation 9 ppm

a The present atmospheric levels (PAL) for CO2, 02, and CH4 (assumed uniformly mixed) arc 320 ppm, 21°7o by volume, and 1.5 ppm, respectively. The HzO distribution is shown in Fig. 2. 42 MOI{SS AND KUItN

80 ...... I ...... I '" ..... I ' ...... I ...... I ...... I ...... "tO $ 5 .4 ~3 ~2 6C _ ~.. ~. ~. ~...... -..~\"""'~ _

-

40

~ 30_-20 "'''. ,o ,~,

I III ''''I , ,*"f-~'I J,,.,l t . j,.,,,l , ,,*,

OZONE MIXING RATIO (g/g) Fro. 1. Ozoile mixing ratios (g/g) used in the evolving atmospheric models. Values illustrated are based on the work of Levine (1975). The column abundance for each model is : Model l, 0.347 atm-cm; Model 2, 0.562 atm-cm; Model 3, 0.250 atm-cm; Model 4, 0.069 atm-cm; Model 5, 0.012 atm-cm; Model 6, 0.0008 atm-cm. See Table I for relation of model number to approximaie geologic time. model beginning with Model 4 of the Each water vapor profile represents near Algonkian period as shown on Fig. 2. saturation at the stratospheric elevations. No tropopause, and thus cold trap, was The earliest model, Model 7, which may apparent in these calculated temperature be representative of 4 to 4.5 billion profiles and water vapor would most likely years ago, represents a have been transported to higher elevations. and is the most uncertain of the models

80 - \ I,~,3,7

70- \ Ev. 60- \o

1"" • ~_4o-~- II'\ "~,. ~'.. -

"1-L~ 50 I 4\\ 5 6.. -- 20 I \\\."'-.\ '\ "" - tO ~ . - II i i iiiiiii 1 iIIllld L IttJuil i i L ILU,~'"I'~JDItH

WATER VAPOR MIXING RATIO (g/g) l"m. 2. Water wH)or mixing r'O,ios (g/g) used in the models of tile evolving atm.sphere. See 'Fable I for relation of model nulul)er to approximate geoh)gic time. PALEOATMOSPHEIHC TEMPIgI/.ATUIIES 4:~

develope

"I'AI+;IA +] 1I

NBSOIgPTI()N I )ATA AND ]IEFERENCES

Consti(uent Band lleference

TerrestriM Ozone 9.6 ~m Walshaw (1957)

Carbon dioxide 15 um lh)dgers and WMshaw (1966)

Water vap()r l (ota( ion ban(l 0 -1000 ('m I{o(tgers and W'dshaw (1966) 6.3 .mn Ba)M 1200 -2200 em -1

Anllll()llitl, 6. I ttm St:~(istical model semiempirically curve ill, I O. 5 ~m to data of Frmwe and Williams (1966)

Met bane 3.3 ~.m (?ess and Khetan (1973) except Pre-Al'ctman, 7. (i /am Bur(.h el al. (1962) for Pre-Ar(.hean model

Poilu' ( )zone tlarlley band 2500 ~ ttuggins band 3200 .;, Lindzen "uld Will (1973) Chappuis b~md 6000 ,X

Ca,'bon dioxide l .4, 1.6, 2.0, 2.7, 4.3, tfoward et al., (1973) 4.8, and 5.8 unt

IcVa( e r v,+tpo r 0.g, 0.9, 1.1, 1.38, 1.9, l{odgers (1967) 2.7, 3.3, and 6.3 >m

,) ,] Methane o.. ~m Same as for terrestrial wavelenglhs 7.6 ,am model has a different specific heat and much different from what we observe thus a unique dry adiabatic lapse rate. today. A more detailed model is not The critical convective lapse rate Fv~ is justified since no information is available then determined from Pp~ = PeD'I'I~/FD, on possible water vapor variations over where P,~ and FD are the present-day geologic time. values for the convective and dry adiabatic We have also not considered a variable lapse rates and reD is the dry adiabatic solar constant. Margulis and Lovelock lapse rqte for the particular model. Values (1974) indicate that a change in the solar for I'ea and FeD are given in Table IIl. constant of -4-10% would have caused The surface temperature was determined catastrophic events which have no basis by adjusting the radiative convective in geologic records. On the other hand temperature profile until the out-going there are investigators who believe the flux to space and absorbed solar energy solar output may have increased nearly agreed within 0.5%. A planetary albedo 40 c/~. of 30% was used which includes not only RESULTS the albedo of the surface but clouds as well. Thus implicit in this assumption is that A comparison of the thermal structure global cloud cover in the past was not for the present-day model and the U. S. PAI,EOAT.~IOSPHEIHC TEMPEI~ATUII ES 45

TABLE III VALUES OF Cp AND LAPSE RATES FOR EACH ~/[ODELa

Atmospheric model (~p Dry adiabatic Radiative (erg gm -~ °K-') lapse rate convective (°K km-Q lapse rate (°K km-1)

l. Present era 1.00 X 107 9.77 6.5 2. Ice Age 1.25 X 107 7.82 5.2 3. Cambrian 0.97 X 107 10.14 6.78 4. Algoukian 1.02 X 107 9.58 6.37 5. Cryptozoic 1.44 X l() 7 8.57 5.7 6. Archean 1.22 X 107 8.00 5.32 7. Pre-Archean 1.07 X 107 9.14 (;.03

See Table I for composition corresponding to model number.

Standard Atmosphere is shown in Fig. 3. studies. We find that doubling the carbon The agreement is quite good, particularly dioxide amount would increase the surface in the stratospheric regions. Our tempera- temperature by 2.9°K, while a reduction tures in the stratosphere especially near to one-half decreases the temperature by the tropopause are somewhat larger than 2.3°K. Manabe and Wetherald (1967) those of Manabe and Strickler (1964) but calculated these changes to be 2.4 and this is due to differences in water vapor 2.30K, respectively. Reck (1976) inves- ~nd ozone concentration (see, e.g., Manabe tigated the change in the thermal structure and Wetherald, 1967) and in the treatment due to ozone variations and found for a of the boundary flux. 50% ozone reduction, the temperatures at We have also compared changes in 10 and 100 mbar decreased by about 8.7 surface temperature, for various amounts and 7.5°K, respectively. We calculated of absorbing gases, with those from previous temperature reductions of 6 and 7°K, respectively. Thus, our model gives results 40 comparable to those of previous studies. The radiative convective temperature profiles for each model atmosphere are shown on Fig. 4. Model 3, the Cambrian E 25 US STD model (0.1 PAL O= and 3.5 PAL CO2) I ~. ----RAD EQUtI_ I-" ,' /~: .... RAO CONV indicates a troposphere slightly warmer ~.9 20 //, .... ~ & - /( L: SmCKLeR than we find today; this is due to the 3:15 (19641 larger amount of CO2 and thus an increased IO "greenhouse effect." A weak tropopause

,,, • is apparent and the stratosphere is about 5 10 to 15°K colder than at similar elevations 0 I I in the present atmosphere. Because of the 180 200 220 240 280 280 3CO smaller amount of ozone (see Fig. 1), TEMPERATURE, °K the ultraviolet radiation penetrates to FIG. 3. Temperatures for the present-day model lower levels in the atmosphere creating a compared with the U. S. Standard Atmosphere, Mid-Latitude Spring/Fall profile. Also shown is smaller heating in the stratosphere (and radiative convective profile from Manabe and thus lower temperature) and a somewhat Strickler (1964) with average cloudiness. higher temperature further down near the .Ill .M()ItSS ANI) KITI[N

Ix(q)()pause. hi addition, the larger :mmunl. I[ '/I ' I '/ of carbon dioxide contributes to the lower- ing of temperature in the stratosphere, in 35 .5 4 /3 this case 5 to 10°K (see, e.g., Manabe and Wetherald, 1967). Since carbon dioxide •.. ,..\ causes an increase in tropospheric tempera- '~25 \ ... I\ ture, a lowering of temperature in the %° \ _ stratosphere is necessary in order that the ~,~;1"~ / 2 ~¢E ACE Earth atmosphere system remain in radi'L- ~'~/. I\ 2/ 3 CAMBRIAN I-- / {'.~/. 4 ALGONKIAN / I ~, 5 c~rozoJc tion bahmce, i.e., the outgoing planetary J P, "'.~. 6 A.,~CI.,~:.e.'~ -q radiation bal.mce the absorbeng with existence were probably much different carbon dioxide contributes to the increased from what we find today. In any case, if an tropospheric temperature. The stratospheric :~ppreciable concentration of methane were temperature is determined primarily by present, then absorption of solar radiation carbon dioxide. by methane would permit a well=developed Models 5 aim 6 which represent early tropopause and a very stable high-tempera= periods in the Earth's history cont'fin so ture str'~tosphere, which coul

TABLE IV temperatures and the effect they would

SURFACE TEMPERATURE CHANOE FOR PROPOSED have upon stratospheric processes. In ATMOSPHERIC MObELS RELATIVE TO particular, the eddy diffusion coefficient PRESENT-DAY MODEL (292.8°K)a was probably quite different than that Model Temperature change used in present-day studies, especially (°K) when the carbon dioxide concentration was much larger than we find today. These Cambrian 2.5 results indicate that the stratospheric Algonkian 11.5 regions were considerably less stable in Cryptozoic 13.0 Archean 12.5 prior eras, which could have significantly influenced the dynamics as well as the a See Table I for atmospheric composition. distributions of photochemically produced minor constituents. In addition, the effect present in such small concentrations that it of such lower stratospheric temperature has little effect on the surface temperature. on chemical reaction rates may be signif- The Ice Age model, Model 2, demon- icant. For example, the rate constant for strates the necessity for including with the ozone formation O + 02 4- M ~ 03 4- M carbon dioxide reduction, the corresponding is increase in ozone which should have occurred if such variation in carbon KI~ = 1.S X 10-35 exp(lOOO/RT) dioxide was due to biological processes. If cm 6 molec-2 see-1, the carbon dioxide is lowered to 0.65 PAL, while the destruction of ozone can occur as then the surface temperature would drop 03 -~- O --~ 202, with rate about 2.3°K, but when the corresponding change in ozone is included (see Fig. 1), K13 = 1.9 × 10-11 exp(--4600/RT) the temperature reduction is near 17°K. cm 3 molec-1 see-1. One should note that although the ozone column abundance has increased to about If the carbon dioxide column abundance 0.56 atm-cm, the distribution with height were greater than about 5 PAL, which is significantly altered. The large amount of may have corresponded to times earlier ozone above about 20 km produces a larger than 0.8 billion years ago, then the rate contribution to the outward flux from the constant for formation would be about stratosphere which requires a lower tropo- twice as large as the value used today, spheric temperature in order to maintain while the rate constant for destruction radiative balance. The smaller troposphere would only be one-twentieth as large. Thus, and lower stratosphere ozone concentra- it is not sufficient for these early studies tions accentuate the surface temperature to simply incorporate the present-day reduction. Our major conclusion is not temperature structure. Fortunately, Levine the magnitude of the temperature change, (1975) used a nearly isothermal strato- but to indicate the importance of the sphere in calculating his ozone concentra- coupled carbon dioxide-ozone variations tions which corresponds closely to our induced by biological processes. Indeed, Model 4 and appears to represent an one would expect other variations during average stratospheric temperature over an ice age, such as albedo, cloud cover, and geologic time. water vapor amount, to influence the surface Evolution of water vapor in the Earth's temperature as well. atmosphere is a subject which has not been Perhaps the most significant result of adequately addressed and represents per- this study is the colder stratospheric haps the most uncertain aspect of the 48 MOI{SS AND KUHN model atmospheric composition. To assess tion in carbon (lioxide occurred, the sttrface the impact of this constituent on the temperature decreased to its present-day temperature profile and surface tempera- value. ture, a "dry" model, representing a one- hundredfold decrease from the present-day ACKNOWLEDGMENTS mean water vapor model, was incorporated This paper is based upon the principal author's into the Arehean model atmosphere. The dissertation submitted to the University of Michigan temperature profile in the stratosphere in parti'd fulfilhnent of the requirements for the degree of Doctor of Philosophy. Pumuit of this changed only slightly, being some 2 to 4°K degree was under the auspices of the Civilian cooler. However, the surface temperature Institutions Directorate, U. S. Air Force Institute decreased 24°K. The reduced water vapor of Technology. Computer funds were provided by content results in a smaller "greenhouse lhe Department of Atmospheric and ()ceanic effect," thus a larger amount of energy Science, University of Michigan. A part of lhis work was supported by NASA (]rant NS11-7308. from the surface and lower troposphere escapes to space, which requires lower REFEI/ENCES surface and tropospheric temperatures if ABELSON, P. H. (1966). Chemical events on lhe radiative balance is to be maintained. primitive earth. Nat. Aead. Sci. Proc. 55, 13(i5- 1372. SUMMARY BERKNER, L., AND MARSm~LI,, L. (1964). The history of oxygenic concemration in the Earlh's Radiative convective temperature pro- atmosphere. Discuss. Faraday Soc. LorMon 37, files for the paleoatmosphere, extending 121-14I. back in time to 4.5 billion years, have BERKNER, L., AND MARSHALL, L. (1965). On the been calculated for an "~tmosphere initially origin and rise of oxygen concenlration in the rich in c,arbon dioxide, deficient in oxygen, earth's almosphere. J. A tmos. Sci. 22, 225-261. BERKNER, g., AND MARSHALL,L. 11966). Limitation and evolving to the present composition. on oxygen concentration in a primitive planetary ()nly within the last 1 billion years, or for atmosphere. J. Atmos. Sci. 23, 133-143. carbon dioxide abundances less than 5 BERKNER, L., AND MARSHALL, L. (1967). The rise PAL, and within a methane dominated of oxygen in 1he Earth's atmosphere with notes atmosphere, if indeed one did occur, was (m the Marlian almosphere. Advan. Geophgs. 12, 309-333. there a tropopause similar to that of the BuncH, 1). W., (;RYVNAK, ])., S1N(mETON, E. B., present day. FRANCF, W. L., AND WILLIAMS, I). 11962). The majority of the models, which ]nfra-red absorption by carbon dioxide, waler may represent most of geoh)gic time, vapor and minor atmospheric constiluen~s. Res. exhibit steadily decreasing temperatures Rep. Geophys. Res. Dir. AFCPdr62-698. Cnss, It. ])., AND KHETAN, S. (1973). Radialive with height at pressures where the current transfer wilhin the "mnospheres of lhe major •~tmosphere displays an inversion. Thus 1)l'mels. J. Qmmt. Spcetro.sc. Radiot. Transfer the use of present-day str:~tospheric temper- 13, 995-1009. atures in studies of atmospheric chemical CLOUD, P. (196S). AImospheric and hydrospheric evolution is justified for only about the evolulion on the primitive Earth. Science 160~ 729- 736. most recent 300 million years, if the c.trbon ELLIS, J., KANTOR, MINZNER, |{., AND QU1ROZ, R., dioxide-ozone atmosphere as studied by Fds. (1973). Comlnittee on the Extension of the Rutten, Berkner, and Marshall, trod Levine Standard Almosphere, Preliminary ](eport. represents conditions in the Earth's past. Fox, S., AND 5,IcCANLEG R. (1968). Could life Surface teinperatures during much of originate now? Natur. Hist. 77, 26~-31). ItOLLAND, It. D. (1962). Model for the evolution of geologic history would appear to have been lhe Earlh's almosphere. In Petrologic Studies: A some 10°K warmer than currently found. Volume to Honor A. F. Bu&tington, p. 447-477. As oxygen content, and by association an ]{OLLAND~ It. 1). (1963). On the chemical evolution accompanying increase in ozone and reduc- of the lerl'es/rial and cylherian almospheres. ]n PALEOATMOSPtIERIC TEMPERATU[IES 49

Origin and Evolution of Atmospheres and Oceans composition of the Preeambrian atmosphere. In (Brancazio and Cameron, Eds.), p. 86. Wiley, Crust of the Earth (A. Poldervaart, Ed.) Geolog. New York/London. Soc. Amer. Special Paper 62. ttOWARD, J. N., BURCH, D. W., AND WILLIAMS, D. RASOOL, S. I. (1966). Primitive atmospheres of the (1956). Infrared transmission of synthetic atmo- Earth. Nature 212, 1255--1276. spheres. II. Absorption by carbon dioxide. J. Opt. RASOOL, S. I. (1967). Evolution of the Earth's Soc. Amer. 45, 237-241. atmosphere. Science 157, 1466-1467. JASTROW, R. (1964). Planetary atmospheres. In RATNER, M. I., AND WALKER, J. C. G. (1972). Space Exploration and the Solar System (B. Ross, Atmospheric ozone and the history of life. J. Ed.), p. 236. Academic Press, New York. Atnws. Sci. 29, 803-808. LASAGA, A. C., HOLLAND, H. D., AND DWYER, M. J. RECK, R. A. (1976). Stratospheric ozone effects on (1971). Primordial oil slick. Science 174, 53-55. temperature. Science 192, 557-559. LEVlNE, J. S. (1975). The evolution of stratospheric RODGERS, C. D., AND WALS~tAW, C. D. (1966). The ozone. Ph.D. Thesis, Univemity of Michigan. computation of infrared cooling rate in planetary LINDZEN, R.. S., AND WILL, D. I. (1973). Analytic atmospheres. Quart. J. Roy. Meteorol. Soc. 92, fnrmula for heating due to ozone. J. Atmos. Sci. 67-92. 30, 513-515. RODOERS, C. D. (1967). The radiative heat balance M'mabe, S., and Strickler, R. F. (1964). Thermal of the troposphere and lower stratosphere. MIT equilibrium of the atm()sphere with a conveetive Dept. Meteor., Plan, Circ. Prog. Report A2. adjustment. J. Atmos. Sci. 21, 361-385. RUTTEN, ~[. G. (1966). Geologic data on atmospheric MANABE, S., AND WETHERALD, e~. T. (1967). history. Palaeogeography, Palaeoclimatology, Pa- Thermal equilibrium of the atmospheres with a laeoecology 2, 47-57. given distribution of relative humidity. J. Atmos. RUTTEN, M. G. (1971). The Origin of Life by Natural Sci. 24, 241-259. Causes. Elsevier, New York. MAnGULIS, L., AND LOVELOCE, J. E. 0974). SAGAS, C., AND MULLEN, G. (1972). Evolution of Biological modulation of the Earth's atmosphere. atmospheres and surface temperatures. Science Icarus 21, 471-489. 177, 52-56. McGovERN, W. E. (1969). The primitive Earth: WALKER, J. C. G. (1974). Stability of atmospheric Thermal models of the upper atmosphere for a oxygen. Amer. J. Sci. 274, 193-214. methane dominated environment. J. Atmos. Sci. WALSHAW, C. D. (1957). Integrated absorption by 26, 623-635. the 9.6 um band of ozone. Quart. J. Roy. Meteorol. RANKAMA, K. (1955). Geologic evidence of chemical Soc. 83, 315-321.