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Paleoatmospheric Temperature Structure

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Paleoatmospheric Temperature Structure 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 Earth's evolving atmosphere have been cah.ulated. If the atmosphere evolved from one rich in carbon dioxide, and deficient in oxygen, 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 carbon dioxide--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 atmospheres 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 Cambrian, Algonkian, Cryptozoic, binations suggested by Rutten (1966, and Archean 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 reducing atmosphere 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<l. It has gener'flly been held that radiation is given by the earth had a reducing atmosphere in its early history, and geologic evidence F(Uo) = ~ ~'Ir,'(Uo)i B,,'(O)do~ points to its existence as recently as 2 i billion years ago (Rankama, 1955; Rutten, 1966, 1971; Cloud, 1968). Additional evi= dence is found in the analysis of volcanic gases (Holland, 1962, 1963). Indirect support may also be found from the laboratory experiments that attempt to create basic proteins and amino acids (Fox and McCauley, 1968; Lasaga et al., where rf ~ is the mean flux transmissivity 1971). over spectral interval of width 6~, and The degree to which the a~mosphere B,~(0) and B,j(U) are the Planek functions was reducing is currently undecided, and for the surface and the level corresponding its composition is also a subject open to to mass path U, respectively. debate with the arguments centering on Solar heating rates for ozone were a methane versus carbon dioxide dominated obtained from the divergence of the energy atmosphere. For this very early atmo- deposition rate Q, as given by Lindzen sphere, we assumed a methane concentra- and Will (1973), tion of 20% by volume and ammonia of ~T/St = (gU/Cp)~O/6p, 9 ppm. where U is the absorber mass path and ~Q/~p is the energy deposition divergence. METHODOLOGY For the other constituents, the solar Radiative equilibrium temperature pro- heating is given as a function of the files were calculated by a forward difference integrated absorption A, iterative method. Heating rates (~T/~t) ~T/~t = (gS/C,)~A/~p, were determined from the equation where S is the incident solar flux. Absorp- 5T/St = (g/Cp)~F/6p, tion data used in this study are summarized in Table II.
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