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Evolution of Atmospheres and Surface Temperatures Author(S): Carl Sagan and George Mullen Source: Science, New Series, Vol Earth and Mars: Evolution of Atmospheres and Surface Temperatures Author(s): Carl Sagan and George Mullen Source: Science, New Series, Vol. 177, No. 4043 (Jul. 7, 1972), pp. 52-56 Published by: American Association for the Advancement of Science Stable URL: http://www.jstor.org/stable/1733927 . Accessed: 10/12/2014 08:53 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. American Association for the Advancement of Science is collaborating with JSTOR to digitize, preserve and extend access to Science. http://www.jstor.org This content downloaded from 128.103.149.52 on Wed, 10 Dec 2014 08:53:18 AM All use subject to JSTOR Terms and Conditions (6). This variation has profound conse- quences for the surface temperatures of the terrestrial planets (7). The main- sequence brightening of the sun is one Reports of the most reliable conclusions drawn from the modern theory of stellar evolu- tion, which explains in considerable de- tail the observed Hertzsprung-Russell Earth and Mars: Evolution of Atmospheres diagram. The models of solar evolution used in this report give an age for the and Surface Temperatures sun in excellent agreement with the age determined on independent grounds for Abstract. Solar evolution implies, for contemporary albedos and atmospheric Earth, the moon, and the meteorites. composition, global mean temperatures below the freezing point of seawater less The principal uncertainties in such cal- than 2.3 aeons ago, contrary to geologic and paleontological evidence. Ammonia culations are in the age of the sun and mixing ratios of the order of a few parts per million in the middle Precambrian its initial abundance of helium. Much atmosphere resolve this and other problems. Possible temperature evolutionary larger possible errors in such parameters tracks for Earth and Mars are described. A runaway greenhouse effect will occur as thermonuclear reaction rates or opac- on Earth about 4.5 aeons from now, when clement conditions will prevail on ities have much smaller effects on Mars. dL/dt (8). Katz (8) concludes that (1/L) (dL/dt) is in error by at most The present surface temperature of dows, and the other emitted by the 25 percent for the best contemporary Earth represents an energy balance be- atmosphere into space in wavelength evolutionary models. A variety of calcu- tween the visible and near-infrared sun- regions of strong atmospheric absorp- lations of main-sequence solar evolu- light that falls on the planet and the tion. In the latter case we consider the tion give a variation, AL, of 30 to 60 middle-infrared thermal emission that emission to occur from the skin tem- percent over geologic time (6). The best leaves. In the absence of an atmo- perature of the approximately isother- present estimate of AL is 40 ? 10 per- sphere this equilibrium is written /4S X mal outer boundary of an atmosphere cent. For most of the following calcula- (1 - A) = eaTe4, where S is the solar in radiative equilibrium, which is, in tions, we conservatively adopt AL = 30 constant; A is the Russell-Bond spheri- the Eddington approximation, at a percent. cal albedo of Earth, a reflectivity inte- temperature of 2-1/4Te. Thus, We then run the sun backward grated over all frequencies; e is the through time and assume initially that - Ax, mean emissivity of Earth's surface in /45(I A-) = EeBi (Ts) + the terrestrial atmospheric composition, the middle infrared; a is the Stefan- e, and A remain constant. The results Boltzmann constant; and Te is the ef- BjHee pec(2-/h ) (1) from Eq. 1 are shown in Fig. 1. We see fective equilibrium temperature of (at- that the global temperature of Earth mosphereless) Earth. The factor 1/4 is Here BAis the Planck specific intensity, dropped below the freezing point of the ratio of the area 7rR2 that intercepts and the wavelength intervals AX are seawater less than 2.3 aeons ago (1 aeon sunlight to the area 47rR2 that emits chosen to pack with adequate density is 109 years); 4.0 to 4.5 aeons ago thermal infrared radiation to space. those wavelength regions where BA is global temperatures were about 263?K. When the best estimates of these param- changing rapidly. The equation is solved Had we used 50 percent for AL, the eters are used, a value for Te of 250? iteratively for Ts on an electronic com- freezing point of seawater would have to 255?K is obtained; this is far less puter. The adopted step-function ap- been reached about 1.4 aeons ago, and than the observed mean surface tem- proximation to the actual nongray ab- temperatures 4.0 to 4.5 aeons ago which is due to rota- perature, T,, of Earth, 286? to sorption spectrum, would have been about 245?K. Be- 288 K. The difference is due to the tion-vibration transitions in Earth's cause of albedo instabilities (discussed with greenhouse effect, in which visible and atmosphere, is compared the mea- below) it is unlikely that extensive near-infrared sunlight penetrates through sured transmission spectrum in (1). The liquid water could have existed any- Earth's atmosphere relatively unim- resulting values of T, are shown in Table where on Earth with such global mean The value of e from studies peded, but thermal emission by Earth's 1. correct is, temperatures. surface is absorbed by atmospheric con- of a wide variety of minerals (2), closer The presence of pillow lavas, mud stituents that have strong absorption to 0.9 than to 1.0. Extensive calculations cracks, and ripple marks in rocks from bands in the middle infrared. Thus, time (3) based on measurements made from the Swaziland supergroup strongly variations in S, A, e, or atmospheric Earth yield values for A of 0.33 to 0.35, implies abundant liquid water 3.2 aeons made composition may induce important and an analysis of observations ago (9). The earliest known microfos- changes in Ts. The present heat flow over 5 years by meteorological satellites sils (10, 11), 3.2 ? 0.1 aeons old, in- from the interior of Earth is about (4) yields 0.30 for A. Since we are clude blue-green algae, which would be 2 X 10-5 the solar constant and plays a concerned with differential effects, we very difficult to imagine on a frozen - negligible role in determining Ts. have adopted A 0.35 to secure agree- Earth. Algal stromatolites, 2.0 to 2.8 To calculate Ts, allowing for the ment with the observed Ts in our ap- aeons old, exist in various parts of the greenhouse effect, we divide the emer- proximation (5). world (12, 13). If they are intertidal gent flux into two parts, one emitted by The solar constant is varying; the (13), there must have been at least the surface at temperature Ts directly luminosity, L, of the sun has increased meters of liquid water; if they are sub- into space through atmospheric win- by about 40 percent in geologic time tidal (14), much greater depths are im- 52 SCIENCE, VOL. 177 This content downloaded from 128.103.149.52 on Wed, 10 Dec 2014 08:53:18 AM All use subject to JSTOR Terms and Conditions ... plied. The time required for surface may be somewhat less, but the fraction than the contemporary global average, water to accumulate sediments in geo- of Earth covered by ice, snow, and about 1 g cm-2. The only surviving synclinal trough suggests (15) the pres- glaciation will be very much larger. The alternative appears to be that the ence of extensive bodies of water on albedos of thick deposits of ice or snow atmosphere of Earth 1 or 2 aeons Earth 4 aeons ago or more. Finally, are 0.50 to 0.70. A decline in the glo- ago contained some constituent or con- liquid water is almost certainly neces- bal temperature of Earth is likely to in- stituents, not now present, with signifi- sary for the origin of life; if we believe crease rather than decrease the albedo, cant absorption in the middle infrared, that life began shortly after the forma- but in any case the albedo decline re- in the vicinity of the Wien peak of tion of Earth (16), liquid water must quired to explain the discrepancy ap- Earth's thermal emission. A large num- have been present for most of the period pears to be out of the question. Indeed, ber of candidate molecules were in- between 3.5 and 4.5 aeons ago. Thus, detailed global climatic models (17) vestigated. The ideal molecule should even using our most conservative value suggest that a relative increase in A of provide significant absorption in the of AL, we find a serious discrepancy only 2 percent is enough to induce ex- present window from 8 to 13 ,um, even between theory and observation. tensive glaciation on Earth, which im- in low abundances. Large amounts of This discrepancy indicates an error plies that the present climate is ex- CO, SO,, 03, and the various oxides in at least one of our initial assump- tremely sensitive to albedo. of nitrogen are inadequate, as are many tions. There are only three likely sources This leaves changes in atmospheric times the contemporary abundances of of error: S, A, and the atmospheric composition as a possible explanation.
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