Figure 4.30 shows the OLR as a function of surface pressure for a pure CO2 atmosphere subject to Martian gravity. The results span the range of surface pressure from those similar to the thin atmosphere of present Mars up to the thick atmospheres commonly hypothesized for Early Mars 6. The calculations were carried out for a fixed surface temperature of 270K, since we are
6 There is no strong reason to exclude the possibility of a substantial amount of N2 in the Early Martian atmosphere. Addition of N2 to the atmosphere would increase surface pressure and enhance CO2 absorption.
primarily interested in the question of how much CO2 there would have to be in order to warm Early Mars up to near the freezing point and permit the widespread liquid water at the surface that is seemingly demanded by the surface geology of the ancient Martian terrain. Results are shown for two different variants of the all-troposphere model. In the first, the atmosphere is on the dry CO2 ideal gas adiabat throughout its depth. This profile is inconsistent at high surface pressure, however, since it becomes supersaturated aloft. For this reason, we also include results in which the temperature profile is on the one-component condensing CO2 adiabat, which is on the dry adiabat where unsaturated but pinned to the Clausius-Clapeyron result when it becomes saturated (as in Fig. 2.6). With condensation, the surface pressure cannot be increased beyond 35.4bar at a surface temperature of 270K, since the surface becomes saturated at that point and no further CO2 can be added to the atmosphere without causing condensation. This does not pose a very significant constraint on the climate of Early Mars, however; a more important limitation is the amount of mass that could plausibly be lost from the primordial Martian atmosphere in the past four billion years. The effect of condensation aloft on OLR in essence, increases the amount of CO2 needed to warm Early Mars to the point where it is unclear that so much atmosphere could be lost.
At surface pressures comparable to that of Present Mars, the CO2 greenhouse effect reduces the OLñ by 35W/m2, and it would take 267W/m2 of absorbed solar radiation to maintain a surface temperature of 270K. The required solar heating is well below the 440W/m2 solar forcing at the subsolar point. Assuming the OLñ to scale with the fourth power of temperature for fixed surface pressure, this would support a temperature of 301K at the subsolar point, in contrast with a temperature of 292K in the absence of the atmospheric greenhouse effect. The atmosphere exerts only a modest warming effect on the surface temperature of Present Mars. To be sure, most of the planet is much colder; the absorbed solar flux averaged over the surface of the planet is only 110W/m2, which supports a temperature of 216K with the greenhouse effect and 210K without. Recall, however, that the planetary mean budget is not very meaningful on a planet like Present Mars with no ocean and little atmosphere to average out the diurnal variations. A thin layer of the rocky surface will be quite warm within a circle centered on the subsolar point, but the nightside surface falls to temperatures well below 216K.
At higher CO2, the OLñ decreases, approximately logarithmically in surface pressure for pressures above 104Pa. At pressures above 1bar, however, condensation becomes important, and the consequent increase in temperature aloft limits the decline of OLR This limitation is quite important for the climate of Early Mars. Taking into account the relatively high albedo caused by molecular reflection from a thick CO2 atmosphere, the absorbed solar radiation for Early Mars at a time when the solar flux is 30% reduced compared to today is about 70W/m2. This would be sufficient to sustain a 270K surface temperature with a surface pressure of 3.6bar if it weren't for the effects of condensation. When condensation is taken into account, however, fully 10 bars of CO2 are necessary to bring the surface temperature up to 270K 7. In fact, given the increase in albedo associated with scattering of solar radiation in a 10bar atmosphere, even 10bars is likely to prove insufficient. The effect of atmospheric scattering on albedo will be quantified in Chapter 5. In that chapter we will also discuss the potential for the scattering greenhouse effect from CO2 ice clouds to warm Early Mars. As time progresses toward the present, and the Sun gets brighter, it becomes progressively easier to warm Mars to the point where liquid water can persist at the surface. The climate history of Mars is a race between the brightening Sun and the loss of atmosphere, which seems to have been lost by the latter.
7The implications of CO2 condensation for the gaseous greenhouse effect on Early Mars were first discussed in: Kasting JF 1991, Icarus 94. The reader is also referred there for a more comprehensive treatment of the radiative transfer problem, including the effects of water vapor and a stratosphere. The conclusions are broadly similar to those based on our homebrew radiation model
T = 270K, Mars gravity
T = 270K, Mars gravity
Figure 4.30: The OLR vs surface pressure for a pure CO2 atmosphere. The results were done with a 10-term exponential sum code based on a 100mb reference pressure, and including the temperature scaling of both the continuum and line absorption. Calculations were done for a ground temperature of 270K, for Martian gravity. The dashed line shows the OLR for the case in which the temperature profile is on the dry ideal gas CO2 adiabat, while the solid line incorporates the effect of condensation on the temperature profile.
The continuum absorption in the CO2 window region is extremely important to these results. Without continuum absorption, the OLR for a 2bar atmosphere would be over 50W/m2 higher. The temperature scaling of the continuum affects the results by 10W/m2 or more. Whether or not one can account for prevalent liquid water on Early Mars by a gaseous CO2 greenhouse effect hinges on a matter of 10W/m2 of flux or so, and therefore the importance of the continuum is disconcerting. To settle this question, one must get the CO2 continuum right, and that is far from clear at this point, in view of the rather sparse experimental and theoretical results on the subject.
Now what about Venus? Are we finally equipped to say that we can account for the high surface temperature of Venus in terms of the CO2 greenhouse effect? Unfortunately, not quite. The problem is that the high albedo of Venus means that the climate is maintained by a relative trickle of absorbed solar radiation, while the high surface temperature means that the infrared emission at wavenumbers higher than 2300cm-1 would exceed 3800 W/m2 if the atmosphere were transparent in that spectral region. Unlike the Earthlike case, the atmospheric opacity there matters very much; however the HITRAN database does not include the weak absorption lines needed to accurately determine the atmospheric opacity at high wavenumbers. Extensions to the database suitable for use in Venusian conditions are described in the Further Readings at the end of this chapter. We will not pursue detailed calculations with the extended database, since one must, after all, stop somewhere. Instead, we will make use of a highly simplified treatment of the short wave thermal emission which at least tells us how close we are to being able to explain the temperature of Venus. Specifically, we use exponential sums based on HITRAN for the spectral region with lower wavenumbers than 2300cm-1, but represent the emission from higher wavenumbers by assuming that there is a radiating pressure prad such that the atmosphere radiates to space like a blackbody with temperature T(prad) throughout the high wavenumber spectral region. This is essentially the same approach as we took in formulating the simplest model of the greenhouse effect in Chapter 3, except that this time we apply the radiating-level concept only to the high wavenumber part of the emission. It is equivalent to stating that the absorptivity in the high wavenumber region is sufficiently large to make the layer of the atmosphere between prad and the ground optically thick throughout the high wavenumber region. Because of the shape of the Planck function, as prad is made smaller and T(prad) is made colder, the peak emission shifts to lower wavenumbers and in consequence the shortwave emission is sharply curtailed.
With these approximations the OLR can be written as OLR<(Tg) + OLR>(Tg,prad) where OLR< is computed for the low wavenumber spectral region alone using exponential sums and where v1 is the frequency cutoff for the high wavenumber region, B is the Planck function and T(prad,Tg) is computed using the dry CO2 adiabat. The OLR thus computed must be balanced against the absorbed solar radiation to determine the surface temperature. At present, the solar radiation absorbed by Venus amounts to 163 W/m2. Assuming a 93bar surface pressure, this is in balance with a surface temperature of 652K if there is no emission at all from the high wavenumber region, i.e. if prad = 0. This is a limiting case giving the maximum temperature that can be obtained with CO2 alone regardless of how optically thick the high wavenumber region may be. The fact that this is still somewhat short of the observed 720K surface temperature of Venus means that a modest additional source of atmospheric opacity other than CO2 is still needed to close the remaining gap in explaining the surface temperature. If prad is increased to 10 bars, the equilibrium temperature only drops to 633K, so it is only necessary for CO2 to be essentially opaque in the high wavenumber region at pressures of 10 bars or greater. On the other hand, if CO2 were really transparent at high wavenumbers, i.e. prad = 93bar, then the surface temperature would drop all the way to 461K, which is well below the observed value. Detailed radiation modeling of the high wavenumber region is consistent with a value prad « 10bar, so it appears that the CO2 greenhouse effect alone gets us almost all the way to explaining the high surface temperature. The remaining opacity needed to bring the surface temperature up to 720K is provided by Venus' high sulfuric acid clouds,the trace of water vapor in the atmosphere, and sulfur dioxide (in order of importance). The sulfur dioxide clouds are not good infrared absorbers, and exert their greenhouse effect through infrared scattering, as discussed in Section 5.
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