Spectroscopic properties of selected greenhouse gases

Now we will provide a survey of the infrared absorption properties of a few common greenhouse gases, with particular emphasis on the "big 3" that determine much of climate evolution of Earth, Mars and Venus from the distant past through the distant future: CO2, H2O and CH4. In each case, the spectral results shown are for the dominant isotopic form of the gas, e.g. 12C16O2 for the case of carbon dioxide. Other isotopic forms (isotopologues) can have significantly different spectra, particularly when the substitution of a heavier or lighter isotope changes the symmetry of the molecule, as in HDO or 12C16O18O. The reader should keep these isotopic effects in mind, since the asymmetric molecules can have have strong absorption in parts of the spectrum where the symmetric molecule has essentially no absorption lines at all. In such cases, the asymmetric isotopologues can be radiatively important even if they are present only in small quantities. When such is the case, one needs to know the isotopic composition of an atmosphere before one can accurately compute the climate. This is a considerable challenge for atmospheres that cannot be directly observed.

This section will deal only with that part of absorption that can be identified as being caused by nearby spectral lines associated with energy transitions of the molecule in question; the continuum absorption which is not so directly associated with spectral lines will be discussed separately. Although CH4 is a greenhouse gas on Titan, most of its contribution there comes from continuum absorption rather than its line spectrum.

Although we focus on some of the more conventional examples, the reader is encouraged to keep an open mind with regard to what might be a greenhouse gas. At present, NO2 and SO2 do not exist in sufficient quantities on any known planet to be important as a greenhouse gas, but with different atmospheric chemistries occuring in the past or on as-yet undiscovered planets, the situation could well be different. For that matter, things like S«O2 that we consider rocks on Earth could be gases and clouds on "roasters" - extrasolar gas giants in near orbits - and there one ought to give some thoughts to their effect on thermal infrared.

When interpreting the absorption spectra to be presented below, it is useful to keep the Planck function in mind. Absorption is not very important where there is little flux to absorb, so the relevant part of the absorption curve varies with the temperature of the planet under consideration. For Titan at 100K, 3 of the emission is at wavenumbers below 350 cm 1. For Earth at 280K , 3 of the emission occurs below 1000 cm-1 . Mars is slightly colder, and the threshold wavenumber is therefore a bit less. For Venus at 737K, 3 of the emission is below 2550 cm-1, but moreover the flux beyond this wavenumber amounts to over 4000 W/m2. This near-infrared flux is vastly in excess of the mere 170W/m2 of absorbed solar radiation which maintains the Venusian climate. For Venus one needs to consider the absorption out to higher wavenumbers than for Earth or Mars, and given the large fluxes involved and the huge mass of CO2 present, exquisite attention to detail and to the effect of weak lines that can normally be ignored is required. For the aforementioned roaster planets, the "thermal" emission extends practically out to the visible range.

An ideal greenhouse gas absorbs well in the thermal infrared part of the spectrum but is transparent to incoming solar radiation. The following survey concentrates on thermal infrared - the part of the spectrum that is involved in OLR- but it should be remembered that some of the gases discussed, such as Methane, absorb quite strongly in the solar near-infrared spectrum.

Figure 4.17: The minimum, 25th percentile, median, 75th percentile, and maximum absorption coefficients in bands of width 50 cm-1, computed for CO2 in air from spectral line data in the HITRAN database. The left panel shows results at an air pressure of 100mb, whereas the right panel gives results at 1bar. Both are calculated at a temperature of 260K.

This can compromise their effectiveness as greenhouse gases when they reach concentrations high enough that the solar absorption becomes significant. Even the weaker solar absorption from CO2 and H2O can affect the thermal structure of atmospheres in significant ways. The implications of real-gas solar absorption will be taken up in more detail in Chapters 5.

Carbon Dioxide

We have already introduced a fair amount of information about the absorption properties of CO2 but here we will present the data in a more systematic and general way, which will make it easier to compare CO2 with other greenhouse gases. In a line graph of a wildly varying function like the absorption, such as shown in Figure 4.7, only only sees the maximum and minimum defining the envelope of the absorption. There is no useful information about the relative probabilities of the values in between. To get around these problems, we divide up the spectrum into slices of a fixed width ( 50 cm-1 in the results presented throughout this section), and then compute the minimum, maximum, median and the 25th and 50th percentiles of the log of the absorption in each band. By plotting these statistics vs. wavenumber, it is possible to present a fairly complete picture of the probability distribution of the absorption. To make the absorption data easier to interpret, we exponentiate the median , quartiles, min and max, and plot the resulting values on a logarithmic vertical axis. Plots of this sort for CO2 at a temperature of 260K are shown in Figure 4.17. The left panel is computed at a pressure of 100mb while the right panel is computed at 1000mb. Both results are for air-broadened lines. As for the other absorption spectra we shall discuss, these results are for the dominant isotopic form of CO2, i.e. 12C16O2. Other isotopic forms can have substantially different properties, particularly the asymmetric forms involving one heavy oxygen and one ligher oxygen.

For Earthlike and Marslike temperatures, only the lower frequency absorption region, from about 400 — 1100cm-1 affects the OLR, since there is little emission in the range of the higher frequency band. For Earth, the higher frequency band can contribute to Solar absorption, since the Solar radiation reaching the Earth in that part of the spectrum amounts to 7.2W/m2 (or about

3W/m2 at the orbit of Mars). However, most of the absorption of Solar near-infrared, whether by water vapor or CO2, occurs at higher frequencies. Venus, however, has significant surface emission in the range of the higher frequency group, which therefore has a significant effect on that planet's OLR.

The absorption spectrum depends on temperature and pressure, and on whether the lines are broadened by collision with air or by collisions with molecules of the same type (e.g. CO2 with CO2 in the present case); rather than present page upon page of graphs, the strategy is to show the results for a single standard temperature and pressure, and make use of appropriate temperature and pressure weighted equivalent paths to apply the standard absorption to a wider variety of atmospheric circumstances. We will adopt T = 260K, p = 100mb and air-broadening as our standard conditions when discussing other greenhouse gases in this section. The comparison of the two panels of Figure 4.17 illustrates the nature of the pressure scaling. Increasing the pressure by a factor of 10 shifts the minimum, median and quartiles upward by a similar factor. The main exception to the scaling is the maximum absorption in each band, which is reduced and becomes more tightly clustered to the median. This is the expected behavior, since increased pressure reduces the absorption near the centers of absorption lines. Since this part of the spectrum is rare, and absorbs essentially everything hitting it anyway, the errors in pressure scaling near the line centers are of little consequence. A bit of numerical experimentation indicates that the linear pressure scaling works quite well for pressures below 1 or 2 bars. At higher pressures (certainly by 10 bar) the lines overlap to such an extent that the whole probability distribution collapses on the median, in which case the absorption can be described as a smooth function of the wavenumber, and loses its statistical character. The other gases to be discussed have similar behavior under pressure, and so we will not repeat the description separately for each gas.

To understand a planet's radiation balance, the main thing we need to understand is where in the spectrum the atmosphere is optically thick, and where it is optically thin. Pressure exerts by far the strongest modifying influence on the standard-state absorption coefficients given in Figure 4.17. Hence, we will first discuss the effect of CO2 on the optical thickness of several planetary atmospheres in terms of the 260K air-broadened coefficients using pressure-adjusted paths. Later we will make a few remarks about how self-broadening and temperature affect the results.

The strong line pressure-weighted equivalent path for a well mixed greenhouse gas with specific concentration q is £ = 2 q(p1 — p2)/(p0g cos 0). If we take the reference pressure po = 100mb, the equivalent paths can be multipled by the absorption coefficients in the left panel of Figure 4.17 to obtain optical thickness. Some typical values of the equivalent path are given in Table 4.1. Although Mars at present has much more CO2 per square meter in its atmosphere than modern Earth, the equivalent paths are quite similar in the two cases because the total pressure on Mars is so much lower. For Earth and Mars temperatures only the lower frequency absorption group is of interest, and within this group it is only the dominant spike in absorption near 675cm-1 that contributes significantly to the absorption. Both atmospheres have optical thicknesses exceeding unity within the wavenumber band from roughly 610 — 750cm-1 and are optically thin outside this band. The weak absorption shoulder occurring to the high-wavenumber side of 870cm-1 has little effect for modern Earth or Mars. For any given wavenumber range, the 10% of the atmosphere nearest the ground (i.e. the lowest 100mb on Earth) is one fifth as optically thick as the atmosphere as a whole, meaning that a substantial part of the back-radiation of infrared to the surface attibutable to CO2 comes from the lowest part of the atmosphere. In contrast, because of low pressure aloft, the uppermost 10% of the atmosphere, which may loosely be thought of as the stratosphere, is comparatively optically thin. If CO2 were the only factor in play, the greenhouse effect of the present Earth and Mars atmospheres would be quite similar. The two planets are rendered qualitatively different primarily by the greater role of water vapor in the

Mod. Earth

Early Earth

Mod. Mars

Early Mars

Venus

Whole atm

47.

15000.

30.

106

109

Bottom 10%

9.

2900.

5.

2 • 105

2 • 108

Top 10%

.5

160.

.3

104

107

Top 1%

.005

1.5

.003

100.

105

Table 4.1: Pressure-weighted equivalent paths for various planetary situations, in units of kg/m2. The weighted path is based on a 100mb reference pressure, so these paths are intended to be used with the absorption coefficients in the left-hand panel of Figure 4.17 . A mean slant path cos 0 = 2 is assumed. The Modern Earth case is based on 300ppmv CO2 in a 16ar atmosphere, while the Early Earth case assumes 10% (molar) CO2 in a 16ar atmosphere. Modern Mars is based on a 10mb pure CO2 atmosphere, while Early Mars assumes a 26ar pure CO2 atmosphere. The Venus case consists of a 906ar pure CO2 atmosphere.

Table 4.1: Pressure-weighted equivalent paths for various planetary situations, in units of kg/m2. The weighted path is based on a 100mb reference pressure, so these paths are intended to be used with the absorption coefficients in the left-hand panel of Figure 4.17 . A mean slant path cos 0 = 2 is assumed. The Modern Earth case is based on 300ppmv CO2 in a 16ar atmosphere, while the Early Earth case assumes 10% (molar) CO2 in a 16ar atmosphere. Modern Mars is based on a 10mb pure CO2 atmosphere, while Early Mars assumes a 26ar pure CO2 atmosphere. The Venus case consists of a 906ar pure CO2 atmosphere.

warmer atmosphere of modern Earth, and by differences in vertical temperature structure between the two atmospheres (arising largely from differences in solar absorption).

On Early Earth - either during the high CO2 phase after a long-lived Snowball, or during the Faint Young Sun period - the CO2 may have been 10% or more of the atmosphere by molar concentration. In this case, the equivalent paths are vastly greater than at present. The Earth atmosphere in this case is optically thick from about 520 — 830cm-1, and the higher wavenumber shoulder just barely begins to be significant. It becomes rapidly more so as the CO2 molar concentration is increased beyond 10% . This is good to keep in mind when doing radiation calculations at very high CO2, since many approximate radiation codes designed for the modern Earth only incorporate the effect of the principal absorption feature centered on 675cm-1. Even with such high CO2 concentrations, the atmosphere is optically thick in only a limited portion of the spectrum, so that the net greenhouse effect will be modest unless other greenhouse gases come into play. This remark is particularly germane to Snowball Earth, where the cold temperatures allow little water vapor in the atmosphere. Without help from water vapor, CO2 has only limited power to warm up a Snowball Earth to the point of deglaciation.

On a hypothetical Early Mars with a 26ar pure CO2 atmosphere, the equivalent path is orders of magnitude greater than the Early Earth case. This renders the atmosphere nearly opaque within the wavenumber range 500 — 1100cm-1. However a great deal of OLR can still escape through the CO2 window regions, so continuum absorption, water vapor and other greenhouse gases will play a key role in deciding whether the gaseous greenhouse effect can explain a warm,wet Early Mars climate.

Since the equivalent path assumes absorption increases linearly with pressure, the equivalent paths given for the bottom 10% and for the entirety of the Venus atmosphere yield overestimates of the true optical depths, given that the increase of absorption with pressure weakens substantially above 106ars. Even assuming that the equivalent paths are overestimated by a factor of 10, the implied optical depths for the lowest 96ars of the Venus atmosphere, and for the entire Venus atmosphere, remain so huge that these layers can be considered essentially completely opaque to infrared outside the CO2 window regions. In fact even the top 16ar ( about 1%) of the Venus atmosphere has an optical thickness greater than unity throughought the 500 — 1100cm-1 and 1800 — 2500cm-1 spectral regions. Within these regions, essentially all the OLR comes from the relatively cold top 16ar of the atmosphere.

The window region, where CO2 has no absorption lines, presents a challenge to the explanation of the surface temperature of Venus, particularly since the peak of the Planck function for the observed Venusian surface temperature lies in this region. In fact, if the 1200 — 1700cm-1 band were really completely transparent to infrared, then emission through this region alone would reduce the Venus surface temperature to a mere 355K (assuming a globally averaged absorbed solar radiation of 163W/m2). Some energy also leaks out through the low frequency window region, which would reduce the temperature even further. We must plug the hole in the spectrum if we are to explain the high surface temperature of Venus. The high altitude sulfuric acid clouds of Venus play some role, by reflecting infrared back to the surface; there may also be some influence of the less common isotopes of CO2, since asymmetric versions of the molecule (e.g. made with one 16O and one 18O) can have lines in the window region. The principal factor at play is the continuum, absorption to be discussed in Section 4.4.8. Figure 4.17 was computed taking into account only the relatively nearby contributions of each absorption line (within roughly 1000 line widths), whereas collisions can allow some absorption to occur much farther from the line centers. This far-tail absorption spills over into the window region, particularly at high pressure. It cannot be reliably described in terms of the Lorentz line shape, and therefore requires separate consideration.

The difficulties posed by Venus do not end with the window region¿ For planets having Earthlike temperatures, the thermal radiation beyond 2300cm-1 is insignificant, so we needn't be too concerned about the absorption properties there. However, for a planet with a surface temperature of 700K, the ground emission on the shortwave side of 2300cm-1 is 3853 W/m2, compared to under 200W/m2 of absorbed solar radiation for Venus. In these circumstances it simply won't do to assume the atmosphere transparent at high wavenumbers The HITRAN spectral database is a monumental accomplishment, but it is still rather Earth-centric, and lacks the weak lines needed to deal with high temperature atmospheres; there may also be continuum absorption in the shortwave region, especially at high pressures. In order to deal with the high wavenumber part of the Venus problem, one needs to employ specialized high-temperature CO2 databases, which are less verified and more in a state of flux than HITRAN. Among specialized databases in use for Venus, the HITEMP database (described in the supplementary reading at the end of this Chapter) is particularly convenient, because it at least uses the same data format as HITRAN. It will be left to the reader to explore the use of this database. Suffice it to say that there appears to be sufficient absorption in the high wavenumber region to raise the radiating level to altitudes where the temperature is low enough that one may not need to consider shortwave emission in computing OLR.

The preceding discussion was based on air-broadened absorption at 260K, whereas self-broadened data would be more appropriate to the pure-CO2 atmospheres and in all cases one must think about whether the increase of line strength with temperature substantially alters the picture presented. A re-calculation of Figure 4.17 for self-broadened pure CO2 indicates that the self-broadened absorption is generally about 30% stronger than the air-broadened case,though there are a few bands in which the enhancement is as little as 13%. This is quantitatively significant, but the enhancement factor is too small to alter the general picture presented above. The temperature dependence can have a more consequential effect. In the strong line approximation, valid away from line centers, the temperature affects the absorption only in the form of the product of line strength and line width, S(T)y(p,T), which yields a temperature dependence of the form KCO2 ~ exp(— T*/T) for some coefficient T*. The coefficient differs from line to line, but we can still attempt to fit this form to the computed temperature dependence of the median absorption within each 50cm-1 band. The result is shown in Figure 4.18. This still only gives an incomplete picture of the effect of temperature on absorption, since the other quartiles may have different scaling coefficients. Within an exponential-sum framework, however, one can do little else than pick a base temperature most appropriate to the planet under consideration, compute the probabilility distribution for that case,and then assume that each absorption coefficient in a band scales with the same function of temperature. This procedure in any event gives an estimate of the magnitude

4500 4000 3500 3000 „ 2500 2000 1500 1000 500

4500 4000 3500 3000 „ 2500 2000 1500 1000 500

500 1000 1500 2000 2500 3000 Wavenumber (cm )

1 1 1 1 1 1 1

1.4

1

1.3

s

1.2

j

*

1

G

1.1

*

1

0.9

0 500 1000 1500 2000 2500 3000 Wavenumber (cm )

500 1000 1500 2000 2500 3000 Wavenumber (cm )

0 500 1000 1500 2000 2500 3000 Wavenumber (cm )

Figure 4.18: Left panel: Temperature dependence coefficient for air-broadened CO2 at 100mb. The coefficient is computed for the median absorption in bands of width 50cm-1, as shown in Figure 4.17. The median absorption within each band increases with temperature in proportion to exp(-T*/T). Right panel: The ratio of self-broadened to air-broadened median absorption coefficients.

of the temperature effect. From the Figure, it is seen that the temperature dependence varies greatly with wavenumber. It is low near the principal absorption spike at 675cm-1, with T* as low as 1000K. This value increases the absorption by a factor of 1.7 going from 260K to 300K, and decreases absorption by a factor of 2 going from 260K to 220K. Where T* = 3000K, the corresponding ratios are 4.7 and .14 . Therefore CO2 is significantly more optically thick than our previous estimates in the warmer-lower reaches of the present Earth atmosphere, and significantly less optically thick in the cold tropopause regions. For the 737K surface temperature of Venus, the absorption is enhanced by a factor of 12 when T* = 1000K but by a substantial factor of 1750 when T* = 3000K. This just makes an already enormously optically thick part of the atmosphere even thicker. Outside the window regions, most of the atmosphere of Venus is in the optically thick limit where very slow radiative diffusion transfers heat; infrared radiative cooling in the deeper parts of the Venus atmosphere is determined almost exclusively by what is going on in the window regions.

Water Vapor

Figure 4.19 shows the standard-state absorption spectrum for water vapor. Unlike CO2, the H2O molecule, which has more complex geometry, has lines throughout the spectrum, so there is no completely transparent window region. Water vapor nonetheless has two window regions where the absorption is very weak; it will turn out that continuum absorption from far tails excluded from the computation in the figure substantially increases the absorption in these window regions (Section 4.4.8). The peak absorption coefficient for water vapor has a similar magnitude to that for CO2, but water vapor absorbs well over a far broader portion of the spectrum than CO2. In particular, the H2O absorption has a peak within both the 1000cm-1 and longwave window regions of CO2. This critically affects the greenhouse warming on Earth and on Early Mars, but it plays little role on present-day Venus, which has little water vapor in its atmosphere. It should not be concluded that water vapor overwhelms the greenhouse effect of CO2, however. It would be more precise to say that the water vapor greenhouse effect complements that of CO2. CO2 absorbs strongly near the peak of the Planck function for Earthlike temperatures, but the water vapor absorption is nearly two orders of magnitude weaker there. Further, for Earthlike planets, water vapor condenses and therefore disappears in colder regions of the planet; it is only the long-lived CO2 greenhouse effect that can persist in cold parts of the atmosphere.

Figure 4.19: As in Figure 4.17, but for H2O. The continuum regions marked on the figure are regions where the measured absorption substantially exceeds that computed from the spectral lines.

On a planet without a substantial condensed water reservoir, water vapor could be a well-mixed noncondensing greenhouse gas much like CO2 on modern or early Earth. In most known cases of interest, though, atmospheric water vapor is in equilibrium with a reservoir -an ocean or glacier - which fills the atmosphere to the point that the atmospheric water vapor content is limited by the saturation vapor pressure. The prime cases of interest are water vapor feedback on Earth and on Early Mars, and the runaway greenhouse on Early Venus. The runaway greenhouse is also relevant to the ultimate far-future fate of the Earth, and the evolution of hypothetical water-rich extrasolar planets. The status of water vapor as a greenhouse gas whose concentration is limited,via condensation, by temperature does not derive from any special properties of water. One tends to focus on a role of this sort for water simply because planets that are "habitable" to the only example of life with which we are presently familiar seem to require a planet with liquid water and an operating temperature range in which the saturation vapor pressure is high enough for water vapor to be present in sufficient quantities to be active as a greenhouse gas. On present and past Mars, as well on a hypothetical early Snowball Earth, CO2 can be limited by condensation, and on Titan today CH4 condenses, while NH3 and other gases have condensation layers on the gas giant planets.

First, let's think about the effect of water on OLR, supposing that the atmosphere is saturated at each altitude. The water vapor greenhouse effect is determined by a competition between two factors. Water vapor causes the greatest optical thickness near the ground, where both pressure-broadening and saturation vapor pressure are highest. However, a strong greenhouse effect requires optical thickness at higher altitudes, where the temperature is substantially colder than the surface, in order to reduce the radiating temperature of the planet. For this reason, water vapor in the mid to upper troposphere is more important than water vapor near the ground. Consider a typical Earth tropical case, on the moist adiabat with 300K temperature near the ground. If the low level air is saturated, then the equivalent path of the lowest 100mb of the atmosphere is about 400kg/m2. This is sufficient to make the lower atmosphere optically thick except within the window regions, so that the atmosphere would radiate to the ground at the near-surface air temperature except within the windows. Most of the infrared cooling of the ground occurs in the windows, but we'll see eventually that at temperatures of 300K and above, the continuum substantially closes off the window region as well. This near-surface opacity doesn't much affect the OLR, however. Near 400mb, the temperature is about 260K,and in saturation the equivalent path between 400mb and 500mb is only 25kg/m2. This relatively small amount of water vapor is still sufficient to make the layer optically thick between 1350cm-1 and 1900cm-1, as well as on the low frequency side of 450cm-1. This substantially reduces the OLR. At the tropopause level, in contrast, the temperature is about 200K, the pressure is 100mb, and the equivalent path from 100mb to 200mb is only .01kg/m2. At such low concentrations, water vapor is optically thin practically throughout the spectrum. At lower surface temperatures, the dominant greenhouse effect of water vapor comes from correspondingly lower altitudes. With a 273K surface temperature, the 400mb temperature on the dry air adiabat is only 210K, and the water vapor opacity is inconsequential there. One has to go down to about 600 — 700mb, where the path is about 2kg/m2, to get a significant water vapor greenhouse effect. On a low CO2 Snowball Earth soon after freeze-up, where the tropical surface temperature is under 250K, the water vapor greenhouse effect is essentially negligible. The water vapor greenhouse effect only starts to play a role when the planet has warmed to the point that the tropical temperatures approach the melting point.

As was the case for CO2, the absorption coefficient for water vapor decays roughly exponentially with distance in wavenumber space from each peak of absorption. This has similar consequences for OLR as were discussed previously in connection with CO2. Because of the exponential envelope of absorption, doubling or halving the water vapor content of a layer of the atmosphere has approximately the same effect on the optical thickness of that layer regardless of whether the base amount being doubled or halved is very large (say 200 kg/m2) or very small (say 2 kg/m2). There may not be much water to work with in the Earth's mid troposphere, but nonetheless halving or doubling the amount would have a significant effect on OLR. This remark is particularly significant because there are dynamical effects which in fact keep the Earth's mid-troposphere substantially undersaturated. Although there are regions with relative humidity as low as 10%, it would still significantly increase the OLR if the relative humidity were reduced still more to 5%, and conversely it would significantly decrease the OLR if the relative humidity were increased to 20%. Because of the spectral position of the absorption peaks relative to the shape of the Planck curve, the effect of water vapor concentration on OLR is not as precisely logarithmic as is the case for CO2 . Nonetheless, it is fair to say that the change in water vapor content relative to the amount initially present gives a more true idea of the radiative impact of the change than would the change in the absolute number of kilograms of water present in a layer.

With regard to water vapor, then, it is clear that subsaturation is important. However, the determination of the degree of subsaturation involves intrinsically fluid dynamical processes, and we will not have much to say about this important issue in this book. Similar considerations would apply to any radiatively active condensible substance in a planetary atmosphere.

Figure 4.20 shows the temperature dependence and the ratio of self to air-broadened absorption for water vapor. The general range of temperature sensitivity is much the same as it was for CO2 . However, whereas self-broadened absorption for CO2 is only a few tens of percents stronger than air-broadened absorption, the self-broadened H2 O absorption is fully five to seven times stronger than the air-broadened case. This is extremely important to the runaway greenhouse, which involves portions of the atmosphere which consist largely of water vapor. Moreover, when a species has a molar concentration in air of, say, 10% or less one wouldn't ordinarily have to worry much about self-broadening, since collisions with air are so much more common than self-collisions. However, because of the great amplification of self-broadened absorption for water vapor, the self-broadening in fact starts to become dominant even at molar concentrations of around 10%. At the Earth's surface, this concentration is achieved at a temperature of 320K. With a dry air partial pressure of 100mb, this concentration would be achieved at temperatures near 280K; this situation is relevant to a hot planet on the verge of a runaway greenhouse. The strong

Figure 4.20: Left panel: Temperature dependence coefficient for air-broadened H2O at 100mb, as defined in Fig. 4.18. Right panel: Ratio of self-broadened to air-broadened median absorption for H2O at 100mb and 260K. As usual, medians are computed in bands of width 50cm-1.

enhancement of self-broadened absorption relative to air-broadened absorption is far in excess of what would be anticipated from simple effects associated with the different molecular weights of the colliders. The sensitivity to the nature of the colliding molecule raises interesting questions about the effect of collisions with other molecules. Would CO2 broadened coefficients be more like the air-broadened or self-broadened case? The answer to this question has some impact on the climates of Early Mars and Early Earth, which are often assumed to have had substantial amounts of CO2 in their atmospheres. Unfortunately, laboratory measurements bearing on the subject are hard to come by.

Next we turn our attention to aspects of the absorption which govern the runaway greenhouse effect for a planet with a water-saturated atmosphere. Specifically, we revisit the question of the Kombayashi-Ingersoll limit, which is the limiting OLR such a planet can have in the limit of large surface temperature. As discussed for the grey gas case in Section 4.3.3, the limiting OLR is approximately determined by the temperature at the pressure level where the optical thickness between that level and the top of the atmosphere becomes unity. For a grey gas this characteristic pressure was independent of wavenumber, whereas for a real gas it is quite strongly wavenum-ber dependent. To keep things simple, we'll consider a saturated pure water vapor atmosphere. In this case, if the temperature at a given altitude is T, the corresponding pressure is psai(T), determined by Clausius-Clapeyron. The equivalent path from this altitude to zero pressure is asei/1 Psai(T)2/(pogcos 0), where po is the standard reference pressure (100mb for use with Figure 4.19) and aself is the ratio of self-broadened to air-broadened absorption (about 6). By using this path together with the absorption coefficients in Figure 4.19, we can estimate the maximum effective radiating temperature as a function of wavenumber. Based on the median absorption in each band, the radiating temperature varies from about 245K at 100cm-1 to 278K at 500cm-1 to 350K at the valley of the window region near 1000cm-1. The high values of radiating temperature in the window region lead to large estimates of the Kombayashi-Ingersoll limit. As a crude estimate, if we assume that the planet radiates at 350K in the window regions between 544 and 1314 cm-1, and on the high wavenumber side of 1950cm-1, then the OLR would be about 520W/m2 even if the planet didn't radiate at all in the rest of the spectrum. The Kombayashi-Ingersoll limit is strongly affected by the absorption in the window regions, and we will see in Section 4.4.8 that the absorption here is dominated by a continuum which is not captured by the nearby line contribution. The estimate of the Kombayashi-Ingersoll limit for H2O (and CO2) will be completed in Section 4.6, after we have discussed the continuum.

Methane

Figure 4.21 shows the standard-state absorption spectrum for methane. From the standpoint of OLR on Modern and Early Earth, and perhaps on Early Mars, the most important absorption feature is that near 1300 cm-1, which occurs in a part of the spectrum where water vapor and CO2 absorption are weak, but where the Planck function still has significant amplitude at Earthlike temperatures. In contrast with water vapor, the very long wave absorption (below 1000 cm-1) is so weak that it does not significantly affect OLR in any atmosphere likely to have existed on an Earthlike or Marslike planet. Titan has extremely large amounts of methane in its atmosphere, which could in principle make the very longwave group important. Even there, however, the weakening of the absorption due to the very cold temperatures makes this absorption group fairly insignificant. For atmospheres containing appreciable amounts of oxygen, methane oxidizes rather quickly to CO2, so it is hard to build up very large concentrations. The Earth's pre-industrial climate had about lppmv of methane in it, and the intensive agriculture of the past century may eventually come close to doubling this concentration. The associated equivalent paths are quite small - on the order of .06kg/m2. For paths this small, Earth's atmosphere has an optical thickness of only .14 based on the median absorption coefficient occurring the 1300cm-1 peak. For methane paths typical of oxygenated atmospheres, one gets significant absorption only from the upper quartile of absorption coefficients, and a short distance from the dominant peak one only gets significant absorption very near the line centers. In this case, the ditch in OLR dug by methane is a very narrow feature centered on 1300cm-1. In an anoxic atmosphere, as Earth's is likely to have been earlier than about 2.7 billion years ago, the rate of methane destruction is much lower, and it is believed that production of methane by methanogenic (methane-producing) bacteria could have driven methane concentrations to quite large values. With 100ppmv of methane in an Earthlike atmosphere, the equivalent path is about .6kg/m2, and based on the median absorption coefficient the atmosphere becomes optically thick from about 1200 — 1400cm-1. If the methane concentration builds up to 1% of the atmosphere, then the equivalent path is nearly 600%/m2, and the atmosphere becomes optically thick from 1150 — 1750cm-1; for such high concentrations, the shoulder to the right of the absorption peak starts to become important. There are also some speculations that abiotic processes could have led to high Methane concentrations on Early Mars, or on the prebiotic Earth.

Beyond what is shown in Figure 4.21, Methane has strong absorption bands that extend well into the Solar near-IR. These are not terribly important at concentrations up to a few hundred ppmv in a 16ar atmosphere, but when Methane makes up a percent or so of the atmosphere, it can absorb most of the incident solar energy between 2500 and 9000 cm-1. At higher concentrations, significant absorption can extend even into the visible range.

It is often said that, molecule for molecule, CH4 is a better greenhouse gas than CO2. However, this is more a reflection of the relative abundances of CH4 and CO2 in the present Earth atmosphere than it is a statement about any intrinsic property of the gases; in fact, the absorption coefficients for the two gases are quite similar in magnitude, and CH4 absorbs in a part of the spectrum that is less well placed to intercept outgoing terrestrial radiation than is the case for CO2. The high effectiveness of CH4 relative to CO2 in the present atmosphere of Earth stems from the fact that currently there is rather a lot of CO2 in the air (380ppmv and rising) but rather little CH4 (1.7ppmv and also rising). In a situation like this, one has already depleted infrared of those frequencies that are most strongly absorbed by CO2, so when adding CO2 one is adding "new absorption" in spectral regions where the absorption is relatively weak. Hence, it takes a large amount of the gas to have much radiative effect. In contrast, when starting with a small amount of CH4, when one adds more, one adds "new absorption" where the absorption

Figure 4.21: As in Figure 4.17, but for CH4.

Figure 4.22: Left panel: Temperature dependence coefficient for air-broadened CH4 at 100mb, as defined in Fig. 4.18. Right panel: Ratio of self-broadened to air-broadened median absorption for CH4 at 100mb and 260K. As usual, medians are computed in bands of width 50cm-1.

coefficient is quite strong, since the strongly absorbing part of the spectrum is not yet depleted. This behavior depends crucially on the lack of significant overlap between the Methane and CO2 absorption regions.

The temperature scaling coefficient for CH4 is shown in Figure 4.22. It is in the same general range as for the cases discussed previously. The ratio of self to air broadening for CH4 is similar to that for CO2, throughout the spectral range of most importance for OLR. In the solar near-IR the self-broadened absorption can be nearly twice the air-broadened absorption. For Methane, the self-broadening is mostly of academic interest, since the methane concentration is too low for self-collisions to be significant in atmospheres encountered or envisioned so far. Titan and similar cryogenic atmospheres are potentially an exception to this remark, but there the absorption is dominated by a continuum that is not clearly related to the absorption lines under consideration here.

Because Titan has a surface temperature on the order of 100K, the peak of the Planck function occurs at about the third of the wavenumber where the peak is for Earthlike temperatures. In consequence, there is little thermal emission in the vicinity of the dominant 1300cm-1 absorption group. It is only the longwave absorption group that is potentially of interest. The lower atmosphere of Titan contains up to 20% CH4, which with Titan's low surface gravity yields an actual (not equivalent) mass path of nearly 15000kg/m2. However, due to the strong reduction of line strength with temperature, the median absorption is well under 10-6m2/kg in the longwave group, even when broadened by a pressure of 1.5bar. The radiative effect of Methane on Titan arises mainly from a collisional continuum of the sort described in Section 4.4.8.

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