A v2U2 rcHc GMmk Trc124

We usually also define a characteristic escape time given by Te = Hc/ve (s).

clearly this must be appreciably less than the age of the Solar System (~1017 s) for the loss of a given species from any particular planet to be important for the climate; on earth, oxygen is safe, by this criterion at least, while hydrogen and helium are long gone (Table 12.2). on Jupiter, the combination of low temperature and high gravity means that this condition is not met, even for hydrogen (Table 12.3). Jeans' formula successfully explains why the larger bodies have denser atmospheres, and why the terrestrial planets are depleted in the lightest gases, despite production rates that can be high.

Table 12.2 Exospheric escape time, Te (s), for reduction of exospheric density by Jeans escape for the Earth's atmosphere, assuming the exobase is at 500 km altitude, at temperature 1480 K and the gravitational acceleration is 8.43 ms -2. Also given are the scale height, H (km), the most probable speed, U, and the mean expansion velocity, ve, (km s-1).

Table 12.2 Exospheric escape time, Te (s), for reduction of exospheric density by Jeans escape for the Earth's atmosphere, assuming the exobase is at 500 km altitude, at temperature 1480 K and the gravitational acceleration is 8.43 ms -2. Also given are the scale height, H (km), the most probable speed, U, and the mean expansion velocity, ve, (km s-1).

parameter

H

h2

He

o

H

1460

730

365

91

U

4.96

3.51

2.48

1.24

Ve

7.32 x 10-2

8.71 x 10-4

9.94x 10-8

7.14 x 10-32

Te

2.0 x 104

8.38 x 105

3.67 x 109

1.28 x 1033

Table 12.3 Thermal escape times , Te (s), according to Jeans theory for various gases on four planets and the Moon. T(K) is the temperature and g is the gravity (m s-2) at the critical level, rc (km).

parameter

Moon

Mercury

Mars

Venus

Jupiter

T

300

600

365

700

155

rc

1738

2439

3590

6255

69500

g

1.62

3.76

3.32

8.27

26.2

Te(H)

3.55x 103

3.32x 103

1.39x 104

5.71 x105

5.14x 10617

Te(He)

2.03x104

1.40 x105

2.66x 108

2.85x 1016

1.18x 102455

Te(o)

2.25x 109

7.37x 1013

1.04x 1028

7.87x 1061

1.03x 109820

Te(Ar)

3.29x 1020

2.57x 1032

1.97x 1068

6.20x 10153

6.61 x1024522

Te(Kr)

3.53x 1041

9.09x 1066

4.45x 10142

4.67x 10322

3.72x10s1445

However, it is also the case that the Moon should have retained a significant atmosphere of the heavier gases if Jeans' formula is correct and if thermal escape is the only mechanism that applies. By the same argument, there should be much stronger fractionation of the noble gases than is actually observed. clearly, processes other than Jeans escape are at work. In particular, it is now realized that a sufficiently rapid flow of a light molecule like hydrogen could carry off heavier gases as a result of collisional interactions, i.e. aerodynamic drag. The theory of this process, sometimes called 'blowoff', suggest a linear dependence on mass, making it potentially much more efficient than the exponential rate in the Jeans equation, provided of course that the carrier flow is sufficiently strong. This would not be the case in Earth's present atmosphere, but fits very well with some theoretical expectations for the T-Tauri phase of the Sun, when the output of solar ultraviolet radiation is thought to have been 100 times the present level. This would provide a copious supply of hydrogen, by the dissociation of water, and a high level of heating in the upper atmosphere, producing a large flux of hydrogen to space on Venus and Mars, as well as Earth. The fact that the life-free planets have no residual oxygen suggests that the flow of hydrogen may have been sufficient to remove the oxygen from the water, as well, or it may have reacted with minerals in the surface.

In addition to the escape processes that are possible for neutral molecules and atoms that have a Maxwellian distribution of velocities, a number of non-thermal escape mechanisms are also known to operate. Shortwave (A <100 nm) solar radiation dissociates and ionizes the constituents of the tenuous upper layers of the atmosphere, and imparts to the fragments a non-Maxwellian or 'suprathermal' distribution of velocities. In addition to any enhanced thermal escape that then occurs, the fact that the particles are charged renders them subject to electromagnetic forces due to the solar wind and the magnetic fields surrounding the planet. Near the Earth's poles, for instance, where the magnetic field lines extend into space rather than reconnecting with the planet, a substantial outflow of charged particles, mainly protons, occurs (the 'polar wind'). These charged particles, and those in the solar wind itself, can also sweep neutral particles away.

A purely mechanical loss process that is thought to have been particularly important on Mars, and must also have occurred on Earth to some extent in the early life of the Solar System, is impact erosion. This is the atmospheric loss that occurs when a planet is bombarded with one or more large meteorites, particularly when the blow is oblique, directing the energy of the blast through the atmosphere and out into space. Clearly the actual mass of gas removed depends on the size and frequency of the colliding objects as well as the geometry of the collision and the mass of the planet, with more material being removed from a smaller planet, because of its smaller gravitational field. Thus impact erosion is relatively inefficient on Earth and Venus, while the impact of a sufficiently large and fast object (more than 3 km across and travelling at least 14 km/s) will create a plume on Mars that expands faster than the escape velocity and that could sweep away much of the atmosphere at a stroke.

12.2 The evolution of the Earth's climate

The age of the Earth from geological records is estimated at about 4.5 billion years (Byr) old. The Precambrian Era (4.5-0.54 Byr) is the longest geological record and comprises the early Precambrian, or Archean Eon (4.5-2.5 Byr), and the Proterozoic Eon (2.5-0.54 Byr). The Archean was a time extending back to the consolidation of the planet and covers the early chemical and mineralogical evolution of the Earth's crust and atmosphere. The initial atmosphere, a remnant of the Earth's formation (duration about 100 million years) by accretion from the Solar Nebula that rotated around the early sun was probably lost due to such processes as bombardment by other bodies, a stronger solar wind than today's, and diffusion to space.

12.2.1 The Precambrian atmosphere

The Earth's early atmosphere is thought to have outgassed from the Earth's interior and would have been reducing, composed of CH4, H2, with minor amounts of H2O, CO, N2, H2, NH3, Ar and He. Most of the H2O condensed to form oceans that became a sink for soluble gases. This reducing atmosphere was thought to play an important role in the formation of amino acids, and hence to the origin of life on Earth, under the action of enhanced (see Chapter 5) solar ultraviolet radiation. The lifetime of such a reducing atmosphere is thought to be only about one million years as H2 would have readily escaped to space. As the atmosphere was depleted of H2, methane would have been oxidized to CO2 by reactions with the products of H2O photolysis (see Chapter 7), and NH3 converted to N2 by photolysis. Outgassing contributions of CO2 and N2 from volcanic and tectonic activity would have resulted in an atmosphere that basically consisted of CO2 and N2, with H2O a trace gas in the atmosphere through condensation. This atmosphere lacked O2 (only present as a trace gas), i.e. it was anoxic. The widespread occurrence of redbeds (oxidized subaerial deposists) at 1.8 Byr suggests significant oxygen production at that time, whilst observations from banded iron formations (BIFs) and paleosols indicate that atmospheric oxygen levels were low before 2 Byr, consistent with the small values of buried organic carbon. It is worth noting that today both Mars and Venus have CO2-N2 atmospheres, while Saturn's satellite Titan has an N2-CH4 atmosphere.

12.2.2 The faint-young-Sun paradox

Conventional theories of stellar evolution (see Chapter 5), imply that the Sun has brightened by about 30% since it first joined the main sequence some 4.6 Byr ago. If the Earth had the same atmosphere as today and similar continental-oceanic distribution, such a weak young Sun would have produced extensive and persistent glaciations throughout most of the Precambrian. Geological evidence suggests, on the contrary, that Precambrian glaciations were rare and confined to two periods, one in the early Proterozoic between 2.5 and 2 Byr and the other in the late Proterozoic between 1 and 0.54 Byr. Rather than a totally frozen Earth, the geological record indicates the presence of substantial expanses of liquid water on the Earth's surface as early as 3.8 Byr. For much of the Proterozoic, the Earth's surface may have been warmer rather than cooler, than its present mean value of 288 K. Although there are uncertainties in all palaeo-temperature estimates, chert and phosphate measurements suggested that, during the Archean, surface temperatures, at least at some locations, could have been as high as 350 K.

One way of resolving the faint-young-Sun paradox is to assume a compensating change in the Earth's atmosphere such as would be produced by a stronger CO2 greenhouse effect than today. This stronger greenhouse would gradually diminish owing to the weathering of silicate rocks on the land and the deposition of carbonates as ocean sediments. On timescales of millions of years, the CO2 cycle is completed by outgassing to the atmosphere as tectonic processes transport and transform the sediments at subduction zones (areas on Earth where two tectonic plates collide, the denser sliding underneath into the mantle). The compensation of the enhanced Precambrian greenhouse needs to be controlled by a mechanism that varies the atmospheric CO2 as the Sun brightens, maintaining an approximate balance between the strength of the incoming solar radiation and the atmospheric CO2-H2O greenhouse.

12.2.3 Greenhouse-weathering evolution model

Walker et al. (1981) suggested that the required negative feedback controlling the Earth's surface temperature as the Sun brightened could have been provided by a temperature-dependent CO2 weathering rate. Carver and Vardavas (1994) developed an evolutionary CO2 weathering model incorporating the weathering rate mechanism and have shown that it can account, at least semiquantitatively, for one of the main features of Precambrian climate. This was the rarity in the geological record of extensive and persistent Precambrian glaciations, and their restriction to two time periods, one in the Early Proterozoic and the other in the late Proterozoic. According to their model, the Early Proterozoic glaciations were caused by increased surface-area weathering due to a major episode of continental land building that began about 3 Byr. The Late Proterozoic glaciations resulted from biologically enhanced weathering due to the proliferation of life forms that marked the transition from the Proterozoic to the Phanerozoic Eon (0.54 Byr-present).

12.2.3.1 Weathering of CO2 The brightening of the Sun with time can be represented by (Gough 1981)

where y is the time in Byr since the Earth formed (today corresponds to y = 4.6) and S(y) is the solar flux in units of the present flux S(4.6) = 1. For an atmosphere with CO2 content A(y), the surface temperature T(y) calculated using a one-dimensional radiative-convective climate model (with moist lapse rate, water-vapour feedback and global mean relative humidity set at 0.77, see Chapter 11) can be approximated by the simplified greenhouse equation

T(y) = 288 + [0.6/v2][Av(y) - 1] - 508[1 - r0'25S0'25(y)], (12.6)

flg. 12.2. Outgassing rate G for the fast and slow models with time in billion years before the present. Also shown is the incoming solar flux relative to today's value. (Carver and Vardavas 1994)

where A(y) is measured in units of the present atmospheric CO2 level (PAL), so that A(4.6) = 1, r = (1 - a(y))/(1 - 0.32), and v = 0.3 to fit the results of the radiative-convective model, and a(y) is the planetary albedo. The ice-albedo feedback is approximated by assuming a planetary albedo equal to 0.32 for T > 288 K, rising to 0.46 at T = 260 K, and to 0.6 for T < 232 K. This simplified model gives a global mean surface temperature rise of 1.5 K for a doubling of the present CO2 level, whilst a 2% increase in the incoming solar radiation increases the global mean surface temperature by 2.5 K. The weathering rate and the organic-carbon burial rate determine the sequestering of atmospheric CO2 by the land surface. The rate at which CO2 is removed from the atmosphere increases with surface temperature owing to the increased rate of snowmelt runoff and the increased reaction of water in equilibrium with atmospheric CO2 as it percolates through the soil and porous rocks. The weathering rate depends on some power (0 < n < 1) of the CO2 atmospheric pressure A(y), and upon the rate of dissolution of rocks by running water and on the runoff rate, both of which depend on the temperature T(y) itself. The weathering rate also depends upon the land area L(y), measured in units of the present land area L(4.6) = 1, and upon the weatherability W(y) of the exposed land surface. Changes in weatherability occur as processes of biological evolution and physical erosion provide soil and vegetative cover to replace the original bare rock. Moist soil in continuous contact with rock will weather atmospheric CO2 at a much faster rate than will bare rock alone. The presence of organisms in the soil assists in the

retention of soil moisture while vegetation cover stabilizes soil formation against erosion. The proliferation of life forms thus leads to accelerated soil weathering.

The burial and decay of organic products enhances the weathering process through the release of CO2 in the soil, while organic carbon burial is a sink for atmospheric CO2 via photosynthesis. Episodes of continental rifting and orogeny also result in enhanced rates of weathering but also in soil erosion. Erosion can deliver nutrients for biological production but commonly exposes organic carbon resulting in its oxidation so that part of the organic carbon returns to the atmosphere.

We assume that these complex physical and biological processes can be characterized by a function W(y) that measures the relative effectiveness in sequestering CO2 from the atmosphere of ancient land surfaces with that of the present land surface. Thus, at present W(4.6) = 1 and throughout the Precambrian W(y) < 1. At equilibrium, the weathering rate R(y) at which CO2 is removed from the atmosphere must equal the rate G(y) at which it is returned to the atmosphere by outgassing, so that

R(y) = An(y)L(y)W(y) exp[(T(y) - 288)/TJ = G(y), (12.7)

where we take n = 0.4 and Tc = 15, based on estimates of these values. The coupled eqns (12.5, 12.6 and 12.7), involving the evolution of the solar flux, evolution of CO2 outgassing-weathering and simplified greenhouse equation, define the feedback processes and determine the evolution of global mean surface temperature and atmospheric CO2.

12.2.3.2 Outgassing model We consider both slow and fast outgassing models for the rate G(y). In the slow model, G(y) is assumed to follow the approximately exponential decline in the Earth's interior heat from radioactive decay. In the fast model it is assumed that after a period of rapid emission in the Early Archean, the rate G(y) approached its present value at about 3.5 Byr and remained essentially constant thereafter. The higher outgassing during the Archean is assumed to have resulted from a greater juvenile emission that was more than sufficient to compensate for a smaller secondary emission due to reduced metamorphism. The two models for the outgassing rate along with the variation in the incoming solar flux are shown in Fig. 12.2.

12.2.3.3 Land-formation model The representations of the development of the land surface area are based on isotopic and geochemical analyzes that support formation as opposed to no-growth models that suggest that the crust was formed early in the Earth's history (prior to 4 Byr). The growth models propose extensive episodic land-surface growth in the Early Proterozoic with only minor additions since that time. These conclusions are based in part on the analysis of zircon populations in the Late Archean (3.0-2.4 Byr) sediments. Geological evidence indicates rapid continental growth starting at about 3 Byr with only

flg. 12.3. Rapid-land formation models with Fc representing the time of maximum continental land formation, as a function of time in billion years before the present. The preferred model for surface-temperature computations was taken to correspond to Fc = 2.8. (Carver and Vardavas 1994)

small areas of continental crust before that time and minor later additions. In Fig. 12.3 are shown rapid land formation models with Fc representing the time of maximum continental land formation.

12.2.3.4 Weatherability model The assumed variation of the weatherability due to biological evolutionary factors W(y) is based on the work of Schartzman and Volk (1991) who suggested that W(y) was of the order of 0.001-0.01 for the abiotic Earth, rising to about 0.2 with the microbial colonization of the Archean Earth that marked the transition from abiotic to biotic land surfaces some 3.9 Byr. The value of W is assumed to have remained fairly constant throughout the Early Proterozoic rising during the late Proterozoic to approach unity at the end of the Phanerozoic. The Late Proterozoic (1.0-0.54 Byr) was a geologically and biologically important period of change. Geological evidence suggests that during the early part of this period there was increased tectonic activity with episodes of global rifting and orogeny, conditions favourable to subsequent weathering, erosion, and through runoff to sedimentation. These processes result in increased nutrient release that can promote enhanced biological activity and organic-carbon burial both on land and in the oceans. During most of the Riphean Epoch (0.9-0.6 Byr) 13C/12C enrichment in sedimentary carbonates indicates high rates of organic carbon burial (reduced availability of 12 C for the formation of sedimentary rocks) suggesting enhanced marine biological activity.

TIME GYR BP

flG. 12.4. Weatherability W(y) models, where W is the weatherability arising from biological evolution through geological time in billion years before the present. (Carver and Vardavas 1994)

TIME GYR BP

flG. 12.4. Weatherability W(y) models, where W is the weatherability arising from biological evolution through geological time in billion years before the present. (Carver and Vardavas 1994)

We note that plants preferentially take up 12C during photosynthesis. It is not unreasonable to assume that if the nutrient release from the land led to increased biological activity in the oceans there was also enhanced biological activity on the land itself. It may be noted that specific glacial episodes (e.g. Varangian about 0.6 Byr, Sturtian about 0.78 Byr) during this period are correlated with dips in the 13 C enrichment and hence with a reduced rate of organic-carbon burial. This can be explained by a scenario in which the biologically enhanced weathering was the precursor to a reduction in atmospheric CO2 that led to a weaker greenhouse that triggered the specific glacial episodes. During the glacial episodes, runoff would have been reduced resulting in a drop in organic-carbon burial and hence in 13C enrichment.

We interpret the overall enhanced carbon burial rate during the Late Proterozoic as indicating increased biological activity leading to more effective soil weathering of CO2. The changes that begun about 1 Byr involved the gradual extinction of the Proterozoic biosphere and its replacement by evolving multicellular organisms in the approach to the Phanerozoic. Accordingly, we allow W to increase from about 1 Byr to approach W = 1 at the end of the Phanerozoic with steps of 0.4 Byr, corresponding to the development of higher land plants and a final increase to present values following the evolution of flowering plants, the angiosperms, about 0.1 Byr. In Fig. 12.4 we show various models for the weatherability variation with time. The preferred model is that with W(2) = 0.25, where W(2) corresponds to Proterozoic weatherability.

1000

1000

flg. 12.5. Evolution of surface temperature and atmospheric CO2 amount (PAL = present atmospheric level) with time in billion years before the present. (Carver and Vardavas 1994)

12.2.4 Surface temperature and CO2 evolution

The evolution of atmospheric CO2 and the consequent climate change have been calculated for the preferred model parameters. We have chosen the fast out-gassing rate. The maximum in the rate of continental land formation was set at 2.8 Byr and the weatherability was taken to correspond to the curve with a value of 0.25 during the Proterozoic. The calculated evolution of the atmospheric CO2 level and the evolution of the global mean surface temperature are shown in Fig. 12.5. After initially hot conditions, the surface temperature falls as the land area increases and the model suggests that glaciations become possible for the first time only during the period 2.5-2.0 Byr. We note that the model gives a CO2 level of about 100 PAL at about 2.5 Byr. After about 1 Byr there is a rapid drop in atmospheric CO2 that results in a second surface-temperature minimum near 0.75 Byr, suggesting that the glaciations found between 1-0.54 Byr were caused by the fall in the atmospheric CO2 content produced by the increased weatherability of the land surface. There is a strong correlation between the minima of the model temperature curve and the main periods of Precambrian glaciations indicating that the model can account for the broad features of the Precambrian climate if we associate the early Proterozoic glaciations with a major episode of continental land building and the late Proterozoic glaciations with the enhanced weatherability of the land surface due to the proliferation of new life forms that marked the transition from the Proterozoic to the Phanerozoic Eon.

12.3 Comparative climatology of the terrestrial planets

12.3.1 Mercury

The surface temperature on Mercury is dominated by the interaction of the solar flux directly with the surface, with the thin atmosphere playing a negligible role. The axis of rotation has a very small obliquity, which normally would mean the absence of seasons; however, the climate retains an interesting degree of complexity due to the large eccentricity of the orbit, and the unusual synchronization of the rotation of the planet with its orbit, such that two days last three years (Table 12.4). If we simplify the real situation and assume that the surface of

Table 12.4 Physical data for Mercury, compared to the same quantities for the Earth.

Mercury

Earth

Orbital and rotational data

Mean distance from Sun (108 km)

0.579

1.496

Eccentricity

0.2056

0.0167

Obliquity (deg)

0

23.45

Siderial period (days)

87.97

365.26

Rotational period (hs)

1407.5

23.93

Solar day (days)

115.88

1

Solar constant (kW m~2 )

6.3 to 14.5

1.366

Solid body data

Mass (1024 kg)

0.3302

5.976

Radius (km)

2439

6373

Surface gravity (m s~2)

3.63

9.82

Atmospheric data

Principal composition

He, Na

N2, O2

Mean surface temperature (K)

~ 400

288

Mean surface pressure (atm)

< 10~12

1

Mass (kg)

~ 1300

5.1xl018

Mercury is a smooth sphere, and has the same albedo (reflectivity integrated over wavelength) everywhere, then a straightforward energy-balance calculation gives the results shown in Fig. 12.6 for the variation of temperature with time at different locations around the equator. The odd shape of the curves is a result of the eccentric orbit and the coupling between the orbit and spin of the planet. At higher latitudes, similar curves apply but with a smaller range of temperatures. The maximum does not fall below 100 °C until about 5° from the pole, however, while the nighttime minimum is well below the freezing point of CO2 everywhere. In reality, variations in composition and topography introduce additional variations in the temperature distribution, one intriguing consequence of which is that Mercury apparently has thick deposits of ice in craters near the poles that are permanently shaded from the Sun.

Another interesting feature of Mercury that relates to its origin and evolution, and therefore also to those of the Earth, is its high mean density. The planet must consist predominantly of metals, probably mostly iron since this has the

0 20 40 60 80 100 120 140 160 180 Time (Earth days)

flg. 12.6. Surface temperatures at the equator on Mercury, calculated from a radiative energy balance model with a simple 'billiard ball' planet with no topography and uniform albedo and emissivity. Results for three different longitudes (degrees West relative to local noon at perihelion) are shown. (Source: ESA)

highest cosmic abundance. This massive core may still be partially liquid, like the Earth's, despite calculations indicating that Mercury is small enough to have cooled throughout by now, since it exhibits a magnetic field that is too strong to exist without an active dynamo. This suggests that there must be an active heat source in the core, presumably a relatively high concentration of radioactive elements. Inferences like these provide valuable information about the distribution of elements in the circumsolar accretion disk when the planetary system formed.

Mercury, in terms of its geology and place in the inner Solar System is undoubtedly a terrestrial planet, but its atmosphere is so thin it more resembles the terrestrial exosphere, a tenuous region that has only a long-term relationship to the climate at the Earth's surface, mainly through atmospheric escape processes. There are also interesting questions concerning the volatile inventory on Mercury, since polar deposits, apparently of water ice at least several tens of metres thick, were discovered by Earth-based observers using radar mapping at large radio telescopes. There exists no obvious source for water in these amounts, and the investigation of the problem is likely to yield answers that will lead to a better understanding of the origin of water on all the planets.

12.3.2 Venus

On Venus, an extreme case of the greenhouse effect raises the surface temperature to around 730 K, which is higher than the melting points of lead, zinc and tin, in spite of the fact that the net solar input is significantly less than for the Earth. Apparently, the very high albedo of Venus (76% compared to around 30% for

Cloud mass density (mgrr3) .00001 .0001 .001 .01 0.1 1 10 100

Cloud mass density (mgrr3) .00001 .0001 .001 .01 0.1 1 10 100

Temperature (K)

flG. 12.7. Atmospheric temperature and cloud density profiles on Venus, as measured by the Pioneer Venus probes in December 1979. The main cloud layers on Venus have a high reflectivity in the near-infra-red and visible parts of the spectrum, and a high absorptivity in the thermal infrared. The atmosphere is 100 times more massive than Earth's and is 95% carbon dioxide. For the amount of energy escaping as thermal radiation from below the clouds to match that absorbed from the Sun, the temperature at the surface has to become very high.

Temperature (K)

flG. 12.7. Atmospheric temperature and cloud density profiles on Venus, as measured by the Pioneer Venus probes in December 1979. The main cloud layers on Venus have a high reflectivity in the near-infra-red and visible parts of the spectrum, and a high absorptivity in the thermal infrared. The atmosphere is 100 times more massive than Earth's and is 95% carbon dioxide. For the amount of energy escaping as thermal radiation from below the clouds to match that absorbed from the Sun, the temperature at the surface has to become very high.

the Earth) more than offsets its greater proximity to the Sun (Table 12.1 and Fig. 12.7). The sulphuric acid of which the Venusian clouds are composed forms droplets that scatter very conservatively, diffusing a fraction of the incoming sunlight down to the surface. At the same time, they are opaque in the infrared, so clouds made of concentrated sulphuric acid droplets have a higher optical depth in the thermal infra-red than they do in the near infra-red and visible part of the spectrum. The cloud blanket therefore makes a contribution to the backwarming effect, which outweighs the albedo effect overall when combined with the contribution of around a million times as much CO2 as the Earth, plus substantial traces of water vapour and other greenhouse gases.

The solar constant at Venus is about twice that at the Earth, at 2626 W m~2. Assuming an albedo of A = 0.76 and dividing by the ratio of the area of the spherical planet to its cross-sectional area, the mean solar power absorbed by the atmosphere is therefore 157 W m~2. Equating this to the outgoing blackbody flux aT^, where a is the Stefan-Boltzmann constant, gives TE = 230 K for the effective radiating temperature of the planet. This is much lower than the surface temperature of Venus, which is 730 K, and is in fact approximately the temperature at the cloud tops (Fig. 12.8). This is to be expected since the clouds

0 2000 4000 6000 8000 10000

Wavenumber (cm-1)

flG. 12.8. The atmospheric transmission of a vertical column on Venus, above the 50 mb level (fine line) and above the surface (bold line). The top frame is for CO2 only; the middle frame for H2O only, and the bottom frame is for all gases, including CO, OCS, HCl, and HF, as well as CO2 and H2O. The cloud opacity is not included in any of these calculations. (After Crisp and Titov 1997)

are optically thick in the thermal infra-red, and their effective upper boundary is at the relatively low pressure of about 50 mb, i.e. above about 99.95% of the total mass of the atmosphere.

While the cloud opacity dominates the net optical depth of the atmosphere above about 50 km, and scattering by cloud particles is the main factor producing the high albedo of Venus, in the lower atmosphere the gaseous constituents, especially carbon dioxide and water vapour, take over. Figure 12.8 shows the atmospheric transmission for a vertical path from the surface to space, and from the 50 mb level to space, computed separately for two of the principal greenhouse gases, and then for all of the infra-red active gases known to have significant abundances. Even before the contribution of absorption in the cloud and haze layers is considered, it can be seen that Venus' atmosphere is opaque at every wavelength except for some narrow transparency windows in the near-infra-red. As with the Earth, this sort of calculation can be incorporated into a full radiative transfer model, which allows the energy balance at every level in the atmosphere to be computed. An added difficulty for Venus is that the cloud properties are not known in the deep atmosphere (and indeed they seem to be very variable) which makes it difficult, in particular, to calculate the penetration of sunlight through the clouds, and the energy deposited at each level, including the surface. Some current models avoid this problem by constraining their codes to give the intensity at solar wavelengths that has been measured near the surface by Soviet and American probes. Another problem is the fact that even quite well-studied gases like CO2 and H2O have spectral properties that are poorly determined

0 2000 4000 6000 8000 10000

Wavenumber (cm-1)

at the very high temperatures and pressures that prevail on Venus. Finally, the abundances and variability of all of the greenhouse gases except CO2 remain poorly known in the lower atmosphere.

Despite all of these difficulties, a number of studies have shown that models can be constructed that, with some reasonable assumptions, do account for the observed thermal structure of Venus' atmosphere by a combination of thermal balance at the surface, with space, and in the stratosphere, and convective equilibrium in the troposphere. The high surface temperature results from the very deep and thermally opaque atmosphere containing large quantities of efficient greenhouse absorbers, in particular CO2, H2O, and the H2SO4 clouds.

It still remains to explain why the Venusian atmosphere is so massive. It has been estimated that the amount of CO2 that once was in the Earth's atmosphere and is now locked in coral reefs and other carbonate rocks, after having first dissolved in the ocean, is of the same order as that which is still in the atmosphere on Venus. The implication is that the Earth, by being cool enough to condense liquid water on its surface, escaped having a much thicker CO2 atmosphere. Also, Venus may be much more volcanically active than Earth, and even today volcanoes may be pumping large amounts of carbonic and sulphurous gases into the atmosphere, continually reinforcing the greenhouse effect. This could, in time, subside.

As long ago as 1952, when it was known that the atmosphere was predominantly CO2, although not that it was so hot or so dense, Harold Urey suggested that the reaction of atmospheric carbon dioxide with common surface minerals might have a role in determining the surface pressure. On theoretical and abundance grounds, the most likely process to dominate is the equilibrium balance between calcium carbonate, silica and calcium silicate

and indeed we now know that the temperature and pressure on the surface of Venus at the present time fall on the equilibrium phase curve for this reaction. Not only that, but if we also plot the surface temperature as a function of surface pressure in the simple radiative-convective equilibrium model described in outline above, it can be seen that the two intersect at a point that is strikingly close to the surface conditions measured by the Venera landers (Fig. 12.9).

This agreement strongly suggests that the high-pressure, high-temperature state of the climate on Venus can be attributed to the balance for a pure CO2 atmosphere in equilibrium with the common minerals likely to be abundant on Venus. Although possibly no more than a coincidence, the existence of a straightforward account for the extreme state of Venus' climate, which is otherwise very difficult to explain, makes it hard to set it aside, at least without a further examination using more complex models and more data from new missions to the planet, both unavailable at present.

Surface Temperature (K)

flG. 12.9. Phase curves for the surface temperature and pressure on Venus, corresponding to radiative-convective equilibrium in the atmosphere (Taylor 2006), and to chemical equilibrium between CO2 in the atmosphere and in surface minerals. (Calculated using the data provided by Adamcik and Draper 1963)

Surface Temperature (K)

flG. 12.9. Phase curves for the surface temperature and pressure on Venus, corresponding to radiative-convective equilibrium in the atmosphere (Taylor 2006), and to chemical equilibrium between CO2 in the atmosphere and in surface minerals. (Calculated using the data provided by Adamcik and Draper 1963)

However, it has often been noted that the temperature dependence of the mineral equilibrium is such that the present climate would be unstable if it was produced in this way. The strong dependence of atmospheric CO2 amount on surface temperature represented by the phase curve shown in Fig. 12.9 means that any small perturbation in the surface temperature, either positive or negative, leads to positive feedback and dramatic changes in atmospheric CO2, resulting in runaway heating or cooling, respectively. Also, even if the regolith on Venus has the necessary supply of silicate minerals, it is not clear how they can be in sufficiently intimate contact with the atmosphere. Finally, the surface of Venus is not at a single uniform temperature; topography alone leads to temperature contrasts of more than 100 K, corresponding to differences in CO2 pressure for Urey equilibrium that would be far out of hydrostatic balance. Other surface-atmosphere reactions are undoubtedly involved, and may be important. Some aspect of these and other complexities not yet understood may act to stabilise the climate, at least against moderate perturbations, somewhat as the complexity of Earth's climate achieves an overall quasistable regime despite the disequilibrium state of most of its components. The strong suggestion that heterogeneous reactions, involving the atmosphere and the regolith, control the climate gives a high priority to plans for long-lived missions to the surface of Venus, possibly including mobility on the surface and the return of samples to the Earth. The climate itself makes that extremely difficult, of course, and it is not clear how many years or decades must pass before the space agencies will be up to the challenge. It may be premature to think too deeply about global change on Venus while there is much still to be understood about the present climate, but recent data do suggest that major change has occurred. The ratio of heavy to normal hydrogen

Earihlike Venus P0 = 1 bar T0 = 375 K

Albedo = 0.3 P0=63bar T0=715K

Earihlike Venus P0 = 1 bar T0 = 375 K

Albedo = 0.3 P0=63bar T0=715K

Surface

Temperature, K

flG. 12.10. Simple climate models for Venus, corresponding to; a) the present day, b) a decrease in albedo to 0.3, and c) atmospheric loss of CO2 such that the surface pressure falls to 1 bar. A measured profile, obtained by the radio-occultation experiment on the Magellan orbiter on 5 October 1991 at latitude 67N, is shown for comparison. (Taylor 2006)

isotopes on Venus is more than 100 times greater than that on Earth, a fact that is generally interpreted in terms of the loss of a global ocean from Venus over the first few billion years of its existence. In this paradigm, water vapour near the top of the atmosphere is dissociated by solar ultraviolet radiation and the hydrogen is lost to space, with the lighter isotope lost at a higher rate due to gravitational fractionation of the water vapour, enriching the residue we now observe. Some have speculated that the long, deep, sinuous channels cut into the surface of Venus by some unknown agent and seen in radar images obtained by the Magellan spacecraft must have been produced by flowing water, suggesting that Venus was cooler in the not-too-distant past. Finally, the amount of sulphur dioxide detected spectroscopically in Venus' atmosphere has shown very large variations on the timescale of a decade, suggesting that the level of volcanic activity on Venus varies considerably. The effect of this on the global climate is not known, but model calculations suggest it could be considerable. Like the Earth, we would expect Venus to respond to changes in external forcing, such as any long-term variation in total solar irradiance. However, again like the Earth, the Sun in the recent epoch has been stable enough that this factor is probably negligible compared to others. For a change of 0.1% in solar output, similar to those measured currently by spacecraft orbiting the Earth, a Venus climate model predicts a change in mean surface temperature of only 0.05 K. The spread in surface temperatures expected due to topographical variations is around three orders of magnitude greater than this. Volcanism seems much more likely to be an important agent for climate change in the relatively short term, particularly since Venus appears to be much more volcanically active than Earth. This evidence includes the observed disequilibrium in the atmosphere of the sulphurous gases that play a large role in the production and maintenance of the cloud layer, and consequently the high planetary albedo. If, at some point in the future, vol-canism ceased on Venus and the cloud regime relaxed to one much more like the Earth, the albedo may fall from the present 0.76 to an Earth-like 0.3. Neglecting for the moment all other consequences, such as atmospheric composition changes (except those in CO2 due to adjustment to the Urey equilibrium at the surface), the model stratospheric temperature may increase to around 273 K, while the surface temperature and pressure fall to about 715 K and 63 bar, respectively (Fig. 12.10).

A further consequence of a complete cessation in volcanic activity is that the greenhouse effect would become less efficient through the removal from the atmosphere of some of the more chemically active minor constituents, such as SO2, H2S and COS, as they move closer to their equilibrium values with the surface. The loss of atmospheric water due to dissociation and exospheric escape of hydrogen may no longer be compensated by emission from the interior, as presumably it is at present. Any loss of atmospheric infra-red opacity, due to weaker absorption in the bands of these species, moves the tropopause downwards to a higher pressure level, resulting in falling surface temperatures and pressures as radiative-convective equilibrium is maintained. This large cooling perturbation leads to the steady take-up of atmospheric CO2 by the surface, although it remains to be shown that this is physically possible in the absence of liquid water to facilitate the exchange, particularly since the carbon dioxide content of the current atmosphere is sufficient to produce a layer of carbonate around 1 km thick if entirely converted to surface rock.

Venus without active volcanism might thus become more Earth-like. Venus has about the same amount of N2 in its present-day atmosphere as the Earth; the selective removal of CO2 could at some point leave a composition of 99% N2, 0.5% Ar, 0.5% H2O, and 0.035% CO2, with a surface pressure in the region of 1 bar. In this case, the mean surface temperature would be a relatively balmy 70 C. This is the Venus that was imagined by our forebears, by extrapolation from the Earth, before the importance of the greenhouse effect and the true state of Venus' climate had been realized.

12.3.3 Mars

The present-day atmosphere of Mars is ^10000 times thinner than that of Venus, with a mean surface pressure of about 6.5 mbar, and, like Venus, is composed also mainly of CO2. The atmosphere of Mars is also warmed by the interaction of both solar and thermal radiation with airborne particles, in this case windblown dust from the surface. This is present in variable quantities, depending on dust-storm activity and other meteorological factors, often in significant quantities at heights up to 50 km above the surface. The dust opacity is in fact the main contributor to the Martian greenhouse effect, exceeding even that of carbon dioxide under most conditions. The role of water vapour in the radiative energy balance of the Martian atmosphere is very small, since the amounts present at the the low prevailing temperatures on Mars are generally insignificant in terms of their contribution to the net opacity of the atmosphere. Under normal conditions, the greenhouse effect on Mars due to all constituents produces a much smaller enhancement of surface temperature than on Earth or Venus. Using A = 0.25 for the albedo of Mars, and 593 W m~2 for the mean solar flux reaching Mars' orbit, a global energy-balance calculation finds that the effective radiating temperature of the planet is T = 210 K. Compared to an observed mean surface temperature of 218 K, this indicates a small greenhouse effect of about 8 K. Under very dusty conditions, this can increase five- or even tenfold.

Of all the planets, including Earth, the clearest evidence for large-scale climate change in the past is found on present-day Mars. Today's frozen rocks and desert bear unmistakable features of rivers, lakes and seas. It is now generally accepted, on the basis of extensive orbital imaging of fluvial features (like the example in Fig. 12.11) and mineralogical evidence (most recently from the Mars Exploration Rovers, Spirit and Opportunity, operating as robot geologists on the surface), that Mars must have had a warm, wet climate in the past with liquid water on the surface. Precisely how warm, how wet, what produced these conditions and when they prevailed, all remain subjects of intense debate. The leading theory is that Mars may in the past have had a much thicker atmosphere, probably still consisting primarily of CO2, but, being warmer, holding much more water vapour, and possibly increased levels of other constituents including methane. Together with an enhanced cloud cover, these might have produced a greenhouse effect large enough to raise the temperature and pressure to values that could support liquid water on the surface.

The large change since then may have originated in the high eccentricity of Mars' orbit and the large fluctuations in sunfall that result from resonances between this and other orbital parameters. Alternatively, the heating could have been primarily due to volcanic activity, which has since subsided. In this case, water vapour, CO2 and other gases and particles from the interior of Mars could have warmed the planet by greenhouse action and produced lakes and rivers for as long as the volcanoes were sufficiently active. Yet another possibility is that Mars lost enough of its early atmosphere in a collision with a large asteroid to cause temperatures to fall below the freezing point of water. The resulting loss of water vapour and clouds from the remaining atmosphere would further reduce the surface temperature and eventually lead to the situation we find today, where the water that remained after the collision mostly lies frozen beneath the surface and in the polar caps. We still do not know whether the present Martian climate is stable or simply a stage in a gradual decline in surface pressure and temperature that has been going on since volcanic activity ceased.

flG. 12.11. Features are seen all over Mars that, like these river-valley networks, were formed by flowing water, which also apparently collected into large bodies or seas, whose coastlines can still be discerned. Their existence implies a warmer, wetter climate on Mars in the past, although the details of what this was like, and how and when Mars changed to its present cold, dry state, remain to be understood.

The development of global mean models for Mars is more capricious than for Venus because the temperature profile is very variable, with season, time of day, and location on the planet. It also depends strongly on the amount of airborne dust, which again is highly variable and dependent on the wind field, including unpredictable factors such as the onset of dust storms and the frequency of occurrence of dust 'devils'. The latter occur in desert regions of the Earth and are now known to be extremely common on Mars, to the extent that they have been belatedly recognized as a key factor in maintaining a high level of airborne dust even when the atmosphere is otherwise relatively quiescent.

The results of an attempt to represent the temperature profile on Mars using a simple radiative-convective model are shown in Fig. 12.12. A solar constant of 593 W m-2 and global mean albedo 0.25, give 210 K for the effective radiating temperature of Mars, a predicted stratospheric temperature of 177 K, and a surface temperature, calculated from a single-slab greenhouse model, of 250 K. Since the adiabatic lapse rate g/cp is 4.5 K km-1 on Mars, the tropopause should occur at approximately 16.2 km above the surface in the absence of dust.

flG. 12.11. Features are seen all over Mars that, like these river-valley networks, were formed by flowing water, which also apparently collected into large bodies or seas, whose coastlines can still be discerned. Their existence implies a warmer, wetter climate on Mars in the past, although the details of what this was like, and how and when Mars changed to its present cold, dry state, remain to be understood.

140 160 180 200 220 240 260 280 300 320 340 36C

iemperature (K)

flG. 12.12. Temperature profiles for the atmosphere of Mars, calculated assuming; a) an atmosphere without suspended dust; b) including the radiative effects of a model dust profile, and c) possible past conditions where the surface pressure was higher, and the temperature was warm enough for liquid water to be present. The shaded area encloses the range of measured temperature profiles obtained by Mariner 9 circa 1971.

This is not what is normally observed, however, since airborne dust is ubiquitous. Its effect, for a typical level of dust loading, is to reduce the lapse rate to about 1 K km-1, which raises the tropopause dramatically to 36.6 km. With this refinement, the model curve b) falls within the shaded area representing observed temperatures on Mars. Retaining the same model dust distribution, it is now straightforward to run models in which the surface pressure is increased, to simulate the conditions thought to have prevailed on early Mars. Curve c in Fig. 12.12 shows the result of assuming the same surface pressure on Mars as on present-day Earth, while retaining a composition of pure CO2 on the smaller planet.

The result suggests that global mean temperatures, well above the freezing point of liquid water, were possible if this amount of CO2 were present then. It might be argued that the possibility of rain would reduce the dust loading of the air and tend to restore the CO2 adiabatic lapse rate; in this case the model predicts even higher surface temperatures, and considerably less than 1 bar of surface pressure would be sufficient to permit the existence of liquid water.

Of course, simple model predictions have to be treated with caution since other factors, not represented in the model, can be important and, may radically alter the conclusions drawn. First, the Sun is thought to have been less bright by 25 to 30% during its early life, possibly including the period when Mars seems to have been warmer. Second, a thicker early atmosphere probably was much cloudier (with CO2 as well as water clouds) and hence Mars may have had a much higher albedo. Some modellers conclude that the greenhouse effect cannot have produced the warm, early Mars suggested by the geological evidence, unless the atmosphere contained gases other than carbon dioxide and water vapour in substantial quantities. One of the prime candidates to produce the missing opacity is methane, which was recently detected in the Martian atmosphere, although in tiny quantities much too small to affect the climate.

12.4 The giant planets

The outer regions of the atmospheres of the gas giant planets Jupiter, Saturn, Uranus, and Neptune, have almost Earth-like temperature and pressure regimes, where the vertical profile is controlled by radiative-convective equilibrium much as on the terrestrial planets (Fig. 12.13). The key processes are those that are familiar to us on our planet, for instance, the absorption and transmission of sunlight in gaseous absorbers and clouds, and the transfer of latent heat as condensates. Along with quite different atmospheric compositions (mainly hydrogen and helium, with substantial traces of ammonia, methane, and water) the important differences from the Earth-like inner planets is that they lack solid surfaces (except possibly in their deep interiors) and they have internal sources of energy that are of the same order as that arriving externally from the Sun. The origin of the latter is uncertain, but it is probably produced by the conversion of potential energy to heat as the planet slowly contracts under its own gravitational field and heavier elements move towards the core. The required rate of contraction is a few cm per year, which of course is quite undetectable.

Taking Jupiter as the largest, closest and therefore best-studied example, energy-balance calculations based solely on its distance from the Sun (five times that of Earth) and its albedo (0.35) predict that its effective emitting temperature should be about 110 K. If we add the internal power of about 30 W m~2, estimated from spacecraft measurements of the total infra-red flux leaving the planet, then this increases to 130 K. The predicted stratospheric temperature based on this is 109 K, which is close to the value observed by spacecraft radio occultation measurements and during the descent of the Galileo entry probe. The heat flux from the interior, along with the high opacity of the atmosphere in the thermal infra-red at pressures higher than about 0.25 bar, guarantees that the deep atmosphere is convective, with a lapse rate g/cp = 2 K km-1, and this is also close to that observed (Fig. 12.13).

The smaller giant planets have smaller internal energy sources than Jupiter (that on Uranus has so far proved undetectable), and different concentrations of methane and other gases that are radiatively active in the infra-red. When these differences are taken into account, they are found to behave in broadly the same way as Jupiter, with a quasi-isothermal stratosphere overlying a virtually bottomless, convective troposphere. All have complex cloud structures,

50 100 150 200 Temperature (K)

250 300

50 100 150 200 Temperature (K)

250 300

flG. 12.13. Temperature profiles for the four giant outer planets, measured by the NASA Voyager spacecraft using infra-red sounding and the radio-occultation method. (Taylor 2005)

as would be expected from the combination of deep convection and low upper-tropospheric temperatures, with water, ammonia, and (except on Jupiter that is too warm) methane, among the species that condense. The existence of multiple cloud and aerosol layers, the long path lengths and high pressures, compared to Earth, which mean that processes such as pressure-induced dipole and quadru-pole absorption bands of hydrogen dominate the opacity below the tropopause, and limited knowledge of the detailed composition, all make the construction of detailed radiative-dynamical equilibrium models for the giant planets difficult. Given also that there are few reliable measurements with which to compare, climate studies involving radiative models are in their infancy for the outer planets.

12.5 Titan's atmosphere and haze

Saturn's biggest moon, Titan, is the only natural satellite in the Solar System that is surrounded by a dense atmosphere. Titan has been the focus of scientific investigation from its first observation in the seventeenth century, by the Dutch mathematician, physicist and astronomer Christian Huygens, to the present space missions and the dedicated ground-based observations. Titan is larger than the planet Mercury, and not much smaller than Mars, but has a thicker atmosphere even than that of the Earth with a surface pressure of around 1.5 bar, and with the same primary constituent, nitrogen. Titan is ten times more distant from the Sun than Earth and so very cold. The principal minor constituents are a few per cent of methane and other hydrocarbons, some of which flg. 12.14. The main features of the climate system on Titan include an atmospheric temperature profile with a distinct troposphere, stratosphere and thermosphere and at least two distinct types of cloud and haze. Instruments on the Cassini spacecraft recently discovered fluvial features and lakes on the surface, probably primarily created and filled by liquid methane rainfall.

form oily haze layers composed of light hydrocarbons. A steady drizzle from these, plus seasonal rain from the lower-level methane clouds, contributes to the production of lakes, rivers and shorelines on the surface (Fig. 12.14). The cloud cover, with a global, high-altitude haze of organic material produced by photochemistry and patchy, lower-level methane clouds, is reminiscent in structure and total N2 content (if not overall composition), of that of Venus. Methane is the principal greenhouse gas and, allowing also for contributions by the pressure-induced bands of nitrogen and hydrogen, and by the clouds, its presence raises the surface temperature by about 12 K above the radiative equilibrium temperature of 82 K. The Huygens probe recorded a mean lapse rate of about 1.2 K km-1 during its descent (the dry lapse rate g/cp is about 1.3 K km-1) and a temperature of 93.65 + 0.25 K at a pressure of 1467 + 15 hPa at its landing site.

At Saturn's mean distance from the Sun, the solar constant is only 15 W m-2, or about 1% of that at Earth. Titan has an albedo of 0.25, which works out, using a simple energy balance model to an effective emitting temperature of 84 K. A one-layer greenhouse model estimates 100 K for the surface temperature and the optically thin approximation gives 71 K for the stratospheric temperature. The dry adiabatic lapse rate g/cp = 1.3 K km-1 on Titan, so the tropopause (based on the definition of the troposphere having a negative temperature gradient, and not on convective equilibrium) should fall at approximately 22.3 km above the surface. These global mean values compare reasonably well to the profile in

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