Habitable Zone Limits for Dry Planets
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ASTROBIOLOGY
Volume 11, Number 5, 2011
ª Mary Ann Liebert, Inc.
DOI: 10.1089/ast.2010.0545
Habitable Zone Limits for Dry Planets
Yutaka Abe,1 Ayako Abe-Ouchi,2 Norman H. Sleep,3 and Kevin J. Zahnle 4
Abstract
Most discussion of habitable planets has focused on Earth-like planets with globally abundant liquid water. For
an ‘‘aqua planet’’ like Earth, the surface freezes if far from its sun, and the water vapor greenhouse effect runs
away if too close. Here we show that ‘‘land planets’’ (desert worlds with limited surface water) have wider
habitable zones than aqua planets. For planets at the inner edge of the habitable zone, a land planet has two
advantages over an aqua planet: (i) the tropics can emit longwave radiation at rates above the traditional
runaway limit because the air is unsaturated and (ii) the dry air creates a dry stratosphere that limits hydrogen
escape. At the outer limits of the habitable zone, the land planet better resists global freezing because there is less
water for clouds, snow, and ice. Here we describe a series of numerical experiments using a simple three-
dimensional global climate model for Earth-sized planets. Other things (CO2, rotation rate, surface pressure)
unchanged, we found that liquid water remains stable at the poles of a low-obliquity land planet until net
insolation exceeds 415 W/m2 (170% that of modern Earth), compared to 330 W/m2 (135%) for the aqua planet.
At the outer limits, we found that a low-obliquity land planet freezes at 77%, while the aqua planet freezes at
90%. High-obliquity land and aqua planets freeze at 58% and 72%, respectively, with the poles offering the last
refuge. We show that it is possible that, as the Sun brightens, an aqua planet like Earth can lose most of its
hydrogen and become a land planet without first passing through a sterilizing runaway greenhouse. It is
possible that Venus was a habitable land planet as recently as 1 billion years ago. Key Words: Venus—Habitable
zone—Extrasolar terrestrial planets—Water—Planetary atmospheres. Astrobiology 11, 443–460.
1. Introduction loss of hydrogen to space. In either case, the end result would
be a dry planet, although, as we discuss below, the details of
M ost previous studies of the habitable zone implicitly
assume an ocean-covered planet with abundant liquid
water, like present Earth. We call such a planet an ‘‘aqua
the two evolutions can be very different. Kasting et al. (1993)
used the threshold for fast hydrogen escape, rather than the
classic runaway greenhouse effect, to define the inner
planet1.’’ If the aqua planet is too far away from its star, the boundary of the continuously habitable zone.
ice-albedo feedback brings complete freezing (Budyko, 1969). We can imagine another kind of habitable planet that has
If the aqua planet is too close to its star, like Venus, the at- only a small amount of water and no oceans; it might be
mosphere fills with water vapor (steam). This triggers a run- covered by vast dry deserts, but it might also have locally
away greenhouse effect that culminates in the complete abundant water. We call such a dry planet a ‘‘land planet.’’
evaporation of the oceans (Ingersoll, 1969). But before the The fictional planet known as Arrakis or Dune (Dune, Her-
oceans evaporate, the atmosphere becomes humid at all alti- bert, 1965) provides an exceptionally well-developed exam-
tudes, the cold trap disappears, and hydrogen escape is rapid ple of a habitable land planet. In its particulars, Dune
(Kasting, 1988). This starts a race between evaporation and the resembles a bigger, warmer Mars with a breathable oxygen
atmosphere. Like Mars, Dune is depicted as a parched desert
planet, but there are signs that water flowed in the prehis-
1
The less awkward ‘‘ocean planet’’ is already in use to describe a toric past. Dune has small water ice caps at the poles and
class of possible planets in which water is a major constituent,
something like Jupiter’s satellite Ganymede, only bigger and
more extensive deep polar aquifers. The tropics are exceed-
warmer. As we define it, an aqua planet is a superset that includes ingly dry, but the polar regions are cool enough and moist
both ‘‘ocean planets’’ and planets like Earth with oceans. enough to have morning dew. A comparison with Saturn’s
1
Department of Earth and Planetary Science, University of Tokyo, Tokyo, Japan.
2
Atmosphere Ocean Research Institute, University of Tokyo, Kashiwa, Japan.
3
Department of Geophysics, Stanford University, Stanford, California, USA.
4
NASA Ames Research Center, Moffett Field, California, USA.
443
444 ABE ET AL.
moon Titan is also apt: Titan has modest polar methane lakes We compute radiative transfer by using a two-stream
separated by a vast desert that spans the tropics and tem- k-distribution scheme (Nakajima and Tanaka, 1986) that in-
perate zones. Dune is sparsely inhabited by a mix of indig- cludes 18 wavenumber channels that are divided into several
enous and terran flora and fauna. Although Dune is a work (1 to 6) subchannels. The total number of subchannels is 37.
of fiction, the planet Dune provides a qualitative model of a We included both the large-scale clouds and the cumulus
land planet that raises several important issues regarding clouds in the radiant flux calculation. We used either liquid
habitability, which include how much water is enough and or ice cloud properties for radiative transfer in the clouds,
what actually sets the inner edge to the habitable zone. depending on the liquid fraction determined by temperature.
The runaway greenhouse effect on land planets has not On a land planet, we ignored rivers and underground
previously been discussed. The greenhouse effect of a land water transport. These assumptions are consistent with our
planet differs from that of an aqua planet because atmospheric assumption of a flat planet. Thus, the distribution of
circulation controls the latitudinal surface water distribution groundwater is completely determined, locally, by the bal-
(Abe et al., 2005). The tropical atmosphere and the stratosphere ance between precipitation and evaporation. For the soil of a
can both be extremely dry on a land planet, so that conven- land planet, we used a bucket model (Manabe, 1969). The
tional runaway greenhouse and hydrogen escape thresholds change of soil moisture is predicted as a net contribution of
may not apply. In this paper, we investigate the limits for the rainfall, evaporation, and snow melt. The rate of evaporation
solar flux that cause complete freezing or evaporation of liquid from the soil surface is a function of the soil moisture and
water on a land planet, using a general circulation model. We the ‘‘potential evaporation,’’ that is, the hypothetical evapo-
close by considering a particular scenario in which land ration rate from a completely wet surface. The potential
planets can evolve from aqua planets. evaporation from the surface is calculated by a bulk for-
mula, thus proportional to the surface wind and difference
in the absolute humidity between the air and surface. When
2. Climate Model
soil moisture exceeds 10 cm, the surface is assumed to
We formulated models to investigate short-term stability be completely wet. When soil moisture is less than 10 cm,
under the assumption that water sequestered in deep aqui- the evaporation rate is assumed proportional to the soil
fers and in hydrous minerals does not evaporate and con- moisture.
tribute to a runaway greenhouse. We qualitatively discuss The snowpack is expressed as a single reservoir, the size of
long-term processes in a later section of this paper. which is prognostically determined by the balance between
We created an idealized three-dimensional land-planet new snowfall and snowmelt. Snowmelt occurs whenever the
model by removing the oceans, topography, and vegetation surface skin temperature exceeds the melting temperature.
from CCSR/NIES AGCM5.4g, which is a general circulation Ice and snow Bond albedo models are the same as those for
model (GCM) developed for modeling Earth’s climate by the the Earth model, with the albedo of snow-covered ground
Center for Climate System Research, University of Tokyo increasing linearly from 0.5 to 0.75 as the temperature de-
and the Japanese National Institute for Environmental Re- creases from 273 K to 258 K. The fraction of snow cover is
search (Numaguti, 1999). We assumed a circular orbit and assumed to be unity when the snow depth exceeds 100 kg/
zero obliquity. The model processes and parameters are m2. Below this critical value, it is assumed to be proportional
unmodified from their terrestrial application, except for the to the square root of the snow thickness. The ground albedo
removal of topography, surface runoff, and ozone radiation without snow cover is fixed at the typical desert value of 0.3.
effects. The background atmosphere consists of one bar of In all the numerical experiments, the initial condition was
air. We set CO2 concentration in the atmosphere to 345 ppm. a steady state circulation with a uniform distribution of
We performed a series of numerical experiments by varying groundwater. We prepared the initial conditions as follows.
the solar flux and varying the amount of water available. First, we ran the model keeping the land surface saturated
Apart from the changes listed above, the model is the until the hydrologic cycle approached steady state. Then, we
same model used for terrestrial studies (Numaguti, 1999). reset the surface water distribution to the uniform distribu-
The scheme for large-scale transport in the model uses the tion with given total water content. We considered three
spectral transform method in the horizontal directions and cases with different total water content: 20, 40, and 60 cm.
grid discretization in the vertical coordinate (the ‘‘sigma’’ Note that 40 cm depth of water is sufficient to cause the
coordinate, defined as the ratio of the pressure aloft to the runaway greenhouse effect, while 20 cm is twice the satura-
surface pressure). The horizontal resolution is triangular tion depth in the model and larger than the annual net
truncation up to 21 wavenumbers, and the equivalent hori- evaporation from the saturated surface. Hence, an initial
zontal grid size is about 5.6 in longitude and latitude. The water content larger than 20 cm does not affect the hydro-
number of vertical levels is 20 at non-uniform spacing. logic cycle at equilibrium, but it takes longer to reach
We compute two types of precipitation: large-scale con- equilibrium.
densation and cumulus convection. For large-scale conden- To compare land planets to aqua planets, we performed a
sation, we applied a prognostic cloud water scheme based on series of parallel experiments for aqua planets. The aqua
Le Treut and Li (1991). We represented cumulus precipita- planet model is basically the same as the land planet model
tion with a simplified version of the Arakawa-Schubert except for the treatment of the surface boundary condition.
scheme (Arakawa and Schubert, 1974; Moorthi and Suarez, On an aqua planet, the landless surface is covered by a 50 m
1992). We recorded precipitation at the surface as snow or deep slab ocean. Thus, the surface is always kept wet irre-
rain, depending on whether the wet bulb temperature at the spective of the balance between precipitation and evapora-
lower atmospheric layer was below or above the freezing tion. In other words, we implicitly assumed water transport
point, respectively. at the surface. However, we did not consider heat transport
HABITABLE ZONE LIMITS FOR DRY PLANETS 445
through oceans. The surface albedo of oceans is 0.07. Ice and Complete freezing on our model land planet occurs when
snow albedo models are the same as in the land planet the Sun is dimmed to 77% of the solar constant (the present
models. Owing to the large thermal inertia of an aqua planet level of sunshine incident on Earth). On the other hand,
compared to a land planet, we computed 60 or more years of complete freezing of the model aqua planet occurs at 90%.
model time for each solar flux value to obtain the steady- Thus, a land planet shows stronger resistance to complete
state hydrological cycle. freezing. Physically, the tropics of a land planet are dry and
characterized by very low absolute humidity (Abe et al.,
3. Limits of Habitability 2005). The tropics of the land planet are thus less cloudy and
less susceptible to snowfall than those of an aqua planet. This
3.1. Cold outer limit
results in a lower albedo and larger net insolation on a land
There are three possible surface states of a cold planet. planet and hence a warmer climate. Figure 1 compares
(1) No permanent ice or snow exists on the planet. Seasonal average surface temperatures of land and aqua planets as
ice and snow may exist. (2) Permanent ice or snow par- functions of latitude and insolation. Figure 2 compares lo-
tially covers the planet, like on the present Earth. (3) Per- cations of the ice line on the land and aqua planets.
manent ice or snow covers the entire surface of the planet. Land planets are less humid and have weaker greenhouse
This ‘‘snowball’’ state may have occurred on ancient effects than aqua planets. This effect is, however, negligibly
Earth (e.g., Hoffman and Schrag, 2002). Snowball Earth small at the freezing limit, because in either case the cold
seems not to have led to obvious mass extinction on Earth atmosphere contains very little water vapor. The different
(oxygenic photosynthesis survived unscathed); it is possible freezing limit is due to the difference of albedo. A land planet
that biota persisted in the subsurface and around liquid has a lower albedo than an aqua planet at the same mean
water oases. surface temperature. One reason is that land planets have
FIG. 1. Average surface temperatures as functions of latitude and insolation for aqua planets (above) and land planets
(below). Obliquity is zero. Color images available online at www.liebertonline.com/ast
446 ABE ET AL. FIG. 2. Permanent ice cover as functions of latitude and insolation for aqua planets (above) and land planets (below). Planetary freezing points are indicated. Color images available online at www.liebertonline.com/ast fewer clouds, because they are less humid. The other reason et al. (2005) classified habitable planets into four types based on is that less snow accumulates on land planets than on aqua whether the planet is wet or dry and whether the obliquity of planets. This occurs not just because the atmosphere is drier the planet is high or low. It is well known that, if the obliquity is but also because daytime temperatures are higher due to high enough, the polar regions receive more insolation over small thermal inertia. the course of the year than the equator. Such high-obliquity In Fig. 2 it can be seen that the idealized aqua planet has planets have different freezing limits than Earth-like ‘‘upright’’ bigger ice caps than Earth for insolation of 100%. One reason planets. Figure 3 illustrates these different freezing regimes for for this difference is that we assume a swamp ocean with no low-obliquity (23.5) and high-obliquity (60) land planets meridional heat transport in the ocean. Another reason is (Abe and Abe-Ouchi, 2003). Figure 4 does the same for aqua that the obliquity is assumed to be zero in Fig. 2. Figures 3 planets. At 23.5, the patterns of ice cover differ from what they and 4 show that obliquity strongly influences the distribution are at 0, but the global freezing limits are unchanged. At 60, of ice and snow, as expected. the patterns of ice cover are qualitatively different. For the land Figures 3 and 4 illustrate something else as well. Based on planet, the equator becomes icy rather easily, but the poles idealized GCM experiments, such as those discussed here, Abe resist freezing until insolation drops below 58% (Fig. 3). High-
FIG. 3. Permanent and seasonal (northern summer) snow and ice cover (above) and temperatures (below) as functions of
latitude and insolation for land planets at different obliquities (Abe and Abe-Ouchi, 2002, 2003). Planetary freezing points are
indicated. Increasing obliquity greatly expands the habitable zone of land planets against global freezing. Color images
available online at www.liebertonline.com/ast
447
448 ABE ET AL.
FIG. 4. Permanent ice cover and seasonal ice (left) and northern summer temperatures (right) as functions of latitude and
insolation for aqua planets at 23.5 (top) and 60 obliquities (bottom). Planetary freezing points are indicated. Increasing obliquity
also greatly expands the habitable zone of aqua planets against global freezing, although not as much as for land planets.
obliquity aqua planets also resist freezing better than low- greenhouse occurs when there is enough water vapor in the
obliquity aqua planets, with the poles offering refugia until atmosphere that the atmosphere is optically thick to thermal
insolation drops below 72% (Fig. 4). radiation. For an aqua planet, the saturation vapor pressure,
Recent work by Spiegel et al. (2010) extended the outer the temperature, and the optical depth are interrelated by the
edge of the habitable zone still farther by combining the ef- physical properties of water. The saturation vapor pressure
fect of high obliquity with the effect of orbital eccentricity. is a function of temperature. Therefore, the constraint im-
For such a planet the Milankovich cycles become huge. The posed by saturation makes the optical depth a function of
maximum effect occurs when the summer pole points to- temperature. In the limit of an optically thick atmosphere,
ward the Sun at perihelion. Such a planet can be seasonally the maximum rate that thermal radiation can be emitted to
habitable in the conventional sense when its mean insolation space is a fixed quantity known as the ‘‘runaway greenhouse
falls as low as 25% (i.e., a semimajor axis approaching 2 AU). limit’’ or the ‘‘critical flux.’’ For a gray absorber (a substance
More broadly, there may not be a true outer limit to the that
R 1 is4 equally opaque to all wavelengths), the limit is
conventional habitable zone. Greenhouse effects can be made 0 T e d, where r is the Stefan-Boltzmann constant, s is
stronger by adding more greenhouse gases—it has not been the optical depth, a & 3/2 is a geometric factor to account for
proved that there is a limit to this if the greenhouse gases are the slanting path of the average ray through the atmo-
carefully chosen. On the other hand, the particular CO2-H2O spheres, and s(T) is determined by the saturation vapor
combination seen on Earth, Mars, and Venus does seem to pressure and the opacity of water vapor. An important
have an outer limit brought on by condensing both of the qualification for real atmospheres containing gases in addi-
active gases (Abe, 1993). In the one-dimensional global av- tion to water vapor is that the critical flux is a function of
erage, the CO2-H2O outer limit is *30% (Abe, 1993), set by relative humidity (Nakajima et al., 1992; Abe, 1993; Renno,
CO2 condensation, and one might expect it to be lower still 1997; Ishiwatari et al., 2002). If the relative humidity is de-
for high obliquity and high eccentricity. pressed, as can happen in the subsiding branch of the Hadley
circulation in an atmosphere that is mostly some other gas
(e.g., N2), the critical flux is increased.
3.2. Hot inner limit
There are two possible warm states for aqua planets (Fig.
The inner edge of the habitable zone is usually set by 5). (1) If insolation in the tropics exceeds the critical flux but
the onset of the runaway greenhouse effect. The runaway the global average insolation is less than the critical flux, low
HABITABLE ZONE LIMITS FOR DRY PLANETS 449
occurs because the tropics of the land planet have very low
relative humidities and essentially no unevaporated water
(Abe et al., 2005). The third choice is illustrated by panel (c) in
Fig. 5.
The critical solar flux for the runaway greenhouse in our
aqua planet models, 330–350 W/m2, agrees with previous
results for a 1-bar air atmosphere Earth. Abe’s (1993) critical-
flux one-dimensional radiative-convective equilibrium
models give *310, 330, and 350 W/m2 for 100%, 75%, and
50% relative humidity, respectively. The three-dimensional
dynamic model of Ishiwatari et al. (2002), which self-consis-
tently computes relative humidity, generates results as a
function of insolation that closely resemble the products of a
one-dimensional model with *60% of the relative humidity.
The corresponding critical flux is between 330 and 350 W/
m2. Ishiwatari et al. attributed the low effective humidity to
subsidence in the Hadley circulation.
Liquid water is stable on the land planet to at least 415 W/
m2, which is 170% of the present Earth’s insolation (Fig. 6).
The transition is abrupt over a numerical step with 1% in-
solation change. In the three cases considered here, the net
insolation jumps to *450 W/m2, well above the critical flux.
The ordinary direction of solar evolution is from left to right,
because after it reaches the main sequence at 50 million years
the Sun brightens as it ages. Net global average insolations
between 415 W/m2 and 450 W/m2 are only attainable in this
model when evolving from right to left. Evolution from right
to left can occur as a planet cools after a giant impact, or it
can occur very early, between 30 and 50 million years after
FIG. 5. Schematic diagrams of insolation and radiation of
heat to space as a function of latitude. (a) The total insolation
is below the critical flux. Radiation at high latitudes removes
the excess at low latitudes. (b) The average insolation is
above the critical flux. No steady state is possible with liquid
water at the surface. (c) A land planet radiates above the
critical flux at low latitudes. Color images available online at
www.liebertonline.com/ast
latitudes emit thermal radiation at the critical flux, and the
excess heat is transported to the high latitudes and emitted
there. The present Earth is in this state. This state is illus-
trated by panel (a) of Fig. 5. (2) But if the global average
insolation exceeds the critical flux, the high latitudes are
overwhelmed, and the planetary thermal radiation is limited
by the critical flux everywhere. In such a state, the insolation
and planetary radiation are out of balance [panel (b), Fig. 5].
In the conventional runaway greenhouse effect, the atmo-
sphere heats up until nearly all the water on the surface and FIG. 6. The total water on the surface of the land planet as a
in the atmosphere has evaporated, at which point the satu- function of net insolation. The red cases assume that the total
inventory of water is equivalent to a layer of water 60 cm
ration vapor pressure no longer limits the temperature at
thick (most of which is near the poles). The purple and blue
which the planet can radiate. Because the aqua planet holds a cases assume 40 and 20 cm, respectively. All the water is in
lot of water, the surface would get extremely hot, and the the atmosphere above the threshold at 415 W/m2. For the
planet would be sterilized. 60 cm case, this gives 0.1 bar of water vapor. The jump be-
A third state is available for a land planet. The dry low- tween 415 W/m2 and 450 W/m2 is caused by increased at-
latitude area can emit a flux larger than the critical flux. This mospheric absorption by water vapor.
450 ABE ET AL. the origin of the Solar System, when the Sun fades as it modern Earth where liquid water is present. For example, the approaches the zero-age main sequence. vapor pressure of water is *2 mbar in the summer and The relation between the runaway greenhouse and the 0.25 mbar in the winter in the dry valleys of Antarctica (Doran complete evaporation of all surface water or the polar ice cap et al., 2002). Brine at - 21C has a partial pressure of 1 mbar. is not as simple for the land planet as it is for the aqua planet. Transient liquid water is therefore reasonable on a land planet. For a very dry land planet, complete evaporation of surface There are multiple equilibrium states at elevated insola- water may occur without a significant contribution to the tion. The runaway state with all surface water in vapor form greenhouse effect by water vapor. Hence, Nakajima et al. is stable below what we have been calling the runaway (1992) defined the runaway greenhouse state as the state threshold. The system exhibits hysteresis, analogous to the with solar flux larger than the critical flux. However, as history-dependent consequences of the ice-albedo feedback, shown above, surface water exists near the poles of land in which ice-covered and ice-free solutions are both possible planets at insolations well above the critical flux. In this for a given insolation. When we start from a state with polar paper, we have also referred to the solar flux that causes caps and liquid water and raise the insolation, we obtain the complete evaporation of surface water or ice cap as the results described above. But if we start from the runaway runaway greenhouse threshold. Fortunately, in the cases state, where all the water is water vapor, and decrease in- discussed here, the state without surface water or ice is also solation, polar ice or water does not form even when inso- the runaway greenhouse state in the classical sense. lation is reduced to just 120% of the solar constant (320 W/ The climate of the land planet is moderate below the m2 at the lower albedo appropriate to the runaway states). runaway greenhouse threshold even above the critical flux, The lower limit of the runaway state decreases with in- especially at the higher latitudes (Fig. 7). Permanent ice caps creasing total water. It is likely that the runaway state is are stable near the poles. Even the equatorial temperature of stable at insolation levels as low as the classical critical flux *75C is well within the limits of thermophilic microbes. for the runaway greenhouse if abundant water is available. Below the runaway greenhouse threshold, the absolute Thus, both runaway states and the state with liquid water humidity is independent of the total amount of water available are stable between the critical flux (310 W/m2 at 100% hu- on the ground (Fig. 8), provided it is sufficient to maintain the midity) and the runaway threshold (415 W/m2). humidity in the model. Atmospheric circulation controls the Figure 9 addresses the albedo of the land planet before and spatial distribution of water on the planet’s surface. Increasing after it passes through the critical flux. The plot shows evo- the total amount of available water merely augments the high- lution in both directions. The albedo jump that accompanies latitude cold traps without changing the absolute humidity. the transition from the habitable state to the runaway green- Thus, the threshold determined here is valid as long as the cold house state (solid symbols) does not cause the runaway but traps can accommodate the available water. rather is a result of the runaway. In Fig. 7, as the runaway is The model global vapor pressure in Fig. 8 reaches 6 mbar of approached from the left, the albedo declines as the net in- water and permanent ice disappears just before the runaway solation increases. Just before runaway, the albedo is very greenhouse threshold. This absolute humidity occurs on nearly equal to the adopted surface albedo of 0.3. At the FIG. 7. The mean surface temperature as a function of net insolation (as percentage of the flux incident on Earth today) and latitude for the land planet. Contours and colors are labeled in degrees Celsius. Color images available online at www .liebertonline.com/ast
HABITABLE ZONE LIMITS FOR DRY PLANETS 451
FIG. 8. The global average precipitable
water in the land-planet model atmo-
sphere as a function of net insolation is
independent of the total available water
below the threshold. Solid symbols are for
evolution from left to right. The green-
house becomes unstable when there are
*4 cm of water vapor in the air, equiva-
lent to 6 mbar partial pressure. For com-
parison, Venus now has the equivalent of
1.3 cm of water. All the water is in the
atmosphere above the threshold. There is
a slight nonconservation of water in the
model as the threshold is passed. Open
symbols are for evolution from right to
left—such solutions can be realized by
starting in the runaway greenhouse state
and reducing net insolation. The plot il-
lustrates hysteresis. Color images avail-
able online at www.liebertonline.com/ast
runaway, the albedo drops discontinuously to *0.23. De- with a thick atmosphere. The range is essentially zero on Ve-
creasing albedo as the runaway threshold is approached is nus, *4 K on Titan, a few 10 K on Earth, and somewhat more
caused by decreasing cloud cover and retreating polar caps. than Earth on Mars (Lorenz et al., 2001). Simple extrapolation
The discontinuity at the runaway is caused by atmospheric and interpolation to a dry planet, however, is not straightfor-
absorption of sunlight by water vapor, because the amount of ward. The average wind velocity is higher on a planet, like
water in the atmosphere jumps from nearly zero to significant. Mars, with a tenuous atmosphere than one with a dense at-
In this study, we have only considered very dry planets mosphere, like Venus. Both Earth and Mars have significant
for which scattering by water vapor is modest. Wetter land obliquity where sunlight hits the polar regions in the summer.
planets would have wetter atmospheres with more scattering For Earth (but not Mars, whose atmosphere is so thin that
and thus less-pronounced albedo jumps at runaway. This elevation has little effect on surface temperature), the elevated
behavior was confirmed by using a simple radiation model. South Pole and low-lying North Pole is important. The latent
Hence, the albedo jump at the transition may not be a gen- heat of water, CO2, and methane is significant on Earth, Mars,
eral feature of land planet runaways but may instead be and Titan, respectively. Ocean currents also transport heat on
peculiar to the very dry cases we have considered here. Earth. We note that Lorenz et al. (2001) suggested that circu-
lation adjusts to maximum entropy dissipation. But the esti-
mate of the entropy dissipation may require full dynamic
3.3. Application to other planets
calculations; dynamic properties such as the rotation rate of a
Our models indicate that the runaway greenhouse thresh- planet affect the circulation and, thus, affect the equator to pole
old is significantly closer to the Sun for a land planet than for heat transport. Hence, quantitative estimation is difficult.
an aqua planet. We retained several properties of Earth in our A thin atmosphere is ineffective at damping daily tem-
model, including its concentration of CO2 and its atmospheric perature fluctuations. Frost thus may form on the coldest
pressure. Carbon dioxide figures directly in the efficacy of the nights, especially if the planet rotates slowly. This enhances
greenhouse. The temperature enhancement from Earth’s habitability unless the surface becomes too hot for life. The
greenhouse is *33 K. Much of the effect is the result of water frost, particularly where it is within pore spaces in the soil,
vapor rather than the direct effect of CO2. With regard to may melt to liquid water in the morning. Carbonate forma-
atmospheric pressure, the land planet remains stable for thin tion in the droplets is the classical mechanism by which the
atmosphere cases above the traditional greenhouse threshold atmospheric pressure of Mars near the triple point of water is
because latitudinal energy transport is inefficient enough that maintained (Kahn, 1985).
cold traps persist at the poles. We qualitatively discuss the As a thought experiment, we could move Mars well inside
effects relevant to a tenuous atmosphere. Earth’s orbit. We could make the move slowly (as with stellar
Empirically, the pole-to-equator temperature difference on a evolution of a real planet) so that a large cryptic CO2 reservoir
planet with a thin atmosphere is greater than that on a planet (if such exists) would have time enough to react with silicates
452 ABE ET AL.
FIG. 9. The albedo of the land planet as a
function of net insolation. The red, purple and
blue cases have the same meaning as in Fig. 8.
The albedo decreases monotonically as net in-
solation increases and clouds become rare and
polar caps retreat. The albedo jump between
415 W/m2 and 450 W/m2 when evolving from
left to right is caused by water vapor absorbing
sunlight. The absence of an albedo jump when
evolving from right to left shows that the low
albedo is caused by absorption of sunlight by
atmospheric water vapor. Color images avail-
able online at www.liebertonline.com/ast
to form carbonates. The polar water and subsurface cryo- 3.4. Clouds
sphere would melt with most of the water entering (or re-
Clouds are a major uncertainty in any discussion of the
maining in) the subsurface. The still tenuous atmosphere
limits of the habitable zone. Clouds can warm or cool.
would inefficiently transfer heat from the equator to the poles,
High clouds such as cirrus tend to warm the planet. Hence,
which would act as cold traps. The greenhouse effect would
expanding their global coverage can expand the habitable
be weak because the atmosphere would be thin. The result
zone outward (Forget and Pierrehumbert, 1997; Goldblatt
would resemble a habitable Dune-like planet.
and Zahnle, 2010; Rondanelli and Lindzen, 2010). Low
Some seasonality aids habitability by producing transient
clouds by contrast have their biggest effect on the albedo.
liquid water. However, too much seasonality precludes good
More-extensive low cloud cover cools the planet. Hence,
cold traps and puts too much water vapor in the air. Cru-
removing low clouds pushes the outer limit of the habit-
dely, any transfer mechanism with an annual flux compa-
able zone outward (Rosing et al., 2010), while increasing
rable to, or greater than, the average water vapor content of
them can stave off the greenhouse runaway at the inner
the air can have a significant effect on humidity. Present
edge of the habitable zone. Which, if any, of these effects
Mars has a significant obliquity and an elliptical orbit. Water
actually takes place on real planets is a fit topic for further
thus seasonally moves between the poles, and the most ef-
research.
fective cold traps change over many millennia as the orbital
parameters evolve. If we made our thought-planet’s orbit
4. Long-Term Stability
more circular and reduced its obliquity, the poles would
become more effective cold traps. There are three issues that govern long-term stability of a
A nearly despun planet, analogous to Mercury, has good climate. One is stellar evolution: the star inexorably bright-
polar cold traps (e.g., Harmon et al., 2001). There is, however, ens, so that at some point the net insolation comes to exceed
a tendency for snow and frost to fall on the dark side and what a planet with liquid water can process. Our Sun is now
evaporate at dawn. This maintains some humidity. A fully brightening at a rate of about 9% per billion years, and the
despun planet has a huge cold trap on the backside and pace is quickening.
clement conditions at twilight ( Joshi, 2003). A fully despun A second issue comprises geological sources and sinks of
land planet that kept one hemisphere facing the Sun would key volatiles. A moribund geological cycle can leave gases
resemble the upright land planets we have discussed here; such as CO2 forever fixed in dead rocks. It is popular to
the Sun-facing hemisphere would play the role of the tropics attribute Mars’s fate in part to a feeble rock cycle.
for the upright planet. Most incident sunlight would be re- A third issue is hydrogen escape. This would seem espe-
radiated through a dry atmosphere; hence the runaway cially germane to land planets, which by construction have
greenhouse limit for a dry planet would be much closer to little water to lose. The amount of available water in our
the star than it would be for an aqua planet. models is small, tens of centimeters globally averagedHABITABLE ZONE LIMITS FOR DRY PLANETS 453
equivalent depth. The amount in the atmosphere at the is condensible, it can be cold trapped (like H2O on Earth or
runaway greenhouse threshold is even smaller, *4 cm. Mars, or H2SO4 on Venus).
We address the effects of topography, hydrogen escape, The diffusion-limited escape flux relates hydrogen escape
and long-term planetary geochemistry in this section. to the total mixing ratio of all H-containing species in the
stratosphere (Walker, 1977, p 164). The upward flux /i of a
conserved species i in an isothermal atmosphere is
4.1. Topography and cold traps
Our models did not include trapped water, as the short- 1 1 qfi
/i ¼ fi bia ( ) (bia þ Kzz Na ) (1)
term climate does not depend on its amount. The long-term Ha Hi qz
available quantity of water thus can be much greater than an
equivalent thickness of centimeters. For example, present In this expression, fi refers to the mixing ratio; bia is the
Earth has voluminous traps, including an equivalent *60 m binary diffusion coefficient of i in air [for H2 in air bia = 1.9 ·
in its ice caps. During the last ice age, continental glaciers 1019(T/300 K)0.75 cm - 1 s - 1]; Ha and Hi are the scale heights of
contained a few times this thickness. With the present to- air and i, respectively [Hi mkTi g, where T is temperature, mi is
pography, an ice-age dry Earth would have closed basins in mass (grams), and g is gravity]; Kzz (cm2/s) describes the
the Arctic Ocean and between East and West Antarctica vertical eddy mixing; and Na is the number density (cm - 3)
(Lythe and Vaughan, 2001). of the atmosphere. The homopause is the altitude where
Topography allows the greenhouse to remain stable be- molecular diffusion and Eddy mixing are equal, bia = KzzNa.
yond the flat-planet greenhouse limit. If present Earth were Below the homopause, bia < < KzzNa, the atmosphere is well
dry, the most effective polar cold traps would be in East mixed, and vertical transport is relatively fast. The maximum
Antarctica. The Gamburtsev-Vostok region has an ice-un- flux is obtained when vfi/vz = 0 above the homopause. This is
loaded elevation of over 2 km [data from Lythe and the diffusion-limited flux, which can also be written
Vaughan (2001)]. Continental glaciation probably started
there (DeConto and Pollard, 2003). In the absence of albedo bia (mi ma )g
/lim (H2 ) ¼ ft (H2 ) (2)
effects, it would be *10 K cooler than if it were at sea level. kT
It would be much cooler than the ocean abyss of a dry
planet. where ft(H2) represents the total mixing ratio of hydrogen in
Topography allows for localized liquid water on a dry all forms at the homopause. It is noteworthy that the diffu-
planet, even if the humidity is too low for rain. Ice melts near sion-limited flux is independent of the eddy diffusion coef-
the edge of ice caps, and snow and frost melt on warm days. ficient. The diffusion limit assumes that escape is otherwise
The water does not immediately completely evaporate. As in easy, that is, that the diffusion-limited flux is smaller than the
the Dry Valleys of Antarctica, it flows through rivulets even energy-limited flux. For Earth with H2 and air and T = 200 K
though the humidity is far lower than equilibrium with liq- this evaluates to
uid water (McKay et al., 1985). Some of the water accumu-
lates in ice-covered ponds. The rest continues down hill, Flim (H2 ) ¼ 2 · 108 fi (H2 ) mol=s (3)
some in streams and some in aquifers. The groundwater
eventually returns to the surface at springs and evaporates. If Because we have assumed that there are no sources or
their annual water budget is small compared to the amount sinks of H in the stratosphere, ft(H2) can be evaluated any-
in the atmosphere, the springs and rivulets have little effect where in the stratosphere. For simplicity, we assume that
on the global humidity. H2O is the major hydrogen carrier, so that ft(H2) & f (H2O).
Although expressions 1–3 implicitly assume that ft(H2) < <
1, they can be applied for ft(H2) & 1 if the background at-
4.2. Hydrogen escape mosphere does not escape. However, a moist greenhouse with
Kasting (1988) proposed that the inner edge of the habit- f(H2O) & 1 poses other problems that render the issue moot: it
able zone is set by hydrogen escape rather than by the is unlikely that chemistry will convert H2O to H2 quickly
runaway greenhouse effect. Kasting defined a ‘‘moist enough, and the escape is likely to be energy limited.
greenhouse’’ state as a temperate atmosphere with a moist The upper limit set by available stellar EUV radiation is
stratosphere. Moist greenhouse atmospheres permit rapid called the energy-limited escape flux (Watson et al., 1981).
hydrogen escape. When stratospheric water vapor mixing The energy-limited escape flux is approximated by
ratios exceed 0.1%, hydrogen escape to space can become fast
enough that an ocean of water can be lost in less than the age 4pR3 eSEUV
of the solar system. Thus the planet can lose its water to Fel (4)
GMmi
space before it suffers a classic thermal meltdown.
There are four important bottlenecks to H escape from an where eSEUV represents the effective stellar EUV heating
Earth-like atmosphere. First there must be energy for escape. (including heating efficiency e) relative to the modern Sun.
The chief source of energy for H escape is solar extreme Watson et al. used erg/cm2/s for the global average at Earth,
ultraviolet (EUV) (k < 100 nm) that can be absorbed directly averaged over the solar cycle. For H2 escape, this evaluates to
by H or H2. Second, H or H2 diffuse through the background
atmosphere to reach altitudes where escape actually occurs. Fel (H2 ) ¼ 4 · 106 SEUV mol=s (5)
Third, if the carrier of hydrogen is something other than H or
H2, for example, H2O on Earth or CH4 on Titan, the chem- Comparing Eqs. 3–5 shows that the energy limit takes over
istry that makes H2 can be a bottleneck. Fourth, if the carrier from the diffusion limit for stratospheric water vapor mixing454 ABE ET AL.
ratios exceeding 2%. This corresponds to the loss of an ocean popause. Whether the stratosphere is wetter or drier as a
of water in 600 million years. consequence is hard to say.
The modern Sun is a relatively weak EUV source com-
pared to other Sun-like stars or to the Sun itself in the past,
4.3. Weathering and interior chemical cycles
with, SEUVf(t/4.57) - 1 where t refers to the age of the Sun in
billions of years. Thus at t = 200 million years, the energy- The vigorous rock cycle on Earth shuttles volatiles be-
limited flux at Venus would equal the diffusion-limited flux tween surface and interior reservoirs. Volcanism and meta-
for a 100% water vapor stratosphere, and the lifetime of an morphism discharge volatiles to Earth’s surface. Weathering
ocean of water would be just 14 million years. The example is sequesters volatiles within rocks, some of which are deeply
extreme, but it illustrates how fast escape can be if conditions buried and metamorphosed or subducted into the mantle.
favor it. We discuss some possible consequences of the rock cycle on
Absolute humidities on land planets are predicted to be the habitability of land planets here.
very low, while the greenhouse is stable (Fig. 10). Figure 11 The Urey CO2 cycle is a part of this cycling that stabilizes
shows how long different planets retain their water. Land climate on modern Earth. Metamorphism and volcanism
planets and aqua planets are compared. For the aqua planets, vent CO2 to the surface. Weathering of silicate rocks releases
we use stratospheric water vapor mixing ratios computed by divalent cations that react with the gas, which sequesters it in
using two non-gray one-dimensional radiative-convective carbonates. On current Earth, increased CO2 leads to higher
models independently developed for Earth-like atmospheres surface temperatures, more weathering, and a stabilizing
with 1-bar background atmospheres. The aqua planets lose sink.
their hydrogen faster and at lower levels of insolation than Here, we examine the analogous cycles on a land planet.
the land planets do, even if the land planets have 1000-fold We assume that water is cold trapped at the poles. The in-
less water to begin with. stantaneous flux of CO2 and water from the interior does not
In general, predicting the water vapor content of the depend on the details of this entrapment. It does, however,
stratosphere is complicated by the nature of the cold trap. On depend on the past volatile history of the planet, that is,
Earth today, the stratospheric cold trap is determined by the subduction of volatiles into the mantle and the presence of
cold, high equatorial tropopause. These are colder than is volatile-rich rocks at depths where crustal metamorphism
typical of the tropopause, and as a result the stratosphere is occurs. We thus quantify the source on an active land planet,
drier than a one-dimensional radiative-convective model using Earth for analogy. We will then examine sinks neces-
would predict. sary to balance the sources, and we will show that volatiles
Dust is another factor that may affect the humidity of the produce stabilizing climatic feedback on a land planet.
land planet’s stratosphere. A land planet’s atmosphere is The fluxes from the interior of the volatile-rich Earth
certainly going to be dusty. A dusty atmosphere may sup- provide an upper limit to the fluxes expected from a similar
press convection, while raising the temperature of the tro- but dry planet. These internal sources are trivial compared to
FIG. 10. The absolute humidity (given as a
volume mixing ratio) at the top of the land-
planet model atmosphere as a function of net
insolation is independent of the total available
water below the threshold. Symbols have the
same meaning as in Fig. 8. Above the thresh-
old, all the planet’s water is in the atmosphere.
The dependence of stratospheric water in the
runaway state on the total amount of water
shows that the dry runaway atmospheres
have cold traps and clouds. Color images
available online at www.liebertonline.com/astHABITABLE ZONE LIMITS FOR DRY PLANETS 455 FIG. 11. How long land planets and aqua planets hold their water. Hydrogen escape is computed in the diffusion limit (Eq. 1). The energy limit (Eq. 2) is shown for comparison. Stratospheric water vapor mixing ratios for land planets are taken from Fig. 10; strato- spheric water for aqua planets is taken from two competing non-gray one-dimensional radiative-convective models of the runaway greenhouse effect (Kasting, 1988; Abe and Matsui, 1988). The pertinent difference be- tween the Kasting and Abe and Matsui models is the stratospheric temperature at low levels of insolation; Kasting assumes 200 K while Abe and Matsui assume 150 K. For aqua planets an ocean of water is pre- sumed to be 2.7 km deep. Land planets are presumed to have much less water, corre- sponding to 2.7 and 27 m global inventories. Nevertheless, the land planets hold on to their water longer and nearer the Sun than do the aqua planets. Color images available online at www.liebertonline.com/ast those of the meteorological cycle. The volcanic water flux, sink for CO2 is carbonate either within sediments or inter- 2 · 1013 mol/yr on Earth, comes mainly from arc volcanoes stitially within hard rock. Weathering reactions that liberate (Oppenheimer, 2003; Wallace, 2005). It returns recently the divalent cations in carbonates from rock do not proceed subducted water to the surface (Staudigel, 2003; Rüpke et al., significantly without liquid water. This requirement sets 2004). The annual flux is equivalent to a global thickness of limits on the efficacy of the cold traps on a warm land planet 7 lm, which is negligible compared to the precipitable water and a lower limit on the global absolute humidity. in the model land planet’s atmosphere. The global CO2, An example to consider is that of a very cold planet where mainly from metamorphism, is *6 · 1012 mol/yr (Brantley no ice ever melts. Degassed CO2 enters the atmosphere, and and Koepenick, 1995). The annual flux changes the global degassed water enters the cold traps. The former process has partial pressure by 0.005 Pa or equivalently changes the the most immediate effect. The global climate becomes concentration in a 1-bar atmosphere by 0.04 ppm per annum. warmer. Eventually, it is warm enough that water is tran- Interior volatile fluxes, however, do add up significantly siently present and comes in contact with rock. This facili- over geological time. We use the flux from ‘‘depleted’’ mantle tates carbonate formation. The climate buffers at the at mid-oceanic ridges to estimate the fluxes on a land planet. temperature where carbonate formation balances the out- That is, we presume that there are few volatile-rich rocks at gassing, analogous to the Urey cycle. depth available for metamorphism and that any subducted Transient melting also acts as a stabilizing effect by oceanic crust and arc volcanics are volatile-poor. Saal et al. opening additional sinks for water that would otherwise be (2002) gave ridge-axis water and CO2 fluxes of 5 · 1012 and trapped in ice caps. The Dry Valleys of Antarctica provide 1012 mol/yr, respectively. an analogy. Liquid water reacts with rocks to form hy- The water flux is significant, compared with probable drous minerals. Water flows into perennially ice-covered traps and sinks, 170 m equivalent thickness per billion years. lakes and into aquifers where it comes into further contact This volume could be reasonably stored in ice sheets or with rock. Mountains are local cold traps that gather water aquifers. Hydrous minerals provide another potentially vo- where it both may melt and charge low-latitude aquifers. luminous sink. For example, greenstone is *10% water (e.g., Overall, processes that increase the availability of transient Staudigel, 2003; Rüpke et al., 2004). water without greatly increasing global humidity favor a In contrast, outgassing of CO2 at our quoted rate of stable dry greenhouse. Sluggish but nonzero CO2 fluxes fa- 1012 mol/yr quickly overwhelms the climate in the absence vor stability. of a rock sink. This flux increases the molecular fraction in a The greenhouse becomes too strong to stabilize surface 1-bar atmosphere to 0.006 in 1 million years and would ac- water/ice if the planet cannot sequester CO2 as fast as it is cumulate as a dense 8-bar atmosphere in 1 billion years. In degassed while maintaining low absolute humidity. Once general, CO2 outgassing would have significant effects un- unstable, the dry greenhouse does not readily return to its less the planet was essentially dead, that is, fluxes < 10 - 3 of previous state. Evaporation of water trapped in glaciers and those of Earth. As with water, plausible rock sinks for the aquifers increases the precipitable water to an equivalent flux exist. A global equivalent thickness of 74 m of CaCO3 thickness of meters. Virtually all this water must escape to would sequester 1 billion years of CO2 output. space for clement conditions to return. Moreover, multiple Here, we concentrate on CO2, as it has the most rapid equilibrium states provide a hysteresis effect that inhibits effects on the climate of a land planet. The only voluminous return to the cool wet state. As the surface becomes hotter,
456 ABE ET AL.
CO2 from degassing enters the atmosphere. As with Venus, It is interesting to ask whether an aqua planet like Earth
the gas does not readily react with rocks in the absence of can evolve into a land planet while remaining habitable.
liquid water. Buildup of CO2 may prevent a previously wet There are (at least) three hurdles: (1) most of the water needs
planet, like future Earth, from emerging from a runaway to escape before the temperature runs away; (2) a full run-
greenhouse as a habitable land planet. away, if it happens, is very hard to reverse, and, as noted
above, it takes very little water to make a runaway; and (3)
Earth might pass through moist greenhouse states that are
5. Earth and Venus
too hot for life to survive the transition.
Figure 12 compares aqua planet and land planet runaway Figure 13 addresses the first and third of these issues with
greenhouse limits for Earth and Venus as a function of time. a one-dimensional approximation, which is the appropriate
The calculation uses the standard main sequence solar lu- choice for an aqua planet entering the moist greenhouse. The
minosity evolution (Sackmann et al., 1993). The Sun reaches one-dimensional model is limited to determine whether most
the main sequence at 50 Myr. This is the same time scale in of the water can escape and whether the moist greenhouse
which the planets accrete. At this time, accretional energy, state is habitable. To address the actual transition from aqua
much of it delivered to the atmosphere in the form of geo- to land planet would require three-dimensional modeling of
thermal heat as the interiors of the planets cooled, would transitional states that we have not yet attempted. We use
have been as important as solar energy in determining the Kasting’s model to describe the relation between net outgo-
climates of Earth and Venus (Abe and Matsui, 1985, 1986; ing thermal radiation FIR and (i) the surface temperature Ts
Matsui and Abe, 1986a, 1986b; Zahnle et al., 1988). Accre- and (ii) the mixing ratio of water ft(H2O) in the stratosphere.
tional energy ensures that both Earth and Venus would The escape rate is taken to be the smaller of the diffusion-
have been in the runaway greenhouse states much of the limited flux and the energy-limited flux. Excess oxygen lib-
time during accretion. Thus, the initial condition for both erated by H escape is not addressed; it is implicitly presumed
planets is hot. to react with crustal rocks and then be folded into the mantle
In Fig. 12, we assume Bond albedos between 0.3 and 0.35 as ferric iron.
for aqua planets. These are comparable to Earth today and to Figure 13 addresses three cases. If we assume a constant
Bond albedos for Jupiter, Saturn, Uranus, and Neptune, albedo, here 0.3, Earth will not lose an ocean of water before
which are examples of deep cloudy atmospheres; the albedo the classic thermal runaway takes place. The moist green-
of a cloudy water-vapor atmosphere might well be higher. house regime does not last long enough. For a wide range of
For Earth, albedos between 0.3 and 0.35 place the onset of parameters (not shown), Earth would lose about 0.2–0.3
the moist greenhouse effect between 7 and 8 Gyr. Kasting oceans of water (about 1 km) before the surface temperature
(1988) considered a single suite of deep water-cloud models runs away. This amount of escape is determined by the pace
that admitted a wide range of outcomes, with albedos be- of solar luminosity evolution ca. 7 Gyr, and is independent of
tween 0.35 and 0.8, depending on cloud cover and cloud the size of the ocean (i.e., 1 km is lost whether the ocean is
altitude. But Kasting’s standard model does not include initially 1 or 10 km deep).
clouds. In this model, Earth has a very low effective albedo When we do the same calculation for Kasting’s (1988)
of 0.2 when it encounters the moist greenhouse *1 billion model, we get the result that Kasting anticipated: a full ocean
years from now. The low albedo stems from absorption of of water escapes before the surface temperature runs away.
sunlight by water vapor. For land planets, we assume al- This happens because the thicker wetter atmosphere is a
bedos between 0.25 and 0.3. If Earth were a land planet, it better Rayleigh scatterer; thus the albedo increases as the Sun
would remain habitable until 9.5 Gyr, which is *5 billion gets brighter. This is a negative feedback that prolongs the
years from now. moist state and thus permits a great deal more H escape
FIG. 12. Aqua planet and land planet runaway
thresholds are shown for Earth and Venus in the
context of the main sequence evolution of the Sun.
Luminosity increases while X-ray and EUV emis-
sions decrease; the latter are important drivers of
hydrogen escape. We assume constant Bond al-
bedos between 0.3 and 0.35 for aqua planets and
between 0.25 and 0.3 for land planets. Earth will
cease being a habitable ocean world some 2.5 bil-
lion years from now. If it were a land planet, Earth
could be habitable for an additional 2–2.5 billion
years. Venus has an uncertain beginning. It may or
may not have had liquid water oceans. But in
principle Venus could have been a habitable land
planet as recently as 1 billion years ago. Color
images available online at www.liebertonline
.com/astHABITABLE ZONE LIMITS FOR DRY PLANETS 457
before the true runaway takes place. This sort of negative occupies an ambiguous position in regard to the runaway
feedback is a general property of any model in which albedo greenhouse effect. If an aqua planet, both runaway and
increases as the stratosphere gets wetter. Because this sort of nonrunaway states are plausible at first. The critical albedo is
relationship between stratospheric humidity and albedo is *0.32. With a nominal, Earth-like albedo of 0.30, Venus is
plausible, it is plausible that many or most aqua planets will predicted to be in runaway when the Sun hits the main se-
be able to lose an ocean of water before the surface tem- quence; if a land planet, Venus would have been habitable
perature actually runs away. until fairly recently.
However, even models that successfully rid Earth of most of Figure 14 addresses cases in which Venus begins as an aqua
its water before evaporating all of it get quite warm (Fig. 13). In planet and evolves into a land planet. The three cases assume
Kasting’s model, which contains *1 bar of gases other than constant albedo and 1 bar atmospheres. In all three cases,
water, significant hydrogen escape does not occur until the Venus loses *1 Earth ocean of water. The moist greenhouse is
surface temperature reaches *350 K, and escape is not complete more efficient for Venus than Earth because the young Sun’s
before Ts approaches 400 K. Although plausibly habitable, such luminosity evolves more slowly and the incident EUV is
conditions are not exploited by complex life on Earth. greater. Thus, it seems likely that an early habitable Venus
Workarounds are a thinner atmosphere or another abun- would have lost the bulk of its water before its liquid water
dant carrier of hydrogen. A thinner atmosphere helps be- wholly evaporated. Whether this evolution ends with a hab-
cause, other things equal, water’s stratospheric mixing ratio, itable land planet is an open question. As discussed above, a
and hence the diffusion-limited flux, would be greater (and a runaway greenhouse on a land planet is reversible only if the
thicker atmosphere—say 10 bar of CO2—makes things net insolation is reduced to the critical flux for an aqua planet.
worse). What this means is that the same amount of hydro- If the liquid water wholly evaporated at any point in the
gen escape occurs at cooler surface temperatures. The other evolution, the result would be an irreversible runaway state.
possibility—a different H carrier (H2 and CH4 are the most
plausible)—removes the ocean with no direct connection to 6. Conclusions
the runaway greenhouse effect.
Venus is an interesting case because it would have en- A pale blue dot is not the only model for an Earth-like
countered these thresholds in the past (Fig. 12). Early Venus habitable planet. There is an excess amount of water on our
1.2 500
Ts Ts
Ocean Volume
1 450
constant
albedo=0.3
Ocean Volume (Earth Oceans)
Surface Temperature
0.8 400
Kasting 1988
Ts
0.6 350
albedo
0.4 300
0.2 250
albedo
0 200
4 5 6 7 8 9
Time (Gyr)
NOW
FIG. 13. Three scenarios of Earth’s future encounter with the runaway greenhouse effect. With constant albedo (green), the
encounter takes place at 7.1 Gyr. Escape removes only 20% of a terrestrial ocean (solid curve), and a classic temperature
runaway occurs (dashed curve). Kasting’s model (black) features a low albedo of 0.2 when Earth encounters the runaway,
which puts the runaway at 5.5 Gyr. Thereafter the albedo (dotted curve) rises by Rayleigh scattering. The rising albedo keeps
Earth in the moist runaway state for the 0.8 billion years needed for an ocean of hydrogen to escape. The surface temperature
rises from 350 to 400 K during this time. The third model begins with constant albedo but then raises albedo to maintain a
surface temperature of 350 K. Surface temperatures in all three models are one-dimensional global averages that use Kasting’s
relationship between FIR and Ts. Color images available online at www.liebertonline.com/astYou can also read
