Lecture 3: Terrestrial
Planets
Adam P. Showman
University of Arizonaon sabbatical at Peking University

Recap of qualitative dynamical regimes:

Showman et al. (2013b, “Atmospheric circulation of terrestrial exoplanets”
in the book Comparative Climatology of Terrestrial Planets)

Key dynamical length scales
In the extratropics, the natural horizontal length scale associated with geostrophic
adjustment (and other processes involving the interaction of gravity and rotation) is the
Rossby deformation radius,

where c is the gravity wave speed. In the tropics the equivalent natural length scale,called the equatorial deformation radius, iswhere b=df/dy is the gradient of the Coriolis parameter with northward distance, y.

Extratropics
Ro << 1; dynamics is in geostrophic balance
Geostrophy enables large horizontal temperature contrasts (cf Charney 1963)

where F=U2/gD is a Froude number and Ro=U/fL is the Rossby number. Here D is the depth of thesystem, U is wind speed, f is Coriolis parameter, L is horizontal lengthscale, and g is gravity. For
Earth-like parameters, we obtain a temperature difference of ~0.01.
Large horizontal temperature contrasts and sloping isentropes imply that extratropics are generally
baroclinically unstable. In analytic theory, the most unstable zonal wavelength is typically ~4LD,
with growth rates scaling withFor Earth-like conditions, these imply length scales of ~4000 km andgrowth timescales of 3-5 days.
Baroclinic instabilities generate eddies that dominate much of the
dynamics, controlling equator-pole heat fluxes, temperature
contrasts, meridional mixing rates, vertical stratification, and jet
formation

Tropics
Ro ~ 1; dynamics is inherently ageostrophic
Horizontal temperature contrasts tend to be small (cf Charney 1963)

which is significantly smaller than in the extratropical case. Inserting Earth parameters
gives ~0.001.

Baroclinic instability less important or negligible (compared to the extratropics)

Temperature structure regulated by Hadley circulations and wave adjustment,
contributing to the relatively small horizontal temperature differences, the so-called “weaktemperature gradient” or WTG regime.

Let’s look at some GCM experiments to illustrate these mechanisms
and address the following questions:• How do fundamental mechanisms of atmospheric circulation vary withrotation rate, atmospheric mass/composition, incident stellar flux, etc? How
do these parameters affect strength, width, location, properties of Hadley
cell, jet streams, mixing rates, temperature distributions, wind speeds, etc?

• Why are equator-to-pole temperature differences on Venus and Titan somuch smaller than on Earth? Why is that of Mars greater? What controls
the equator-pole temperature contrast generally?

• Implications for habitability?

•

Implications for observations of terrestrial exoplanets?

Observations

Reference Earth GCM experiment

Kaspi & Showman (2015)

Latitudem = moist static energy= CpT + gz + Lq

vm = vm + v'm'
T = temperaturez = geopotentials = specific humidity
L = latent heat of vaporization

LatitudeKaspi & Showman (2015)

Energy flux (PW)

vm
v'm'

Energy flux (PW)

Meridional temperature distribution (Earth case)

Eddy length scale decreases inversely with rotation rate, as expected from analytic
theory. Note the greater equator-pole temperature differences at high rotation rate.

Kaspi & Showman (2015)

Effect of planetary rotation on baroclinic eddies

Kaspi & Showman (2015)

Mid-troposphere vorticity

Streamfunction(color)zonal wind(contours)

Effect of planetary rotation

Temp(color)mom flux(contours)

At fast rotation
rates, the HC isconfined near
the equator, andthe barocliniczone exhibits
multiple eddydriven jets.

Kaspi & Showman (2015)

Width of Hadleycell (HC)increases withdecreasing
rotation rate,
becoming nearly
global at theslowest rotation
rates.

Effect of planetary rotation

Meridional energy flux (PW)

Equator to pole temp. diff.

The smaller eddies in the more rapidly rotating models are less efficient attransporting thermal energy, and the Hadley cell is narrower, both of which
contribute to greater equator-to-pole temperature difference at fast rotation rate.

Rotation Period (hours)

Rotation Period (hours)

Kaspi & Showman (2015)

Surface temperature

Incident stellar flux

LatitudeLatitude (deg)Kaspi & Showman (2015)

Atmospheric Mass
Energy flux (PW)

Surface temperature

Vary surface pressure, keeping gravity constant at Earth value(bar)Kaspi & Showman (2015)

LatitudeLatitudeKaspi & Showman (2015)

Summary• Rotation rate, atmospheric mass, solar constant, planetary mass andplanetary mean density have an order unity affect on the dynamical
structure of the circulation, including the equator to pole temperature
gradient.
• The equator to pole temperature gradient is important in characterizing
climate and habitability (e.g., it is important for determining whether aplanet can enter a snowball state).
Temperature gradients increase

Temperature gradients decrease• Faster rotation• Larger planetary mass
• Larger planetary density• Larger atmospheric mass
• Larger solar flux
• Larger radiative time scale

Extratropics: Role of baroclinic eddies in controlling thermal structure

Meridional temperature gradient

Schneider & Walker (2006)

Vertical stratification

Some numerical evidence suggests that baroclinic instabilities cause the extratropics
to adjust to a state where isentropes slope by a scale height over a planetary radius(implying that vertical stratification scales with meridional temperature gradient).
This could explain this property of Earth’s extratropics. More on this in the lecture
on jets.

Rossby waves

Mechanisms of extratropical jet formation: role of
Rossby waves
Grouppropagation

In the extratropics,
regions of Rossby
wave generation
correspond toeastward eddy-driven
jets. Regions of
Rossby wave
damping correspondto westward flow.

Phase
propagation

Phase
propagationGroup
propagation

Mechanisms of jet formation: role of Rossby waves
Grouppropagationu’v’<0Phase
propagation

The eddy acceleration
term is positive(eastward) in theregion of Rossby
wave generation, andnegative (westward)
in the region of
Rossby wave
damping/breaking.

u’v’>0Phase
propagationGroup
propagation

Zonal jets

Schneider & Walker (2006)

Hadley circulation
Regulates the thermal structure in the tropics. Exerts a significant effect on the mean climate.
Although the real Hadley cell has strong 3D structure, it can be idealized as a 2D circulation—
unlike the case of heat transport by baroclinic eddies in the extratropics.
All the terrestrial planets with thick atmospheres—Earth, Mars, Venus, Titan—have Hadleycirculations.
Planetary rotation exerts strong control over the Hadley circulation. It’s useful to think about thelimit where the upper branch conserves angular momentum about the rotation axis,

where a is planetary radius. If the ascending branch is at the equator and exhibits zero zonal wind,then the zonal wind in the upper (poleward flowing) branch is

For Earth conditions, this yields wind speeds of 134 m/s, 1000 m/s, and infinite at latitudes of 30 o,
67o, and the poles. This is of course impossible, and implies that rotation, if sufficiently strong, will
confine the Hadley circulation to low latitudes.
This eastward upper tropospheric wind, which peaks near the outer edge of the Hadley cell, is thesubtropical jet.

Effect of planetary rotation

Note howwidth of
Hadley cellincreases withdecreasing
rotation rate,
becoming
nearly global
at the slowest
rotation rates.

Temperature
gradients are
relatively weakacross most of
the Hadley
cell.

Temp
(color)mom flux(contours)

Kaspi & Showman (2015)

Streamfunction(color)zonal wind(contours)

Hadley circulation
The Hadley circulation can exhibit different regimes depending on the extent to which the upper
branch is angular-momentum conserving. Consider the zonal-mean zonal wind equation from 3D
primitive equations, using pressure as a vertical coordinate:

where w=dp/dt is the vertical velocity in pressure coordinates. Overbars and primes denote zonalmeans and deviations therefrom. Denote the eddy terms by –S and consider the statistical steadystate:For Earth, the first term on the right side is not dominant, so that we can write (e.g., Held 2000,
Walker & Schneider 2006):

where RoH = -z/f is a Rossby number associated with the Hadley circulation.
Essentially, RoH is a measure of the strength of eddies on the Hadley cell, which exhibits different
behaviors depending on whether RoH is large or small.

Hadley circulation
The Hadley circulation exhibits different behavior depending on whether RoH is large or small.
When eddy accelerations are negligible, then S=0, and for non-zero circulations the absolute
vorticity must therefore be zero within the upper branch, i.e., f+z=0, or, in other words, RoH1.
The definitions of relative vorticity and angular momentum imply that

A circulation with zero absolute vorticity therefore exhibits angular momentum that is constantwith latitude. This is simply the angular-momentum conserving limit. The Hadley cell in this limit
is thermally driven.

On the other hand, eddy accelerations are often important in shaping the Hadley circulation. If
RoH<<1, then the zonal momentum balance iswhich means that the strength of the Hadley circulation is solely controlled by the amplitude of theeddy acceleration (and not, at least directly, by thermal forcing).
Real Hadley circulations lie between these two extremes.

Hadley circulations
For Earth and Mars, the primary eddy effects result from absorption of equatorwardpropagating Rossby waves that reach critical levels on the flanks of the subtropical jets.
These waves break and cause a net westward torque, removing angular momentum.
This implies that the angular momentum in the upper branch decreases with latitude
away from the equator, and helps explain why the subtropical jet is a factor of several
weaker than the angular-momentum conserving limit would suggest.
There is strong seasonality—if the rising branch is located off the equator, as occurs
during solstice, then the so-called “winter cell” (the cell that crosses over the equator into
the winter hemisphere) will have strongly westward winds near the equator, which tend
to lack critical levels and is therefore relatively transparent to the waves.
RoH varies from ~0.3-0.4 in the equinoctal and summer cells to ~0.7-0.8 in the winter cell
(Schneider & Bordoni 2008, Bordoni & Schneider 2008).

Wave adjustment

Kuo & Polvani (1997)

The “dam break” problem for the non-rotating case:

Showman et al. (2013b, “Atmospheric circulation of terrestrial exoplanets”
in the book Comparative Climatology of Terrestrial Planets)

In a 3D tropical atmosphere,
wave adjustment erases
horizontal temperature
differences

Timescale arguments associated with adjustment•

Generally one might crudely expect that if
small fractional temperature differences

large fractional temperature differences•

Relevant damping timescales include friction and radiative timescales. Dynamicaltimescales can be horizontal wave propagation timescales, although advection androtation timescales may be relevant. The precise timescale comparison is thus
probably more complex than shown above (e.g., see Komacek & Showman 2016).

•

The adjustment timescale is often much shorter than the mixing timescale.

•For synchronously rotating Earth-like planets, these arguments suggest large
temperature differences if atmospheric pressure <~ 0.1 bar. For hot Jupiters, theysuggest large temperture differences if the planet is hot enough.

This has important implications for atmospheric collapse on synchronously rotating
planets (e.g., Joshi et al. 1997), and for explaining IR data for hot Jupiters.

Weak damping

Moderate damping

Strong damping

Showman et al. (2013a)

Equatorial superrotation is expected on tidally locked exoplanets
Axisymmetric forcing

Heng & Vogt (2010)

Joshi et al. (1997)

Synchronously locked

See also Merlis & Schneider (2010), Wordsworth et al. (2011), Edson et al. (2011)

Showman & Polvani (2 011, ApJ 738, 71)

Showman & Polvani (2011) showed that the superrotation
results from momentum transport by standing, planetaryscale waves driven by the day-night thermal forcing

That’s it for theoretical aspects.
Now let’s do a brief observational tourof the Solar System’s terrestrial planet
climates.

Earth as a planet•

Earth is the largest terrestrial planet, with a 1bar N2 atmosphere and trace amounts of CO2
and water vapor sufficient to keep temperatures
above freezing.

•

The 3.7-km deep ocean is 260 times theatmosphere mass, implying that Earth has more
fluid volatiles at its surface than any other solid
object in the solar system.

•

Viewing Earth as a planet leads to major
questions: why is the atmosphere made mostly of
N2? Why does it have this mass? Why isn’t theocean ten times more or less massive? Is it acoincidence that the ocean volume is large
enough to cover most of the globe but smallenough to allow continents to stick abovewater?
What processes control Earth’s climate—what are the fundamental global climate feedbacks,
how do they interact with the circulation and how do they relate to planetary climate
and habitability in general?

Zonal-mean zonal wind

Earth as a planet: circulation••

Earth has a Hadley cell at low latitudes anda baroclinic zone at high latitudes, leading tosubtropical and eddy-driven jet streams inthe midlatitudes, relatively flat temperaturepatterns in the tropics, and steeper
isentropes in the midlatitudes.

Mean-meridional streamfunction

The Hadley cell transports heat poleward in
the tropics, and baroclinic instabilities do soin the extratropics.

Isentropes

Much of this structure remains poorly
understood at a deep level. We still do nothave a predictive theory for what controls
Hadley cell width, strength, andtemperature constrasts, nor for the equatorpole temperature difference, nor for whatsets the rate at which baroclinic instabilities
transport heat poleward under given
background conditions

Peixoto & Oort (1992)

Answering these questions requires a “planetary perspective,”
and will be aided by comparison to other planets.

Salby (1996)•

Earth precipitation/vegetation regimes are controlled by its circulation

Peixoto & Oort (1983)

Annual-mean
Precipitation

Width/strength of the Hadley cell and width/structure of the baroclinic zone
determine the location of rainforests and deserts
So what would happen if Earth were rotating faster or slower, if the atmosphericmass were different, if the gravity were different, if the sunlight were different?
These are planetary questions!

•

Venus, geophysically, is a near-twin of Earth:radius and mass 94% and 81% of Earth’s.
Bulk interior composition probably very
similar. Orbits at 0.728 AU.

•

But atmosphere is very different: sulfuric acidcloud layer gives bond albedo of 0.75, reflecting
most of the sunlight•

90 bars of CO2 (~300,000 times more than
Earth!).

•

Venus therefore exhibits a monstrous
greenhouse effect—surface temperature of 740
K—despite absorbing less sunlight than Earth!

•

Venus is a slow rotator: siderial day 243 Earthdays; solar day 117 Earth days. Thisdrastically changes the dynamics (compared to
Earth)•

There is very little horizontal temperature
variability below 60-km altitude, due to a
combination of the massive atmosphere andslow rotation.

Seiff (1983)

Venus

Climate: Why is Venus so different from Earth?
•

Earth’s CO2 is maintained by the carbonatesilicate cycle—a climate feedbacks that keeps
atmospheric CO2 levels low and keeps most of
the carbon stored in carbonate rocks.

•

This cycle relies on the existence of the oceans,
which greatly speed up the loss of atmospheric
CO2.

•

Earth keeps its oceans because the atmosphericcold trap keeps water out of the upper
atmosphere.

•

BUT if Venus ever had oceans, the cold trap may have been less effective, allowing
gradual loss of ocean…. at which point CO2 would start building up in the atmosphere.
D/H on Venus is 100 times the Earth value, consistent with this idea.

•

This raises obvious questions: Did oceans ever exist (can we find evidence for them)?
What does the high D/H ratio imply about initial water abundance? What are the noble
gas abundances and what do they imply about volatile inventories supplied to Venus?
What are the conditions (atmospheric composition, solar flux) under which oceans are
lost? How does the carbonate-silicate feedback cycle really work on Earth or on planets

Venus circulation/clouds
Due to the slow rotation, Venus,
dynamically, is an “all tropics” planet—
Rossby number >> 1 everywhere.

•

Unlike Earth, Venus exhibits a global(equator-to-pole) Hadley circulation.

•

The atmosphere superrotates, carrying
cloud-level air around the planet in 4
days—60 times faster than the underlying
planet moves!

•

This means that the atmosphere has much
more angular momentum per unit mass
than the planet itself—a major puzzle.

•

The clouds form a global deck at about 5060 km altitude, which may trigger local
convection and gravity waves that may be
important for the circulation.

•

Despite the clouds, the planet is very dry

Gierasch et al. (1997)

Schubert (1983)

•

Mars
•

Mars has a thin (0.006 bar) atmosphere of CO2. Liquid water is not stable at the surface.

•

Greenhouse effect is weak due to low pressure, despite having a column abundance of CO2~15 times greater than that on Earth. Atmospheric dust has a strong effect on thermal
structure.

•

Mars has the most Earth-like weather of any planet in the Solar system, because of its similar
length of day (24.6 hours) and axial tilt (25 deg).

•

So circulation regime is similar: Hadley cell at low latitudes, geostrophic flow comprising abaroclinic zone and jet streams at high latitudes, where Ro~0.1. Heat transported to poles by
baroclinic instabilities.

•

Mars gives an example of weather andclimate on a dry world. Comparing the
behavior of Hadley cell, jets, instabilities on
Mars and Earth can yield insights into theseprocesses generally, and the role of moisturein them.

Mars•

Because of the thin atmosphere, the radiative time constant is short on Mars, leading
to larger equator-pole and day-night temperature differences. This leads to fasterwinds and strong seasonal cycles.

Zonal wind (m/sec)

solstice

Smith (2008)

Diagnosis of
zonal winds
from observed
temperaturesusing thermalwind analysis:

Temperature (K)equinoxMars climate: dust storms

How these dust storms
work, including why
they sometimes become
global, is not wellunderstood!

Water ice on Mars
Liquid water is not stable at Mars’ surface today, but the planet has significant
reservoirs of ice at high latitudes. We know from the Gamma Ray Spectrometer on
the Mars Odyssey spacecraft that the uppermost ~1 m of much of the polar regions ofMars (latitudes > 60 deg) is dominated by a hydrogen-bearning material, probably
water ice. The ice could extend significantly deeper.

Boynton et al. (2002)•

•The topography within 10
deg of both poles is locallyelevated, and is known
from radar, imaging, andother data to consist of awater-ice deposit ~2 km
thick and ~1000 km across.
These are the north andsouth polar layered deposits.

•

Outcrops and radar exhibit
fine-scale layering,probably layers of a few %dust intermixed with theice. This layering records
episodic deposition
associated with climate
cycles over millions ofyears.

Byrne (2009, Annu. Rev.)

Mars polar caps

Ice ages on Mars•

Both poles have water ice caps 1-2 km deep,and subsurface ice exists to latitudes ~60 deg,
where it is stable.

•

Yet, evidence exists for ice glaciers at low
latitudes where the ice is not currently stable•

Mars’ obliquity oscillates, and climate
models show that, at high obliquity, ice isstable at low latitudes (and less so at poles)•

Thus, we seem to be witnessing a form of ice
ages on Mars—ice oscillates between low andhigh latitudes in response to Milankovitch
cycles•There are numerous unanswered questions
about how this works and analogies with
Milankovitch cycles and ice ages on Earth.

Byrne (2009)
Low-latitude glaciers (Head et al. 2005, Shean etal. 2007):Long-term climate on Mars

Numerous channels and valley
networks suggest that Mars had awarmer, wetter past.

But how warm? How wet? Did it
once have a thicker CO2 atmospherewith a significant greenhouse effect?
If so, where did the atmosphere go?
And was the planet ever habitable?

Titan•Titan is an icy satellite of Saturn with a thick (1.5 bar)
N2 atmosphere and a surface temperature of 97 K. The“bedrock” is H2O. Radius 2500 km, gravity 1.3 m/s2.

•

Methane forms a hydrological cycle like water on
Earth—methane evaporates out of surface lakes, forms
clouds, and rains, carving valleys in the ice.

•

Only other terrestrial planet besides Earth with a thickN2 atmosphere, and with an active hydrological cycle!

•

Photolysis of atmospheric methane leads to escape ofhydrogen to space and production of higher-orderhydrocarbons, many of which are liquids or solids.
This produces a global, opaque, high-altitude hazelayer, which obscures the surface from view. Thesematerials slowly settle down onto the surface.

•

If not resupplied, all of Titan’s atmospheric methane would be destroyed by photolysis
in ~107 years. The existence of atmospheric methane thus suggests that methane isresupplied from the surface to the atmosphere.

•It was thought in the 1980s to ~2000 that, over solar-system history, photolysis of all thatmethane would lead to a global layer of ethane ~0.5 km thick. Thus global oceans of ethane(and dissolved methane) were predicted.

•

Groundbased data, Cassini and Hugyens showed that there is no global ocean but a desert-likelandscape with river valleys, sand dunes, etc, with lakes near the poles.

•

It’s unclear where the missing organics are. Some may be below-ground in an aquifer. Somemay be in solid form. Or perhaps Titan didn’t always have abundant atmospheric methane
over its history, which would mean that less ethane would have been produced.

Thermal structure and humidity•

Titan has a well-defined troposphere 40
km thick, overlain by a stratosphere anda thermosphere. Here are measurementsfrom the Huygens probe. Wiggles arecaused by atmospheric waves.

•

Methane is cold trapped at thetropopause, but because of the low latent
heat of methane, the effect is not strong.
The (constant) mole fraction of methane
in the stratosphere is only a factor ofseveral less than at the surface.

•This helps enable irreversible methane
destruction/loss over time.

•

This differs from Earth, wherestratospheric water vapor is ~104 times
less than at the tropical surface.

Fulchignoni et al. (2005)

Niemann et al. (2005)

Titan circulation•

Titan is a slow rotator (16 day period), meaning it
is (nearly) an “all tropics” world•

Hadley cell is nearly global; like Venus, Titan
lacks an extensive “baroclinic zone”•

Like Venus, Titan’s atmosphere superrotates.
Comparisons of Venus and Titan may help
elucidate the mechanism.

•

Hazes exhibit considerable structure andseasonality, and rainstorms can be monitoredfrom Earth and spacecraft

Fulchignoni et al. (2005)

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(p.4) http://claspresearch.engin.umich.edu/groups/admg/baroclinic_wave_T850hPa_day9.jpg(p.34) https://disc.gsfc.nasa.gov/education-and-outreach/additional/sciencefocus/images/ITCZ_GOES_large.jpg(p.36左)http://eoimages.gsfc.nasa.gov/images/imagerecords/57000/57752/land_shallow_topo_204
8.jpg(p.37上) http://nssdc.gsfc.nasa.gov/image/planetary/venus/pvo_uv_790226.jpg(p.38) https://upload.wikimedia.org/wikipedia/commons/5/55/Carbon_cyclecute_diagram.jpeg(p.40) http://free-photos-ls01.gatag.net/images/lgf01a201306282100.jpg(p.42左上) http://www.universetoday.com/wpcontent/uploads/2011/10/MarsDustStorms.jpg(p.42右上)
http://cache.boston.com/universal/site_graphics/blogs/bigpicture/mars_06_20/mars13.jpg(p.42下) http://imgsrc.hubblesite.org/hu/db/images/hs-2001-31-a-small_web.jpg(p.46左上) http://solarviews.com/raw/mars/islands.gif(p.46右上) http://solarviews.com/raw/mars/network.gif(p.46左下) http://photojournal.jpl.nasa.gov/jpeg/PIA00414.jpg

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(p.47)
https://upload.wikimedia.org/wikipedia/commons/8/84/Titan_in_natural_color_Cassini.jpg(p.48左) https://media1.britannica.com/eb-media/63/97263-004-BE71CA07.jpg(p.48中) http://photojournal.jpl.nasa.gov/jpegMod/PIA08630_modest.jpg(p.48右) http://nssdc.gsfc.nasa.gov/planetary/titan/huygens_titan_09.jpg(p.50左下) https://www.nasa.gov/images/content/151384main_pia08211_detail.jpg(p.50中下) http://conservapedia.com/images/4/43/Titan_haze_2007.jpg(p.50右下) https://apod.nasa.gov/apod/image/0410/titan1_cassini_big.jpg(p.50中右) http://www2.keck.hawaii.edu/science/titan/041007_nb2108_128.png