Contents
1 Dynamical basics, part 1
3
1.1 What drives the atmospheric circulation? . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Conservation laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3 Large-scale circulation: Basic force balances . . . . . . . . . . . . . . . . . . . . . . . 10
1.3.1 Vertical momentum balance: hydostaticity . . . . . . . . . . . . . . . . . . . . 10
1.3.2 Horizontal momentum balance on rapidly rotating planets: geostrophy andthe importance of rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2

Dynamical basics, part 1

Chapter 1

Dynamical basics, part 1

Showman et al. (2013, “Atmospheric circulation ofterrestrial exoplanets,” in Comparative Climatologyof Terrestrial Planets, Univ. Arizona Press)

Here we survey the basic dynamical regimes and mechanisms that occur inplanetary atmospheres. Before presenting any theory, let’s describe qualitatively the kind of regimes that exist. This shows the atmospheric circulationof a generic terrestrial exoplanet:

There are two basic regimes:• Tropics: In the tropics is the Hadley circulation, whereby air rises near
the equator, moves poleward in the upper troposphere, sinks at ∼20–30◦
latitude, and returns to the equator near the surface. This is an efficient means of transporting heat and contributes to the relative constanttemperatures with latitude in the tropics. However, Earth’s rotationprohibits the Hadley cell from extending to the poles. The poleward
movement of air in the upper branch of the Hadley cell causes an eastward deflection due to the Coriolis force, which leads to the so-called
subtropical jets.
• Extratropics: Poleward of ∼30◦ , dynamical instabilities lead to warm

4

Dynamical basics, part 1

and cold eddies (∼1000-3000 km across in the case of Earth) that transport heat poleward. This is called the baroclinic zone and the instability
responsible for producing these eddies is called baroclinic instability. This
is not such an efficient heat-transport mechanism and so the latitudinaltemperature gradient is larger in midlatitudes. The eddies converge momentum into their latitude region, generating the so-called eddy-driven
jet.

Peixoto & Oort (1992)

Let’s look at a few observations for Earth. This shows the annual-meansurface and 200 mbar (∼tropopause) winds. Note weak equatorial winds,
moving slightly westward at the surface. Midlatitude winds are eastward
and get very strong in the upper troposphere. This is the signature ofjet streams.

Showman notes

5

From Peixoto & Oort (1992).

Pressure

Pressure

Pressure

This shows vertical structure of east-west (“zonal”) wind, the streamfunction of the so-called meridional circulation (i.e., the circulation in thelatitude-height plane), and the structure of the longitudinal-mean isentropes:

Peixoto & Oort (1983).

This circulation pattern controls the geographic distribution of vegetation.
The abundant rainfall associated with the rising branch of the Hadley cell
leads to the tropical rainforests (Brazil, central Africa, southeast Asia). The
dearth of rainfall associated with the descending branch of the Hadley cell
leads to the abundant deserts at ∼20–30◦ latitude (the Sahara, central Asia,
the American Southwest, Australia, and South Africa). The midlatitude peakin cloudiness and precipitation associated with the baroclinic zone leads toabundant temperate forests in midlatitudes.

6

Dynamical basics, part 1

Salby (1996)

Poleward heat transport in thebaroclinic zone involves continual
growth and decay of eddies. These
eddies cause the fronts andmulti-thousand-km-long arc-shaped
clouds seen in weather maps andsatellite images at high latitudes andcause most winter weather in the
U.S., Europe, and other midlatitude
locations. They also cause themeanders on the jet stream seen in
the geopotential heights of the
500-mbar surface:Showman, Menou & Cho (2010).

Now let’s look at the circulation of the giant planets.

Jupiter, Saturn, Uranus, and Neptune have radii of 11, 9, 4, and 4 times
that of Earth. They are completely fluid planets with no solid surfaces andShowman notes

7

thus challenge our understanding of how atmospheric circulation should behave in the absence of a surface. They are also rapid rotators, with rotation
periods ranging from 10 hours on Jupiter to 17 hours for Uranus. Cloudtracking shows that the circulation is dominated by zonal jets with speeds
peaking at ∼200 m sec−1 on Jupiter and ∼400 m sec−1 or more on Saturn and
Neptune. These clouds are at pressures of ∼1 bar within a factor of a few.
How winds can be so fast despite the weak solar forcing is not well understood.

1.1

What drives the atmospheric circulation?

Atmospheric circulation is fundamentally a coupled radiation-dynamics problem. In the absence of circulation, the vertical temperature profiles would relax into a local radiative equilibrium, which would be very hot on the daysideand cold at the poles/nightside. The radiative heating rate would everywhere
be zero. When a circulation operates, however, horizontal temperature contrasts imply horizontal pressure contrasts, which drive winds. The winds inturn drive the atmosphere away from radiative equilibrium by transporting
heat from hot regions to cold regions (e.g., from the equator to the poles on
Earth). This deviation from radiative equilibrium allows net radiative heating and cooling to occur, thus maintaining the horizontal temperature andpressure contrasts that drive the winds. Spatial contrasts in thermodynamic
heating/cooling therefore drive the circulation, yet it is the existence of thecirculation that gives rise to these heating/cooling patterns in the first place.

The coupled nature of
the problem can beillustrated with thisflow chart, which represents an infinite loopof cause-and-effect:1

1
See Showman, Menou & Cho (2010), “Atmospheric circulation of exoplanets,” in Exoplanets [S. Seager, Ed.],
Univ. Arizona Press; online at arXiv 0911.3170.

8

Dynamical basics, part 1

On the Earth,for example, theequator and poles
are not in radiativeequilibrium. The
equator is subject
to net heating,the poles to net
cooling, and it is
the mean latitudinal heat transportthat is both responsible for and Figure 1.1: Earth’s energy balance vs latitude, averaged over the year.
driven by these net Blue is absorbed sunlight and red is OLR. Because the circulation mutes
the latitudinal temperature contrasts, the OLR exhibits weaker latitude
imbalances.
variation than absorbed sunlight, and this is what allows the net heating at the equator and net cooling at the poles—which in turn drives
the circulation. Data are an annual-average for 1987 obtained from theNASA Earth Radiation Budget Experiment (ERBE) project. (Source:
M. Pidwirny, www.physicalgeography.net.)

1.2

Conservation laws

Atmospheric circulation is fundamentally controlled by the laws governing
the conservation of momentum, mass, and energy.
Conservation of momentum: This is essentially F = ma applied to a
fluid. The acceleration of a fluid parcel, which is just the rate of change ofthe parcel’s velocity with time, dv
dt , is the sum of the forces per mass thatact on the parcel:
dv
1= − ∇p + g − 2Ω × v + F
dtρwhere p is pressure, ρ is density, g is gravity, Ω is rotation rate, v is
velocity, and F is friction. On the right-side, the forces that act toaccelerate the parcel are the pressure-gradient force, gravity, Coriolis
force, and friction. The Coriolis force acts perpendicularly to both theplanetary rotation vector, Ω, and to the velocity, v. An important rule
to remember is that, in the horizontal force balance, the Coriolis force
acts to the right of the fluid motion in the northern hemisphere and toShowman notes9

the left of the fluid motion in the southern hemisphere.2 3 Friction is
generally small except within a few cm of a planetary surface. However,small-scale turbulent mixing can cause accelerations of the large-scale
flow that in some cases exhibit qualitative similarities to friction. In
models that do not explicitly resolve such small-scale turbulence, thisis often represented with a frictional term.
In a Cartesian frame, where x is eastward, y northward, and z upward,
the momentum equations are
du
1 ∂p
=−
+ 2Ωv sin φ − 2Ωw cos φ + Fx
dt
ρ ∂x
1 ∂p
dv
=−
− 2Ωu sin φ + Fy
dt
ρ ∂y
dw
1 ∂p
=−
− g + 2Ωu cos φ + Fz
dt
ρ ∂z
where u, v, and w are the eastward, northward, and upward velocity
components, φ is latitude, and Fx , Fy , and Fz are the eastward, northward, and vertical frictional forces.
Conservation of mass: Also called the continuity equation, this is
1 dρ+∇·v =0
ρ dtwhich simply states that fractional changes in the volume of a fluid parcel(i.e. nonzero divergence) must be accompanied by changes in the density.
For order of magnitude considerations, it often suffices to treat the fluid
as incompressible, leading to∇·v =0Conservation of thermal energy: This is just the first law of thermodynamics, which is
dT
1 dp
cp
=Q+
dt
ρ dt
2

Northern and southern hemispheres are here defined as those where Ω · k > 0 and < 0, respectively, where k is
the local vertical (upward) unit vector.
3
On a spherical planet, the Coriolis force can intuitively be understood as representing two physical effects. Whena fluid parcel moves poleward (equatorward), conservation of angular momentum about the planetary rotation axis
tends to deflect the parcel eastward (westward). When a fluid parcel moves eastward (westward) relative to theplanetary surface, there is an acceleration away from (toward) the rotation axis. It can be seen that, in both cases,
the force is to the right (left) of the motion in the northern (southern) hemisphere.

10

Dynamical basics, part 1

or alternately
cp

θ
dθ
= Q
dt
T

where θ is potential temperature, θ = T (p0 /p)R/cp , where p0 is a reference
pressure. Q is thermodynamic heating due to radiation, conduction, latentheating, etc.
Together, this set constitutes five equations (the east-west, north-south, andvertical momentum equations, continuity equation, and thermodynamic energy equation) in six unknowns: the three velocity components (u, v, w), ρ,p, and T (or alternately θ). The system is closed by specifying an equationof state, typically ideal gas.
In all of the above equations, the time derivatives on the left-hand sides givethe time rate of change following an individual air parcel as it moves around.
This is called the material or total derivative and, for any scalar quantity
ψ, is given bydψ∂ψ=+ v · ∇ψdt
∂t
The term v · ∇ψ is called the advection term, because it represents the advection (transport) of ψ by the flow.

1.3

Large-scale circulation: Basic force balances

We now consider some basic aspects of the large-scale circulation. In thissection we consider the dominant force balances, in the vertical and horizontal
momentum equations, for typical large-scale circulations. We do this by
estimating the magnitudes of the terms in the equations, allowing small terms
to be thrown out and exposing the dominant balances.
1.3.1

Vertical momentum balance: hydostaticity

Atmospheres are shallow, with horizontal scales greatly exceeding verticalones. Consider the magnitudes of terms in the vertical momentum equation
for a typical terrestrial planet. Let U , W , L, H, τ , and P be the characteristic
magnitudes of horizontal and vertical velocity, horizontal and vertical lengthscale, evolution time scale for the circulation, and pressure change acrossvertical scale H. Terms in the vertical momentum equations have magnitudes

Showman notes

11

1 ∂p
∂w
+ v · ∇w = −− g + 2Ωu cos φ
∂t
ρ ∂z
W
UW
P
g
ΩU
τ
L
ρH
10−7
10−7
10
10
10−3
where the numerical estimates are in m sec−2 and use H ∼ 10 km, L ∼103 km, τ ∼ 105 sec, U ∼ 10 m sec−1 , W ∼ 10−2 m sec−1 , and P ∼ 1 bar,
relevant to Earth.
Clearly, hydrostatic balance dominates. But much of this is a static balancethat has nothing to do with meteorological motions. What we want to do issubtract off the static, background state and look at the balances associatedsolely with meteorological motions. Define p = p0 (z) + p0 and ρ = ρ0 (z) + ρ0 ,where p0 (z) and ρ0 (z) are the time-independent basic-state pressure and den0sity and, by construction, ∂p∂z ≡ −ρ0 g. Primed quantities are the deviations
from this basic state caused by dynamics. Substituting these expressions into
the momentum equation, we obtain


1 ∂p0
∂w
0
+ v · ∇w = −+ ρ g + 2Ωu cos φ
∂t
ρ ∂z
W
UW
∆P ∆ρ
g
ΩU
τ
L
ρH
ρ
10−7 10−7
0.1
0.1
10−3
where the basic-state hydrostatic balance has been subtracted off. The terms
in parentheses give only the flow-induced contributions to the vertical pressure gradient and weight (they go to zero in a static atmosphere). In the−2order-of-magnitude estimate, ∆p ∼ 1000 Pa and ∆ρare the characρ ∼ 10teristic pressure and fractional density perturbations associated with midlatitude large-scale meteorology on Earth, and the numerical values are again
in m sec−2 . The terms in the parentheses on the right side still dominate
by several orders of magnitude. Thus, even after we cancel out the mean
(hydrostatic) pressure gradient and gravity, we find that the meteorologicallyinduced pressure perturbations are in hydrostatic balance with the density
perturbations:∂p0+ ρ0 g ≈ 0∂zTherefore, vertical accelerations are negligible in the force balance
and, for the large-scale circulation, we can replace the vertical momentum equation with “local” hydrostatic balance:
∂p
= −ρg
∂z

12

Dynamical basics, part 1

This analysis can be formalized, and doing so shows that local hydrostaticbalance is a good assumption provided that (i) L2 /H 2  1, and (ii) the fluid
is stably stratified (see Vallis 2006, Atmospheric and oceanic fluid dynamics,
pp. 80-84). Note that this does NOT mean vertical motions do not occur:
they still occur, but the accelerations are simply so small that we do not needto keep track of them in the vertical momentum equation.

1.3.2

Horizontal momentum balance on rapidly rotating planets: geostrophy
and the importance of rotation

A similar scale analysis of the horizontal momentum equation can be performed as follows:∂v
1 ∂p+ v · ∇v = −− 2Ωu sin φ
∂t
ρ ∂y
U
U2
∆P
ΩU
τ
L
ρL
10−4
10−4
10−3
10−3
where again the numbers are m sec−2 . The scaling analysis indicates thatthe time-derivative and advection terms are significantly smaller than thepressure gradient and Coriolis terms, which approximately balance. This canbe formalized by defining the Rossby number, which is just the ratio ofhorizontal advection to Coriolis accelerations:
Ro =

U
fL

where f ≡ 2Ω sin φ is called the “Coriolis parameter.” Thus, whenver Ro 
1, the dominant horizontal momentum balance is between pressure-gradientand Coriolis accelerations. This is called geostrophic balance.

Showman notes

13

The dynamics at Ro << 1 are significantly different from those at Ro & 1.
So we can use this to define regimes:• Extratropics: Regime of Ro  1. Rotationally dominated (geostrophically balanced to leading order). In the presence of latitudinally varying
stellar forcing, can develop significant temperature differences and baroclinic instabilities.
• Tropics: Regime of Ro & 1. Dynamics are ageostrophic, though rotation still usually plays a role. Hadley circulation and wave adjustment
mechanisms tend to maintain small temperature differences.

This gives estimates for the midlatitudes:

Venus
Earth
Mars
Titan
Jupiter
SaturnUranus
NeptuneHD 189733b
Brown dwarf
Earth-sized planet inhabitable zone of M star

RotationΩL−1
U (m/sec)
period(sec )
(km)
Ro
−7
10
243 days
3 × 10
3000
10
−5
10
24 hours
7.3 × 10
1000
0.1
−5
10
24.6 hours 7.1 × 10
1000
0.1
−6
10
16 days
4.5 × 10
1000
2
−4
30
10 hours
1.7 × 10
5000
0.02
−4
4
150
11 hours 1.65 × 10
10
0.05
−5
4
100
17 hours
9.7 × 10
10
0.1
−4
4
200
16 hours
1.1 × 10
10
0.1
−5
1000?
2.2 days
3 × 1050,000?
0.5−4430-300? ∼3-5 hours 4 × 10
10 ?
0.01–0.1−610?
30 days2 × 103000?
∼2?

We can see that Earth, Mars, Jupiter, Saturn, Uranus, Neptune, andbrown dwarfs exhibit geostrophic balance at mid-to-high latitudes, but ofcourse f → 0 at the equator so geostrophy breaks down there. Slowly rotating
planets like Titan and Venus have Ro & 1 across the whole planet, at leastin the upper troposphere and above where winds are fast. Tidally locked hot
Jupiters, due to faster wind speeds and modestly slower rotation than Earth,14

Dynamical basics, part 1

may have Ro ∼ 1, while tidally locked terrestrial planets in the habitablezones of M dwarfs also have Ro & 1 due to their slow rotation periods.
When geostrophy holds, we can write the approximate horizontal momentum balance as
1 ∂p
ρ ∂y
1 ∂p
fv ≈
ρ ∂x

fu ≈ −

What does this mean? Geostrophy implies that the horizontal winds tend
to flow parallel to the intersection of isobars with a horizontal plane. This is
why the pressure field is so useful on a midlatitude weather map: the winds
simply flow along isobars, so one knows the approximate wind field even if
only the isobars, but not winds, are plotted. Importantly, this phenomenon
differs drastically from common intuition, in which air flows from high to low
pressure. In the midlatitudes of rapidly rotating planets, nature does notabhor a vacuum but rather organizes a cyclone around it.

Isobars (black),
isotherms (red)
and
winds
(arrows) near
850 mbar level,in the bottom
part of the troposphere above
the boundary
layer.

Showman notes

Anotherexample, thisone from the
500-mbar level.
This shows theuppertropospheric
jet stream andthe baroclinic
eddies(associatedwith baroclinic
instabilities) as
seen from overthe north pole.
For March 4,
1984 (Salby
1996).
Jupiter’s Great Red Spot, from Choi et al. (2007, Icarus 188, 35-46).

15

Dynamical basics, part 1

Geostrophy also explains
why currents generally flow
parallel to the contours oftime-mean ocean surface
topography (when waves andtides are subtracted off): thehorizontal pressure gradients
just below the ocean surface
are proportional to the
topographic gradients.
Satellite measurements ofglobal ocean topography
therefore determine thesurface currents.
Vertical
Structure of geostrophy: The thermal wind::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
When Ro  1, geostrophy generally holds at all heights except near the surface, where friction becomes strong. This leads to a tight coupling between
the winds and temperatures, or more precisely between horizontal temperature gradients and vertical gradients of the horizontal wind.
To illustrate, imagine a geostrophicallybalanced atmosphere in the presence of ahorizontal temperature gradient. In thewarm air column, the air is less dense
than in the cold air column. Because themass per area contained between isobars
2
p1 and p2 is p1 −p
in hydrostatic balance,g
the isobars are more widely spaced in thewarm air column than the cold air
column. As the diagram makes evident,
this changes the magnitude, andpotentially even the sign, of thehorizontal pressure-gradient force as you
consider different altitudes. When thesepressure gradients are geostrophicallybalanced, this leads to strong variationsin the horizontal wind with altitude.
Thus, in a geostrophic atmosphere, horizontal temperature gradients imply
vertical shear of the horizontal wind. This is called the thermal-wind relationship.
As shown in the diagram, this allows a weather system to be a cyclone at thesurface and an anticyclone at the tropopause (or vice versa).

Measurements from NASA
Topex-Poseidon spacecraft

16

Showman notes

17

Doing this for an atmosphere is complicated by the fact that density is notconstant, but the situation becomes simple if we convert from height to pressure as a vertical coordinate. To do so, express a pressure increment
 
 
 
∂p
∂p
∂p
dp =
dx +
dy +
dz
∂x z
∂y z
∂z x
which implies that    
 
 
∂z
∂p
∂p
∂z
∂Φ
=−
= ρg
=ρ
∂x
∂z
∂x
∂x
∂x
 z
 x,y  p
 p
 p
∂p
∂p
∂z
∂z
∂Φ
=−
= ρg
=ρ
∂y z
∂z x,y ∂y p
∂y p
∂y p
where hydrostatic balance has been used between the second and third stepsand Φ is the gravitational potential (often called “geopotential” in the dynamics literature). This implies that, in the horizontal momentum equations, thepressure gradient force can simply be represented as gradients of geopotential on isobars rather than gradients of pressure on constant-heightsurfaces.
∂Φ∂ΦGeostrophy is then just f u = − ∂y p and f v = ∂x p . Differentiating thiswith pressure,
 


∂u
∂ RT
∂ ∂Φ
f
=
=−
∂p
∂y ∂p
∂y
p p
 


∂v
∂ ∂Φ
∂ RT
f
=
=−
(1.1)
∂p ∂x ∂p∂x
p p
where we have used the fact that, in pressure coordinates, hydrostatic balance
p
1
is ∂Φ
∂p = − ρ , and we have expressed ρ = RT using ideal gas. Absorbing thepressure on the righthand side into the derivative, and assuming R is constant,yields the thermal-wind equations for an ideal-gas atmosphere:
 
∂u
∂T
f
=R
∂ ln p
∂y
 p
∂v
∂T
f
= −R
∂ ln p∂x pHere are some examples. Deep ocean currents are generally weak, and the fastsurface currents exist in a thermal-wind balance with horizontal temperature
gradients. This shows the oceanic Gulf Stream and rings (∼100-km sized
vortices that spin off the Gulf Stream):Dynamical basics, part 1

Olson (1991), Ann. Rev. Earth
Planet. Sci. 19, 283-311

18

Figure 1.2: A warm-core ring showing
isotherms (dashed) and contours of azimuthal current speed (solid), with direction indicated.

Mars: Top panels show zonal- and seasonal-mean temperature (K), measured by the Mars Global Surveyor spacecraft (Smith 2008). Bottom panels
show zonal- and seasonal-mean zonal winds (m/sec) derived from the temperatures assuming thermal-wind balance and zero wind at the surface. Leftcolumn is equinox and right column is northern winter solstice. Notice (i)that greatest vertical wind shear occurs at latitudes where temperature gradients are strongest, and (ii) that predominant wind speed in midlatitudes iseastward.

19

Zonal-mean zonal winds( m sec−1 )Temp (K)Showman notes

June-July-Aug

Dec-Jan-Feb

Annual average

Earth: Left panels show zonal- and time-mean temperatures (◦ C) and rightpanels show zonal- and time-mean zonal winds (m/sec) from observations(Peixoto & Oort 1992). Again notice that (i) peak wind shears occur at latitudes with peak temperature gradients, and (ii) predominant wind direction
is eastward.

20

Dynamical basics, part 1

On the giant planets,
temperatures above theclouds generally exhibit acorrelation with jet shear(cold in anticyclonicregions and warm incyclonic regions), implying
through thermal wind
that, in the upper
troposphere and lower
stratosphere, the jets tend
to decay with altitude
above the clouds. Some
exceptions exist. Thisshows Saturn, but asimilar picture holds forthe other three giant
planets. The details of
why this occurs are notwell understood.

Read et al. (2009), Planet. Space Sci. 57, 1682-1698

It is important to emphasize that thermal-wind balance is not a mechanism to explain the generation and maintenance of particular wind andtemperature patterns; rather, it is simply a statement of force balance. All
we really know from thermal-wind balance is that, wherever there are large
horizontal temperature gradients, there will be large vertical wind shears.
There exist an infinite number of possible configurations for the wind andtemperatures in such a balance, so one needs additional physics to determine
what controls the particular temperature/wind pattern on any given planet.
Still, insofar as the time-mean horizontal temperature gradients are predominantly north-south, with the equator being hotter than the pole and thegreatest temperature gradients in midlatitudes, thermal-wind balance makes
several useful statements:• It shows why the time-mean zonal (east-west) winds are stronger than
meridional (north-south) winds. In other words, given the temperature
distribution, thermal-wind balance provides a partial explanation for thezonally “banded” appearance of the winds on planets.
• Given that temperature gradients peak in midlatitudes, thermal-windhelps explain why the zonal wind shear—hence the upper-troposphericzonal winds themselves—are greater at midlatitudes than in the tropics
or at the poles on Earth and Mars. This is the latitude of the jet streams,
so thermal-wind balance would appear to play a role in showing how thewinds increase with height in the jet streams.

Showman notes21• Since the equator is generally hotter than the poles on terrestrial planets,
thermal-wind balance implies that the zonal wind increases (i.e., becomes
more eastward) with altitude. Assuming the surface winds are weak, this
explains the predominantly eastward nature of the tropospheric winds,
especially in midlatitudes.
It is also worth emphasizing that, since thermal-wind balance only constrains
the vertical wind shear, and not the wind itself, it says nothing about what
controls the wind at the surface.

Reference• Choi, D.S., Banfield, D., Gierasch, P., Showman, A.P., 2007: Velocity andvorticity measurements of Jupiter’s Great Red Spot using automated cloudfeature tracking, Icarus, 188, 35-46.
• Olson, D.B., 1991: Rings in the ocean, Annu. Rev. Earth Planet. Sci., 19,283-311.
• Peixóto, J.P., Oort, A.H., 1983: The atmospheric branch of the hydrologicalcycle and climate, Variations in the Global Water Budget, 5-65.
• Peixóto, J.P., Oort, A.H., 1992: Physics of Climate, American Institute ofPhysics, pp.520.
• Read, P.L., Conrath, B.J., Fletcher, L.N., Gierasch, P.J., Simon-Miller, A.A.,
Zuchowski, L.C., 2009: Mapping potential vorticity dynamics on saturn: Zonal
mean circulation from Cassini and Voyager data, Planet. Space Sci., 57, 16821698.
• Salby, M.L., 1996: Fundamentals of Atmospheric Physics, Academic Press,
pp.627.
• Showman, A.P., Cho, J.Y-K., Menou, K., 2010: Atmospheric circulation of
exoplanets, Exoplanets, University of Arizona Press, 471-576.
• Showman, A.P., Wordsworth, R.D., Merlis, T.M., Kaspi, Y., 2013: Atmospheric circulation of terrestrial exoplanets, Comparative Climatology of Terrestrial Planets, University of Arizona Press, 277-326.
• Smith, M.D., 2008: Spacecraft observations of the Martian Atmosphere, Annu.
Rev. Earth Planet. Sci., 36, 191219.
• (p.5)

http://eoimages.gsfc.nasa.gov/images/imagerecords/57000/

57752/land_shallow_topo_2048.jpg• (p.8)

http://www.physicalgeography.net/fundamentals/images/rad_balance_ERBE_1987.jpg• (p.14) https://commons.wikimedia.org/wiki/File:GFS_850_MB.PNG• (p.16) http://sealevel.jpl.nasa.gov/images/ostm/newsroom/press-releases/
images/topo_arrows.gif