Today’s Lecture: General circulation
Reference
Hartmann, Global Physical Climatology (1994), Ch. 2, 3, 6
Peixoto and Oort, Ch. 4, 6, 7
Kuhlbrodt et al. (2007), linked from course webpage
5.2 – General circulation of the atmosphere
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Atmospheric transport in response to radiative imbalance
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Mean meridional circulation and eddy circulation
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Energy transport
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Angular-momentum transport
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Moisture transport
Radiative balance requires atmospheric transport
Figures from Hartmann (1994) unless noted
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As we saw in the previous section, the net radiative energy
balance of the atmosphere is Ra = O(−100 W m−2 ); fairly
constant in latitude
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The radiative energy loss is balanced by latent (LP) and
sensible (SH) heat flux from land and ocean; but these are
strong functions of latitude
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Meridional advective atmospheric energy transport (∆Fa ) is
required to provide local energy balance
Streamfunction
The zonal-mean continuity equation (zonal flow is integrated out) is
1
∂
RE cos φ ∂φ
([v̄ ] cos φ) +
∂[ω̄]
=0
∂p
(5.13)
For a non-divergent flow, velocity components can be written with the aid of a streamfunction:
[v̄ ] =
[ω̄] =
g
∂ΨM
2π RE cos φ ∂ p
−g
∂ΨM
2π RE2 cos φ ∂φ
(5.14)
(5.15)
(5.14) and (5.15) satisfy (5.13); normalization, including the minus sign, is convention – but the relative minus sign is
required. To calculate ΨM , first impose boundary condition ΨM = 0 at TOA, then integrate (5.14):
ΨM =
2π RE cos φ
g
p
Z
[v̄ ] dp0
(5.16)
0
The normalization is chosen to give units of kg s−1 (mass streamfunction); the cos φ factor is required to ensure constant
ΨM for constant meridional flow. Mass transport is tangent to contours of the streamfunction. Mass flow between two
contours is equal to ∆ΨM .
Note the corrected typo in (2.9)
Mean meridional circulation
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Hadley cell with rising branch in the ITCZ and descending in
the subtropics
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Transport is from winter hemisphere to summer hemisphere at
the surface, summer hemisphere to winter hemisphere at
altitude → transport of potential energy, latent heat, sensible
heat
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Mass transport by mean circulation is small outside the
Hadley cell
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This is where (temporal and zonal) fluctuations in the
circulation are important – eddy transport
Averaging operators
Temporal mean
A = A(λ, φ, p) =
1
Z
τ
τ /2
and the zonal mean
[A] = [A](φ, p, t ) =
A(λ, φ, p, t ) dt
(5.17)
A(λ, φ, p, t ) d λ
(5.18)
−τ /2
1
2π
Z
2π
0
The instantaneous value of A is given by
A = A + A0
where
A0
(5.19)
is called the fluctuating component of A. Likewise
A = [ A] + A∗
(5.20)
where A∗ is the departure from the zonal mean.
Decomposition of a field into time-average and fluctuating, zonally symmetric and zonally asymmetric components:
A = [Ā] + [A0 ] + Ā∗ + A0∗
(5.21)
Decomposition of the flow
Products of fields contain covariance terms (where fluctuations do not average to zero)
AB = ĀB̄ + A0 B0
(5.22)
[AB] = [A][B] + [A∗ B∗ ]
i h
i
h i h ih i h
AB = Ā B̄ + Ā∗ B̄∗ + A0 B0
(5.23)
(5.24)
The terms in (5.24) are the mean circulation, stationary eddies, and transient eddies. To take a concrete example, the
decomposition of northward flux of sensible heat is
h i
h ih i
cp vT = cp v̄
h
i
h
T̄ + cp v̄ ∗ T̄ ∗ + cp v 0 T 0
i
This week’s homework will analyze the relative importance of each contribution as a function of latitude.
(5.25)
Meridional energy transport
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Recall static energy (2.61): sum of potential energy
(PE), sensible heat (SH) and latent heat (LH)
h = gz + cp T + Llv q
(5.26)
The (divergence of) poleward transport of these energy
terms balances the atmospheric energy budget.
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Mean transport dominates in the Hadley cell – but note
large terms of opposite signs
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Eddy transport, especially in winter (large temperature
gradient), dominates in midlatitudes
5.3 – General circulation of the oceans
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Meridional overturning circulation
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Definition
Functions in the climate system: meridional heat transport, heat storage in the deep ocean
Meridional overturning circulation
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Definition: meridional–vertical
circulation
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Function:
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meridional heat
transport
vertical heat storage
(also CO2
storage)
Structure:
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Upwelling processes that
transport volume from depth
to near the ocean surface
Surface currents that transport
relatively light water toward
high latitudes
Deepwater formation regions
where waters become denser
and sink
Deep currents closing the
loop
Timescales: millennial
Figure: Kuhlbrodt et al., 2007
The global conveyor belt
Meridional overturning circulation
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Upwelling processes that transport volume from
depth to near the ocean surface
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Surface currents that transport relatively light
water toward high latitudes
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Deepwater formation regions where waters
become denser and sink
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Deep currents closing the loop
Deepwater formation
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Density dictates vertical motion
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Temperature of all oceans is approximately
−2◦ C at the poleward boundary (ice formation)
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Whether water is dense enough to sink is
decided mainly by salinity
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Sufficient salinity is reached in the north Atlantic
and under the Antarctic ice sheets (due to brine
production during freezing)
Figure: Kuhlbrodt et al., 2007
Surface circulation
Murman
Greenland
Irminger
Arctic Circle
60
Norway
North
Atlantic
drift
o
Alaska
Oyeshio
Labrador
45 o
30
o
15
o
North Pacific
California
Kuroshio
Gulf
Stream
Florida
Canaries
North Equatorial
Equatorial Countercurrent
0o
C.C.
South Equatorial
-15 o
-30
o
Peru
or
Humboldt
-45 o
-60
Benguala
Agulhas
N. Eq. C.
Eq.C.C.
S. Eq. C.
West Australia
Falkland
West wind drift
or
Antarctic Circumpolar
West wind drift
or
Antarctic Circumpolar
warm currents
cool currents
Figure: Stewart 2008
S. Eq. C.
Somali
Brazil
East
Australia
o
Guinea
N. Eq. C.
Equator
N. north
S. south
Eq. equatorial
C. current C.C. counter current
Partitioning between atmospheric and oceanic transport
Figures: Trenberth and Caron (2001), Wunsch (2005)
Partitioning of meridional transport between oceans
Note the anomalous equatorward transport in
the South Atlantic Ocean
Figure: Hartmann (1994)
Oceanic heat uptake
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Ocean warming dominates the global energy uptake
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Warming of the ocean accounts for about 93% of the energy
uptake between 1971 and 2010
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Warming of the upper (0 to 700 m) ocean accounts for about 64%
of the total
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Figure: IPCC AR5
Energy uptake is equivalent to 0.4 W m−2 (global average), or
0.55 W m−2 (ocean average)