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Ocean circulation, dynamics and thermodynamics….
Equation of state for seawater
General T/S properties of the upper ocean
Heat balance of the upper ocean
Upper ocean circulation
Deep circulation
OCN/ATM/ESS 587
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ρ = ρ (S, T, p, ……) [Determined from laboratory experiments]
[ S = salinity; T = temperature; p = pressure ]
Seawater is a complex chemical system that contains traces of nearly all naturally occurring elements. The dissolved part of seawater is about 78% NaCl by mass.
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The chemical composition of seawater….
Amazingly, the proportions of the major constituents of seawater are nearly constant everywhere.
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This constancy of proportions means that to a good approximation, only one component of seawater needs to be measured, and all of the other can be inferred from it. (what are the limitations?)
Instead of characterizing a seawater sample by knowing all of its chemical components, we can characterize the sample by a single parameter. We shall call this parameter the salinity.
Salinity = Mass of salt/(Mass of salt + Mass of water)
Typical ocean salinity ∼ 0.035 = 35 PSU
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How well do we need to measure S? The section of S along 43° S in the S. Pacific shows that there is considerable detail at signal levels ≤ 0.01 PSU.
34.72
34.70
34.60
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Temperature (continued)….
Seawater is slightly compressible. What are the implications of this?
[warming][cooling]
Adiabatic changes in temperature: changes in temperature when there are no changes in heat.
dQ = dq − dW (1st Law of thermodynamics)
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Temperature (continued)….
In situ temperature T increases as depth inceases.
Potential temperature θ does not increase with depth.
T θ
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Density….
ρ = ρ (S, T, p) is the symbolic equation of state.
Over the water column, ρ varies by a few per cent.
ρsurf ∼ 1.021 g/cm3 ; ρbot ∼ 1.071 g/cm3 [typical values]
In the upper ocean, ρ ∼ ρ (S, T) . In the deep sea, ρ ∼ ρ (p) .
Define the parameter σ as a more useful representation of density:
σ = (ρ − 1) × 1000 (cgs) ; σ = ρ − 1000 (mks)
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Typical profiles in the ocean….
σtT
S
[ from Ocean Station P, 50°N, 145°W ]
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Typical profiles (continued)….
•
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Equation of state….
The equation of state for seawater is nonlinear. This has major implications to ocean mixing.
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Ocean circulation: surface currents….
[ 0-500 dbar dynamic ht; maximum range ~ 2 m] [notice E/W asymmetry]
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The pressure field of the upper ocean relative to a depth of 1000 dbar (∼1000 m), from Argo data
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Seasonal variation in SST
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Seasonal variation in SSS….
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The Heat Balance of the Earth (and the ocean’s role)….
Solar heating is ultimately the source of all energy at the Earth’s surface, except for tides and geothermal heating.
The atmosphere and ocean exchange heat and energy in a complicated set of feedbacks.
Recall the 1st law of thermodynamics….Heat is conserved.
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The heat content in the upper 300 m of the ocean has varied over the past 50 years, generally increasing…where has this heat come from?
[from Levitus]
[heating rate ∼ 0.6 °C/century]
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ΔT
ΔS
Δρ
Upper ocean changes in the past 25 years
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ΔT
ΔS
Δρ
Average changes in temperature, salinity, and density in the world ocean as a function of latitude since the middle of the last century, determined using 2004-2008 Argo float observations
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The concept of a flux….
amount of stuff S per unit time
area A
The flux of S is defined as the amount of S crossing the area A per unit time; a flux is just (amount)/(area × time).
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atmosphere
ocean/land/cryosphere/biosphere
The global heat balance (schematic)….
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The heat balance of the ocean….
where QT = net heat input to the Earth (∼ 0 watts/m2)
QS = direct solar input (∼ +150 watts/m2)
QB = black body radiation (∼ −50 watts/m2)
QH = sensible heat loss (∼ −10 watts/m2)
QE = evaporative heat loss (∼ −90 watts/m2)
QV = advective heat transport (0 watts/m2)
QG = geothermal heating (∼ +0.01 watts/m2)
QT = QS + QB + QH + QE + QV + QG
[note: there are errors and uncertainties associated with each of these estimates]
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QS for the Pacific….
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QB for the Pacific….
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The concept of flux-gradient diffusion….
The flux is proportional to the gradient of the concentration, with the constant of proportionality being the diffusivity κ.
[note: this is generally true in the molecular case only]
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QH , conductive (or sensible) heat flux….
Since the ocean is generally at a different temperature than the atmosphere, there will be a conduction of heat between them (recall the two blocks).
Fourier’s Law of heat conduction:
F ∝ − ∇T or
F = − K ∇T[K = diffusivity]
So, QH = c ∂T/∂z, c = ρCpK
[this is an empirical result]
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QH, continued….
Note 1: K = K (T, wind, sea state, humidity…..)∼ 10 – 103 cm2/sec at the sea surface
Note 2: Strictly, the concept of a diffusivity K only applies to laminar flows. Where turbulence occurs (everywhere !), this formulation serves as a parameterization only (“eddy diffusivity”).
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QH for the Pacific….
[note the east-west asymmetry]
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Evaporative heat flux, QE….
The latent heat of evaporation L for fresh water is
L = 2494 joules/kg @ 2 °C
This much energy must be supplied in order for the state transition from liquid to vapor to occur. In the oceanic case, the energy will be extracted from surface seawater in the form of heat, thus having a net cooling effect.
This evaporated seawater will appear as water vapor in the atmosphere, and the latent heat L will be released into the atmosphere upon condensation of the water vapor.
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QE, continued….
Note: QE is generally the largest term in the heat balance equation, after direct solar input QS.
How can QE be estimated? In general the evaporation rate and associated heat flux are a complicated function of a number of variables and can only be estimated empirically,
QE = QE(Toc, Tatm, S, wind, sea state, humidity,….)
Many estimates of the evaporative heat flux exist, using a variety of parameterizations. Estimated errors are not small, in general.
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QE for the Pacific….
[note the east-west asymmetry]
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QT = QS + QB + QH + QE + QV + QG = 0
= Qsurf + QV + QG ≈ Qsurf + QV = 0
where Qsurf = QS + QB + QH + QE
The heat balance….
What is the total surface heat flux from the ocean, Qsurf ?
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Qsurf for the Pacific….
[note east-west asymmetry]
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QS QE
QH Σ
Global heating at the sea surface….
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Qsurf for the Atlantic…. [note east-west asymmetry](watts/m2)
-250
-150
-50 -100
0
+75
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QV , advective heat flux….
Qsurf + QV = 0 [Globally, QV = 0, but this might not be true locally.]
If there is a gain or loss of heat from the sea surface, then the ocean must export or import heat in order to keep the system in thermodynamical equilibrium.
Result: Ocean Circulation.
Thus,
ocean oceansurf vQ dA Q dA= −∫∫ ∫∫
[The integration proceeds over the surface area of a sector of ocean, including the surface, sidewalls, and the bottom.]
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QV, continued….
an ocean losing/gaining heat at the sea surface
an ocean losing/gaining heat via advection through the sides
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QV, continued….
ocean oceansurf vQ dA Q dA= −∫∫ ∫∫
(1) (2)
If (1) > 0 (ocean gains heat from the atmosphere), then (2) < 0 (ocean circulation must transport heat away)
If (1) < 0 (ocean loses heat to the atmosphere), then (2) > 0 (ocean circulation must transport heat in)
Globally, the surface heat budget for the ocean has been estimated from bulk formulae, marine observations, satellites, etc. If we have an estimate of Qsurf, we should be able to estimate Qv.
+ → flux in, − → flux out
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QV continued….
Global ocean heat transport, basin integrated
units: 1013 watts
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QV, averaged along latitude by ocean….
[note: Atlantic is different]
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QV (continued)….
Parameterization of Qv :
Let V equal a velocity normal to some surface,and let T be the temperature of the water flowing with V. The heat transport associated with V and Tis then
QV = ρCVT
where C is the heat capacity and ρ the density.
Check the units:
[heat/area/time, a flux by definition]3 2
heat heatv
M LQ CL M C T L T
⎡ ⎤⎡ ⎤ ⎡ ⎤ ⎡ ⎤= =⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦⎣ ⎦
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QV , continued….
QV = ρCVT
Note the meaning of this parameterization:
Increasing either the temperature, or the flow, will increase the heat transport.
Also note that
warm water flowing north = cold water flowing south(T>0, V>0) (T<0, V<0)
[note: T is measured relative to some reference temperature]
[consider the Atlantic]
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QV , continued….
Northward heat transport by the ocean and atmosphere
•
•
•
•
•
•• Ocean• Atmosphere• Total
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Ocean circulation: surface currents….
[ 0-500 dbar dynamic ht; maximum range ~ 2 m] [notice E/W asymmetry]
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The upper ocean circulation is largely wind-driven.
Annual mean wind stress
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Winds: symmetric; Ocean circulation: asymmetric….why?
wind
ocean circ.
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Large-scale asymmetric gyre….possible
Large-scale symmetric gyre….not possible
[See Stommel (1948) for the details]
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The surface mixed layer in the ocean….
summerwinter mixed layer
[western N. Atlantic]
[ thermostad remainsafter winter ]
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http://flux.ocean.washington.edu
Typical wintermixed layer in the western N. Atlantic, 3/98
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Model results,western N. Atlanticmode water
winter
summer
N S
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mode water
Mode water, resulting from winter mixed layer,exists over much of the western N. Atlantic
N S
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EDW Temperature
80oW 70oW 60oW 50oW 40oW 30oW 20oN
30oN
40oN
50oN
18
1818
Te
mp
era
ture
(oC
)
1717.217.417.617.81818.218.418.618.819
EDW Thickness
80oW 70oW 60oW 50oW 40oW 30oW 20oN
30oN
40oN
50oN
10020
0
400
Th
ickn
ess
(m
)
0
50
100
150
200
250
300
350
400
450
Depth of the Upper Boundary of EDW
80oW 70oW 60oW 50oW 40oW 30oW 20oN
30oN
40oN
50oN
100
100
200200
300
De
pth
(m
)
0
50
100
150
200
250
300
350
400
450
Upper ocean propertiesin March, 1998
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⇒ Low NAO ~ Colder SST in the subtropics
High NAO Low NAO
The North Atlantic Oscillation (NAO)….
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1961 1966 1971 1976 1981 1986 1991 1996 2001−5
0
5W
inte
r N
AO
Inde
x EDW Volume
1961 1966 1971 1976 1981 1986 1991 1996 20010
2
4
6
8
Vol
ume
(1014
m3 )
1961 1966 1971 1976 1981 1986 1991 1996 2001−5
0
5
Win
ter
NA
O In
dex
EDW Temperature
1961 1966 1971 1976 1981 1986 1991 1996 200117
17.5
18
18.5
19
Tem
pera
ture
(o C)
1961 1966 1971 1976 1981 1986 1991 1996 2001−5
0
5
Win
ter
NA
O In
dex
EDW Heat Content
Year1961 1966 1971 1976 1981 1986 1991 1996 2001
0
1.5
3
4.5
6
Hea
t Con
tent
(x1
022 J
)
Long-term variability of western N. Atlantic mode water….
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Mode waters in the world ocean….
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Winter mixed layer depth in the N. Pacific….
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Stommel’sT-O2diagram, suggesting locations of deep water sources
(1958)
Deep circulation….
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•
•
• Stommel’s deep water sources
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Source function for tritium (HTO) input to the ocean(tritium half-life ≈ 12.5 years)
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Tritium in the thermoclineof the world ocean, 1970s
Atlantic
Pacific
Indian
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Tritium in the western N. Atlantic, 1972
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Deep convection and the conveyor belt….
[ apparent time scale: ~1000 years, from 14C ]
Importance of the global deep circulation• long term memory (~ 1 ky)• storage of heat (cold)• sequestration of carbon