density and the equation of state - ccpo€¦ · density and the equation of state ... •...
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Density and the Equation of State • Accurate measurements of density can only be done in
the lab, not in situ (no density sensor).
• Therefore, density is usually calculated from temperature, salinity and pressure using the Equation of State.
• Importance of density for physical oceanography: - ocean stratification, stability and mixing
- ocean currents (geostrophic) depend on horizontal changes in density
- water masses formation and propagation
Downslope
descent
Bottom friction
Dynamics of density
currents and overflows
)(
)()/(
3
3
mV
kgmmkg
),,( PST
eddies
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In situ and potential density
(cgi units) ρ=1.0275 g/cm3 = (SI units) 1027.5 kg/m3
• “Sigma” units: σ = ρ kg/m3 – 1000 kg/m3 = 27.5
σS,T,p = ρ(S,T,P) – 1000 Sigma: in situ density as a
function of salinity, temperature & pressure
σt = ρ(S,T,0) – 1000 Sigma-t: density a particle of water would have at the surface (atmospheric pressure)
σθ = ρ(S,θ,0) – 1000 Sigma-θ: potential density a particle of water would have if raised to the surface adiabatically (function of potential temperature)
Other units: specific volume α = 1/ρ (for geostrophic calc.; later)
σS,T,p specific volume anomaly = αS,T,p – α35,0,p
σt thermosteric anomaly S,T = αS,T,0 – α35,0,0
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measured with CTD calculated properties
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489.1069)1000,5,35(343.1023)0,25,35( Example:
UNESCO
EOS:
Best polynomial
fit to many
observations
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A simple (linear) Equation of State:
ρ = ρ0 + [-(T-T0) + (S-S0) + kp]
– averages values & expansion coefficients:
ρ0=1027 kg/m3, T0=10°C, S=35‰
Thermal expansion: =0.15 kg/(m3 °C)
Salinity contraction: =0.78 kg/(m3 ‰)
Pressure compressibility: k=0.0045 kg/(m3 db),
– When can we use a Linear EOS? • if T,S,p have small variations
• simple process studies
– Accuracy of linear EOS: about ±0.5 kg/m3
– Accuracy of complete EOS: about ±0.001 kg/m3
Note: In the real ocean , & k are not constant, but vary with T,S & P
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Effects of Temperature and Salinity on Density
T
1
S
1
Thermal Expansion Saline Contraction
x 10-4 oC-1 x 10-4 S-1
Density changes by 0.2 kg/m3 for a T change of 1oC,
and by 0.8 kg/m3 for a S change of 1ppt.
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Greater influence of salinity on density
90 % of Ocean Water
Mean T & S for
World Ocean
(not linear)
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• How much σt will change
if S changes by +0.5‰ ?
• How much σt will change
if T changes by +1°C
T\S 0‰ 20‰ 40‰
30°C 0.39 0.38 0.38
10°C 0.41 0.39 0.39
0°C 0.43 0.40 0.40
T\S 0‰ 20‰ 40‰
30°C -0.30 -0.33 -0.35
10°C -0.09 -0.14 -0.18
0°C +0.07 -0.01 -0.17
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Typical density distribution in the ocean
pycnocline: the region
of large change of
density with depth
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T
S
density
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A word of caution about potential
density
“Sigma-4” units
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σθ
σ4
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T-S Diagrams: plots of observed salinity vs.
temperature. Why so useful?
•Water properties change at the surface, but
after sinking to deeper layers only small
changes occur in their properties
•Study water masses and their geographical
distribution
•Study mixing between water masses
•Study motion of water in the deep ocean
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T-S Diagram
Mixing of 2
water types
initial
profile
after
mixing
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T-S Diagram
Mixing of 2
water types
Mixing of 3
water types
initial
profile
after
mixing
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T-S diagram:
useful tool to
diagnose water
masses and how
they mix with each
other
100m
700m
1500m
Antarctic
Bottom Waters
N. Atlantic
Deep Water
Mediterranean
Water
Atlantic
Central Waters
Surface
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Static Stability
• The water’s static stability determines the tendency of
water mass to move vertically, it also affects mixing:
• High stability- minimal vertical movement and mixing
(oceans are mostly stably stratified)
• Low stability- more vertical movement and mixing
(unstable stratification will rapidly mixed until stable or neutral
stability reached)
ρ1
ρ2
ρ
z
Change in potential
energy per unit
volume when parcel
is moved up by
distance Z1 is
PE=(ρ2- ρ1)gZ1
Z1
unstable stable Neutrally
stable
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Stability in continuously stratified ocean:
zE
12c
g
More accurate formula to
account for compressibility
change in deep ocean use
gravity over square of speed of
sound
Oceanographer often use another measure of stability:
Brünt-Väisälä frequency:
Where oscillations have period given by T=2/N
(faster oscillations in more stable stratification)
z
gN
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Weak stratification Strong stratification
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Sound in the sea • Since penetration of visible light is limited in the
ocean, we can not use it to transfer information or to collect data.
• Therefore, sound waves play a much more important role in oceanography than it does in the atmosphere:
– Echo-sounders to measure depth or find ship wrecks
– SONAR to detect submarines or school of fish
– Underwater communication (humans, marine mammals- whales, dolphins..)
– Measuring ocean currents (ADCP)
– Measuring climate change (acoustic thermometry)
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Different types of waves
Longitudinal waves Transverse waves
particle motion parallel particle motion perpendicular
to wave propagation to wave propagation
Orbital waves
particle motion is circular
Sound Waves
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Speed of sound depends on temperature, salinity and depth
C = 1449 + 4.6 T – 0.055 T 2 + 1.4 (S – 35) + 0.017 D (m/s)
k=compressibility
ρ=density
V=volume
P=pressure
c=speed of sound in water (~1500 m/s)
(about 4-5 times faster than in the atmosphere)
Note: without compressibility there would be
no sound, as sound waves propagate through
small fluctuations in pressure
Compressibility and the speed of sound
kc
P
V
Vk
1,
1
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Speed of sound in the ocean:
increases by ~4m/s per 1°C by ~1.5m/s per 1‰ and 18m/s per 1000m
sound channel
Pressure effect
Temperature effect
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The sound channel
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However, Acoustic Thermometry became a controversial issue
and much of the efforts have shifted from measuring climate to
studies of the impact on marine mammals…
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Next Classes:
• Global sun-earth heat balances and heat
transports in the ocean
• Local heat balances and temperature
changes (daily, seasonally, etc.)
• Salt-Fresh Water balances
• Mid-term exam – Monday, Sep. 23, 2013