SIO 210
Physical properties of seawater
(Lectures 2 and 3)
First lecture:
Second and third lectures:
1. Depth and Pressure
1. Salinity
2. Temperature
2. Density
3. Heat
3. Freezing point, sea ice
4. Potential temperature
4. Potential and neutral
density, stability, BruntVaisala freq.
5. Sound speed
6. Tracers: Oxygen,
nutrients, transient tracers
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1. Salinity
•“Salinity” in the oldest sense is the mass of matter (expressed in grams)
dissolved in a kilogram of seawater = Absolute salinity
•Units are parts per thousand (o/oo) or “psu” (practical salinity units), or
unitless (preferred UNESCO standard, since salinity is mass/mass, but
this has now changed again, in 2010)
•The concept of salinity is useful because all of the constituents of sea
salt are present in almost equal proportion everywhere in the ocean.
•This is an empirical “Law of equal proportions”
•(There are really small variations that are of great interest to marine
chemists, and which can have a small effect on seawater density, but we
mostly ignore them; note that the new definition of salinity in TEOS-10*
takes these small variations into account.)
*TEOS-10 is “Thermodynamic Equation of State 2010”
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Salinity
•Typical ocean salinity is 34 to 36 (i.e. 34 to 36 gm seasalt/kg
seawater)
•Measurements:
Oldest: evaporate the seawater and weigh the salts
Old: titration method to determine the amount of chlorine, bromie
and iodine (prior to 1957)
Modern: Use seawater conductivity, which depends mainly on
temperature and, much less, on salinity, along with accurate
temperature measurement, to compute salinity.
Modern conductivity measurements:
(1) in the lab relative to a reference standard
(2) profiling instrument (which MUST be calibrated to (1))
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Sea Salt: what is in it?
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Millero et al. (Deep-Sea Res. I, 2008)
Conductivity and salinity profiles
Data from northern (subpolar) N. Pacific
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DPO Figure 3.2
X
Salinity
Bottles for
collecting water
samples
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Autosalinometer for
running salinity
analyses relative to
standard seawater
CTD
(conductivity,
temperature,
pressure) for
measuring
conductivity in a
profile (on the
fly)
DPO Chapter S16
Salinity accuracy and precision
Accuracy
Precision
Old titration salinities (pre-1957)
0.025 psu
0.025 psu
Modern lab samples releative to reference
standard
0.002 psu
0.001 psu
Profiling instruments without lab samples
?
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?
“Absolute salinity” (TEOS-10)
Absolute salinity = reference salinity + correction for
other stuff
SA = SR + δSA
Reference salinity SR = 35.16504/35 * Practical salinity =
1.0047*psu
Reference salinity has been corrected for new knowledge (since
1978) about sea water stoichiometry as well as new published
atomic weights.
The correction δSA is for dissolved matter that doesn’t contribute
to conductivity variations: silicate, nitrate, alkalinity
Millero et al. (2008), IOC, SCOR and IAPSO (2010), McDougall et al. (2010)
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Surface salinity
Note range of values and general distribution
Surface salinity (psu) in winter (January, February, and March north of the equator; July, August, and
September south of the equator) based on averaged (climatological) data from Levitus et al. (1994b).
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DPO Figure 4.15
Surface salinity
Aquarius satellite salinity tour
http://podaac.jpl.nasa.gov/AnimationsImages/Animations
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Atlantic salinity section
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DPO Figure 4.11b
What sets salinity? Precipitation + runoff minus
evaporation (cm/yr)
Salinity is set by freshwater inputs and exports since the total amount of
salt in the ocean is constant, except on the longest geological timescales
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NCEP climatology DPO 5.4
Return to Atlantic potential temperature:
what about this inversion – why is it vertically stable?
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S. Atlantic (25°S)
X
We now see how the water column can be stable with a temperature
minimum, since there is also a large salinity minimum.
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2. Seawater density 
Seawater density depends on S, T, and p
 = (S, T, p)
units are mass/volume (kg/m3)
Specific volume
(alpha) α= 1/
units are volume/mass (m3/kg)
Pure water has a maximum density (at 4°C,
atmospheric pressure) of
(0,4°C,1bar) = 1000 kg/m3 = 1 g/cm3
Seawater density  ranges from about 1022 kg/m3 at
the sea surface to 1050 kg/m3 at bottom of ocean,
mainly due to compression
Talley SIO 210 (2014)
Equation of state (EOS) for seawater
• Common way to express density is as
an anomaly (“sigma”)
 (S, T, p) = (S, T, p) - 1000 kg/m3
• The EOS is nonlinear
• This means it contains products of T, S,
and p with themselves and with each
other (i.e. terms like T2, T3, T4, S2, TS,
etc.)
Talley SIO 210 (2014)
Seawater density
Seawater density is determined empirically with lab
measurements.
New references: TEOS-10 and Millero et al. (linked to notes)
UNESCO tables (computer code in fortran, matlab, c) (see link to
online lecture notes)
Talley SIO 210 (2014)
From Gill textbook Appendix
Equation of state for seawater
See course website link for correction to DPO Section 3.5.5
• (S, T, p)
• Changes in  as a function of T,S,p:



d 
dT  dS  dp
T
S
p
 dT  dS  dp
• Thermal expansion coefficient
Generally positive for seawater
• Haline contraction coefficient
Positive
• Adiabatic compressibility
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Positive

1 
 
 T
1 

 S
1 

 p
Seawater density dependence on
pressure
For water parcel at 0°C, S = 35 (psu)
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DPO Figure 3.4
Dependence of density on T, P
T
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p
Seawater density, freezing point
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DPO Figure 3.1
Where does most of the volume of the
ocean fit in temperature/salinity space?
75% of ocean is 0-6°C, 34-35 psu
50% is 1.3-3.8°C, 34.6-34.7 psu (=27.6 to 27.7 kg/m3)
Mean temperature and salinity are 3.5°C and 34.6 psu
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DPO Figure 3.1
3. Digression to freezing point and sea ice
• Freezing point temperature decreases with
increasing salinity
• Temperature of maximum density decreases
with increasing salinity
• They cross at ~ 25 psu (brackish water).
• Most seawater has maximum density at the
freezing point
• Why then does sea ice
float?
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Sea ice and brine rejection
• Why then does sea ice float? (because it is
actually less dense than the seawater, for
several reasons…)
• Brine rejection: as sea ice forms, it excludes
salt from the ice crystal lattice.
• The salt drips out the bottom, and the sea ice
is much fresher (usually ~3-4 psu) than the
seawater (around 30-32 psu)
• The rejected brine mixes into the seawater
below. If there is enough of it mixing into a
thin enough layer, it can measurably increase
the salinity of the seawater, and hence its
density
• This is the principle mechanism for forming
the densest waters of the world ocean.
http://www.youtube.com/watch?v=CSlHYlbVh1c
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Surface density  (winter)
Surface density  (kg m–3) in winter (January, February, and March north of the equator; July,
August, and September south of the equator) based on averaged (climatological) data from Levitus
and Boyer (1994) and Levitus et al. (1994b).
Talley SIO 210 (2014)
DPO Figure 4.16
4. Potential density: compensating for
compressibility
Adiabatic compression has 2 effects on density:
(1) Changes temperature (increases it)
(2) Mechanically compresses so that molecules are
closer together
As with temperature, we are not interested in this
purely compressional effect on density. We wish
to trace water as it moves into the ocean.
Assuming its movement is adiabatic (no sources
of density, no mixing), then it follows surfaces
that we should be able to define. This is
actually very subtle because density depends on
both temperature and salinity.
Talley SIO 210 (2014)
Potential density: compensating for
compressibility
Sigma-t: This outdated (DO NOT USE THIS)
density parameter is based on temperature
and a pressure of 0 dbar
t = (S, T, 0)
Potential density: reference the density  (S,
T, p) to a specific pressure, such as at the
sea surface, or at 1000 dbar, or 4000 dbar,
etc.
 = 0 = (S, , 0)
1 = (S, 1, 1000)
…..
4 = (S, 4, 4000)
Talley SIO 210 (2014)
Potential density: compensating for
compressibility
Potential density: reference the density  (S,
T, p) to a specific pressure, such as at the
sea surface, or at 1000 dbar, or 4000 dbar,
etc.
First compute the potential temperature AT
THE CHOSEN REFERENCE PRESSURE
Second compute density using that potential
temperature and the observed salinity at
that reference pressure.
 = 0 = (S, , 0)
1 = (S, 1, 1000)
…..
4 = (S, 4, 4000)
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Potential density profiles ( &
4): note different
absolute range of values because of different ref. p
DPO Figure 4.17
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An important nonlinearity for the EOS
• Cold water is more compressible than
warm water
• Seawater density depends on both
temperature and salinity.
(Compressibility also depends, much
more weakly, on salinity.)
• Constant density surfaces flatten in
temperature/salinity space when the
pressure is increased (next slide)
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Potential density:
density computed
relative to 0 dbar
and 4000 dbar

4
DPO Figure 3.5
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Potential
density:
reference
pressures
Therefore 2 water
parcels that are the
same density or
unstably stratified
close to the sea
surface will have a
different
relationship at high
pressure
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DPO Figure 3.5
Atlantic section of potential density
referenced to 0 dbar ( )
Note deep potential density inversion - need to use deeper
reference pressures to show vertical stability
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Atlantic section of potential density
referenced to 0 dbar (sea surface): 
Need to use deeper reference pressures to check local
vertical stability (e.g. 4)
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Atlantic section of potential density
referenced to 4000 dbar: 4
Potential density  inversion vanishes with use of deeper
reference (4 ): in fact, extremely stable!!
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Isopycnal analysis: track water parcels
through the ocean
• Parcels move mostly adiabatically
(isentropically). Mixing with parcels of
the same density is much easier than
with parcels of different density,
because of ocean stratification
• Use isopycnal surfaces as an
approximation to isentropic surfaces
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Isopycnal analysis: an isopycnal surface
from the Pacific Ocean
Depth
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Salinity
WHP Pacific Atlas (Talley, 2007)
Isopycnal analysis: an isopycnal surface
from the Pacific Ocean
Potential temp.
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Salinity
WHP Pacific Atlas (Talley, 2007)
Neutral density n
• To follow a water parcel as it travels down and
up through the ocean:
• Must change reference pressure as it changes
its depth, in practical terms every 1000 dbar
• Neutral density provides a continuous
representation of this changing reference
pressure. (Jackett and McDougall, 1997)
• Ideal neutral density: follow actual water
parcel as it moves, and also mixed (change T
and S). Determine at every step along its
path where it should fall vertically relative to
the rest of the water. This is the true path of
the parcel.
• Practically speaking we can’t track water
parcels.
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Atlantic section of “neutral density”: n
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Brunt-Vaisala frequency
• Frequency of internal waves (period is time between
successive crests, frequency is 1/period or 2p/period)
• Internal waves are (mostly) gravity waves
• Restoring force depends on g (gravitational
acceleration) AND
• Restoring force depends on the vertical stratification
• So frequency depends on g and stratification
17
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19
Brunt-Vaisala frequency
• The ocean stratification is quantified by
the measured value of  /z
• The stratification creates a restoring
force on the water;if water is dispaced
vertically, it oscillates in an internal
wave with frequency
N = sqrt(-g/ x  /z)
If the water is more stratified, this
frequency is higher. If less stratified,
frequency is lower.
Talley SIO 210 (2014)
Brunt-Vaisala frequency
Practical calculation of  /z to get exact
frequency, and also an exact measure of how
stable the water column is:
Use a reference pressure for the density in the
middle of the depth interval that you are
calculating over (for instance, you might have
observations every 10 meters, so you would
reference your densities at the mid-point of
each interval, I.e. change the reference
pressure every 10m.
Calculation
(right panel) is
noisy since it’s a
derivative
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DPO Figure 3.6
Brunt-Vaisala frequency
Values of Brunt-Vaisala frequency:
0.2 to 6 cycles per hour
These are the frequencies of “internal
waves”
Compare with frequency of surface waves,
which is around 50-500 cycles per hour
(1 per minute to 1 per second)
Internal waves are much slower than
surface waves since the internal water
interface is much less stratified than the
sea-air interface, which provide the
restoring force for the waves.
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5. Ocean acoustics: sound speed
Seawater is compressible/elastic  supports
compressional waves or pressure waves
Sound speed:
Adiabatic compressibility of seawater
(if compressibility is large then c is small;
if compressibility is small then c is large:
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Sound speed cs and Brunt-Vaisala
frequency (N) profiles

N

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cs
Ocean acoustics
• Sound is a compressional wave
• Sound speed cs is calculated from the
change in density for a given change in
pressure
1/cs2 = /p at constant T, S
This quantity is small if a given change
in pressure creates only a small
change in density (I.e. medium is
only weakly compressible)
• Sound speed is much higher in water
than in air because water is much less
compressible than air
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Sound speed profile: contributions of
temperature and pressure to variation of cs
• Warm water is less compressible than cold
water, so sound speed is higher in warm water
• Water at high pressure is less compressible
than water at low pressure, so sound speed is
higher at high pressure
• These competing effects create a max. sound
speed at the sea surface (warm) and a max.
sound speed at great pressure, with a
mininum sound speed in between
• The sound speed minimum is an acoustic
waveguide, called the “SOFAR” channel
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Sound speed profile: contributions of
temperature and pressure to variation of c
Temperature
contribution
T
SOFAR channel
c
S
Pressure
contribution
At Ocean Weather Station PAPA in the Gulf of Alaska at 39°N
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DPO Figure 3.7
Sound speed equation
Sound speed c has a complicated equation of state
(dependence on T, S, p), but approximately:
c = 1448.96 + 4.59T – 0.053T2 + 1.34 (S – 35) + 0.016p
(gives c in m/s if T in °C, S in psu, p in dbar)
• c increases ~5m/s per °C
• c increases ~1m/s per psu S
• linear increase with pressure/depth
Typical sound speed profiles in open ocean
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Sound channel, or SOFAR channel (a wave guide)
Mid-latitude
High-latitude
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6. Tracers
• Use tracers to help determine pathways
of circulation, age of waters
• Conservative vs. non-conservative
• Natural vs. anthropogenic
• We will return to this topic in “Typical
distributions” lectures
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Tracers on isopycnal surfaces
Oxygen
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Chloroflourocarbons
WHP Pacific Atlas (Talley, 2007)
Tracers on isopycnals
3He
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14C
WHP Pacific Atlas (Talley, 2007)