1. SIO 210 Physical properties of seawater (Lectures 2 and 3)
Second and third lectures:
1. Salinity
2. Density
3. Freezing point, sea ice
4. Potential and neutral density, stability, Brunt-Vaisala freq.
5. Sound speed
6. Tracers: Oxygen, nutrients, transient tracers
First lecture:
1. Depth and Pressure
2. Temperature
3. Heat
4. Potential temperature
Talley SIO 210 (2014)

2. 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”
Talley SIO 210 (2014)

3. 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))
Talley SIO 210 (2014)

4. Sea Salt: what is in it? Millero et al. (Deep-Sea Res. I, 2008)
Talley SIO 210 (2014)

5. Conductivity and salinity profilesX
Conductivity and salinity profiles
Data from northern (subpolar) N. Pacific
DPO Figure 3.2
Talley SIO 210 (2014)

6. Salinity
CTD (conductivity, temperature, pressure) for measuring conductivity in a profile (on the fly)
Autosalinometer for running salinity analyses relative to standard seawater
Bottles for collecting water samples
DPO Chapter S16
Talley SIO 210 (2014)

7. Salinity accuracy and precision
Accuracy Precision
Old titration salinities (pre-1957)
0.025 psu psu
Modern lab samples releative to reference standard
0.002 psu psu
Profiling instruments without lab samples
? ?
Talley SIO 210 (2014)

8. “Absolute salinity” (TEOS-10)
Absolute salinity = reference salinity + correction for other stuff
SA = SR + δSA
Reference salinity SR = /35 * Practical salinity = *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)
Talley SIO 210 (2014)

9. 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).
DPO Figure 4.15
Talley SIO 210 (2014)

10. Surface salinity Aquarius satellite salinity tour
Talley SIO 210 (2014)

11. Atlantic salinity section
DPO Figure 4.11b
Talley SIO 210 (2014)

12. 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
NCEP climatology DPO 5.4
Talley SIO 210 (2014)

13. Return to Atlantic potential temperature: what about this inversion – why is it vertically stable?
Talley SIO 210 (2014)

14. X
S. Atlantic (25°S)
We now see how the water column can be stable with a temperature minimum, since there is also a large salinity minimum.
Talley SIO 210 (2014)

15. 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)

16. Equation of state (EOS) for seawater
Common way to express density is as an anomaly (“sigma”)
 (S, T, p) = (S, T, p) 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)

17. Seawater density From Gill textbook Appendix
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)
Rescan this!
From Gill textbook Appendix
Talley SIO 210 (2014)

18. 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:
Thermal expansion coefficient
Haline contraction coefficient
Adiabatic compressibility
Generally positive for seawater
Positive
Positive
Talley SIO 210 (2014)

19. Seawater density dependence on pressure
For water parcel at 0°C, S = 35 (psu)
DPO Figure 3.4
Talley SIO 210 (2014)

20. Dependence of density on T, P
Add plot with dependence on salinity
Talley SIO 210 (2014)

21. Seawater density, freezing point
Return to in Distributions lecture
DPO Figure 3.1
Talley SIO 210 (2014)

22. Where does most of the volume of the ocean fit in temperature/salinity space?
75% of ocean is 0-6°C, psu
50% is °C, psu (=27.6 to 27.7 kg/m3)
Mean temperature and salinity are 3.5°C and 34.6 psu
First set of slides repeats what was shown in physical properties lectures
DPO Figure 3.1
Talley SIO 210 (2014)

23. 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?
Talley SIO 210 (2014)

24. 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 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.
Staudigel video under sea ice. Look about 10 minutes in for brinicles.
Talley SIO 210 (2014)

25. Surface density  (winter)
Surface density sq (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).
DPO Figure 4.16
Talley SIO 210 (2014)

26. 4. Potential density: compensating for compressibility
Adiabatic compression has 2 effects on density:
Changes temperature (increases it)
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)

27. 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)

28. 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)
Talley SIO 210 (2014)

29. Potential density profiles ( & 4): note different absolute range of values because of different ref. p
DPO Figure 4.17
Talley SIO 210 (2014)

30. 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)
Talley SIO 210 (2014)

31. Potential density: density computed relative to 0 dbar and 4000 dbar  4
DPO Figure 3.5
Talley SIO 210 (2014)

32. 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
DPO Figure 3.5
Talley SIO 210 (2014)

33. Atlantic section of potential density referenced to 0 dbar ( )
Note deep potential density inversion - need to use deeper reference pressures to show vertical stability
Talley SIO 210 (2014)

34. 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)
Talley SIO 210 (2014)

35. Atlantic section of potential density referenced to 4000 dbar: 4
Potential density  inversion vanishes with use of deeper reference (4 ): in fact, extremely stable!!
Talley SIO 210 (2014)

36. 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
Talley SIO 210 (2014)

37. Isopycnal analysis: an isopycnal surface from the Pacific Ocean
Depth Salinity
WHP Pacific Atlas (Talley, 2007)
Talley SIO 210 (2014)

38. Isopycnal analysis: an isopycnal surface from the Pacific Ocean
Potential temp. Salinity
WHP Pacific Atlas (Talley, 2007)
Talley SIO 210 (2014)

39. 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.
Talley SIO 210 (2014)

40. Atlantic section of “neutral density”: n
Talley SIO 210 (2014)

41. 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 19
Talley SIO 210 (2014)

42. 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)

43. 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
DPO Figure 3.6
Talley SIO 210 (2014)

44. 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 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.
Talley SIO 210 (2014)

45. 5. Ocean acoustics: sound speed
Seawater is compressible/elastic  supports compressional waves or pressure waves
Send
Therefore, a 20 Hz sound in the water is 75m long whereas a 20 Hz sound in air is 17m long.
Sound speed:
Adiabatic compressibility of seawater
(if compressibility is large then c is small;
if compressibility is small then c is large:
Talley SIO 210 (2014)

46. Sound speed cs and Brunt-Vaisala frequency (N) profiles N cs 
Talley SIO 210 (2014)

47. Sound is a compressional wave
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
Talley SIO 210 (2014)

48. 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
Talley SIO 210 (2014)

49. Sound speed profile: contributions of temperature and pressure to variation of c
Temperature contribution
SOFAR channel T c S
Pressure contribution
At Ocean Weather Station PAPA in the Gulf of Alaska at 39°N
DPO Figure 3.7
Talley SIO 210 (2014)

50. • c increases ~5m/s per °C • c increases ~1m/s per psu S
Sound speed equation
Sound speed c has a complicated equation of state (dependence on T, S, p), but approximately:
c = T – 0.053T (S – 35) p
(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
send
Typical sound speed profiles in open ocean
Talley SIO 210 (2014)

51. Sound channel, or SOFAR channel (a wave guide)
Mid-latitude
High-latitude
send
Talley SIO 210 (2014)

52. Animation of sound paths and staggered arrivals:
each path has a different traveltime….
transmitter
receiver
send
Talley SIO 210 (2014)

53. Typical sound frequencies
Frequency
application
10-500Hz
whales
50-400Hz
Tomography, thermometry
5-15kHz
Acoustic navigation, pingers, deep echosounders
10-100kHz
dolphins
75-300kHz
ADCPs (100m-600m range)
40-400kHz
Zooplankton/fish sonars
send
Talley SIO 210 (2014)

54. 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
Talley SIO 210 (2014)

55. Tracers on isopycnal surfaces
Oxygen Chloroflourocarbons
WHP Pacific Atlas (Talley, 2007)
Talley SIO 210 (2014)

56. Tracers on isopycnals 3He 14C WHP Pacific Atlas (Talley, 2007)
Talley SIO 210 (2014)