1. Ch.2: Physical Properties of Sea Water (0.5week)
Ch.2: Physical Properties of Sea Water (0.5week)
2.1: Temperature
2.2: Salinity
2.3: Density
2.4: Tracers
2.5: Sound

2. 2.1: Temperature
K=273+C
Heat capacity Q= ρCpT, ρ~ 1000 Kg/m3, Cp=4000 J/Kg
Pure water, maximum density at 4oC, freezing point: 0oC
Sea water, maximum density at -2oC, freezing point: -2oC

3. Values of density st (curved lines) and the loci of maximum density and freezing point (at atmospheric pressure) for seawater as functions of temperature and salinity. The full density r is st with units of kg/m3.
27.4

4. Pressure
1 Pa = 1 N/m2
1 bar = 106 dynes/cm2 = 105 Pa (atmosphere usage.., whole atmosphere column ~= 1 bar)
1 dbar = 105 dynes/cm2 = 104 Pa = 0.1 bar (ocean usage 1 dbar ~= 1 m water)
The relation between depth and pressure, using a station in the northwest Pacific at 41° 53’N, 146° 18’W.
Obs error:
Pressure is measured with an electronic instrument called a “transducer”. The accuracy reaches up to 2% at 6000m, 3 dbar. This accuracy is sufficient for other variables, T, S, ….. but insufficient to calculate horizontal pressure gradient accurately to give the ocean currents (which is very weak at ~1 dbar over thousands of kilometers).
Therefore, ocean currents need to be calculated using other methods, such as geotrophic method or directly measured.

5. Potential temperature:
Potential temperature:
Water is slightly compressible, temperature increases with higher pressure, about 0.1 to 0.2Co in 1 km depth (<1oK for the entire depth), much smaller than the atmosphere at ~9.8Co/1 km.
Potential temperature is the temperature that a water parcel would have if moved adiabatically to another pressure, most often used, at the surface.
The potential temperature is a function of salinity, temperature and pressure (in situ)
θ(S, T, p)

6. (a) Potential temperature (q) and temperature (T) (°C), (b) conductivity (mmho), and (c) salinity in the northeastern North Pacific (36° 30’N, 135°W).

7. 2.2: Salinity Salinity : because water dissolve materials the most.
1. Major constituents of the solutes:
The principle of constant proportion:
One striking feature is that the proportion of the chemical ingredients in seawater is unvarying in all oceans, although the total amount (i.e. salinity) changes from place to place. (Dittmar (1884) used 77 samples from Challenge expedition, confirming the hypothesis of Forchhammer (1865)).
The primary solutes in seawater are cations (+) and anions (-).
(no local source/sink, conservative properties)
Salt ions: by weight (%)
Chlorine (Cl-)
Sodium (Na+)
Sulphate (SO4 2-)
Magnesium (Mg2+)
Calcium (Ca2+)
Potassium (K+)
total here 99
Bicarbonate(HCO3 -)
Bromide (Br-)
Boric acid (H3BO3)
Strontium (Sr 2+)
Fluoride (F-)
total here 99.99

8. Other constituents:
The seawater also contains small amount of other constituents, in addition to salt ions. Although small amount, some of these solutes are very important. These solutants can be used as tracers, although they may not be conserved and are affected by external processes such as biological acitivity.
Nutrients:
due to biological uptake and release, these are nonconservative properties.
concentration (ppm) (parts per million)
Phosphorus (P)
Nitrogen (N)
Silicon (Si)
Gases (desolved): in dry air (%) in surface water (%)
Nitrogen (N2),
Oxygen (O2),
Carbon dioxide (C02), (a lot in the ocean !)
Tracers:
concentration (ppb , parts per billion)
Lithium (Li)
Iodine (I)
Zinc (Z)

9. 2. Salinity
Absolute Salinity = total dissolved matter (g) / salt water (kg)
= (roughly) 35 o/oo (ppt, parts per thousand)
<==measured by evaporation to dryness, before 1900,
= *chlorinity = chlorine/salt water ( Cl= % * absolute salinity)
<==measured by titration with silver nitrate, , accuracy
= conductivity /conductivity of standard water (psu, practical salinity unit)
<==measured by electric conductivity , after 1980, accuracy
see next figure for example

10. (a) Potential temperature (q) and temperature (T) (°C), (b) conductivity (mmho), and (c) salinity in the northeastern North Pacific (36° 30’N, 135°W).

11. 3. Source / sink of seawater components:
sources sinks
Chloride: Volcanoes Evaporative deposition as NaCl (salt rock)
River influx Net air transfer
Sodium: River influx Evaporative deposition as NaCl(salt rock)
Net air transfer
Basalt-seawater reactions......
The original sources of most of the chemicals dissolved in seawater are the continents, where rocks of various type, composed predominantly of silicates minerals, are chemically (e.g. reaction resulted acid water ) and mechanically weathered (heat/cooling). These elements are then mainly carried into the ocean through river influx . (2.5-4x1015g/year). In addition, Volcanic emanations along the crest of the spreading ocean ridges and in volcanic arcs of subduction zones inject large amounts of salt ions.
The major sinks are chemical reactions (evaporites deposit), exchange with air, and biological processes (shell, ....).
Questions:
* How can salinity maintains the quasi-equilibrium for over a billion years ? (conservation of salt )
* Furthermore, Why the constant proportion principle ?

12. 2.3: Density ρ(S,T,P)= 1021 ~ 1070 kg/m3 ~ 1 g/cm3
This is about 1000 times that of the air .
Since the density is around 1, it is convenient to define it in the sigma unit as:
σS,T,P=ρ(S,T,P)-1000 kg/m3 = 21 ~ 70 (sigma)
Since the compressibility is small for water, in most cases, the pressure effect can beneglected, so we take p=0. The resulted sigma is called sigma-t, and defined as:
σt (S,T)= σS,T,0
Effect of temperature and salinity on density is most conveniently seen in the so called T-S diagram, as in the next figure. Generally, density increases with higher salinity and lower temperature. In the simplest form, neglecting the nonlinearity and pressure effect, the density can be expressed as a linear equation of state
ρ ≈ ρ0 + α(T-T0) + β(S-S0)
where
α=dρ/dT is the thermoal expansion coefficient
β=-dρ/dS is the haline contraction coefficient.
However, the effect of T and S on density can be very nonlinear, especially with temperature near the freezing point. In other words, the two coefficients changes with T, S, P significantly, especially ρα 53x10-6 K-1 at 0oC to 257x10-6 K-1 at 20oC. (ρβ ranges from 785x10-6 psu-1 at 0oC to 744x10-6 psu-1 at 20oC) (all for surface p=0 and S=35 psu). This leads to nonlinearity in the equation of state.
a) the change of density with temperature decreases towards lower temperature, especially at low salinity as in high latitude or estuarine, while the change of density with salinity is almost the same for all the T and S. As such, density is determined mainly by temperature at higher temperature, but but density at low temperature as in the high latitude and in estuarine.
b) Fresher, s<27 ==> maximum density is reached before freezing =>ice can form on the surface => shorter mixing time;
Saltier, s>27 ==> first freeze, before reaching maximum density => the entire water column has to be cooled before freezing => longer mixing time.
1oC
2oC
4oC
-2oC

13. Equation of state: A. Gill, Appendix 3, UNESCO, 1981)
Step 3
Step 3a
Step 3b
Step 1
Step 3c
Step 2

14. T-S diagram
Values of density st (curved lines) and the loci of maximum density and freezing point (at atmospheric pressure) for seawater as functions of temperature and salinity. The full density r is st with units of kg/m3.
FIGURE 3.1
27.4

15. Effect of pressure on density:
Density also increases with depth, almost linearly
Increase in density with pressure for a water parcel of temperature 0°C and salinity 35.0 at the sea surface.
Since the pressure effect does not contribute to horizontal difference and therefore has no impact on horizontal pressure gradient and in turn circulation, this effect should be removed. The simplest way, earlier way, is to simply use the density at the surface pressure σt = σS,T,0. However, although this removes pressure effect on density, it does not remove the density effect on temperature (temperature is slightly higher at higher pressure! Up to 1oC at the ocean bottom as shown in the previous figure). Now, the effect of pressure is removed by using potential temperature in density such that the density is called potential density: the potential density is the density that the water parcel would have if it is moved adiabatically to the reference pressure. That is one first calculate the potential temperature θ at the surface pressure 0 dbar and then the potential density is
σθ=σt(S, θ).
Due to nonlinearity, at depth, the potential temperature is usually calculated at deeper depths, and the associated potential density will also be referenced to different pressure level. The standard levels are 1000, 2000, 3000 and 4000 dbar, the corresponding density will be called σ1, σ2, σ3 and σ4, respectively.
σ1 (S, θ1)= σS, θ1,1000, σ2 (S, θ2)= σS, θ2,2000, σ3 (S, θ3)= σS, θ3,3000, σ4 (S, θ4)= σS, θ4,4000.

16. Further (nonlinear) effects of temperature and salinity on density:
Cabbeling
The nonlinear contour of density on T and S leads to a mixing of different water masses (different T, S sources after mixing on the straight-line in T,S diagram) ) of the same density leads to heavier density, or cabbeling (Witty, 1902). Cabbeling has been found important in the Antarctic region in producing bottom water with two very different water masses.
b) Thermobaricity
Colder water is more compressible than warm water. Two water
parcels of the same initial density, but different T,S when submerged to the same pressure. The colder water will be denser because it has a higher
compressibility, as shown in the figures to the right. Potential density
relative to (a) 0 dbar (and (b) 4000 dbar as a function of potential
temperature (relative to 0 dbar) and salinity. Parcels labeled 1 and 2
have the same density at the sea surface, but different density at
depth. The parcels labeled 2 represents Mediterranean overflow
water (MOW, saltier) and Nordic Seas overflow water (NSOW,
fresher) source waters at their sills. When they sink to the bottom, the
Nordic Sea water becomes heavier, because it is colder and
therefore more compressible (denser toward depth)! Therefore, the
cold and fresh water tend to be at the bottom. Thermobaricity favors a
cold/fresh bottom water below warm/salty water. This effect has been
found important in the Arctic Ocean defining the relative vertical
stratification of the Canadian and Eurasian Basin Deep Waters.
c) Double diffusion
The molecular diffusivity is higher for temperature than for density and this difference in diffusivity can be scaled up to eddy diffusivity. This leads to the double diffusive instability. A warm/salty over cold/fresh stratification can become unstable. An initial W/S pulse will be cooled quickly by the higher temperature diffusivity while maintaining the high salinity. So, it become cold and salty and therefore heavier than the cold/fresh water below to become unstable. Opposite to thermobaricity, double diffusion destabilize warm/salty over cold/fresh stratification. σθ σ4
MOW
NSOW
cabbeling
W, S
C, F
C, S
Double diffusive instability

17. Isentropic surfaces, potential density and neutral densities
Below the surface mixed layer, because of the weak diabatic mixing, water parcels tend to flow adiabatically, i.e. along an isentropic surface. An isentropic surface is one along which water parcels can move adiabatically, that is, without external input of heat or salt.
If there is no salt, density is determined by temperature and pressure only. Given a reference pressure, one can define the isentropic surface uniquely as the potential density surface. However, with salt effect, a water parcel can be mixed with adjacent water of different T and S quasi-laterally and adiabatically, and will then possess different density. That is the density of the parcel will depend on its pass way due to the effect of thermobaricity (as shown in the previous example of Mediterranean water against Nordic Seas water) and cabbeling. Therefore, there is no longer a uniquely defined isentropic surface, even in the absence of diabatic mixing!
Potential density surfaces can be used approximately for isentropic surface. But the potential density depends on the reference pressure and is best used not too far away from the reference pressure. The discontinuous standard reference pressure, although effective, is not idea. This idea can be extended to a continuous reference pressure follow the water parcel. This leads to the idea of neutral density surface. However, the definition of neutral density depends on the location (x, y and p) of the origin of the water parcel and is defined only for a range of temperature and salinity in the open ocean. One current version of neutral density is calculated for water parcel from the middle of Pacific using climatological T, S observations. Both potential density and neutral density are approximation of the isentropic surface. Neutral density is used for large vertical excursions of hundreds of meters.

18. Static stability and Brunt-Vaisala frequency
Static stability E=-(1/ρ)dρ/dz or for large vertical excursion, using local potential density as E=-(1/ρ)dσn/dz. When stability becomes negative, the column becomes grativtationally unstable.
The Brunt-Vasala frequency is N2=-(g/ρ)dσn/dz. For a stable ocean, in the upper ocena, g=10 m/s2, dσ=2 g/cm3, H=500m, we have N2=0.4*103 /s, which corresponds to a period τ=2π/N=103 s ~15 min. This is pretty fast. In the deep ocean, the stratification is much weaker, the Brunt Vasala frequency can be up to 6 hours. The Brunt Vaisala frequency is much higher in the atmosphere, with period of minutes.
(a) Potential density and (b) Brunt-Väisälä frequency (cycles/h) and period (minutes) for a profile in the western North Pacific.
FIGURE 3.6

19. Static Stability:
For a stable stratification, the density of environment has to be lighter towards the top, and vise versa. A unstable stratification will lead to convection that lowers the center of gravity of the environmental fluid to provide the potential energy to be changed to kinetic energy for convection.
Stable,
Unstable, ρ2 ρ3 ρ1
ρ1<ρ2<ρ3, N2>0
ρ1>ρ2>ρ3, N2<0
unstable, potential energy higher than uniform case Z
stable, potential energy lower than uniform case
center
of mass ρ ρ

20. 2.4: Tracers
Due to the difficulty in measuring ocean currents in the interior ocean, circulation has been inferred from tracers. Salinity has been used as a rough tracer for deep ocean circulation because it is influenced by the surface E-P and does not change density too much unless very cold. But, it is not conservative such that it is not a very good tracer for many purposes.
Dissolved oxygen (O2):
Oxygen enters the ocean surface from the atmosphere, and is also produced in the surface through photosynthesis by planktons (100% saturation in the mixed layer) and is then consumed by respiration of by zooplankton, bacteria and other creatures. Its content decreases rapidly with depth below the mixed layer, because it is consumed by respiration of bacteria and by nitrify bacteria. Therefore, oxygen decreases with water age away from the surface.
Nutrients: (Silica (SiO2), Phosphate (PO43-), nitrogen compond: Ammonium (ion, NH4+), Nitrite (anion, NO2-), Nitrate (ion, NO3-))
Nutrients are crucial for life in the ocean and are consumed in the surface where life is abundant, and is then produced in the deep ocean, so its content increases with depth and age, almost a mirror image with oxygen.
Silicon (Si): Silica (SiO2) used by some organisms to form their shells and re-enters the water column as their hard parts dissolves as they fall to the ocean floor. Some silica accumulates over the ocean floor and provides another source; some silica enters from mid-ocean ridge vents.
Nitrogen: enters the water as the biological (bacteria) dissolves the soft part of the organism.
Phosphate and Ammonium are immediate decay product. Nitrifying bacteria occurs through the water column and leads to Nitrite and finally Nitrate.
Redfield Ratios: nitrate/oxygen, phosphate/oxygen remains constant
because oxygen is consumed and nutrients are generated. (Redfield, 1934).
Carbon tracers:
dissloved inorganic carbon, organic carbon, alkalinity and pH. Sources: natural and anthrophgenic.
Isotopes:
d18O=O18/O16 : positive from surface evaporation, negative from precipitation and glacial melting glacial (very negative), a good indicator of high latitude prep and melting
d14C=C14/C12 : Source: cosmic ray bombardment on nitrogen, and enters the ocean through gas exchange, with half-life time of 5730 years. a good indicator of water age

21. 2.5: Sound
Sound wave in water is like the eletromagnetic wave in the atmosphere.
Sound wave is produced by the adiabatic compressibility of the water (air). Water is less compressible and therefore sound wave propagates about 4.5 times faster than in the air (1500 m/s vs. 344 m/s)
Sound speed
C=(dρ/dP|θ,S )1/2 = (ρβ)1/2 , where β=(1/ρ)dρ/dP|θ,S adiabatic compressibility
Sound speed is high when the water is less compressible. Since higher temperature and higher pressure make water less compressible, sound speed is higher at the surface (warmer) and deep ocean (higher pressure). This forms a sound speed minimum in the mid-ocean depth of about 700-m. This minimum depth range is called SOFAR (Sound Fixing And Ranging) channel. (see figure next). At high latitude where suface is cold, the minimum speed will be in the surface ocean. Sound wave can propagate a long distance in SOFAR channel.
For station Papa in the Pacific Ocean at 39°N, 146°W, August, 1959: (a) temperature (°C) and salinity (psu) profiles, (b) corrections to sound speed due to salinity, temperature, and pressure, (c) resultant in situ sound-speed profile showing sound-speed minimum (SOFAR channel).
SOFAR
FIGURE 3.7

22. Sound ray diagrams: (a) from a shallow source for a sound-speed profile initially increasing with depth in upper mixed layer to a shallow minimum and then decreasing, and (b) from a sound source near the speed minimum in the sound channel for a typical open ocean sound-speed profile.
Instruments:
Echo Sounding: finding the depth of the ocean by beaming vertically.
Acoustic Doppler speed log: detecting the speed of ship relative to water
Acoustic Tomography: multiple arrays of sound beams to retract the open ocean temperature structure, sea ice,….
FIGURE 3.8

23. 2.6: Light
Light is attenuated almost entirely in the top 100 m of the surface water, which is the euphotic zone where photosynthesis occurs.

24. Light process
Schematic of optical processes in seawater. Adapted and simplified from Mobley (1995), with added indicators of seawater heating and photosynthesis, as well as satellite observation of ocean color.
FIGURE 3.9

25. FIGURE 3.10 Ocean color S(z,λ)=S(0, λ)exp(-Kλz)
(a) Attenuation coefficient kl, as a function of wavelength l (mm) for clearest ocean water (solid line) and turbid coastal water (dashed line). (b) Relative energy reaching 1, 10, and 50 m depth for clearest ocean water and reaching 1 and 10 m for turbid coastal waters.
Blue and green penetrates the most in clear water, as the ocean color in the open ocean
Coastal water towards green and yellow.
FIGURE 3.10

26. FIGURE 3.11 Ocean color dependence on chlorophyll low chl high chl
Example of observations of water-leaving radiance observed by the Multi-angle Imaging Spectro Radiometer (MISR), with bands observed by satellite color sensors indicated. Solid curves: low chlorophyll water (0.01 mg/m3). Dotted curves: high chlorophyll water (10.0 mg/m3). The two lower curves have the atmospheric signal removed.
low chl
high chl
FIGURE 3.11

27. S< 27.4
S> 27.4
2.7: Sea Ice
1oC
2oC
4oC
-2oC
Sea ice formation: Pure ice density kg/m3, vs. water kg/m3 (at 0oC)
Fresh water type (S< 27.4) and salty water type (S >27.4)
Initial freezing (especially fast freezing) traps some salt in “brine cell”, and
can have salinity of up to 15 psu. Later, gravity draws down the brine cell and reduces the
salinity of the sea ice. Sea ice has a much lower salinity (4-10 psu 1st year, 1-3 psu 2nd year..).
Brine rejection: Formation of sea ice injects salt into nearby water, making the surrounding water saltier and heavier and sinking.
This is a major mechanism for the formation of deep ocean water masses, especially for the Antarctic Bottom Water and
North Pacific Intermediate Water.
Sea Ice Motion: ridging, leads, polynya…
Schematics of polynya formation: (a) latent heat polynya kept open by winds and (b) sensible heat polynya kept open by tidal mixing with warmer subsurface waters (after Hannah et al., 2009).