SIO 210
Physical properties of seawater
(3 lectures)
First lecture:
1. Accuracy and precision;
other definitions
2. Depth and Pressure
3. Temperature
Second and third lectures:
1. Salinity
2. Density
3. Freezing point, sea ice
4. Heat
4. Potential and neutral
density, Brunt-Vaisala freq.
5. Potential temperature
5. Sound speed
6. Tracers: Oxygen,
nutrients, transient tracers
Talley SIO 210 (2015)
SIO 210 Properties of Seawater
Reading for this and the next 2 lectures:
DPO Chapter 3.1 to 3.6
DPO Chapter 4.2 to 4.6
Extra: DPO Java Ocean Atlas examples for Chapter 3
Stewart chapter 6, and just look at Gill Appendix 3
Study questions: see website
Talley SIO 210 (2015)
1. Definitions for measurements
Accuracy: reproducibility relative to a chosen
standard
Precision: repeatability of an observation by a
given instrument or observing system
A very precise measurement could be wildly
inaccurate.
Mean: average value
Median: center of distribution (equal number of
values above and below)
Mode: most common value
Talley SIO 210 (2015)
2. Depth and pressure
Ocean range: 0-6000 meters (mean 3734 m, median 4093 m,
mode 4400 m since file had depths by 100 m intervals)
Talley SIO 210 (2015)
FIGURE 2.2
2. Depth and Pressure
Pressure (mostly) results from overlying mass of water
(and air); total mass depends on the water density and
height
Ocean range: 0-6000 dbar (get to this unit below) (note
that 1 dbar is equivalent to about 1 m)
Pressure is a force per unit area
Newton’s law: F = ma where F and a are 3-D vector
force and acceleration, and m is mass.
Units of force: mass x length / (time)2
cgs: 1 dyne = 1 gm cm / sec 2
mks: 1 Newton = 1 kg m / sec 2
Talley SIO 210 (2015)
2. Depth and Pressure
Units of pressure: dyne/cm2 and N/m2
1 Pascal = 1 N/m2
1 bar = 106 dynes/cm2 = 105 N/m2
approximately the atmospheric pressure at sea level
1 atmosphere = 1000 millibar = 1 bar
1 decibar = 0.1 bar
Decibar or “dbar” is the most common pressure unit used in
oceanography because it is so close to 1 m, given the density
of seawater: approximately the pressure for 1 meter of
seawater. (Don’t use the abbreviation “db” because dB is used
for decibels – sound intensity.)
Talley SIO 210 (2015)
2. Relation of pressure to depth (1)
“Hydrostatic balance”
From Newton’s law, use the force balance in the vertical
direction
vertical acceleration = (vertical forces)/mass
vertical acceleration = vertical pressure gradient force + gravity
Pressure gradient (difference) force (“pgf”) is upward due to
higher pressure below and lower pressure above
pgf = - (pressure/depth) = -(p/z)
(since z increases upward and p increases downward)
Gravitational force per unit volume is downward = - g
where  is the density of seawater,  ~1025 kg/m3
Talley SIO 210 (2015)
2. Relation of pressure to depth (2)
We now assume vertical acceleration is approximately zero, so
the vertical pressure gradient (pressure difference force) almost
exactly balances the downward gravitational force. This is called
“hydrostatic balance”.
0 = vertical pgf + gravitational force
0 = - (p/z) - g
We can then solve for the change in pressure for a given change in depth.
For:
z = 1 meter, density  ~1025 kg/m3, and g = 9.8 m/s2, we get
p = -  g z = (1025 kg/m3)(9.8 m/s2)(1 m) =
10045 kg/(m s2) = 0.10045 bar = 1.0045 dbar
Talley SIO 210 (2015)
2. Pressure vs. depth for actual ocean
profile
Z
Talley SIO 210 (2015)
DPO Figure 3.2
2. Pressure measurements
Reading the
reversing
thermometers
Old: pair of mercury reversing
thermometers
Talley SIO 210 (2015)
Modern
(post 1960s)
- quartz
transducers
that produce
digital output
DPO Chapter S16
2. Pressure measurement accuracy and
precision
Old-fashioned
reversing
thermometers
Quartz
pressure sensor
on modern
(1970s to
present)
instrument
Talley SIO 210 (2015)
Accuracy
Precision
~5 dbar
?
3 dbar
0.5 dbar
(0.1% of range)
(0.01% of range)
3. Temperature, heat and potential temperature
• Temperature is measure of energy at molecular level
• Temperature units: Kelvin and Celsius
• TK Kelvin is absolute temperature, with 0 K at the
point of zero entropy (no motion of molecules)
• TC Celsius 0°C at melting point at standard
atmosphere (and no salt, etc)
• TK = TC + 273.16°
• Ocean temperature range: freezing point to about 30°
or 31°C
• (Freezing point is < 0°C because of salt content)
Talley SIO 210 (2015)
3. Surface temperature (°C)
Note total range and general distribution of temperature
Talley SIO 210 (2015)
DPO Figure 4.1: Winter data from Levitus and Boyer (1994)
Pacific
potential
temperature section
(“potential” defined on later slides)
Note total range and general distribution of temperature
Talley SIO 210 (2015)
DPO Fig. 4.12a
3. Temperature
• Temperature is defined in statistical
mechanics in terms of heat energy
• T = temperature, Q is heat, S is entropy
• Heat content is zero at absolute zero
temperature (Kelvin scale)
•dQ = TdS
Heat is not 0 at 0°C!!!!
Talley SIO 210 (2015)
4. Heat
Energy: 1 Joule = 1 kg m2 / sec2
Heat is energy, so units are Joules = J
Q = total amount of heat
dQ/dT = Cp where Cp is heat capacity
q= heat per unit volume = Q/V, units are J/m3
dq/dT =  cp where cp is specific heat = Cp/mass
For seawater, typical values (with a wide range) are:
cp ~3850 J/kg °C and  ~ 1025 kg/m3
Talley SIO 210 (2015)
4. Heat flux
Heat change per unit time
1 Watt = 1 W = 1 J/sec
Flux of heat from air into ocean or vice versa:
Heat/(unit time x unit area)
Units are
Talley SIO 210 (2015)
Joules/(sec m2) = (J/sec)/m2 = W/m2
4. What sets temperature?
Surface heat flux (W/m2) into ocean
Map shows the annual mean (total for all seasons)
DPOcooling
Figure S5.8 (in supplement to Chapter 5)
Yellow: heating. Blue:
Talley SIO 210 (2015)
5. Potential temperature
Water (including seawater) is (slightly) compressible
If we compress a volume of water adiabatically (no exchange of
heat or salt), then its temperature increases. (“adiabatic
compression”)
We are interested in tracking water parcels from the sea surface
down into the ocean. We are not interested in the adiabatic
compression effect on temperature. We prefer to track
something that is conserved following the parcel.
“Potential temperature” 
Is defined as the temperature a parcel of water has if moved
adiabatically (without heat exchanges or mixing) to the sea
surface.
Potential temperature is always lower than measured
temperature except at the sea surface (where they are the same
by definition)
Talley SIO 210 (2015)
5. Potential temperature expressions
The change in temperature with pressure that is due
solely to pressure is called the “adiabatic lapse rate”:
Γ(S,T,p) =  T/ p (> 0)
In the atmosphere, the adiabatic lapse rate is equivalent
to 6.5°C per 1000 m altitude.
In the ocean, the adiabatic lapse rate is about 0.1°C per
1000 m depth (1000 dbar pressure).
Potential temperature is defined as
 (S,T, p)  T 

pref
p
(S,T, p')dp'
Again: potential temperature is always lower than measured
temperature except at the sea surface (where they are the same by
definition) (pref = 0 dbar, p is > 0 dbar)
Talley SIO 210 (2015)
5. Pressure effect on temperature:
Mariana Trench (the most extreme example because of
its depth)
Note the measured
temperature has a minimum
around 4000 dbar and
increases below that.
Potential temperature is
almost exactly uniform
below 5000 m: the water
column is “adiabatic”.(This is
because all of the water in this trench
spilled into it over a sill that was at
about 5000 m depth.)
X
Talley SIO 210 (2015)
DPO Figure 4.9
5. Temperature
and potential
temperature
difference in S.
Atlantic (25°S)
Note that this water
column has a
temperature and
potential temperature
minimum at about
1000 m (must be
balanced by a salinity
feature).
X
Talley SIO 210 (2015)
5. Temperature
and potential
temperature
difference in S.
Atlantic (25°S)

T
Note that this water
column has a
temperature and
potential temperature
minimum at about
1000 m (must be
balanced by a salinity
feature).
X
Talley SIO 210 (2015)
5. Atlantic temperature and potential
temperature sections for contrast
Temperature
Talley SIO 210 (2015)
Potential temperature
Summary: definitions
Accuracy
Precision
Mean
Median
Mode
Pressure
Newton’s Law
Hydrostatic balance
Dyne
Newton
Decibar
Talley SIO 210 (2015)
Temperature
Kelvin
Celsius
Heat and heat flux
Joule
Watt
Potential temperature
Adiabatic lapse rate