1.
Difference between accuracy and precision, and units used in
oceanographic measurements:
2.
Pressure and depth:
- Definition:
Pressure is the force per unit area exerted by water (or
air in the atmosphere) on either side of the unit area.
- Units:
The units of force are (mass length / time2) which you
can remember from Newton's Law F = ma. The units of
pressure are (force / length2) or (mass /[length ×
time2]).
- cgs:
dynes/cm^2.
- mks:
Newtons/m2 and 1 Pascal = 1 Newton/m^2.
- Atmospheric
pressure is usually measured in bars. 1 bar = 106
dynes/cm2 = 105 Pascal.
- Ocean
pressure is usually measured in decibars. 1 dbar =
10-1 bar = 105 dyne/cm2 = 104 Pascal.
3.
Temperature, heat and potential temperature:
3.3.
Potential temperature
Pressure in the ocean increases greatly downward. A
parcel of water moving from one pressure to another will be
compressed or expanded. When a parcel of water is compressed
adiabatically, that is, without exchange of heat, its
temperature increases. (This is true of any fluid or gas.)
When a parcel is expanded adiabatically, its temperature
decreases. The change in temperature which occurs solely due
to compression or expansion is not of interest to us, as it
does not represent a change in heat content of the fluid.
Therefore if we wish to compare the temperature of water at
one pressure with water at another pressure, we should remove
this effect of adiabatic compression/expansion.
Thus, "potential temperature" is the
temperature which a water parcel has when moved adiabatically
to another pressure. In the ocean, we commonly use the sea
surface as our "reference" pressure for potential temperature
- we compare the temperatures of parcels as if they have been
moved, without mixing or diffusion, to the sea surface. Since
pressure is lowest at the sea surface, potential temperature
(computed at surface pressure) is ALWAYS lower than the actual
temperature unless the water is lying at the sea surface.
4. Salinity and conductivity:
4.1
Salinity:
- Definition:
Salinity is roughly the number of grams of dissolved matter
per kilogram of seawater. This was the original definition,
and at one time salinity was determined by evaporating the
water and weighing the residual. The dissolved matter in
seawater affects its density (see section 5 below), hence
the importance of measuring salinity. The "law" of constant
proportions (Dittmar, 1884), formalized the observation that
the composition of the dissolved matter in seawater does not
vary much from place to place. Why constant proportions?
Salts come from weathering of continents and deep-sea vents,
etc - the input is very very slow (order 100,000 years)
compared with the mixing rate of the whole ocean (which is
order 1000 years). Thus it is possible to measure just one
component of the dissolved material and then estimate the
total amount of dissolved material (salinity). This approach
was used until the 1950's. The main constituent of sea salt
is Cl, the second largest is Na, followed by many other
constituents (see Pickard and Emery for table). In
actuality, there is a slight variation in the proportions,
and recommendations are underway to formulate new
definitions of salinity which depend on the actual
constituents - this may likely take the form of
geographically-dependent tables of corrections to the
quantity which is measured (usually conductivity). The total
amount of salt in the world oceans does not change except on
the longest geological time scales. However, the salinity
does change in response to freshwater inputs from rain and
runoff, and freshwater removal through evaporation.
- Units: in the
original definition, salinity units were ‰ (parts per
thousand). This was replaced by the "practical salinity
unit" or PSU. Most recently, the recommendation of the SCOR
working group on salinity is that salinity be unitless, as
the measurement is now based on conductivity and is not
precisely related to the mass of dissolved material.
- How is salinity measured?
- Evaporate and weigh residual, determine amount of
chlorine, bromine and iodine to give "chlorinity", through
titration with silver nitrate. Then relate salinity to
chlorinity, where S = 1.80655 Cl.
Accuracy is 0.025 (less than 2 places). This method was
used until the International Geophysical Year in 1957.
- Or, measure conductivity and relate it to salinity (see
next).
5.
Density, potential density and neutral density:
For mapping general circulation, it is more useful to use
density (hereafter ρ) as our vertical coordinate than pressure
since we assume that water parcels much more nearly conserve
density than pressure. Thus we often map properties on
isopycnal surfaces. However, the isopycnals which we choose
must have the effect of changing pressure removed since most
of the density variation in the ocean is due to pressure,
which has no bearing on sources of heat/salt for water
parcels. Thus we introduce the concept of potential density or
neutral surfaces, which attempt to remove the effect of
pressure changes on density.
5.1. Density
- Definition:
Seawater density depends on temperature,
salinity and pressure. Colder water is denser. Saltier
water is denser. High pressure increases density. The
dependence is nonlinear. An empirical equation of state
is used, based on very careful laboratory measurements
(See Gill, Appendix 3).
- Discussion:
- The
density of freshwater is 1000 kg/m3.
Typical densities for seawater are only slightly
higher: 1020 to 1050 kg/m3, with most of
this range being due to pressure. The range of
densities at the sea surface is about 1020 to 1029
kg/m3.
- Density
as a function of temperature for pure and salty
water:
Fresh water (S=0) at atmospheric pressure (p=0) has
maximum density at temperature 4°C.
(Thus colder fresh water is less dense, which has
implications for lake overturn and ice floating.) As
salinity is increased, the density maximum moves to
lower temperature. At a salinity of about 24.7, the
maximum density is at the freezing point.
- Other
expressions for density ρ:
- σ
= ρ - 1000;
- ɑ
(specific volume) = 1/ρ.
6. Sound speed:
The speed of sound in water is approximately 1500 m/s.
It depends on pressure and on temperature. The higher the
pressure, the higher the sound speed (in a sense, the water is
more "rigid" and so the speed increases). The higher the
temperature, the higher the sound speed. In most areas of the
ocean, the warm water at the surface and the high pressure at
the bottom produce a sound speed profile which is maximum at the
surface and bottom, with a minimum in between. This sound speed
minimum is referred to as the SOFAR channel. Where temperature
is low or inverted near the surface, then there is no surface
maximum in sound speed and the SOFAR channel is found at the sea
surface (typical of the subpolar and polar regions). Where there
is a sound speed minimum, it functions as a wave guide.
Figure. Profiles of potential density, Brunt-Väisälä
frequency, potential temperature, sound speed from
the eastern subtropical North Pacific.
7. Sea ice:
The freezing point of seawater is lower than that of
freshwater. As sea water freezes, it forms pockets of salt. The
salt (brine) leaches out of the bottom of the ice and the brine
drips into the water below the ice. Thus sea ice when melted is
considerably fresher than the original water which was frozen. The
"brine rejection" process creates dense water below the sea ice
formation area. This can be an important contributor to dense
water formation in a global sense as the densest waters are formed
at high latitudes, and often involve sea ice.
The faster that sea ice is frozen, the less likely that the
salt can escape. Thus the saltiest sea ice is formed at the lowest
temperatures. Sverdrup et al. (1942 text) tabulate the salinity of
ice formed from water which starts at salinity 30. When frozen at
an air temperature of -16C, the salinity of the ice is 5.6. When
frozen at an air temperature of -40C, the salinity of the ice is
10.2.
Study questions:
1.
What is the difference between accuracy and precision?
2. What properties of seawater determine its density?
3. What is the pressure at the bottom of the ocean relative to sea
surface pressure? What unit of pressure is very similar to 1
meter?
4. What happens to the temperature of a parcel of water (or any
fluid or gas) when it is compressed adiabatically? What quantity
describes the effect of compression on temperature? How
does this quantity differ from the measured temperature? (Is it
larger or smaller at depth?)
5. What are the two effects of adiabatic compression on density?
What quantity is used to minimize the effect of compression on
density? Is cold water more or less compressible than warm
water?
6. What is salinity and why do we use a single chemical
constituent (which one?) to determine it? What other physical
property of seawater i is used to determine salinity? What are
the problems with both of these methods?
7. What is an equation of state? What unique properties of
seawater arise from non-linearities in the equation of state?
8. Why do we use different reference pressure levels for potential
density? (see answer to 6)
9. What is a neutral surface or path?
10. What are the significant differences between freezing pure
water and freezing seawater? What happens to the salt in frozen
seawater?
11. Fresh water has a density maximum at a temperature above the
freezing point, which allows ice to float. Is this also true for
sea water? 12. Why does ice formed from sea water float?
13.
Why is there a sound speed minimum in the middle of the water
column?
Quantitative
questions:
A simplified formula for the speed of sound in water is:
C = 1449 + 4.6T - 0.055T2 +
1.4(S-35) + 0.017D (m/s)
where T is temperature (°C), S
is salinity and D is depth in meters. Suppose an experiment is
set up to measure the mean ocean temperature with a sound
source and receiver located 5,000 km apart. Assume the sound
path follows a mean depth of 1000m, where the mean salinity is
35 psu. Based on this setting, answer the questions below:
1. If the travel time between source and receiver is 56
minutes and 28.25 seconds, what is the mean temperature of the
water?
2. Suppose the water between the sound source and receiver
were to warm by 0.15°C. What would be the change in the
acoustic travel time?
3. Suppose, instead, that a warm eddy drifted into the sound
path. The eddy has a width of 200 km and a temperature anomaly
of 1°C at 1000m. What is the change in acoustic travel time?A
5m deep swimming pool is filled with seawater so that the
level is 1 cm below the rim (e.g. 4.99 m of water). If the
water is well mixed and initially at 10C and 35 PSU. If the
water is uniformly heated, how hot would the water be when it
started leaking over the rim? How much heat (J/m2)
is required to heat the water to this point? If the heating
rate is 100 W/m2, how long would this take?
Further reading and
resources:
Last
modified: Sep 2016