SIO 210 housekeeping Tutorials: Math tutorials (finalize time) (M or W 3-4) Course material...

SIO 210 housekeeping

Tutorials:

Math tutorials (finalize time) (M or W 3-4)

Course material tutorials (finalize 2 times)

Exam format: in-class, closed book but you may bring 1 page of your own notes (both sides, any fontsize OK)

Course url: http://www-pord.ucsd.edu/~ltalley/sio210

Email: [email protected] SIO210 or SIO 210 in the subject line to help me see your email

Talley SIO 210 (2013)

http://www-pord.ucsd.edu/~ltalley/sio210

mailto:[email protected]

SIO 210 Physical properties of seawater (3 lectures)

First lecture:

1. Depth and Pressure

2. Temperature

3. Heat

4. Potential temperature

Course url: http://www-pord.ucsd.edu/~ltalley/sio210Talley SIO 210 (2013)

Second and third lectures:

1. Salinity

2. Density

3. Freezing point, sea ice

4. Potential and neutral density, Brunt-Vaisala freq.

5. Sound speed

6. Tracers: Oxygen, nutrients, transient tracers

http://www-pord.ucsd.edu/~ltalley/sio210

NASA SST animation


http://podaac.jpl.nasa.gov/AnimationsImages/Animations

SIO 210 Properties of Seawater

These 2 powerpoint presentations include only the figures, not the blackboard work or notes.

Reading for this and the next 2 lectures:

DPO Chapter 3.1 to 3.6; 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


Definitions

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

Ocean range: 0-6000 meters (mean 3734 m, median 4093 m, mode 4400 m since file had depths by 100 m intervals)

1. Depth

Talley SIO 210 (2013)FIGURE 2.2

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

1. Pressure


1. 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.)


1. 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


1. 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


1. Pressure vs. depth for actual ocean profile

Z

DPO Figure 3.2Talley SIO 210 (2013)

1. Pressure measurements

Reading the reversing thermometers

Old: pair of mercury reversing thermometers

New - quartz transducers that produce digital output

DPO Chapter S16Talley SIO 210 (2013)

1. Pressure measurement accuracy and precision

Accuracy Precision

~5 dbar ?

3 dbar 0.5 dbar

(0.1% of range) (0.01% of range)


Old-fashioned reversing thermometers

Quartz pressure sensor on modern instrument

2. Temperature, heat and potential temperature

• Temperature units: Kelvin and Celsius• Kelvin is absolute temperature, with 0 K at the

point of zero entropy (no motion of molecules)• 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)


Surface temperature (°C)

DPO Figure 4.1: Winter data from Levitus and Boyer (1994)Talley SIO 210 (2013)

Note total range and general distribution of temperature

Pacific potential temperature section (“potential” defined on later slides)

Talley SIO 210 (2013) DPO Fig. 4.12aNote total range and general distribution of temperature

2. 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


2. HeatEnergy: 1 Joule = 1 kg m2 / sec2

Heat is energy, so units are Joules

Heat change per unit time: 1 Watt = 1 J/sec

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


2. Heat flux

Flux of heat from air into ocean or vice versa:

Heat/(unit time x unit area)

Units are Joules/(sec m2) = (J/sec)/m2 = W/m2

Where 1 Watt = 1 W = 1 J/sec


What sets temperature? Surface heat flux (W/m2) into ocean

DPO Figure 5.12Yellow: heating. Blue: coolingMap shows the annual mean (total for all seasons)


Heat flux and temperature change: sample calculation

Compute the temperature change over 1 month in a volume of fluid that is 1m2 in surface area and 100 m thick, if the heat flux through the sea surface is 150 W/m2. (Net heat flux is due to solar radiation and various heat loss terms – later lecture.)

i.e. dq/dt = 150 W/m2

Total heat flux into the column of water is

dQ = (dq/dt)*Area*time =

(150 W/m2)(1 m2)(30 days) = 3.8888 x 108 J

Total heat change of the water column in terms of temperature:

dQ = (Volume) cp dT since dq = dQ/volume

Thus dT = (3.8888 x 108 J)/(100 m3 x 1025 kg/m3 x 3850 J/kg°C)

= 0.99 °C or ~ 1°CTalley SIO 210 (2013)

2. (cont.) Potential temperatureWater (including seawater) is 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.

Define “potential temperature” as the temperature a parcel of water has if moved adiabatically (without heat exchanges or mixing) to the sea surface.

Use the Greek letter to denote potential temperature.

Potential temperature is always lower than measured temperature except at the sea surface (where they are the same by definition)


Potential temperature expressions

€

θ(S,T, p) = T + Γ(S,T, p')dp'p

pref

∫

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

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)


Pressure effect on temperature:Mariana Trench (the most extreme example because of its

depth)

DPO Figure 4.9

X

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.)


Temperature and potential temperature

difference in S. Atlantic (25°S)

X

Note that this water column has a temperature and potential temperature minimum at about 1000 m (must be balanced by a salinity feature).


Atlantic temperature and potential temperature sections for contrast

Temperature Potential temperature


SIO 210 housekeeping Tutorials: Math tutorials (finalize time) (M or W 3-4) Course material...

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