Density and the Equation of State • Accurate measurements of density can only be done in

the lab, not in situ (no density sensor).

• Therefore, density is usually calculated from temperature, salinity and pressure using the Equation of State.

• Importance of density for physical oceanography: - ocean stratification, stability and mixing

- ocean currents (geostrophic) depend on horizontal changes in density

- water masses formation and propagation

Downslope

descent

Bottom friction

Dynamics of density

currents and overflows

)(

)()/(

3

3

mV

kgmmkg

),,( PST

eddies

In situ and potential density

(cgi units) ρ=1.0275 g/cm3 = (SI units) 1027.5 kg/m3

• “Sigma” units: σ = ρ kg/m3 – 1000 kg/m3 = 27.5

σS,T,p = ρ(S,T,P) – 1000 Sigma: in situ density as a

function of salinity, temperature & pressure

σt = ρ(S,T,0) – 1000 Sigma-t: density a particle of water would have at the surface (atmospheric pressure)

σθ = ρ(S,θ,0) – 1000 Sigma-θ: potential density a particle of water would have if raised to the surface adiabatically (function of potential temperature)

Other units: specific volume α = 1/ρ (for geostrophic calc.; later)

σS,T,p specific volume anomaly = αS,T,p – α35,0,p

σt thermosteric anomaly S,T = αS,T,0 – α35,0,0

measured with CTD calculated properties

489.1069)1000,5,35(343.1023)0,25,35( Example:

UNESCO

EOS:

Best polynomial

fit to many

observations

A simple (linear) Equation of State:

ρ = ρ0 + [-(T-T0) + (S-S0) + kp]

– averages values & expansion coefficients:

ρ0=1027 kg/m3, T0=10°C, S=35‰

Thermal expansion: =0.15 kg/(m3 °C)

Salinity contraction: =0.78 kg/(m3 ‰)

Pressure compressibility: k=0.0045 kg/(m3 db),

– When can we use a Linear EOS? • if T,S,p have small variations

• simple process studies

– Accuracy of linear EOS: about ±0.5 kg/m3

– Accuracy of complete EOS: about ±0.001 kg/m3

Note: In the real ocean , & k are not constant, but vary with T,S & P

Effects of Temperature and Salinity on Density

T

1

S

1

Thermal Expansion Saline Contraction

x 10-4 oC-1 x 10-4 S-1

Density changes by 0.2 kg/m3 for a T change of 1oC,

and by 0.8 kg/m3 for a S change of 1ppt.

Greater influence of salinity on density

90 % of Ocean Water

Mean T & S for

World Ocean

(not linear)

• How much σt will change

if S changes by +0.5‰ ?

• How much σt will change

if T changes by +1°C

T\S 0‰ 20‰ 40‰

30°C 0.39 0.38 0.38

10°C 0.41 0.39 0.39

0°C 0.43 0.40 0.40

T\S 0‰ 20‰ 40‰

30°C -0.30 -0.33 -0.35

10°C -0.09 -0.14 -0.18

0°C +0.07 -0.01 -0.17

Typical density distribution in the ocean

pycnocline: the region

of large change of

density with depth

T

S

density

A word of caution about potential

density

“Sigma-4” units

σθ

σ4

T-S Diagrams: plots of observed salinity vs.

temperature. Why so useful?

•Water properties change at the surface, but

after sinking to deeper layers only small

changes occur in their properties

•Study water masses and their geographical

distribution

•Study mixing between water masses

•Study motion of water in the deep ocean

T-S Diagram

Mixing of 2

water types

initial

profile

after

mixing

T-S Diagram

Mixing of 2

water types

Mixing of 3

water types

initial

profile

after

mixing

T-S diagram:

useful tool to

diagnose water

masses and how

they mix with each

other

100m

700m

1500m

Antarctic

Bottom Waters

N. Atlantic

Deep Water

Mediterranean

Water

Atlantic

Central Waters

Surface

Static Stability

• The water’s static stability determines the tendency of

water mass to move vertically, it also affects mixing:

• High stability- minimal vertical movement and mixing

(oceans are mostly stably stratified)

• Low stability- more vertical movement and mixing

(unstable stratification will rapidly mixed until stable or neutral

stability reached)

ρ1

ρ2

ρ

z

Change in potential

energy per unit

volume when parcel

is moved up by

distance Z1 is

PE=(ρ2- ρ1)gZ1

Z1

unstable stable Neutrally

stable

Stability in continuously stratified ocean:

zE

12c

g

More accurate formula to

account for compressibility

change in deep ocean use

gravity over square of speed of

sound

Oceanographer often use another measure of stability:

Brünt-Väisälä frequency:

Where oscillations have period given by T=2/N

(faster oscillations in more stable stratification)

z

gN

Weak stratification Strong stratification

Sound in the sea • Since penetration of visible light is limited in the

ocean, we can not use it to transfer information or to collect data.

• Therefore, sound waves play a much more important role in oceanography than it does in the atmosphere:

– Echo-sounders to measure depth or find ship wrecks

– SONAR to detect submarines or school of fish

– Underwater communication (humans, marine mammals- whales, dolphins..)

– Measuring ocean currents (ADCP)

– Measuring climate change (acoustic thermometry)

Different types of waves

Longitudinal waves Transverse waves

particle motion parallel particle motion perpendicular

to wave propagation to wave propagation

Orbital waves

particle motion is circular

Sound Waves

Speed of sound depends on temperature, salinity and depth

C = 1449 + 4.6 T – 0.055 T 2 + 1.4 (S – 35) + 0.017 D (m/s)

k=compressibility

ρ=density

V=volume

P=pressure

c=speed of sound in water (~1500 m/s)

(about 4-5 times faster than in the atmosphere)

Note: without compressibility there would be

no sound, as sound waves propagate through

small fluctuations in pressure

Compressibility and the speed of sound

kc

P

V

Vk

1,

1

Speed of sound in the ocean:

increases by ~4m/s per 1°C by ~1.5m/s per 1‰ and 18m/s per 1000m

sound channel

Pressure effect

Temperature effect

The sound channel

However, Acoustic Thermometry became a controversial issue

and much of the efforts have shifted from measuring climate to

studies of the impact on marine mammals…

Next Classes:

• Global sun-earth heat balances and heat

transports in the ocean

• Local heat balances and temperature

changes (daily, seasonally, etc.)

• Salt-Fresh Water balances

• Mid-term exam – Monday, Sep. 23, 2013