SIO 210 Physical properties of seawater (Lectures 2...

SIO 210 Physical properties of seawater (Lectures 2 and 3) Fall, 2016 L. Talley

Talley SIO 210 (2016)

First lecture:

1.  Accuracy and precision; other definitions

2.  Depth and Pressure

3.  Temperature

4.  Salinity and absolute salinity

5.  Density

6.  Sea ice, freezing point

Second (and third) lectures:

7. Heat

8. Potential temperature and conservative temperature

9. Potential density

10. Neutral density

11. Stability, Brunt-Vaisala frequency

12. Sound speed

13. Tracers: Oxygen, nutrients, transient tracers

7. 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 = ρ cp where cp is specific heat = Cp/mass

So dq = ρ cp dT

For seawater, typical values (with a wide range) are:

cp ~3850 J/kg °C and ρ ~ 1025 kg/m3


7. 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 Joules/(sec m2) = (J/sec)/m2 = W/m2


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

Yellow: heating. Blue: coolingMap shows the annual mean (total for all seasons)Talley SIO 210 (2016)

DPO Figure S5.8 (in supplement to Chapter 5)

8. 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” θ

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 (2016)

8. 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) Talley SIO 210 (2016)

8. 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.)


8. 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).


8. 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).


Tθ

8. Atlantic temperature and potential temperature sections for contrast

Temperature Potential temperatureTalley SIO 210 (2016)

9. Potential density: compensating for compressibility

Adiabatic compression has 2 effects on density:

(1)  Changes temperature (increases it)

(2)  Mechanically compresses so that molecules are closer together

As with temperature, we are not interested in this purely compressional effect on density. We wish to trace water as it moves into the ocean. Assuming its movement is adiabatic (no sources of density, no mixing), then it follows surfaces that we should be able to define. This is actually very subtle because density depends on both temperature and salinity.



Sigma-t: This outdated (DO NOT USE THIS) density parameter is based on temperature and a pressure of 0 dbar

σt = σ(S, T, 0)

Potential density: reference the density σ (S, T, p) to a specific pressure, such as at the sea surface, or at 1000 dbar, or 4000 dbar, etc.

σθ = σ0 = σ(S, θ, 0) σ1 = σ(S, θ1, 1000) ….. σ4 = σ(S, θ4, 4000)



Potential density: reference the density σ (S, T, p) to a specific pressure, such as at the sea surface, or at 1000 dbar, or 4000 dbar, etc.

First compute the potential temperature AT THE CHOSEN REFERENCE PRESSURE

Second compute density using that potential temperature and the observed salinity at that reference pressure.

σθ = σ0 = σ(S, θ, 0) σ1 = σ(S, θ1, 1000) ….. σ4 = σ(S, θ4, 4000)


9. Potential density profiles (σθ & σ4): note different absolute range of values because of different ref.

p

DPO Figure 4.17Talley SIO 210 (2016)

9. An important nonlinearity for the Equation of State

•  Cold water is more compressible than warm water

•  Seawater density depends on both temperature and salinity. (Compressibility also depends, much more weakly, on salinity.)

•  Constant density surfaces flatten in temperature/salinity space when the pressure is increased (next slide)


9. Potential density: density computed relative to 0 dbar and 4000 dbar

σθ

σ4


9. Potential density: reference pressures

Therefore 2 water parcels that are the same density or unstably stratified close to the sea surface will have a different relationship at high pressure


9. Atlantic section of potential density referenced to 0 dbar (sea surface): σθ

Need to use deeper reference pressures to check local vertical stability (e.g. σ4) Talley SIO 210 (2016)

9. Atlantic section of potential density referenced to 4000 dbar: σ4

Potential density σθ inversion vanishes with use of deeper reference (σ4 ): in fact, extremely stable!!


9. Isopycnal analysis: track water parcels through the ocean

•  Parcels move mostly adiabatically (isentropically). Mixing with parcels of the same density is much easier than with parcels of different density, because of ocean stratification

•  Use isopycnal surfaces as an approximation to isentropic surfaces


9. Isopycnal analysis: an isopycnal surface from the Pacific Ocean

Depth Salinity

WHP Pacific Atlas (Talley, 2007)Talley SIO 210 (2016)

9. Isopycnal analysis: an isopycnal surface from the Pacific Ocean

Potential temp. Salinity


10. Neutral density γn •  To follow a water parcel as it travels down and

up through the ocean: •  Must change reference pressure as it changes

its depth, in practical terms every 1000 dbar

•  Neutral density provides a continuous representation of this changing reference pressure. (Jackett and McDougall, 1997)

•  Ideal neutral density: follow actual water parcel as it moves, and also mixed (change T and S). Determine at every step along its path where it should fall vertically relative to the rest of the water. This is the true path of the parcel.

•  Practically speaking we can’t track water parcels.


10. Atlantic section of “neutral density”: γn


11. Brunt-Vaisala frequency •  Frequency of internal waves (period is time between

successive crests, frequency is 1/period or 2π/period) •  Internal waves are (mostly) gravity waves •  Restoring force depends on g (gravitational

acceleration) AND •  Restoring force depends on the vertical stratification •  So frequency depends on g and stratification

17 19


11. Brunt-Vaisala frequency

•  The ocean stratification is quantified by the measured value of Δρ /Δz

•  The stratification creates a restoring force on the water;if water is dispaced vertically, it oscillates in an internal wave with frequency N = sqrt(-g/ρ x Δρ /Δz)

If the water is more stratified, this frequency is higher. If less stratified, frequency is lower.



Practical calculation of Δρ /Δz to get exact frequency, and also an exact measure of how stable the water column is:

Use a reference pressure for the density in the middle of the depth interval that you are calculating over (for instance, you might have observations every 10 meters, so you would reference your densities at the mid-point of each interval, I.e. change the reference pressure every 10m.

Calculation (right panel) is noisy since it’s a derivative



Values of Brunt-Vaisala frequency: 0.2 to 6 cycles per hour

These are the frequencies of “internal waves”

Compare with frequency of surface waves, which is around 50-500 cycles per hour (1 per minute to 1 per second)

Internal waves are much slower than surface waves since the internal water interface is much less stratified than the sea-air interface, which provide the restoring force for the waves.


Seawater is compressible/elastic ! supports compressional waves or pressure waves

Sound speed:

Adiabatic compressibility of seawater (if compressibility is large then c is small; if compressibility is small then c is large:

12. Ocean acoustics: sound speed


12. Sound speed cs and Brunt-Vaisala frequency (N) profiles

σθ

θ cs

N


12. Ocean acoustics

•  Sound is a compressional wave •  Sound speed cs is calculated from the

change in density for a given change in pressure 1/cs

2 =Δρ /Δp at constant T, S This quantity is small if a given change

in pressure creates only a small change in density (I.e. medium is only weakly compressible)

•  Sound speed is much higher in water than in air because water is much less compressible than air


12. Sound speed profile: contributions of temperature and pressure to variation of cs

•  Warm water is less compressible than cold water, so sound speed is higher in warm water

•  Water at high pressure is less compressible than water at low pressure, so sound speed is higher at high pressure

•  These competing effects create a max. sound speed at the sea surface (warm) and a max. sound speed at great pressure, with a mininum sound speed in between

•  The sound speed minimum is an acoustic waveguide, called the “SOFAR” channel


c = 1448.96 + 4.59T – 0.053T2 + 1.34 (S – 35) + 0.016p (gives c in m/s if T in °C, S in psu, p in dbar)

• c increases ~5m/s per °C• c increases ~1m/s per psu S• linear increase with pressure/depth

Sound speed c has a complicated equation of state (dependence on T, S, p), but approximately:

Typical sound speed profiles in open ocean

12. Sound speed equation


12. Sound channel, or SOFAR channel (a wave guide)

Mid-latitude

High-latitude


Frequency application

10-500Hz whales

50-400Hz Tomography, thermometry

5-15kHz Acoustic navigation, pingers, deep echosounders

10-100kHz dolphins

75-300kHz ADCPs (100m-600m range)

40-400kHz Zooplankton/fish sonars

Typical sound frequencies


13. Tracers

•  Use tracers to help determine pathways of circulation, age of waters

•  Conservative vs. non-conservative – Conservative tracers do not interact with

their environment except by mixing, and at their localized sources. Examples are salinity, potential temperature, potential density, chlorofluorocarbons

– Non-conservative tracers are changed chemically or biologically within the water column. Many examples: oxygen, nutrients, helium-3

•  Natural vs. anthropogenic •  We will return to this topic in “Typical

distributions” lectures Talley SIO 210 (2016)

13. Tracers on isopycnal surfaces

Oxygen Chloroflourocarbons


13. Tracers on isopycnals

δ3He Δ14C


SIO 210 Physical properties of seawater (Lectures 2...

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