Unit 1: Properties of Seawater

G. CowlesMAR 555 Fall, 2009

1

Unit 1:Properties of Seawater

Introductory Physical Oceanography (MAR 555) - Fall 2009

Prof. G. Cowles


2

Key Concepts:

1. The Earth2. Coordinate Systems and Projections

3. Features of the World’s Oceans

4. Local Setting: Gulf of Maine

5. Properties of Seawater: T & S

6. Equation of State

7. Potential Temperature and Density

8. Stability and Stratification

9. Characteristics of the Worlds Oceans


3

The Earth: Our Oblate Spheroid

• Not quite round (due to rotation)• Probably not flat• Equatorial Radius: 6378.1370 km• Polar Radius: 6356.7523 km• Spins CCW from a point of view

of astronaut above North Pole• Spins CCW around sun from

point of view of astronaut on North Star

• 71% covered with water


4

Earth’s Orbit: Principal Axes of Rotation

• Earth’s rotation around its own axis is slowing down due to tides

• Note occasional increases due to abrupt changes in moment of inertia

• Spin direction of principal axes has same direction relative to orbital plane: Prograding planet

S

To Distant Star

Solar Day: 86400 seconds• Time between success zeniths of the

sun for a fixed observer • Day is 86400 seconds (24*3600)• Angular Speed of Solar Day

2π/86400s = 7.2722e-5 rad/s

Inertial “Day”: ~86164 seconds• Time between success zeniths of a

distance star for a fixed observer • Inertial Ang. Speed 7.2921150e-5 rad/s• This is the Angular Velocity we will use

for dynamics

Difference ~ 1 degree/day, why?


5

Geographic Coordinate System

• Latitude: E-W (90°S-90°N) or (-90° < Lat < 90°), huge influence on ocean dynamics

• Longitude: N-S (-180° < Long < 180°) or (180°W to 180E°)

• Lat/Lon pairs uniquely specify a point on the Earth (reverse mapping not injective)

• Meridional: Along a line of longitude• Zonal: Along a line of latitude

• Tropics of Cancer (~23.5N) and Tropics of Capricorn (~23.5S) – Within this band Sun will reach zenith at some point during year.

• Polar Circles (~66.5 N/S) – Area between these and poles will experience full 24 hours of day and night at least once a year.

Important Latitudes

• Tropics (a.k.a. low-latitude), between Tropics of C’s

• Temperate (a.k.a. mid-latitudes), between Tropics and Polar Circles

• Polar (a.k.a. high-latitude, frigid zone), between Polar Circles and Poles.

Climate / Dynamics Zones


6

Real Distances

• At the equator, 1 degree of long or lat is about 111 km.• Moving poleward, 1 degree of latitude varies slightly from 111 km

due to ellipticity of the Earth• Longitude varies greatly, 1 degree of longitude at the Poles is 0 km.• Rough calculation of km/degree longitude is 111*sin(latitude)• At SMAST (41.60N, 70.91W), degree of longitude is about 75km• Very rough rule of thumb in general: 100km /degree• 0.1° resolution ocean model ~10 km resolution


7

Projections: A curved surface in 2D

• Popular Conical Projection: Mercator• Useful Properties for Navigation pertaining to Rhumb Lines• Key issue: Greatly Exaggerated Landmass near Poles• Greenland appears as big as Africa but actually is 15x smaller• Conicals centered on the equator have trouble at poles: Singularity

Mercator Projection of Earth! Artificial stretching: Circles actually all equivalent in area


8

Projections: Local Coordinate Systems

Projection Software• M_Map (Matlab)• GIS• Proj (http://trac.oscgeo.org/proj/)• Pyproj (python wrapper for proj)

• Localized regions O(100K) can work in Earth-Attached Euclidean (Cartesian) coordinate systems

• Governing equations are simplified in Cartesian coordinates

• Coordinates are more intuitive as they are real distances

• Common projection: Lambert Conformal• Geographic Coords are standardized,

(x,y) Euclidean pairs depend on details of projection!


9

Oceanic Dimensions

Ocean covers 71% of the Earth’s Surface• Pacific: 181e6 km2

• Atlantic: 106e6 km2

• Indian: 74e6 km2

Ocean (and Atmosphere) are extremely thin layers of fluid

• Horizontal Scale (L): O (10000 km)• Vertical Scale (H): O (1 km)• Pacific: Similar ratio of dimensions to

a sheet of paper• Ratio of length scales: Aspect Ratio• H/L very small: Plays a Major Role in

the Dynamics


10

Ocean Depths: Histogram

Depth / Elevation Statistics• Average Depth: 3730m• Maximum Depth: 11,524m• Maximum Elevation on Land:

8840m• Average Land Elevation: 840m


11

Typical Cross-Basin Profile (Exaggerated Vertical Scale!!)

Shore• Land-Water Interface• Continual Reworking• Adjustment to

Glacial, Seasonal, Tidal Time Scales and Storm Events

Continental Shelf• Majority of Worlds

Fisheries• Gradual Slope• Shelf Width Varies• Storm Events

Shelf Slope• Steep (Relatively)

Gradient• Gravity-driven mud

flows

Shelf Break


12

Features: Canyons and Sills

Canyons• Sharp features in the

relatively gentle cont. shelf• Generated by runoff from

previous retreated glaciers• Notable in our region:

Hudson Canyon

Sills• Shallow Regions separating

Two Deeper Regions. Control the Exchange of Water (both Volume and Type) between them.

Example: Fjords


13

The Geoid

Cause• Perturbations in gravity

caused by features in the seafloor warp the sea surface.

• Note a rise in SSH over an object of large mass!

What is it?• Even if we shutoff all

external forcing (wind, sun, tides, etc.) and let the ocean come to rest, it would not be ‘flat’ (i.e. distance between surface and satellite not constant)

Why Care• We can use this to detect

seafloor features using measured sea surface height (SSH) from satellites

• We need to know position of geoid to subtract it out and obtain real SSH anomalies (tides and such)


14

Georges Bank

Georges Basin

Jordan Basin

Wilkinson Basin

NE Channel- Sill Depth: 230m

Great South Channel- Sill Depth: 70m

Canyons

Canadia


15

Properties of Seawater

Examples• Temperature (Kinetic Energy)• Salinity (Dissolved Salts)• Density (‘Heaviness’)• Dissolved Oxygen Content• Optical Absorbance

=> Scalar (state) variables that we can measure, observe, and/or estimate

Estimating Density• Salinity/Temp can be measured in

situ using relatively cheap instruments

• Using an equation of state, these properties can then be used to estimated density quite accurately

Tracing Water Masses• S/T provide cheap markers for

water masses

Light Profiles• Absorbance helps estimate how

light penetrates the water column, influencing heating and photosynthesis

Utility


16

TemperatureWhat is it?• Measure of the Internal Kinetic

Energy of a Substance• Fundamental Unit is Kelvin• At 0K, no Internal Kinetic Energy

How is it Measured• Absolute Temp is very difficult to

measure• Solution: use an interpolating device,

calibrated to absolute scale at two known points, e.g. a thermometer.

• Temperature (T) typically reported using the temperature anomaly scale °C, where T(°C) = T(K) – 273.15 where T=0 °C is the freezing point of water at 1 atm.

Mercury Thermometers• Slow• Accurate to about .001 °C• Early ocean measurements used

Reversing models

Platinum Resistance• Mechanism: Electrical

conductivity is temperature dependent

• Expensive, primarily used for calibration

Semiconductor Resistance (Thermistor)• Fast• Accurate to about .001 °C• Commonly Used

Remote Sensing: Radiometers• AVHRR instruments on satellites• Convert sensed infrared into electric

signals• Incredible Temporal and Spatial

Coverage• Surface Only!!


17

Avg. Sea Surface Temperature Distributions


18

SalinityWhat is it?• Measure of total amount of dissolved salts in g / kg• Chlorine (55%), Sodium (30.6%), Sulfate (7.7%)• These ratios are nearly constant through the ocean – mixing?• If units are dimensionless, should I specify o/oo, or PSU (see below)?

- 1800s: Chemical Methods: Measure Chl, uses constant ratios of salts to determine total salts and S

- 1900s: Electrical Conductivity: Measure K, link to Chl through complex relation, derive S from constant ratio assumption.

- 1970: Cox et al- Ratios aren’t constant enough for good accuracy. However, some good news: Conductivity correlates better with density than Chl measurements. What we really want is a measure of salt that can accurately be used to determine density.

- 1978: Development of the Practical Salinity Standard based on conductivity: Unit: Practical Salinity Unit (PSU).

- Today: Accurate to +/- .005

Background


19

Average SSS Distributions

Tropics, Evaporation > Precipitation

Poles, Precipitation > Evaporation

Med and Red Seas, Hot Dry WindsLead Drive Massive Evaporation


20

T-S StatsMean Values in the Ocean: T: 3.52°C (75% between 0° and 4°)

S: 34.72 (75% between 34.5 and 35)

Pacific is Fresher (S = 34.62) than the Atlantic (S = 34.90)

Ocean is cold! – Warm water is confined to shallow depths

High Salinity Zones: Red Sea (> 40 ) and Dead Sea (293)

Seabird CTD


21

Pressure (Static) and Depth

What is it?• Force per unit area• Units: N/m^2 (ak.a. Pascals, Pa) (S.I.)• Units: bar (100 kPa)• Decibar: 10 kPa (oceanographer)

How is it Calculated

How is it measured• Diaphragm: Membrane with Strain Gauge• Quartz Resonator: Frequency depends on applied

pressure• Accuracy +/- 0.5 dbar

€

P= ρgdz +Pah

0

∫

€

P≈ ρgz+Pa

€

P 1m≈ 9.81*1025*1m =10055kPa ≈1dbar

Constant density approx.

Note:


22

DensityVolume: V (m3)

Mass: m (kg)

ρ = m/V (kg/m3)

In practice, Absolute Density is extremely tedious to measure

Solution: Estimate in situ using an Equation of State

ρ = ρ(T,S,p)

• Coastal applications, influence of p may be ignored• Areas of high suspended sediment load must include mass of dry material• Standards Maintained by UNESCO• Matlab/Python/Ruby Functions on the Web• Online EOS Calculators

0 0

03

-33 3 3

( ) ( )

1027 10 S=35psu

kg kg kg =.15 =.78 = 4.5 10

(m )( ) (m )( ) (m )( )

o

o

a T T b S S kp

where

kgT C

m

a b kC psu decibar

Linearized EOS (For Estimates Only!)


23

Density Anomaly

Most seawater density is typically 1020-1030 kg/m3 It is common then to use sigma density defined as:

€

σ(S,T, p)= ρ (S,T, p) −1000kg /m3

Working within oceanic layers, the influence of pressure (i.e compressibility) may be ignored giving the “sigma-t” density anomaly.

€

σ t= σ (S,T,0)


24

Partial Phase Diagram at 1 ATM

• S < 24.7, maximum density occurs at higher temp than freezing• Ice (solid phase) floats on liquid• As surface is cooled, colder, denser water sinks until temperature of max density reached.

Further cooling produces relatively lighter water which eventually freezes• At typical ocean salinities (34-35), seawater remains liquid until nearly -2C


25

Issue: In Situ Temperature and Salinity

Unstable water Column?


26

Potential Temperature and DensityDepth (m)

100

1000

Parcel 1

Parcel 2

T1, P1

T2, P2

P: water pressureT: water temperature

If T2>T1, does it means that the water parcel 2 is warmer ?

Answer: NO! The water is slightly compressible and these two water parcels have different pressures


27

Potential Temperature and DensityHow could we compared two water parcels with different pressures?

T(P): in-situ water temperature

T(Po) = : potential temperature

Adiabatically (no thermal contact with the surrounding water)

Reference pressure level

Replacing T by the potential density, we can define the potential density (sigma-) as

€

σ =(θ ,S,Po) −1000


28

Static Stability: Two Layer Stratification

Work (specific) Required to Move Parcel Up a Layer

€

ΔPE = (ρ 2 − ρ1)gΔz

ρ2

zρ1

• Low Density on High = Stable• Increasing Density with Depth = Stable• Work requires source of energy, either

mechanical (Mixing) or thermal (Heating/Cooling)

• ρ1 = ρ2 No work required to move water parcel => no change in potential energy (neutral stability)

• In reality, density of the ocean increases with depth.


29

Typical Profiles

Thermocline: Temperature GradientHalocline: Salinity GradientPycnocline: Density Gradient

Stratified Water


30

Static Stability: Continuously Stratified

€

E = −1

ρ

dρ

dzStability Measure

E > 0: StableE2 > E1: E2 more stableE = 0: Neutrally StableE < 0: Unstable (Convection will occur)

Buoyancy Frequency N (s-1):

€

N 2 = gE = −g

ρ

dρ

dz

z

ρ

• Natural frequency of oscillation of a fluid parcel at z• ρ is true density (not anomaly)• We will revisit this when we explore dynamical stability in the context of

mixing in Unit8.


31

Light – Beers Law

€

dI

dz= −cI

€

I = I0e−cz

c: attenuation coefficient (depends on level of suspended material)I: incident light at the surface (W/m2)

Light profile assuming attenuation does not depend on depth

Note: Pay attention to the orientation of the z-coordinate


32

Data Sources – Examples:Realtime Data: Ocean Observing Systems (OOS)• GoMOOS• NERACOOS• MACOORA• NDBC• other COOS’s

Archival Data• NODC (point + field data)• NDBC (point data)

Future Data – Model Predictions• NeCOFS: FVCOM model, Gulf of Maine• SCCOOS: ROMS model, Southern Cali• GoMOOS: POM model, Gulf of Maine


33

Review:

1. The Earth2. Coordinate Systems and Projections

3. Features of the Worlds Oceans

4. Local Setting: Gulf of Maine

5. Properties of Seawater: T & S

6. Equation of State

7. Potential Temperature and Density

8. Stability and Stratification

9. Characteristics of the Worlds Oceans

Documents

Unit 1: Properties of Seawater