Transcript MAR 555

Introductory Physical Oceanography
(MAR 555) - Fall 2009
Prof. G. Cowles
Unit 1:
Properties of Seawater
G. Cowles
MAR 555
Fall, 2009
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Key Concepts:
1. The Earth
2. 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
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MAR 555
Fall, 2009
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The Earth: Our Oblate Spheroid
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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
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Earth’s Orbit: Principal Axes of Rotation
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To Distant Star
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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
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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
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?
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Geographic Coordinate System
Important
Latitudes
• Tropics of Cancer (~23.5N) and Tropics of
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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.
Climate / Dynamics Zones
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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
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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.
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Real Distances
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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
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Projections: A curved surface in 2D
Mercator Projection of Earth!
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Artificial stretching: Circles actually
all equivalent in area
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
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Projections: Local Coordinate Systems
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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!
Projection Software
• M_Map (Matlab)
• GIS
• Proj (http://trac.oscgeo.org/proj/)
• Pyproj (python wrapper for proj)
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Oceanic Dimensions
Ocean covers 71% of the Earth’s Surface
• Pacific: 181e6 km2
• Atlantic: 106e6 km2
• Indian: 74e6 km2
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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
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Ocean Depths: Histogram
Depth / Elevation Statistics
• Average Depth: 3730m
• Maximum Depth: 11,524m
• Maximum Elevation on Land:
8840m
• Average Land Elevation: 840m
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Typical Cross-Basin Profile (Exaggerated Vertical Scale!!)
Shelf Break
Shore
• Land-Water Interface
• Continual Reworking
• Adjustment to
Glacial, Seasonal,
Tidal Time Scales
and Storm Events
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Continental Shelf
• Majority of Worlds
Fisheries
• Gradual Slope
• Shelf Width Varies
• Storm Events
Shelf Slope
• Steep (Relatively)
Gradient
• Gravity-driven mud
flows
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Features: Canyons and Sills
Sills
• Shallow Regions separating
Two Deeper Regions.
Control the Exchange of
Water (both Volume and
Type) between them.
Example: Fjords
Canyons
• Sharp features in the
relatively gentle cont. shelf
• Generated by runoff from
previous retreated glaciers
• Notable in our region:
Hudson Canyon
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The Geoid
What is it?
Cause
• Even if we shutoff all
• Perturbations in gravity
external forcing (wind,
caused by features in the
sun, tides, etc.) and let the
seafloor warp the sea
ocean come to rest, it
surface.
would not be ‘flat’ (i.e.
• Note a rise in SSH over
distance between surface
an object of large mass!
and satellite not constant)
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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)
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Canadia
Jordan Basin
Wilkinson Basin Georges Basin
NE Channel- Sill
Depth: 230m
Georges Bank
Great South ChannelSill Depth: 70m
Canyons
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Properties of Seawater
=> Scalar (state) variables that we can measure, observe, and/or estimate
Examples
• Temperature (Kinetic Energy)
• Salinity (Dissolved Salts)
• Density (‘Heaviness’)
• Dissolved Oxygen Content
• Optical Absorbance
Utility
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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
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Temperature
What 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.
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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
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• Surface Only!!
Avg. Sea Surface Temperature Distributions
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Salinity
What 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)?
Background
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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
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Average SSS Distributions
Tropics, Evaporation > Precipitation
Med and Red Seas, Hot Dry Winds
Lead Drive Massive Evaporation
Poles, Precipitation > Evaporation
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T-S Stats
Mean 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)
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Seabird CTD
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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
0
P
 gdz P
a
P gzPa
Constant density approx.
h
Note:
P 1m  9.81*1025*1m 10055kPa 1dbar
How is it measured
with Strain Gauge
• Diaphragm: Membrane
• Quartz Resonator: Frequency depends on applied
 pressure
• Accuracy +/- 0.5 dbar
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Density
In practice, Absolute Density is extremely tedious to
measure
Volume: V (m3)
Mass: m (kg)
Solution: Estimate in situ using an Equation of State
ρ = m/V (kg/m3)
ρ = ρ(T,S,p)
Linearized EOS (For Estimates Only!)



a
(
TT
0)
b
(
SS
0)
k
p
w
h
e
r
e
k
g
o


1
0
2
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T

1
0
CS
=
3
5
p
s
u

0
3
m
k
g
k
g
k
g
3
a
=
.1
5 3o
b
=
.7
83
k
=
4
.5
1
0
3
(
m
)
(C
)
(
m
)
(
p
s
u
)
(
m
)
(
d
e
c
i
b
a
r
)
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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
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Density Anomaly
Most seawater density is typically 1020-1030 kg/m3
common then to use sigma density defined as:
It is
 (S,T, p) (S,T, p) 1000 kg/m
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Working within oceanic layers, the influence of pressure (i.e
compressibility) may be ignored giving the “sigma-t” density
anomaly.
 t  (S,T,0)
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
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Partial Phase Diagram at 1 ATM
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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
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At
typical ocean salinities (34-35), seawater remains liquid until nearly -2C
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Fall, 2009
Issue: In Situ Temperature and Salinity
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Unstable water Column?
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Potential Temperature and Density
Depth (m)
Parcel 1
100
P: water pressure
T: water temperature
T1, P1
Parcel 2
1000
T2, P2
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
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Potential Temperature and Density
How could we compared two water parcels with different pressures?
Reference pressure level
T(Po) = : potential temperature
Adiabatically (no thermal contact with the
surrounding water)
T(P): in-situ water temperature
Replacing T by the potential density, we can define the potential density (sigma-) as
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  (,S,Po ) 1000
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Static Stability: Two Layer Stratification
Work (specific) Required to Move Parcel Up a Layer
PE  (2  1)gz
z
ρ1
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ρ2
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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.
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Typical Profiles
Stratified Water
Thermocline: Temperature Gradient
Halocline: Salinity Gradient
Pycnocline: Density Gradient
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Static Stability: Continuously Stratified
1 d
E 
 dz
Stability Measure
E > 0: Stable
E2 > E1: E2 more stable
E = 0: Neutrally Stable
E < 0: Unstable (Convection will occur)
z

Buoyancy Frequency N (s-1):
g d
N  gE  
 dz
2
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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.
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Light – Beers Law
dI
 cI
dz
I  I0e
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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
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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
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Review:
1. The Earth
2. 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
G. Cowles
MAR 555
Fall, 2009
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