11

MATH 2240 Introduction to Oceanography

and MeteorologyDr. Alex Sen GuptaClimate Change Research CentreRoom 454 Matthews BuildingE-Mail: a.sengupta@unsw.edu.au Consultation Tuesday 11-1pm

Class Time: Friday 9-11Room 3037 Red Centre WestLectures and tutorials are combined.

Introduction to Oceanography and Meteorology

Topics We Will Cover – 6 Chapters1. Introduction to the ocean and atmosphere2. Dynamics: The Equations of Motion

The vertical and horizontal equations, Geostrophic balance, thermal wind and fronts.

3. Unforced motion – wavesLong surface Waves, Wave diffraction and steepening, Vorticity

4. Wind Forced motionEkman Transport, Storm Surges, Upwelling, Ekman pumping

5. Atmospheric CirculationRadiation Balance, Hadley/Walker Cells, Baroclinic instabilities

6. Meso-Scale Atmospheric CirculationE.g. Thunderstorms and Cyclones

Course ScheduleCourse ScheduleTuesday Time Topic Important Dates Week 1 13th March 9-11am Chapter 1 Introduction Week 2 20th March 9-11am Chapter 2 Dynamics Week 3 27th April 9-11am Chapter 2 Dynamics Assignment 1 – 10 %

Due Monday 20th AprilWeek 4 3rdApril 9-11am Chapter 3 Ocean Waves

Easter BreakWeek 6 24th April 9-11am Chapter 3 Ocean Waves Assignment 2 -20%

Due Friday 8th MayWeek 7 1st May 9-11am Chapter 4 Wind Forced Motion Week 8 8th May 9-11am Chapter 4 Wind Forced Motion Week 9 15th May 9-11am Chapter 5 Atmospheric Circulation Assignment 3 – 20%

Due Monday 1st JuneWeek 10 22nd May 9-11am Chapter 5 Atmospheric Circulation Week 11 29th May 9-11am Chapter 6 Meso Scale Atmos Circulation Week 12 5th June 9-11am Chapter 6 Meso Scale Atmos Circulation

All assignments due at 12 noon on the assigned day at the school office. Assignments Handed in late will incur a 10% reduction in the mark per day. Assignments handed in More than 7 days late will not receive a mark.

Assessment Tasks and FeedbackAssessment Tasks and Feedback

Course material: http://web.maths.unsw.edu.au/~alexg/

Text BooksText BooksThere is no prescribed text for this course.• A number of reference books are available on the course web site.

• Ocean Circulation, the Open University• http://engineering.dartmouth.edu/~cushman/books/GFD.html

Comprehensive notes will be made available on the course web site.Equipment needed:Please bring a pen, pencil and calculator to class each week.

Chapter 1 IntroductionTopics We Will Cover Today1. Introduction to the ocean and atmosphere2. Properties of the ocean

– Temperature– Salinity– Pressure– Density

3. Properties of the Atmosphere– Composition– Temperature– Vertical Structure– Water Vapour– Atmospheric Pressure– Density

4. The Earth as a heat Engine5. Distinctions between the Atmosphere and Ocean6. Units / Co-ordinate System / Nomenclature

Oceanography and MeteorologyOceanography and Meteorology• The study of the dynamics of the oceans and the

atmosphere• Governed by simple physical laws• Solutions require advanced mathematical methods

– Solutions to differential equations– Numerical analysis– Non-linear dynamics– Computational mathematics– Optimisation– Statistical analyses– Fourier Analysis– Time Series Analysis

ApplicationsApplicationsEnvironmental Disasters

ApplicationsApplicationsPower Generation

ApplicationsApplicationsNavigation

ApplicationsApplicationsBiology/Fisheries

ApplicationsApplicationsWeather prediction

• Weather Prediction• Climate Prediction• Climate Change• ENSO

ApplicationsApplicationsClimate Prediction

GeophysicalGeophysicalFluidFluid

DynamicsDynamics

Oceanic and Atmospheric Phenomena

100 y

Month

mins

Time Scale

2 yrs

days

Molecular Waves Turbulence

Fronts

El Nino

Climate Change

N. AtlanticOscillation

Eddies

1 km 10000 kmSpatial Scale

cms 10 m 100 km

Boundarycurrents

Upwelling Diurnal cycle

Deep waterformation

Weather

Hail storm

Oceanic and Atmospheric Phenomena

Properties of the oceans

Water covers ~71% of world surfaceAverage depth 3800mPacific Ocean 46%Atlantic Ocean 23%Indian Ocean 20% Others 11%

Q. What is the volume of the ocean?Q, What is the aspect ratio of the ocean (i.e a typical depth H divided by a typical length, L)?Q. Is the aspect ratio of a piece of paper? (a 500 sheet ream of paper has a width of ~5cm)?The aspect ratio turns out to have important consequences for the magnitude of typical velocites in the horizontal compared to vertical directions

Properties of the oceans

Measuring the OceanEcho sounders (time taken to bounce a sound wave)Gravity measurements – the slope of the surface is affected by the gravitational attraction of underlying bathymetry features (see Giod)

Properties of the OceanTemperature (T)•Temperature is important because it reflects the amount of heat held and transported by the ocean.

•Plays important role in circulation via density

•The temperature range in the ocean varies from -2°C at the poles to >28°C at the equator.

•The temperature of the ocean is primarily influenced by the heating at the air-sea interface.

Global Sea Surface TemperatureGlobal Sea Surface Temperature

Properties of the oceans

The ocean has a massive thermal inertia compared to the atmosphereCalculate the heat required to heat the atmosphere by 1C?With this amount of heat what volume of water could you heat up by 1C?By calculating the surface area of the worlds ocean, what depth does this volume correspond to?

•Density of water: ~1000kgm-3

•Specific heat capacity of air C=1000J/kg/K•Specific heat capacity of water C=4000J/kg/K

H=mCΔT, m=mass

HOMEWORK!

Temperature distribution with depthTemperature distribution with depth

Temperature distribution with depthTemperature distribution with depth

Salinity• Total dissolved solids (mainly sodium chloride, or “table salt”)• About 3.5% by weight (i.e 35kg of salt in 1000kg of pure water

on average)• Usually expressed as 35psu (practical salinity units, psu, or no

units at all)

What sets the salinity in the ocean?

Properties of the Ocean

Salinity• Total dissolved solids (mainly sodium chloride, or “table salt”)• About 3.5% by weight (i.e 35kg of salt in 1000kg of pure water

on average)• Usually expressed as 35psu (practical salinity units, or ppt

parts per thousand – they are the same)• Varies geographically according to Evaporation, precipitation,

rivers, ice formation and ice melt.• Plays an important part in ocean circulation, through influence

on density

Properties of the OceanProperties of the

oceans

Salinity changes with depth:Salinity changes with depth:PolarTemperateTropical

PressurePressure• Ocean pressure is the weight of seawater per

unit area (force per unit area). • It is mainly a function of depth.• Pressure in the ocean increases at a rate of

about 1 “atmosphere” OR “bar” per 10 m of water.

• Or pressure increases by 1 dbar per 1 m of water.

• At 4000m, P=4000tonnes/m2 i.e. one person trying to hold up 100 jumbo jets

• Differences in pressure area one of major drivers of ocean circulation

Stiletto vs Elephant

Density in the ocean Density in the ocean (ρ)(ρ)• Density is the mass of sea water per unit volume.

Kg / m3

• Density depends on salinity, temperature and pressure.

- Density increases with increasing salinity

- Density increases with decreasing temperature

• Seawater density ranges from 1020 – 1030 kg/m³, the average density is 1025 kg/m³

Density (continued)(continued)

• Density increases with pressure, as the pressure force squashes water into a smaller volume.

• Lighter water is - warmer- fresher

• Denser water is - colder- more saline

• Generally for stability, less dense water overlies more dense water – otherwise convection

The Equation of State

For regions where T and S vary little, we may assume a linear equation of state.

Where alpha and beta are nearly constant expansion coefficients for T and S.

Density Structure of the OceanDensity Structure of the Ocean

Thermocline – Sharp temperature gradientHalocline – Sharp salinity gradientPycnocline – Sharp density gradient

Composition

•N2 ( 75% by mass)

•O2 (23.2% by mass)

•Others (1.3% e.g. argon, CO2)

•Water vapour, also exists in small amounts, 0- 4% over the desert and oceans.

Composition of AirComposition of AirThe earth's atmosphere is a very thin layer that surrounds a very large planet.

Water vapour is important to weatherproduction since it exists in gaseous, liquid, and solid phases and absorbs radiant energy from the earth – GREENHOUSE GAS.

Based on temperature, the atmosphere is divided into four layers: the troposphere, stratosphere, mesosphere, and thermosphere.

Temperature in Temperature in the Atmospherethe Atmosphere

99.9% of mass of the atmosphere is below the Stratopause

The The TroposphereTroposphere• The troposphere extends from the

earth's surface to ~ of 12 km. • Pressure ranges 1000 to 200mb. • Temperature generally decreases

with increasing height up to the tropopause (top of the troposphere); this is near 200mb/12km– Temperature range ~ 15°C (surface) to

~ -57°C at the tropopause. – The layer ends at the point where

temperature no longer varies with height. This area, known as the tropopause, marks the transition to the stratosphere.

The The TroposphereTroposphere

• Winds increase with height up to the jet stream.

• The moisture concentration decreases with height up to the tropopause. – The air is much drier above the

tropopause, in the stratosphere. – The sun's heat that warms the earth's

surface is transported upwards largely by convection and is mixed by updrafts and downdrafts.

• The troposphere is 70% N2 and 21% O2. The lower density of molecules higher up would not give us enough to survive.

Vertical temperature in the atmosphere

Sun's radiation: near infrared (37%), visible (44%), and ultraviolet (7%) Earth's radiation is mostly far infrared

Heated by radiation from the earth (most is absorbed at lower levels)Unstable conditions cause convection and mixing of heat upwards

Increased temperature mainly due to absorption of solar UV radiation by ozone

Increased warming by O2absorption of solar radiation

Pressure in the Pressure in the AtmosphereAtmosphere

• Air pressure is the pressure exerted by the air in the column above that height

• Atmospheric Pressure decreases with height above the earth.

• Pressure at sea level 1040-970mb (or hPa)

Density in the AtmosphereDensity in the Atmosphere• Air density decreases with increasing altitude (as

does air pressure). It also decreases with increasing temperature or humidity. At sea level and 20°C, air has a density of approximately 1.2 kg/m3.

pRT

ρ =

VDhumid

D V

ppR T R T

ρ = +

As the molecular mass of water is less than average molecular mass of air, humid are is actually less dense than dry air

Energy reaching the Earth affected by:• Angle of the sun (overhead at low latitudes)•Albedo (ice covered poles reflect much of the energy back to space without heating the planet)

Ruddiman (2000)

What drives the climate system? What drives the climate system?Seasonal changes in insolation (animation)

The sun’s energy is reflected more strongly by the land than by the ocean. Greatest reflection occurs over the white ice surfaces.

The proportion of reflected energy is the ALBEDO

Unequal heating of tropics and poles and resulting radiation imbalanceslow latitudes:- more outgoing longwave radiation- but more than compensated by intense

incoming solar radiationnet heating

high latitudes:- low net incoming solar radiation

(low angle of sun & high albedo)- exceeds outgoing longwave

net cooling

What drives the climate system?

Conservation of energy: If the energy IN exceeds the energy OUT then warming will occur.

Averaged over the whole planet energy IN is balanced by energy OUT.

BUT there is a net energy GAIN at low-latitudes (the tropics) and a net energy LOSS at high-latitudes (the poles).

So why doesn’t the tropics keep getting warmer and the poles keep getting colder?

There has to be a transfer of heat from the equator to the poles

What drives the climate system?

To compensate for the polar cooling and tropical heating:

Both ocean & atmosphere transport the excess heat polewards

Pole

war

d he

at tr

ansp

ort P

W

What drives the climate system?

As a fluid (e.g. ocean/ atmosphere) warms (cools) it becomes less (more) dense. If a heavy fluid (high density) sits above a light fluid convection will occur.

Convection is a very efficient way if transporting heat.

The equator-pole temperature gives rise to convective motion in both the atmosphere and ocean

What drives the climate system?

What drives the climate system? ATMOSPHERE

No Rotation

With rotation (Coriolis)

• Ocean currents transfer heat poleward. Major currents, such as the Gulf Stream,and the EAC transport tremendous amounts of heat poleward and contribute to the development of many types of weather phenomena.

• They also warm the climate of nearby locations. Conversely, cold southward flowing currents, such as the California current, cool the climate of nearby locations.

What drives the climate system?

Net heat lostfrom ocean

Net heat lostfrom ocean

Net heat to ocean

What drives the climate system? There is also a convective ‘overturning circulation’ The Water CycleThe Water Cycle• Most water vapour in the

atmosphere comes from the oceans.

• Most of the precipitation falling over land finds its way back to oceans.

• About two-thirds returns to the atmosphere via the water cycle.

• Oceans act as an abundant moisture source for the atmosphere and a heat source and sink (storage).

• The exchange of heat and moisture has profound effects on atmospheric processes near and over the oceans.

Z is usually positive downwards….

Negative depth doesn’t make sense!

OceanCoordinate

System

Used for all calculations from now on….

xy

z

u

w

v

Oceans

z (altitude)

x (longitude)

y (latitude)

Atmosphere

Coordinate systems and Notation

GradientsGradientsA Gradient is a measure of how a quantity (pressure, salt, temperature, density) changes with direction:e.g

In most applications in oceanography, the gradient term in an equation, such as:

Can be approximated as

Δρ , Δρ , ΔρΔx Δy Δz

ρ2 – ρ1x2 – x1

ΔρΔx=

etc , ,dxd

dxdT ρ

xT

dxdT

ΔΔ

≅

Change

1st year maths!

Where is the temperature gradient bigger?

100m

1000m

dT/dx ~ 2oC/1000m = 0.002 oC m-1

dT/dx ~ 2oC/100m = 0.02 oCm-1

Where is the temperature gradient bigger?

100m

1000m

What can you say about the gradient?

0dudx

>

What can you say about the gradient?

What can you say about the gradient?

Units

Force N (Newtons)

1 bar = 100 PaPa = Nm-2

Distinctions between the Distinctions between the Atmosphere and OceanAtmosphere and Ocean

• Length, velocity and timescales vary.• Landmasses affect ocean circulation, • No lateral boundaries in the atmosphere.• Salinity - Affects density in the ocean.• Forcing mechanisms in the ocean, gravity, (tides), winds.• Terminology and conventions... In meteorology we refer

to winds by the direction of origin (e.g. A northerly) however in the ocean we refer to the direction of travel, (e.g. A southward current).

Length Velocity and Time ScalesLength Velocity and Time Scales

6161

Review:Review:Important ocean properties, T, S, pressure, density. Important atmosphere properties, T, water vapor/humidity,

pressure, density, trace gasesMajor horizontal and vertical differences in propertiesClimate system is a giant heat engine: ocean and

atmosphere are fluids whose motion redistributes the imbalance in earth’s heat gain and loss. (other source of energy is gravity via tides)

Very different distance, velocity and timescales in the motion of ocean and atmosphere

Coming upComing up

F ma or1 a Fm

=

= Σ

Motion in the ocean …

Equations of motion, simply a restatement of Newton’s laws for a fluid on a rotating planet