AOSS 401, Fall 2007Lecture 1

September 5, 2007

Richard B. Rood (Room 2525, SRB)rbrood@umich.edu

734-647-3530Derek Posselt (Room 2517D, SRB)

dposselt@umich.edu734-936-0502

Name of Course

• Geophysical Fluid Dynamics

• What it really is …– Introduction to Dynamic Meteorology– Fluid dynamics of the neutral atmosphere on

a rotating planet.

• How many are weather, climate, space?

Text Book

• Holton, James R.• An Introduction to Dynamic

Meteorology, Volume 88, Fourth Edition (International Geophysics) – Hardcover: 535 pages – Publisher: Academic Press; 4 edition (March

31, 2004) – Language: English – ISBN: 0123540151

Where does it fit in?

• AOSS 321– First 2 (+) Chapters of Holton

• AOSS 401– Chapters 3 – 6+ of Holton (No chapter 5,

Allison Steiner’s course.)

• AOSS 451– Chapters > 7 of Holton (waves and stability)

Other recommended reference (1)

• Hess, Seymour L.• Introduction to Theoretical Meteorology

– Hardcover: 362 pages – Publisher: Krieger Pub Co (February 1979) – Language: English – ISBN: 0882758578

• A clear intuitive introduction to basic concepts of meteorology.

Other recommended text (2)

• Dutton, John A.• The Ceaseless Wind: An Introduction to the

Theory of Atmospheric Motion (Dover Phoenix Editions)– Hardcover: 640 pages – Publisher: Dover Publications (May 1, 2002) – Language: English – ISBN: 0486495035

• Rigorous mathematical approach with thorough introduction of background material.

Other recommended reference (3)

• Martin, Jonathan E.Mid-Latitude Atmospheric Dynamics – Paperback: 324 pages – Publisher: Wiley; 1st edition (2006) – Language: English – ISBN: 0470864656

• Focuses on mid-latitude cyclones with good introduction to the principles of atmospheric dynamics

Other recommended reference (4)

• Lynch, Amanda H. and Cassano, John J.Applied Atmospheric Dynamics – Paperback: 280 pages – Publisher: Wiley; 1st edition (2006) – Language: English – ISBN: 0470861738

• Example driven dynamics text book with focus on weather systems, includes a CD

Class News

• Ctools site (AOSS 401 001 F07)– Calendar (completed for whole semester)– Syllabus– Lectures

• Posted on day of

– Homework (and solutions)

• Course is being taught by– Richard Rood– Derek Posselt

Class news: Schedule issues

• Currently 4.5 hours are scheduled for a 4.0 hour course. (So we have some flexibility; we can “cancel” 4 classes)– There will be no class on September 14– There will be no class on October 12– There will be no class on November 21– When to schedule final exam?

Dynamical meteorology

• “Dynamic meteorology is the study of those motions of the atmosphere that are associated with weather and climate.”

• Meteorologists generally divide the theory-based description of their science into two major divisions– Dynamic meteorology– Physical meteorology

Dynamical meteorology

• Dynamic meteorology is associated with the fluid dynamics of the atmosphere. – Resolved waves– Dynamical systems such as hurricanes– Dissipation of these waves and dynamical

systems– General circulation that results from it all …

• Ultimately how does heat transported by the atmosphere contribute to the maintenance of the global energy balance

Physical meteorology

• Physical meteorology is associated with thermodynamics - radiative transfer, cloud physics

• Turbulence, viscosity, unresolved wave motions, etc., sit at the interface of dynamic and physical meteorology

• Water and the energy associated with phase changes of water strongly link dynamical and physical meteorology

Why is dynamic meteorology important?

• Core element of the scientific investigation of the atmosphere – meteorology

• Central to weather and weather forecasting– Propagation of dynamic systems is at the heart of

weather forecasting• Central to distribution and variability of trace

constituents – chemistry, air quality• Central to exchange of energy, constituents,

between atmosphere and land and ocean• Climate, climate change, impact of climate

change on ecosystems and human enterprise

Why is dynamic meteorology important?

• It’s required to get a degree in meteorology.

• It’s very, very interesting.

Do you see yourself on that list?

• Why are you taking this class?– Required?

• What do you want to get out of it?– Is there something that really interests you?

Characteristics of Dynamic Meteorology(Why is it hard?)

• Mathematically based• Uses calculus (and algebra)• Uses vectors

– Can you think of math as simplifying?

• Principles of dynamic meteorology are largely drawn from fluid dynamics, but without any previous study of fluid dynamics.

Characteristics of Dynamic Meteorology(Why is it hard?)

• We are required to work in a rotating, spherical coordinate system

• The concept of scale analysis• Which you will ultimately use in all aspects of your

life, if you don’t use it already.

• Complexity

But, the physics are simple!

• Conservation principle– Momentum– Mass– Energy

• Newtonian physics, Newton’s laws of motion applied to the atmosphere.– force = mass x acceleration– acceleration = change of velocity with time– velocity = change of position with time

But, the physics are simple!

• Newtonian physics, Newton’s laws of motion applied to the atmosphere.F = ma

a = dv/dt

v = dx/dt

This is at the starting point.

Are you comfortable with this?

Conservation (continuity) principle

• There are certain parameters, for example, energy, momentum, mass (air, water, ozone, number of atoms, … ) that are conserved. – “classical” physics, we’re not talking about general or special

relativity!– Simple stuff, like billiard balls hitting each other, ice melting

• Conserved? That means that in an isolated system that the parameter remains constant; it’s not created; it’s not destroyed.

• Isolated system? A collection of things, described by the parameter, that might interact with each other, but does not interact with other things. Nothing comes into or goes out of the system … or, perhaps, nothing crosses the boundary that surrounds the system.

Conservation (continuity) principle

• There are many other things in the world that we can think of as conserved. For example, money.– We have the money that we have.

• If we don’t spend money or make money then the money we have tomorrow is the same as the money we had yesterday.

Mtomorrow = Myesterday

That’s not very interesting, or realistic

Conservation (continuity) principle(with “production” and “loss”)

Mtomorrow = Myesterday + I - E

Let’s get some money and buy stuff.

Income

Expense

Conservation (continuity) principle(with the notion of time)

Mtomorrow = Myesterday + N(I – E)

SalaryIncome per month = I

RentExpense per month = EN = number of months

I = NxI and E= NxE

Income

Expense

Some algebra and some thinking

Mtomorrow = Myesterday + N(I – E)

Rewrite the equation to represent the difference in money

(Mtomorrow - Myesterday ) = N(I – E)

This difference will get more positive or more negative as time goes on.Saving money or going into debt.

Divide both sides by N, to get some notion of how difference changes with time.

(Mtomorrow - Myesterday )/N = I – E

Conservation (continuity) principle

• dM/dt = Production – Loss

This is at the starting point.Are you comfortable with this?

Picture of Earth: What can you say about this figure?

Some basics of Earth’s atmosphere

• Atmosphere is composed of air, which is a mixture of gases, which is treated as an ideal gas, and which below ~ altitude of 1.0 x 105 m (100 km) behaves like a fluid – a continuum.

• Hint: Know and use the ideal gas law.

• What is a continuum?

Some basics of Earth’s atmosphere

Earth: radius ≡ a = 6.37 x 106 m

atmosphere: depth ~ 1.0 x 105 m

Mountain: height ~ 5.0 x 103 m

Ocean Land Biosphere

Some basics of Earth’s atmosphere

Troposphere: depth ~ 1.0 x 104 m

Troposphere------------------ ~ 2Mountain

Troposphere------------------ ~ 1.6 x 10-3

Earth radius

Scale analysis tells us that the troposphere is thin relative to the size of the Earth and that mountains extend half way through the troposphere.

Some basics of Earth’s atmosphere

Troposphere: depth ~ 900 mb

Do you know these units?

Pressure:mb = millibarshPa=hecto Pascals

Scale analysis tells us that most of the mass of the atmosphere is in the troposphere.

So what is this course (1)?

• First part of this course is review and practice– Defining the forces that act in the atmosphere

• Pressure gradient• Apparent forces that come from a rotating coordinate system• Gravity• Friction

– Pressure as a vertical coordinate• Geopotential and pressure

– Describing d ( )/dt in a rotating, spherical coordinate system.

So what is this course (2)?

• Equations of motions.

• First part is followed by use of scale analysis to look at some particular aspects of atmospheric flow.

• Balanced flow– Thermal wind

• Then expect to have a test.

So what is this course (3)?

• Then we are going to look at some important concepts of dynamic meteorology– Vorticity, Potential vorticity– Divergence (vertical wind)

• Link between physics and dynamics

– Large-scale waves in middle latitudes (quasi-geostrophic approximation, barotropic and baroclinic)

• Weather, jet streams, tracer variability, …

• Then expect to have another test.– You will know how to derive the vorticity equation

So what is this course (4)?

• Scale analysis and motion at different scales– Different types of waves

• Dispersion relationship, phase and group velocity

– Introduction to hurricane dynamics

– You will know how to calculate “wave-like” solutions

• Special topics?

• Final exam

What is in this course and how does it link to the text.

• Chapter 1• Chapter 2• Chapter 3

– TEST 1

• Chapter 4– TEST 2

• Chapter 6• Chapter 7 (introduction)

– Final Exam (Covers entire course)

} Fast Review

Tests, Projects, Homework, Exams

• TEST 1 (30%)• TEST 2 (30%)• FINAL EXAM (40%)

• HOMEWORK– Will be assigned. It is primarily for your benefit.– I will try to assign problems that investigate concepts and

techniques.– I will try to assign problems that are directly relevant to tests.– If you choose to do the homework and turn it in, then it will be

considered at grading time; that is, it can compensate for deficiencies on the tests ~ 5%.

– If you don’t do the homework, then you will probably NOT do well on the exams.

A simple programming exercise

• We are going to develop a simple program based on the hydrostatic equation to expose– Vertical structure of the atmosphere– Pressure as a vertical coordinate– Wave motion

– Matlab, C++, ?

Picture of Earth: What can you say about this figure?

Dynamic Atmosphere:Extratropical storm systems

• Satellite image• Storm system in

the Gulf of Alaska• Scale of the

motion:3000-5000 km

• What are the differences/similarities of these weather systems?

Conceptual Ideas

• Weather map with isobars: Lines connecting equal pressure levels

Weather maps: http://www.wunderground.com

Dynamic atmosphere: Hurricanes

• Satellite image• Tropical storm

that originates over warm ocean water

• Scale of the motion:1000 km

Weather

• National Weather Service– http://www.nws.noaa.gov/– Model forecasts:

http://www.hpc.ncep.noaa.gov/basicwx/day0-7loop.html

• Weather Underground– http://www.wunderground.com/cgi-bin/findweather/getForecast?

query=ann+arbor

– Model forecasts: http://www.wunderground.com/modelmaps/maps.asp?model=NAM&domain=US

Dynamic atmosphere: Tornadoes

• Photo• Funnel cloud

that emerges from a thunderstorm

• Scale of the motion:<1 km

Martian dust devil tracksWhat are these?

Some fundamental notions you will learn.

• The importance of the conservation equation• Atmospheric motions organize in distinct spatial and temporal

scales• Most of the dynamic disturbances of the atmosphere can be

classified as either:– Waves– Vortices

• There is a mean circulation of the atmosphere which is known as the general circulation.– What does this do?

• The atmosphere has two dominate balances, at least away from the tropics:– Hydrostatic balance– Geostrophic balance

• It is the deviations from this balance which we are most interested in.

Sunset from surface of Mars

Final Slide

• Review the book

• There will be homework posted before the next class.– Due next Wednesday

• Questions