Transcript AOSS 401, Fall 2006 Lecture 1 September 6, 2006

AOSS 401, Fall 2007
Lecture 1
September 5, 2007
Richard B. Rood (Room 2525, SRB)
[email protected]
734-647-3530
Derek Posselt (Room 2517D, SRB)
[email protected]
734-936-0502
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)
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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
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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
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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 theorybased 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”)
Income
Mtomorrow = Myesterday + I - E
Let’s get some money and buy stuff.
Expense
Conservation (continuity) principle
(with the notion of time)
Income
Mtomorrow = Myesterday + N(I – E)
Salary
Income per month = I
Rent
Expense per month = E
N = number of months
I = NxI and E= NxE
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
atmosphere: depth ~ 1.0 x 105 m
Mountain: height ~ 5.0 x 103 m
Ocean
Land
Earth: radius ≡ a = 6.37 x 106 m
Biosphere
Some basics of Earth’s atmosphere
Troposphere
------------------ ~ 2
Mountain
Troposphere
------------------ ~ 1.6 x 10-3
Earth radius
Troposphere: depth ~ 1.0 x 104 m
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
Do you know these units?
Pressure:
mb = millibars
hPa=hecto Pascals
Troposphere: depth ~ 900 mb
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
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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 (quasigeostrophic 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
} Fast Review
– TEST 1
• Chapter 4
– TEST 2
• Chapter 6
• Chapter 7 (introduction)
– Final Exam (Covers entire course)
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/day07loop.html
• Weather Underground
– http://www.wunderground.com/cgibin/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
are these?
MartianWhat
dust
devil tracks
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