1. AOSS 401, Fall 2007 Lecture 1 September 5, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu 734-936-0502

2. 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?

3. 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

4. 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)

5. 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.

6. 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.

7. 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

8. 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

9. Class News Ctools site (AOSS 401 001 F07)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

10. 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?

11. 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

12. 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

13. 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

14. 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

15. Why is dynamic meteorology important? It’s required to get a degree in meteorology. It’s very, very interesting.

16. 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?

17. 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.

18. 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

19. 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

20. 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?

21. 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.

22. 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. M tomorrow = M yesterday That’s not very interesting, or realistic

23. Conservation (continuity) principle (with “production” and “loss”) M tomorrow = M yesterday + I - E Let’s get some money and buy stuff. Income Expense

24. Conservation (continuity) principle (with the notion of time) M tomorrow = M yesterday + N(I – E) Salary Income per month = I Rent Expense per month = E N = number of months I = NxI and E= NxE Income Expense

25. Some algebra and some thinking M tomorrow = M yesterday + N(I – E) Rewrite the equation to represent the difference in money (M tomorrow - M yesterday ) = 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. (M tomorrow - M yesterday )/N = I – E

26. Conservation (continuity) principle dM/dt = Production – Loss This is at the starting point. Are you comfortable with this?

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

28. 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 10 5 m (100 km) behaves like a fluid – a continuum. Hint: Know and use the ideal gas law. What is a continuum?

29. Some basics of Earth’s atmosphere Earth: radius ≡ a = 6.37 x 10 6 m atmosphere: depth ~ 1.0 x 10 5 m Mountain: height ~ 5.0 x 10 3 m OceanLandBiosphere

30. Some basics of Earth’s atmosphere Troposphere: depth ~ 1.0 x 10 4 m Troposphere ------------------ ~ 2 Mountain 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.

31. Some basics of Earth’s atmosphere Troposphere: depth ~ 900 mb Do you know these units? Pressure: mb = millibars hPa=hecto Pascals Scale analysis tells us that most of the mass of the atmosphere is in the troposphere.

32. 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.

33. 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.

34. 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

35. 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

36. 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

37. 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.

38. 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++, ?

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

40. 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?

41. Conceptual Ideas Weather map with isobars: Lines connecting equal pressure levels Weather maps: http://www.wunderground.comhttp://www.wunderground.com

42. Dynamic atmosphere: Hurricanes Satellite image Tropical storm that originates over warm ocean water Scale of the motion:1000 km

43. Weather National Weather Service –http://www.nws.noaa.gov/http://www.nws.noaa.gov/ –Model forecasts: http://www.hpc.ncep.noaa.gov/basicwx/day0- 7loop.html http://www.hpc.ncep.noaa.gov/basicwx/day0- 7loop.html Weather Underground –http://www.wunderground.com/cgi- bin/findweather/getForecast?query=ann+arborhttp://www.wunderground.com/cgi- bin/findweather/getForecast?query=ann+arbor –Model forecasts: http://www.wunderground.com/modelmaps/maps.asp ?model=NAM&domain=US http://www.wunderground.com/modelmaps/maps.asp ?model=NAM&domain=US

44. Dynamic atmosphere: Tornadoes Photo Funnel cloud that emerges from a thunderstorm Scale of the motion:<1 km

45. Martian dust devil tracks What are these?

46. 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.

47. Sunset from surface of Mars

48. Final Slide Review the book There will be homework posted before the next class. –Due next Wednesday Questions