AOSS 401, Fall 2013 Lecture 1 Introduction / Forces September 3 , 2013

1. AOSS 401, Fall 2013Lecture 1Introduction / ForcesSeptember 3, 2013 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Cell: 301-526-8572

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, geosci?

3. Class News • Ctools site (AOSS 401 001 F13) • Syllabus • Lectures • 2013 • Previous lectures from 2010 • Homework (and solutions will be added) • 2013 • Previous homework from 2010 • Reference materials and readings • Course is being taught by • Richard Rood

4. 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

5. Where does it fit in? • AOSS 321 • First 2 (+) Chapters of Holton • AOSS 401 • Chapters 3, 4, and 6 of Holton • Parts of 5, 7, 9, and 11 • AOSS 451 • Chapters > 7 of Holton (waves and stability)

6. Other recommended reference (1) • 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

7. Other recommended reference (2) • 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.

8. Tests • There will be two exams – each 25 % of grade 50% total

9. Homework • Homework will be assigned regularly and will contain problems that are directly relevant to examinations. The homework is designed to help you to learn the course material and prepare for exams, and will count toward 25% of your final grade. The lowest homework score will be dropped; the remaining homework sets will count toward your grade.

10. Readings, Discussion • This year we will have readings and discussions. This will include short write ups and class presentations on the papers. • This will count 25% of grades.

11. So what is this course (1)? • 1.4-1.6 Fundamental forces in the atmosphere, atmospheric vertical structure • 1.6, 2.1-2.3 Coordinate systems, material derivative, Eulerian and Lagrangian reference frames • 2.4, Ch. 3 Scale analysis and the equations that govern the motion of the atmosphere • Ch. 3 Balance of forces on a rotating planet, including thermal wind

12. So what is this course (2)? • Ch. 4 Vorticity, potential vorticity, and links between divergence and vertical motion • Ch. 6 Extratropical waves and mid-latitude cyclones, quasi-geostrophic balance

13. So what is this course (3)? • Some material from: • Boundary layer dynamics, Ekman layer, Ekman pumping, and the spin-down of cyclones • Ch. 7 Waves in the atmosphere, including use of perturbation theory • Ch. 9, 11 Tropical waves and hurricanes, application of scale analysis to the tropics, balance of forces and thermal wind in the tropics

14. So when you are through • You will know how to do scale analysis • You will know how to derive the vorticity equation • You will know the wave equation and how to seek “wave-like” solution • Something more about weather and climate

15. 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.

16. A little about yourself? • Why are you taking this class? • What do you want to get out of it? • Is there something that really interests you?

17. Review Homework

18. 1.1) Homework Question • Forces in the atmosphere and the equations of motion • 1a. Forces in the atmosphere can be divided into surface, body, and apparent forces. Write a brief description of each. • 1b. Write down the equations of motion corresponding to the u, v, and w components of the wind. Assume a Cartesian (x, y, z) coordinate system. • 1c. Each of the body, surface, and apparent forces in the atmosphere can be linked to terms in the equations of motion. Identify each force in the equations you wrote down for part 1b, and identify it as a surface, body, or apparent force.

19. 1.2) Homework question • 2. Following an air parcel the time rate of change of temperature can be expressed as the difference between heating and cooling. If the heating is a constant, H, and the cooling is proportional to the temperature, then the conservation equation for temperature can be written as: 2a. What are the units of H and λ? 2b. If T is in equilibrium, it does not change with time. - What is the equilibrium value of T?

20. 1.3) Homework question • 3. The Earth rotates around an axis which extends from pole to pole. This is indicated in the figure. You may assume the Earth is a perfect sphere. 3a. What are the components of angular velocity at latitude Φ in a coordinate system tangential to the Earth’s surface? 3b. What is the direction of the centrifugal force at a point on the surface? 3c. What is the magnitude of the centrifugal force due only to the Earth’s rotation at a point on the surface. 3d. What are the components of the centrifugal force in the tangential coordinate system? Ω a Φ = latitude Earth

21. Homework • These three questions and their answers are posted in resources on C-Tools • Finish working through them by the next class • There is a lot of intro and review material at the end of this lecture. • Look through it

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

23. 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?

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

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

26. Weather • National Weather Service • Model forecasts: • Weather Underground • Model forecasts: • NCAR Research Applications Program

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

28. Martian dust devil tracks What are these?

29. Material that you should review

30. 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

31. 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

32. 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

33. 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

34. Characteristics of This Course in Dynamic Meteorology • Mathematically based • Uses calculus (and algebra) • Uses vectors • Can you think of math as simplifying? • Expected mathematical knowledge • Principles of dynamic meteorology are largely drawn from fluid dynamics.

35. Characteristics of This Course in Dynamic Meteorology • 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

36. 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

37. 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?

38. 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. • Is the Earth an isolated system?

39. 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

40. Conservation (continuity) principle(with “production” and “loss”) Income Mtomorrow = Myesterday + I - E Let’s get some money and buy stuff. Expense

41. 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

42. 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

43. Conservation (continuity) principle • dM/dt = Production – Loss • This is at the starting point.

44. Return to Earth

45. 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?

46. Some basics of Earth’s atmosphere atmosphere: depth ~ 1.0 x 105 m Mountain: height ~ 5.0 x 103 m Ocean Land Biosphere Earth: radius ≡ a = 6.37 x 106 m

47. 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.

48. 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.

49. Outline • Conservation of Momentum • Forces • Pressure gradient force • Viscous force • Gravitational Force • Coriolis Force • Centrifugal Force Should be review. So we are going fast. You have the power to slow me down.

50. Newton’s Law of Motion F = ma Force = mass x acceleration In general we will work with force per unit mass; hence, a = F/m And with the definition of acceleration Boldwill represent vectors.