Atmospheric Science 4310 / 7310

1. Atmospheric Science 4310 / 7310 Atmospheric Thermodynamics By Anthony R. Lupo

2. Syllabus • Atmospheric Thermodynamics • ATMS 4310 • MTWR 9:00 – 9:50 / 4 credit hrs. • Location: 1-120 Agruculture Building • Class Ref#: 15505 • Instructor: A.R. Lupo • Address: 302 E ABNR Building • Phone: 88-41638 • Fax: 88-45070 • Email: lupo@bergeron.snr.missouri.edu or LupoA@missouri.edu • Homepage: www.missouri.edu/~lupoa/author.html • Class Homepage:www.missouri.edu/~lupoa/atms4310.html • Office hours: MTWR 10:00 – 10:50 • 302 E ABNR Building

3. Syllabus • Grading Policy:“Straight” • 97 – 100 A+ 77 – 79 C+ • 92 – 97 A 72 – 77 C • 89 – 92 A- 69 – 72 C- • 87 – 89 B+ 67 – 69 D+ • 82 – 87 B 62 – 67 D • 79 – 82 B- 60 – 62 D- • < 60 F • Grading Distribution: • Final Exam 20% • 2 Tests 40% • Homework/Labs 35% • Class participation 5% (Note, you WILL lose 1 point for each unexcused absence, up to 5 points. This IS a half-letter grade, keep that in mind!) • Attendance Policy:“Shouldn’t be an issue!”

4. Syllabus • Texts: • Holton, J.R., 2004: An Introduction to Dynamic Meteorology, 4th Inter, 535 pp. (Required) • Bluestein, H.B., 1992: Synoptic-Dynamic Meteorology in the Mid-latitudes Vol I: Priciples of Kinematics and Dynamics. Oxford University Press, 431 pp. • Hess, S.L., 1959: An Introduction to Theoretical Meteorology. Robert E. Kreiger Publishing Co., Inc., 362 pp. • Zdunkowski, W., and A. Bott, 2003: Dynamics of the Atmosphere: A course in Theoretical • Meteorology. Cambridge University Press, 719 pp. (a good math review) • Zdunkowski, W., and A. Bott, 2004: Thermodynamics of the Atmosphere: A course in Theoretical Meteorology. Cambridge University Press, 251 pp. • Various relevant articles from AMS and RMS Journals. • Course Prerequisites: • Atmospheric Science 1050, Calculus through Math 1700, Physics 2750, or their equivalents. Senior standing or the permission of the Instructor.

5. Syllabus • Calendar: “Wednesday is Lab exercise day” • Week 1: 21 22 23 24 August  Introduction and Friday makeup arrangements. Intro. To Atms. 4310. Lab 1: The Thermodynamic diagram and upper air information. • Week 2: 28 29 30 31 August / September  Fri. makeup 1, 1 September. Lab 2: Adiabatic Motions in the Atmosphere. • Week 3: hh 5 6 7 September  Mon., Labour Day Holiday / Fri makeup 2, 8 September. Lab 3: The Thermodynamic Diagram: Examining Moist Processes. • Week 4: 11 12 13 14 September  Fri. makeup 3, 15 September, Lab 5 Lab 4: The Thickness Equation and it’s Uses in Operational Meteorology. (move up other labs) • Week 5: 18 19 20 21 September  Friday make up 4, 22 September, Lab 5 the Lapse Rates of Special Atmospheres. Test 1 22 Sept., covering material to 19 Sept.? • Week 6: 25 26 27 28 September  Friday 29 September makeup 5. • Lab 6: Using Thermodynamic diagrams to Determine Water Vapor Variables. • Week 7: 2 3 4 5 October  Friday makeup 6, 6 October. Lab 7: Estimating Vertical Motions Using the First Law of Thermodynamics.

6. Syllabus • Week 8: nn nn nn nn October  No Class, UCAR-NCAR member rep meetings and Heads and Chairs. Lab 8: Atmospheric Stability I: Special Forecasting Problems: Fog Formation. • Week 9: nn nn nn nn October  Gone to Cleveland, OH – NWA meet. • Lab 9: Atmospheric Stability II: Special Forecasting Problems: Air Pollution. • Week 10: 23 24 25 26 October  Makeup 7, 27 October • Lab 10: Severe Weather: The Synoptic-Scale sets the table. • Week 11: 30 31 1 2 October / November  Makeup 8, 3 November Test covering material to 1 November. Lab 11: Using Thermodynamic diagrams in forecasting Convective Outbreaks. • Week 12: nn nn nn nn November  Severe and Local Storms Conference in Saint, Louis, MO. Lab 12: Estimating Various Stability Indicies in real-time. • Week 13: 13 14 15 16 November  Makeup number 9, 17 November Lab 13: Severe Weather I: Using thermodynamic diagrams: Super Cell Formation and Wind Gust Estimation. • Week 14: hh hh hh hh November  No classes Turkey day week! • Week 15: 27 28 29 30 November / December  Make up number 10, 1 December. Lab 14: Severe Weather II: Using thermodynamic diagrams: Hail Formation • Week 16: 4 5 6 7 December  Makeup 11, 8 Dec., Final 8 Dec.? • Lab 15: Severe Weather III: Using thermodynamic diagrams: Maximum Windgust and Microburst. • Finals Week: 11 – 15 December

7. Syllabus • ATMS 4310 Final Exam • The Exam will be quasi-comprehensive. Most of the material will come from the final third of the course, however, important concepts (which I will explicitly identify) will be tested. All tests and the final exam will use materials from the Lab excercises! Thus, all material is fair game! The final date and time is: • Friday, 15 December 2006 – 10:30 am to 12:30 pm in ABNR 1-120 • University Important Dates Calendar • August 14-18 FS2006 Regular Registration • August 16 Residence Halls open 9:00 a.m. • August 18 Easy Access registration - noon - 6:00 p.m. • August 21 Classwork begins 8:00 a.m. • August 21 Late Registration and Add/Drop - Late fee assessed • beginning August 21 • August 28 Last day to register, add, or change sections • August 29-Sept. 25 Drop Only • September 4 Labor day Holiday • September 5 Last day to change grading option • September 18 (Census Day) - Last day to register for CDIS courses • for Fall • September 25 Last day to drop course without grade

8. Syllabus • TBA WS2007 Early Registration Appointments • October 30 Last day to withdraw from a course - FS2006 • November 15 Last day to change divisions • November 18 Thanksgiving recess begins, close of day • November 27 Classwork resumes, 8:00 a.m. • December 8 Fall semester classwork ends • December 8 Last day to withdraw from University • December 9 Reading Day • December 11 Final examinations begin • December 15 Fall semester ends at close of day • December 15-16 Commencement Weekend • *Please note: This calendar is subject to change

9. Syllabus • Syllabus ** • Introductory and Background Material, including a math review (Calculus III) • The Thermodynamics of Dry Air • Hydrostatics • The Thermodynamics of Moist Air • Static Stability and Convection • Vertical Stability, Instability, and Convection* • Cloud Microphysics * • The Thunderstorm and Non-hydrostatic Pressure * • * These topics will be taught if there is time. All Lecture schedules are tentative! • ** Students with special need are encouraged to schedule an appointment with me as soon as possible!

10. Syllabus • Special Statements: • ADA Statement (reference: MU sample statement) • Please do not hesitate to talk to me! • If you need accommodations because of a disability, if you have emergency medical information to share with me, or if you need special arrangements in case the building must be evacuated, please inform me immediately. Please see me privately after class, or at my office. • Office location: 302 E ABNR Building Office hours : ________________ • To request academic accommodations (for example, a notetaker), students must also register with Disability Services, AO38 Brady Commons, 882-4696. It is the campus office responsible for reviewing documentation provided by students requesting academic accommodations, and for accommodations planning in cooperation with students and instructors, as needed and consistent with course requirements. Another resource, MU's Adaptive Computing Technology Center, 884-2828, is available to provide computing assistance to students with disabilities. • Academic Dishonesty (Reference: MU sample statement and policy guidelines) • Any student who commits an act of academic dishonesty is subject to disciplinary action.

11. Syllabus • The procedures for disciplinary action will be in accordance with the rules and regulations of the University governing disciplinary action. • Academic honesty is fundamental to the activities and principles of a university. All members of the academic community must be confident that each person's work has been responsibly and honorably required, developed, and presented. Any effort to gain an advantage not given to all students is dishonest whether or not the effort is successful. The academic community regards academic dishonesty as an extremely serious matter, with serious consequences that range from probation to expulsion. When in doubt about plagiarism, paraphrasing, quoting, or collaboration, consult the instructor. In cases of suspected plagiarism, the instructor is required to inform the provost. The instructor does not have discretion in deciding whether to do so. • It is the duty of any instructor who is aware of an incident of academic dishonesty in his/her course to report the incident to the provost and to inform his/her own department chairperson of the incident. Such report should be made as soon as possible and should contain a detailed account of the incident (with supporting evidence if appropriate) and indicate any action taken by the instructor with regard to the student's grade. The instructor may include an opinion of the seriousness of the incident and whether or not he/she considers disciplinary action to be appropriate. The decision as to whether disciplinary proceedings are instituted is made by the provost. It is the duty of the provost to report the disposition of such cases to the instructor concerned.

12. Syllabus • Lab Exercise Write-up Format: All lab write-ups are due at the beginning of the next ‘lab’ Wednesday. Grading format also given. • Total of 100 pts Name • Lab # • Atms 4310 • Neatness and Grammar 10 pts Date Due • Title • Introduction: brief discussion of relevant background material (5 pts) • Purpose: brief discussion of why performed (5 pts) • Data used: brief discussion of data used if relevant (5 pts) • Procedure: (15 pts) • 1. • 2.

13. Syllabus • Results: brief discussion of results (50 pts) • observations • discussion (answer all relevant questions here) • Summary and Conclusions (10 pts) • summary • conclusions • Write-ups need to be the appropriate length for the exercise done. If one section does not apply, just say so. However, one should never exceed 6 pages for a particular write – up. That’s too much! Finally, answer all questions given in the assignment.

14. Day 1 • Thermodynamics  the study of initial and final equilibrium states of a "system" which has been subjected to a specified energy process or transformation. • “System”  a specific sample of matter (air parcels) • We will concentrate on the “macroscale” or parcel properties only! We will not look at the microscale (molecular level) that’s atmospheric physics (Dr. George, Dr. Fox).

15. Day 1

16. Day 1 • Variables of state: (thermodynamic variables) • pressure (hPa, mb) (Force Area-1) • Temperature (oC, K, oF) • Volume (typically m3 [kg-1]), but typically assume “unit” mass)

17. Day 1 • Laws of thermodynamics: • Equation of State • 1st law of thermodynamics (conservation of energy) • 2nd law of thermodynamics (entropy) (direction of heat flow) (warm to cold) • We will review Dimensions and Units, and conventions.

18. Day 1 • Atmospheric science derives a set of standard measurements or unit system, such that everyone everywhere will be on the same page. • AMS endorsed the SI (Systeme International) or International system of Units (BAMS, 1974, Aug.) • The basic units are: Length, Mass, Time (meter, m; kilo, kg; second, s)

19. Day 1 • A derived unit combines basic units: example, pressure: • Force /Area = kg m s-2 / m2 = kg m-1 s-2 = Pascals • 1000 Pa = 1 kPa = 10 hPa = 10 mb • Temperature (Kelvin, or absolute scale; Celsius (1742) Farenheit (1714)). • Coordinate System: (Cartesian)

20. Day 1 • Coordinate system: tangent to Earth’s surface which is really a sphere (curvature for most applications and approximations can be neglected). • Cartesian coordinates: x,y,z,t => x,y,p,t, or x,y,q,t • Could also use natural coordinates: • s(treamline),n(normal),z,t • Spherical coordinates • r(adius),q(longitude),f(latitude)

21. Day 2 • Wind • Wind direction: direction from which the wind blows, and compass direction, not Cartesian! • West wind: is blowing from 270o. • Wind direction: increasing with time or height: veering: decreasing with time or height: backing

22. Day 2 • Remember: Direction of math = 270 – compass (meteorology) direction. • Vector representation in Geophysical Fluid Dynamics • Remember the atmosphere is a fluid, and a fluid is liquid or gas. Thus, the primitive equations will be valid in any atmosphere, terrestrial (extraterrestrial).

23. Day 2 • Scalar quantity  A quantity with magnitude only (e.g., wind • speed has units m s-1) (zero order tensor) • Vector  (first order Tensor) A quantity with magnitude and direction (e.g., wind velocity)

24. Day 2 • Wind…

25. Day 2 • Dyadic (2nd order Tensor) has a magnitude and two directions! • Example: stress (Force per unit area), where A is the vector of some magnitude equal to the area and in the direction of the normal. • In English: Magnitude, direction (1) of the force, and (2) on which surface applied

26. Day 2 • An example… • Example Stress: Force = Area times Stress (has same units as pressure)

27. Day 2 • Vector Analysis: • Vector Notations: • A A • |A| = magnitude of A

28. Day 2 • Vectors are equal if they have equal magnitude and directions!! • The unit vector: any vector of unit length! • where is a vector of unit length • Cartesian Unit vectors: vectors of unit length in the positive x,y,z direction, respectively.

29. Day 2 • Natural coordinates are: • Vector components (2 dimensions), but we can extend to infinite number of directions: • Magnitude of A  |A| =  (Ax2 + Ay2)

30. Day 2 • Vector addition and subtraction: • 1) A + B = C • 2) A+B = B + A = C • 3) A - B = C

31. Day 2 • Addition Subtraction

32. Day 2 • Here’s how: • Associative rule: • (A+B) + C = A + (B+C) • Negative Vector: Is a vector of the same magnitude, but opposite direction.

33. Day 2 • Vector multiplication: • Scalar x Vector: • In the atmospheric sciences: The wind vector (2-D 3 – D):

34. Day 2 /3 • Vector products • The dot product (also the “scalar” or “inner”) product: • A dot B = |A||B|cos(q) • Physically: The dot product is the PROJECTION of vector B onto Vector A in direction of A!

35. Day 2/3 • Projection (mathworld.wolfram.com) (excellent math site):

36. Day 3 • Properties of the Dot Product: • commutative • A dot B = B dot A • associative • A dot (B dot C) = (A dot B) dot C • distributive • A dot (B + C) = A dot B + A dot C

37. Day 3 • Dot product of perpendicular vector = 0 • In order for the dot product to have a value, the B vector must have a component parallel to vector A! • Recall: cos(0o) = 1 and cos(90o) = 0 • Thus, i dot j, and j dot k, etc… = 0, and i dot i = 1, etc…

38. Day 3 • Orthogonal Vectors (Orthogonality property): When the angle between two vectors is 90o, or the dot product is zero, two vectors are said to be “orthogonal”. • Other Dot Product Rules: • 1) A dot A = |A||A| cos(0) = A2 • 2) A dot mA = mA2

39. Day 3 • Dot product of two vectors (here’s how): • Remember “Foil”? “AxBx (i dot i) + Ax By ( i dot j) + Ay Bx (j dot i) + Ay By (j dot j)”

40. Day 3 • Ok, now you try = ? • Answer????? Ax • Cross Product (or vector product) = • A x B = |A||B|sin(q)

41. Day 3 • What is it (again courtesy of Mathworld site)?

42. Day 3 • Einstien notation – permutation: • Q: "What do you get when you cross a mountain-climber with a mosquito?" • A: "Nothing: you can't cross a scaler with a vector," • Q: "What do you get when you cross an elephant and a grape?" • A: "Elephant grape sine-of-theta."

43. Day 3 • The cross product of two vectors is a third vector that is mutually perpendicular to the two vectors and the plane containing these vectors. • Q: Remember your Physics? • The positive direction of A x B may be determined by the “right hand (or corkscrew)” rule. Just curl your fingers from A to B, and your right thumb (vector C) is the result! (“ayyyy”)

44. Day 3 • Evaluating the cross product of A and B in the cartesian coordinate system. • The vector or cross product is NOT commutative!

45. Day 3 • Try the right hand rule to show that we cannot switch order • Also, remember sin(-90o) = -1.0 • The cross product is distributive: • A X (B +C) = (A x B) + (A x C)

46. Day 3/4 • The cross product of a vector with itself equals 0!! • q = 0 so, sin(0) = 0, or A x A = |A||A|sin(0) = 0 • Cross products of unit vectors and the “cyclical” property of the cross product: • 1) i x i = 0, i x j = k, i x k = -j • 2) j x i = -k, j x j = 0, j x k = i • 3) k x i = j, k x j = -i, k x k = 0

47. Day 4 • A x B = C , B x C = A, C x A = B • Another “trick” or property: • Unit vector k x Ah = Horizontal vector of length |A| turned 90o to the left of A (try it with right hand rule - horizontal vector!!!) • -k x Ah = A vector of length A turned 90o to the right of A

48. Day 4 • Multiple Vector Products • Scalar Triple product: • A dot (B x C) = a scalar value • This is also “cyclical” • A dot (Bx C) = B dot (C x A) = C dot (A x B)

49. Day 4 • Or dot and cross product may be interchanged: • A dot ( B x C) = (A x B) dot C • Triple vector product: • (A x (B xC)) = Vector quantity • A x (B xC) = (A dot C ) B – (A dot B) C • The result is a third vector in the plane of B and C!!!

50. Day 4 • But, • (A x B) x C not equal to A x (B x C) • since for former result is in the plane of A and B!!