ATM S 441 - Autumn 2012

Textbook: J. Holton and G. Hakim, 2012: An Introduction to Dynamic Meteorology, 5th Ed. Elsevier Academic Press. Errata for this text are posted here.

Overview: The purpose of the course, together with ATMS 442/504,is to obtain a thorough understanding of the basic physical processes describing atmospheric motions, with particular emphasis on midlatitude high and low pressure systems. In this course we will consider both the fundamental governing equations, some elementary consequences of those equations and build up to a discussion of atmospheric oscillations.

Midlatitude cyclone on Sept. 26, 2011

Grading: The grade will be based on two midterms (25% each), a final (30%) and homework problems (20%).

Midterm 1: Nov 5th (Mon). Covering material in the assigned reading in Chapters 1 and 2. Closed book, but you can bring a 5"x 8" index card (the big ones) with equations and notes to class. Blank index cards will be handed out in class on the Oct 29th. Values for physical constants will be provided as required on the test.

Midterm 2: November 28th (Wed). Covering material in the assigned reading in Chapter 3 and through Section 4.3 of Chapter 4. Closed book, but you can bring a second 5"x 8" index card with equations and notes to class. You can also bring your index card from the last midterm. A piece of paper cut to 5"x 8" size can be used instead of a card.

Final: December 10th (Mon) 8:30-10:30 AM. One-half will be comprehensive and one-half will cover material in Sections 4.4, 4.5 and the assigned reading in Chpt 5. Closed book, but you can bring your two previous index cards along with a third new one.

Problem Set 1: On pp. 27 do 1.2, 1.5, 1.8

A1: On p. 28, do M1.1(a) using the scripts provided by the authors (available here as: coriolis.m, xprim1.m and xprim2.m). Then download these modified files: coriolis_cHH.m, xprim2_cHH.m into the same directory with the files from the authors, and repeat M1.1(a) typing "coriolis_cHH" instead of "coriolis".

How do the results shown in Figures 1 and 2 differ between these two scripts?
What is the difference in the mathematical equations solved by the original and modified scripts?
Which of the approximate equation sets is more self-consistent?

A2: On p. 29 do M1.3. Use the modified script coriolis_cHH.m . (Although there is little difference in the results produced by the two scripts).

A3: Set the Earth's angular velocity (omega) to zero in coriolis_cHH.m and compute trajectories (using the modified script) for a case with initial latitude = 60 deg, u = 100 m/s, v=0 and run time = 5 days. Explain why the curves in Figures 1 and 2 look so different.

(due Wed Oct 10th)

Problem Set 2: On pp. 27-28 do 1.12, 1.13, 1.16, 1.17. On pp. 65, do 2.1, 2.2

(due Wed Oct 17th)

Problem Set 3: On pp. 65-66 do 2.5 through 2.8, 2.10, 2.12. In 2.10 assume geostrophic (not gradient-wind) balance. (due Wed. Oct 24th)

Problem Set 4: On pp. 89-90 do 3.1 through 3.5. Also redo problem 2.10 on p. 65 as written; compare your new answer with that you should have obtained (125 m² s^-2) when you assumed geostrophic instead of gradient wind balance. Also convert both of these geopotential differences to height differences and compare those. (due Wed. Oct 31st)

Problem Set 5: On pp. 90-92 do 3.10, 3.11, 3.20 and 3.21.

A4: Using only the wind information on these 850 and 500 hPa charts: (winds are in knots, half barb / full barb / triangle = 5 / 10 / 50 knts)

Explain why the mean air temperatures on the equatorward side of the jet (running from Washington to the Gulf Coast) should be warmer than those on poleward side.
Make a rough estimate of the horizontal gradient in the mean temperature of the 850-500-hPa layer in the vicinity of Little Rock, Arkansas.

(due Fri. Nov 9th)

Problem Set 6: On page 122-123 do 4.1, 4.2, 4.3, 4.6, 4.7, 4.11 and problems S1 and S2 on this sheet (due Fri Nov. 16)

Problem Set 7: Do problems 1-3 on this sheet (due Wed. Nov. 21)

Problem Set 8: Do problems 1-4 on this sheet (due Mon. Dec 3)

Math Review by Profs. Anthony Broccoli and Robert Harnack

Vector Analysis Review by Profs. Anthony Broccoli and Robert Harnack

Significant figures: Rules; Behavior during mathematical manipulations.

Chapter 1: Introduction (read by indicated date)

Chapter 2: Basic Conservation Laws

10/8 pp. 31-34
10/10: Sec 2.2 & 2.3, pp. 35-41
10/12: Sec 2.4, pp. 41-45
10/15: Sec 2.5, pp. 45-49
10/19: Sec 2.6-2.7.3, pp. 50-56
- 500 hPa heights seen from space
- Cumulus congestus time lapse (24mb file)

Chapter 3: Elementary Applications of the Basic Equations

Chapter 4: Circulation, Vorticity, and Potential Vorticity

11/2: Through the end of Sec. 4.1, pp. 95-99
11/9: Sec. 4.2, pp. 100-104.
11/16: Sec. 4.3, pp. 104-110
11/19: Sec 4.4, pp. 110-115
11/21: Sec 4.5, pp. 115-120

Conservation of SW PV demonstrated in Prof. Rhines lab (more here)
- Water column over mountain
- Column moving off mountain developing cyclonic relative vorticity
- Stretched column clearly showing cyclonic vorticity (red dye). Water columns that shrank as they moved over mountain show anticyclonic curvature (blue dye).

Chapter 5: Atmospheric Oscillations

11/30 Through Sec. 5.2.2, and 5.2.4, pp. 127-133, 135-136
12/5 Sec. 5.3.2, pp. 139-144
- Fluid particles and wave motion
- Group velocity animation: Frequency dispersion of surface gravity waves on deep water. The red dot moves with the phase velocity, and the green dots propagate with the group velocity. In this deep-water case, the phase velocity is twice the group velocity. The red dot overtakes two green dots, when moving from the left to the right of the figure.

Atmospheric Motions I