METEO 521 Feldstein SP2015

Dynamic Meteorology

Dynamic Meteorology

Spring 2015
Course Outline

  • T refers to the textbook; N refers to the notes on ANGEL.
  1. Introduction
    1. Goals and scope of the course
    2. Observations  (N/obs.pdf)
  2. Preliminaries
    1. Review equations of motion (read T1.1-1.6)
      1. The lecture will focus on advection and diff  
      2. (N/diffusivity.pdf)
    2. Incompressibility
      1. Sound waves (T1.8, N/soundwave.pdf)

      2. Compressible and incompressible fl w (T1.9)

      3. Incompressibility approximation

      4. Boussinesq approximation (T2.4)

      5. Anelastic approximation (T2.5)

  3. Effect of rotation and stratification

    1. Equations of motion in rotating, 
    2. spherical coordinates (read T2.1-2.3)
    3. Hydrostatic balance/approximation (T2.7, N/geo.hydro.pdf)
    4. Geostrophic balance/approximation (T2.8)
    5. Thermal wind balance (T2.8, N/thermalwind.pdf)
    6. Static stability (read T2.9)
    7. Introduction and gravity waves (T2.10.1)
  4. Gravity waves.
    1. Shallow water system as a tool (T3.1)
    2. Reduced gravity equations (T3.2; read T3.3)
    3. Thermal wind balance revisited (T3.4)
    4. Introduction of potential vorticity (PV) (T3.6)
    5. Shallow water waves (T3.7, N/Kelvinwaves.pdf)
    6. Geostrophic adjustment (T3.8, N/adjustment.poincare.pdf)
    7. Isentropic coordinates (read T3.9)
  5. Vorticity and Potential Vorticity
    1. Preliminaries (read T4.1-4.4)
    2. Potential vorticity conservation (T4.5, N/vor.pv.pdf)
    3. Potential vorticity and Kelvin’s circulation theorem
    4. General form of PV; application to various fl    and fl ws (T4.6-4.8)
  6. Simplified equations for ocean and atmosphere
    1. Quasi-Geostrophic scaling (T5.1)
    2. The shallow water quasi-geostrophic equations (T5.3)
    3. The continuously stratified quasi-geostrophic system (T5.4)
    4. Rossby waves (T5.7, 5.8; read T5.A, N/zonal.prop.pdf and meridional.disp.pdf)
    5. Refractive index
  7. Instabilities
    1. Synoptic dynamics (extratropical cyclones and fronts)
    2. Synoptic dynamics (tropical cyclones and hurricanes)
    3. Kelvin-Helmholtz instability (read T6.1)
    4. Instability of parallel shear fl w (T6.2)
    5. Necessary condition for instability (T6.3)
    6. Baroclinic instability (T6.4, N/instability.pdf)
    7. The Eady problem (T6.5)
    8. The two-layer baroclinic instability (T6.6, 6.7)
  8. Planetary boundary layer
    1. Planetary boundary layer and its structure Atmospheric turbulence
    2. Secondary circulations and Ekman pumping 

Course Structure

There will be two mid-terms and a final exam. Each mid-term will contribute 20%, and the final will contribute 30% to your final  grade. The dates for the mid-term exams are near February 24 and April 9.

Problem sets:

Problem sets will be given about every two weeks. The problem sets will contribute 20% to your final grade.

Lab project:

Hand-on laboratory experiments can help us understand key concepts and theories that are unique to rotating fl  Laboratory-experiment report and class presentation will contribute 10% to your final grade.

  1. The class will be divided into five groups. Each group will be comprised of 2 (for one experiment 3) students. The experiments will take place in 529 Walker. Practice times are 4:00-5:00pm on the previous Thursday in 529 Walker. The following experiments are to be performed:
    • Exp 1. Taylor Columns (February 10)
    • Exp 2. Fronts, geostrophic adjustment (February 17)
    • Exp 3. General circulation - Hadley Circulation (March 3)
    • Exp 4. General circulation - Eddies (March 24)
    • Exp 5. General circulation -Ekman layers (March 31)
  2. Each group will practice the experiment of its choice prior to the class; perform the demonstration in front of the class; and explain what we are supposed to learn from the experiment. Each member of the group must participate in all of these three activities. In addition, each group is required to write a short report (2-3 pages long). This report may include
    • (a) an experimental log which can supplement the log available on the “Weather in a Tank” web page (,
    • (b) a discussion of what has been learned from the experiment, and
    • (c) an observed analog of the experiment (e.g., examples from weather maps, analyses from the literature, etc.). In the report, briefl describe how each member of the group contributed to the report.
  3. Your credit will be given based on (a) clarity of demonstration, (b) clarity of explanations (i.e., what we are trying to learn from the experiment, and how this is related to the class material), and (c) the report.
  4. Time line: Let me know your choice of experiment (first come, fi choice) and the members of your group by Jan 20.

Prerequisite: Meteo 520.

Textbook: Atmospheric and Oceanic Fluid Dynamics. Vallis, 2006, Cambridge University Press.


  1. Atmosphere-ocean dynamics. Gill, 1983, Academic Press. Call#: GC190.G54 1982 (reserved)
  2. Geophysical Fluid Dynamics.  Pedlosky, 1986.  Springer-Verlag.  Call#:  QC809.F5P43 1987 (reserved)
  3. Introduction to circulating atmospheres, James, Ian N. 1994. Cambridge University Press. Call#: QC880.4.A8J34 1994
  4. Middle Atmospheric Dynamics.   Andrews,  Holton,  and Leovy,  1998.   Academic Press. Call#:  QC881.2.M53A53 1987
  5. An introduction to fl    dynamics.  Batchelor, 1967.  Batchelor.  Cambridge University Press. Call#: QA911.B33
  6. Fluid Mechanics, 1990. Kundu. Academic Press.
  7. Lectures on geophysical fl    dynamics, 1998.  Salmon.  Oxford University Press.  Call#: QC809.F5S25 1998.
  8. Meteo 521 lecture notes. Peter Bannon.
  9. An Introduction to Dynamic Meteorology.    Holton 1992.    Academic Press.    Call#: QC880.H65 1992
  10. Atmospheric Science:  In Introductory Survey.  Wallace and Hobbs 1977.  Academic Press. Call#: QC861.2.W34


T Th 9:45am-11:00am 101 Walker Building


Steven Feldstein
516 Walker Building

Office hours: by appointment

Goals and Scope of Meteo 521


  • introduce some of the important concepts in dynamic meteorology
  • provide a theoretical basis for understanding weather and climate


This course does not cover the entire spectrum of atmospheric motion; this course focuses on large-scale atmospheric motion for which rotation and stable stratification are central. However, as the concepts to be covered in this course are fundamental to atmospheric motion, the same conceptual approach (e.g., scaling, adjustment, concept of balanced fl ws) can often be applied to other atmospheric phenomena at smaller scales.

Basic mathematics such as calculus, vector calculus, and partial diff  tial equations will be extensively used.

Academic Integrity

Students in this class are expected to write all their code individually, but are encouraged to work on exercises and assignments in groups.

Quizzes and the final project are completely individual. Students may only communicate with the instructors and TAs during quizzes and regarding the final project.

Students are not to copy any answers from another student or external resources and present them as their own. Students who present other people's work as their own will receive at least a 0 on the assignment and may well receive an F or XF in the course.  Please see: Earth and Mineral Sciences Academic Integrity Policy:, which this course adopts.


The student is responsible for learning the material in the lectures. Attendance will not be taken and does not affect the final grade. Students must be present at quizzes to receive a score. If you are going to miss a lecture for a legitimate reason, let the instructor know (preferably ahead of time), and the instructor will help you catch up to speed.

This course abides by the Penn State Class Attendance Policy 42-27 at, Attendance Policy E-11:, and Conflict Exam Policy 44-35: Please also see Illness Verification Policy:, and Religious Observance Policy: Students who miss class for legitimate reasons will be given a reasonable opportunity to make up missed work, including exams and quizzes.  Students are not required to secure the signature of medical personnel in the case of illness or injury and should use their best judgment on whether they are well enough to attend class or not; the University Health Center will not provide medical verification for minor illnesses or injuries. Other legitimate reasons for missing class include religious observance, family emergencies, and regularly scheduled university-approved curricular or extracurricular activities.  Students who encounter serious family, health, or personal situations that result in extended absences should contact the Office of Student and Family Services for help:  Whenever possible, students participating in University-approved activities should submit to the instructor a Class Absence Form available from the Registrar's Office:, at least one week prior to the activity.

Accommodations for Students with Disabilities

If the course format fails to provide for your needs due to a disability, please talk to the course instructor. The instructor will make every effort to accommodate you.

Penn State welcomes students with disabilities into the University's educational programs. Every Penn State campus has an office for students with disabilities. The Office for Disability Services (ODS) at provides contact information for every Penn State campus: ( For further information, please visit the Office for Disability Services website (

In order to receive consideration for reasonable accommodations, you must contact the appropriate disability services office at the campus where you are officially enrolled, participate in an intake interview, and provide documentation based on the documentation guidelines ( If the documentation supports your request for reasonable accommodations, your campus’s disability services office will provide you with an accommodation letter. Please share this letter with your instructors and discuss the accommodations with them as early in your courses as possible. You must follow this process for every semester that you request accommodations.

Weather Delays

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Disclaimer Statement

Please note that the specifics of this Course Syllabus can be changed at any time, and you will be responsible for abiding by any such changes. Changes will be posted to Angel.

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