Course Syllabus

GFD II - Balanced Dynamics

(ATM S 542, Spring 2021)

***This course is scheduled to run synchronously at your scheduled class time via Zoom. These Zoom class sessions will be recorded. The recording will capture the presenter’s audio, video and computer screen. Student audio and video will be recorded if they share their computer audio and video during the recorded session. The recordings will only be accessible to students enrolled in the course to review materials. These recordings will not be shared with or accessible to the public.

The University and Zoom have FERPA-compliant agreements in place to protect the security and privacy of UW Zoom accounts. Students who do not wish to be recorded should:

  • Change their Zoom screen name to hide any personal identifying information such as their name or UW Net ID, and
  • Not share their computer audio or video during their Zoom sessions.


  • Class meets: MWF 2:30-3:20pm
  • Office hour: Tu/W 2:30-3:30pm (on Zoom)
  • Prerequisites:ATM S 509/OCEAN 512 and AMATH 402 or equivalents.
  • Purpose of the course: To develop i) understanding of and own perspective on the dynamics of large-scale flows in the atmosphere, and ii) ability to interpret real atmospheric circulation.
  • TextbookHolton, J. R., and G. Hakim, 2012: An Introduction to Dynamic Meteorology (5th Ed.).
  • Other textbooks
    Lorenz, E. N., 1967: The Nature and Theory of the General Circulation of the Atmosphere.
    Gill, A. E., 1982: Atmosphere-Ocean Dynamics.  
    Pedlosky, J. P., 1987: Geophysical Fluid Dynamics (2nd Ed.).
    Andrews, D. G, J. R. Holton, and C. B. Leovy, 1987: Middle Atmosphere Dynamics.
    Vallis, G. K., 2006: Atmospheric and Oceanic Fluid Dynamics.
    Hoskins, B. J., and I. N. James, 2014: Fluid Dynamics of the Midlatitude Atmosphere. 
  • Content: Course will include lectures, homework, exercises, and exams. Basic concepts listed below will be taught in lectures. Exercises and homework will be used to strengthen the understanding of the basic concepts.
  • Course Outline (subject to change at any time)

1. QG Theory

a.    Scale analysis
b.    2D QG theory and planetary waves
c.    Ekman modification 
d.    3D QG theory for a compressible fluid; potential vorticity
e.    Potential vorticity and inversion

2. Baroclinic Instability

a.    The concept of instability 
b.    Rayleigh necessary condition for instability
c.    Barotropic instability
d.    Baroclinic instability: the Eady model

3. Extratropical Planetary Waves

a.    Vertical propagation
b.    Horizontal propagation and group velocity
c.    Forcing of barotropic stationary waves by orography
d.    Waves in a slowly varying mean state

4. Tropical Dynamics

a.    Scale analysis 
b.    Equatorially trapped modes (Matsuno 1966) 
c.    Moisture mode dynamics

  • Grading:

Problem-solving homework: 70%
Quizzes: 30%

  • Note: No makeup tests will be provided unless the absence is excused in advance.
  • Class overview
Week Course material Reading/Reference


Ch. 0: Introduction
Course introduction, Equations of motion, Scale analysis, Shallow water Rossby wave

Scale analysis of the equations of motion
  • Holton and Hakim, Ch. 2.4
Rossby waves
  • Holton and Hakim, Ch. 5.7


Ch 1. Quasi-geostrophic motions
a) Shallow water QG system

2D QG scaling
  • Vallis, Ch. 5.1.1, 5.3.1
  • Pedlosky, Ch. 3.1-12
3D QG scaling
  • Holton and Hakim, Ch. 6.2
  • Vallis, Ch. 5.1.2, 5.4
  • Pedlosky, Ch. 6.1-6


Ch 1. Quasi-geostrophic motions
b) Continuously stratified QG system
c) Spin-down

Ch 2. Instability
Concept of barotropic and baroclinic Instability


  • Holton and Hakim, Ch. 8
  • Vallis, Ch. 2.12
  • Pedlosky, Ch. 4.1-7

Concept of barotropic and baroclinic instability

  • Hoskins and James, Ch. 9.8, Ch. 14.1-2


Ch 2. Instability
a) Necessary condition for instability
b)The Eady stability problem

Necessary condition for instability

  • Holton and Hakim, Ch. 7.4.1-7.4.2
  • Vallis, Ch. 6.1-3
  • Pedlosky, Ch. 7.1-5


Ch 2. Instability
b) The Eady stability problem

Baroclinic instability, The Eady stability problem

  • Holton and Hakim, Ch. 7.4.3
  • Hoskins and James, Ch. 14.3-4
  • Vallis, Ch. 6.4-5, 6.7.2
  • Pedlosky, Ch. 7.6-7


Ch 3. Planetary wave propagation
a) Vertical propagation

Planetary wave propagation
  • Holton and Hakim, Ch. 10.5
  • Vallis, Ch. 13.1-3


Ch 3. Planetary wave propagation
a) Vertical propagation
b) Meridional propagation

Planetary wave propagation
  • Held (1983)
  • Hoskins and Karoly (1981)


Ch 3. Planetary wave propagation
b) Meridional propagation

Sardeshmukh and Hoskins (1988) discussion

Ch 4. Tropical dynamics
a) Scale analysis

Scale analysis for tropical motion
  • Holton and Hakim, Ch. 11
  • Charney (1963, 1969)


Ch 4. Tropical dynamics
b) Equatorial waves

Equatorial waves
  • Matsuno (1966)
  • Kiladis et al. (2009)


Ch 4. Tropical dynamics
c) Moisture mode dynamics

Moisture mode dynamics

  • Adames and Kim (2016)