Course Syllabus

Atmospheric Motions I

(ATM S 441/503, Autumn 2018)


  • Office hour: Tu/W 11:30-12:30pm (ATG 608)
  • PrerequisitesAMATH 353 or MATH 309; MATH 324 or equivalents.
  • Purpose of the course: Develop an understanding of why large-scale midlatitude weather systems behave as they do. As an example we might consider a simple question; why does the wind blow almost parallel to the height contours on a 500-mb map?
  • TextbookHolton, J. R., and G. Hakim, 2013: An Introduction to Dynamic Meteorology (5th Ed.).
  • ContentCourse will include lectures, quizes and homeworks. Homeworks will consist of problems similar to those in the text. [NOTE: Graduate students registered for ATM S 503 will attend the 441 but may have additional problem assignments and will be graded separately from the undergraduates registered for 441]
  • Course Outline (subject to change at any time)

I. Introduction: Fundamental forces, rotating coordinates, Coriolis force, atmospheric statics.

II. Basic conservation laws: Momentum equation, continuity equation, thermodynamic energy equation, scale analysis.

III. Elementary applications of the basic equations: Isobaric coordinates, geostrophic flow, intertial flow, cyclostrophic flow, gradient wind, thermal wind, vertical motion.

IV. Circulation, vorticity, and potential vorticity: Circulation theorem, vorticity, potential vorticity, barotropic vorticity equation.

V. Atmospheric oscillations: Linear perturbation theory, basic properties of waves, linear waves.

  • Grading:

Homework: 30%
Quiz: 30%
Exams: 30%
Participation: 10%

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


09/26: Course introduction (slides)
09/28: Math essentials (handout), Equations of motion (handout)

Introduction to Dynamic Meteorology
  • Holton and Hakim, Ch. 1.1


10/01: Fundamental forces (handout)
10/03: Apparent forces I (handout)
10/05: Apparent forces II

Fundamental forces
  • Holton and Hakim, Ch. 1.2
Apparent forces
  • Holton and Hakim, Ch. 1.3


10/08: Hypsometric equation (handout)
10/10: Scale analysis of the equations of motion (handout)
10/12: Geostrophic and hydrostatic balance

Hypsometric equation
  • Holton and Hakim, Ch. 1.4.1
Scale analysis
  • Holton and Hakim, Ch. 1.6
Scale analysis of the equations of motion
  • Holton and Hakim, Ch. 2.4


10/15: Continuity equation (handout)
10/17: Quiz I
10/19: Thermodynamic energy equation I (handout)

Continuity equation
  • Holton and Hakim, Ch. 2.6
Thermodynamic energy equation
  • Holton and Hakim, Ch. 2.7


10/22: Thermodynamic energy equation II (handout)
10/24: Basic equations in pressure coordinate (handout)
10/26: Natural coordinate (handout)
Basic equations in isobaric coordinates
  • Holton and Hakim, Ch. 3.1


10/29: Natural coordinate II, Balanced flow (handout)
10/31: Quiz II 
11/02: Balanced flow II (handout)

Balanced flow
  • Holton and Hakim, Ch. 3.2


11/05: Thermal wind (handout)
11/07: Mid-term 
11/09: Mid-term discussion

Thermal wind

  • Holton and Hakim, Ch. 3.4


  • Holton and Hakim, Ch. 4.2


11/12: No class (Veteran's day)
11/14: Vorticity and vorticity equation (handout
11/16: Circulation (handout)

The circulation theorem
  • Holton and Hakim, Ch. 4.1

Vorticity equation
  • Holton and Hakim, Ch. 4.3


11/19: Potential vorticity (handout)
Shallow water equation (handout
11/23: No class (Thanksgiving day)

Potential vorticity
  • Holton and Hakim, Ch. 4.4
Shallow water equations
  • Holton and Hakim, Ch. 4.5


11/26: Quiz III
11/28: Rossby waves (handout)
11/30: Rossby waves II (handout)

Rossby waves
  • Holton and Hakim, Ch. 5.7
The perturbation method
  • Holton and Hakim, Ch. 5.1
Free barotropic Rossby waves
  • Holton and Hakim, Ch. 5.7.1 


12/03: Shallow water gravity waves (handout)
12/05: Quiz IV
12/07: Class review
Shallow water waves
  • Holton and Hakim, Ch. 5.3.2


Course Summary:

Date Details