METEO 521: Dynamic Meteorology

Instructor: Prof. Fuqing Zhang,

Syllabus for METEO521: Dynamic Meteorology

Spring 2017 

Instructor: Prof. Fuqing Zhang, 627A Walker Building,, 865-0470

Office hours: By appointments 

Scope: 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 flows) can often be applied to other atmospheric phenomena at smaller scales.

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

Homework: Problem sets will be assigned roughly every other week. You are expected to work independently to solve the problems though discussions among classmates are allowed. Plagiarism will not be tolerated. Late homework will be penalized 20% each day after the due date; it will not be accepted after the 5th day past due.

Grading: Homework (20%), two in-class exams (25% each), and a final exam (30%).

Textbook: Atmospheric and Oceanic Fluid Dynamics (Vallis 2006) 


  1. Introduction to Dynamic Meteorology (Holton and Hakim 2013)            
  2. Atmospheric-Ocean Dynamics (Gill 1983)             

Course Outline

  1. Preliminaries 
    • Review equations of motion (read T1.1-1.6)

    • Incompressibility

    • Sound waves (T1.8)
    • Compressible and incompressible flow (T1.9)
    • Incompressibility approximation
    • Boussinesq approximation (T2.4)

    • Anelastic approximation (T2.5) 
  1. Effect of rotation and stratification
    • Equations of motion in rotating, spherical coordinates (read T2.1-2.3)
    • Hydrostatic balance/approximation (T2.7)
    • Geostrophic balance/approximation (T2.8)

    • Thermal wind balance (T2.8)
    • Static stability (read T2.9)

    • Introduction and gravity waves (T2.10.1)
  2. Gravity Waves
    • Shallow water system as a tool (T3.1)
    • Reduced gravity equations (T3.2; read T3.3)
    • Thermal wind balance revisited (T3.4)
    • Introduction of potential vorticity (PV) (T3.6)

    • Shallow water waves (T3.7)
    • Geostrophic adjustment (T3.8)
    • Isentropic coordinates (read T3.9)
  1. Vorticity and Potential Vorticity
    • Preliminaries (read T4.1-4.4)

    • Potential vorticity conservation (T4.5)
Potential vorticity and Kelvin’s circulation theorem
General form of PV; application to various fluids and flows (T4.6-4.8)
  1. Simplified equations for ocean and atmosphere
    • Quasi-Geostrophic scaling (T5.1)

    • The shallow water quasi-geostrophic equations (T5.3)

    • The continuously stratified quasi-geostrophic system (T5.4)

    • Rossby waves (T5.7, 5.8; read T5.A) 
  1. Instabilities
    • Synoptic dynamics (extratropical cyclones and fronts)
    • Synoptic dynamics (tropical cyclones and hurricanes)
    • Kelvin-Helmholtz instability (read T6.1)

    • Instability of parallel shear flow (T6.2)
    • Necessary condition for instability (T6.3)
    • Baroclinic instability (T6.4)
    • The Eady problem (T6.5)

    • The two-layer baroclinic instability (T6.6, 6.7) 
  1. Planetary boundary layer
    • Planetary boundary layer and its structure
    • Atmospheric turbulence
    • Secondary circulations and Ekman pumping 

Academic integrity statement

Students in this class are expected to write up their problem sets individually, to work the exams on their own, and to write their papers in their own words using proper citations. Class members may work on the problem sets in groups, but then each student must write up the answers separately. Students are not to copy problem or exam answers from another person’s paper and present them as their own; students may not plagiarize text from papers or websites written by others. 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: undergrad students/academics/integrity policy, which this course adopts.

Accommodations for students with disabilities

Penn State welcomes students with disabilities into the University’s educational pro- grams. Every Penn State campus has an office for students with disabilities. The Office for Disability Services (ODS) Web site provides contact information for every Penn State campus: For further information, please visit the site: http.

In order to receive consideration for reasonable accommodations, you must contact the appropriate disability services office at the campus where you are officially enrolled, documentation: http. If the documentation supports your request for reasonable accommodations, your campus 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.

Other statements as applicable

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