Figure: Hurricane Isabel on the Chesapeake Bay, Cape Anne, Maryland, 2003. The pier in the picture is normally several feet above the water.

Introduction

This is the collection of lectures, assignments, and other resources for CLIMATE/EARTH 401 at the University of Michigan.

The name of the course is Geophysical Fluid Dynamics. It is the second of a three-part series in dynamical meteorology. CLIMATE/EARTH 321 is the first in the series. Since many take the course without taking the first course, the relevant material from that course is reviewed. Hence, this is effectively an introduction to dynamical meteorology with a focus on middle-latitude, quasi-geostrophic theory. There are brief introductions to other topics, including tropical waves and hurricanes.

The course is divided into these major topics

  1. Structure and organization of atmosphere, Conservation laws and balanced systems, Fundamental forces, Mathematical techniques
  2. Coordinate systems, Material derivatives, Eulerian and Lagrangian frames of reference.
  3. Scale analysis, Simplified equations of motion, Wave motions
  4. Balance of forces on a rotating planet, Thermal wind
  5. Divergence, Vorticity, Potential Vorticity, Vertical motion and divergence
  6. Extratropical waves, Mid-latitude cyclones, Quasi-geostrophic balance
  7. Tropical features
  8. Special topics

Lectures, slides, and supporting resources

Note:

  • It is often more reliable to download the lectures rather than listen to them in the Preview.
  • If you use the Preview, then the PDF of the slides are more reliable than the Powerpoint.
  1. Introduction to Class
    1. What is this class about? ( ~ 6:00 minute lecture, slides, pdf
    2. Mathematical requirements: See Additional Resource, below, for more links to calculus refreshers ( ~ 7:00 minute lecture, slides, pdf)
      1. Definitions of important vector operations (slides, pdf)
      2. PDF_Schaum_Vector_Analysis_for_review (pdf)
    3. What you should know from CLIMATE 321 (slides, pdf)
    4. Homework, tests, and grades (under construction)
    5. Text and reference materials (slides, pdf)
      1. Chapter 1, Holton 4th Edition (pdf)
      2. Chapter 2, Holton 4th Edition (pdf)
      3. Chapter 1, Martin (pdf)
      4. Good text: Different Emphasis, Environmental Fluid Mechanics by B. Cushman-Roisin
  2. Introduction to Dynamics
    1. Dynamic meteorology ( ~ 8:00 minute lecture, slides, pdf)
    2. Basic structure of Earth’s atmosphere (~ 16:00 minute lecture, slides, pdf)
      1. Description of Atmosphere: Figures, Units, and Constant (slides, pdf)
    3. Dynamics organizes the atmosphere ( ~ 16:30 minute lecture, slides, pdf
      1. Popular article on turbulence from CBC
      2. Non-rotating fluid video (MIT)
      3. Rotating fluid video (MIT)
      4. Severe convective storms: Past, Present, and Future (Victor Gensini, NIU): This is a excellent seminar that includes discussions of how tornadoes have changed (or not!) as the climate has warmed.
    4. Systems and balance: This lecture, from my climate change class (CLIMATE/EAS 480), is an introduction to the idea that Earth’s climate (and weather) are in a balance that we are used to. Plus, it is useful to think about how dynamics will change with a warming climate. It, also, serves an introduction on how to think about problem solving. ( ~ 19:30 minute lecture, slides, pdf)
  3. Underlying physical principles
    1. Conservation principle: This lecture, from my climate change class (CLIMATE/EAS 480), introduces the conservation principle ( ~ 18.30 minute lecture, slides, slide show, pdf)
      1. Conservation of thermodynamic energy: Introduction  ( ~ 5:30 minute lecture,  slides, pdf)
        1. Simple video on heat and heat transfer (Crash Chemistry): conduction, radiant heat, convection
        2. More general introduction video on conservation of energy and different types of energy (GCSE Physics): open and closed systems
      2. Conservation of mass: Introduction: Includes open, closed, and isolated systems  (~ 3:00  minute  lecture,  slides,  pdf)
        1. Simple video on conservation of mass from a chemical perspective (Fuse School)
        2. Mass versus weight video (Khan Academy)
    2. Ideal gas law and hydrostatic equation ( ~15 minute lecture,  slides, pdf)
      1. Highs and lows of air pressure (UCAR)
    3. Newton’s laws of motion: Includes the concept of idealized “parcel” of fluid ( ~11:00 minute lectureslidespdf)
  4. Forces: Includes introductory lecture on the “idealized parcel” used to derive all forces ( ~ 2:30 minute lecture), which is extracted from the lecture on gravity. See also, Conservation of mass lecture.
    1. Body forces
      1. Gravity: Includes the concept of idealized “parcel” of fluid ( ~ 9:00 minute lecture, slides, pdf)
    2. Surface forces
      1. Pressure-gradient force ( ~ 7:00 minute lecture, slides, pdf)
      2. Viscous force ( ~ 7:00 minute lecture, slides, pdf)
        1. Viscous force details (slides, pdf)
        2. Relationship between viscosity and turbulence: Turbulence and viscosity are not the same.
    3. Apparent Forces
      1. Rotating coordinate systems (~ 9:00 minute lecture, slides, pdf) (This lecture does introduce the Coriolis force in a straightforward mathematical way. It is really all you need to form the equations of motion, but it is not very visual or physically intuitive. See, also, resources with the Coriolis force, below.)
        1. Non-rotating fluid video (MIT)
        2. Rotating fluid video (MIT)
      2. Angular momentum ( ~ 11:30 lecture, slides, pdf)
        1. What is angular momentum (minutephysics)
        2. Angular momentum from Bozeman Science AP physics
      3. Centrifugal forces (~ 21:00 minute lecture, slides, pdf)
        1. Ball on a string video
      4. Coriolis force ( ~11:30 minute lecture, slides, pdf)
        1. Coriolis movie from University of Illinois (This is one of the oldest online movies that I am aware of. I think it pre-dates Google. It remains one of the best for the Coriolis force. Note, in particular when viewed from above, the ball looks like it moves in a straight line.)
        2. Coriolis movie from National Geographic
        3. What is the Coriolis effect from SciJinks (NOAA)
        4. The Coriolis effect (“A fairly simple explanation”)
        5. How do ocean currents work?  (YouTube, Jennifer Verduin)
        6. How does the Gulf Stream work? (YouTube, Kurzgesagt)
  5. Points of View: Coordinate Systems, Lagrangian, and Eulerian frames of reference
    1. The foundation
      1. The idealized parcel ( ~ 2:30 minute lecture)
      2. Rotating coordinate systems (~ 9:00 minute lecture, slides, pdf)
      3. Tangential coordinates ( ~ 6:30 minute lecture, slides, pdf)
    2. Eulerian and Lagrangian frames of reference ( ~ 8:30 minute lecture, slides, pdf)
      1. Eulerian and Lagrangian figures and exercises (slides, pdf)
      2. Mount Pinatubo Particle Model movie from NASA (SVS)
  6. The Material Derivative: ( ~ 12:00 minute lecture, slides, pdf)
    1. Eulerian and Lagrangian figures and exercises (slides, pdf)
  7. Mass Conservation: The Continuity Equation ( ~ 10:30 minute lecture, slides, pdf)
  8. Pressure as a Vertical Coordinate
    1. Definition of geopotential ( ~ 16:30 minute lecture, slides, pdf)
    2. Pressure as vertical coordinate (the pressure gradient force) ( ~ 12:00 minute lecture, slides, pdf)
    3. Material derivative in pressure coordinates (slides, pdf)
    4. Mass continuity in pressure coordinates (slides, pdf)
    5. Hydrostatic equation in pressure coordinates (slides, pdf)
    6. Thermodynamic equation in pressure coordinates (slides, pdf)
  9. Scale Analysis: For Large-Scale Mid-latitudes
    1. Scale analysis: Time scale ( ~ 13:00 minute lecture, slides, pdf)
    2. Scale analysis: Horizontal momentum equation (Geostrophic Balance) ( ~ 12:00 minute lecture, slides, pdf)
    3. Scale analysis: The ageostrophic wind ( ~12:30 minute lecture, slides, pdf)
    4. Scale analysis: Vertical momentum equation ( ~ 7:00 lecture, slides, pdf)
    5. Scale analysis: Continuity equation ( ~ 13:00 minute lecture, slides, pdf)
  10. Thermodynamic Energy Equation
    1. Conservation of thermodynamic energy: Introduction  ( ~ 5:30 minute lectureslides, pdf) (This is a repeat from lecture in 3.1.1. That section, 3.1, has more background material.)
    2. Thermodynamic equation for the atmosphere (slides, pdf)
    3. Potential temperature (slides, pdf)
    4. Lapse rate ( ~ 9:00 minute lecture, slides, pdf)
      1. Buoyancy Wave (slides, pdf)
    5. Thermodynamic equation in pressure coordinates (slides, pdf)
  11. The Thermal Wind
    1. Thermal wind: Derivation of the equation ( ~ 7:00 minute lecture, slides, pdf)
    2. Thermal wind: Relationship to thickness (lecture, slides, pdf)
    3. Thermal wind: Interpretation (lecture, slides, pdf)
  12. Wind Estimates: Geostrophic Wind, Gradient Wind, Balanced Flows (to come)
  13. Vorticity
    1. Vorticity 1: Introduction, definition, curl, and divergence ( ~ 10:30 minute lecture, slides, pdf)
      1. GIF Animation of Hummingbird Wing Shedding Vortices
      2. 1961 video from NASA Langley Learning Center 
      3. Video: Circulation, vorticity, and potential vorticity (Nick Hall – this is a concise, mathematical approach. Might be better for review than introduction.)
      4. Chapter from CGD@NCAR: Vorticity, circulation, and potential vorticity (Nicely presented. Might be better for review than introduction.)
    2. Vorticity 2: Absolute, planetary, and relative vorticity ( ~13:30 minute lecture; slides, pdf)
    3. Vorticity 3: Derivation of conservation of vorticity ( ~ 8:30 minute lecture, slides, pdf)
    4. Vorticity 4: Divergence term (slides, pdf)
    5. Vorticity 5: Tilting term (slides, pdf)
    6. Vorticity 6: Solenoidal or baroclinic term (slides, pdf)
    7. Vorticity 7: Advection (slides, pdf)
    8. Vorticity 8: Scaling of vorticity equation (slides, pdf)
  14. Barotropic Potential Vorticity
    1. Definition and introduction ( ~ 8:00 minute lecture, slides, pdf)
    2. Barotropic potential vorticity ( ~ 6:30 minute lecture, slides, pdf)
    3. Potential vorticity interpretation and mountain wave (slides, pdf)
    4. Vorticity in the atmosphere interpretation (slides, pdf)
  15. Quasi-Geostrophic (QG) Theory
    1. QG1: Scaled equations in pressure coordinates: Momentum ( ~ 16:00 minute lecture, slides, pdf)
    2. QG2: Scaled equations in pressure coordinates: Continuity and Thermodynamic ( ~ 12:00 lecture, slides, pdf)
    3. QG3: Vorticity equation and barotropic geopotential tendency ( ~ 5:30 minute lecture, slides, pdf)
      1. QG3.1: Description of the derivation of the vorticity equation (slides, pdf)
      2. QG3.2: Barotropic longwave ( ~ 7:30 lecture, slides, pdf)
      3. QG3.3: Barotropic longwave and vorticity advection (slides, pdf)
    4. QG4: Baroclinic geopotential tendency ( ~18:00 minute lecture, slides, pdf)
      1. QG4.1: Geopotential tendency and thickness (slides, pdf)
      2. QG4.2: Omega equation ( ~ 16 minute lecture, slides, pdf)
    5. QG5: Images used for discussion and summary of quasi-geostrophic theory and mid-latitude cyclones. (slides, pdf)
    6. QG6: Images used for discussion of waves, weather, and climate (slides, pdf)
  16. Vertical Wind Synthesis
    1. Kinematic, Adiabatic, and Diabatic Estimates (slides, pdf)
    2. Omega equation ( ~ 16 minute lecture, slides, pdf) (This is same as 15.4.2)

 

Homework and In-class Exercises

Homework

Homework 1 (slides, pdf)

Homework 2 (slides, pdf)

Homework 3 (slides, pdf)

Homework 4 (slides, pdf)

Homework 5 (slides, pdf)

Homework 6 (slides, pdf)

Homework 7 (slides, pdf)

Homework 8 (slides, pdf)

In-class Exercises and Figures

  1. Wind Vectors (slides, pdf)
  2. Pressure Forces (slides, pdf)
  3. Independent and Dependent Variables (slides, pdf)
  4. Smoke Transport, September 2020 (slides, pdf)
  5. Hydrostatic Integrations: Isothermal &  Linear (slides, pdf)
  6. Eulerian and Lagrangian Frames of Reference: Examples & Exercises (slides, pdf)
  7. Material Derivative (Eulerian – Lagrangian Station problem) (slides, pdf)
  8. Geostrophic Observed Winds and Friction (slides, pdf)
  9. Hurricane: Vertical Structure (slides, pdf)
  10. Thermal Low and Surface Pressure (slides, pdf, key ppt, key pdf)
  11. Tropical Tidbits Discussion Hurricane Delta (2020)
  12. Geostrophic and Thermal Wind Exercise (slides, pdf, key ppt, key pdf)
  13. Easterly Flow over Mountain & Barotropic (slides, pdf)
  14. Using the Complex Exponential to Solve the Wave Equation (slides, pdf)
  15. Analysis of Dispersion Relation (slides, pdf)
  16. Tornado Analysis and Discussion
    1. What Causes a Tornado (NOAA)
    2. Climate Change and Tornadoes (John Allen, The Conversation)
    3. Chasing the World’s Largest Tornado (National Geographic)
    4. Simulation of El Reno 2011 Tornado (by Leigh Orf, U Wisconsin)

 

Additional resources:

If you need to review calculus

Paul’s Online Notes

Wolfram: Introduction to Calculus

Schaum’s Outline of Calculus

 

USGS: The Water Cycle for Adults and Advanced Students

 

Maps and data.

Extraordinary visualizations of Earth’s dynamics from Earth @ nullschool.net (Navigation on the bottom left, which is a little obscure.)

Observations, predictions, assimilation at NASA Global Modeling and Assimilation Office. (Includes constituents)

Real time weather date at Research Applications Lab at National Center for Atmospheric Research.

Tropical Tidbits. (Excellent collection of model forecasts, observations, and weather discussions of hurricanes)