__Units and constants__

- Derived units for dynamics
- Useful constants
- Constants and conversions from Penn State webpage
- Unit conversion technique

__Math basics and basic forces__

- Taylor series, vector math, and the pressure gradient force
- Pressure gradient force brief quiz
- Review example on calculating derivatives. More information on formal method from UC Davis is here. Derivatives shortcuts discussed here and here. Online derivative calculator here.
- Calculating derivative using centered finite difference technique
- Gravitational and viscous forces
- Cool stuff - Online calculator for vectors
- Cool stuff - What is gravity? It's the curvature of spacetime. Learn about Einstein's General Theory of Relativity in this video. Mind-blowing!

__Reference frames__

- Basic discussion on references frames
- Reference frames, centrifugal force and Coriolis force
- COMET video on Coriolis force (requires COMET account)
- Earth rotation rate and sidereal day
- a) More information on the sidereal day. b) Video

__Recorded lecture on units, math basics, and reference frames (quick review of previous in-class lectures)__

__Vertical pressure gradient relationships__

- Hydrostatic equation and thickness equation (from Wallace and Hobbs)
- Thickness equation derivation (from Stull)
- Refresher on virtual temperature. Also see http://www.cimms.ou.edu/~doswell/virtual/virtual.html and page 14 in my stability notes here
- Good explanation of hydrostatic equation (from weatherprediction.com)
- Good explanation of thickness and relationship to mean temperature in layers (from weatherprediction.com)
- COMET module on thickness
- Relationship of thickness to tropospheric cold-core cyclones, warm-core cyclone, cold-core anticyclones, and warm-core anticyclones
- More description on warm-core and cold-core systems
- Example thickness application: the rain-snow line
- Real-time model example of rain-snow line: click on 1000-500 mb thickness product here

__Recorded lecture on vertical pressure gradient relationships__

__Upper-level maps__

- Pressure gradient coordinate transformation
- Relationship between pressure gradient force on constant heights and isobaric levels
- General discussion on isobaric maps
- Isohyse definition. Isohypse (also called "height lines") are shown on constant pressure charts for mandatory levels.
- Uses for upper-air maps
- Current constant pressure maps at University of Wisconsin and Unisys Weather

__Recorded lecture on upper-level maps__

__Surface pressure__

- Is static pressure the weight per unit area? For practical purposes, yes. 1) Proof for x,y, z system . 2) Description of weight . 3) What is a kilogram?
- Optional reading. Oddly enough, this definition of pressure may not be completely true for the spherical earth and other planet geometries. See this BAMS article.
- Surface pressure relationship when including troposphere and stratosphere. A tropospheric "warm-core" high is cold-core in stratosphere, and tropospheric "cold-core" low is warm-core in stratosphere. From Hirschberg and Fritsch (1991).
- Why is pressure so low in a tropical cyclone? Warm-core in upper-troposphere! Mathematically, it's the dp/p term (manifested as a ln). Explanation here.

__Recorded lecture on surface pressure__

__Surface pressure adjustment and the sigma coordinate system__

- Different coordinate systems: 1) Sigma ; 2) Hybrid sigma-pressure ; 3) Hybrid sigma-isentrope ; 4) COMET module on vertical coordinate systems
- Adjustment to mean sea level pressure, method from Stull
- Adjustment to mean sea level pressure, method used in mesoscale model MM5
- Adjustment to mean sea level pressure, using a table (COMET module)
- Adjustment to ground pressure from mean sea level pressure, method used in mesoscale model MM5

__Recorded lecture on surface pressure adjustment and the sigma coordinate system__

__Altimeter equation__

- Derivation of height equation for altimeters (Problem 1.16 in HH)
- Issues with altimeters
- A pilot's discussion on altimeters
- Altimeter calculator online

__Recorded lecture on altimeter equation__

__Length scale analysis__

__Recorded lecture on length scale analysis__

__Review of material for test on Feb 3__