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  • Home
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  • Synoptic lab
    • Syllabus
    • Take-home exams
    • Homework
    • Tropical Cyclones
      • Tropical cyclone climatology and overview
      • Tropical cyclone life cycle and motion
      • Tropical cyclone structure
      • Hurricane forecasting learning material
      • Hurricane forecasting tools
      • Storm surge
      • TUTTs and LA/MS flood event of 2016
    • Ocean applications
      • Waves
      • Tides
      • Miscellaneous ocean products
    • Streamlines
    • Regression, MOS, and NBM
    • Forecasting baroclinic systems and other products
      • Analysis
      • Model guidance
      • Model Output Statistics and National Blend of Models
      • Useful forecast products
  • Synoptic class
    • Syllabus
    • Exam Information
    • Homework
    • Stability
      • The Basics
      • The SkewT and related diagnostic tools
      • POP, air mass thunderstorms, sea breeze thunderstorms
      • Severe Weather
    • Map analysis
      • Upper-level synoptic charts
      • Contouring
      • Surface analysis and fronts
      • Vertical structure
      • Jet Streaks
    • Dynamics
      • Review of dynamics
      • Dynamics applications
      • QG Theory and the Omega equation
      • Cyclogenesis and baroclinic instability
    • Modeling
    • Fog
    • Winter Weather
  • Intro Dynamics
    • Syllabus
    • Homework
    • Sample exam questions
    • Introduction (Chap. 1, HH)
    • Basic equations of meteorology (Chap. 2, HH)
    • Imbedded processes in equations of meteorology (Chap. 3, HH). Exam 2 material
    • Imbedded processes in equations of meteorology (Chap. 3, HH). Exam 3 material
    • Planetary boundary layer
    • Vorticity (Chap.4, HH)
    • Pertubation method and atmospheric waves (Chap 5, HH)
  • Numerical methods
    • Syllabus
    • Homework
    • Number Series
    • Interpolation
    • Basic matrix math
    • Filters And Fourier Analysis
    • Numerical derivatives
    • Numerical integration, random numbers, and Monte Carlo
    • Numerical solutions of differential equations and atmospheric modeling
    • Parameterization, data assimilation, and overview on WRF model
    • Final computer exercises
  • Dashboard
​Fourier (Harmonic) series
  • The basics (from "ask a mathematician")
  • The mathematics (from Lamar University)
  • The fundamental equations with sine as the first term - a Fourier series; computing harmonic coefficients; computing signal power; computing explained variance
  • The fundamental equations with cosine as the first term. (This version is slightly more common in the literature.)
Imaginary numbers and Fourier series
  • Wait! What? The beauty of a bizarre notion. (Note: the term "imaginary number" originated in the 17th century as a derogatory term, see Wiki) 
  • Intuitive understanding of Euler's formula
  • The fundamental equations for complex Fourier series
  • Examples of converting between complex Fourier series and real version of Fourier series. Courtesy Nathan Pflueger of Amherst University
  • Supplementary material on complex Fourier series. Courtesy Swarthmore College.
Normal modes
  • Animation, example of drum normal modes
  • Normal modes and using them for wave solutions
  • Linearization of equations by perturbation method
Dispersion
  • Dispersion relationship, phase speed, and group velocity
  • 1) Animation of phase speed and group velocity 2) Another animation 3) Animation of dispersive vs nondispersive waves 4) General video on wave dispersion
  • Video lecture on wave dispersion. Courtesy Dr. Hillary Weller. Accompanying notes to video. 
  • Video of boat wake dispersion.
Atmospheric waves
  • Basic discussion of wave types in the atmosphere
  • Summary figure on atmospheric wave types
  • Characteristics of atmospheric wave types
  • General (intermediate) water waves, shallow water waves, and deepwater waves. Which one is NOT dispersive? Video on ocean wave dispersion
Dispersion and phase speed derivations responsible for on exam
  • Rossby waves. Their westward propagation mechanism relates to how vorticity is redistributed. Graphic showing mechanism.
  • Sound waves. Aside --- converting thermodynamic equation to its natural log version
  • Waves on a discontinuity (like ocean waves)
Alternate derivations of Rossby waves from sine wave
  • Alternate Rossby wave derivation
Dr. Fitz's derivations on atmospheric waves (supplemental, not required for class, some steps incomplete but could still be helpful to students)
  • Alternate derivation of sound waves (shorter version!)
  • Inertial-buoyancy waves
  • Kelvin waves
  • Inertia-gravity waves
  • Inertia-buoyancy waves
  • Equatorial waves
  • 2D Rossby wave, non-divergent classical version
  • 2D Rossby wave, weakly divergent flow
  • Rossby wave in a dishpan
Excellent technical overview on waves from Japan Meteorological Agency, including alternative derivations to dispersion relationships (supplemental material)
  • Technical details
  • Linear wave theory 
Recorded lectures
  • Waves, dispersion, and Fourier series. Audio only.
  • Dispersion derivations. Audio only.
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  • Home
  • Contact information
  • Synoptic lab
    • Syllabus
    • Take-home exams
    • Homework
    • Tropical Cyclones
      • Tropical cyclone climatology and overview
      • Tropical cyclone life cycle and motion
      • Tropical cyclone structure
      • Hurricane forecasting learning material
      • Hurricane forecasting tools
      • Storm surge
      • TUTTs and LA/MS flood event of 2016
    • Ocean applications
      • Waves
      • Tides
      • Miscellaneous ocean products
    • Streamlines
    • Regression, MOS, and NBM
    • Forecasting baroclinic systems and other products
      • Analysis
      • Model guidance
      • Model Output Statistics and National Blend of Models
      • Useful forecast products
  • Synoptic class
    • Syllabus
    • Exam Information
    • Homework
    • Stability
      • The Basics
      • The SkewT and related diagnostic tools
      • POP, air mass thunderstorms, sea breeze thunderstorms
      • Severe Weather
    • Map analysis
      • Upper-level synoptic charts
      • Contouring
      • Surface analysis and fronts
      • Vertical structure
      • Jet Streaks
    • Dynamics
      • Review of dynamics
      • Dynamics applications
      • QG Theory and the Omega equation
      • Cyclogenesis and baroclinic instability
    • Modeling
    • Fog
    • Winter Weather
  • Intro Dynamics
    • Syllabus
    • Homework
    • Sample exam questions
    • Introduction (Chap. 1, HH)
    • Basic equations of meteorology (Chap. 2, HH)
    • Imbedded processes in equations of meteorology (Chap. 3, HH). Exam 2 material
    • Imbedded processes in equations of meteorology (Chap. 3, HH). Exam 3 material
    • Planetary boundary layer
    • Vorticity (Chap.4, HH)
    • Pertubation method and atmospheric waves (Chap 5, HH)
  • Numerical methods
    • Syllabus
    • Homework
    • Number Series
    • Interpolation
    • Basic matrix math
    • Filters And Fourier Analysis
    • Numerical derivatives
    • Numerical integration, random numbers, and Monte Carlo
    • Numerical solutions of differential equations and atmospheric modeling
    • Parameterization, data assimilation, and overview on WRF model
    • Final computer exercises
  • Dashboard