Numerical Weather Prediction

Meteorology 526

Numerical Weather Prediction
Fall Semester, 2017

TuTh  12:05 – 1:20 pm                                                          
126 Walker Building

Dr. David R. Stauffer
621 Walker Building
Office Hours: After class and by appointment

Text: Thomas T. Warner, Numerical Weather and Climate Prediction, Cambridge University Press, 2011.

Selected papers from open literature (OL)

Course handouts

Dale R. Durran, Numerical Methods for Wave Equations in Geophysical Fluid Dynamics, Springer.1999.  (On reserve, additional background material for course notes, printed copy (EMS Library) and e-book (

Course Outline: Topics/Reading

  • Intro. to NWP, systems of equations for atmosphere and oceans, scale analysis, approximations to equations, averaging and filter scales, parameterization, ‘gray’ zones 1-12, 119-121, OL

  • Map projections, model grids and vertical coordinates, generalized vertical coordinates, boundary conditions 24-40, 89-95 96-117, OL

  • Review of wave motions, shallow-water model, linearization,phase and group velocity, hydrostatic vs. nonhydrostatic wave modes, geostrophic adjustment 12-16, 236-240, OL

  • Model initialization, objective analysis, spinup and insertion noise, nudging and digital filters, statistical (OI, Kalman filter EnKF) and variational (3DVAR, 4DVAR / adjoint) methods, hybrid methods 198-250, OL

  • EXAM I

  • Finite differences, the advection equation, truncation error, computational modes, false (numerical) diffusion, linear numerical stability analysis 17-23, 51-53, 58-72

  • Numerical issues / necessities, the diffusion equation, smoothing and filtering, nonlinear, computational instability, aliasing, effective resolution 72-89, 95

  • Series expansion methods, spectral, finite element, pseudospectral methods  42-51 

  • Computational efficiency and accuracy, grid-staggering, multi-step, multi-stage, time-splitting schemes, semi-Lagrangian, semi-implicit methods  53-58, 75-80, 358-364


  • Ensemble methods, coupled model applications, verification methods, model analysis techniques 252-282, 378-400, 294-319, 343-357, OL


*Basic shallow water model code / graphics software will be provided to the class


  • EXAMS (2) 60 %
  • Problem sets, shallow-water model assignments 10 %
  • Final paper – Extended shallow-water model studies 30 %

Academic Integrity: Students in this class are expected to write up their problem sets / modeling studies individually, to work the exams on their own, and to write their papers in their own words using their results and proper citations. Class members may work on the problem sets in groups, but then each student must write up the answers separately. Please see: Earth and Mineral Sciences Academic Integrity Policy, which is adopted by this course: To learn more, see Penn State's "Plagiarism Tutorial for Students."  

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For example, uploading completed labs, homework, or other assignments to any study site constitutes a violation of this policy.

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