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."  

Course Copyright: All course materials students receive or to which students have online access are protected by copyright laws. Students may use course materials and make copies for their own use as needed, but unauthorized distribution and/or uploading of materials without the instructor’s express permission is strictly prohibited. University Policy AD 40, the University Policy Recording of Classroom Activities and Note Taking Services addresses this issue. Students who engage in the unauthorized distribution of copyrighted materials may be held in violation of the University’s Code of Conduct, and/or liable under Federal and State laws.

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

Accommodations for Students with Disabilities:  Penn State welcomes students with disabilities into the University's educational programs. Every Penn State campus has an office for students with disabilities. The Student Disability Resources (SDR) website provides contact information for every Penn State campus: ( For further information, please visit the Student Disability Resources website (

In order to receive consideration for reasonable accommodations, you must contact the appropriate disability services office at the campus where you are officially enrolled, participate in an intake interview, and provide documentation: If the documentation supports your request for reasonable accommodations, your campus’s 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.

Attendance: This course abides by the Penn State Attendance Policy E-11:, and Conflict Exam Policy 44-35: Please also see Illness Verification Policy:, and Religious Observance Policy: Students who miss class for legitimate reasons will be given a reasonable opportunity to make up missed work, including exams and quizzes.  Students are not required to secure the signature of medical personnel in the case of illness or injury and should use their best judgment on whether they are well enough to attend class or not; the University Health Center will not provide medical verification for minor illnesses or injuries. Other legitimate reasons for missing class include religious observance, military service, family emergencies, regularly scheduled university-approved curricular or extracurricular activities, and post-graduate, career-related interviews when there is no opportunity for students to re-schedule these opportunities (such as employment and graduate school final interviews).  Students who encounter serious family, health, or personal situations that result in extended absences should contact the Office of the Assistant Vice President for Student Affairs (AVPSA) and Student Care and Advocacy for help:  Whenever possible, students participating in University-approved activities should submit to the instructor a Class Absence Form available from the Registrar's Office:, at least one week prior to the activity.

Weather Delays: Campus emergencies, including weather delays, are announced on Penn State News and communicated to cell phones, email, the Penn State Facebook page, and Twitter via PSUAlert (Sign up at:

Reporting Bias-Motivated Incidents: Penn State takes great pride to foster a diverse and inclusive environment for students, faculty, and staff.  Acts of intolerance, discrimination, or harassment due to age, ancestry, color, disability, gender, gender identity, national origin, race, religious belief, sexual orientation, or veteran status are not tolerated ( and can be reported through Educational Equity via the Report Bias webpage.

Counseling and Psychological Services: Many students at Penn State face personal challenges or have psychological needs that may interfere with their academic progress, social development, or emotional wellbeing.  The university offers a variety of confidential services to help you through difficult times, including individual and group counseling, crisis intervention, consultations, online chats, and mental health screenings.  These services are provided by staff who welcome all students and embrace a philosophy respectful of clients’ cultural and religious backgrounds, and sensitive to differences in race, ability, gender identity and sexual orientation.  Services include the following:

Document Actions