UBC ATSC 507 - Numerical Weather Prediction (NWP)

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Calendar Description:  Scientific basis of weather forecasting, grid-point and spectral numerics, physics parameterizations, data assimilation, initial and boundary conditions, ensemble methods, verification, numerical forecast process, post-processing, operational models.  Prerequisites: any fluid-dynamics course, any numerical-methods course, and computer-programming skills.  (3 credits)

Motivation:

• Over 90% of modern weather forecasts are made by numerical weather prediction (NWP), with little adjustment by humans.
• NWP methods apply to scales from global climate models (GCMs) to operational short-range weather forecasts to turbulence.
• Output from NWP forecasts guide wind- and hydro-energy management, pollutant dispersion, and storm prediction.
• UBC ATSC has a major research program in NWP.  Many ATSC grad students use NWP models as a research tool/method. 

 
Course Structure:

• Weeks 1-2:  Lectures by the instructor. Homework assignments involving derivations and textbook reading.
• Weeks 3-13:  In addition to lectures , readings, and homeworks, some use of Just-in-Time Teaching (JiTT) including group discussions and other CWSEI methods.  Homework assignments involving problem-solving for some idealized components of NWP. 
• Weeks 4, 7:  Install and run the WRF model to evaluate different numerics and parameterizations. Also, in-depth discussion of FV3 and MPAS models.
• Last days:  Synthesis.  Students will debate the pros and cons of key physics parameterizations used in WRF.

 
Topics: 

1. scientific basis for NWP (governing eqs.)
2. vertical coordinate transformations (terrain following, sigma)
3. the WRF model
4. horizontal coordinate transformations (map projections, map factors)
5. finite-difference methods
6. errors associated with finite-difference methods
7. lateral boundary conditions and nesting (from readings)
8. finite-volume methods, and associated models (FV3 & MPAS)
9. physics parameterization schemes
10. smoothing and filtering
11. semi-Lagrangian methods
12. data assimilation
13. ensemble methods
14. verification methods
15. probability forecasting
16. post-processing methods
17. operational forecasting
    

 
Context:

• This is an elective for ATSC Masters students (thesis, non-thesis, and co-op) and ATSC PhD students.
• The course is open to all UBC graduate students having the prereqs.  Grad students in engineering (aerodynamics, fluid dynamics), oceanography, geology, environmental science, and perhaps computer science might be interested.
• It differs from engineering computational fluid dynamics (CFD) in the large horizontal scales of motion with limited vertical scales in the troposphere, the strong influence of the earth's rotation via Coriolis force, the extremely large Reynolds number (inertial forces are much larger than frictional forces), the importance of static stability in modulating vertical motions, and the influence of subgrid physical processes such as cloud microphysics, radiation and turbulence.

 
Operation:
Instructor:  Prof. Roland Stull, with occasional guest lectures by others.   Course to be offered every other year. 
Assignments:
    • Textbook readings each week from the required textbook.  Occasional readings from journal papers and other textbooks.
    • Written homework assignments each week (derivations or problem solving or programming)
    • Capstone project by student teams to design and program a simple NWP model.
Discussions and debates by students during weeks 3-10 to expose their understanding of the readings.
Exams: One written final exam during the normal exam period.

 
Discussion of Prerequisites: 
    • Fluid dynamics:  any of ATSC 404, 414, EOSC 512, or a fluid-dynamics course in engineering, physics, etc. covering:
            Basic atmospheric (primitive) eqs of motion (dynamics, thermodynamics, continuity, state, etc.).
            Roles of dynamics, physics, and numerics in weather models
            Approximations:  hydrostatic, Boussinesq, Reynolds, anelastic, shallow-fluids, barotropic vs. baroclinic.

    • Numerical methods:  any of ATSC 409, ATSC 506, EOSC 511 or similar courses in engineering, physics, etc. covering:
            Taylor Series, finite-difference calculus, grid points (aligned and staggered)
            Interpolation and extrapolation, curve fitting, roots of equations, linear algebra methods
            Numerical integration, numerical solution of ordinary and partial differential eqs.
                including leapfrog, Runge-Kutta, etc.  Explicit, implicit, and semi-implicit methods.
            Spatial differencing methods.  Eulerian, Lagrangian, and semi-Lagrangian.  Stencil rules. 
            Discretized equations of motion.  Role of initial and boundary conditions.
            Truncation error.  Linear stability in advection and diffusion terms. 
            Phase and group speed errors.  Aliasing.  Numerical diffusion.  Numerical stability criteria: CFL

    • Computer programming:  any one of EOSC 211 (matlab), CPSC 189 (Python), ATSC 212 (sci. programming),
            or similar courses in other depts that cover scientific programming.  Or demonstrated programming skill.

    Note:  If a student from another dept has similar courses but without the full coverage listed above, the student can still be successful because each of these topics will be briefly reviewed in the first weeks of the course, and are covered in the textbook.  We want this course to be accessible to a wide range of grad students.  Contact the instructor to discuss your own situation.

 
Methods & Activities: 

1. textbook readings
2. journal-paper readings
3. derivations
4. understanding the workings of the WRF model (i.e., not a"black box")
5. running WRF
6. WRF physics intercomparisons
7. student presentations in class
8. what-if demos using spreadsheets
9. samples of code
10. homeworks
11. projects
12. crunching numbers
13. in-class lab work (e.g., graphical interpretation of time-diff. schemes)
14. laptops in class to follow TA's guidance in setting-up WRF
15. guest lectures
16. flexibility in the computational tools you can use