UBC ATSC 507 - Numerical Weather Prediction (NWP)

Lecture Topics, Readings, Homework Assignments, and Learning Goals - 2023


Under construction.

Topic Schedule - 2023
2023 Topics

Week 1.   17-19 Jan

Scientific Basis for NWP.    Approximations.   Flux form.
Week 2a.    24 Jan Coordinate Transformations:  Vertical & Horizontal.
Week 2b & 3.    26, 31 Jan & 2 Feb
Installing and Running WRF.
Week 4.    7-9 Feb Finite-difference Methods - Spatial & Temporal.
Week 5.    14-16 Feb Finiite-difference Errors - Part 1:   Amplitude Error Analysis of Linear Eqs;   the von Neuman method.
Holiday.    21-23 Feb Spring Break. No classes.
Week 6.    28 Feb - 2 Mar Finite-difference Errors - Part 2: Amplitude Error Analysis (continued).
Week 7.    7-9 Mar Finite-volume Methods. MPAS model. FV3 model.
Week 8.    14-16 Mar Finite-difference Errors - Part 3: Phase & Group-speed Errors, Nonlinear stability.
Week 9.    21-23 Mar Chaos, ensemble methods, probabilistic forecasts
Week 10.    28-30 Mar Postprocessing Methods
Week 11.    4-6 Apr Semi-Lagrangian Methods; Smoothing and Filtering; Verification Methods
Week 12.    11-13 Apr (no classes for this course)
Week 13.    19 Apr Physics Schemes (presentations by students)
   
   
   
   
   

 


 

Ignore the remainder of this web page. It is from past terms, and will be deleted soon.
( Stull is gradually moving the material to the new web pages above.)

 

Lect.
#
Date (2020)
Topics
(& instructor:
Roland Stull or Tim Chui)

Learning Goals
At the end of the class meeting, you should be able to:
Assignments.  Legend:
C = Coiffier 2011: Fundamentals of NWP,
S = Stull 2017: Practical Meteorology (NWP chapter only),
W = Warner 2011: Numerical Weather & Clim. Pred.,
c = chapter, p = page

12
9 Feb 2020

Acoustic split time differencing

(Lecture by Tim Chui)


    For the Acoustic Time-splitting lecture:

    • Before class, skim paper by paper by Wicker and Skamarock (2002) on split time differencing:
      https://journals.ametsoc.org/doi/pdf/10.1175/1520-0493%282002%29130%3C2088%3ATSMFEM%3E2.0.CO%3B2

    Homework 5: See this link for the assignment on acoustic time splitting.

    .
    18, 20 Feb
    Spring Break / Reading Week


    13
    ????

    Vapor display software

    , presented by Nadya Moisseeva.
    • open WRF output in the Vapor program to create 3-D visualizations of your forecasts. BEFORE class, use the instructions on this link to install Vapor on your own laptop.
    Also, download the sample WRF output file to your own laptop, which is the forecast for a strong low off the BC coast that caused damaging winds on 20 Dec 2018.  Bring your laptop to class.

    In class, Nadya will show you how to use Vapor to view the WRF output.
    22
    16 Mar

    9. Spectral methods


    1. Fourier series and Fourier transforms, used to describe variations along parallels.
    2. Legendre polynomials, used to describe variation along meridions.
    3. Orthogonality properties.
    4. Applying Fourier series to simplified eqs. of motion.
    5. Spectral methods in global models
    6. Operational spectral models: GFS & ECMWF
    7. Pros and cons of spectral methods.

    • start with the variation of a weather variable with distance (such as T vs. x) and convert it into a Fourier series.
    • convert simple equations of motion into forecast equations for spectral amplitude.
    • integrate (i.e., time-step) these equations forward in time to get forecasts of spectral amplitude, and then do an inverse Fourier transform to recover the physical signal.
    • summarize the steps needed to utilize the spectral method for spherical domains such as Earth's atmosphere.
    • relate truncation type (triangular, trapezoidal, rhomboidal) and order to the effective horizontal resolution
    • BEFORE class, Read Warner section 3.2.2 (p42-51) about spectral methods.

    • Stull - Spectra Methods lecture notes - part a
    • Stull - Spectra Methods lecture notes - part b
    • Stull - Spectra Methods lecture notes - part c
    • Coiffier - chapter on spectral methods - annotated

    • HW 10 - Spectral: 
      1) Given the polynomial y = 0.5*x + x*SIN(2*PI*x/10) for 0 ≤ x ≤ 20.
        (a) plot this function
        (b) analytically integrate it, to find the exact solution.
        (c) use Gauss quadrature to numerically integrate it (using the eqs and tables in the handout, not any built-in integration function) for the following number of key points (m or n=):  (i) 2 ,  (ii) 4 , (iii) 6 , (iv) 8 , and discuss how Gaussian quadrature converges to the exact solution.  Show your work on your spreadsheet, or matlab, or your computer program.

      2) search the internet fo find the type of truncation and its highest order M used for operational runs of (a)  ECMWF.   Relate these to Warner's L1-L4 on p49, and show the corresponding values (km) for the different measures of horizontal resolution.

      3) Plot eq. (4.22) of Coiffier similar to his Fig 4.2, but for:  (a) m=0 with n=1 to 4, (b) m=1 with n=1 to5, and (c) m=2 with n=2 to 6. 

      4) Use Fourier methods similar to the class demo, so you can derive the Ordinary Differential Eq (ODE) for:  ∂T/∂t + Uo*∂T/∂x = K∂2T/∂x2, where Uo and K are constants.
      .
    .
    .
    Pseudo-spectral methods

    ( not covered in 2020)
    .
    .
    Semi-Lagrangian
    tbd
    See Dr. May Wong's lecture slides on Semi-Lagrangian methods (not covered in 2020)
    .
    .
    Smoothing & Filtering
    1. Notation
    2. DFT filter
    3. Smoothing, including low-pass, high-pass, band-pass, and general filters.

    • explain the relationship between smoothing and filtering
    • use the discrete fourier transform (DFT) to create any arbitrary filter
    • compare running-mean vs. ideal filters.
    • explain what filtering is used in WRF and why it is used.
    During the online class:
    • Stull - Smoothing & Filtering lecture notes (not covered in 2020)

    Reading AFTER class:
    • WRF-ARW4 Tech Note - Chapter 4

    HW xx - Topic: Smoothing & Filtering. (not assigned in 2020)
    1) What are the weights in a 5-point smoother (applied once) that is equivalent to a 3-point smoother ( 0.25 / 0.50 / 0.25 ) applied twice?
    2) For a continuous (not discrete) problem, derive the filter response function for the case where the smoother weights are given by the following sinc function:   w(tau) = 2*B* [sin(2*pi*B*tau) ] / (2*pi*B*tau) , where B = bandwidth (=the cutoff wavenumber for the filter).  Note, this w(tau) function is already normalized; namely, the area under the w(tau) curve = 1. 
    Hint:   the definite integral of the sinc function is
    sinc
     

    .
    .
    Data Assimilation
    1. Overview, observations, background
    2. Model spin-up to balance mass and flow fields
    3. Optimal interpolation and Bratseth's Successive Correction schemes
    4. Variational data assimilation (3D & 4D)
    5. Advanced and hybrid assimilation methods

    Data Assimilation
    • explain why numerical models need initial conditions
    • define data assimilation
    • list 3 major methods of doing data assimilation
    • indentify the factors that cause certain observations or grid-point values to be weighted less than other.
    • show how the Cressman, Barnes, and Bratseth schemes are all types of successive correction assimilation methods.
    • identify optimum interpolation as a least-squares approach.
    • show how optimum interpolation method can be re-written as a cost function for a variational approach
    • explain the basic concepts of 3-D Var and 4-D Var.
    • Regarding initialization & data assimilation: Read Stull p762-767, and
    • Read Warner p198-251 in Ch 6 on initial conditions, and
    • Read WRF-ARW4 Tech Note chapter 5 on Initial Conditions .
    • Read WRF-ARW4 Tech Note  Chapter 11 on Variational Data Assimilation.
    • .
    • AFTER class:   

    HW xx  Topic -  Data Assimilation.  (not covered in 2020)

    1) Analytically derive eq. (20.20) of Stull's NWP chapter by finding the analysis value "A" that gives the minimum cost function "J" as defined by Stull's eq. (20.21).
    24
    2 Apr
    Verification
    • calculate verification statistics for continuous, binary, and probabilistic forecasts.
    • explain pros and cons of each verification statistics
    • identify the range of values of each statistic, and explain which values are good and bad.
    • compare the forecast skill of NWP models from different organizations worldwide.

    See Stull's Verification lecture slides-2020

    HW 11  Topic: Forecast Verification
    From Stull's Practical Meteorology book, chapter 20
    https://www.eoas.ubc.ca/books/Practical_Meteorology/prmet102/Ch20-nwp-v102.pdf
    Do the following exercises at the end of chapter 20 ,from the "Applied " section of exercises:
    • A19,
    • A20,
    • A21,
    • A22,
    • A23 (exercise a)

    25
    7 Apr
    Post-processing, Catch-up & Review
    • explain the reasons for statistical post-processing of NWP forecasts
    • use different statistical methods to perform post-processing
    • compare MOS , Perfect-prog, and other methods.

    See Dr. Thomas Nipen's lecture slides on Probabilistic Forecasts


    See Stull's lecture slides on post-processing, operational forecasting, and terrain issues

    Also listen to ECMWF's lecture on new developments in statistical post-processing:
    https://confluence.ecmwf.int/download/attachments/45754015/TK_StatisticalPostrocessing_2015.mp4 

    26
    16 Apr - instead of a final exam
    Student presentations on WRF-ARW4 Physics Schemes, with selections from:
    • radiation - Rachel
    • microphysics
    • cumulus convection - Eve
    • shallow cumulus
    • boundary layers
    • land-surface - Abhi
    • surface layer - Christina
    • boundary layer - Chris
    • fire physics
    • etc.
    Most of these topics are covered in Chapter 8 of the WRF-ARW4 Tech Note.

    • list 3 of each of the schemes that was discussed by you and your classmates.
    • identify the default schemes used in WRF, and show how to change these schemes via the namelist.
    • give talks on NWP topics with confidence
    • BEFORE class, Re-read Table 20-1 in Stull.  
    • Also, READ the portions of Warner chapters 4 & 5 that apply to your presentation topics (see HW below), and read the sections of WRF-ARW Tech Note Chapter 8 that applies to your topic.
    HW 12  Topic: Physics options in WRF
    • Chat online with  your classmates so you can each pick a different physics category (i.e., no students doing the same category).  Please slack me to tell me your category.
    • Read the one section in Warner chapters 4 & 5 related to YOUR physics category.  Also read the associated WRF info for your physics category.
    • As we discussed earlier, create a 30-minute presentation (plus/minus 10 min) summarizing the different WRF Physics options (and their main characteristics, advantages, disadvantages) for the NWP Physics category assigned to you in previous emails.
    • Create handouts to be emailed to your classmates (& for the TA and I).
    • Give your presentation to the class via Zoom or other online mechanism that I will set up.







    Ignore all below this line



    topics needing a home:




    1. Finite-element methods.
    2. Consistency of vertical and horizontal grid increments.






    • BEFORE class, continue working on your presentation for next week.
    • Read WRF-ARW Tech Note chapter 6 on lateral boundary conditions,
    • Read WRF-ARW Tech Note chapter 7 on nesting.
    • Read Warner section 3.5 on lateral boundary conditions.







    END OF COURSE