README               January 15, 2022

                     by Hiromasa Yoshimura
                        Meteorological Research Institute, Japan Meteorological Agency


Output data in shallow water model and advection model experiments.
This data is used in the following paper.

[Paper]

  Yoshimura, H.: Improved double Fourier series on a sphere and its application to a semi-implicit 
       semi-Lagrangian shallow water model.
        (Geoscientific Model Development, 2022)

[Directory]

  (N  : Truncation wavenumber.)
  (IxJ: Number of longitudinal and latitudinal grid points.)
  (dfs: Double Fourier Series)
  (sh : Spherical Harmonics)
      
  Williamson1_euler/  Williamson test case 1, Eulerian    (Output time interval is 24 hour)
    N42_128x64/         N=42,  IxJ=128x64
    N106_320x160/       N=106, IxJ=320x160
    N213_640x320/       N=213, IxJ=640x320
    N639_1920x960/      N=639, IxJ=1920x960
      
  Williamson1/        Williamson test case 1, semi-Lagrangian (Output time interval is 24 hour)
    N63_128x64/         N=63,  IxJ=128x64
    N159_320x160/       N=159, IxJ=320x160
    N319_640x320/       N=319, IxJ=640x320
    N959_1920x960/      N=959, IxJ=1920x960
      
  Williamson2/        Williamson test case 2   (Output time interval is 24 hour)
    N63_128x64/         N=63,  IxJ=128x64
    N63_128x64_1hr/     N=63,  IxJ=128x64        (Output time interval is 1 hour)
    N159_320x160/       N=159, IxJ=320x160
    N319_640x320/       N=319, IxJ=640x320
    N959_1920x960/      N=959, IxJ=1920x960

  Williamson5/        Williamson test case 5   (Output time interval is 24 hour)
    N42_128x64/         N=42,  IxJ=128x64
    N63_128x64/         N=63,  IxJ=128x64
    N106_320x160/       N=106, IxJ=320x160
    N159_320x160/       N=159, IxJ=320x160
    N213_640x320/       N=213, IxJ=640x320
    N319_640x320/       N=319, IxJ=640x320
    N639_1920x960/      N=639, IxJ=1920x960
    N959_1920x960/      N=959, IxJ=1920x960
      
  Williamson6/        Williamson test case 6   (Output time interval is 24 hour)
    N63_128x64/         N=63,  IxJ=128x64
    N159_320x160/       N=159, IxJ=320x160
    N319_640x320/       N=319, IxJ=640x320
    N959_1920x960/      N=959, IxJ=1920x960

  Galewsky/           Galewsky test case   (Output time interval is 24 hour)
    N10239_30720x15360/  N=10239. IxJ=30720x15360

  Galewsky_like/      Galewsky-like test case   (Output time interval is 24 hour)
    N10239_30720x15360/  N=10239. IxJ=30720x15360

      dfsold_grid0/        Old DFS model using Grid [0].
      dfs_grid0/           New DFS model using Grid [0].
      dfs_grid1/           New DFS model using Grid [1].
      dfs_grid-1/          New DFS model using Grid [-1].
      sh/                  SH model.
    
  truncation_error/   Check of the error due to meridional wavenumber truncation
    N42_J64/       N=42, J=64
    N63_J64/       N=63, J=64

  test_Laplacian_Helmholtz/   Accuracy test with the Laplacian operator and the Helmholtz equation
    N42_128x64/         N=42,  IxJ=128x64
    N106_320x160/       N=106, IxJ=320x160
    N213_640x320/       N=213, IxJ=640x320
    N639_1920x960/      N=639, IxJ=1920x960


[Data]

  *.nc : NetCDF file
  *.ncctl: Grads contol file for NetCDF file (text file).

  data.nc, data.ncctl: Simulated lon-lat data.
    Variables: h (height), u (zonal wind), v (meridional wind), vor (vorticity), div (divergence).

  vor.nc, vor.ncctl: Simulated lon-lat vorticity data after 144-hour integration.
                     (For Galewsky test case.)
    Variables: vor (vorticity)

  norm.nc, norm.ncctl: Error of predicted height (for Williamson test case 2).
    Variables: norm_L1 (L1 norm), norm_L2 (L2 norm), norm_Lmax (Lmax norm).

  spectrum.nc, spectrum.ncctl: Kinetic Energy spectrum.
    Variables: KE_VOR (Kinetic Energy (Vorticity)), KE_DIV (Kinetic Energy (Divergence)).

  weight_lat.nc, weight_lat.ncctl: Latitudinal weight.
    Variables: wgt (latitudinal weight)

  STDOUT: Standard Output file

  In 'truncation_error' directory

    initial.nc, initial.ncctl : Initial values before truncation
    orszag.nc, orszag.ncctl   : Values after truncation in Orszag's DFS method
    cheong.nc, cheong.ncctl   : Values after truncation in Cheong's method (old DFS method)
    new.nc   , new.ncctl      : Values after truncation in CNew DFS method
    cheong_interp.nc, cheong_interp.ncctl
                              : Values interpolated between grids after truncation in Cheong's method (old DFS method)
    new_interp.nc   , new_interp.ncctl
                              : Values interpolated between grids after truncation in new DFS method
    legendre_initial.nc, legendre_initial.ncctl : Initial values before truncation in SH method
    legendre.nc, legendre.ncctl                 : Values after truncation in SH method
      lon: Wavenumber
      lat: Latitude


  - Output REAL(4) binary files and grads control files were converted to NetCDF files by using cdo.
    > cdo -f nc4 -z zip_5 import_binary aaa.ctl aaa.nc
    https://code.mpimet.mpg.de/projects/cdo/
    http://cola.gmu.edu/grads/
    

[Web site]

  https://climate.mri-jma.go.jp/pub/archives/Yoshimura_DFS_SW_Testcase/