| 1 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
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| 2 | ! |
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| 3 | ! This program creates a remapping grid file for Gaussian lat/lon |
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| 4 | ! grids (for spectral transform codes). |
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| 5 | ! |
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| 6 | !----------------------------------------------------------------------- |
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| 7 | ! |
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| 8 | ! CVS:$Id$ |
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| 9 | ! |
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| 10 | ! Copyright (c) 1997, 1998 the Regents of the University of |
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| 11 | ! California. |
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| 12 | ! |
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| 13 | ! Unless otherwise indicated, this software has been authored |
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| 14 | ! by an employee or employees of the University of California, |
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| 15 | ! operator of the Los Alamos National Laboratory under Contract |
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| 16 | ! No. W-7405-ENG-36 with the U.S. Department of Energy. The U.S. |
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| 17 | ! Government has rights to use, reproduce, and distribute this |
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| 18 | ! software. The public may copy and use this software without |
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| 19 | ! charge, provided that this Notice and any statement of authorship |
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| 20 | ! are reproduced on all copies. Neither the Government nor the |
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| 21 | ! University makes any warranty, express or implied, or assumes |
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| 22 | ! any liability or responsibility for the use of this software. |
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| 23 | ! |
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| 24 | !*********************************************************************** |
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| 25 | |
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| 26 | program convert_gauss |
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| 27 | |
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| 28 | !----------------------------------------------------------------------- |
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| 29 | ! |
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| 30 | ! This file creates a remapping grid file for a Gaussian grid |
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| 31 | ! |
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| 32 | !----------------------------------------------------------------------- |
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| 33 | |
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| 34 | use kinds_mod |
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| 35 | use constants |
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| 36 | use iounits |
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| 37 | use netcdf_mod |
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| 38 | |
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| 39 | implicit none |
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| 40 | |
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| 41 | !----------------------------------------------------------------------- |
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| 42 | ! |
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| 43 | ! variables that describe the grid |
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| 44 | ! |
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| 45 | ! T42: nx=128 ny=64 |
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| 46 | ! T62: nx=192 ny=94 |
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| 47 | ! |
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| 48 | !----------------------------------------------------------------------- |
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| 49 | |
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| 50 | integer (kind=int_kind), parameter :: |
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| 51 | & nx = 192, ny = 94, |
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| 52 | & grid_size = nx*ny, |
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| 53 | & grid_rank = 2, |
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| 54 | & grid_corners = 4 |
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| 55 | |
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| 56 | character(char_len), parameter :: |
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| 57 | & grid_name = 'T62 Gaussian Grid', |
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| 58 | & grid_file_out = 'remap_grid_T62.nc' |
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| 59 | |
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| 60 | integer (kind=int_kind), dimension(grid_rank) :: |
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| 61 | & grid_dims |
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| 62 | |
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| 63 | !----------------------------------------------------------------------- |
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| 64 | ! |
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| 65 | ! grid coordinates and masks |
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| 66 | ! |
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| 67 | !----------------------------------------------------------------------- |
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| 68 | |
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| 69 | integer (kind=int_kind), dimension(grid_size) :: |
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| 70 | & grid_imask |
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| 71 | |
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| 72 | real (kind=dbl_kind), dimension(grid_size) :: |
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| 73 | & grid_center_lat, ! lat/lon coordinates for |
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| 74 | & grid_center_lon ! each grid center in degrees |
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| 75 | |
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| 76 | real (kind=dbl_kind), dimension(grid_corners,grid_size) :: |
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| 77 | & grid_corner_lat, ! lat/lon coordinates for |
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| 78 | & grid_corner_lon ! each grid corner in degrees |
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| 79 | |
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| 80 | !----------------------------------------------------------------------- |
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| 81 | ! |
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| 82 | ! other local variables |
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| 83 | ! |
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| 84 | !----------------------------------------------------------------------- |
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| 85 | |
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| 86 | integer (kind=int_kind) :: i, j, iunit, atm_add |
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| 87 | |
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| 88 | integer (kind=int_kind) :: |
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| 89 | & ncstat, ! general netCDF status variable |
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| 90 | & nc_grid_id, ! netCDF grid dataset id |
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| 91 | & nc_gridsize_id, ! netCDF grid size dim id |
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| 92 | & nc_gridcorn_id, ! netCDF grid corner dim id |
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| 93 | & nc_gridrank_id, ! netCDF grid rank dim id |
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| 94 | & nc_griddims_id, ! netCDF grid dimension size id |
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| 95 | & nc_grdcntrlat_id, ! netCDF grid center lat id |
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| 96 | & nc_grdcntrlon_id, ! netCDF grid center lon id |
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| 97 | & nc_grdimask_id, ! netCDF grid mask id |
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| 98 | & nc_grdcrnrlat_id, ! netCDF grid corner lat id |
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| 99 | & nc_grdcrnrlon_id ! netCDF grid corner lon id |
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| 100 | |
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| 101 | integer (kind=int_kind), dimension(2) :: |
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| 102 | & nc_dims2_id ! netCDF dim id array for 2-d arrays |
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| 103 | |
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| 104 | real (kind=dbl_kind) :: dlon, minlon, maxlon, centerlon, |
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| 105 | & minlat, maxlat, centerlat |
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| 106 | |
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| 107 | real (kind=dbl_kind), dimension(ny) :: gauss_root, gauss_wgt |
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| 108 | |
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| 109 | !----------------------------------------------------------------------- |
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| 110 | ! |
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| 111 | ! compute longitudes of cell centers and corners. set up alon |
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| 112 | ! array for search routine. |
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| 113 | ! |
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| 114 | !----------------------------------------------------------------------- |
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| 115 | |
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| 116 | grid_dims(1) = nx |
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| 117 | grid_dims(2) = ny |
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| 118 | |
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| 119 | dlon = 360./nx |
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| 120 | |
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| 121 | do i=1,nx |
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| 122 | |
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| 123 | centerlon = (i-1)*dlon |
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| 124 | minlon = centerlon - half*dlon |
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| 125 | maxlon = centerlon + half*dlon |
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| 126 | |
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| 127 | do j=1,ny |
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| 128 | atm_add = (j-1)*nx + i |
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| 129 | |
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| 130 | grid_center_lon(atm_add ) = centerlon |
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| 131 | grid_corner_lon(1,atm_add) = minlon |
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| 132 | grid_corner_lon(2,atm_add) = maxlon |
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| 133 | grid_corner_lon(3,atm_add) = maxlon |
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| 134 | grid_corner_lon(4,atm_add) = minlon |
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| 135 | end do |
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| 136 | |
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| 137 | end do |
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| 138 | |
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| 139 | !----------------------------------------------------------------------- |
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| 140 | ! |
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| 141 | ! compute Gaussian latitudes and store in gauss_wgt. |
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| 142 | ! |
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| 143 | !----------------------------------------------------------------------- |
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| 144 | |
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| 145 | call gquad(ny, gauss_root, gauss_wgt) |
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| 146 | do j=1,ny |
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| 147 | gauss_wgt(j) = pih - gauss_root(ny+1-j) |
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| 148 | end do |
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| 149 | |
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| 150 | !----------------------------------------------------------------------- |
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| 151 | ! |
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| 152 | ! compute latitudes at cell centers and corners. set up alat |
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| 153 | ! array for search routine. |
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| 154 | ! |
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| 155 | !----------------------------------------------------------------------- |
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| 156 | |
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| 157 | do j=1,ny |
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| 158 | centerlat = gauss_wgt(j) |
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| 159 | |
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| 160 | if (j .eq. 1) then |
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| 161 | minlat = -pih |
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| 162 | else |
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| 163 | minlat = ATAN((COS(gauss_wgt(j-1)) - |
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| 164 | & COS(gauss_wgt(j )))/ |
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| 165 | & (SIN(gauss_wgt(j )) - |
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| 166 | & SIN(gauss_wgt(j-1)))) |
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| 167 | endif |
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| 168 | |
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| 169 | if (j .eq. ny) then |
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| 170 | maxlat = pih |
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| 171 | else |
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| 172 | maxlat = ATAN((COS(gauss_wgt(j )) - |
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| 173 | & COS(gauss_wgt(j+1)))/ |
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| 174 | & (SIN(gauss_wgt(j+1)) - |
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| 175 | & SIN(gauss_wgt(j )))) |
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| 176 | endif |
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| 177 | |
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| 178 | do i=1,nx |
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| 179 | atm_add = (j-1)*nx + i |
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| 180 | grid_center_lat(atm_add ) = centerlat*360./pi2 |
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| 181 | grid_corner_lat(1,atm_add) = minlat*360./pi2 |
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| 182 | grid_corner_lat(2,atm_add) = minlat*360./pi2 |
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| 183 | grid_corner_lat(3,atm_add) = maxlat*360./pi2 |
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| 184 | grid_corner_lat(4,atm_add) = maxlat*360./pi2 |
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| 185 | end do |
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| 186 | |
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| 187 | end do |
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| 188 | |
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| 189 | !----------------------------------------------------------------------- |
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| 190 | ! |
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| 191 | ! define mask |
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| 192 | ! |
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| 193 | !----------------------------------------------------------------------- |
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| 194 | |
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| 195 | grid_imask = 1 |
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| 196 | |
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| 197 | !----------------------------------------------------------------------- |
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| 198 | ! |
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| 199 | ! set up attributes for netCDF file |
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| 200 | ! |
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| 201 | !----------------------------------------------------------------------- |
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| 202 | |
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| 203 | !*** |
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| 204 | !*** create netCDF dataset for this grid |
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| 205 | !*** |
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| 206 | |
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| 207 | ncstat = nf_create (grid_file_out, NF_CLOBBER, |
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| 208 | & nc_grid_id) |
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| 209 | call netcdf_error_handler(ncstat) |
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| 210 | |
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| 211 | ncstat = nf_put_att_text (nc_grid_id, NF_GLOBAL, 'title', |
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| 212 | & len_trim(grid_name), grid_name) |
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| 213 | call netcdf_error_handler(ncstat) |
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| 214 | |
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| 215 | !*** |
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| 216 | !*** define grid size dimension |
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| 217 | !*** |
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| 218 | |
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| 219 | ncstat = nf_def_dim (nc_grid_id, 'grid_size', grid_size, |
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| 220 | & nc_gridsize_id) |
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| 221 | call netcdf_error_handler(ncstat) |
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| 222 | |
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| 223 | !*** |
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| 224 | !*** define grid corner dimension |
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| 225 | !*** |
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| 226 | |
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| 227 | ncstat = nf_def_dim (nc_grid_id, 'grid_corners', grid_corners, |
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| 228 | & nc_gridcorn_id) |
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| 229 | call netcdf_error_handler(ncstat) |
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| 230 | |
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| 231 | !*** |
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| 232 | !*** define grid rank dimension |
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| 233 | !*** |
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| 234 | |
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| 235 | ncstat = nf_def_dim (nc_grid_id, 'grid_rank', grid_rank, |
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| 236 | & nc_gridrank_id) |
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| 237 | call netcdf_error_handler(ncstat) |
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| 238 | |
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| 239 | !*** |
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| 240 | !*** define grid dimension size array |
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| 241 | !*** |
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| 242 | |
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| 243 | ncstat = nf_def_var (nc_grid_id, 'grid_dims', NF_INT, |
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| 244 | & 1, nc_gridrank_id, nc_griddims_id) |
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| 245 | call netcdf_error_handler(ncstat) |
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| 246 | |
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| 247 | !*** |
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| 248 | !*** define grid center latitude array |
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| 249 | !*** |
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| 250 | |
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| 251 | ncstat = nf_def_var (nc_grid_id, 'grid_center_lat', NF_DOUBLE, |
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| 252 | & 1, nc_gridsize_id, nc_grdcntrlat_id) |
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| 253 | call netcdf_error_handler(ncstat) |
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| 254 | |
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| 255 | ncstat = nf_put_att_text (nc_grid_id, nc_grdcntrlat_id, 'units', |
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| 256 | & 7, 'degrees') |
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| 257 | call netcdf_error_handler(ncstat) |
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| 258 | |
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| 259 | !*** |
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| 260 | !*** define grid center longitude array |
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| 261 | !*** |
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| 262 | |
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| 263 | ncstat = nf_def_var (nc_grid_id, 'grid_center_lon', NF_DOUBLE, |
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| 264 | & 1, nc_gridsize_id, nc_grdcntrlon_id) |
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| 265 | call netcdf_error_handler(ncstat) |
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| 266 | |
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| 267 | ncstat = nf_put_att_text (nc_grid_id, nc_grdcntrlon_id, 'units', |
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| 268 | & 7, 'degrees') |
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| 269 | call netcdf_error_handler(ncstat) |
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| 270 | |
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| 271 | !*** |
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| 272 | !*** define grid mask |
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| 273 | !*** |
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| 274 | |
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| 275 | ncstat = nf_def_var (nc_grid_id, 'grid_imask', NF_INT, |
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| 276 | & 1, nc_gridsize_id, nc_grdimask_id) |
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| 277 | call netcdf_error_handler(ncstat) |
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| 278 | |
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| 279 | ncstat = nf_put_att_text (nc_grid_id, nc_grdimask_id, 'units', |
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| 280 | & 8, 'unitless') |
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| 281 | call netcdf_error_handler(ncstat) |
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| 282 | |
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| 283 | !*** |
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| 284 | !*** define grid corner latitude array |
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| 285 | !*** |
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| 286 | |
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| 287 | nc_dims2_id(1) = nc_gridcorn_id |
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| 288 | nc_dims2_id(2) = nc_gridsize_id |
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| 289 | |
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| 290 | ncstat = nf_def_var (nc_grid_id, 'grid_corner_lat', NF_DOUBLE, |
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| 291 | & 2, nc_dims2_id, nc_grdcrnrlat_id) |
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| 292 | call netcdf_error_handler(ncstat) |
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| 293 | |
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| 294 | ncstat = nf_put_att_text (nc_grid_id, nc_grdcrnrlat_id, 'units', |
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| 295 | & 7, 'degrees') |
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| 296 | call netcdf_error_handler(ncstat) |
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| 297 | |
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| 298 | !*** |
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| 299 | !*** define grid corner longitude array |
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| 300 | !*** |
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| 301 | |
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| 302 | ncstat = nf_def_var (nc_grid_id, 'grid_corner_lon', NF_DOUBLE, |
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| 303 | & 2, nc_dims2_id, nc_grdcrnrlon_id) |
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| 304 | call netcdf_error_handler(ncstat) |
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| 305 | |
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| 306 | ncstat = nf_put_att_text (nc_grid_id, nc_grdcrnrlon_id, 'units', |
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| 307 | & 7, 'degrees') |
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| 308 | call netcdf_error_handler(ncstat) |
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| 309 | |
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| 310 | !*** |
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| 311 | !*** end definition stage |
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| 312 | !*** |
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| 313 | |
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| 314 | ncstat = nf_enddef(nc_grid_id) |
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| 315 | call netcdf_error_handler(ncstat) |
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| 316 | |
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| 317 | !----------------------------------------------------------------------- |
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| 318 | ! |
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| 319 | ! write grid data |
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| 320 | ! |
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| 321 | !----------------------------------------------------------------------- |
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| 322 | |
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| 323 | ncstat = nf_put_var_int(nc_grid_id, nc_griddims_id, grid_dims) |
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| 324 | call netcdf_error_handler(ncstat) |
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| 325 | |
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| 326 | ncstat = nf_put_var_int(nc_grid_id, nc_grdimask_id, grid_imask) |
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| 327 | call netcdf_error_handler(ncstat) |
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| 328 | |
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| 329 | ncstat = nf_put_var_double(nc_grid_id, nc_grdcntrlat_id, |
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| 330 | & grid_center_lat) |
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| 331 | call netcdf_error_handler(ncstat) |
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| 332 | |
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| 333 | ncstat = nf_put_var_double(nc_grid_id, nc_grdcntrlon_id, |
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| 334 | & grid_center_lon) |
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| 335 | call netcdf_error_handler(ncstat) |
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| 336 | |
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| 337 | ncstat = nf_put_var_double(nc_grid_id, nc_grdcrnrlat_id, |
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| 338 | & grid_corner_lat) |
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| 339 | call netcdf_error_handler(ncstat) |
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| 340 | |
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| 341 | ncstat = nf_put_var_double(nc_grid_id, nc_grdcrnrlon_id, |
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| 342 | & grid_corner_lon) |
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| 343 | call netcdf_error_handler(ncstat) |
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| 344 | |
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| 345 | ncstat = nf_close(nc_grid_id) |
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| 346 | call netcdf_error_handler(ncstat) |
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| 347 | |
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| 348 | !----------------------------------------------------------------------- |
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| 349 | |
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| 350 | end program convert_gauss |
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| 351 | |
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| 352 | !*********************************************************************** |
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| 353 | |
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| 354 | subroutine gquad(l,root,w) |
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| 355 | |
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| 356 | !----------------------------------------------------------------------- |
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| 357 | ! |
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| 358 | ! This subroutine finds the l roots (in theta) and gaussian weights |
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| 359 | ! associated with the legendre polynomial of degree l > 1. |
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| 360 | ! |
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| 361 | !----------------------------------------------------------------------- |
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| 362 | |
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| 363 | use kinds_mod |
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| 364 | use constants |
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| 365 | |
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| 366 | implicit none |
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| 367 | |
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| 368 | !----------------------------------------------------------------------- |
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| 369 | ! |
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| 370 | ! intent(in) |
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| 371 | ! |
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| 372 | !----------------------------------------------------------------------- |
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| 373 | |
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| 374 | integer (kind=int_kind), intent(in) :: l |
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| 375 | |
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| 376 | !----------------------------------------------------------------------- |
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| 377 | ! |
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| 378 | ! intent(out) |
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| 379 | ! |
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| 380 | !----------------------------------------------------------------------- |
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| 381 | |
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| 382 | real (kind=dbl_kind), dimension(l), intent(out) :: |
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| 383 | & root, w |
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| 384 | |
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| 385 | !----------------------------------------------------------------------- |
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| 386 | ! |
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| 387 | ! local |
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| 388 | ! |
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| 389 | !----------------------------------------------------------------------- |
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| 390 | |
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| 391 | integer (kind=int_kind) :: l1, l2, l22, l3, k, i, j |
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| 392 | |
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| 393 | real (kind=dbl_kind) :: |
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| 394 | & del,co,p1,p2,p3,t1,t2,slope,s,c,pp1,pp2,p00 |
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| 395 | |
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| 396 | !----------------------------------------------------------------------- |
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| 397 | ! |
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| 398 | ! Define useful constants. |
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| 399 | ! |
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| 400 | !----------------------------------------------------------------------- |
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| 401 | |
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| 402 | del= pi/float(4*l) |
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| 403 | l1 = l+1 |
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| 404 | co = float(2*l+3)/float(l1**2) |
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| 405 | p2 = 1.0 |
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| 406 | t2 = -del |
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| 407 | l2 = l/2 |
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| 408 | k = 1 |
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| 409 | p00 = one/sqrt(two) |
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| 410 | |
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| 411 | !----------------------------------------------------------------------- |
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| 412 | ! |
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| 413 | ! Start search for each root by looking for crossing point. |
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| 414 | ! |
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| 415 | !----------------------------------------------------------------------- |
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| 416 | |
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| 417 | do i=1,l2 |
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| 418 | 10 t1 = t2 |
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| 419 | t2 = t1+del |
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| 420 | p1 = p2 |
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| 421 | s = sin(t2) |
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| 422 | c = cos(t2) |
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| 423 | pp1 = 1.0 |
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| 424 | p3 = p00 |
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| 425 | do j=1,l1 |
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| 426 | pp2 = pp1 |
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| 427 | pp1 = p3 |
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| 428 | p3 = 2.0*sqrt((float(j**2)-0.250)/float(j**2))*c*pp1- |
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| 429 | & sqrt(float((2*j+1)*(j-1)*(j-1))/ |
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| 430 | & float((2*j-3)*j*j))*pp2 |
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| 431 | end do |
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| 432 | p2 = pp1 |
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| 433 | if ((k*p2).gt.0) goto 10 |
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| 434 | |
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| 435 | !----------------------------------------------------------------------- |
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| 436 | ! |
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| 437 | ! Now converge using Newton-Raphson. |
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| 438 | ! |
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| 439 | !----------------------------------------------------------------------- |
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| 440 | |
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| 441 | k = -k |
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| 442 | 20 continue |
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| 443 | slope = (t2-t1)/(p2-p1) |
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| 444 | t1 = t2 |
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| 445 | t2 = t2-slope*p2 |
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| 446 | p1 = p2 |
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| 447 | s = sin(t2) |
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| 448 | c = cos(t2) |
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| 449 | pp1 = 1.0 |
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| 450 | p3 = p00 |
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| 451 | do j=1,l1 |
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| 452 | pp2 = pp1 |
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| 453 | pp1 = p3 |
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| 454 | p3 = 2.0*sqrt((float(j**2)-0.250)/float(j**2))*c*pp1- |
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| 455 | & sqrt(float((2*j+1)*(j-1)*(j-1))/ |
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| 456 | & float((2*j-3)*j*j))*pp2 |
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| 457 | end do |
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| 458 | p2 = pp1 |
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| 459 | if (abs(p2).gt.1.e-10) goto 20 |
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| 460 | root(i) = t2 |
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| 461 | w(i) = co*(sin(t2)/p3)**2 |
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| 462 | end do |
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| 463 | |
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| 464 | !----------------------------------------------------------------------- |
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| 465 | ! |
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| 466 | ! If l is odd, take care of odd point. |
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| 467 | ! |
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| 468 | !----------------------------------------------------------------------- |
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| 469 | |
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| 470 | l22 = 2*l2 |
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| 471 | if (l22 .ne. l) then |
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| 472 | l2 = l2+1 |
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| 473 | t2 = pi/2.0 |
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| 474 | root(l2) = t2 |
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| 475 | s = sin(t2) |
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| 476 | c = cos(t2) |
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| 477 | pp1 = 1.0 |
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| 478 | p3 = p00 |
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| 479 | do j=1,l1 |
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| 480 | pp2 = pp1 |
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| 481 | pp1 = p3 |
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| 482 | p3 = 2.0*sqrt((float(j**2)-0.250)/float(j**2))*c*pp1- |
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| 483 | & sqrt(float((2*j+1)*(j-1)*(j-1))/ |
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| 484 | & float((2*j-3)*j*j))*pp2 |
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| 485 | end do |
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| 486 | p2 = pp1 |
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| 487 | w(l2) = co/p3**2 |
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| 488 | endif |
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| 489 | |
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| 490 | !----------------------------------------------------------------------- |
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| 491 | ! |
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| 492 | ! Use symmetry to compute remaining roots and weights. |
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| 493 | ! |
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| 494 | !----------------------------------------------------------------------- |
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| 495 | |
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| 496 | l3 = l2+1 |
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| 497 | do i=l3,l |
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| 498 | root(i) = pi-root(l-i+1) |
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| 499 | w(i) = w(l-i+1) |
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| 500 | end do |
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| 501 | |
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| 502 | !----------------------------------------------------------------------- |
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| 503 | |
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| 504 | end subroutine gquad |
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| 505 | |
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| 506 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
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