| 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: convertgauss.F90,v 1.3 2002-11-14 17:11:07 eong Exp $ |
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| 9 | ! CVS $Name: $ |
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| 10 | ! |
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| 11 | ! Copyright (c) 1997, 1998 the Regents of the University of |
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| 12 | ! California. |
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| 13 | ! |
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| 14 | ! Unless otherwise indicated, this software has been authored |
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| 15 | ! by an employee or employees of the University of California, |
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| 16 | ! operator of the Los Alamos National Laboratory under Contract |
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| 17 | ! No. W-7405-ENG-36 with the U.S. Department of Energy. The U.S. |
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| 18 | ! Government has rights to use, reproduce, and distribute this |
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| 19 | ! software. The public may copy and use this software without |
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| 20 | ! charge, provided that this Notice and any statement of authorship |
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| 21 | ! are reproduced on all copies. Neither the Government nor the |
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| 22 | ! University makes any warranty, express or implied, or assumes |
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| 23 | ! any liability or responsibility for the use of this software. |
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| 24 | ! |
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| 25 | !*********************************************************************** |
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| 26 | |
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| 27 | subroutine convertgauss(GGrid, nx, ny) |
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| 28 | |
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| 29 | !----------------------------------------------------------------------- |
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| 30 | ! |
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| 31 | ! This file creates a remapping grid file for a Gaussian grid |
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| 32 | ! |
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| 33 | !----------------------------------------------------------------------- |
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| 34 | |
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| 35 | use m_AttrVect,only : AttrVect |
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| 36 | ! use m_GeneralGrid,only : MCT_GGrid_init => init |
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| 37 | use m_GeneralGrid,only : MCT_GGrid_initUnstructured => initUnstructured |
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| 38 | use m_GeneralGrid,only : MCT_GGrid_indexIA => indexIA |
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| 39 | use m_GeneralGrid,only : MCT_GGrid_indexRA => indexRA |
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| 40 | use m_GeneralGrid,only : GeneralGrid |
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| 41 | use m_die |
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| 42 | use m_stdio |
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| 43 | |
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| 44 | implicit none |
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| 45 | |
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| 46 | !----------------------------------------------------------------------- |
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| 47 | ! |
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| 48 | ! variables that describe the grid |
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| 49 | ! |
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| 50 | ! T42: nx=128 ny=64 |
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| 51 | ! T62: nx=192 ny=94 |
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| 52 | ! |
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| 53 | !----------------------------------------------------------------------- |
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| 54 | |
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| 55 | type(GeneralGrid), intent(out) :: GGrid |
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| 56 | integer, intent(in) :: nx |
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| 57 | integer, intent(in) :: ny |
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| 58 | |
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| 59 | integer :: grid_size |
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| 60 | |
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| 61 | integer, parameter :: & |
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| 62 | grid_rank = 2, & |
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| 63 | grid_corners = 4 |
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| 64 | |
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| 65 | integer, dimension(grid_rank) :: & |
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| 66 | grid_dims |
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| 67 | |
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| 68 | !----------------------------------------------------------------------- |
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| 69 | ! |
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| 70 | ! grid coordinates and masks |
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| 71 | ! |
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| 72 | !----------------------------------------------------------------------- |
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| 73 | |
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| 74 | integer, dimension(:), allocatable :: & |
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| 75 | grid_imask |
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| 76 | |
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| 77 | real, dimension(:), allocatable :: & |
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| 78 | grid_area , & ! area weights |
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| 79 | grid_center_lat, & ! lat/lon coordinates for |
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| 80 | grid_center_lon ! each grid center in degrees |
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| 81 | |
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| 82 | real, dimension(:,:), allocatable :: & |
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| 83 | grid_corner_lat, & ! lat/lon coordinates for |
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| 84 | grid_corner_lon ! each grid corner in degrees |
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| 85 | |
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| 86 | |
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| 87 | !----------------------------------------------------------------------- |
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| 88 | ! |
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| 89 | ! defined constants |
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| 90 | ! |
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| 91 | !----------------------------------------------------------------------- |
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| 92 | |
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| 93 | real, parameter :: & |
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| 94 | zero = 0.0, & |
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| 95 | one = 1.0, & |
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| 96 | two = 2.0, & |
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| 97 | three = 3.0, & |
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| 98 | four = 4.0, & |
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| 99 | five = 5.0, & |
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| 100 | half = 0.5, & |
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| 101 | quart = 0.25, & |
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| 102 | bignum = 1.e+20, & |
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| 103 | tiny = 1.e-14, & |
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| 104 | pi = 3.14159265359, & |
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| 105 | pi2 = two*pi, & |
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| 106 | pih = half*pi |
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| 107 | |
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| 108 | !----------------------------------------------------------------------- |
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| 109 | ! |
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| 110 | ! other local variables |
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| 111 | ! |
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| 112 | !----------------------------------------------------------------------- |
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| 113 | |
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| 114 | character(len=*),parameter :: myname_= 'convertgauss' |
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| 115 | |
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| 116 | integer :: i, j, k, p, q, r, ier, atm_add |
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| 117 | |
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| 118 | integer :: center_lat, center_lon, & |
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| 119 | corner_lat, corner_lon, & |
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| 120 | imask, area |
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| 121 | |
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| 122 | real :: dlon, minlon, maxlon, centerlon, & |
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| 123 | minlat, maxlat, centerlat |
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| 124 | |
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| 125 | real, dimension(ny) :: gauss_root, gauss_wgt, gauss_lat |
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| 126 | |
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| 127 | real, dimension(:), pointer :: PointData |
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| 128 | integer :: offset |
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| 129 | |
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| 130 | !----------------------------------------------------------------------- |
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| 131 | ! |
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| 132 | ! compute longitudes of cell centers and corners. set up alon |
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| 133 | ! array for search routine. |
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| 134 | ! |
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| 135 | !----------------------------------------------------------------------- |
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| 136 | |
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| 137 | grid_size = nx*ny |
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| 138 | |
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| 139 | allocate(grid_imask(grid_size), & |
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| 140 | grid_area(grid_size), & |
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| 141 | grid_center_lat(grid_size), & |
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| 142 | grid_center_lon(grid_size), & |
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| 143 | grid_corner_lat(grid_corners,grid_size), & |
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| 144 | grid_corner_lon(grid_corners,grid_size), stat=ier) |
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| 145 | |
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| 146 | if(ier/=0) call die(myname_,"allocate(grid_imask... ", ier) |
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| 147 | |
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| 148 | grid_dims(1) = nx |
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| 149 | grid_dims(2) = ny |
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| 150 | |
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| 151 | dlon = 360./nx |
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| 152 | |
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| 153 | do i=1,nx |
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| 154 | |
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| 155 | centerlon = (i-1)*dlon |
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| 156 | minlon = centerlon - half*dlon |
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| 157 | maxlon = centerlon + half*dlon |
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| 158 | |
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| 159 | do j=1,ny |
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| 160 | atm_add = (j-1)*nx + i |
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| 161 | |
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| 162 | grid_center_lon(atm_add ) = centerlon |
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| 163 | grid_corner_lon(1,atm_add) = minlon |
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| 164 | grid_corner_lon(2,atm_add) = maxlon |
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| 165 | grid_corner_lon(3,atm_add) = maxlon |
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| 166 | grid_corner_lon(4,atm_add) = minlon |
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| 167 | end do |
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| 168 | |
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| 169 | end do |
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| 170 | |
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| 171 | !----------------------------------------------------------------------- |
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| 172 | ! |
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| 173 | ! compute Gaussian latitudes and store in gauss_wgt. |
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| 174 | ! |
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| 175 | !----------------------------------------------------------------------- |
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| 176 | |
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| 177 | call gquad(ny, gauss_root, gauss_wgt) |
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| 178 | do j=1,ny |
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| 179 | gauss_lat(j) = pih - gauss_root(ny+1-j) |
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| 180 | end do |
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| 181 | |
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| 182 | !----------------------------------------------------------------------- |
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| 183 | ! |
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| 184 | ! compute latitudes at cell centers and corners. set up alat |
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| 185 | ! array for search routine. |
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| 186 | ! |
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| 187 | !----------------------------------------------------------------------- |
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| 188 | |
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| 189 | do j=1,ny |
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| 190 | centerlat = gauss_lat(j) |
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| 191 | |
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| 192 | if (j .eq. 1) then |
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| 193 | minlat = -pih |
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| 194 | else |
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| 195 | minlat = ATAN((COS(gauss_lat(j-1)) - & |
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| 196 | COS(gauss_lat(j )))/ & |
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| 197 | (SIN(gauss_lat(j )) - & |
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| 198 | SIN(gauss_lat(j-1)))) |
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| 199 | endif |
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| 200 | |
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| 201 | if (j .eq. ny) then |
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| 202 | maxlat = pih |
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| 203 | else |
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| 204 | maxlat = ATAN((COS(gauss_lat(j )) - & |
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| 205 | COS(gauss_lat(j+1)))/ & |
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| 206 | (SIN(gauss_lat(j+1)) - & |
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| 207 | SIN(gauss_lat(j )))) |
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| 208 | endif |
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| 209 | |
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| 210 | do i=1,nx |
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| 211 | atm_add = (j-1)*nx + i |
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| 212 | grid_center_lat(atm_add ) = centerlat*360./pi2 |
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| 213 | grid_corner_lat(1,atm_add) = minlat*360./pi2 |
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| 214 | grid_corner_lat(2,atm_add) = minlat*360./pi2 |
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| 215 | grid_corner_lat(3,atm_add) = maxlat*360./pi2 |
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| 216 | grid_corner_lat(4,atm_add) = maxlat*360./pi2 |
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| 217 | grid_area(atm_add) = gauss_wgt(j)*pi2/nx |
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| 218 | end do |
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| 219 | |
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| 220 | end do |
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| 221 | |
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| 222 | !----------------------------------------------------------------------- |
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| 223 | ! |
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| 224 | ! define mask |
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| 225 | ! |
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| 226 | !----------------------------------------------------------------------- |
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| 227 | |
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| 228 | grid_imask = 1 |
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| 229 | |
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| 230 | !----------------------------------------------------------------------- |
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| 231 | ! |
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| 232 | ! intialize GeneralGrid |
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| 233 | ! |
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| 234 | !----------------------------------------------------------------------- |
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| 235 | |
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| 236 | ! call MCT_GGrid_init(GGrid=GGrid, & |
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| 237 | ! CoordChars="grid_center_lat:& |
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| 238 | ! &grid_center_lon", & |
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| 239 | ! WeightChars="grid_area", & |
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| 240 | ! OtherChars="grid_corner_lat_1:& |
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| 241 | ! &grid_corner_lat_2:& |
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| 242 | ! &grid_corner_lat_3:& |
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| 243 | ! &grid_corner_lat_4:& |
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| 244 | ! &grid_corner_lon_1:& |
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| 245 | ! &grid_corner_lon_2:& |
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| 246 | ! &grid_corner_lon_3:& |
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| 247 | ! &grid_corner_lon_4", & |
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| 248 | ! IndexChars="grid_imask", & |
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| 249 | ! lsize=grid_size) |
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| 250 | |
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| 251 | ! Create and fill PointData(:) array for unstructured-style GeneralGrid_init |
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| 252 | |
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| 253 | allocate(PointData(2*grid_size), stat=ier) |
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| 254 | if(ier /= 0) then |
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| 255 | write(stderr,'(2a,i8)') myname_, & |
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| 256 | ':: allocate(PointData(...) failed with ier=',ier |
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| 257 | call die(myname_) |
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| 258 | endif |
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| 259 | |
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| 260 | do i=1,grid_size |
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| 261 | offset = 2 * (i-1) |
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| 262 | PointData(offset+1) = grid_center_lat(i) |
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| 263 | PointData(offset+2) = grid_center_lon(i) |
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| 264 | end do |
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| 265 | |
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| 266 | call MCT_GGrid_initUnstructured(GGrid=GGrid, & |
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| 267 | CoordChars="grid_center_lat:& |
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| 268 | &grid_center_lon", & |
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| 269 | CoordSortOrder="grid_center_lat:& |
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| 270 | &grid_center_lon", & |
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| 271 | WeightChars="grid_area", & |
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| 272 | OtherChars="grid_corner_lat_1:& |
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| 273 | &grid_corner_lat_2:& |
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| 274 | &grid_corner_lat_3:& |
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| 275 | &grid_corner_lat_4:& |
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| 276 | &grid_corner_lon_1:& |
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| 277 | &grid_corner_lon_2:& |
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| 278 | &grid_corner_lon_3:& |
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| 279 | &grid_corner_lon_4", & |
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| 280 | IndexChars="grid_imask", & |
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| 281 | nDims=2, nPoints=grid_size, & |
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| 282 | PointData=PointData) |
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| 283 | |
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| 284 | deallocate(PointData, stat=ier) |
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| 285 | if(ier /= 0) then |
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| 286 | write(stderr,'(2a,i8)') myname_, & |
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| 287 | ':: deallocate(PointData...) failed with ier=',ier |
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| 288 | call die(myname_) |
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| 289 | endif |
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| 290 | |
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| 291 | ! center_lat = MCT_GGrid_indexRA(GGrid,'grid_center_lat') |
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| 292 | ! center_lon = MCT_GGrid_indexRA(GGrid,'grid_center_lon') |
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| 293 | corner_lat = MCT_GGrid_indexRA(GGrid,'grid_corner_lat_1') |
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| 294 | corner_lon = MCT_GGrid_indexRA(GGrid,'grid_corner_lon_1') |
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| 295 | area = MCT_GGrid_indexRA(GGrid,'grid_area') |
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| 296 | imask = MCT_GGrid_indexIA(GGrid,'grid_imask') |
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| 297 | |
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| 298 | ! GGrid%data%rattr(center_lat,1:grid_size) = & |
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| 299 | ! grid_center_lat(1:grid_size) |
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| 300 | ! GGrid%data%rattr(center_lon,1:grid_size) = & |
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| 301 | ! grid_center_lon(1:grid_size) |
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| 302 | GGrid%data%rattr(area,1:grid_size) = & |
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| 303 | grid_area(1:grid_size) |
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| 304 | GGrid%data%iattr(imask,1:grid_size) = & |
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| 305 | grid_imask(1:grid_size) |
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| 306 | |
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| 307 | do p = 1,grid_corners |
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| 308 | GGrid%data%rattr(corner_lat+p-1,1:grid_size) = & |
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| 309 | grid_corner_lat(p,1:grid_size) |
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| 310 | GGrid%data%rattr(corner_lon+p-1,1:grid_size) = & |
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| 311 | grid_corner_lon(p,1:grid_size) |
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| 312 | enddo |
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| 313 | |
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| 314 | deallocate(grid_imask, grid_area, & |
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| 315 | grid_center_lat, grid_center_lon, & |
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| 316 | grid_corner_lat, grid_corner_lon, & |
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| 317 | stat=ier) |
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| 318 | |
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| 319 | if(ier/=0) call die(myname_,"deallocate(grid_imask... ", ier) |
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| 320 | |
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| 321 | |
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| 322 | !----------------------------------------------------------------------- |
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| 323 | |
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| 324 | end subroutine convertgauss |
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| 325 | |
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| 326 | !*********************************************************************** |
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| 327 | |
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| 328 | subroutine gquad(l,root,w) |
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| 329 | |
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| 330 | !----------------------------------------------------------------------- |
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| 331 | ! |
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| 332 | ! This subroutine finds the l roots (in theta) and gaussian weights |
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| 333 | ! associated with the legendre polynomial of degree l > 1. |
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| 334 | ! |
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| 335 | !----------------------------------------------------------------------- |
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| 336 | |
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| 337 | use m_die |
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| 338 | |
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| 339 | implicit none |
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| 340 | |
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| 341 | !----------------------------------------------------------------------- |
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| 342 | ! |
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| 343 | ! intent(in) |
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| 344 | ! |
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| 345 | !----------------------------------------------------------------------- |
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| 346 | |
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| 347 | integer, intent(in) :: l |
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| 348 | |
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| 349 | !----------------------------------------------------------------------- |
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| 350 | ! |
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| 351 | ! intent(out) |
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| 352 | ! |
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| 353 | !----------------------------------------------------------------------- |
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| 354 | |
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| 355 | real, dimension(l), intent(out) :: root, w |
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| 356 | |
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| 357 | !----------------------------------------------------------------------- |
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| 358 | ! |
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| 359 | ! defined constants |
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| 360 | ! |
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| 361 | !----------------------------------------------------------------------- |
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| 362 | |
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| 363 | real, parameter :: & |
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| 364 | zero = 0.0, & |
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| 365 | one = 1.0, & |
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| 366 | two = 2.0, & |
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| 367 | three = 3.0, & |
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| 368 | four = 4.0, & |
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| 369 | five = 5.0, & |
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| 370 | half = 0.5, & |
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| 371 | quart = 0.25, & |
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| 372 | bignum = 1.e+20, & |
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| 373 | tiny = 1.e-14, & |
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| 374 | pi = 3.14159265359, & |
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| 375 | pi2 = two*pi, & |
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| 376 | pih = half*pi |
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| 377 | |
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| 378 | !----------------------------------------------------------------------- |
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| 379 | ! |
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| 380 | ! local |
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| 381 | ! |
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| 382 | !----------------------------------------------------------------------- |
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| 383 | |
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| 384 | integer :: l1, l2, l22, l3, k, i, j, loop_counter |
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| 385 | |
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| 386 | real :: del,co,p1,p2,p3,t1,t2,slope,s,c,pp1,pp2,p00 |
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| 387 | |
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| 388 | !-----MUST adjust tolerance for newton convergence-----! |
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| 389 | |
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| 390 | ! Modify tolerance level to the precision of the real numbers: |
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| 391 | ! Increase for lower precision, decrease for higher precision. |
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| 392 | |
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| 393 | real, parameter :: RTOL = 1.0e4*epsilon(0.) |
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| 394 | |
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| 395 | !------------------------------------------------------! |
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| 396 | |
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| 397 | !----------------------------------------------------------------------- |
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| 398 | ! |
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| 399 | ! Define useful constants. |
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| 400 | ! |
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| 401 | !----------------------------------------------------------------------- |
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| 402 | |
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| 403 | del= pi/float(4*l) |
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| 404 | l1 = l+1 |
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| 405 | co = float(2*l+3)/float(l1**2) |
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| 406 | p2 = 1.0 |
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| 407 | t2 = -del |
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| 408 | l2 = l/2 |
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| 409 | k = 1 |
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| 410 | p00 = one/sqrt(two) |
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| 411 | |
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| 412 | !----------------------------------------------------------------------- |
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| 413 | ! |
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| 414 | ! Start search for each root by looking for crossing point. |
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| 415 | ! |
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| 416 | !----------------------------------------------------------------------- |
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| 417 | |
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| 418 | do i=1,l2 |
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| 419 | 10 t1 = t2 |
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| 420 | t2 = t1+del |
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| 421 | p1 = p2 |
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| 422 | s = sin(t2) |
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| 423 | c = cos(t2) |
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| 424 | pp1 = 1.0 |
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| 425 | p3 = p00 |
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| 426 | do j=1,l1 |
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| 427 | pp2 = pp1 |
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| 428 | pp1 = p3 |
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| 429 | p3 = 2.0*sqrt((float(j**2)-0.250)/float(j**2))*c*pp1- & |
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| 430 | sqrt(float((2*j+1)*(j-1)*(j-1))/ & |
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| 431 | float((2*j-3)*j*j))*pp2 |
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| 432 | end do |
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| 433 | p2 = pp1 |
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| 434 | if ((k*p2).gt.0) goto 10 |
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| 435 | |
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| 436 | !----------------------------------------------------------------------- |
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| 437 | ! |
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| 438 | ! Now converge using Newton-Raphson. |
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| 439 | ! |
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| 440 | !----------------------------------------------------------------------- |
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| 441 | |
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| 442 | k = -k |
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| 443 | loop_counter=0 |
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| 444 | 20 continue |
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| 445 | loop_counter=loop_counter+1 |
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| 446 | slope = (t2-t1)/(p2-p1) |
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| 447 | t1 = t2 |
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| 448 | t2 = t2-slope*p2 |
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| 449 | p1 = p2 |
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| 450 | s = sin(t2) |
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| 451 | c = cos(t2) |
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| 452 | pp1 = 1.0 |
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| 453 | p3 = p00 |
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| 454 | do j=1,l1 |
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| 455 | pp2 = pp1 |
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| 456 | pp1 = p3 |
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| 457 | p3 = 2.0*sqrt((float(j**2)-0.250)/float(j**2))*c*pp1- & |
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| 458 | sqrt(float((2*j+1)*(j-1)*(j-1))/ & |
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| 459 | float((2*j-3)*j*j))*pp2 |
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| 460 | end do |
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| 461 | p2 = pp1 |
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| 462 | |
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| 463 | if(loop_counter > 1e4) then |
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| 464 | call die("subroutine gquad",& |
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| 465 | "ERROR:: Precision of reals is too low. & |
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| 466 | & Increase the magnitude of RTOL.",0) |
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| 467 | endif |
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| 468 | |
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| 469 | if (abs(p2).gt.RTOL) goto 20 |
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| 470 | root(i) = t2 |
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| 471 | w(i) = co*(sin(t2)/p3)**2 |
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| 472 | end do |
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| 473 | |
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| 474 | !----------------------------------------------------------------------- |
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| 475 | ! |
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| 476 | ! If l is odd, take care of odd point. |
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| 477 | ! |
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| 478 | !----------------------------------------------------------------------- |
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| 479 | |
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| 480 | l22 = 2*l2 |
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| 481 | if (l22 .ne. l) then |
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| 482 | l2 = l2+1 |
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| 483 | t2 = pi/2.0 |
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| 484 | root(l2) = t2 |
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| 485 | s = sin(t2) |
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| 486 | c = cos(t2) |
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| 487 | pp1 = 1.0 |
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| 488 | p3 = p00 |
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| 489 | do j=1,l1 |
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| 490 | pp2 = pp1 |
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| 491 | pp1 = p3 |
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| 492 | p3 = 2.0*sqrt((float(j**2)-0.250)/float(j**2))*c*pp1- & |
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| 493 | sqrt(float((2*j+1)*(j-1)*(j-1))/ & |
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| 494 | float((2*j-3)*j*j))*pp2 |
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| 495 | end do |
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| 496 | p2 = pp1 |
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| 497 | w(l2) = co/p3**2 |
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| 498 | endif |
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| 499 | |
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| 500 | !----------------------------------------------------------------------- |
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| 501 | ! |
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| 502 | ! Use symmetry to compute remaining roots and weights. |
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| 503 | ! |
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| 504 | !----------------------------------------------------------------------- |
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| 505 | |
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| 506 | l3 = l2+1 |
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| 507 | do i=l3,l |
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| 508 | root(i) = pi-root(l-i+1) |
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| 509 | w(i) = w(l-i+1) |
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| 510 | end do |
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| 511 | |
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| 512 | !----------------------------------------------------------------------- |
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| 513 | |
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| 514 | end subroutine gquad |
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| 515 | |
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| 516 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
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