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.f,v 1.3 2000/04/19 22:05:57 pwjones Exp $ |
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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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