1 | !> @file src/inifor_transform.f90 |
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2 | !------------------------------------------------------------------------------! |
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3 | ! This file is part of the PALM model system. |
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4 | ! |
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5 | ! PALM is free software: you can redistribute it and/or modify it under the |
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6 | ! terms of the GNU General Public License as published by the Free Software |
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7 | ! Foundation, either version 3 of the License, or (at your option) any later |
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8 | ! version. |
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9 | ! |
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10 | ! PALM is distributed in the hope that it will be useful, but WITHOUT ANY |
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11 | ! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR |
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12 | ! A PARTICULAR PURPOSE. See the GNU General Public License for more details. |
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13 | ! |
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14 | ! You should have received a copy of the GNU General Public License along with |
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15 | ! PALM. If not, see <http://www.gnu.org/licenses/>. |
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16 | ! |
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17 | ! Copyright 2017-2019 Leibniz Universitaet Hannover |
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18 | ! Copyright 2017-2019 Deutscher Wetterdienst Offenbach |
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19 | !------------------------------------------------------------------------------! |
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20 | ! |
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21 | ! Current revisions: |
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22 | ! ----------------- |
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23 | ! |
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24 | ! |
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25 | ! Former revisions: |
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26 | ! ----------------- |
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27 | ! $Id: inifor_transform.f90 3866 2019-04-05 14:25:01Z knoop $ |
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28 | ! Use PALM's working precision |
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29 | ! Improved coding style |
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30 | ! |
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31 | ! |
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32 | ! 3785 2019-03-06 10:41:14Z eckhard |
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33 | ! Remove basic state pressure before computing geostrophic wind |
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34 | ! - Introduced new level-based profile averaging routine that does not rely on |
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35 | ! external weights average_profile() |
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36 | ! - Renamed original weights-based routine average_profile() -> |
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37 | ! interp_average_profile() |
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38 | ! Average geostrophic wind components on coarse COSMO levels instead of fine PALM levels |
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39 | ! - Introduced new profile interpolation routine for interpolating single |
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40 | ! profiles from COSMO to PALM levels |
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41 | ! - Renamed original array variant interpolate_1d() -> interpolate_1d_arr() |
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42 | ! |
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43 | ! |
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44 | ! |
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45 | ! 3716 2019-02-05 17:02:38Z eckhard |
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46 | ! Include out-of-bounds error message in log |
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47 | ! |
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48 | ! |
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49 | ! 3680 2019-01-18 14:54:12Z knoop |
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50 | ! Check if set of averaging columns is empty |
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51 | ! |
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52 | ! |
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53 | ! 3618 2018-12-10 13:25:22Z eckhard |
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54 | ! Prefixed all INIFOR modules with inifor_, removed unused variables |
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55 | ! |
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56 | ! |
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57 | ! 3615 2018-12-10 07:21:03Z raasch |
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58 | ! bugfix: abort replaced by inifor_abort |
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59 | ! |
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60 | ! 3614 2018-12-10 07:05:46Z raasch |
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61 | ! unused variables removed |
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62 | ! |
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63 | ! 3613 2018-12-07 18:20:37Z eckhard |
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64 | ! Use averaged heights profile for level-based averaging instead of modified |
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65 | ! COSMO heights array |
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66 | ! |
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67 | ! |
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68 | ! 3557 2018-11-22 16:01:22Z eckhard |
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69 | ! Updated documentation |
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70 | ! |
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71 | ! |
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72 | ! 3537 2018-11-20 10:53:14Z eckhard |
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73 | ! bugfix: working precision added |
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74 | ! |
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75 | ! 3447 2018-10-29 15:52:54Z eckhard |
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76 | ! Renamed source files for compatibilty with PALM build system |
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77 | ! |
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78 | ! |
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79 | ! 3395 2018-10-22 17:32:49Z eckhard |
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80 | ! Switched addressing of averaging regions from index bounds to list of columns |
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81 | ! Added routines for the computation of geostrophic winds including: |
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82 | ! - the downward extrapolation of density (linear) and |
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83 | ! - pressure (hydrostatic equation) and |
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84 | ! - rotation of geostrophic wind components to PALM frame of reference |
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85 | ! |
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86 | ! 3183 2018-07-27 14:25:55Z suehring |
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87 | ! Introduced new PALM grid stretching |
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88 | ! Removed unnecessary subroutine parameters |
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89 | ! Renamed kcur to k_intermediate |
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90 | ! |
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91 | ! |
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92 | ! 3182 2018-07-27 13:36:03Z suehring |
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93 | ! Initial revision |
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94 | ! |
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95 | ! |
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96 | ! |
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97 | ! Authors: |
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98 | ! -------- |
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99 | !> @author Eckhard Kadasch (Deutscher Wetterdienst, Offenbach) |
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100 | ! |
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101 | ! Description: |
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102 | ! ------------ |
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103 | !> The transform module provides INIFOR's low-level transformation and |
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104 | !> interpolation routines. The rotated-pole transformation routines phirot2phi, |
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105 | !> phi2phirot, rlarot2rla, rla2rlarot, uv2uvrot, and uvrot2uv are adapted from |
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106 | !> int2lm's utility routines. |
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107 | !------------------------------------------------------------------------------! |
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108 | #if defined ( __netcdf ) |
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109 | MODULE inifor_transform |
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110 | |
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111 | USE inifor_control |
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112 | USE inifor_defs, & |
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113 | ONLY: BETA, G, P_SL, PI, RD, T_SL, TO_DEGREES, TO_RADIANS, wp |
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114 | USE inifor_types |
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115 | USE inifor_util, & |
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116 | ONLY: get_basic_state, real_to_str, str |
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117 | |
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118 | IMPLICIT NONE |
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119 | |
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120 | CONTAINS |
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121 | |
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122 | |
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123 | SUBROUTINE interpolate_1d(in_arr, out_arr, outgrid) |
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124 | TYPE(grid_definition), INTENT(IN) :: outgrid |
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125 | REAL(wp), INTENT(IN) :: in_arr(:) |
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126 | REAL(wp), INTENT(OUT) :: out_arr(:) |
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127 | |
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128 | INTEGER :: k, l, nz |
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129 | |
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130 | nz = UBOUND(out_arr, 1) |
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131 | |
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132 | DO k = nz, LBOUND(out_arr, 1), -1 |
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133 | |
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134 | ! |
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135 | !-- TODO: Remove IF clause and extrapolate based on a critical vertical |
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136 | !-- TODO: index marking the lower bound of COSMO-DE data coverage. |
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137 | !-- Check for negative interpolation weights indicating grid points |
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138 | !-- below COSMO-DE domain and extrapolate from the top in such cells. |
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139 | IF (outgrid%w(1,k,1) < -1.0_wp .AND. k < nz) THEN |
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140 | out_arr(k) = out_arr(k+1) |
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141 | ELSE |
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142 | out_arr(k) = 0.0_wp |
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143 | DO l = 1, 2 |
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144 | out_arr(k) = out_arr(k) + & |
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145 | outgrid%w(1,k,l) * in_arr(outgrid%kkk(1,k,l) ) |
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146 | ENDDO |
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147 | ENDIF |
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148 | ENDDO |
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149 | |
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150 | END SUBROUTINE interpolate_1d |
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151 | |
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152 | |
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153 | !------------------------------------------------------------------------------! |
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154 | ! Description: |
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155 | ! ------------ |
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156 | !> Interpolates linearly in the vertical direction in very column (i,j) of the |
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157 | !> output array outvar(i,j,:) using values of the source array invar. In cells |
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158 | !> that are outside the COSMO-DE domain, indicated by negative interpolation |
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159 | !> weights, extrapolate constantly from the cell above. |
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160 | !> |
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161 | !> Input parameters: |
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162 | !> ----------------- |
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163 | !> invar : Array of source data |
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164 | !> |
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165 | !> outgrid%kk : Array of vertical neighbour indices. kk(i,j,k,:) contain the |
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166 | !> indices of the two vertical neighbors of PALM-4U point (i,j,k) on the |
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167 | !> input grid corresponding to the source data invar. |
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168 | !> |
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169 | !> outgrid%w_verti : Array of weights for vertical linear interpolation |
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170 | !> corresponding to neighbour points indexed by kk. |
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171 | !> |
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172 | !> Output papameters: |
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173 | !> ------------------ |
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174 | !> outvar : Array of interpolated data |
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175 | !------------------------------------------------------------------------------! |
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176 | SUBROUTINE interpolate_1d_arr(in_arr, out_arr, outgrid) |
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177 | TYPE(grid_definition), INTENT(IN) :: outgrid |
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178 | REAL(wp), INTENT(IN) :: in_arr(0:,0:,0:) |
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179 | REAL(wp), INTENT(OUT) :: out_arr(0:,0:,:) |
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180 | |
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181 | INTEGER :: i, j, k, l, nz |
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182 | |
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183 | nz = UBOUND(out_arr, 3) |
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184 | |
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185 | DO j = LBOUND(out_arr, 2), UBOUND(out_arr, 2) |
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186 | DO i = LBOUND(out_arr, 1), UBOUND(out_arr, 1) |
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187 | DO k = nz, LBOUND(out_arr, 3), -1 |
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188 | |
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189 | ! |
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190 | !-- TODO: Remove IF clause and extrapolate based on a critical vertical |
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191 | !-- TODO: index marking the lower bound of COSMO-DE data coverage. |
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192 | !-- Check for negative interpolation weights indicating grid points |
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193 | !-- below COSMO-DE domain and extrapolate from the top in such cells. |
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194 | IF (outgrid%w_verti(i,j,k,1) < -1.0_wp .AND. k < nz) THEN |
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195 | out_arr(i,j,k) = out_arr(i,j,k+1) |
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196 | ELSE |
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197 | out_arr(i,j,k) = 0.0_wp |
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198 | DO l = 1, 2 |
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199 | out_arr(i,j,k) = out_arr(i,j,k) + & |
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200 | outgrid%w_verti(i,j,k,l) * & |
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201 | in_arr(i,j,outgrid%kk(i,j,k, l) ) |
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202 | ENDDO |
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203 | ENDIF |
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204 | ENDDO |
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205 | ENDDO |
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206 | ENDDO |
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207 | END SUBROUTINE interpolate_1d_arr |
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208 | |
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209 | |
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210 | !------------------------------------------------------------------------------! |
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211 | ! Description: |
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212 | ! ------------ |
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213 | !> Interpolates bi-linearly in horizontal planes on every k level of the output |
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214 | !> array outvar(:,:,k) using values of the source array invar(:,:,:). The source |
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215 | !> (invar) and interpolation array (outvar) need to have matching dimensions. |
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216 | !> |
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217 | !> Input parameters: |
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218 | !> ----------------- |
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219 | !> invar : Array of source data |
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220 | !> |
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221 | !> outgrid%ii,%jj : Array of neighbour indices in x and y direction. |
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222 | !> ii(i,j,k,:), and jj(i,j,k,:) contain the four horizontal neighbour points |
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223 | !> of PALM-4U point (i,j,k) on the input grid corresponding to the source |
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224 | !> data invar. (The outgrid carries the relationship with the ingrid in the |
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225 | ! form of the interpolation weights.) |
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226 | !> |
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227 | !> outgrid%w_horiz: Array of weights for horizontal bi-linear interpolation |
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228 | !> corresponding to neighbour points indexed by ii and jj. |
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229 | !> |
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230 | !> Output papameters: |
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231 | !> ------------------ |
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232 | !> outvar : Array of interpolated data |
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233 | !------------------------------------------------------------------------------! |
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234 | SUBROUTINE interpolate_2d(invar, outvar, outgrid, ncvar) |
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235 | ! |
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236 | !-- I index 0-based for the indices of the outvar to be consistent with the |
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237 | !-- outgrid indices and interpolation weights. |
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238 | TYPE(grid_definition), INTENT(IN) :: outgrid |
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239 | REAL(wp), INTENT(IN) :: invar(0:,0:,0:) |
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240 | REAL(wp), INTENT(OUT) :: outvar(0:,0:,0:) |
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241 | TYPE(nc_var), INTENT(IN), OPTIONAL :: ncvar |
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242 | |
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243 | INTEGER :: i, j, k, l |
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244 | |
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245 | ! |
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246 | !-- TODO: check if input dimensions are consistent, i.e. ranges are correct |
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247 | IF ( UBOUND(outvar, 3) .GT. UBOUND(invar, 3) ) THEN |
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248 | message = "Output array for '" // TRIM(ncvar%name) // "' has ' more levels (" // & |
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249 | TRIM(str(UBOUND(outvar, 3))) // ") than input variable ("//& |
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250 | TRIM(str(UBOUND(invar, 3))) // ")." |
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251 | CALL inifor_abort('interpolate_2d', message) |
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252 | ENDIF |
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253 | |
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254 | DO k = 0, UBOUND(outvar, 3) |
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255 | DO j = 0, UBOUND(outvar, 2) |
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256 | DO i = 0, UBOUND(outvar, 1) |
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257 | outvar(i,j,k) = 0.0_wp |
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258 | DO l = 1, 4 |
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259 | |
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260 | outvar(i,j,k) = outvar(i,j,k) + & |
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261 | outgrid%w_horiz(i,j,l) * invar( outgrid%ii(i,j,l), & |
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262 | outgrid%jj(i,j,l), & |
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263 | k ) |
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264 | ENDDO |
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265 | ENDDO |
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266 | ENDDO |
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267 | ENDDO |
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268 | |
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269 | END SUBROUTINE interpolate_2d |
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270 | |
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271 | |
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272 | !------------------------------------------------------------------------------! |
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273 | ! Description: |
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274 | ! ------------ |
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275 | !> Compute the horizontal average of the in_arr(:,:,:) and store it in |
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276 | !> out_arr(:) |
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277 | !------------------------------------------------------------------------------! |
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278 | SUBROUTINE average_2d(in_arr, out_arr, ii, jj) |
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279 | REAL(wp), INTENT(IN) :: in_arr(0:,0:,0:) |
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280 | REAL(wp), INTENT(OUT) :: out_arr(0:) |
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281 | INTEGER, INTENT(IN), DIMENSION(:) :: ii, jj |
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282 | |
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283 | INTEGER :: i, j, k, l |
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284 | REAL(wp) :: ni |
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285 | |
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286 | IF (SIZE(ii) /= SIZE(jj)) THEN |
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287 | message = "Length of 'ii' and 'jj' index lists do not match." // & |
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288 | NEW_LINE(' ') // "ii has " // str(SIZE(ii)) // " elements, " // & |
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289 | NEW_LINE(' ') // "jj has " // str(SIZE(jj)) // "." |
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290 | CALL inifor_abort('average_2d', message) |
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291 | ENDIF |
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292 | |
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293 | IF (SIZE(ii) == 0) THEN |
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294 | message = "No columns to average over; " // & |
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295 | "size of index lists 'ii' and 'jj' is zero." |
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296 | CALL inifor_abort('average_2d', message) |
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297 | ENDIF |
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298 | |
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299 | DO k = 0, UBOUND(out_arr, 1) |
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300 | |
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301 | out_arr(k) = 0.0_wp |
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302 | DO l = 1, UBOUND(ii, 1) |
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303 | i = ii(l) |
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304 | j = jj(l) |
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305 | out_arr(k) = out_arr(k) + in_arr(i, j, k) |
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306 | ENDDO |
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307 | |
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308 | ENDDO |
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309 | |
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310 | ni = 1.0_wp / SIZE(ii) |
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311 | out_arr(:) = out_arr(:) * ni |
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312 | |
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313 | END SUBROUTINE average_2d |
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314 | |
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315 | |
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316 | !------------------------------------------------------------------------------! |
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317 | ! Description: |
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318 | ! ------------ |
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319 | !> Three-dimensional interpolation driver. Interpolates from the source_array to |
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320 | !> the given palm_grid. |
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321 | !> |
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322 | !> The routine separates horizontal and vertical |
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323 | !> interpolation. In the horizontal interpolation step, the source_array data is |
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324 | !> interpolated along COSMO grid levels onto the intermediate grid (vertically |
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325 | !> as coarse as COSMO, horizontally as fine as PALM). |
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326 | !------------------------------------------------------------------------------! |
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327 | SUBROUTINE interpolate_3d(source_array, palm_array, palm_intermediate, palm_grid) |
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328 | TYPE(grid_definition), INTENT(IN) :: palm_intermediate, palm_grid |
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329 | REAL(wp), DIMENSION(:,:,:), INTENT(IN) :: source_array |
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330 | REAL(wp), DIMENSION(:,:,:), INTENT(OUT) :: palm_array |
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331 | REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: intermediate_array |
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332 | INTEGER :: nx, ny, nlev |
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333 | |
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334 | nx = palm_intermediate%nx |
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335 | ny = palm_intermediate%ny |
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336 | nlev = palm_intermediate%nz |
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337 | |
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338 | ! |
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339 | !-- Interpolate from COSMO to intermediate grid. Allocating with one |
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340 | !-- less point in the vertical, since scalars like T have 50 instead of 51 |
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341 | !-- points in COSMO. |
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342 | ALLOCATE(intermediate_array(0:nx, 0:ny, 0:nlev-1)) ! |
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343 | |
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344 | CALL interpolate_2d(source_array, intermediate_array, palm_intermediate) |
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345 | |
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346 | ! |
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347 | !-- Interpolate from intermediate grid to palm_grid grid, includes |
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348 | !-- extrapolation for cells below COSMO domain. |
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349 | CALL interpolate_1d_arr(intermediate_array, palm_array, palm_grid) |
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350 | |
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351 | DEALLOCATE(intermediate_array) |
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352 | |
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353 | END SUBROUTINE interpolate_3d |
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354 | |
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355 | |
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356 | !------------------------------------------------------------------------------! |
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357 | ! Description: |
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358 | ! ------------ |
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359 | !> Average data horizontally from the source_array over the region given by the |
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360 | !> averaging grid 'avg_grid' and store the result in 'profile_array'. |
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361 | !------------------------------------------------------------------------------! |
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362 | SUBROUTINE interp_average_profile(source_array, profile_array, avg_grid) |
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363 | TYPE(grid_definition), INTENT(IN) :: avg_grid |
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364 | REAL(wp), DIMENSION(:,:,:), INTENT(IN) :: source_array |
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365 | REAL(wp), DIMENSION(:), INTENT(OUT) :: profile_array |
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366 | |
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367 | INTEGER :: i_source, j_source, k_profile, k_source, l, m |
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368 | |
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369 | REAL :: ni_columns |
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370 | |
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371 | profile_array(:) = 0.0_wp |
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372 | |
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373 | DO l = 1, avg_grid%n_columns |
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374 | i_source = avg_grid%iii(l) |
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375 | j_source = avg_grid%jjj(l) |
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376 | |
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377 | ! |
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378 | !-- Loop over PALM levels |
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379 | DO k_profile = avg_grid%k_min, UBOUND(profile_array, 1) |
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380 | |
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381 | ! |
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382 | !-- Loop over vertical interpolation neighbours |
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383 | DO m = 1, 2 |
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384 | |
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385 | k_source = avg_grid%kkk(l, k_profile, m) |
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386 | |
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387 | profile_array(k_profile) = profile_array(k_profile) & |
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388 | + avg_grid%w(l, k_profile, m) & |
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389 | * source_array(i_source, j_source, k_source) |
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390 | ! |
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391 | !-- Loop over vertical interpolation neighbours m |
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392 | ENDDO |
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393 | |
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394 | ! |
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395 | !-- Loop over PALM levels k_profile |
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396 | ENDDO |
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397 | |
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398 | ! |
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399 | !-- Loop over horizontal neighbours l |
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400 | ENDDO |
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401 | |
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402 | ni_columns = 1.0_wp / avg_grid%n_columns |
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403 | profile_array(:) = profile_array(:) * ni_columns |
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404 | |
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405 | ! |
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406 | !-- Constant extrapolation to the bottom |
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407 | profile_array(1:avg_grid%k_min-1) = profile_array(avg_grid%k_min) |
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408 | |
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409 | END SUBROUTINE interp_average_profile |
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410 | |
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411 | |
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412 | !------------------------------------------------------------------------------! |
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413 | ! Description: |
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414 | ! ------------ |
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415 | !> Average data horizontally from the source_array over the region given by the |
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416 | !> averaging grid 'avg_grid' and store the result in 'profile_array'. |
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417 | !------------------------------------------------------------------------------! |
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418 | SUBROUTINE average_profile( source_array, profile_array, avg_grid ) |
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419 | |
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420 | TYPE(grid_definition), INTENT(IN) :: avg_grid |
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421 | REAL(wp), DIMENSION(:,:,:), INTENT(IN) :: source_array |
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422 | REAL(wp), DIMENSION(:), INTENT(OUT) :: profile_array |
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423 | |
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424 | INTEGER :: i_source, j_source, l, nz, nlev |
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425 | |
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426 | REAL(wp) :: ni_columns |
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427 | |
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428 | nlev = SIZE( source_array, 3 ) |
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429 | nz = SIZE( profile_array, 1 ) |
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430 | |
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431 | IF ( nlev /= nz ) THEN |
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432 | message = "Lengths of input and output profiles do not match: " // & |
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433 | "cosmo_pressure(" // TRIM( str( nlev ) ) // & |
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434 | "), profile_array(" // TRIM( str( nz ) ) // ")." |
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435 | CALL inifor_abort('average_pressure_perturbation', message) |
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436 | ENDIF |
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437 | |
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438 | profile_array(:) = 0.0_wp |
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439 | |
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440 | DO l = 1, avg_grid%n_columns |
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441 | |
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442 | i_source = avg_grid%iii(l) |
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443 | j_source = avg_grid%jjj(l) |
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444 | |
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445 | profile_array(:) = profile_array(:) & |
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446 | + source_array(i_source, j_source, :) |
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447 | |
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448 | ENDDO |
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449 | |
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450 | ni_columns = 1.0_wp / avg_grid%n_columns |
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451 | profile_array(:) = profile_array(:) * ni_columns |
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452 | |
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453 | END SUBROUTINE average_profile |
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454 | |
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455 | |
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456 | !------------------------------------------------------------------------------! |
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457 | ! Description: |
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458 | ! ------------ |
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459 | !> This is a sister routine to average_profile() and differes from it in that |
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460 | !> it removes the COSMO basic state pressure from the input array before |
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461 | !> averaging. |
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462 | !------------------------------------------------------------------------------! |
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463 | SUBROUTINE average_pressure_perturbation( cosmo_pressure, profile_array, & |
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464 | cosmo_grid, avg_grid ) |
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465 | |
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466 | TYPE(grid_definition), INTENT(IN) :: cosmo_grid, avg_grid |
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467 | REAL(wp), DIMENSION(:,:,:), INTENT(IN) :: cosmo_pressure |
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468 | REAL(wp), DIMENSION(:), INTENT(OUT) :: profile_array |
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469 | |
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470 | INTEGER :: i_source, j_source, l, nz, nlev |
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471 | |
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472 | REAL(wp) :: ni_columns |
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473 | REAL(wp), DIMENSION(:), ALLOCATABLE :: basic_state_pressure |
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474 | |
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475 | nlev = SIZE( cosmo_pressure, 3 ) |
---|
476 | nz = SIZE( profile_array, 1 ) |
---|
477 | |
---|
478 | IF ( nlev /= nz ) THEN |
---|
479 | message = "Lengths of input and output profiles do not match: " // & |
---|
480 | "cosmo_pressure(" // TRIM( str( nlev ) ) // & |
---|
481 | "), profile_array(" // TRIM( str( nz ) ) // ")." |
---|
482 | CALL inifor_abort('average_pressure_perturbation', message) |
---|
483 | ENDIF |
---|
484 | |
---|
485 | ALLOCATE( basic_state_pressure(nz) ) |
---|
486 | profile_array(:) = 0.0_wp |
---|
487 | |
---|
488 | DO l = 1, avg_grid%n_columns |
---|
489 | i_source = avg_grid%iii(l) |
---|
490 | j_source = avg_grid%jjj(l) |
---|
491 | |
---|
492 | ! |
---|
493 | !-- Compute pressure perturbation by removing COSMO basic state pressure |
---|
494 | CALL get_basic_state( cosmo_grid%hfl(i_source,j_source,:), BETA, & |
---|
495 | P_SL, T_SL, RD, G, basic_state_pressure ) |
---|
496 | |
---|
497 | profile_array(:) = profile_array(:) & |
---|
498 | + cosmo_pressure(i_source, j_source, :) & |
---|
499 | - basic_state_pressure(:) |
---|
500 | |
---|
501 | ! |
---|
502 | !-- Loop over horizontal neighbours l |
---|
503 | ENDDO |
---|
504 | |
---|
505 | DEALLOCATE( basic_state_pressure ) |
---|
506 | |
---|
507 | ni_columns = 1.0_wp / avg_grid%n_columns |
---|
508 | profile_array(:) = profile_array(:) * ni_columns |
---|
509 | |
---|
510 | END SUBROUTINE average_pressure_perturbation |
---|
511 | |
---|
512 | |
---|
513 | |
---|
514 | |
---|
515 | !------------------------------------------------------------------------------! |
---|
516 | ! Description: |
---|
517 | ! ------------ |
---|
518 | !> Extrapolates density linearly from the level 'k_min' downwards. |
---|
519 | !------------------------------------------------------------------------------! |
---|
520 | SUBROUTINE extrapolate_density(rho, avg_grid) |
---|
521 | REAL(wp), DIMENSION(:), INTENT(INOUT) :: rho |
---|
522 | TYPE(grid_definition), INTENT(IN) :: avg_grid |
---|
523 | |
---|
524 | REAL(wp) :: drhodz, dz, zk, rhok |
---|
525 | INTEGER :: k_min |
---|
526 | |
---|
527 | k_min = avg_grid%k_min |
---|
528 | zk = avg_grid%z(k_min) |
---|
529 | rhok = rho(k_min) |
---|
530 | dz = avg_grid%z(k_min + 1) - avg_grid%z(k_min) |
---|
531 | drhodz = (rho(k_min + 1) - rho(k_min)) / dz |
---|
532 | |
---|
533 | rho(1:k_min-1) = rhok + drhodz * (avg_grid%z(1:k_min-1) - zk) |
---|
534 | |
---|
535 | END SUBROUTINE extrapolate_density |
---|
536 | |
---|
537 | |
---|
538 | !------------------------------------------------------------------------------! |
---|
539 | ! Description: |
---|
540 | ! ------------ |
---|
541 | !> Driver for extrapolating pressure from PALM level k_min downwards |
---|
542 | !------------------------------------------------------------------------------! |
---|
543 | SUBROUTINE extrapolate_pressure(p, rho, avg_grid) |
---|
544 | REAL(wp), DIMENSION(:), INTENT(IN) :: rho |
---|
545 | REAL(wp), DIMENSION(:), INTENT(INOUT) :: p |
---|
546 | TYPE(grid_definition), INTENT(IN) :: avg_grid |
---|
547 | |
---|
548 | REAL(wp) :: drhodz, dz, zk, rhok |
---|
549 | INTEGER :: k, k_min |
---|
550 | |
---|
551 | k_min = avg_grid%k_min |
---|
552 | zk = avg_grid%z(k_min) |
---|
553 | rhok = rho(k_min) |
---|
554 | dz = avg_grid%z(k_min + 1) - avg_grid%z(k_min) |
---|
555 | drhodz = 0.5_wp * (rho(k_min + 1) - rho(k_min)) / dz |
---|
556 | |
---|
557 | DO k = 1, k_min-1 |
---|
558 | p(k) = constant_density_pressure(p(k_min), zk, rhok, drhodz, & |
---|
559 | avg_grid%z(k), G) |
---|
560 | ENDDO |
---|
561 | |
---|
562 | END SUBROUTINE extrapolate_pressure |
---|
563 | |
---|
564 | |
---|
565 | !------------------------------------------------------------------------------! |
---|
566 | ! Description: |
---|
567 | ! ------------ |
---|
568 | !> Takes the averaged pressure profile <p> and sets the lowest entry to the |
---|
569 | !> extrapolated pressure at the surface. |
---|
570 | !------------------------------------------------------------------------------! |
---|
571 | SUBROUTINE get_surface_pressure(p, rho, avg_grid) |
---|
572 | REAL(wp), DIMENSION(:), INTENT(IN) :: rho |
---|
573 | REAL(wp), DIMENSION(:), INTENT(INOUT) :: p |
---|
574 | TYPE(grid_definition), INTENT(IN) :: avg_grid |
---|
575 | |
---|
576 | REAL(wp) :: drhodz, dz, zk, rhok |
---|
577 | INTEGER :: k_min |
---|
578 | |
---|
579 | k_min = avg_grid%k_min |
---|
580 | zk = avg_grid%z(k_min) |
---|
581 | rhok = rho(k_min) |
---|
582 | dz = avg_grid%z(k_min + 1) - avg_grid%z(k_min) |
---|
583 | drhodz = 0.5_wp * (rho(k_min + 1) - rho(k_min)) / dz |
---|
584 | |
---|
585 | p(1) = constant_density_pressure(p(k_min), zk, rhok, drhodz, & |
---|
586 | 0.0_wp, G) |
---|
587 | |
---|
588 | END SUBROUTINE get_surface_pressure |
---|
589 | |
---|
590 | |
---|
591 | FUNCTION constant_density_pressure(pk, zk, rhok, drhodz, z, g) RESULT(p) |
---|
592 | |
---|
593 | REAL(wp), INTENT(IN) :: pk, zk, rhok, drhodz, g, z |
---|
594 | REAL(wp) :: p |
---|
595 | |
---|
596 | p = pk + ( zk - z ) * g * ( rhok + 0.5*drhodz * (zk - z) ) |
---|
597 | |
---|
598 | END FUNCTION constant_density_pressure |
---|
599 | |
---|
600 | !-----------------------------------------------------------------------------! |
---|
601 | ! Description: |
---|
602 | ! ----------- |
---|
603 | !> This routine computes profiles of the two geostrophic wind components ug and |
---|
604 | !> vg. |
---|
605 | !-----------------------------------------------------------------------------! |
---|
606 | SUBROUTINE geostrophic_winds(p_north, p_south, p_east, p_west, rho, f3, & |
---|
607 | Lx, Ly, phi_n, lam_n, phi_g, lam_g, ug, vg) |
---|
608 | |
---|
609 | REAL(wp), DIMENSION(:), INTENT(IN) :: p_north, p_south, p_east, p_west, & |
---|
610 | rho |
---|
611 | REAL(wp), INTENT(IN) :: f3, Lx, Ly, phi_n, lam_n, phi_g, lam_g |
---|
612 | REAL(wp), DIMENSION(:), INTENT(OUT) :: ug, vg |
---|
613 | REAL(wp) :: facx, facy |
---|
614 | |
---|
615 | facx = 1.0_wp / (Lx * f3) |
---|
616 | facy = 1.0_wp / (Ly * f3) |
---|
617 | ug(:) = - facy / rho(:) * (p_north(:) - p_south(:)) |
---|
618 | vg(:) = facx / rho(:) * (p_east(:) - p_west(:)) |
---|
619 | |
---|
620 | CALL rotate_vector_field( & |
---|
621 | ug, vg, angle = meridian_convergence_rotated(phi_n, lam_n, phi_g, lam_g)& |
---|
622 | ) |
---|
623 | |
---|
624 | END SUBROUTINE geostrophic_winds |
---|
625 | |
---|
626 | |
---|
627 | !-----------------------------------------------------------------------------! |
---|
628 | ! Description: |
---|
629 | ! ----------- |
---|
630 | !> This routine computes the inverse Plate Carree projection, i.e. in projects |
---|
631 | !> Cartesian coordinates (x,y) onto a sphere. It returns the latitude and |
---|
632 | !> lngitude of a geographical system centered at x0 and y0. |
---|
633 | !-----------------------------------------------------------------------------! |
---|
634 | SUBROUTINE inv_plate_carree(x, y, x0, y0, r, lat, lon) |
---|
635 | REAL(wp), INTENT(IN) :: x(:), y(:), x0, y0, r |
---|
636 | REAL(wp), INTENT(OUT) :: lat(:), lon(:) |
---|
637 | |
---|
638 | REAL(wp) :: ri |
---|
639 | |
---|
640 | ! |
---|
641 | !-- TODO check dimensions of lat/lon and y/x match |
---|
642 | |
---|
643 | ri = 1.0_wp / r |
---|
644 | |
---|
645 | lat(:) = (y(:) - y0) * ri |
---|
646 | lon(:) = (x(:) - x0) * ri |
---|
647 | END SUBROUTINE |
---|
648 | |
---|
649 | |
---|
650 | !-----------------------------------------------------------------------------! |
---|
651 | ! Description: |
---|
652 | ! ------------ |
---|
653 | !> Computes the reverse Plate-Carree projection of a x or y position on a |
---|
654 | !> Cartesian grid. |
---|
655 | !> |
---|
656 | !> Input parameters: |
---|
657 | !> ----------------- |
---|
658 | !> xy : x or y coordinate of the Cartasian grid point [m]. |
---|
659 | !> |
---|
660 | !> xy0 : x or y coordinate that coincides with the origin of the underlying |
---|
661 | !> sperical system (crossing point of the equator and prime meridian) [m]. |
---|
662 | !> |
---|
663 | !> r : Radius of the of the underlying sphere, e.g. EARTH_RADIUS [m]. |
---|
664 | !> |
---|
665 | !> Returns: |
---|
666 | !> -------- |
---|
667 | !> project : Longitude (in case xy = x) or latitude (xy = y) of the given input |
---|
668 | !> coordinate xy. |
---|
669 | !------------------------------------------------------------------------------! |
---|
670 | ELEMENTAL REAL(wp) FUNCTION project(xy, xy0, r) |
---|
671 | REAL(wp), INTENT(IN) :: xy, xy0, r |
---|
672 | REAL(wp) :: ri |
---|
673 | |
---|
674 | ! |
---|
675 | !-- If this elemental function is called with a large array as xy, it is |
---|
676 | !-- computationally more efficient to precompute the inverse radius and |
---|
677 | !-- then muliply. |
---|
678 | ri = 1.0_wp / r |
---|
679 | |
---|
680 | project = (xy - xy0) * ri |
---|
681 | |
---|
682 | END FUNCTION project |
---|
683 | |
---|
684 | |
---|
685 | !------------------------------------------------------------------------------! |
---|
686 | ! Description: |
---|
687 | ! ------------ |
---|
688 | !> For a rotated-pole system with the origin at geographical latitude 'phi_c', |
---|
689 | !> compute the geographical latitude of its rotated north pole. |
---|
690 | !------------------------------------------------------------------------------! |
---|
691 | REAL(wp) FUNCTION phic_to_phin(phi_c) |
---|
692 | REAL(wp), INTENT(IN) :: phi_c |
---|
693 | |
---|
694 | phic_to_phin = 0.5_wp * PI - ABS(phi_c) |
---|
695 | |
---|
696 | END FUNCTION phic_to_phin |
---|
697 | |
---|
698 | |
---|
699 | !------------------------------------------------------------------------------! |
---|
700 | ! Description: |
---|
701 | ! ------------ |
---|
702 | !> For a rotated-pole system with the origin at geographical latitude 'phi_c' |
---|
703 | !> and longitude 'lam_c', compute the geographical longitude of its rotated |
---|
704 | !> north pole. |
---|
705 | !------------------------------------------------------------------------------! |
---|
706 | REAL(wp) FUNCTION lamc_to_lamn(phi_c, lam_c) |
---|
707 | REAL(wp), INTENT(IN) :: phi_c, lam_c |
---|
708 | |
---|
709 | lamc_to_lamn = lam_c |
---|
710 | IF (phi_c > 0.0_wp) THEN |
---|
711 | lamc_to_lamn = lam_c - SIGN(PI, lam_c) |
---|
712 | ENDIF |
---|
713 | |
---|
714 | END FUNCTION lamc_to_lamn |
---|
715 | |
---|
716 | |
---|
717 | !------------------------------------------------------------------------------! |
---|
718 | ! Description: |
---|
719 | ! ------------ |
---|
720 | !> Set gamma according to whether PALM domain is in the northern or southern |
---|
721 | !> hemisphere of the COSMO rotated-pole system. Gamma assumes either the |
---|
722 | !> value 0 or PI and is needed to work around around a bug in the |
---|
723 | !> rotated-pole coordinate transformations. |
---|
724 | !------------------------------------------------------------------------------! |
---|
725 | REAL(wp) FUNCTION gamma_from_hemisphere(phi_cg, phi_ref) |
---|
726 | REAL(wp), INTENT(IN) :: phi_cg |
---|
727 | REAL(wp), INTENT(IN) :: phi_ref |
---|
728 | |
---|
729 | LOGICAL :: palm_origin_is_south_of_cosmo_origin |
---|
730 | |
---|
731 | palm_origin_is_south_of_cosmo_origin = (phi_cg < phi_ref) |
---|
732 | |
---|
733 | IF (palm_origin_is_south_of_cosmo_origin) THEN |
---|
734 | gamma_from_hemisphere = PI |
---|
735 | ELSE |
---|
736 | gamma_from_hemisphere = 0.0_wp |
---|
737 | ENDIF |
---|
738 | END FUNCTION gamma_from_hemisphere |
---|
739 | |
---|
740 | |
---|
741 | !------------------------------------------------------------------------------! |
---|
742 | ! Description: |
---|
743 | ! ------------ |
---|
744 | !> Computes the geographical coordinates corresponding to the given rotated-pole |
---|
745 | !> coordinates. |
---|
746 | !> |
---|
747 | !> In INIFOR, this routine is used to convert coordinates between two |
---|
748 | !> rotated-pole systems: COSMO-DE's rotated-pole system, and one centred at the |
---|
749 | !> PALM-4U domain centre. In this case, the PALM-4U system is thought of as the |
---|
750 | !> rotated-pole system and the routine is used to rotate back to COSMO-DE's |
---|
751 | !> system which is thought of as the geographical one. |
---|
752 | !> |
---|
753 | !> Input parameters: |
---|
754 | !> ----------------- |
---|
755 | !> phir(:), lamr(: ): latitudes and longitudes of the rotated-pole grid |
---|
756 | !> |
---|
757 | !> phip, lamp: latitude and longitude of the rotated north pole |
---|
758 | !> |
---|
759 | !> gam: "angle between the north poles. If [gam] is not present, the other |
---|
760 | !> system is the real geographical system." (original phiro2rot |
---|
761 | !> description) |
---|
762 | !> |
---|
763 | !> Output parameters: |
---|
764 | !> ------------------ |
---|
765 | !> phi(:,:), lam(:,:): geographical latitudes and logitudes |
---|
766 | !------------------------------------------------------------------------------! |
---|
767 | SUBROUTINE rotate_to_cosmo(phir, lamr, phip, lamp, phi, lam, gam) |
---|
768 | REAL(wp), INTENT(IN) :: phir(0:), lamr(0:), phip, lamp, gam |
---|
769 | REAL(wp), INTENT(OUT) :: phi(0:,0:), lam(0:,0:) |
---|
770 | |
---|
771 | INTEGER :: i, j |
---|
772 | |
---|
773 | IF ( SIZE(phi, 1) .NE. SIZE(lam, 1) .OR. & |
---|
774 | SIZE(phi, 2) .NE. SIZE(lam, 2) ) THEN |
---|
775 | PRINT *, "inifor: rotate_to_cosmo: Dimensions of phi and lambda do not match. Dimensions are:" |
---|
776 | PRINT *, "inifor: rotate_to_cosmo: phi: ", SIZE(phi, 1), SIZE(phi, 2) |
---|
777 | PRINT *, "inifor: rotate_to_cosmo: lam: ", SIZE(lam, 1), SIZE(lam, 2) |
---|
778 | STOP |
---|
779 | ENDIF |
---|
780 | |
---|
781 | IF ( SIZE(phir) .NE. SIZE(phi, 2) .OR. & |
---|
782 | SIZE(lamr) .NE. SIZE(phi, 1) ) THEN |
---|
783 | PRINT *, "inifor: rotate_to_cosmo: Dimensions of phir and lamr do not match. Dimensions are:" |
---|
784 | PRINT *, "inifor: rotate_to_cosmo: phir: ", SIZE(phir), SIZE(phi, 2) |
---|
785 | PRINT *, "inifor: rotate_to_cosmo: lamr: ", SIZE(lamr), SIZE(phi, 1) |
---|
786 | STOP |
---|
787 | ENDIF |
---|
788 | |
---|
789 | DO j = 0, UBOUND(phir, 1) |
---|
790 | DO i = 0, UBOUND(lamr, 1) |
---|
791 | |
---|
792 | phi(i,j) = phirot2phi(phir(j) * TO_DEGREES, & |
---|
793 | lamr(i) * TO_DEGREES, & |
---|
794 | phip * TO_DEGREES, & |
---|
795 | gam * TO_DEGREES) * TO_RADIANS |
---|
796 | |
---|
797 | lam(i,j) = rlarot2rla(phir(j) * TO_DEGREES, & |
---|
798 | lamr(i) * TO_DEGREES, & |
---|
799 | phip * TO_DEGREES, & |
---|
800 | lamp * TO_DEGREES, & |
---|
801 | gam * TO_DEGREES) * TO_RADIANS |
---|
802 | |
---|
803 | ENDDO |
---|
804 | ENDDO |
---|
805 | |
---|
806 | END SUBROUTINE rotate_to_cosmo |
---|
807 | |
---|
808 | |
---|
809 | !------------------------------------------------------------------------------! |
---|
810 | ! Description: |
---|
811 | ! ------------ |
---|
812 | !> Rotate the given vector field (x(:), y(:)) by the given 'angle'. |
---|
813 | !------------------------------------------------------------------------------! |
---|
814 | SUBROUTINE rotate_vector_field(x, y, angle) |
---|
815 | REAL(wp), DIMENSION(:), INTENT(INOUT) :: x, y !< x and y coodrinate in arbitrary units |
---|
816 | REAL(wp), INTENT(IN) :: angle !< rotation angle [deg] |
---|
817 | |
---|
818 | INTEGER :: i |
---|
819 | REAL(wp) :: sine, cosine, v_rot(2), rotation(2,2) |
---|
820 | |
---|
821 | sine = SIN(angle * TO_RADIANS) |
---|
822 | cosine = COS(angle * TO_RADIANS) |
---|
823 | ! |
---|
824 | !-- RESAHPE() fills columns first, so the rotation matrix becomes |
---|
825 | !-- |
---|
826 | !-- rotation = [ cosine -sine ] |
---|
827 | !-- [ sine cosine ] |
---|
828 | rotation = RESHAPE( (/cosine, sine, -sine, cosine/), (/2, 2/) ) |
---|
829 | |
---|
830 | DO i = LBOUND(x, 1), UBOUND(x, 1) |
---|
831 | |
---|
832 | v_rot(:) = MATMUL(rotation, (/x(i), y(i)/)) |
---|
833 | |
---|
834 | x(i) = v_rot(1) |
---|
835 | y(i) = v_rot(2) |
---|
836 | |
---|
837 | ENDDO |
---|
838 | |
---|
839 | END SUBROUTINE rotate_vector_field |
---|
840 | |
---|
841 | |
---|
842 | |
---|
843 | !------------------------------------------------------------------------------! |
---|
844 | ! Description: |
---|
845 | ! ------------ |
---|
846 | !> This routine computes the local meridian convergence between a rotated-pole |
---|
847 | !> and a geographical system using the Eq. (6) given in the DWD manual |
---|
848 | !> |
---|
849 | !> Baldauf et al. (2018), Beschreibung des operationelle KuÌrzestfrist- |
---|
850 | !> vorhersagemodells COSMO-D2 und COSMO-D2-EPS und seiner Ausgabe in die |
---|
851 | !> Datenbanken des DWD. |
---|
852 | !> https://www.dwd.de/SharedDocs/downloads/DE/modelldokumentationen/nwv/cosmo_d2/cosmo_d2_dbbeschr_aktuell.pdf?__blob=publicationFile&v=2 |
---|
853 | !------------------------------------------------------------------------------! |
---|
854 | FUNCTION meridian_convergence_rotated(phi_n, lam_n, phi_g, lam_g) & |
---|
855 | RESULT(delta) |
---|
856 | |
---|
857 | REAL(wp), INTENT(IN) :: phi_n, lam_n, phi_g, lam_g |
---|
858 | REAL(wp) :: delta |
---|
859 | |
---|
860 | delta = atan2( COS(phi_n) * SIN(lam_n - lam_g), & |
---|
861 | COS(phi_g) * SIN(phi_n) - & |
---|
862 | SIN(phi_g) * COS(phi_n) * COS(lam_n - lam_g) ) |
---|
863 | |
---|
864 | END FUNCTION meridian_convergence_rotated |
---|
865 | |
---|
866 | !------------------------------------------------------------------------------! |
---|
867 | ! Description: |
---|
868 | ! ------------ |
---|
869 | !> Compute indices of PALM-4U grid point neighbours in the target |
---|
870 | !> system (COSMO-DE) by rounding up and down. (i,j) are the indices of |
---|
871 | !> the PALM-4U grid and (ii(i,j,1-4), jj(i,j,1-4)) contain the indices |
---|
872 | !> of the its four neigbouring points in the COSMO-DE grid. |
---|
873 | !> |
---|
874 | !> |
---|
875 | !> COSMO-DE grid |
---|
876 | !> ------------- |
---|
877 | !> jj, lat |
---|
878 | !> ^ j |
---|
879 | !> | \ i |
---|
880 | !> jj(i,j,2/3) + ... 2 ---\--------/------ 3 |
---|
881 | !> | | ^ \ / | |
---|
882 | !> | | |wp \ / | |
---|
883 | !> | | v \ / | |
---|
884 | !> latpos + ............ o/ (i,j) | |
---|
885 | !> | | : | |
---|
886 | !> | | :<----wl---->| |
---|
887 | !> jj(i,j,1/4) + ... 1 -------:----------- 4 |
---|
888 | !> | : : : |
---|
889 | !> | : : : |
---|
890 | !> | : lonpos : |
---|
891 | !> L-----+--------+------------+------> ii, lon |
---|
892 | !> ii(i,j,1/2) ii(i,j,3/4) |
---|
893 | !> |
---|
894 | !> |
---|
895 | !> Input parameters: |
---|
896 | !> ----------------- |
---|
897 | !> source_lat, source_lon : (rotated-pole) coordinates of the source grid (e.g. |
---|
898 | !> COSMO-DE) |
---|
899 | !> |
---|
900 | !> source_dxi, source_dyi : inverse grid spacings of the source grid. |
---|
901 | !> |
---|
902 | !> target_lat, target_lon : (rotated-pole) coordinates of the target grid (e.g. |
---|
903 | !> COSMO-DE) |
---|
904 | !> |
---|
905 | !> Output parameters: |
---|
906 | !> ------------------ |
---|
907 | !> palm_ii, palm_jj : x and y index arrays of horizontal neighbour columns |
---|
908 | !> |
---|
909 | !------------------------------------------------------------------------------! |
---|
910 | SUBROUTINE find_horizontal_neighbours(cosmo_lat, cosmo_lon, & |
---|
911 | palm_clat, palm_clon, & |
---|
912 | palm_ii, palm_jj) |
---|
913 | |
---|
914 | REAL(wp), DIMENSION(0:), INTENT(IN) :: cosmo_lat, cosmo_lon |
---|
915 | REAL(wp), DIMENSION(0:,0:), INTENT(IN) :: palm_clat, palm_clon |
---|
916 | REAL(wp) :: cosmo_dxi, cosmo_dyi |
---|
917 | INTEGER, DIMENSION(0:,0:,1:), INTENT(OUT) :: palm_ii, palm_jj |
---|
918 | |
---|
919 | REAL(wp) :: lonpos, latpos, lon0, lat0 |
---|
920 | INTEGER :: i, j |
---|
921 | |
---|
922 | lon0 = cosmo_lon(0) |
---|
923 | lat0 = cosmo_lat(0) |
---|
924 | cosmo_dxi = 1.0_wp / (cosmo_lon(1) - cosmo_lon(0)) |
---|
925 | cosmo_dyi = 1.0_wp / (cosmo_lat(1) - cosmo_lat(0)) |
---|
926 | |
---|
927 | DO j = 0, UBOUND(palm_clon, 2)!palm_grid%ny |
---|
928 | DO i = 0, UBOUND(palm_clon, 1)!palm_grid%nx |
---|
929 | ! |
---|
930 | !-- Compute the floating point index corrseponding to PALM-4U grid point |
---|
931 | !-- location along target grid (COSMO-DE) axes. |
---|
932 | lonpos = (palm_clon(i,j) - lon0) * cosmo_dxi |
---|
933 | latpos = (palm_clat(i,j) - lat0) * cosmo_dyi |
---|
934 | |
---|
935 | IF (lonpos < 0.0_wp .OR. latpos < 0.0_wp) THEN |
---|
936 | message = "lonpos or latpos out of bounds " // & |
---|
937 | "while finding interpolation neighbours!" // NEW_LINE(' ') // & |
---|
938 | " (i,j) = (" // & |
---|
939 | TRIM(str(i)) // ", " // TRIM(str(j)) // ")" // NEW_LINE(' ') //& |
---|
940 | " lonpos " // TRIM(real_to_str(lonpos*TO_DEGREES)) // & |
---|
941 | ", latpos " // TRIM(real_to_str(latpos*TO_DEGREES)) // NEW_LINE(' ') // & |
---|
942 | " lon0 " // TRIM(real_to_str(lon0 *TO_DEGREES)) // & |
---|
943 | ", lat0 " // TRIM(real_to_str(lat0*TO_DEGREES)) // NEW_LINE(' ') // & |
---|
944 | " PALM lon " // TRIM(real_to_str(palm_clon(i,j)*TO_DEGREES)) // & |
---|
945 | ", PALM lat " // TRIM(real_to_str(palm_clat(i,j)*TO_DEGREES)) |
---|
946 | CALL inifor_abort('find_horizontal_neighbours', message) |
---|
947 | ENDIF |
---|
948 | |
---|
949 | palm_ii(i,j,1) = FLOOR(lonpos) |
---|
950 | palm_ii(i,j,2) = FLOOR(lonpos) |
---|
951 | palm_ii(i,j,3) = CEILING(lonpos) |
---|
952 | palm_ii(i,j,4) = CEILING(lonpos) |
---|
953 | |
---|
954 | palm_jj(i,j,1) = FLOOR(latpos) |
---|
955 | palm_jj(i,j,2) = CEILING(latpos) |
---|
956 | palm_jj(i,j,3) = CEILING(latpos) |
---|
957 | palm_jj(i,j,4) = FLOOR(latpos) |
---|
958 | ENDDO |
---|
959 | ENDDO |
---|
960 | |
---|
961 | END SUBROUTINE find_horizontal_neighbours |
---|
962 | |
---|
963 | |
---|
964 | !------------------------------------------------------------------------------! |
---|
965 | ! Description: |
---|
966 | ! ------------ |
---|
967 | !> Computes linear vertical interpolation neighbour indices and weights for each |
---|
968 | !> column of the given palm grid. |
---|
969 | !------------------------------------------------------------------------------! |
---|
970 | SUBROUTINE find_vertical_neighbours_and_weights_interp( palm_grid, & |
---|
971 | palm_intermediate ) |
---|
972 | TYPE(grid_definition), INTENT(INOUT) :: palm_grid |
---|
973 | TYPE(grid_definition), INTENT(IN) :: palm_intermediate |
---|
974 | |
---|
975 | INTEGER :: i, j, k, nx, ny, nz, nlev, k_intermediate |
---|
976 | LOGICAL :: point_is_below_grid, point_is_above_grid, & |
---|
977 | point_is_in_current_cell |
---|
978 | REAL(wp) :: current_height, column_base, column_top, h_top, h_bottom, & |
---|
979 | weight |
---|
980 | |
---|
981 | nx = palm_grid%nx |
---|
982 | ny = palm_grid%ny |
---|
983 | nz = palm_grid%nz |
---|
984 | nlev = palm_intermediate%nz |
---|
985 | |
---|
986 | ! |
---|
987 | !-- in each column of the fine grid, find vertical neighbours of every cell |
---|
988 | DO j = 0, ny |
---|
989 | DO i = 0, nx |
---|
990 | |
---|
991 | k_intermediate = 0 |
---|
992 | |
---|
993 | column_base = palm_intermediate%h(i,j,0) |
---|
994 | column_top = palm_intermediate%h(i,j,nlev) |
---|
995 | |
---|
996 | ! |
---|
997 | !-- scan through palm_grid column and set neighbour indices in |
---|
998 | !-- case current_height is either below column_base, in the current |
---|
999 | !-- cell, or above column_top. Keep increasing current cell index until |
---|
1000 | !-- the current cell overlaps with the current_height. |
---|
1001 | DO k = 1, nz |
---|
1002 | |
---|
1003 | ! |
---|
1004 | !-- Memorize the top and bottom boundaries of the coarse cell and the |
---|
1005 | !-- current height within it |
---|
1006 | current_height = palm_grid%z(k) + palm_grid%z0 |
---|
1007 | h_top = palm_intermediate%h(i,j,k_intermediate+1) |
---|
1008 | h_bottom = palm_intermediate%h(i,j,k_intermediate) |
---|
1009 | |
---|
1010 | point_is_above_grid = (current_height > column_top) !22000m, very unlikely |
---|
1011 | point_is_below_grid = (current_height < column_base) |
---|
1012 | |
---|
1013 | point_is_in_current_cell = ( & |
---|
1014 | current_height >= h_bottom .AND. & |
---|
1015 | current_height < h_top & |
---|
1016 | ) |
---|
1017 | |
---|
1018 | ! |
---|
1019 | !-- set default weights |
---|
1020 | palm_grid%w_verti(i,j,k,1:2) = 0.0_wp |
---|
1021 | |
---|
1022 | IF (point_is_above_grid) THEN |
---|
1023 | |
---|
1024 | palm_grid%kk(i,j,k,1:2) = nlev |
---|
1025 | palm_grid%w_verti(i,j,k,1:2) = - 2.0_wp |
---|
1026 | |
---|
1027 | message = "PALM-4U grid extends above COSMO-DE model top." |
---|
1028 | CALL inifor_abort('find_vertical_neighbours_and_weights', message) |
---|
1029 | |
---|
1030 | ELSE IF (point_is_below_grid) THEN |
---|
1031 | |
---|
1032 | palm_grid%kk(i,j,k,1:2) = 0 |
---|
1033 | palm_grid%w_verti(i,j,k,1:2) = - 2.0_wp |
---|
1034 | |
---|
1035 | ELSE |
---|
1036 | ! |
---|
1037 | !-- cycle through intermediate levels until current |
---|
1038 | !-- intermediate-grid cell overlaps with current_height |
---|
1039 | DO WHILE (.NOT. point_is_in_current_cell .AND. k_intermediate <= nlev-1) |
---|
1040 | k_intermediate = k_intermediate + 1 |
---|
1041 | |
---|
1042 | h_top = palm_intermediate%h(i,j,k_intermediate+1) |
---|
1043 | h_bottom = palm_intermediate%h(i,j,k_intermediate) |
---|
1044 | point_is_in_current_cell = ( & |
---|
1045 | current_height >= h_bottom .AND. & |
---|
1046 | current_height < h_top & |
---|
1047 | ) |
---|
1048 | ENDDO |
---|
1049 | |
---|
1050 | IF (k_intermediate > nlev-1) THEN |
---|
1051 | message = "Index " // TRIM(str(k_intermediate)) // & |
---|
1052 | " is above intermediate grid range." |
---|
1053 | CALL inifor_abort('find_vertical_neighbours', message) |
---|
1054 | ENDIF |
---|
1055 | |
---|
1056 | palm_grid%kk(i,j,k,1) = k_intermediate |
---|
1057 | palm_grid%kk(i,j,k,2) = k_intermediate + 1 |
---|
1058 | |
---|
1059 | ! |
---|
1060 | !-- compute vertical weights |
---|
1061 | weight = (h_top - current_height) / (h_top - h_bottom) |
---|
1062 | palm_grid%w_verti(i,j,k,1) = weight |
---|
1063 | palm_grid%w_verti(i,j,k,2) = 1.0_wp - weight |
---|
1064 | ENDIF |
---|
1065 | |
---|
1066 | ENDDO |
---|
1067 | |
---|
1068 | ENDDO |
---|
1069 | ENDDO |
---|
1070 | |
---|
1071 | END SUBROUTINE find_vertical_neighbours_and_weights_interp |
---|
1072 | |
---|
1073 | |
---|
1074 | !------------------------------------------------------------------------------! |
---|
1075 | ! Description: |
---|
1076 | ! ------------ |
---|
1077 | !> Computes linear vertical interpolation neighbour indices and weights for each |
---|
1078 | !> column of the given averaging grid. |
---|
1079 | !> |
---|
1080 | !> The difference to the _interp variant of this routine lies in how columns |
---|
1081 | !> are adressed. While the _interp variant loops over all PALM grid columns |
---|
1082 | !> given by combinations of all index indices (i,j), this routine loops over a |
---|
1083 | !> subset of COSMO columns, which are sequantlially stored in the index lists |
---|
1084 | !> iii(:) and jjj(:). |
---|
1085 | !------------------------------------------------------------------------------! |
---|
1086 | SUBROUTINE find_vertical_neighbours_and_weights_average( & |
---|
1087 | avg_grid, level_based_averaging & |
---|
1088 | ) |
---|
1089 | |
---|
1090 | TYPE(grid_definition), INTENT(INOUT), TARGET :: avg_grid |
---|
1091 | LOGICAL :: level_based_averaging |
---|
1092 | |
---|
1093 | INTEGER :: i, j, k_palm, k_intermediate, l, nlev |
---|
1094 | LOGICAL :: point_is_below_grid, point_is_above_grid, & |
---|
1095 | point_is_in_current_cell |
---|
1096 | REAL(wp) :: current_height, column_base, column_top, h_top, & |
---|
1097 | h_bottom, weight |
---|
1098 | REAL(wp), POINTER :: cosmo_h(:,:,:) |
---|
1099 | |
---|
1100 | |
---|
1101 | avg_grid%k_min = LBOUND(avg_grid%z, 1) |
---|
1102 | |
---|
1103 | nlev = SIZE(avg_grid%cosmo_h, 3) |
---|
1104 | |
---|
1105 | IF (level_based_averaging) THEN |
---|
1106 | cosmo_h => avg_grid%h |
---|
1107 | ELSE |
---|
1108 | cosmo_h => avg_grid%cosmo_h |
---|
1109 | ENDIF |
---|
1110 | |
---|
1111 | ! |
---|
1112 | !-- in each column of the fine grid, find vertical neighbours of every cell |
---|
1113 | DO l = 1, avg_grid%n_columns |
---|
1114 | |
---|
1115 | IF (level_based_averaging) THEN |
---|
1116 | i = 1 |
---|
1117 | j = 1 |
---|
1118 | ELSE |
---|
1119 | i = avg_grid%iii(l) |
---|
1120 | j = avg_grid%jjj(l) |
---|
1121 | ENDIF |
---|
1122 | |
---|
1123 | column_base = cosmo_h(i,j,1) |
---|
1124 | column_top = cosmo_h(i,j,nlev) |
---|
1125 | |
---|
1126 | ! |
---|
1127 | !-- scan through avg_grid column until and set neighbour indices in |
---|
1128 | !-- case current_height is either below column_base, in the current |
---|
1129 | !-- cell, or above column_top. Keep increasing current cell index until |
---|
1130 | !-- the current cell overlaps with the current_height. |
---|
1131 | k_intermediate = 1 !avg_grid%cosmo_h is indezed 1-based. |
---|
1132 | DO k_palm = 1, avg_grid%nz |
---|
1133 | |
---|
1134 | ! |
---|
1135 | !-- Memorize the top and bottom boundaries of the coarse cell and the |
---|
1136 | !-- current height within it |
---|
1137 | current_height = avg_grid%z(k_palm) + avg_grid%z0 |
---|
1138 | h_top = cosmo_h(i,j,k_intermediate+1) |
---|
1139 | h_bottom = cosmo_h(i,j,k_intermediate) |
---|
1140 | |
---|
1141 | ! |
---|
1142 | !-- COSMO column top is located at 22000m, point_is_above_grid is very |
---|
1143 | !-- unlikely. |
---|
1144 | point_is_above_grid = (current_height > column_top) |
---|
1145 | point_is_below_grid = (current_height < column_base) |
---|
1146 | |
---|
1147 | point_is_in_current_cell = ( & |
---|
1148 | current_height >= h_bottom .AND. & |
---|
1149 | current_height < h_top & |
---|
1150 | ) |
---|
1151 | |
---|
1152 | ! |
---|
1153 | !-- set default weights |
---|
1154 | avg_grid%w(l,k_palm,1:2) = 0.0_wp |
---|
1155 | |
---|
1156 | IF (point_is_above_grid) THEN |
---|
1157 | |
---|
1158 | avg_grid%kkk(l,k_palm,1:2) = nlev |
---|
1159 | avg_grid%w(l,k_palm,1:2) = - 2.0_wp |
---|
1160 | |
---|
1161 | message = "PALM-4U grid extends above COSMO-DE model top." |
---|
1162 | CALL inifor_abort('find_vertical_neighbours_and_weights_average', message) |
---|
1163 | |
---|
1164 | ELSE IF (point_is_below_grid) THEN |
---|
1165 | |
---|
1166 | avg_grid%kkk(l,k_palm,1:2) = 0 |
---|
1167 | avg_grid%w(l,k_palm,1:2) = - 2.0_wp |
---|
1168 | avg_grid%k_min = MAX(k_palm + 1, avg_grid%k_min) |
---|
1169 | ELSE |
---|
1170 | ! |
---|
1171 | !-- cycle through intermediate levels until current |
---|
1172 | !-- intermediate-grid cell overlaps with current_height |
---|
1173 | DO WHILE (.NOT. point_is_in_current_cell .AND. k_intermediate <= nlev-1) |
---|
1174 | k_intermediate = k_intermediate + 1 |
---|
1175 | |
---|
1176 | h_top = cosmo_h(i,j,k_intermediate+1) |
---|
1177 | h_bottom = cosmo_h(i,j,k_intermediate) |
---|
1178 | point_is_in_current_cell = ( & |
---|
1179 | current_height >= h_bottom .AND. & |
---|
1180 | current_height < h_top & |
---|
1181 | ) |
---|
1182 | ENDDO |
---|
1183 | |
---|
1184 | ! |
---|
1185 | !-- k_intermediate = 48 indicates the last section (indices 48 and 49), i.e. |
---|
1186 | !-- k_intermediate = 49 is not the beginning of a valid cell. |
---|
1187 | IF (k_intermediate > nlev-1) THEN |
---|
1188 | message = "Index " // TRIM(str(k_intermediate)) // & |
---|
1189 | " is above intermediate grid range." |
---|
1190 | CALL inifor_abort('find_vertical_neighbours', message) |
---|
1191 | ENDIF |
---|
1192 | |
---|
1193 | avg_grid%kkk(l,k_palm,1) = k_intermediate |
---|
1194 | avg_grid%kkk(l,k_palm,2) = k_intermediate + 1 |
---|
1195 | |
---|
1196 | ! |
---|
1197 | !-- compute vertical weights |
---|
1198 | weight = (h_top - current_height) / (h_top - h_bottom) |
---|
1199 | avg_grid%w(l,k_palm,1) = weight |
---|
1200 | avg_grid%w(l,k_palm,2) = 1.0_wp - weight |
---|
1201 | ENDIF |
---|
1202 | |
---|
1203 | ! |
---|
1204 | !-- Loop over PALM levels k |
---|
1205 | ENDDO |
---|
1206 | |
---|
1207 | ! |
---|
1208 | !-- Loop over averaging columns l |
---|
1209 | ENDDO |
---|
1210 | |
---|
1211 | END SUBROUTINE find_vertical_neighbours_and_weights_average |
---|
1212 | |
---|
1213 | !------------------------------------------------------------------------------! |
---|
1214 | ! Description: |
---|
1215 | ! ------------ |
---|
1216 | !> Compute the four weights for horizontal bilinear interpolation given the |
---|
1217 | !> coordinates clon(i,j) clat(i,j) of the PALM-4U grid in the COSMO-DE |
---|
1218 | !> rotated-pole grid and the neightbour indices ii(i,j,1-4) and jj(i,j,1-4). |
---|
1219 | !> |
---|
1220 | !> Input parameters: |
---|
1221 | !> ----------------- |
---|
1222 | !> palm_grid%clon : longitudes of PALM-4U scalars (cell centres) in COSMO-DE's rotated-pole grid [rad] |
---|
1223 | !> |
---|
1224 | !> palm_grid%clat : latitudes of PALM-4U cell centres in COSMO-DE's rotated-pole grid [rad] |
---|
1225 | !> |
---|
1226 | !> cosmo_grid%lon : rotated-pole longitudes of scalars (cell centres) of the COSMO-DE grid [rad] |
---|
1227 | !> |
---|
1228 | !> cosmo_grid%lat : rotated-pole latitudes of scalars (cell centers) of the COSMO-DE grid [rad] |
---|
1229 | !> |
---|
1230 | !> cosmo_grid%dxi : inverse grid spacing in the first dimension [m^-1] |
---|
1231 | !> |
---|
1232 | !> cosmo_grid%dyi : inverse grid spacing in the second dimension [m^-1] |
---|
1233 | !> |
---|
1234 | !> Output parameters: |
---|
1235 | !> ------------------ |
---|
1236 | !> palm_grid%w_horiz(:,:,1-4) : weights for bilinear horizontal interpolation |
---|
1237 | ! |
---|
1238 | ! COSMO-DE grid |
---|
1239 | ! ------------- |
---|
1240 | ! jj, lat |
---|
1241 | ! ^ j |
---|
1242 | ! | \ i |
---|
1243 | ! jj(i,j,2/3) + ... 2 ---\--------/------ 3 |
---|
1244 | ! | | ^ \ / | |
---|
1245 | ! | | |wp \ / | |
---|
1246 | ! | | v \ / | |
---|
1247 | ! latpos + ............ o/ (i,j) | |
---|
1248 | ! | | : | |
---|
1249 | ! | | :<----wl---->| |
---|
1250 | ! jj(i,j,1/4) + ... 1 -------:----------- 4 |
---|
1251 | ! | : : : |
---|
1252 | ! | : : : |
---|
1253 | ! | : lonpos : |
---|
1254 | ! L-----+--------+------------+------> ii, lon |
---|
1255 | ! ii(i,j,1/2) ii(i,j,3/4) |
---|
1256 | ! |
---|
1257 | !------------------------------------------------------------------------------! |
---|
1258 | SUBROUTINE compute_horizontal_interp_weights(cosmo_lat, cosmo_lon, & |
---|
1259 | palm_clat, palm_clon, palm_ii, palm_jj, palm_w_horiz) |
---|
1260 | |
---|
1261 | REAL(wp), DIMENSION(0:), INTENT(IN) :: cosmo_lat, cosmo_lon |
---|
1262 | REAL(wp) :: cosmo_dxi, cosmo_dyi |
---|
1263 | REAL(wp), DIMENSION(0:,0:), INTENT(IN) :: palm_clat, palm_clon |
---|
1264 | INTEGER, DIMENSION(0:,0:,1:), INTENT(IN) :: palm_ii, palm_jj |
---|
1265 | |
---|
1266 | REAL(wp), DIMENSION(0:,0:,1:), INTENT(OUT) :: palm_w_horiz |
---|
1267 | |
---|
1268 | REAL(wp) :: wlambda, wphi |
---|
1269 | INTEGER :: i, j |
---|
1270 | |
---|
1271 | cosmo_dxi = 1.0_wp / (cosmo_lon(1) - cosmo_lon(0)) |
---|
1272 | cosmo_dyi = 1.0_wp / (cosmo_lat(1) - cosmo_lat(0)) |
---|
1273 | |
---|
1274 | DO j = 0, UBOUND(palm_clon, 2) |
---|
1275 | DO i = 0, UBOUND(palm_clon, 1) |
---|
1276 | |
---|
1277 | ! |
---|
1278 | !-- weight in lambda direction |
---|
1279 | wlambda = ( cosmo_lon(palm_ii(i,j,4)) - palm_clon(i,j) ) * cosmo_dxi |
---|
1280 | |
---|
1281 | ! |
---|
1282 | !-- weight in phi direction |
---|
1283 | wphi = ( cosmo_lat(palm_jj(i,j,2)) - palm_clat(i,j) ) * cosmo_dyi |
---|
1284 | |
---|
1285 | IF (wlambda > 1.0_wp .OR. wlambda < 0.0_wp) THEN |
---|
1286 | message = "Horizontal weight wlambda = " // TRIM(real_to_str(wlambda)) // & |
---|
1287 | " is out bounds." |
---|
1288 | CALL inifor_abort('compute_horizontal_interp_weights', message) |
---|
1289 | ENDIF |
---|
1290 | IF (wphi > 1.0_wp .OR. wphi < 0.0_wp) THEN |
---|
1291 | message = "Horizontal weight wphi = " // TRIM(real_to_str(wphi)) // & |
---|
1292 | " is out bounds." |
---|
1293 | CALL inifor_abort('compute_horizontal_interp_weights', message) |
---|
1294 | ENDIF |
---|
1295 | |
---|
1296 | palm_w_horiz(i,j,1) = wlambda * wphi |
---|
1297 | palm_w_horiz(i,j,2) = wlambda * (1.0_wp - wphi) |
---|
1298 | palm_w_horiz(i,j,3) = (1.0_wp - wlambda) * (1.0_wp - wphi) |
---|
1299 | palm_w_horiz(i,j,4) = 1.0_wp - SUM( palm_w_horiz(i,j,1:3) ) |
---|
1300 | |
---|
1301 | ENDDO |
---|
1302 | ENDDO |
---|
1303 | |
---|
1304 | END SUBROUTINE compute_horizontal_interp_weights |
---|
1305 | |
---|
1306 | |
---|
1307 | !------------------------------------------------------------------------------! |
---|
1308 | ! Description: |
---|
1309 | ! ------------ |
---|
1310 | !> Interpolates u and v components of velocities located at cell faces to the |
---|
1311 | !> cell centres by averaging neighbouring values. |
---|
1312 | !> |
---|
1313 | !> This routine is designed to be used with COSMO-DE arrays where there are the |
---|
1314 | !> same number of grid points for scalars (centres) and velocities (faces). In |
---|
1315 | !> COSMO-DE the velocity points are staggared one half grid spaceing up-grid |
---|
1316 | !> which means the first centre point has to be omitted and is set to zero. |
---|
1317 | !------------------------------------------------------------------------------! |
---|
1318 | SUBROUTINE centre_velocities(u_face, v_face, u_centre, v_centre) |
---|
1319 | REAL(wp), DIMENSION(0:,0:,0:), INTENT(IN) :: u_face, v_face |
---|
1320 | REAL(wp), DIMENSION(0:,0:,0:), INTENT(OUT) :: u_centre, v_centre |
---|
1321 | INTEGER :: nx, ny |
---|
1322 | |
---|
1323 | nx = UBOUND(u_face, 1) |
---|
1324 | ny = UBOUND(u_face, 2) |
---|
1325 | |
---|
1326 | u_centre(0,:,:) = 0.0_wp |
---|
1327 | u_centre(1:,:,:) = 0.5_wp * ( u_face(0:nx-1,:,:) + u_face(1:,:,:) ) |
---|
1328 | |
---|
1329 | v_centre(:,0,:) = 0.0_wp |
---|
1330 | v_centre(:,1:,:) = 0.5_wp * ( v_face(:,0:ny-1,:) + v_face(:,1:,:) ) |
---|
1331 | END SUBROUTINE centre_velocities |
---|
1332 | |
---|
1333 | |
---|
1334 | !------------------------------------------------------------------------------! |
---|
1335 | ! Description: |
---|
1336 | ! ------------ |
---|
1337 | !> Compute the geographical latitude of a point given in rotated-pole cordinates |
---|
1338 | !------------------------------------------------------------------------------! |
---|
1339 | FUNCTION phirot2phi (phirot, rlarot, polphi, polgam) |
---|
1340 | |
---|
1341 | REAL(wp), INTENT (IN) :: polphi !< latitude of the rotated north pole |
---|
1342 | REAL(wp), INTENT (IN) :: phirot !< latitude in the rotated system |
---|
1343 | REAL(wp), INTENT (IN) :: rlarot !< longitude in the rotated system |
---|
1344 | REAL(wp), INTENT (IN) :: polgam !< angle between the north poles of the systems |
---|
1345 | |
---|
1346 | REAL(wp) :: phirot2phi !< latitude in the geographical system |
---|
1347 | |
---|
1348 | REAL(wp) :: zsinpol, zcospol, zphis, zrlas, zarg, zgam |
---|
1349 | |
---|
1350 | zsinpol = SIN(polphi * TO_RADIANS) |
---|
1351 | zcospol = COS(polphi * TO_RADIANS) |
---|
1352 | zphis = phirot * TO_RADIANS |
---|
1353 | |
---|
1354 | IF (rlarot > 180.0_wp) THEN |
---|
1355 | zrlas = rlarot - 360.0_wp |
---|
1356 | ELSE |
---|
1357 | zrlas = rlarot |
---|
1358 | ENDIF |
---|
1359 | zrlas = zrlas * TO_RADIANS |
---|
1360 | |
---|
1361 | IF (polgam /= 0.0_wp) THEN |
---|
1362 | zgam = polgam * TO_RADIANS |
---|
1363 | zarg = zsinpol * SIN (zphis) + & |
---|
1364 | zcospol * COS(zphis) * ( COS(zrlas) * COS(zgam) - & |
---|
1365 | SIN(zgam) * SIN(zrlas) ) |
---|
1366 | ELSE |
---|
1367 | zarg = zcospol * COS (zphis) * COS (zrlas) + zsinpol * SIN (zphis) |
---|
1368 | ENDIF |
---|
1369 | |
---|
1370 | phirot2phi = ASIN (zarg) * TO_DEGREES |
---|
1371 | |
---|
1372 | END FUNCTION phirot2phi |
---|
1373 | |
---|
1374 | |
---|
1375 | !------------------------------------------------------------------------------! |
---|
1376 | ! Description: |
---|
1377 | ! ------------ |
---|
1378 | !> Compute the geographical latitude of a point given in rotated-pole cordinates |
---|
1379 | !------------------------------------------------------------------------------! |
---|
1380 | FUNCTION phi2phirot (phi, rla, polphi, pollam) |
---|
1381 | |
---|
1382 | REAL(wp), INTENT (IN) :: polphi !< latitude of the rotated north pole |
---|
1383 | REAL(wp), INTENT (IN) :: pollam !< longitude of the rotated north pole |
---|
1384 | REAL(wp), INTENT (IN) :: phi !< latitude in the geographical system |
---|
1385 | REAL(wp), INTENT (IN) :: rla !< longitude in the geographical system |
---|
1386 | |
---|
1387 | REAL(wp) :: phi2phirot !< longitude in the rotated system |
---|
1388 | |
---|
1389 | REAL(wp) :: zsinpol, zcospol, zlampol, zphi, zrla, zarg1, zarg2, zrla1 |
---|
1390 | |
---|
1391 | zsinpol = SIN(polphi * TO_RADIANS) |
---|
1392 | zcospol = COS(polphi * TO_RADIANS) |
---|
1393 | zlampol = pollam * TO_RADIANS |
---|
1394 | zphi = phi * TO_RADIANS |
---|
1395 | |
---|
1396 | IF (rla > 180.0_wp) THEN |
---|
1397 | zrla1 = rla - 360.0_wp |
---|
1398 | ELSE |
---|
1399 | zrla1 = rla |
---|
1400 | ENDIF |
---|
1401 | zrla = zrla1 * TO_RADIANS |
---|
1402 | |
---|
1403 | zarg1 = SIN(zphi) * zsinpol |
---|
1404 | zarg2 = COS(zphi) * zcospol * COS(zrla - zlampol) |
---|
1405 | |
---|
1406 | phi2phirot = ASIN(zarg1 + zarg2) * TO_DEGREES |
---|
1407 | |
---|
1408 | END FUNCTION phi2phirot |
---|
1409 | |
---|
1410 | |
---|
1411 | !------------------------------------------------------------------------------! |
---|
1412 | ! Description: |
---|
1413 | ! ------------ |
---|
1414 | !> Compute the geographical longitude of a point given in rotated-pole cordinates |
---|
1415 | !------------------------------------------------------------------------------! |
---|
1416 | FUNCTION rlarot2rla(phirot, rlarot, polphi, pollam, polgam) |
---|
1417 | |
---|
1418 | REAL(wp), INTENT (IN) :: polphi !< latitude of the rotated north pole |
---|
1419 | REAL(wp), INTENT (IN) :: pollam !< longitude of the rotated north pole |
---|
1420 | REAL(wp), INTENT (IN) :: phirot !< latitude in the rotated system |
---|
1421 | REAL(wp), INTENT (IN) :: rlarot !< longitude in the rotated system |
---|
1422 | REAL(wp), INTENT (IN) :: polgam !< angle between the north poles of the systems |
---|
1423 | |
---|
1424 | REAL(wp) :: rlarot2rla !< latitude in the geographical system |
---|
1425 | |
---|
1426 | REAL(wp) :: zsinpol, zcospol, zlampol, zphis, zrlas, zarg1, zarg2, zgam |
---|
1427 | |
---|
1428 | zsinpol = SIN(TO_RADIANS * polphi) |
---|
1429 | zcospol = COS(TO_RADIANS * polphi) |
---|
1430 | zlampol = TO_RADIANS * pollam |
---|
1431 | zphis = TO_RADIANS * phirot |
---|
1432 | |
---|
1433 | IF (rlarot > 180.0_wp) THEN |
---|
1434 | zrlas = rlarot - 360.0_wp |
---|
1435 | ELSE |
---|
1436 | zrlas = rlarot |
---|
1437 | ENDIF |
---|
1438 | zrlas = TO_RADIANS * zrlas |
---|
1439 | |
---|
1440 | IF (polgam /= 0.0_wp) THEN |
---|
1441 | zgam = TO_RADIANS * polgam |
---|
1442 | zarg1 = SIN(zlampol) * (zcospol * SIN(zphis) - zsinpol*COS(zphis) * & |
---|
1443 | (COS(zrlas) * COS(zgam) - SIN(zrlas) * SIN(zgam)) ) - & |
---|
1444 | COS(zlampol) * COS(zphis) * ( SIN(zrlas) * COS(zgam) + & |
---|
1445 | COS(zrlas) * SIN(zgam) ) |
---|
1446 | |
---|
1447 | zarg2 = COS (zlampol) * (zcospol * SIN(zphis) - zsinpol*COS(zphis) * & |
---|
1448 | (COS(zrlas) * COS(zgam) - SIN(zrlas) * SIN(zgam)) ) + & |
---|
1449 | SIN(zlampol) * COS(zphis) * ( SIN(zrlas) * COS(zgam) + & |
---|
1450 | COS(zrlas) * SIN(zgam) ) |
---|
1451 | ELSE |
---|
1452 | zarg1 = SIN (zlampol) * (-zsinpol * COS(zrlas) * COS(zphis) + & |
---|
1453 | zcospol * SIN(zphis)) - & |
---|
1454 | COS (zlampol) * SIN(zrlas) * COS(zphis) |
---|
1455 | zarg2 = COS (zlampol) * (-zsinpol * COS(zrlas) * COS(zphis) + & |
---|
1456 | zcospol * SIN(zphis)) + & |
---|
1457 | SIN (zlampol) * SIN(zrlas) * COS(zphis) |
---|
1458 | ENDIF |
---|
1459 | |
---|
1460 | IF (zarg2 == 0.0_wp) zarg2 = 1.0E-20_wp |
---|
1461 | |
---|
1462 | rlarot2rla = ATAN2(zarg1,zarg2) * TO_DEGREES |
---|
1463 | |
---|
1464 | END FUNCTION rlarot2rla |
---|
1465 | |
---|
1466 | |
---|
1467 | !------------------------------------------------------------------------------! |
---|
1468 | ! Description: |
---|
1469 | ! ------------ |
---|
1470 | !> Compute the rotated-pole longitude of a point given in geographical cordinates |
---|
1471 | !------------------------------------------------------------------------------! |
---|
1472 | FUNCTION rla2rlarot ( phi, rla, polphi, pollam, polgam ) |
---|
1473 | |
---|
1474 | REAL(wp), INTENT (IN) :: polphi !< latitude of the rotated north pole |
---|
1475 | REAL(wp), INTENT (IN) :: pollam !< longitude of the rotated north pole |
---|
1476 | REAL(wp), INTENT (IN) :: phi !< latitude in geographical system |
---|
1477 | REAL(wp), INTENT (IN) :: rla !< longitude in geographical system |
---|
1478 | REAL(wp), INTENT (IN) :: polgam !< angle between the north poles of the systems |
---|
1479 | |
---|
1480 | REAL(wp) :: rla2rlarot !< latitude in the the rotated system |
---|
1481 | |
---|
1482 | REAL(wp) :: zsinpol, zcospol, zlampol, zphi, zrla, zarg1, zarg2, zrla1 |
---|
1483 | |
---|
1484 | zsinpol = SIN(polphi * TO_RADIANS) |
---|
1485 | zcospol = COS(polphi * TO_RADIANS) |
---|
1486 | zlampol = pollam * TO_RADIANS |
---|
1487 | zphi = phi * TO_RADIANS |
---|
1488 | |
---|
1489 | IF (rla > 180.0_wp) THEN |
---|
1490 | zrla1 = rla - 360.0_wp |
---|
1491 | ELSE |
---|
1492 | zrla1 = rla |
---|
1493 | ENDIF |
---|
1494 | zrla = zrla1 * TO_RADIANS |
---|
1495 | |
---|
1496 | zarg1 = - SIN (zrla-zlampol) * COS(zphi) |
---|
1497 | zarg2 = - zsinpol * COS(zphi) * COS(zrla-zlampol) + zcospol * SIN(zphi) |
---|
1498 | |
---|
1499 | IF (zarg2 == 0.0_wp) zarg2 = 1.0E-20_wp |
---|
1500 | |
---|
1501 | rla2rlarot = ATAN2 (zarg1,zarg2) * TO_DEGREES |
---|
1502 | |
---|
1503 | IF (polgam /= 0.0_wp ) THEN |
---|
1504 | rla2rlarot = polgam + rla2rlarot |
---|
1505 | IF (rla2rlarot > 180._wp) rla2rlarot = rla2rlarot - 360.0_wp |
---|
1506 | ENDIF |
---|
1507 | |
---|
1508 | END FUNCTION rla2rlarot |
---|
1509 | |
---|
1510 | |
---|
1511 | !------------------------------------------------------------------------------! |
---|
1512 | ! Description: |
---|
1513 | ! ------------ |
---|
1514 | !> Rotate the given velocity vector (u,v) from the geographical to the |
---|
1515 | !> rotated-pole system |
---|
1516 | !------------------------------------------------------------------------------! |
---|
1517 | SUBROUTINE uv2uvrot(u, v, rlat, rlon, pollat, pollon, urot, vrot) |
---|
1518 | |
---|
1519 | REAL(wp), INTENT (IN) :: u, v !< wind components in the true geographical system |
---|
1520 | REAL(wp), INTENT (IN) :: rlat, rlon !< coordinates in the true geographical system |
---|
1521 | REAL(wp), INTENT (IN) :: pollat, pollon !< latitude and longitude of the north pole of the rotated grid |
---|
1522 | |
---|
1523 | REAL(wp), INTENT (OUT) :: urot, vrot !< wind components in the rotated grid |
---|
1524 | |
---|
1525 | REAL (wp) :: zsinpol, zcospol, zlonp, zlat, zarg1, zarg2, znorm |
---|
1526 | |
---|
1527 | zsinpol = SIN(pollat * TO_RADIANS) |
---|
1528 | zcospol = COS(pollat * TO_RADIANS) |
---|
1529 | zlonp = (pollon-rlon) * TO_RADIANS |
---|
1530 | zlat = rlat * TO_RADIANS |
---|
1531 | |
---|
1532 | zarg1 = zcospol * SIN(zlonp) |
---|
1533 | zarg2 = zsinpol * COS(zlat) - zcospol * SIN(zlat) * COS(zlonp) |
---|
1534 | znorm = 1.0_wp / SQRT(zarg1*zarg1 + zarg2*zarg2) |
---|
1535 | |
---|
1536 | urot = u * zarg2 * znorm - v * zarg1 * znorm |
---|
1537 | vrot = u * zarg1 * znorm + v * zarg2 * znorm |
---|
1538 | |
---|
1539 | END SUBROUTINE uv2uvrot |
---|
1540 | |
---|
1541 | |
---|
1542 | !------------------------------------------------------------------------------! |
---|
1543 | ! Description: |
---|
1544 | ! ------------ |
---|
1545 | !> Rotate the given velocity vector (urot, vrot) from the rotated-pole to the |
---|
1546 | !> geographical system |
---|
1547 | !------------------------------------------------------------------------------! |
---|
1548 | SUBROUTINE uvrot2uv (urot, vrot, rlat, rlon, pollat, pollon, u, v) |
---|
1549 | |
---|
1550 | REAL(wp), INTENT(IN) :: urot, vrot !< wind components in the rotated grid |
---|
1551 | REAL(wp), INTENT(IN) :: rlat, rlon !< latitude and longitude in the true geographical system |
---|
1552 | REAL(wp), INTENT(IN) :: pollat, pollon !< latitude and longitude of the north pole of the rotated grid |
---|
1553 | |
---|
1554 | REAL(wp), INTENT(OUT) :: u, v !< wind components in the true geographical system |
---|
1555 | |
---|
1556 | REAL(wp) :: zsinpol, zcospol, zlonp, zlat, zarg1, zarg2, znorm |
---|
1557 | |
---|
1558 | zsinpol = SIN(pollat * TO_RADIANS) |
---|
1559 | zcospol = COS(pollat * TO_RADIANS) |
---|
1560 | zlonp = (pollon-rlon) * TO_RADIANS |
---|
1561 | zlat = rlat * TO_RADIANS |
---|
1562 | |
---|
1563 | zarg1 = zcospol * SIN(zlonp) |
---|
1564 | zarg2 = zsinpol * COS(zlat) - zcospol * SIN(zlat) * COS(zlonp) |
---|
1565 | znorm = 1.0_wp / SQRT(zarg1*zarg1 + zarg2*zarg2) |
---|
1566 | |
---|
1567 | u = urot * zarg2 * znorm + vrot * zarg1 * znorm |
---|
1568 | v = - urot * zarg1 * znorm + vrot * zarg2 * znorm |
---|
1569 | |
---|
1570 | END SUBROUTINE uvrot2uv |
---|
1571 | |
---|
1572 | END MODULE inifor_transform |
---|
1573 | #endif |
---|
1574 | |
---|