1 | !> @file src/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 2017-2018 Leibniz Universitaet Hannover |
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18 | ! Copyright 2017-2018 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: transform.f90 3395 2018-10-22 17:32:49Z eckhard $ |
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28 | ! Switched addressing of averaging regions from index bounds to list of columns |
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29 | ! Added routines for the computation of geostrophic winds including: |
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30 | ! - the downward extrapolation of density (linear) and |
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31 | ! - pressure (hydrostatic equation) and |
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32 | ! - rotation of geostrophic wind components to PALM frame of reference |
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33 | ! |
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34 | ! 3183 2018-07-27 14:25:55Z suehring |
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35 | ! Introduced new PALM grid stretching |
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36 | ! Removed unnecessary subroutine parameters |
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37 | ! Renamed kcur to k_intermediate |
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38 | ! |
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39 | ! |
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40 | ! 3182 2018-07-27 13:36:03Z suehring |
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41 | ! Initial revision |
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42 | ! |
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43 | ! |
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44 | ! |
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45 | ! Authors: |
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46 | ! -------- |
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47 | ! @author Eckhard Kadasch |
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48 | ! |
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49 | ! Description: |
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50 | ! ------------ |
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51 | !> The transform module provides INIFOR's low-level transformation and |
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52 | !> interpolation routines. The rotated-pole transformation routines phirot2phi, |
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53 | !> phi2phirot, rlarot2rla, rla2rlarot, uv2uvrot, and uvrot2uv are adapted from |
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54 | !> int2lm's utility routines. |
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55 | !------------------------------------------------------------------------------! |
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56 | MODULE transform |
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57 | |
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58 | USE control |
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59 | USE defs, & |
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60 | ONLY: G, TO_DEGREES, TO_RADIANS, PI, dp |
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61 | USE types |
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62 | USE util, & |
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63 | ONLY: real_to_str, str |
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64 | |
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65 | IMPLICIT NONE |
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66 | |
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67 | CONTAINS |
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68 | |
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69 | !------------------------------------------------------------------------------! |
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70 | ! Description: |
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71 | ! ------------ |
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72 | !> Interpolates linearly in the vertical direction in very column (i,j) of the |
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73 | !> output array outvar(i,j,:) using values of the source array invar. In cells |
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74 | !> that are outside the COSMO-DE domain, indicated by negative interpolation |
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75 | !> weights, extrapolate constantly from the cell above. |
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76 | !> |
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77 | !> Input parameters: |
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78 | !> ----------------- |
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79 | !> invar : Array of source data |
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80 | !> |
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81 | !> outgrid % kk : Array of vertical neighbour indices. kk(i,j,k,:) contain the |
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82 | !> indices of the two vertical neighbors of PALM-4U point (i,j,k) on the |
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83 | !> input grid corresponding to the source data invar. |
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84 | !> |
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85 | !> outgrid % w_verti : Array of weights for vertical linear interpolation |
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86 | !> corresponding to neighbour points indexed by kk. |
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87 | !> |
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88 | !> Output papameters: |
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89 | !> ------------------ |
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90 | !> outvar : Array of interpolated data |
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91 | !------------------------------------------------------------------------------! |
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92 | SUBROUTINE interpolate_1d(in_arr, out_arr, outgrid) |
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93 | TYPE(grid_definition), INTENT(IN) :: outgrid |
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94 | REAL(dp), INTENT(IN) :: in_arr(0:,0:,0:) |
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95 | REAL(dp), INTENT(OUT) :: out_arr(0:,0:,:) |
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96 | |
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97 | INTEGER :: i, j, k, l, nz |
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98 | |
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99 | nz = UBOUND(out_arr, 3) |
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100 | |
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101 | DO j = LBOUND(out_arr, 2), UBOUND(out_arr, 2) |
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102 | DO i = LBOUND(out_arr, 1), UBOUND(out_arr, 1) |
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103 | DO k = nz, LBOUND(out_arr, 3), -1 |
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104 | |
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105 | ! TODO: Remove IF clause and extrapolate based on a critical vertical |
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106 | ! TODO: index marking the lower bound of COSMO-DE data coverage. |
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107 | ! Check for negative interpolation weights indicating grid points |
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108 | ! below COSMO-DE domain and extrapolate from the top in such cells. |
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109 | IF (outgrid % w_verti(i,j,k,1) < -1.0_dp .AND. k < nz) THEN |
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110 | out_arr(i,j,k) = out_arr(i,j,k+1) |
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111 | ELSE |
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112 | out_arr(i,j,k) = 0.0_dp |
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113 | DO l = 1, 2 |
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114 | out_arr(i,j,k) = out_arr(i,j,k) + & |
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115 | outgrid % w_verti(i,j,k,l) * & |
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116 | in_arr(i,j,outgrid % kk(i,j,k, l) ) |
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117 | END DO |
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118 | END IF |
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119 | END DO |
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120 | END DO |
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121 | END DO |
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122 | END SUBROUTINE interpolate_1d |
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123 | |
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124 | |
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125 | !------------------------------------------------------------------------------! |
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126 | ! Description: |
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127 | ! ------------ |
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128 | !> Interpolates bi-linearly in horizontal planes on every k level of the output |
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129 | !> array outvar(:,:,k) using values of the source array invar(:,:,:). The source |
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130 | !> (invar) and interpolation array (outvar) need to have matching dimensions. |
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131 | !> |
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132 | !> Input parameters: |
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133 | !> ----------------- |
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134 | !> invar : Array of source data |
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135 | !> |
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136 | !> outgrid % ii, % jj : Array of neighbour indices in x and y direction. |
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137 | !> ii(i,j,k,:), and jj(i,j,k,:) contain the four horizontal neighbour points |
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138 | !> of PALM-4U point (i,j,k) on the input grid corresponding to the source |
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139 | !> data invar. (The outgrid carries the relationship with the ingrid in the |
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140 | ! form of the interpoaltion weights.) |
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141 | !> |
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142 | !> outgrid % w_horiz: Array of weights for horizontal bi-linear interpolation |
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143 | !> corresponding to neighbour points indexed by ii and jj. |
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144 | !> |
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145 | !> Output papameters: |
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146 | !> ------------------ |
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147 | !> outvar : Array of interpolated data |
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148 | !------------------------------------------------------------------------------! |
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149 | SUBROUTINE interpolate_2d(invar, outvar, outgrid, ncvar) |
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150 | ! I index 0-based for the indices of the outvar to be consistent with the |
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151 | ! outgrid indices and interpolation weights. |
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152 | TYPE(grid_definition), INTENT(IN) :: outgrid |
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153 | REAL(dp), INTENT(IN) :: invar(0:,0:,0:) |
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154 | REAL(dp), INTENT(OUT) :: outvar(0:,0:,0:) |
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155 | TYPE(nc_var), INTENT(IN), OPTIONAL :: ncvar |
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156 | |
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157 | INTEGER :: i, j, k, l |
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158 | |
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159 | ! TODO: check if input dimensions are consistent, i.e. ranges are correct |
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160 | IF (UBOUND(outvar, 3) .GT. UBOUND(invar, 3)) THEN |
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161 | message = "Output array for '" // TRIM(ncvar % name) // "' has ' more levels (" // & |
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162 | TRIM(str(UBOUND(outvar, 3))) // ") than input variable ("//& |
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163 | TRIM(str(UBOUND(invar, 3))) // ")." |
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164 | CALL abort('interpolate_2d', message) |
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165 | END IF |
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166 | |
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167 | DO k = 0, UBOUND(outvar, 3) |
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168 | DO j = 0, UBOUND(outvar, 2) |
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169 | DO i = 0, UBOUND(outvar, 1) |
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170 | outvar(i,j,k) = 0.0_dp |
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171 | DO l = 1, 4 |
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172 | |
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173 | outvar(i,j,k) = outvar(i,j,k) + & |
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174 | outgrid % w_horiz(i,j,l) * invar( outgrid % ii(i,j,l), & |
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175 | outgrid % jj(i,j,l), & |
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176 | k ) |
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177 | END DO |
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178 | END DO |
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179 | END DO |
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180 | END DO |
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181 | |
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182 | END SUBROUTINE interpolate_2d |
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183 | |
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184 | |
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185 | SUBROUTINE average_2d(in_arr, out_arr, ii, jj) |
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186 | REAL(dp), INTENT(IN) :: in_arr(0:,0:,0:) |
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187 | REAL(dp), INTENT(OUT) :: out_arr(0:) |
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188 | INTEGER, INTENT(IN), DIMENSION(:) :: ii, jj |
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189 | |
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190 | INTEGER :: i, j, k, l |
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191 | REAL(dp) :: ni |
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192 | |
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193 | IF (SIZE(ii) .NE. SIZE(jj)) THEN |
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194 | message = "Length of 'ii' and 'jj' index lists do not match." // & |
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195 | NEW_LINE(' ') // "ii has " // str(SIZE(ii)) // " elements, " // & |
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196 | NEW_LINE(' ') // "jj has " // str(SIZE(jj)) // "." |
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197 | CALL abort('average_2d', message) |
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198 | END IF |
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199 | |
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200 | DO k = 0, UBOUND(out_arr, 1) |
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201 | |
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202 | out_arr(k) = 0.0_dp |
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203 | DO l = 1, UBOUND(ii, 1) |
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204 | i = ii(l) |
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205 | j = jj(l) |
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206 | out_arr(k) = out_arr(k) +& |
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207 | in_arr(i, j, k) |
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208 | END DO |
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209 | |
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210 | END DO |
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211 | |
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212 | ni = 1.0_dp / SIZE(ii) |
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213 | out_arr(:) = out_arr(:) * ni |
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214 | |
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215 | END SUBROUTINE average_2d |
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216 | |
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217 | |
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218 | SUBROUTINE interpolate_3d(source_array, palm_array, palm_intermediate, palm_grid) |
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219 | TYPE(grid_definition), INTENT(IN) :: palm_intermediate, palm_grid |
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220 | REAL(dp), DIMENSION(:,:,:), INTENT(IN) :: source_array |
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221 | REAL(dp), DIMENSION(:,:,:), INTENT(OUT) :: palm_array |
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222 | REAL(dp), DIMENSION(:,:,:), ALLOCATABLE :: intermediate_array |
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223 | INTEGER :: nx, ny, nlev |
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224 | |
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225 | nx = palm_intermediate % nx |
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226 | ny = palm_intermediate % ny |
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227 | nlev = palm_intermediate % nz ! nlev |
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228 | |
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229 | ! Interpolate from COSMO-DE to intermediate grid. Allocating with one |
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230 | ! less point in the vertical, since scalars like T have 50 instead of 51 |
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231 | ! points in COSMO-DE. |
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232 | ALLOCATE(intermediate_array(0:nx, 0:ny, 0:nlev-1)) ! |
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233 | |
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234 | CALL interpolate_2d(source_array, intermediate_array, palm_intermediate) |
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235 | |
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236 | ! Interpolate from intermediate grid to palm_grid grid, includes |
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237 | ! extrapolation for cells below COSMO-DE domain. |
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238 | CALL interpolate_1d(intermediate_array, palm_array, palm_grid) |
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239 | |
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240 | DEALLOCATE(intermediate_array) |
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241 | |
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242 | END SUBROUTINE interpolate_3d |
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243 | |
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244 | |
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245 | SUBROUTINE average_profile(source_array, profile_array, avg_grid) |
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246 | TYPE(grid_definition), INTENT(IN) :: avg_grid |
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247 | REAL(dp), DIMENSION(:,:,:), INTENT(IN) :: source_array |
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248 | REAL(dp), DIMENSION(:), INTENT(OUT) :: profile_array |
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249 | |
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250 | INTEGER :: i_source, j_source, k_profile, k_source, l, m |
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251 | |
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252 | REAL :: ni_columns |
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253 | |
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254 | profile_array(:) = 0.0_dp |
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255 | |
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256 | DO l = 1, avg_grid % n_columns |
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257 | i_source = avg_grid % iii(l) |
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258 | j_source = avg_grid % jjj(l) |
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259 | |
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260 | DO k_profile = avg_grid % k_min, UBOUND(profile_array, 1) ! PALM levels |
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261 | |
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262 | DO m = 1, 2 ! vertical interpolation neighbours |
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263 | |
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264 | k_source = avg_grid % kkk(l, k_profile, m) |
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265 | |
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266 | profile_array(k_profile) = profile_array(k_profile) & |
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267 | + avg_grid % w(l, k_profile, m) & |
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268 | * source_array(i_source, j_source, k_source) |
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269 | |
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270 | END DO ! m, vertical interpolation neighbours |
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271 | |
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272 | END DO ! k_profile, PALM levels |
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273 | |
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274 | END DO ! l, horizontal neighbours |
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275 | |
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276 | ni_columns = 1.0_dp / avg_grid % n_columns |
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277 | profile_array(:) = profile_array(:) * ni_columns |
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278 | |
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279 | ! Extrapolate constant to the bottom |
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280 | profile_array(1:avg_grid % k_min-1) = profile_array(avg_grid % k_min) |
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281 | |
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282 | END SUBROUTINE average_profile |
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283 | |
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284 | |
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285 | SUBROUTINE extrapolate_density(rho, avg_grid) |
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286 | REAL(dp), DIMENSION(:), INTENT(INOUT) :: rho |
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287 | TYPE(grid_definition), INTENT(IN) :: avg_grid |
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288 | |
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289 | REAL(dp) :: drhodz, dz, zk, rhok |
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290 | INTEGER :: k_min |
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291 | |
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292 | k_min = avg_grid % k_min |
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293 | zk = avg_grid % z(k_min) |
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294 | rhok = rho(k_min) |
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295 | dz = avg_grid % z(k_min + 1) - avg_grid % z(k_min) |
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296 | drhodz = (rho(k_min + 1) - rho(k_min)) / dz |
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297 | |
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298 | rho(1:k_min-1) = rhok + drhodz * (avg_grid % z(1:k_min-1) - zk) |
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299 | |
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300 | END SUBROUTINE extrapolate_density |
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301 | |
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302 | |
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303 | SUBROUTINE extrapolate_pressure(p, rho, avg_grid) |
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304 | REAL(dp), DIMENSION(:), INTENT(IN) :: rho |
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305 | REAL(dp), DIMENSION(:), INTENT(INOUT) :: p |
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306 | TYPE(grid_definition), INTENT(IN) :: avg_grid |
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307 | |
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308 | REAL(dp) :: drhodz, dz, zk, rhok |
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309 | INTEGER :: k, k_min |
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310 | |
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311 | k_min = avg_grid % k_min |
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312 | zk = avg_grid % z(k_min) |
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313 | rhok = rho(k_min) |
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314 | dz = avg_grid % z(k_min + 1) - avg_grid % z(k_min) |
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315 | drhodz = 0.5_dp * (rho(k_min + 1) - rho(k_min)) / dz |
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316 | |
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317 | DO k = 1, k_min-1 |
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318 | p(k) = constant_density_pressure(p(k_min), zk, rhok, drhodz, & |
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319 | avg_grid % z(k), G) |
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320 | END DO |
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321 | |
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322 | END SUBROUTINE extrapolate_pressure |
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323 | |
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324 | |
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325 | !------------------------------------------------------------------------------! |
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326 | ! Description: |
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327 | ! ------------ |
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328 | !> Takes the averaged pressure profile <p> and sets the lowest entry to the |
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329 | !> extrapolated pressure at the surface. |
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330 | !------------------------------------------------------------------------------! |
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331 | SUBROUTINE get_surface_pressure(p, rho, avg_grid) |
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332 | REAL(dp), DIMENSION(:), INTENT(IN) :: rho |
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333 | REAL(dp), DIMENSION(:), INTENT(INOUT) :: p |
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334 | TYPE(grid_definition), INTENT(IN) :: avg_grid |
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335 | |
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336 | REAL(dp) :: drhodz, dz, zk, rhok |
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337 | INTEGER :: k, k_min |
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338 | |
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339 | k_min = avg_grid % k_min |
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340 | zk = avg_grid % z(k_min) |
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341 | rhok = rho(k_min) |
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342 | dz = avg_grid % z(k_min + 1) - avg_grid % z(k_min) |
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343 | drhodz = 0.5_dp * (rho(k_min + 1) - rho(k_min)) / dz |
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344 | |
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345 | p(1) = constant_density_pressure(p(k_min), zk, rhok, drhodz, & |
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346 | 0.0, G) |
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347 | |
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348 | END SUBROUTINE get_surface_pressure |
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349 | |
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350 | |
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351 | FUNCTION constant_density_pressure(pk, zk, rhok, drhodz, z, g) RESULT(p) |
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352 | |
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353 | REAL(dp), INTENT(IN) :: pk, zk, rhok, drhodz, g, z |
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354 | REAL(dp) :: p |
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355 | |
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356 | p = pk + ( zk - z ) * g * ( rhok + 0.5*drhodz * (zk - z) ) |
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357 | |
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358 | END FUNCTION constant_density_pressure |
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359 | |
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360 | !-----------------------------------------------------------------------------! |
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361 | ! Description: |
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362 | ! ----------- |
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363 | !> This routine computes profiles of the two geostrophic wind components ug and |
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364 | !> vg. |
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365 | !-----------------------------------------------------------------------------! |
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366 | SUBROUTINE geostrophic_winds(p_north, p_south, p_east, p_west, rho, f3, & |
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367 | Lx, Ly, phi_n, lam_n, phi_g, lam_g, ug, vg) |
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368 | |
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369 | REAL(dp), DIMENSION(:), INTENT(IN) :: p_north, p_south, p_east, p_west, & |
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370 | rho |
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371 | REAL(dp), INTENT(IN) :: f3, Lx, Ly, phi_n, lam_n, phi_g, lam_g |
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372 | REAL(dp), DIMENSION(:), INTENT(OUT) :: ug, vg |
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373 | REAL(dp) :: facx, facy |
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374 | |
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375 | facx = 1.0_dp / (Lx * f3) |
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376 | facy = 1.0_dp / (Ly * f3) |
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377 | ug(:) = - facy / rho(:) * (p_north(:) - p_south(:)) |
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378 | vg(:) = facx / rho(:) * (p_east(:) - p_west(:)) |
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379 | |
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380 | CALL rotate_vector_field( & |
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381 | ug, vg, angle = meridian_convergence_rotated(phi_n, lam_n, phi_g, lam_g)& |
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382 | ) |
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383 | |
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384 | END SUBROUTINE geostrophic_winds |
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385 | |
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386 | |
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387 | !-----------------------------------------------------------------------------! |
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388 | ! Description: |
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389 | ! ----------- |
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390 | !> This routine computes the inverse Plate Carree projection, i.e. in projects |
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391 | !> Cartesian coordinates (x,y) onto a sphere. It returns the latitude and |
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392 | !> lngitude of a geographical system centered at x0 and y0. |
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393 | !-----------------------------------------------------------------------------! |
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394 | SUBROUTINE inv_plate_carree(x, y, x0, y0, r, lat, lon) |
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395 | REAL(dp), INTENT(IN) :: x(:), y(:), x0, y0, r |
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396 | REAL(dp), INTENT(OUT) :: lat(:), lon(:) |
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397 | |
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398 | REAL(dp) :: ri |
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399 | |
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400 | ! TODO check dimensions of lat/lon and y/x match |
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401 | |
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402 | ri = 1.0_dp / r |
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403 | |
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404 | lat(:) = (y(:) - y0) * ri |
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405 | lon(:) = (x(:) - x0) * ri |
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406 | END SUBROUTINE |
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407 | |
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408 | |
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409 | !-----------------------------------------------------------------------------! |
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410 | ! Description: |
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411 | ! ------------ |
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412 | !> Computes the reverse Plate-Carree projection of a x or y position on a |
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413 | !> Cartesian grid. |
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414 | !> |
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415 | !> Input parameters: |
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416 | !> ----------------- |
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417 | !> xy : x or y coordinate of the Cartasian grid point [m]. |
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418 | !> |
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419 | !> xy0 : x or y coordinate that coincides with the origin of the underlying |
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420 | !> sperical system (crossing point of the equator and prime meridian) [m]. |
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421 | !> |
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422 | !> r : Radius of the of the underlying sphere, e.g. EARTH_RADIUS [m]. |
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423 | !> |
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424 | !> Returns: |
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425 | !> -------- |
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426 | !> project : Longitude (in case xy = x) or latitude (xy = y) of the given input |
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427 | !> coordinate xy. |
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428 | !------------------------------------------------------------------------------! |
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429 | ELEMENTAL REAL(dp) FUNCTION project(xy, xy0, r) |
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430 | REAL(dp), INTENT(IN) :: xy, xy0, r |
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431 | REAL(dp) :: ri |
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432 | |
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433 | ! If this elemental function is called with a large array as xy, it is |
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434 | ! computationally more efficient to precompute the inverse radius and |
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435 | ! then muliply. |
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436 | ri = 1.0_dp / r |
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437 | |
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438 | project = (xy - xy0) * ri |
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439 | |
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440 | END FUNCTION project |
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441 | |
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442 | |
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443 | REAL(dp) FUNCTION phic_to_phin(phi_c) |
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444 | REAL(dp), INTENT(IN) :: phi_c |
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445 | |
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446 | phic_to_phin = 0.5_dp * PI - ABS(phi_c) |
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447 | |
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448 | END FUNCTION phic_to_phin |
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449 | |
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450 | |
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451 | REAL(dp) FUNCTION lamc_to_lamn(phi_c, lam_c) |
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452 | REAL(dp), INTENT(IN) :: phi_c, lam_c |
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453 | |
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454 | lamc_to_lamn = lam_c |
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455 | IF (phi_c > 0.0_dp) THEN |
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456 | lamc_to_lamn = lam_c - SIGN(PI, lam_c) |
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457 | END IF |
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458 | |
---|
459 | END FUNCTION lamc_to_lamn |
---|
460 | |
---|
461 | |
---|
462 | REAL(dp) FUNCTION gamma_from_hemisphere(phi_cg, phi_ref) |
---|
463 | REAL(dp), INTENT(IN) :: phi_cg, phi_ref |
---|
464 | LOGICAL :: palm_centre_is_south_of_cosmo_origin |
---|
465 | |
---|
466 | palm_centre_is_south_of_cosmo_origin = (phi_cg < phi_ref) |
---|
467 | |
---|
468 | IF (palm_centre_is_south_of_cosmo_origin) THEN |
---|
469 | gamma_from_hemisphere = PI |
---|
470 | ELSE |
---|
471 | gamma_from_hemisphere = 0.0_dp |
---|
472 | END IF |
---|
473 | END FUNCTION gamma_from_hemisphere |
---|
474 | |
---|
475 | |
---|
476 | !------------------------------------------------------------------------------! |
---|
477 | ! Description: |
---|
478 | ! ------------ |
---|
479 | !> Computes the geographical coordinates corresponding to the given rotated-pole |
---|
480 | !> coordinates. |
---|
481 | !> |
---|
482 | !> In INIFOR, this routine is used to convert coordinates between two |
---|
483 | !> rotated-pole systems: COSMO-DE's rotated-pole system, and one centred at the |
---|
484 | !> PALM-4U domain centre. In this case, the PALM-4U system is thought of as the |
---|
485 | !> rotated-pole system and the routine is used to rotate back to COSMO-DE's |
---|
486 | !> system which is thought of as the geographical one. |
---|
487 | !> |
---|
488 | !> Input parameters: |
---|
489 | !> ----------------- |
---|
490 | !> phir(:), lamr(: ): latitudes and longitudes of the rotated-pole grid |
---|
491 | !> |
---|
492 | !> phip, lamp: latitude and longitude of the rotated north pole |
---|
493 | !> |
---|
494 | !> gam: "angle between the north poles. If [gam] is not present, the other |
---|
495 | !> system is the real geographical system." (original phiro2rot |
---|
496 | !> description) |
---|
497 | !> |
---|
498 | !> Output parameters: |
---|
499 | !> ------------------ |
---|
500 | !> phi(:,:), lam(:,:): geographical latitudes and logitudes |
---|
501 | !------------------------------------------------------------------------------! |
---|
502 | SUBROUTINE rotate_to_cosmo(phir, lamr, phip, lamp, phi, lam, gam) |
---|
503 | REAL(dp), INTENT(IN) :: phir(0:), lamr(0:), phip, lamp, gam |
---|
504 | REAL(dp), INTENT(OUT) :: phi(0:,0:), lam(0:,0:) |
---|
505 | |
---|
506 | INTEGER :: i, j |
---|
507 | |
---|
508 | IF ( SIZE(phi, 1) .NE. SIZE(lam, 1) .OR. & |
---|
509 | SIZE(phi, 2) .NE. SIZE(lam, 2) ) THEN |
---|
510 | PRINT *, "inifor: rotate_to_cosmo: Dimensions of phi and lambda do not match. Dimensions are:" |
---|
511 | PRINT *, "inifor: rotate_to_cosmo: phi: ", SIZE(phi, 1), SIZE(phi, 2) |
---|
512 | PRINT *, "inifor: rotate_to_cosmo: lam: ", SIZE(lam, 1), SIZE(lam, 2) |
---|
513 | STOP |
---|
514 | END IF |
---|
515 | |
---|
516 | IF ( SIZE(phir) .NE. SIZE(phi, 2) .OR. & |
---|
517 | SIZE(lamr) .NE. SIZE(phi, 1) ) THEN |
---|
518 | PRINT *, "inifor: rotate_to_cosmo: Dimensions of phir and lamr do not match. Dimensions are:" |
---|
519 | PRINT *, "inifor: rotate_to_cosmo: phir: ", SIZE(phir), SIZE(phi, 2) |
---|
520 | PRINT *, "inifor: rotate_to_cosmo: lamr: ", SIZE(lamr), SIZE(phi, 1) |
---|
521 | STOP |
---|
522 | END IF |
---|
523 | |
---|
524 | DO j = 0, UBOUND(phir, 1) |
---|
525 | DO i = 0, UBOUND(lamr, 1) |
---|
526 | |
---|
527 | phi(i,j) = phirot2phi(phir(j) * TO_DEGREES, & |
---|
528 | lamr(i) * TO_DEGREES, & |
---|
529 | phip * TO_DEGREES, & |
---|
530 | lamp * TO_DEGREES, & |
---|
531 | gam * TO_DEGREES) * TO_RADIANS |
---|
532 | |
---|
533 | lam(i,j) = rlarot2rla(phir(j) * TO_DEGREES, & |
---|
534 | lamr(i) * TO_DEGREES, & |
---|
535 | phip * TO_DEGREES, & |
---|
536 | lamp * TO_DEGREES, & |
---|
537 | gam * TO_DEGREES) * TO_RADIANS |
---|
538 | |
---|
539 | END DO |
---|
540 | END DO |
---|
541 | |
---|
542 | END SUBROUTINE rotate_to_cosmo |
---|
543 | |
---|
544 | |
---|
545 | SUBROUTINE rotate_vector_field(x, y, angle) |
---|
546 | REAL(dp), DIMENSION(:), INTENT(INOUT) :: x, y !< x and y coodrinate in arbitrary units |
---|
547 | REAL(dp), INTENT(IN) :: angle !< rotation angle [deg] |
---|
548 | |
---|
549 | INTEGER :: i |
---|
550 | REAL(dp) :: sine, cosine, v_rot(2), rotation(2,2) |
---|
551 | |
---|
552 | sine = SIN(angle * TO_RADIANS) |
---|
553 | cosine = COS(angle * TO_RADIANS) |
---|
554 | ! RESAHPE() fills columns first, so the rotation matrix becomes |
---|
555 | ! |
---|
556 | ! rotation = [ cosine -sine ] |
---|
557 | ! [ sine cosine ] |
---|
558 | rotation = RESHAPE( (/cosine, sine, -sine, cosine/), (/2, 2/) ) |
---|
559 | |
---|
560 | DO i = LBOUND(x, 1), UBOUND(x, 1) |
---|
561 | |
---|
562 | v_rot(:) = MATMUL(rotation, (/x(i), y(i)/)) |
---|
563 | |
---|
564 | x(i) = v_rot(1) |
---|
565 | y(i) = v_rot(2) |
---|
566 | |
---|
567 | END DO |
---|
568 | |
---|
569 | END SUBROUTINE rotate_vector_field |
---|
570 | |
---|
571 | |
---|
572 | |
---|
573 | !------------------------------------------------------------------------------! |
---|
574 | ! Description: |
---|
575 | ! ------------ |
---|
576 | !> This routine computes the local meridian convergence between a rotated-pole |
---|
577 | !> and a geographical system using the Eq. (6) given in the DWD manual |
---|
578 | !> |
---|
579 | !> Baldauf et al. (2018), Beschreibung des operationelle KuÌrzestfrist- |
---|
580 | !> vorhersagemodells COSMO-D2 und COSMO-D2-EPS und seiner Ausgabe in die |
---|
581 | !> Datenbanken des DWD. |
---|
582 | !> https://www.dwd.de/SharedDocs/downloads/DE/modelldokumentationen/nwv/cosmo_d2/cosmo_d2_dbbeschr_aktuell.pdf?__blob=publicationFile&v=2 |
---|
583 | !> |
---|
584 | FUNCTION meridian_convergence_rotated(phi_n, lam_n, phi_g, lam_g) & |
---|
585 | RESULT(delta) |
---|
586 | |
---|
587 | REAL(dp), INTENT(IN) :: phi_n, lam_n, phi_g, lam_g |
---|
588 | REAL(dp) :: delta |
---|
589 | |
---|
590 | delta = atan2( COS(phi_n) * SIN(lam_n - lam_g), & |
---|
591 | COS(phi_g) * SIN(phi_n) - & |
---|
592 | SIN(phi_g) * COS(phi_n) * COS(lam_n - lam_g) ) |
---|
593 | |
---|
594 | END FUNCTION meridian_convergence_rotated |
---|
595 | |
---|
596 | !------------------------------------------------------------------------------! |
---|
597 | ! Description: |
---|
598 | ! ------------ |
---|
599 | !> Compute indices of PALM-4U grid point neighbours in the target |
---|
600 | !> system (COSMO-DE) by rounding up and down. (i,j) are the indices of |
---|
601 | !> the PALM-4U grid and (ii(i,j,1-4), jj(i,j,1-4)) contain the indices |
---|
602 | !> of the its four neigbouring points in the COSMO-DE grid. |
---|
603 | !> |
---|
604 | !> |
---|
605 | !> COSMO-DE grid |
---|
606 | !> ------------- |
---|
607 | !> jj, lat |
---|
608 | !> ^ j |
---|
609 | !> | \ i |
---|
610 | !> jj(i,j,2/3) + ... 2 ---\--------/------ 3 |
---|
611 | !> | | ^ \ / | |
---|
612 | !> | | |wp \ / | |
---|
613 | !> | | v \ / | |
---|
614 | !> latpos + ............ o/ (i,j) | |
---|
615 | !> | | : | |
---|
616 | !> | | :<----wl---->| |
---|
617 | !> jj(i,j,1/4) + ... 1 -------:----------- 4 |
---|
618 | !> | : : : |
---|
619 | !> | : : : |
---|
620 | !> | : lonpos : |
---|
621 | !> L-----+--------+------------+------> ii, lon |
---|
622 | !> ii(i,j,1/2) ii(i,j,3/4) |
---|
623 | !> |
---|
624 | !> |
---|
625 | !> Input parameters: |
---|
626 | !> ----------------- |
---|
627 | !> source_lat, source_lon : (rotated-pole) coordinates of the source grid (e.g. |
---|
628 | !> COSMO-DE) |
---|
629 | !> |
---|
630 | !> source_dxi, source_dyi : inverse grid spacings of the source grid. |
---|
631 | !> |
---|
632 | !> target_lat, target_lon : (rotated-pole) coordinates of the target grid (e.g. |
---|
633 | !> COSMO-DE) |
---|
634 | !> |
---|
635 | !> Output parameters: |
---|
636 | !> ------------------ |
---|
637 | !> palm_ii, palm_jj : x and y index arrays of horizontal neighbour columns |
---|
638 | !> |
---|
639 | !------------------------------------------------------------------------------! |
---|
640 | SUBROUTINE find_horizontal_neighbours(cosmo_lat, cosmo_lon, & |
---|
641 | palm_clat, palm_clon, & |
---|
642 | palm_ii, palm_jj) |
---|
643 | |
---|
644 | REAL(dp), DIMENSION(0:), INTENT(IN) :: cosmo_lat, cosmo_lon |
---|
645 | REAL(dp), DIMENSION(0:,0:), INTENT(IN) :: palm_clat, palm_clon |
---|
646 | REAL(dp) :: cosmo_dxi, cosmo_dyi |
---|
647 | INTEGER, DIMENSION(0:,0:,1:), INTENT(OUT) :: palm_ii, palm_jj |
---|
648 | |
---|
649 | REAL(dp) :: lonpos, latpos, lon0, lat0 |
---|
650 | INTEGER :: i, j |
---|
651 | |
---|
652 | lon0 = cosmo_lon(0) |
---|
653 | lat0 = cosmo_lat(0) |
---|
654 | cosmo_dxi = 1.0_dp / (cosmo_lon(1) - cosmo_lon(0)) |
---|
655 | cosmo_dyi = 1.0_dp / (cosmo_lat(1) - cosmo_lat(0)) |
---|
656 | |
---|
657 | DO j = 0, UBOUND(palm_clon, 2)!palm_grid % ny |
---|
658 | DO i = 0, UBOUND(palm_clon, 1)!palm_grid % nx |
---|
659 | ! Compute the floating point index corrseponding to PALM-4U grid point |
---|
660 | ! location along target grid (COSMO-DE) axes. |
---|
661 | lonpos = (palm_clon(i,j) - lon0) * cosmo_dxi |
---|
662 | latpos = (palm_clat(i,j) - lat0) * cosmo_dyi |
---|
663 | |
---|
664 | IF (lonpos < 0.0 .OR. latpos < 0.0) THEN |
---|
665 | PRINT *, " Error while finding neighbours: lonpos or latpos out of bounds!" |
---|
666 | PRINT *, " (i,j) = (", i, ",",j,")" |
---|
667 | PRINT *, " lonpos ", lonpos*TO_DEGREES, ", latpos ", latpos*TO_DEGREES |
---|
668 | PRINT *, " lon0 ", lon0 *TO_DEGREES, ", lat0 ", lat0*TO_DEGREES |
---|
669 | PRINT *, " PALM lon ", palm_clon(i,j)*TO_DEGREES, ", PALM lat ",palm_clat(i,j)*TO_DEGREES |
---|
670 | STOP |
---|
671 | END IF |
---|
672 | |
---|
673 | palm_ii(i,j,1) = FLOOR(lonpos) |
---|
674 | palm_ii(i,j,2) = FLOOR(lonpos) |
---|
675 | palm_ii(i,j,3) = CEILING(lonpos) |
---|
676 | palm_ii(i,j,4) = CEILING(lonpos) |
---|
677 | |
---|
678 | palm_jj(i,j,1) = FLOOR(latpos) |
---|
679 | palm_jj(i,j,2) = CEILING(latpos) |
---|
680 | palm_jj(i,j,3) = CEILING(latpos) |
---|
681 | palm_jj(i,j,4) = FLOOR(latpos) |
---|
682 | END DO |
---|
683 | END DO |
---|
684 | |
---|
685 | END SUBROUTINE find_horizontal_neighbours |
---|
686 | |
---|
687 | |
---|
688 | SUBROUTINE find_vertical_neighbours_and_weights_interp( palm_grid, & |
---|
689 | palm_intermediate ) |
---|
690 | TYPE(grid_definition), INTENT(INOUT) :: palm_grid |
---|
691 | TYPE(grid_definition), INTENT(IN) :: palm_intermediate |
---|
692 | |
---|
693 | INTEGER :: i, j, k, nx, ny, nz, nlev, k_intermediate |
---|
694 | LOGICAL :: point_is_below_grid, point_is_above_grid, & |
---|
695 | point_is_in_current_cell |
---|
696 | REAL(dp) :: current_height, column_base, column_top, h_top, h_bottom, & |
---|
697 | weight |
---|
698 | |
---|
699 | nx = palm_grid % nx |
---|
700 | ny = palm_grid % ny |
---|
701 | nz = palm_grid % nz |
---|
702 | nlev = palm_intermediate % nz |
---|
703 | |
---|
704 | ! in each column of the fine grid, find vertical neighbours of every cell |
---|
705 | DO j = 0, ny |
---|
706 | DO i = 0, nx |
---|
707 | |
---|
708 | k_intermediate = 0 |
---|
709 | |
---|
710 | column_base = palm_intermediate % h(i,j,0) |
---|
711 | column_top = palm_intermediate % h(i,j,nlev) |
---|
712 | |
---|
713 | ! scan through palm_grid column and set neighbour indices in |
---|
714 | ! case current_height is either below column_base, in the current |
---|
715 | ! cell, or above column_top. Keep increasing current cell index until |
---|
716 | ! the current cell overlaps with the current_height. |
---|
717 | DO k = 1, nz |
---|
718 | |
---|
719 | ! Memorize the top and bottom boundaries of the coarse cell and the |
---|
720 | ! current height within it |
---|
721 | current_height = palm_grid % z(k) + palm_grid % z0 |
---|
722 | h_top = palm_intermediate % h(i,j,k_intermediate+1) |
---|
723 | h_bottom = palm_intermediate % h(i,j,k_intermediate) |
---|
724 | |
---|
725 | point_is_above_grid = (current_height > column_top) !22000m, very unlikely |
---|
726 | point_is_below_grid = (current_height < column_base) |
---|
727 | |
---|
728 | point_is_in_current_cell = ( & |
---|
729 | current_height >= h_bottom .AND. & |
---|
730 | current_height < h_top & |
---|
731 | ) |
---|
732 | |
---|
733 | ! set default weights |
---|
734 | palm_grid % w_verti(i,j,k,1:2) = 0.0_dp |
---|
735 | |
---|
736 | IF (point_is_above_grid) THEN |
---|
737 | |
---|
738 | palm_grid % kk(i,j,k,1:2) = nlev |
---|
739 | palm_grid % w_verti(i,j,k,1:2) = - 2.0_dp |
---|
740 | |
---|
741 | message = "PALM-4U grid extends above COSMO-DE model top." |
---|
742 | CALL abort('find_vertical_neighbours_and_weights', message) |
---|
743 | |
---|
744 | ELSE IF (point_is_below_grid) THEN |
---|
745 | |
---|
746 | palm_grid % kk(i,j,k,1:2) = 0 |
---|
747 | palm_grid % w_verti(i,j,k,1:2) = - 2.0_dp |
---|
748 | |
---|
749 | ELSE |
---|
750 | ! cycle through intermediate levels until current |
---|
751 | ! intermediate-grid cell overlaps with current_height |
---|
752 | DO WHILE (.NOT. point_is_in_current_cell .AND. k_intermediate <= nlev-1) |
---|
753 | k_intermediate = k_intermediate + 1 |
---|
754 | |
---|
755 | h_top = palm_intermediate % h(i,j,k_intermediate+1) |
---|
756 | h_bottom = palm_intermediate % h(i,j,k_intermediate) |
---|
757 | point_is_in_current_cell = ( & |
---|
758 | current_height >= h_bottom .AND. & |
---|
759 | current_height < h_top & |
---|
760 | ) |
---|
761 | END DO |
---|
762 | |
---|
763 | IF (k_intermediate > nlev-1) THEN |
---|
764 | message = "Index " // TRIM(str(k_intermediate)) // & |
---|
765 | " is above intermediate grid range." |
---|
766 | CALL abort('find_vertical_neighbours', message) |
---|
767 | END IF |
---|
768 | |
---|
769 | palm_grid % kk(i,j,k,1) = k_intermediate |
---|
770 | palm_grid % kk(i,j,k,2) = k_intermediate + 1 |
---|
771 | |
---|
772 | ! copmute vertical weights |
---|
773 | weight = (h_top - current_height) / (h_top - h_bottom) |
---|
774 | palm_grid % w_verti(i,j,k,1) = weight |
---|
775 | palm_grid % w_verti(i,j,k,2) = 1.0_dp - weight |
---|
776 | END IF |
---|
777 | |
---|
778 | END DO |
---|
779 | |
---|
780 | END DO |
---|
781 | END DO |
---|
782 | |
---|
783 | END SUBROUTINE find_vertical_neighbours_and_weights_interp |
---|
784 | |
---|
785 | |
---|
786 | SUBROUTINE find_vertical_neighbours_and_weights_average( avg_grid ) |
---|
787 | TYPE(grid_definition), INTENT(INOUT) :: avg_grid |
---|
788 | |
---|
789 | INTEGER :: i, j, k_palm, k_intermediate, l, nlev |
---|
790 | LOGICAL :: point_is_below_grid, point_is_above_grid, & |
---|
791 | point_is_in_current_cell |
---|
792 | REAL(dp) :: current_height, column_base, column_top, h_top, h_bottom, & |
---|
793 | weight |
---|
794 | |
---|
795 | |
---|
796 | avg_grid % k_min = LBOUND(avg_grid % z, 1) |
---|
797 | |
---|
798 | nlev = SIZE(avg_grid % cosmo_h, 3) |
---|
799 | |
---|
800 | ! in each column of the fine grid, find vertical neighbours of every cell |
---|
801 | DO l = 1, avg_grid % n_columns |
---|
802 | |
---|
803 | i = avg_grid % iii(l) |
---|
804 | j = avg_grid % jjj(l) |
---|
805 | |
---|
806 | column_base = avg_grid % cosmo_h(i,j,1) |
---|
807 | column_top = avg_grid % cosmo_h(i,j,nlev) |
---|
808 | |
---|
809 | ! scan through avg_grid column until and set neighbour indices in |
---|
810 | ! case current_height is either below column_base, in the current |
---|
811 | ! cell, or above column_top. Keep increasing current cell index until |
---|
812 | ! the current cell overlaps with the current_height. |
---|
813 | k_intermediate = 1 !avg_grid % cosmo_h is indezed 1-based. |
---|
814 | DO k_palm = 1, avg_grid % nz |
---|
815 | |
---|
816 | ! Memorize the top and bottom boundaries of the coarse cell and the |
---|
817 | ! current height within it |
---|
818 | current_height = avg_grid % z(k_palm) + avg_grid % z0 |
---|
819 | h_top = avg_grid % cosmo_h(i,j,k_intermediate+1) |
---|
820 | h_bottom = avg_grid % cosmo_h(i,j,k_intermediate) |
---|
821 | |
---|
822 | point_is_above_grid = (current_height > column_top) !22000m, very unlikely |
---|
823 | point_is_below_grid = (current_height < column_base) |
---|
824 | |
---|
825 | point_is_in_current_cell = ( & |
---|
826 | current_height >= h_bottom .AND. & |
---|
827 | current_height < h_top & |
---|
828 | ) |
---|
829 | |
---|
830 | ! set default weights |
---|
831 | avg_grid % w(l,k_palm,1:2) = 0.0_dp |
---|
832 | |
---|
833 | IF (point_is_above_grid) THEN |
---|
834 | |
---|
835 | avg_grid % kkk(l,k_palm,1:2) = nlev |
---|
836 | avg_grid % w(l,k_palm,1:2) = - 2.0_dp |
---|
837 | |
---|
838 | message = "PALM-4U grid extends above COSMO-DE model top." |
---|
839 | CALL abort('find_vertical_neighbours_and_weights_average', message) |
---|
840 | |
---|
841 | ELSE IF (point_is_below_grid) THEN |
---|
842 | |
---|
843 | avg_grid % kkk(l,k_palm,1:2) = 0 |
---|
844 | avg_grid % w(l,k_palm,1:2) = - 2.0_dp |
---|
845 | avg_grid % k_min = MAX(k_palm + 1, avg_grid % k_min) |
---|
846 | ELSE |
---|
847 | ! cycle through intermediate levels until current |
---|
848 | ! intermediate-grid cell overlaps with current_height |
---|
849 | DO WHILE (.NOT. point_is_in_current_cell .AND. k_intermediate <= nlev-1) |
---|
850 | k_intermediate = k_intermediate + 1 |
---|
851 | |
---|
852 | h_top = avg_grid % cosmo_h(i,j,k_intermediate+1) |
---|
853 | h_bottom = avg_grid % cosmo_h(i,j,k_intermediate) |
---|
854 | point_is_in_current_cell = ( & |
---|
855 | current_height >= h_bottom .AND. & |
---|
856 | current_height < h_top & |
---|
857 | ) |
---|
858 | END DO |
---|
859 | |
---|
860 | ! k_intermediate = 48 indicates the last section (indices 48 and 49), i.e. |
---|
861 | ! k_intermediate = 49 is not the beginning of a valid cell. |
---|
862 | IF (k_intermediate > nlev-1) THEN |
---|
863 | message = "Index " // TRIM(str(k_intermediate)) // & |
---|
864 | " is above intermediate grid range." |
---|
865 | CALL abort('find_vertical_neighbours', message) |
---|
866 | END IF |
---|
867 | |
---|
868 | avg_grid % kkk(l,k_palm,1) = k_intermediate |
---|
869 | avg_grid % kkk(l,k_palm,2) = k_intermediate + 1 |
---|
870 | |
---|
871 | ! copmute vertical weights |
---|
872 | weight = (h_top - current_height) / (h_top - h_bottom) |
---|
873 | avg_grid % w(l,k_palm,1) = weight |
---|
874 | avg_grid % w(l,k_palm,2) = 1.0_dp - weight |
---|
875 | END IF |
---|
876 | |
---|
877 | END DO ! k, PALM levels |
---|
878 | END DO ! l, averaging columns |
---|
879 | |
---|
880 | END SUBROUTINE find_vertical_neighbours_and_weights_average |
---|
881 | |
---|
882 | !------------------------------------------------------------------------------! |
---|
883 | ! Description: |
---|
884 | ! ------------ |
---|
885 | !> Compute the four weights for horizontal bilinear interpolation given the |
---|
886 | !> coordinates clon(i,j) clat(i,j) of the PALM-4U grid in the COSMO-DE |
---|
887 | !> rotated-pole grid and the neightbour indices ii(i,j,1-4) and jj(i,j,1-4). |
---|
888 | !> |
---|
889 | !> Input parameters: |
---|
890 | !> ----------------- |
---|
891 | !> palm_grid % clon : longitudes of PALM-4U scalars (cell centres) in COSMO-DE's rotated-pole grid [rad] |
---|
892 | !> |
---|
893 | !> palm_grid % clat : latitudes of PALM-4U cell centres in COSMO-DE's rotated-pole grid [rad] |
---|
894 | !> |
---|
895 | !> cosmo_grid % lon : rotated-pole longitudes of scalars (cell centres) of the COSMO-DE grid [rad] |
---|
896 | !> |
---|
897 | !> cosmo_grid % lat : rotated-pole latitudes of scalars (cell centers) of the COSMO-DE grid [rad] |
---|
898 | !> |
---|
899 | !> cosmo_grid % dxi : inverse grid spacing in the first dimension [m^-1] |
---|
900 | !> |
---|
901 | !> cosmo_grid % dyi : inverse grid spacing in the second dimension [m^-1] |
---|
902 | !> |
---|
903 | !> Output parameters: |
---|
904 | !> ------------------ |
---|
905 | !> palm_grid % w_horiz(:,:,1-4) : weights for bilinear horizontal interpolation |
---|
906 | ! |
---|
907 | ! COSMO-DE grid |
---|
908 | ! ------------- |
---|
909 | ! jj, lat |
---|
910 | ! ^ j |
---|
911 | ! | \ i |
---|
912 | ! jj(i,j,2/3) + ... 2 ---\--------/------ 3 |
---|
913 | ! | | ^ \ / | |
---|
914 | ! | | |wp \ / | |
---|
915 | ! | | v \ / | |
---|
916 | ! latpos + ............ o/ (i,j) | |
---|
917 | ! | | : | |
---|
918 | ! | | :<----wl---->| |
---|
919 | ! jj(i,j,1/4) + ... 1 -------:----------- 4 |
---|
920 | ! | : : : |
---|
921 | ! | : : : |
---|
922 | ! | : lonpos : |
---|
923 | ! L-----+--------+------------+------> ii, lon |
---|
924 | ! ii(i,j,1/2) ii(i,j,3/4) |
---|
925 | ! |
---|
926 | SUBROUTINE compute_horizontal_interp_weights(cosmo_lat, cosmo_lon, & |
---|
927 | palm_clat, palm_clon, palm_ii, palm_jj, palm_w_horiz) |
---|
928 | |
---|
929 | REAL(dp), DIMENSION(0:), INTENT(IN) :: cosmo_lat, cosmo_lon |
---|
930 | REAL(dp) :: cosmo_dxi, cosmo_dyi |
---|
931 | REAL(dp), DIMENSION(0:,0:), INTENT(IN) :: palm_clat, palm_clon |
---|
932 | INTEGER, DIMENSION(0:,0:,1:), INTENT(IN) :: palm_ii, palm_jj |
---|
933 | |
---|
934 | REAL(dp), DIMENSION(0:,0:,1:), INTENT(OUT) :: palm_w_horiz |
---|
935 | |
---|
936 | REAL(dp) :: wl, wp |
---|
937 | INTEGER :: i, j |
---|
938 | |
---|
939 | cosmo_dxi = 1.0_dp / (cosmo_lon(1) - cosmo_lon(0)) |
---|
940 | cosmo_dyi = 1.0_dp / (cosmo_lat(1) - cosmo_lat(0)) |
---|
941 | |
---|
942 | DO j = 0, UBOUND(palm_clon, 2) |
---|
943 | DO i = 0, UBOUND(palm_clon, 1) |
---|
944 | |
---|
945 | ! weight in lambda direction |
---|
946 | wl = ( cosmo_lon(palm_ii(i,j,4)) - palm_clon(i,j) ) * cosmo_dxi |
---|
947 | |
---|
948 | ! weight in phi direction |
---|
949 | wp = ( cosmo_lat(palm_jj(i,j,2)) - palm_clat(i,j) ) * cosmo_dyi |
---|
950 | |
---|
951 | IF (wl > 1.0_dp .OR. wl < 0.0_dp) THEN |
---|
952 | message = "Horizontal weight wl = " // TRIM(real_to_str(wl)) // & |
---|
953 | " is out bounds." |
---|
954 | CALL abort('compute_horizontal_interp_weights', message) |
---|
955 | END IF |
---|
956 | IF (wp > 1.0_dp .OR. wp < 0.0_dp) THEN |
---|
957 | message = "Horizontal weight wp = " // TRIM(real_to_str(wp)) // & |
---|
958 | " is out bounds." |
---|
959 | CALL abort('compute_horizontal_interp_weights', message) |
---|
960 | END IF |
---|
961 | |
---|
962 | palm_w_horiz(i,j,1) = wl * wp |
---|
963 | palm_w_horiz(i,j,2) = wl * (1.0_dp - wp) |
---|
964 | palm_w_horiz(i,j,3) = (1.0_dp - wl) * (1.0_dp - wp) |
---|
965 | palm_w_horiz(i,j,4) = 1.0_dp - SUM( palm_w_horiz(i,j,1:3) ) |
---|
966 | |
---|
967 | END DO |
---|
968 | END DO |
---|
969 | |
---|
970 | END SUBROUTINE compute_horizontal_interp_weights |
---|
971 | |
---|
972 | |
---|
973 | !------------------------------------------------------------------------------! |
---|
974 | ! Description: |
---|
975 | ! ------------ |
---|
976 | !> Interpolates u and v components of velocities located at cell faces to the |
---|
977 | !> cell centres by averaging neighbouring values. |
---|
978 | !> |
---|
979 | !> This routine is designed to be used with COSMO-DE arrays where there are the |
---|
980 | !> same number of grid points for scalars (centres) and velocities (faces). In |
---|
981 | !> COSMO-DE the velocity points are staggared one half grid spaceing up-grid |
---|
982 | !> which means the first centre point has to be omitted and is set to zero. |
---|
983 | SUBROUTINE centre_velocities(u_face, v_face, u_centre, v_centre) |
---|
984 | REAL(dp), DIMENSION(0:,0:,0:), INTENT(IN) :: u_face, v_face |
---|
985 | REAL(dp), DIMENSION(0:,0:,0:), INTENT(OUT) :: u_centre, v_centre |
---|
986 | INTEGER :: nx, ny |
---|
987 | |
---|
988 | nx = UBOUND(u_face, 1) |
---|
989 | ny = UBOUND(u_face, 2) |
---|
990 | |
---|
991 | u_centre(0,:,:) = 0.0_dp |
---|
992 | u_centre(1:,:,:) = 0.5_dp * ( u_face(0:nx-1,:,:) + u_face(1:,:,:) ) |
---|
993 | |
---|
994 | v_centre(:,0,:) = 0.0_dp |
---|
995 | v_centre(:,1:,:) = 0.5_dp * ( v_face(:,0:ny-1,:) + v_face(:,1:,:) ) |
---|
996 | END SUBROUTINE centre_velocities |
---|
997 | |
---|
998 | |
---|
999 | FUNCTION phirot2phi (phirot, rlarot, polphi, pollam, polgam) |
---|
1000 | |
---|
1001 | REAL(dp), INTENT (IN) :: polphi !< latitude of the rotated north pole |
---|
1002 | REAL(dp), INTENT (IN) :: pollam !< longitude of the rotated north pole |
---|
1003 | REAL(dp), INTENT (IN) :: phirot !< latitude in the rotated system |
---|
1004 | REAL(dp), INTENT (IN) :: rlarot !< longitude in the rotated system |
---|
1005 | REAL(dp), INTENT (IN) :: polgam !< angle between the north poles of the systems |
---|
1006 | |
---|
1007 | REAL(dp) :: phirot2phi !< latitude in the geographical system |
---|
1008 | |
---|
1009 | REAL(dp) :: zsinpol, zcospol, zphis, zrlas, zarg, zgam |
---|
1010 | |
---|
1011 | zsinpol = SIN(polphi * TO_RADIANS) |
---|
1012 | zcospol = COS(polphi * TO_RADIANS) |
---|
1013 | zphis = phirot * TO_RADIANS |
---|
1014 | |
---|
1015 | IF (rlarot > 180.0_dp) THEN |
---|
1016 | zrlas = rlarot - 360.0_dp |
---|
1017 | ELSE |
---|
1018 | zrlas = rlarot |
---|
1019 | END IF |
---|
1020 | zrlas = zrlas * TO_RADIANS |
---|
1021 | |
---|
1022 | IF (polgam /= 0.0_dp) THEN |
---|
1023 | zgam = polgam * TO_RADIANS |
---|
1024 | zarg = zsinpol * SIN (zphis) + & |
---|
1025 | zcospol * COS(zphis) * ( COS(zrlas) * COS(zgam) - & |
---|
1026 | SIN(zgam) * SIN(zrlas) ) |
---|
1027 | ELSE |
---|
1028 | zarg = zcospol * COS (zphis) * COS (zrlas) + zsinpol * SIN (zphis) |
---|
1029 | END IF |
---|
1030 | |
---|
1031 | phirot2phi = ASIN (zarg) * TO_DEGREES |
---|
1032 | |
---|
1033 | END FUNCTION phirot2phi |
---|
1034 | |
---|
1035 | |
---|
1036 | FUNCTION phi2phirot (phi, rla, polphi, pollam) |
---|
1037 | |
---|
1038 | REAL(dp), INTENT (IN) :: polphi !< latitude of the rotated north pole |
---|
1039 | REAL(dp), INTENT (IN) :: pollam !< longitude of the rotated north pole |
---|
1040 | REAL(dp), INTENT (IN) :: phi !< latitude in the geographical system |
---|
1041 | REAL(dp), INTENT (IN) :: rla !< longitude in the geographical system |
---|
1042 | |
---|
1043 | REAL(dp) :: phi2phirot !< longitude in the rotated system |
---|
1044 | |
---|
1045 | REAL(dp) :: zsinpol, zcospol, zlampol, zphi, zrla, zarg1, zarg2, zrla1 |
---|
1046 | |
---|
1047 | zsinpol = SIN(polphi * TO_RADIANS) |
---|
1048 | zcospol = COS(polphi * TO_RADIANS) |
---|
1049 | zlampol = pollam * TO_RADIANS |
---|
1050 | zphi = phi * TO_RADIANS |
---|
1051 | |
---|
1052 | IF (rla > 180.0_dp) THEN |
---|
1053 | zrla1 = rla - 360.0_dp |
---|
1054 | ELSE |
---|
1055 | zrla1 = rla |
---|
1056 | END IF |
---|
1057 | zrla = zrla1 * TO_RADIANS |
---|
1058 | |
---|
1059 | zarg1 = SIN(zphi) * zsinpol |
---|
1060 | zarg2 = COS(zphi) * zcospol * COS(zrla - zlampol) |
---|
1061 | |
---|
1062 | phi2phirot = ASIN(zarg1 + zarg2) * TO_DEGREES |
---|
1063 | |
---|
1064 | END FUNCTION phi2phirot |
---|
1065 | |
---|
1066 | |
---|
1067 | FUNCTION rlarot2rla(phirot, rlarot, polphi, pollam, polgam) |
---|
1068 | |
---|
1069 | REAL(dp), INTENT (IN) :: polphi !< latitude of the rotated north pole |
---|
1070 | REAL(dp), INTENT (IN) :: pollam !< longitude of the rotated north pole |
---|
1071 | REAL(dp), INTENT (IN) :: phirot !< latitude in the rotated system |
---|
1072 | REAL(dp), INTENT (IN) :: rlarot !< longitude in the rotated system |
---|
1073 | REAL(dp), INTENT (IN) :: polgam !< angle between the north poles of the systems |
---|
1074 | |
---|
1075 | REAL(dp) :: rlarot2rla !< latitude in the geographical system |
---|
1076 | |
---|
1077 | REAL(dp) :: zsinpol, zcospol, zlampol, zphis, zrlas, zarg1, zarg2, zgam |
---|
1078 | |
---|
1079 | zsinpol = SIN(TO_RADIANS * polphi) |
---|
1080 | zcospol = COS(TO_RADIANS * polphi) |
---|
1081 | zlampol = TO_RADIANS * pollam |
---|
1082 | zphis = TO_RADIANS * phirot |
---|
1083 | |
---|
1084 | IF (rlarot > 180.0_dp) THEN |
---|
1085 | zrlas = rlarot - 360.0_dp |
---|
1086 | ELSE |
---|
1087 | zrlas = rlarot |
---|
1088 | END IF |
---|
1089 | zrlas = TO_RADIANS * zrlas |
---|
1090 | |
---|
1091 | IF (polgam /= 0.0_dp) THEN |
---|
1092 | zgam = TO_RADIANS * polgam |
---|
1093 | zarg1 = SIN(zlampol) * (zcospol * SIN(zphis) - zsinpol*COS(zphis) * & |
---|
1094 | (COS(zrlas) * COS(zgam) - SIN(zrlas) * SIN(zgam)) ) - & |
---|
1095 | COS(zlampol) * COS(zphis) * ( SIN(zrlas) * COS(zgam) + & |
---|
1096 | COS(zrlas) * SIN(zgam) ) |
---|
1097 | |
---|
1098 | zarg2 = COS (zlampol) * (zcospol * SIN(zphis) - zsinpol*COS(zphis) * & |
---|
1099 | (COS(zrlas) * COS(zgam) - SIN(zrlas) * SIN(zgam)) ) + & |
---|
1100 | SIN(zlampol) * COS(zphis) * ( SIN(zrlas) * COS(zgam) + & |
---|
1101 | COS(zrlas) * SIN(zgam) ) |
---|
1102 | ELSE |
---|
1103 | zarg1 = SIN (zlampol) * (-zsinpol * COS(zrlas) * COS(zphis) + & |
---|
1104 | zcospol * SIN(zphis)) - & |
---|
1105 | COS (zlampol) * SIN(zrlas) * COS(zphis) |
---|
1106 | zarg2 = COS (zlampol) * (-zsinpol * COS(zrlas) * COS(zphis) + & |
---|
1107 | zcospol * SIN(zphis)) + & |
---|
1108 | SIN (zlampol) * SIN(zrlas) * COS(zphis) |
---|
1109 | END IF |
---|
1110 | |
---|
1111 | IF (zarg2 == 0.0_dp) zarg2 = 1.0E-20_dp |
---|
1112 | |
---|
1113 | rlarot2rla = ATAN2(zarg1,zarg2) * TO_DEGREES |
---|
1114 | |
---|
1115 | END FUNCTION rlarot2rla |
---|
1116 | |
---|
1117 | |
---|
1118 | FUNCTION rla2rlarot ( phi, rla, polphi, pollam, polgam ) |
---|
1119 | |
---|
1120 | REAL(dp), INTENT (IN) :: polphi !< latitude of the rotated north pole |
---|
1121 | REAL(dp), INTENT (IN) :: pollam !< longitude of the rotated north pole |
---|
1122 | REAL(dp), INTENT (IN) :: phi !< latitude in geographical system |
---|
1123 | REAL(dp), INTENT (IN) :: rla !< longitude in geographical system |
---|
1124 | REAL(dp), INTENT (IN) :: polgam !< angle between the north poles of the systems |
---|
1125 | |
---|
1126 | REAL (KIND=dp) :: rla2rlarot !< latitude in the the rotated system |
---|
1127 | |
---|
1128 | REAL (KIND=dp) :: zsinpol, zcospol, zlampol, zphi, zrla, zarg1, zarg2, zrla1 |
---|
1129 | |
---|
1130 | zsinpol = SIN(polphi * TO_RADIANS) |
---|
1131 | zcospol = COS(polphi * TO_RADIANS) |
---|
1132 | zlampol = pollam * TO_RADIANS |
---|
1133 | zphi = phi * TO_RADIANS |
---|
1134 | |
---|
1135 | IF (rla > 180.0_dp) THEN |
---|
1136 | zrla1 = rla - 360.0_dp |
---|
1137 | ELSE |
---|
1138 | zrla1 = rla |
---|
1139 | END IF |
---|
1140 | zrla = zrla1 * TO_RADIANS |
---|
1141 | |
---|
1142 | zarg1 = - SIN (zrla-zlampol) * COS(zphi) |
---|
1143 | zarg2 = - zsinpol * COS(zphi) * COS(zrla-zlampol) + zcospol * SIN(zphi) |
---|
1144 | |
---|
1145 | IF (zarg2 == 0.0_dp) zarg2 = 1.0E-20_dp |
---|
1146 | |
---|
1147 | rla2rlarot = ATAN2 (zarg1,zarg2) * TO_DEGREES |
---|
1148 | |
---|
1149 | IF (polgam /= 0.0_dp ) THEN |
---|
1150 | rla2rlarot = polgam + rla2rlarot |
---|
1151 | IF (rla2rlarot > 180._dp) rla2rlarot = rla2rlarot - 360.0_dp |
---|
1152 | END IF |
---|
1153 | |
---|
1154 | END FUNCTION rla2rlarot |
---|
1155 | |
---|
1156 | |
---|
1157 | SUBROUTINE uv2uvrot(u, v, rlat, rlon, pollat, pollon, urot, vrot) |
---|
1158 | |
---|
1159 | REAL(dp), INTENT (IN) :: u, v !< wind components in the true geographical system |
---|
1160 | REAL(dp), INTENT (IN) :: rlat, rlon !< coordinates in the true geographical system |
---|
1161 | REAL(dp), INTENT (IN) :: pollat, pollon !< latitude and longitude of the north pole of the rotated grid |
---|
1162 | |
---|
1163 | REAL(dp), INTENT (OUT) :: urot, vrot !< wind components in the rotated grid |
---|
1164 | |
---|
1165 | REAL (dp) :: zsinpol, zcospol, zlonp, zlat, zarg1, zarg2, znorm |
---|
1166 | |
---|
1167 | zsinpol = SIN(pollat * TO_RADIANS) |
---|
1168 | zcospol = COS(pollat * TO_RADIANS) |
---|
1169 | zlonp = (pollon-rlon) * TO_RADIANS |
---|
1170 | zlat = rlat * TO_RADIANS |
---|
1171 | |
---|
1172 | zarg1 = zcospol * SIN(zlonp) |
---|
1173 | zarg2 = zsinpol * COS(zlat) - zcospol * SIN(zlat) * COS(zlonp) |
---|
1174 | znorm = 1.0_dp / SQRT(zarg1*zarg1 + zarg2*zarg2) |
---|
1175 | |
---|
1176 | urot = u * zarg2 * znorm - v * zarg1 * znorm |
---|
1177 | vrot = u * zarg1 * znorm + v * zarg2 * znorm |
---|
1178 | |
---|
1179 | END SUBROUTINE uv2uvrot |
---|
1180 | |
---|
1181 | |
---|
1182 | SUBROUTINE uvrot2uv (urot, vrot, rlat, rlon, pollat, pollon, u, v) |
---|
1183 | |
---|
1184 | REAL(dp), INTENT(IN) :: urot, vrot !< wind components in the rotated grid |
---|
1185 | REAL(dp), INTENT(IN) :: rlat, rlon !< latitude and longitude in the true geographical system |
---|
1186 | REAL(dp), INTENT(IN) :: pollat, pollon !< latitude and longitude of the north pole of the rotated grid |
---|
1187 | |
---|
1188 | REAL(dp), INTENT(OUT) :: u, v !< wind components in the true geographical system |
---|
1189 | |
---|
1190 | REAL(dp) :: zsinpol, zcospol, zlonp, zlat, zarg1, zarg2, znorm |
---|
1191 | |
---|
1192 | zsinpol = SIN(pollat * TO_RADIANS) |
---|
1193 | zcospol = COS(pollat * TO_RADIANS) |
---|
1194 | zlonp = (pollon-rlon) * TO_RADIANS |
---|
1195 | zlat = rlat * TO_RADIANS |
---|
1196 | |
---|
1197 | zarg1 = zcospol * SIN(zlonp) |
---|
1198 | zarg2 = zsinpol * COS(zlat) - zcospol * SIN(zlat) * COS(zlonp) |
---|
1199 | znorm = 1.0_dp / SQRT(zarg1*zarg1 + zarg2*zarg2) |
---|
1200 | |
---|
1201 | u = urot * zarg2 * znorm + vrot * zarg1 * znorm |
---|
1202 | v = - urot * zarg1 * znorm + vrot * zarg2 * znorm |
---|
1203 | |
---|
1204 | END SUBROUTINE uvrot2uv |
---|
1205 | |
---|
1206 | END MODULE |
---|
1207 | |
---|