1 | !!---------------------------------------------------------------------- |
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2 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
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3 | !! $Id$ |
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4 | !! Software governed by the CeCILL license (see ./LICENSE) |
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5 | !!---------------------------------------------------------------------- |
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6 | |
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7 | SUBROUTINE obs_int_h2d_init( kpk, kpk2, k2dint, plam, pphi, & |
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8 | & pglam, pgphi, pmask, pweig, pobsmask, & |
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9 | & iminpoints ) |
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10 | !!----------------------------------------------------------------------- |
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11 | !! |
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12 | !! *** ROUTINE obs_int_h2d *** |
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13 | !! |
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14 | !! ** Purpose : Computes weights for horizontal interpolation to the |
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15 | !! observation point. |
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16 | !! |
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17 | !! ** Method : Horizontal interpolation to the observation point using |
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18 | !! model values at the corners of the surrounding grid |
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19 | !! points. |
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20 | !! |
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21 | !! Interpolation Schemes : |
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22 | !! |
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23 | !! 1) k2dint = 0: Distance-weighted interpolation scheme 1 |
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24 | !! |
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25 | !! The interpolation weights are computed as a weighted |
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26 | !! sum of the distance between the model grid points (A) |
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27 | !! and the observation point (B). Distance (s) is computed |
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28 | !! using the great-circle distance formula: |
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29 | !! |
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30 | !! s(AB) = arcos( sin( phiA ) x sin( phiB ) |
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31 | !! + cos( phiA ) x cos( phiB ) |
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32 | !! x cos( lamB - lamA ) ) |
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33 | !! |
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34 | !! 2) k2dint = 1: Distance-weighted interpolation scheme 2 |
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35 | !! |
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36 | !! As k2dint = 0 but with distance (ds) computed using |
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37 | !! a small-angle approximation to the great-circle formula: |
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38 | !! |
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39 | !! ds(AB) = sqrt( ( phiB - phiA )^{2} |
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40 | !! + ( ( lamB - lamA ) * cos( phiB ) )^{2} ) |
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41 | !! |
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42 | !! 3) k2dint = 2: Bilinear interpolation on a geographical grid |
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43 | !! |
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44 | !! The interpolation is split into two 1D interpolations in |
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45 | !! the longitude and latitude directions, respectively. |
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46 | !! |
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47 | !! 4) k2dint = 3: General bilinear remapping interpolation |
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48 | !! |
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49 | !! An iterative scheme that involves first mapping a |
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50 | !! quadrilateral cell into a cell with coordinates |
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51 | !! (0,0), (1,0), (0,1) and (1,1). |
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52 | !! |
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53 | !! 5) k2dint = 4: Polynomial interpolation |
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54 | !! |
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55 | !! The interpolation weights are computed by fitting a |
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56 | !! polynomial function of the form |
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57 | !! |
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58 | !! P(i) = a1(i) + a2(i) * phi + a3(i) * plam |
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59 | !! + a4(i) * phi * plam |
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60 | !! |
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61 | !! through the model values at the four surrounding grid points. |
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62 | !! |
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63 | !! ** Action : |
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64 | !! |
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65 | !! References : Jones, P.: A users guide for SCRIP: A Spherical |
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66 | !! Coordinate Remapping and Interpolation Package. |
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67 | !! Version 1.4. Los Alomos. |
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68 | !! |
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69 | !! http://www.acl.lanl.gov/climate/software/SCRIP/SCRIPmain.html |
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70 | !! |
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71 | !! History : |
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72 | !! ! 97-11 (A. Weaver, N. Daget) |
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73 | !! ! 06-03 (A. Vidard) NEMOVAR migration |
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74 | !! ! 06-10 (A. Weaver) Cleanup |
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75 | !! ! 07-08 (K. Mogensen) Split in two routines for easier adj. |
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76 | !!----------------------------------------------------------------------- |
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77 | !! * Modules used |
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78 | !! * Arguments |
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79 | INTEGER, INTENT(IN) :: & |
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80 | & kpk, & ! Parameter values for automatic arrays |
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81 | & kpk2, & |
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82 | & k2dint ! Interpolation scheme options |
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83 | ! = 0 distance-weighted (great circle) |
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84 | ! = 1 distance-weighted (small angle) |
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85 | ! = 2 bilinear (geographical grid) |
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86 | ! = 3 bilinear (quadrilateral grid) |
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87 | ! = 4 polynomial (quadrilateral grid) |
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88 | REAL(KIND=wp), INTENT(INOUT) :: & |
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89 | & plam, & |
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90 | & pphi ! Geographical (lat,lon) coordinates of |
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91 | ! observation |
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92 | REAL(KIND=wp), DIMENSION(2,2), INTENT(IN) :: & |
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93 | & pglam, & ! Model variable lat |
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94 | & pgphi ! Model variable lon |
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95 | REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(IN) :: & |
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96 | & pmask ! Model variable mask |
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97 | REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(OUT) :: & |
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98 | & pweig ! Weights for interpolation |
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99 | REAL(KIND=wp), DIMENSION(kpk2), INTENT(OUT) :: & |
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100 | & pobsmask ! Vertical mask for observations |
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101 | INTEGER, INTENT(IN), OPTIONAL :: & |
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102 | & iminpoints ! Reject point which is not surrounded |
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103 | ! by at least iminpoints sea points |
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104 | |
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105 | !! * Local declarations |
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106 | INTEGER :: & |
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107 | & jk |
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108 | INTEGER :: & |
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109 | & ikmax, & |
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110 | & iamb1, & |
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111 | & iamb2 |
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112 | REAL(KIND=wp) :: & |
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113 | & zphimm, & |
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114 | & zphimp, & |
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115 | & zphipm, & |
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116 | & zphipp, & |
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117 | & zlammm, & |
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118 | & zlammp, & |
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119 | & zlampm, & |
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120 | & zlampp, & |
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121 | & zphimin, & |
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122 | & zphimax, & |
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123 | & zlammin, & |
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124 | & zlammax |
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125 | REAL(KIND=wp), DIMENSION(kpk2) :: & |
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126 | & z2dmm, & |
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127 | & z2dmp, & |
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128 | & z2dpm, & |
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129 | & z2dpp, & |
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130 | & z2dmmt, & |
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131 | & z2dmpt, & |
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132 | & z2dpmt, & |
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133 | & z2dppt, & |
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134 | & zsum |
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135 | LOGICAL :: & |
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136 | & ll_ds1, & |
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137 | & ll_skip, & |
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138 | & ll_fail |
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139 | |
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140 | !------------------------------------------------------------------------ |
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141 | ! Constants for the 360 degrees ambiguity |
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142 | !------------------------------------------------------------------------ |
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143 | iamb1 = 10 ! dlam < iamb1 * dphi |
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144 | iamb2 = 3 ! Special treatment if iamb2 * lam < max(lam) |
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145 | |
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146 | !------------------------------------------------------------------------ |
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147 | ! Initialize number of levels |
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148 | !------------------------------------------------------------------------ |
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149 | IF ( kpk2 == 1 ) THEN |
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150 | ikmax = 1 |
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151 | ELSEIF ( kpk2 == kpk) THEN |
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152 | ikmax = kpk-1 |
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153 | ENDIF |
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154 | !------------------------------------------------------------------------ |
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155 | ! Initialize the cell corners |
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156 | !------------------------------------------------------------------------ |
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157 | zphimm = pgphi(1,1) |
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158 | zphimp = pgphi(1,2) |
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159 | zphipm = pgphi(2,1) |
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160 | zphipp = pgphi(2,2) |
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161 | zlammm = pglam(1,1) |
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162 | zlammp = pglam(1,2) |
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163 | zlampm = pglam(2,1) |
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164 | zlampp = pglam(2,2) |
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165 | |
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166 | !------------------------------------------------------------------------ |
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167 | ! Treat the 360 degrees ambiguity |
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168 | !------------------------------------------------------------------------ |
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169 | DO WHILE ( ( zlammm < 0.0_wp ).OR.( zlammm > 360.0_wp ) & |
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170 | & .OR.( zlampm < 0.0_wp ).OR.( zlampm > 360.0_wp ) & |
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171 | & .OR.( zlampp < 0.0_wp ).OR.( zlampp > 360.0_wp ) & |
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172 | & .OR.( zlammp < 0.0_wp ).OR.( zlammp > 360.0_wp ) ) |
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173 | |
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174 | IF ( zlammm < 0.0_wp ) zlammm = zlammm + 360.0_wp |
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175 | IF ( zlammm > 360.0_wp ) zlammm = zlammm - 360.0_wp |
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176 | IF ( zlammp < 0.0_wp ) zlammp = zlammp + 360.0_wp |
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177 | IF ( zlammp > 360.0_wp ) zlammp = zlammp - 360.0_wp |
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178 | IF ( zlampm < 0.0_wp ) zlampm = zlampm + 360.0_wp |
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179 | IF ( zlampm > 360.0_wp ) zlampm = zlampm - 360.0_wp |
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180 | IF ( zlampp < 0.0_wp ) zlampp = zlampp + 360.0_wp |
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181 | IF ( zlampp > 360.0_wp ) zlampp = zlampp - 360.0_wp |
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182 | |
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183 | END DO |
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184 | |
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185 | DO WHILE ( ( plam < 0.0_wp ) .OR. ( plam > 360.0_wp ) ) |
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186 | IF ( plam < 0.0_wp ) plam = plam + 360.0_wp |
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187 | IF ( plam > 360.0_wp ) plam = plam - 360.0_wp |
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188 | END DO |
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189 | |
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190 | !------------------------------------------------------------------------ |
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191 | ! Special case for observation on grid points |
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192 | !------------------------------------------------------------------------ |
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193 | ll_skip = .FALSE. |
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194 | IF ( ( ABS( zphimm - pphi ) < 1.0e-6_wp ) .AND. & |
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195 | & ( ABS( zlammm - plam ) < 1.0e-6_wp ) ) THEN |
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196 | z2dmm(:) = 1.0_wp |
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197 | z2dpm(:) = 0.0_wp |
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198 | z2dmp(:) = 0.0_wp |
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199 | z2dpp(:) = 0.0_wp |
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200 | ll_skip = .TRUE. |
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201 | ENDIF |
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202 | IF ( ( ABS( zphipm - pphi ) < 1.0e-6_wp ) .AND. & |
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203 | & ( ABS( zlampm - plam ) < 1.0e-6_wp ) ) THEN |
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204 | z2dmm(:) = 0.0_wp |
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205 | z2dpm(:) = 1.0_wp |
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206 | z2dmp(:) = 0.0_wp |
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207 | z2dpp(:) = 0.0_wp |
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208 | ll_skip = .TRUE. |
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209 | ENDIF |
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210 | IF ( ( ABS( zphimp - pphi ) < 1.0e-6_wp ) .AND. & |
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211 | & ( ABS( zlammp - plam ) < 1.0e-6_wp ) ) THEN |
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212 | z2dmm(:) = 0.0_wp |
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213 | z2dpm(:) = 0.0_wp |
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214 | z2dmp(:) = 1.0_wp |
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215 | z2dpp(:) = 0.0_wp |
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216 | ll_skip = .TRUE. |
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217 | ENDIF |
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218 | IF ( ( ABS( zphipp - pphi ) < 1.0e-6_wp ) .AND. & |
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219 | & ( ABS( zlampp - plam ) < 1.0e-6_wp ) ) THEN |
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220 | z2dmm(:) = 0.0_wp |
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221 | z2dpm(:) = 0.0_wp |
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222 | z2dmp(:) = 0.0_wp |
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223 | z2dpp(:) = 1.0_wp |
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224 | ll_skip = .TRUE. |
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225 | ENDIF |
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226 | |
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227 | IF ( .NOT.ll_skip ) THEN |
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228 | |
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229 | zphimin = MIN( zphimm, zphipm, zphipp, zphimp ) |
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230 | zphimax = MAX( zphimm, zphipm, zphipp, zphimp ) |
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231 | zlammin = MIN( zlammm, zlampm, zlampp, zlammp ) |
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232 | zlammax = MAX( zlammm, zlampm, zlampp, zlammp ) |
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233 | |
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234 | IF ( ( ( zlammax - zlammin ) / ( zphimax - zphimin ) ) > iamb1 ) THEN |
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235 | IF ( iamb2 * zlammm < zlammax ) zlammm = zlammm + 360.0_wp |
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236 | IF ( iamb2 * zlammp < zlammax ) zlammp = zlammp + 360.0_wp |
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237 | IF ( iamb2 * zlampm < zlammax ) zlampm = zlampm + 360.0_wp |
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238 | IF ( iamb2 * zlampp < zlammax ) zlampp = zlampp + 360.0_wp |
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239 | ENDIF |
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240 | |
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241 | zlammin = MIN( zlammm, zlampm, zlampp, zlammp ) |
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242 | IF ( zlammm > ( zlammin + 180.0_wp ) ) zlammm = zlammm - 360.0_wp |
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243 | IF ( zlammp > ( zlammin + 180.0_wp ) ) zlammp = zlammp - 360.0_wp |
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244 | IF ( zlampm > ( zlammin + 180.0_wp ) ) zlampm = zlampm - 360.0_wp |
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245 | IF ( zlampp > ( zlammin + 180.0_wp ) ) zlampp = zlampp - 360.0_wp |
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246 | |
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247 | IF ( plam < zlammin ) plam = plam + 360.0_wp |
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248 | z2dmm = 0.0_wp |
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249 | z2dmp = 0.0_wp |
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250 | z2dpm = 0.0_wp |
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251 | z2dpp = 0.0_wp |
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252 | SELECT CASE (k2dint) |
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253 | |
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254 | CASE(0) |
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255 | CALL obs_int_h2d_ds1( kpk2, ikmax, & |
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256 | & pphi, plam, pmask, & |
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257 | & zphimm, zlammm, zphimp, zlammp, & |
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258 | & zphipm, zlampm, zphipp, zlampp, & |
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259 | & z2dmm, z2dmp, z2dpm, z2dpp ) |
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260 | CASE(1) |
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261 | CALL obs_int_h2d_ds2( kpk2, ikmax, & |
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262 | & pphi, plam, pmask, & |
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263 | & zphimm, zlammm, zphimp, zlammp, & |
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264 | & zphipm, zlampm, zphipp, zlampp, & |
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265 | & z2dmm, z2dmp, z2dpm, z2dpp ) |
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266 | CASE(2) |
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267 | CALL obs_int_h2d_bil( kpk2, ikmax, & |
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268 | & pphi, plam, pmask, & |
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269 | & zlammp, & |
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270 | & zphipm, zphipp, zlampp, & |
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271 | & z2dmm, z2dmp, z2dpm, z2dpp ) |
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272 | CASE(3) |
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273 | CALL obs_int_h2d_bir( kpk2, ikmax, & |
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274 | & pphi, plam, pmask, & |
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275 | & zphimm, zlammm, zphimp, zlammp, & |
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276 | & zphipm, zlampm, zphipp, zlampp, & |
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277 | & z2dmm, z2dmp, z2dpm, z2dpp, ll_fail ) |
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278 | IF (ll_fail) THEN |
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279 | IF(lwp) THEN |
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280 | WRITE(numout,*)'Bilinear weight computation failed' |
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281 | WRITE(numout,*)'Switching to great circle distance' |
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282 | WRITE(numout,*) |
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283 | ENDIF |
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284 | CALL obs_int_h2d_ds1( kpk2, ikmax, & |
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285 | & pphi, plam, pmask, & |
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286 | & zphimm, zlammm, zphimp, zlammp, & |
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287 | & zphipm, zlampm, zphipp, zlampp, & |
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288 | & z2dmm, z2dmp, z2dpm, z2dpp ) |
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289 | ENDIF |
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290 | CASE(4) |
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291 | CALL obs_int_h2d_pol( kpk2, ikmax, & |
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292 | & pphi, plam, pmask, & |
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293 | & zphimm, zlammm, zphimp, zlammp, & |
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294 | & zphipm, zlampm, zphipp, zlampp, & |
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295 | & z2dmm, z2dmp, z2dpm, z2dpp ) |
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296 | END SELECT |
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297 | |
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298 | ENDIF |
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299 | !------------------------------------------------------------------------ |
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300 | ! Compute weights for interpolation to the observation point |
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301 | !------------------------------------------------------------------------ |
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302 | pobsmask(:) = 0.0_wp |
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303 | pweig(:,:,:) = 0.0_wp |
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304 | ! ll_ds1 is used for failed interpolations |
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305 | ll_ds1 = .FALSE. |
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306 | DO jk = 1, ikmax |
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307 | IF (PRESENT(iminpoints)) THEN |
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308 | IF (NINT(SUM(pmask(:,:,jk)))<iminpoints) CYCLE |
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309 | ENDIF |
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310 | zsum(jk) = z2dmm(jk) + z2dmp(jk) + z2dpm(jk) + z2dpp(jk) |
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311 | IF ( zsum(jk) /= 0.0_wp ) THEN |
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312 | pweig(1,1,jk) = z2dmm(jk) |
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313 | pweig(1,2,jk) = z2dmp(jk) |
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314 | pweig(2,1,jk) = z2dpm(jk) |
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315 | pweig(2,2,jk) = z2dpp(jk) |
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316 | ! Set the vertical mask |
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317 | IF ( ( ( z2dmm(jk) > 0.0_wp ) .AND. & |
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318 | & ( pmask(1,1,jk) == 1.0_wp ) ) .OR. & |
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319 | & ( ( z2dmp(jk) > 0.0_wp ) .AND. & |
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320 | & ( pmask(1,2,jk) == 1.0_wp ) ) .OR. & |
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321 | & ( ( z2dpm(jk) > 0.0_wp ) .AND. & |
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322 | & ( pmask(2,1,jk) == 1.0_wp ) ) .OR. & |
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323 | & ( ( z2dpp(jk) > 0.0_wp ) .AND. & |
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324 | & ( pmask(2,2,jk) == 1.0_wp ) ) ) pobsmask(jk)=1.0_wp |
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325 | ELSE |
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326 | ! If the interpolation has failed due to the point |
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327 | ! being on the intersect of two land points retry with |
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328 | ! k2dint = 0 |
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329 | IF ( ( pmask(1,1,jk) /= 0.0_wp ).OR. & |
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330 | & ( pmask(1,2,jk) /= 0.0_wp ).OR. & |
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331 | & ( pmask(2,1,jk) /= 0.0_wp ).OR. & |
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332 | & ( pmask(2,2,jk) /= 0.0_wp ) ) THEN |
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333 | ! If ll_ds1 is false compute k2dint = 0 weights |
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334 | IF ( .NOT.ll_ds1 ) THEN |
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335 | CALL obs_int_h2d_ds1( kpk2, ikmax, & |
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336 | & pphi, plam, pmask, & |
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337 | & zphimm, zlammm, zphimp, zlammp, & |
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338 | & zphipm, zlampm, zphipp, zlampp, & |
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339 | & z2dmmt, z2dmpt, z2dpmt, z2dppt ) |
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340 | ll_ds1 = .TRUE. |
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341 | ENDIF |
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342 | zsum(jk) = z2dmmt(jk) + z2dmpt(jk) + z2dpmt(jk) + z2dppt(jk) |
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343 | IF ( zsum(jk) /= 0.0_wp ) THEN |
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344 | pweig(1,1,jk) = z2dmmt(jk) |
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345 | pweig(1,2,jk) = z2dmpt(jk) |
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346 | pweig(2,1,jk) = z2dpmt(jk) |
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347 | pweig(2,2,jk) = z2dppt(jk) |
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348 | ! Set the vertical mask |
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349 | IF ( ( ( z2dmmt(jk) > 0.0_wp ) .AND. & |
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350 | & ( pmask(1,1,jk) == 1.0_wp ) ) .OR. & |
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351 | & ( ( z2dmpt(jk) > 0.0_wp ) .AND. & |
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352 | & ( pmask(1,2,jk) == 1.0_wp ) ) .OR. & |
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353 | & ( ( z2dpmt(jk) > 0.0_wp) .AND. & |
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354 | & ( pmask(2,1,jk) == 1.0_wp ) ) .OR. & |
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355 | & ( ( z2dppt(jk) > 0.0_wp ) .AND. & |
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356 | & ( pmask(2,2,jk) == 1.0_wp ) ) ) & |
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357 | & pobsmask(jk)=1.0_wp |
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358 | ENDIF |
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359 | ENDIF |
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360 | ENDIF |
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361 | END DO |
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362 | |
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363 | END SUBROUTINE obs_int_h2d_init |
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364 | |
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365 | SUBROUTINE obs_int_h2d( kpk, kpk2, & |
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366 | & pweig, pmod, pobsk ) |
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367 | !!----------------------------------------------------------------------- |
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368 | !! |
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369 | !! *** ROUTINE obs_int_h2d *** |
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370 | !! |
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371 | !! ** Purpose : Horizontal interpolation to the observation point. |
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372 | !! |
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373 | !! ** Method : Horizontal interpolation to the observation point using |
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374 | !! model values at the corners of the surrounding grid |
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375 | !! points. |
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376 | !! |
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377 | !! ** Action : |
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378 | !! |
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379 | !! References : |
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380 | !! |
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381 | !! History : |
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382 | !! ! 97-11 (A. Weaver, N. Daget) |
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383 | !! ! 06-03 (A. Vidard) NEMOVAR migration |
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384 | !! ! 06-10 (A. Weaver) Cleanup |
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385 | !! ! 07-08 (K. Mogensen) Split in two routines for easier adj. |
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386 | !!----------------------------------------------------------------------- |
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387 | !! * Modules used |
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388 | !! * Arguments |
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389 | INTEGER, INTENT(IN) :: & |
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390 | & kpk, & ! Parameter values for automatic arrays |
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391 | & kpk2 |
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392 | REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(IN) :: & |
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393 | & pweig ! Interpolation weights |
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394 | REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(IN) :: & |
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395 | & pmod ! Model variable to interpolate |
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396 | REAL(KIND=wp), DIMENSION(kpk2), INTENT(OUT) :: & |
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397 | & pobsk ! Model profile interpolated to obs (i,j) pt |
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398 | |
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399 | !! * Local declarations |
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400 | INTEGER :: & |
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401 | & jk |
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402 | INTEGER :: & |
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403 | & ikmax |
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404 | REAL(KIND=wp) :: & |
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405 | & zsum |
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406 | !------------------------------------------------------------------------ |
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407 | ! Initialize number of levels |
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408 | !------------------------------------------------------------------------ |
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409 | IF ( kpk2 == 1 ) THEN |
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410 | ikmax = 1 |
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411 | ELSEIF ( kpk2 == kpk) THEN |
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412 | ikmax = kpk-1 |
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413 | ENDIF |
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414 | !------------------------------------------------------------------------ |
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415 | ! Interpolate to the observation point |
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416 | !------------------------------------------------------------------------ |
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417 | pobsk(:) = obfillflt |
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418 | DO jk = 1, ikmax |
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419 | zsum = pweig(1,1,jk) + pweig(1,2,jk) + pweig(2,1,jk) + pweig(2,2,jk) |
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420 | IF ( zsum /= 0.0_wp ) THEN |
---|
421 | pobsk(jk) = ( pweig(1,1,jk) * pmod(1,1,jk) & |
---|
422 | & + pweig(1,2,jk) * pmod(1,2,jk) & |
---|
423 | & + pweig(2,1,jk) * pmod(2,1,jk) & |
---|
424 | & + pweig(2,2,jk) * pmod(2,2,jk) & |
---|
425 | & ) / zsum |
---|
426 | ENDIF |
---|
427 | END DO |
---|
428 | |
---|
429 | END SUBROUTINE obs_int_h2d |
---|
430 | |
---|
431 | SUBROUTINE obs_int_h2d_ds1( kpk2, kmax, & |
---|
432 | & pphi, plam, pmask, & |
---|
433 | & pphimm, plammm, pphimp, plammp, & |
---|
434 | & pphipm, plampm, pphipp, plampp, & |
---|
435 | & p2dmm, p2dmp, p2dpm, p2dpp ) |
---|
436 | !!----------------------------------------------------------------------- |
---|
437 | !! |
---|
438 | !! *** ROUTINE obs_int_h2d_ds1 *** |
---|
439 | !! |
---|
440 | !! ** Purpose : Distance-weighted interpolation scheme (k2dint = 0) |
---|
441 | !! |
---|
442 | !! ** Method : The interpolation weights are computed as a weighted |
---|
443 | !! sum of the distance between the model grid points (A) |
---|
444 | !! and the observation point (B). |
---|
445 | !! |
---|
446 | !! Distance (s) is computed using the great-circle distance formula: |
---|
447 | !! |
---|
448 | !! s(AB) = arcos( sin( phiA ) x sin( phiB ) |
---|
449 | !! + cos( phiA ) x cos( phiB ) x cos( lamB - lamA ) |
---|
450 | !! |
---|
451 | !! ** Action : |
---|
452 | !! |
---|
453 | !! History : |
---|
454 | !! ! 97-11 (A. Weaver, N. Daget) |
---|
455 | !! ! 06-10 (A. Weaver) Cleanup |
---|
456 | !!----------------------------------------------------------------------- |
---|
457 | |
---|
458 | !! * Modules used |
---|
459 | |
---|
460 | !! * Arguments |
---|
461 | INTEGER, INTENT(IN) :: & |
---|
462 | & kpk2, & ! Parameter values for automatic arrays |
---|
463 | & kmax |
---|
464 | REAL(KIND=wp), INTENT(IN) :: & |
---|
465 | & pphi, & ! Geographical location of observation |
---|
466 | & plam, & |
---|
467 | & pphimm, & ! Geographical location of surrounding |
---|
468 | & pphimp, & ! model grid points |
---|
469 | & pphipm, & |
---|
470 | & pphipp, & |
---|
471 | & plammm, & |
---|
472 | & plammp, & |
---|
473 | & plampm, & |
---|
474 | & plampp |
---|
475 | REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(IN) :: & |
---|
476 | & pmask ! Model variable mask |
---|
477 | REAL(KIND=wp), DIMENSION(kpk2), INTENT(OUT) :: & |
---|
478 | & p2dmm, & ! Interpolation weights |
---|
479 | & p2dmp, & |
---|
480 | & p2dpm, & |
---|
481 | & p2dpp |
---|
482 | |
---|
483 | !! * Local declarations |
---|
484 | INTEGER :: & |
---|
485 | & jk |
---|
486 | REAL(KIND=wp) :: & |
---|
487 | & zphi2, & |
---|
488 | & zlam2, & |
---|
489 | & zcola, & |
---|
490 | & za2, & |
---|
491 | & zb2, & |
---|
492 | & zc2, & |
---|
493 | & zphimm2, & |
---|
494 | & zphimp2, & |
---|
495 | & zphipm2, & |
---|
496 | & zphipp2, & |
---|
497 | & zlammm2, & |
---|
498 | & zlammp2, & |
---|
499 | & zlampm2, & |
---|
500 | & zlampp2, & |
---|
501 | & za1mm, & |
---|
502 | & za1mp, & |
---|
503 | & za1pm, & |
---|
504 | & za1pp, & |
---|
505 | & zcomm, & |
---|
506 | & zcomp, & |
---|
507 | & zcopm, & |
---|
508 | & zcopp, & |
---|
509 | & zb1mm, & |
---|
510 | & zb1mp, & |
---|
511 | & zb1pm, & |
---|
512 | & zb1pp, & |
---|
513 | & zc1mm, & |
---|
514 | & zc1mp, & |
---|
515 | & zc1pm, & |
---|
516 | & zc1pp, & |
---|
517 | & zsopmpp, & |
---|
518 | & zsommmp, & |
---|
519 | & zsomm, & |
---|
520 | & zsomp, & |
---|
521 | & zsopm, & |
---|
522 | & zsopp |
---|
523 | |
---|
524 | !------------------------------------------------------------------------ |
---|
525 | ! Distance-weighted interpolation using the great circle formula |
---|
526 | !------------------------------------------------------------------------ |
---|
527 | zphi2 = pphi * rad |
---|
528 | zlam2 = plam * rad |
---|
529 | zcola = COS( zphi2 ) |
---|
530 | za2 = SIN( zphi2 ) |
---|
531 | zb2 = zcola * COS( zlam2 ) |
---|
532 | zc2 = zcola * SIN( zlam2 ) |
---|
533 | |
---|
534 | zphimm2 = pphimm * rad |
---|
535 | zphimp2 = pphimp * rad |
---|
536 | zphipm2 = pphipm * rad |
---|
537 | zphipp2 = pphipp * rad |
---|
538 | |
---|
539 | zlammm2 = plammm * rad |
---|
540 | zlammp2 = plammp * rad |
---|
541 | zlampm2 = plampm * rad |
---|
542 | zlampp2 = plampp * rad |
---|
543 | |
---|
544 | za1mm = SIN( zphimm2 ) |
---|
545 | za1mp = SIN( zphimp2 ) |
---|
546 | za1pm = SIN( zphipm2 ) |
---|
547 | za1pp = SIN( zphipp2 ) |
---|
548 | |
---|
549 | zcomm = COS( zphimm2 ) |
---|
550 | zcomp = COS( zphimp2 ) |
---|
551 | zcopm = COS( zphipm2 ) |
---|
552 | zcopp = COS( zphipp2 ) |
---|
553 | |
---|
554 | zb1mm = zcomm * COS( zlammm2 ) |
---|
555 | zb1mp = zcomp * COS( zlammp2 ) |
---|
556 | zb1pm = zcopm * COS( zlampm2 ) |
---|
557 | zb1pp = zcopp * COS( zlampp2 ) |
---|
558 | |
---|
559 | zc1mm = zcomm * SIN( zlammm2 ) |
---|
560 | zc1mp = zcomp * SIN( zlammp2 ) |
---|
561 | zc1pm = zcopm * SIN( zlampm2 ) |
---|
562 | zc1pp = zcopp * SIN( zlampp2 ) |
---|
563 | |
---|
564 | ! Function for arcsin(sqrt(1-x^2) version of great-circle formula |
---|
565 | zsomm = grt_cir_dis( za1mm, za2, zb1mm, zb2, zc1mm, zc2 ) |
---|
566 | zsomp = grt_cir_dis( za1mp, za2, zb1mp, zb2, zc1mp, zc2 ) |
---|
567 | zsopm = grt_cir_dis( za1pm, za2, zb1pm, zb2, zc1pm, zc2 ) |
---|
568 | zsopp = grt_cir_dis( za1pp, za2, zb1pp, zb2, zc1pp, zc2 ) |
---|
569 | |
---|
570 | zsopmpp = zsopm * zsopp |
---|
571 | zsommmp = zsomm * zsomp |
---|
572 | DO jk = 1, kmax |
---|
573 | p2dmm(jk) = zsomp * zsopmpp * pmask(1,1,jk) |
---|
574 | p2dmp(jk) = zsomm * zsopmpp * pmask(1,2,jk) |
---|
575 | p2dpm(jk) = zsopp * zsommmp * pmask(2,1,jk) |
---|
576 | p2dpp(jk) = zsopm * zsommmp * pmask(2,2,jk) |
---|
577 | END DO |
---|
578 | |
---|
579 | END SUBROUTINE obs_int_h2d_ds1 |
---|
580 | |
---|
581 | SUBROUTINE obs_int_h2d_ds2( kpk2, kmax, & |
---|
582 | & pphi, plam, pmask, & |
---|
583 | & pphimm, plammm, pphimp, plammp, & |
---|
584 | & pphipm, plampm, pphipp, plampp, & |
---|
585 | & p2dmm, p2dmp, p2dpm, p2dpp ) |
---|
586 | !!----------------------------------------------------------------------- |
---|
587 | !! |
---|
588 | !! *** ROUTINE obs_int_h2d_ds2 *** |
---|
589 | !! |
---|
590 | !! ** Purpose : Distance-weighted interpolation scheme (k2dint = 1) |
---|
591 | !! |
---|
592 | !! ** Method : As k2dint = 0 but with distance (ds) computed using a |
---|
593 | !! small-angle approximation to the great-circle distance |
---|
594 | !! formula: |
---|
595 | !! |
---|
596 | !! ds(AB) = sqrt( ( phiB - phiA )^{2} |
---|
597 | !! + ( ( lamB - lamA ) * cos( phiB ) )^{2} ) |
---|
598 | !! |
---|
599 | !! ** Action : |
---|
600 | !! |
---|
601 | !! History : |
---|
602 | !! ! 97-11 (A. Weaver, N. Daget) |
---|
603 | !! ! 06-10 (A. Weaver) Cleanup |
---|
604 | !!----------------------------------------------------------------------- |
---|
605 | |
---|
606 | !!----------------------------------------------------------------------- |
---|
607 | !! * Modules used |
---|
608 | !!----------------------------------------------------------------------- |
---|
609 | !! * Arguments |
---|
610 | INTEGER, INTENT(IN) :: & |
---|
611 | & kpk2, & ! Parameter values for automatic arrays |
---|
612 | & kmax |
---|
613 | REAL(KIND=wp), INTENT(IN) :: & |
---|
614 | & pphi, & ! Geographical location of observation |
---|
615 | & plam, & |
---|
616 | & pphimm, & ! Geographical location of surrounding |
---|
617 | & pphimp, & ! model grid points |
---|
618 | & pphipm, & |
---|
619 | & pphipp, & |
---|
620 | & plammm, & |
---|
621 | & plammp, & |
---|
622 | & plampm, & |
---|
623 | & plampp |
---|
624 | REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(IN) :: & |
---|
625 | & pmask ! Model variable mask |
---|
626 | REAL(KIND=wp), DIMENSION(kpk2), INTENT(OUT) :: & |
---|
627 | & p2dmm, & ! Interpolation weights |
---|
628 | & p2dmp, & |
---|
629 | & p2dpm, & |
---|
630 | & p2dpp |
---|
631 | |
---|
632 | !! * Local declarations |
---|
633 | INTEGER :: & |
---|
634 | & jk |
---|
635 | REAL(KIND=wp) :: & |
---|
636 | & zcosp, & |
---|
637 | & zdlmm, & |
---|
638 | & zdlmp, & |
---|
639 | & zdlpm, & |
---|
640 | & zdlpp, & |
---|
641 | & zdpmm, & |
---|
642 | & zdpmp, & |
---|
643 | & zdppm, & |
---|
644 | & zdppp, & |
---|
645 | & zsomm, & |
---|
646 | & zsomp, & |
---|
647 | & zsopm, & |
---|
648 | & zsopp, & |
---|
649 | & zsopmpp, & |
---|
650 | & zsommmp |
---|
651 | |
---|
652 | !------------------------------------------------------------------------ |
---|
653 | ! Distance-weighted interpolation with a small angle approximation |
---|
654 | !------------------------------------------------------------------------ |
---|
655 | zcosp = COS( pphi * rad ) |
---|
656 | |
---|
657 | zdlmm = plammm - plam |
---|
658 | zdlmp = plammp - plam |
---|
659 | zdlpm = plampm - plam |
---|
660 | zdlpp = plampp - plam |
---|
661 | |
---|
662 | zdpmm = pphimm - pphi |
---|
663 | zdpmp = pphimp - pphi |
---|
664 | zdppm = pphipm - pphi |
---|
665 | zdppp = pphipp - pphi |
---|
666 | |
---|
667 | zsomm = grt_cir_dis_saa( zdlmm, zdpmm, zcosp ) |
---|
668 | zsomp = grt_cir_dis_saa( zdlmp, zdpmp, zcosp ) |
---|
669 | zsopm = grt_cir_dis_saa( zdlpm, zdppm, zcosp ) |
---|
670 | zsopp = grt_cir_dis_saa( zdlpp, zdppp, zcosp ) |
---|
671 | |
---|
672 | zsopmpp = zsopm * zsopp |
---|
673 | zsommmp = zsomm * zsomp |
---|
674 | |
---|
675 | DO jk = 1, kmax |
---|
676 | p2dmm(jk) = zsomp * zsopmpp * pmask(1,1,jk) |
---|
677 | p2dmp(jk) = zsomm * zsopmpp * pmask(1,2,jk) |
---|
678 | p2dpm(jk) = zsopp * zsommmp * pmask(2,1,jk) |
---|
679 | p2dpp(jk) = zsopm * zsommmp * pmask(2,2,jk) |
---|
680 | END DO |
---|
681 | |
---|
682 | END SUBROUTINE obs_int_h2d_ds2 |
---|
683 | |
---|
684 | SUBROUTINE obs_int_h2d_bil( kpk2, kmax, & |
---|
685 | & pphi, plam, pmask, & |
---|
686 | & plammp, pphipm, pphipp, plampp, & |
---|
687 | & p2dmm, p2dmp, p2dpm, p2dpp) |
---|
688 | !!----------------------------------------------------------------------- |
---|
689 | !! |
---|
690 | !! *** ROUTINE obs_int_h2d_bil *** |
---|
691 | !! |
---|
692 | !! ** Purpose : Bilinear interpolation on a geographical grid (k2dint = 2) |
---|
693 | !! |
---|
694 | !! ** Method : The interpolation is split into two 1D interpolations in |
---|
695 | !! the longitude and latitude directions, respectively. |
---|
696 | !! |
---|
697 | !! An iterative scheme that involves first mapping a quadrilateral |
---|
698 | !! cell into a cell with coordinates (0,0), (1,0), (0,1) and (1,1). |
---|
699 | !! |
---|
700 | !! ** Action : |
---|
701 | !! |
---|
702 | !! History : |
---|
703 | !! ! 97-11 (A. Weaver, N. Daget) |
---|
704 | !! ! 06-10 (A. Weaver) Cleanup |
---|
705 | !!----------------------------------------------------------------------- |
---|
706 | |
---|
707 | !! * Arguments |
---|
708 | INTEGER, INTENT(IN) :: & |
---|
709 | & kpk2, & ! Parameter values for automatic arrays |
---|
710 | & kmax |
---|
711 | REAL(KIND=wp), INTENT(IN) :: & |
---|
712 | & pphi, & ! Geographical location of observation |
---|
713 | & plam, & |
---|
714 | & pphipm, & ! Geographical location of surrounding |
---|
715 | & pphipp, & ! model grid points |
---|
716 | & plammp, & |
---|
717 | & plampp |
---|
718 | REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(IN) :: & |
---|
719 | & pmask ! Model variable mask |
---|
720 | REAL(KIND=wp), DIMENSION(kpk2), INTENT(OUT) :: & |
---|
721 | & p2dmm, & ! Interpolation weights |
---|
722 | & p2dmp, & |
---|
723 | & p2dpm, & |
---|
724 | & p2dpp |
---|
725 | |
---|
726 | !! * Local declarations |
---|
727 | INTEGER :: & |
---|
728 | & jk |
---|
729 | REAL(KIND=wp) :: & |
---|
730 | & zdlmp, & |
---|
731 | & zdppm, & |
---|
732 | & zdlpp, & |
---|
733 | & zdppp |
---|
734 | |
---|
735 | !---------------------------------------------------------------------- |
---|
736 | ! Bilinear interpolation for geographical grid |
---|
737 | !---------------------------------------------------------------------- |
---|
738 | zdlmp = ABS(plam - plammp) |
---|
739 | zdppm = ABS(pphi - pphipm) |
---|
740 | zdlpp = ABS(plampp - plam) |
---|
741 | zdppp = ABS(pphipp - pphi) |
---|
742 | |
---|
743 | DO jk = 1, kmax |
---|
744 | p2dmm(jk) = zdlpp * zdppp * pmask(1,1,jk) |
---|
745 | p2dmp(jk) = zdlpp * zdppm * pmask(1,2,jk) |
---|
746 | p2dpm(jk) = zdlmp * zdppp * pmask(2,1,jk) |
---|
747 | p2dpp(jk) = zdlmp * zdppm * pmask(2,2,jk) |
---|
748 | END DO |
---|
749 | |
---|
750 | END SUBROUTINE obs_int_h2d_bil |
---|
751 | |
---|
752 | SUBROUTINE obs_int_h2d_bir( kpk2, kmax, & |
---|
753 | & pphi, plam, pmask, & |
---|
754 | & pphimm, plammm, pphimp, plammp, & |
---|
755 | & pphipm, plampm, pphipp, plampp, & |
---|
756 | & p2dmm, p2dmp, p2dpm, p2dpp, ldfail ) |
---|
757 | !!----------------------------------------------------------------------- |
---|
758 | !! |
---|
759 | !! *** ROUTINE obs_int_h2d_bir *** |
---|
760 | !! |
---|
761 | !! ** Purpose : General bilinear remapping interpolation (k2dint = 3) |
---|
762 | !! |
---|
763 | !! ** Method : An iterative scheme that involves first mapping a |
---|
764 | !! quadrilateral cell into a cell with coordinates |
---|
765 | !! (0,0), (1,0), (0,1) and (1,1). |
---|
766 | !! |
---|
767 | !! ** Action : |
---|
768 | !! |
---|
769 | !! History : |
---|
770 | !! ! 97-11 (A. Weaver, N. Daget) |
---|
771 | !! ! 06-10 (A. Weaver) Cleanup |
---|
772 | !!----------------------------------------------------------------------- |
---|
773 | |
---|
774 | !! * Arguments |
---|
775 | INTEGER, INTENT(IN) :: & |
---|
776 | & kpk2, & ! Parameter values for automatic arrays |
---|
777 | & kmax |
---|
778 | REAL(KIND=wp), INTENT(IN) :: & |
---|
779 | & pphi, & ! Geographical location of observation |
---|
780 | & plam, & |
---|
781 | & pphimm, & ! Geographical location of surrounding |
---|
782 | & pphimp, & ! model grid points |
---|
783 | & pphipm, & |
---|
784 | & pphipp, & |
---|
785 | & plammm, & |
---|
786 | & plammp, & |
---|
787 | & plampm, & |
---|
788 | & plampp |
---|
789 | REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(IN) :: & |
---|
790 | & pmask ! Model variable mask |
---|
791 | REAL(KIND=wp), DIMENSION(kpk2), INTENT(OUT) :: & |
---|
792 | & p2dmm, & ! Interpolation weights |
---|
793 | & p2dmp, & |
---|
794 | & p2dpm, & |
---|
795 | & p2dpp |
---|
796 | LOGICAL, INTENT(OUT) :: & |
---|
797 | & ldfail |
---|
798 | !! * Local declarations |
---|
799 | INTEGER :: & |
---|
800 | & jk |
---|
801 | REAL(KIND=wp) :: & |
---|
802 | & zbiwmm, & |
---|
803 | & zbiwmp, & |
---|
804 | & zbiwpm, & |
---|
805 | & zbiwpp |
---|
806 | |
---|
807 | !---------------------------------------------------------------------- |
---|
808 | ! Bilinear remapping interpolation for general quadrilateral grid |
---|
809 | !---------------------------------------------------------------------- |
---|
810 | CALL bil_wgt( pphimm, pphimp, pphipm, pphipp, & |
---|
811 | & plammm, plammp, plampm, plampp, & |
---|
812 | & zbiwmm, zbiwmp, zbiwpm, zbiwpp, & |
---|
813 | & pphi , plam, ldfail ) |
---|
814 | |
---|
815 | IF ( .NOT.ldfail ) THEN |
---|
816 | DO jk = 1, kmax |
---|
817 | p2dmm(jk) = zbiwmm * pmask(1,1,jk) |
---|
818 | p2dmp(jk) = zbiwmp * pmask(1,2,jk) |
---|
819 | p2dpm(jk) = zbiwpm * pmask(2,1,jk) |
---|
820 | p2dpp(jk) = zbiwpp * pmask(2,2,jk) |
---|
821 | END DO |
---|
822 | ENDIF |
---|
823 | |
---|
824 | END SUBROUTINE obs_int_h2d_bir |
---|
825 | |
---|
826 | SUBROUTINE obs_int_h2d_pol( kpk2, kmax, & |
---|
827 | & pphi, plam, pmask, & |
---|
828 | & pphimm, plammm, pphimp, plammp, & |
---|
829 | & pphipm, plampm, pphipp, plampp, & |
---|
830 | & p2dmm, p2dmp, p2dpm, p2dpp ) |
---|
831 | !!----------------------------------------------------------------------- |
---|
832 | !! |
---|
833 | !! *** ROUTINE obs_int_h2d_pol *** |
---|
834 | !! |
---|
835 | !! ** Purpose : Polynomial interpolation (k2dint = 4) |
---|
836 | !! |
---|
837 | !! ** Method : The interpolation weights are computed by fitting a |
---|
838 | !! polynomial function of the form |
---|
839 | !! |
---|
840 | !! P(i) = a1(i) + a2(i) * phi + a3(i) * plam + a4(i) * phi * plam |
---|
841 | !! |
---|
842 | !! through the model values at four surrounding grid pts (i=1,4). |
---|
843 | !! As k2dint = 0 but with distance (ds) computed using a small- |
---|
844 | !! angle approximation to the great-circle distance formula: |
---|
845 | !! |
---|
846 | !! ds(AB) = sqrt( ( phiB - phiA )^{2} |
---|
847 | !! + ( ( lamB - lamA ) * cos( phiB ) )^{2} ) |
---|
848 | !! |
---|
849 | !! ** Action : |
---|
850 | !! |
---|
851 | !! History : |
---|
852 | !! ! 97-11 (A. Weaver, N. Daget) |
---|
853 | !! ! 06-10 (A. Weaver) Cleanup |
---|
854 | !!----------------------------------------------------------------------- |
---|
855 | |
---|
856 | !! * Arguments |
---|
857 | INTEGER, INTENT(IN) :: & |
---|
858 | & kpk2, & ! Parameter values for automatic arrays |
---|
859 | & kmax |
---|
860 | REAL(KIND=wp), INTENT(IN) :: & |
---|
861 | & pphi, & ! Geographical location of observation |
---|
862 | & plam, & |
---|
863 | & pphimm, & ! Geographical location of surrounding |
---|
864 | & pphimp, & ! model grid points |
---|
865 | & pphipm, & |
---|
866 | & pphipp, & |
---|
867 | & plammm, & |
---|
868 | & plammp, & |
---|
869 | & plampm, & |
---|
870 | & plampp |
---|
871 | REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(IN) :: & |
---|
872 | & pmask ! Model variable mask |
---|
873 | REAL(KIND=wp), DIMENSION(kpk2), INTENT(OUT) :: & |
---|
874 | & p2dmm, & ! Interpolation weights |
---|
875 | & p2dmp, & |
---|
876 | & p2dpm, & |
---|
877 | & p2dpp |
---|
878 | |
---|
879 | !! * Local declarations |
---|
880 | INTEGER :: & |
---|
881 | & jk |
---|
882 | REAL(KIND=wp) :: & |
---|
883 | & zplp |
---|
884 | REAL(KIND=wp), DIMENSION(4,4) :: & |
---|
885 | & zmat, & |
---|
886 | & zmati |
---|
887 | |
---|
888 | !------------------------------------------------------------------------ |
---|
889 | ! Polynomial interpolation |
---|
890 | !------------------------------------------------------------------------ |
---|
891 | zmat(1,1) = 1.0_wp |
---|
892 | zmat(1,2) = 1.0_wp |
---|
893 | zmat(1,3) = 1.0_wp |
---|
894 | zmat(1,4) = 1.0_wp |
---|
895 | zmat(2,1) = plammm |
---|
896 | zmat(2,2) = plammp |
---|
897 | zmat(2,3) = plampm |
---|
898 | zmat(2,4) = plampp |
---|
899 | zmat(3,1) = pphimm |
---|
900 | zmat(3,2) = pphimp |
---|
901 | zmat(3,3) = pphipm |
---|
902 | zmat(3,4) = pphipp |
---|
903 | zmat(4,1) = plammm * pphimm |
---|
904 | zmat(4,2) = plammp * pphimp |
---|
905 | zmat(4,3) = plampm * pphipm |
---|
906 | zmat(4,4) = plampp * pphipp |
---|
907 | |
---|
908 | CALL lu_invmat( zmat, 4, zmati ) |
---|
909 | |
---|
910 | zplp = plam * pphi |
---|
911 | DO jk = 1, kmax |
---|
912 | p2dmm(jk) = ABS( zmati(1,1) + zmati(1,2) * plam & |
---|
913 | & + zmati(1,3) * pphi + zmati(1,4) * zplp ) & |
---|
914 | & * pmask(1,1,jk) |
---|
915 | p2dmp(jk) = ABS( zmati(2,1) + zmati(2,2) * plam & |
---|
916 | & + zmati(2,3) * pphi + zmati(2,4) * zplp ) & |
---|
917 | & * pmask(1,2,jk) |
---|
918 | p2dpm(jk) = ABS( zmati(3,1) + zmati(3,2) * plam & |
---|
919 | & + zmati(3,3) * pphi + zmati(3,4) * zplp ) & |
---|
920 | & * pmask(2,1,jk) |
---|
921 | p2dpp(jk) = ABS( zmati(4,1) + zmati(4,2) * plam & |
---|
922 | & + zmati(4,3) * pphi + zmati(4,4) * zplp ) & |
---|
923 | & * pmask(2,2,jk) |
---|
924 | END DO |
---|
925 | |
---|
926 | END SUBROUTINE obs_int_h2d_pol |
---|
927 | |
---|
928 | SUBROUTINE bil_wgt( pphimm, pphimp, pphipm, pphipp, & |
---|
929 | & plammm, plammp, plampm, plampp, & |
---|
930 | & pbiwmm, pbiwmp, pbiwpm, pbiwpp, & |
---|
931 | & pphi , plam, ldfail ) |
---|
932 | !!------------------------------------------------------------------- |
---|
933 | !! |
---|
934 | !! *** ROUTINE bil_wgt *** |
---|
935 | !! |
---|
936 | !! ** Purpose : Compute the weights for a bilinear remapping |
---|
937 | !! interpolation scheme. |
---|
938 | !! |
---|
939 | !! ** Method : This scheme is appropriate for bilinear interpolation |
---|
940 | !! on a general quadrilateral grid. |
---|
941 | !! This scheme is also used in OASIS. |
---|
942 | !! |
---|
943 | !! This routine is a derivative of the SCRIP software. |
---|
944 | !! Copyright 1997, 1998 the Regents of the University |
---|
945 | !! of California. See SCRIP_Copyright.txt. |
---|
946 | !! |
---|
947 | !! ** Action : |
---|
948 | !! |
---|
949 | !! References : Jones, P.: A user's guide for SCRIP: A Spherical |
---|
950 | !! Coordinate Remapping and Interpolation Package. |
---|
951 | !! Version 1.4. Los Alamos. |
---|
952 | !! |
---|
953 | !! http://www.acl.lanl.gov/climate/software/SCRIP/SCRIPmain.html |
---|
954 | !! |
---|
955 | !! History |
---|
956 | !! ! 97-11 (A. Weaver, N. Daget) |
---|
957 | !! ! 06-03 (A. Vidard) |
---|
958 | !! ! 06-10 (A. Weaver) Cleanup |
---|
959 | !!----------------------------------------------------------------------- |
---|
960 | |
---|
961 | !! * Arguments |
---|
962 | REAL(KIND=wp), INTENT(IN) :: & |
---|
963 | & pphi, & ! Geographical location of observation |
---|
964 | & plam, & |
---|
965 | & pphimm, & ! Geographical location of surrounding |
---|
966 | & pphimp, & ! model grid points |
---|
967 | & pphipm, & |
---|
968 | & pphipp, & |
---|
969 | & plammm, & |
---|
970 | & plammp, & |
---|
971 | & plampm, & |
---|
972 | & plampp |
---|
973 | REAL(KIND=wp), INTENT(OUT) :: & |
---|
974 | & pbiwmm, & ! Interpolation weights |
---|
975 | & pbiwmp, & |
---|
976 | & pbiwpm, & |
---|
977 | & pbiwpp |
---|
978 | LOGICAL, INTENT(out) :: & |
---|
979 | & ldfail |
---|
980 | |
---|
981 | !! * Local declarations |
---|
982 | INTEGER :: & |
---|
983 | & jiter |
---|
984 | INTEGER :: & |
---|
985 | & itermax |
---|
986 | REAL(KIND=wp) :: & |
---|
987 | & zphi, & ! Geographical location of observation |
---|
988 | & zlam, & |
---|
989 | & zphimm, & ! Geographical location of surrounding |
---|
990 | & zphimp, & ! model grid points |
---|
991 | & zphipm, & |
---|
992 | & zphipp, & |
---|
993 | & zlammm, & |
---|
994 | & zlammp, & |
---|
995 | & zlampm, & |
---|
996 | & zlampp, & |
---|
997 | & zdth1, & |
---|
998 | & zdth2, & |
---|
999 | & zdth3, & |
---|
1000 | & zdthp, & |
---|
1001 | & zdph1, & |
---|
1002 | & zdph2, & |
---|
1003 | & zdph3, & |
---|
1004 | & zdphp, & |
---|
1005 | & zmat1, & |
---|
1006 | & zmat2, & |
---|
1007 | & zmat3, & |
---|
1008 | & zmat4, & |
---|
1009 | & zdeli, & |
---|
1010 | & zdelj, & |
---|
1011 | & ziguess, & |
---|
1012 | & zjguess, & |
---|
1013 | & zeps, & |
---|
1014 | & zdeterm, & |
---|
1015 | & z2pi, & |
---|
1016 | & zhpi |
---|
1017 | |
---|
1018 | ! Initialization |
---|
1019 | |
---|
1020 | ! Conversion to radians |
---|
1021 | |
---|
1022 | zphi = pphi * rad |
---|
1023 | zlam = plam * rad |
---|
1024 | zphimm = pphimm * rad |
---|
1025 | zphimp = pphimp * rad |
---|
1026 | zphipm = pphipm * rad |
---|
1027 | zphipp = pphipp * rad |
---|
1028 | zlammm = plammm * rad |
---|
1029 | zlammp = plammp * rad |
---|
1030 | zlampm = plampm * rad |
---|
1031 | zlampp = plampp * rad |
---|
1032 | |
---|
1033 | ldfail = .FALSE. |
---|
1034 | |
---|
1035 | zdth1 = zphipm - zphimm |
---|
1036 | zdth2 = zphimp - zphimm |
---|
1037 | zdth3 = zphipp - zphipm - zdth2 |
---|
1038 | |
---|
1039 | zdph1 = zlampm - zlammm |
---|
1040 | zdph2 = zlammp - zlammm |
---|
1041 | zdph3 = zlampp - zlampm |
---|
1042 | |
---|
1043 | z2pi = 2.0_wp * rpi |
---|
1044 | |
---|
1045 | IF ( zdph1 > 3.0_wp * rpi ) zdph1 = zdph1 - z2pi |
---|
1046 | IF ( zdph2 > 3.0_wp * rpi ) zdph2 = zdph2 - z2pi |
---|
1047 | IF ( zdph3 > 3.0_wp * rpi ) zdph3 = zdph3 - z2pi |
---|
1048 | IF ( zdph1 < -3.0_wp * rpi ) zdph1 = zdph1 + z2pi |
---|
1049 | IF ( zdph2 < -3.0_wp * rpi ) zdph2 = zdph2 + z2pi |
---|
1050 | IF ( zdph3 < -3.0_wp * rpi ) zdph3 = zdph3 + z2pi |
---|
1051 | |
---|
1052 | zdph3 = zdph3 - zdph2 |
---|
1053 | |
---|
1054 | ziguess = 0.5_wp |
---|
1055 | zjguess = 0.5_wp |
---|
1056 | |
---|
1057 | itermax = 100 |
---|
1058 | |
---|
1059 | IF ( wp == sp ) THEN |
---|
1060 | zeps = 1.0e-6_wp ! Single precision |
---|
1061 | ELSE |
---|
1062 | zeps = 1.0e-10_wp ! Double precision |
---|
1063 | ENDIF |
---|
1064 | |
---|
1065 | !------------------------------------------------------------------------ |
---|
1066 | ! Iterate to determine (i,j) in new coordinate system |
---|
1067 | !------------------------------------------------------------------------ |
---|
1068 | jiter_loop: DO jiter = 1, itermax |
---|
1069 | |
---|
1070 | zdthp = zphi - zphimm - zdth1 * ziguess - zdth2 * zjguess & |
---|
1071 | & - zdth3 * ziguess * zjguess |
---|
1072 | zdphp = zlam - zlammm |
---|
1073 | |
---|
1074 | zhpi = 0.5_wp * rpi |
---|
1075 | IF ( zdphp > 3.0_wp * zhpi ) zdphp = zdphp - z2pi |
---|
1076 | IF ( zdphp < -3.0_wp * zhpi ) zdphp = zdphp + z2pi |
---|
1077 | |
---|
1078 | zdphp = zdphp - zdph1 * ziguess - zdph2 * zjguess & |
---|
1079 | & - zdph3 * ziguess * zjguess |
---|
1080 | |
---|
1081 | zmat1 = zdth1 + zdth3 * zjguess |
---|
1082 | zmat2 = zdth2 + zdth3 * ziguess |
---|
1083 | zmat3 = zdph1 + zdph3 * zjguess |
---|
1084 | zmat4 = zdph2 + zdph3 * ziguess |
---|
1085 | |
---|
1086 | ! Matrix determinant |
---|
1087 | zdeterm = zmat1 * zmat4 - zmat2 * zmat3 |
---|
1088 | |
---|
1089 | zdeli = ( zdthp * zmat4 - zmat2 * zdphp) / zdeterm |
---|
1090 | zdelj = ( zmat1 * zdphp - zdthp * zmat3) / zdeterm |
---|
1091 | |
---|
1092 | IF ( ABS( zdeli ) < zeps .AND. ABS( zdelj ) < zeps ) EXIT jiter_loop |
---|
1093 | |
---|
1094 | ziguess = ziguess + zdeli |
---|
1095 | zjguess = zjguess + zdelj |
---|
1096 | |
---|
1097 | ! DJL prevent ziguess and zjguess from going outside the range |
---|
1098 | ! 0 to 1 |
---|
1099 | ! prevents interpolated value going wrong |
---|
1100 | ! for example sea ice concentration gt 1 |
---|
1101 | |
---|
1102 | IF ( ziguess < 0 ) ziguess = 0.0_wp |
---|
1103 | IF ( zjguess < 0 ) zjguess = 0.0_wp |
---|
1104 | IF ( ziguess > 1 ) ziguess = 1.0_wp |
---|
1105 | IF ( zjguess > 1 ) zjguess = 1.0_wp |
---|
1106 | |
---|
1107 | END DO jiter_loop |
---|
1108 | |
---|
1109 | IF ( jiter <= itermax ) THEN |
---|
1110 | |
---|
1111 | ! Successfully found i,j, now compute the weights |
---|
1112 | |
---|
1113 | pbiwmm = ( 1.0_wp - ziguess ) * ( 1.0_wp - zjguess ) |
---|
1114 | pbiwmp = ( 1.0_wp - ziguess ) * zjguess |
---|
1115 | pbiwpm = ziguess * ( 1.0_wp - zjguess ) |
---|
1116 | pbiwpp = ziguess * zjguess |
---|
1117 | |
---|
1118 | ELSEIF ( jiter > itermax ) THEN |
---|
1119 | |
---|
1120 | IF(lwp) THEN |
---|
1121 | |
---|
1122 | WRITE(numout,*)'Obs lat/lon : ',pphi, plam |
---|
1123 | WRITE(numout,*)'Grid lats : ',pphimm, pphimp, pphipm, pphipp |
---|
1124 | WRITE(numout,*)'Grid lons : ',plammm, plammp, plampm, plampp |
---|
1125 | WRITE(numout,*)'Current i,j : ',ziguess, zjguess |
---|
1126 | WRITE(numout,*)'jiter = ',jiter |
---|
1127 | WRITE(numout,*)'zeps = ',zeps |
---|
1128 | WRITE(numout,*)'zdeli, zdelj = ',zdeli, zdelj |
---|
1129 | WRITE(numout,*)' Iterations for i,j exceed max iteration count!' |
---|
1130 | WRITE(numout,*) |
---|
1131 | |
---|
1132 | ldfail = .TRUE. |
---|
1133 | |
---|
1134 | ENDIF |
---|
1135 | |
---|
1136 | ENDIF |
---|
1137 | |
---|
1138 | END SUBROUTINE bil_wgt |
---|
1139 | |
---|
1140 | SUBROUTINE lu_invmat( pmatin, kdim, pmatou ) |
---|
1141 | !!----------------------------------------------------------------------- |
---|
1142 | !! |
---|
1143 | !! *** ROUTINE lu_invmat *** |
---|
1144 | !! |
---|
1145 | !! ** Purpose : Invert a matrix using LU decomposition. |
---|
1146 | !! |
---|
1147 | !! ** Method : |
---|
1148 | !! |
---|
1149 | !! ** Action : |
---|
1150 | !! |
---|
1151 | !! References : |
---|
1152 | !! |
---|
1153 | !! History |
---|
1154 | !! ! 02-11 (A. Weaver, N. Daget) |
---|
1155 | !! ! 06-03 (A. Vidard) |
---|
1156 | !! ! 06-10 (A. Weaver) Cleanup |
---|
1157 | !! ! 06-11 (NEMOVAR task force) Fix declaration of zd. |
---|
1158 | !!----------------------------------------------------------------------- |
---|
1159 | |
---|
1160 | !! * Arguments |
---|
1161 | INTEGER, INTENT(IN) :: & |
---|
1162 | & kdim ! Array dimension |
---|
1163 | REAL(KIND=wp), DIMENSION(kdim,kdim), INTENT(IN) :: & |
---|
1164 | & pmatin |
---|
1165 | REAL(KIND=wp), DIMENSION(kdim,kdim), INTENT(OUT) :: & |
---|
1166 | & pmatou |
---|
1167 | |
---|
1168 | !! * Local declarations |
---|
1169 | INTEGER :: & |
---|
1170 | & ji, & |
---|
1171 | & jj |
---|
1172 | INTEGER, DIMENSION(kdim) :: & |
---|
1173 | & indx |
---|
1174 | REAL(KIND=wp), DIMENSION(kdim,kdim) :: & |
---|
1175 | & zmat |
---|
1176 | REAL(KIND=wp) :: & |
---|
1177 | & zd |
---|
1178 | |
---|
1179 | ! Invert the matrix |
---|
1180 | DO jj = 1, kdim |
---|
1181 | DO ji = 1, kdim |
---|
1182 | pmatou(ji,jj) = 0.0_wp |
---|
1183 | zmat(ji,jj) = pmatin(ji,jj) |
---|
1184 | END DO |
---|
1185 | pmatou(jj,jj) = 1.0_wp |
---|
1186 | END DO |
---|
1187 | CALL lu_decomp( zmat, kdim, kdim, indx, zd ) |
---|
1188 | DO jj = 1, kdim |
---|
1189 | CALL lu_backsb( zmat, kdim, kdim, indx, pmatou(1,jj) ) |
---|
1190 | END DO |
---|
1191 | |
---|
1192 | END SUBROUTINE lu_invmat |
---|
1193 | |
---|
1194 | SUBROUTINE lu_decomp( pmatin, kdim1, kdim2, kindex, pflt ) |
---|
1195 | !!----------------------------------------------------------------------- |
---|
1196 | !! |
---|
1197 | !! *** ROUTINE lu_decomp *** |
---|
1198 | !! |
---|
1199 | !! ** Purpose : Compute the LU decomposition of a matrix |
---|
1200 | !! |
---|
1201 | !! ** Method : |
---|
1202 | !! |
---|
1203 | !! ** Action : |
---|
1204 | !! |
---|
1205 | !! References : |
---|
1206 | !! |
---|
1207 | !! History |
---|
1208 | !! ! 02-11 (A. Weaver, N. Daget) |
---|
1209 | !! ! 06-03 (A. Vidard) |
---|
1210 | !! ! 06-10 (A. Weaver) Cleanup |
---|
1211 | !!----------------------------------------------------------------------- |
---|
1212 | |
---|
1213 | !! * Arguments |
---|
1214 | INTEGER, INTENT(IN) :: & |
---|
1215 | & kdim1, & ! Array dimensions |
---|
1216 | & kdim2 |
---|
1217 | INTEGER, DIMENSION(kdim1), INTENT(OUT) :: & |
---|
1218 | & kindex |
---|
1219 | REAL(KIND=wp), INTENT(OUT) :: & |
---|
1220 | & pflt |
---|
1221 | REAL(KIND=wp), DIMENSION(kdim2,kdim2), INTENT(INOUT) :: & |
---|
1222 | & pmatin |
---|
1223 | |
---|
1224 | !! * Local declarations |
---|
1225 | INTEGER, PARAMETER :: & |
---|
1226 | & jpmax = 100 |
---|
1227 | REAL(KIND=wp), PARAMETER :: & |
---|
1228 | & pptiny = 1.0e-20_wp |
---|
1229 | REAL(KIND=wp), DIMENSION(jpmax) :: & |
---|
1230 | & zvv |
---|
1231 | INTEGER :: & |
---|
1232 | & ji, & |
---|
1233 | & jj, & |
---|
1234 | & jk |
---|
1235 | INTEGER :: & |
---|
1236 | & imax |
---|
1237 | REAL(KIND=wp) :: & |
---|
1238 | & zsum, & |
---|
1239 | & zdum, & |
---|
1240 | & zaamax |
---|
1241 | |
---|
1242 | imax = -1 |
---|
1243 | ! Main computation |
---|
1244 | pflt = 1.0_wp |
---|
1245 | DO ji = 1, kdim1 |
---|
1246 | zaamax = 0.0_wp |
---|
1247 | DO jj = 1, kdim1 |
---|
1248 | IF ( ABS( pmatin(ji,jj) ) > zaamax ) zaamax = ABS( pmatin(ji,jj) ) |
---|
1249 | END DO |
---|
1250 | IF ( zaamax == 0.0_wp ) THEN |
---|
1251 | CALL ctl_stop( 'singular matrix' ) |
---|
1252 | ENDIF |
---|
1253 | zvv(ji) = 1.0_wp / zaamax |
---|
1254 | END DO |
---|
1255 | DO jj = 1, kdim1 |
---|
1256 | DO ji = 1, jj-1 |
---|
1257 | zsum = pmatin(ji,jj) |
---|
1258 | DO jk = 1, ji-1 |
---|
1259 | zsum = zsum - pmatin(ji,jk) * pmatin(jk,jj) |
---|
1260 | END DO |
---|
1261 | pmatin(ji,jj) = zsum |
---|
1262 | END DO |
---|
1263 | zaamax = 0.0_wp |
---|
1264 | DO ji = jj, kdim1 |
---|
1265 | zsum = pmatin(ji,jj) |
---|
1266 | DO jk = 1, jj-1 |
---|
1267 | zsum = zsum - pmatin(ji,jk) * pmatin(jk,jj) |
---|
1268 | END DO |
---|
1269 | pmatin(ji,jj) = zsum |
---|
1270 | zdum = zvv(ji) * ABS( zsum ) |
---|
1271 | IF ( zdum >= zaamax ) THEN |
---|
1272 | imax = ji |
---|
1273 | zaamax = zdum |
---|
1274 | ENDIF |
---|
1275 | END DO |
---|
1276 | IF ( jj /= imax ) THEN |
---|
1277 | DO jk = 1, kdim1 |
---|
1278 | zdum = pmatin(imax,jk) |
---|
1279 | pmatin(imax,jk) = pmatin(jj,jk) |
---|
1280 | pmatin(jj,jk) = zdum |
---|
1281 | END DO |
---|
1282 | pflt = -pflt |
---|
1283 | zvv(imax) = zvv(jj) |
---|
1284 | ENDIF |
---|
1285 | kindex(jj) = imax |
---|
1286 | IF ( pmatin(jj,jj) == 0.0_wp ) pmatin(jj,jj) = pptiny |
---|
1287 | IF ( jj /= kdim1 ) THEN |
---|
1288 | zdum = 1.0_wp / pmatin(jj,jj) |
---|
1289 | DO ji = jj+1, kdim1 |
---|
1290 | pmatin(ji,jj) = pmatin(ji,jj) * zdum |
---|
1291 | END DO |
---|
1292 | ENDIF |
---|
1293 | END DO |
---|
1294 | |
---|
1295 | END SUBROUTINE lu_decomp |
---|
1296 | |
---|
1297 | SUBROUTINE lu_backsb( pmat, kdim1, kdim2, kindex, pvect ) |
---|
1298 | !!----------------------------------------------------------------------- |
---|
1299 | !! |
---|
1300 | !! *** ROUTINE lu_backsb *** |
---|
1301 | !! |
---|
1302 | !! ** Purpose : Back substitution |
---|
1303 | !! |
---|
1304 | !! ** Method : |
---|
1305 | !! |
---|
1306 | !! ** Action : |
---|
1307 | !! |
---|
1308 | !! References : |
---|
1309 | !! |
---|
1310 | !! History |
---|
1311 | !! ! 02-11 (A. Weaver, N. Daget) |
---|
1312 | !! ! 06-03 (A. Vidard) |
---|
1313 | !! ! 06-10 (A. Weaver) Cleanup |
---|
1314 | !!----------------------------------------------------------------------- |
---|
1315 | |
---|
1316 | !! * Arguments |
---|
1317 | INTEGER, INTENT(IN) :: & |
---|
1318 | & kdim1, & ! Array dimensions |
---|
1319 | & kdim2 |
---|
1320 | INTEGER, DIMENSION(kdim1), INTENT(IN) :: & |
---|
1321 | & kindex |
---|
1322 | REAL(KIND=wp), DIMENSION(kdim1), INTENT(INOUT) :: & |
---|
1323 | & pvect |
---|
1324 | REAL(KIND=wp), DIMENSION(kdim2,kdim2), INTENT(IN) :: & |
---|
1325 | & pmat |
---|
1326 | |
---|
1327 | !! * Local declarations |
---|
1328 | INTEGER :: & |
---|
1329 | & ji, & |
---|
1330 | & jii, & |
---|
1331 | & jj, & |
---|
1332 | & jll |
---|
1333 | REAL(KIND=wp) :: & |
---|
1334 | & zsum |
---|
1335 | |
---|
1336 | ! Main computation |
---|
1337 | jii = 0 |
---|
1338 | DO ji = 1, kdim1 |
---|
1339 | jll = kindex(ji) |
---|
1340 | zsum = pvect(jll) |
---|
1341 | pvect(jll) = pvect(ji) |
---|
1342 | IF ( jii /= 0 ) THEN |
---|
1343 | DO jj = jii, ji-1 |
---|
1344 | zsum = zsum - pmat(ji,jj) * pvect(jj) |
---|
1345 | END DO |
---|
1346 | ELSEIF ( zsum /= 0.0_wp ) THEN |
---|
1347 | jii = ji |
---|
1348 | ENDIF |
---|
1349 | pvect(ji) = zsum |
---|
1350 | END DO |
---|
1351 | DO ji = kdim1, 1, -1 |
---|
1352 | zsum = pvect(ji) |
---|
1353 | DO jj = ji+1, kdim1 |
---|
1354 | zsum = zsum - pmat(ji,jj) * pvect(jj) |
---|
1355 | END DO |
---|
1356 | pvect(ji) = zsum / pmat(ji,ji) |
---|
1357 | END DO |
---|
1358 | |
---|
1359 | END SUBROUTINE lu_backsb |
---|