1 | ;+ |
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2 | ; @file_comments |
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3 | ; compute the weight and address needed to interpolate data from |
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4 | ; an "irregular 2D grid" (defined as a grid made of quadrilateral cells) |
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5 | ; to any grid using the bilinear method |
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6 | ; |
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7 | ; @categories |
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8 | ; Interpolation |
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9 | ; |
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10 | ; @param olonin {in}{required} |
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11 | ; longitude of the input data |
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12 | ; |
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13 | ; @param olat {in}{required} |
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14 | ; latitude of the input data |
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15 | ; |
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16 | ; @param omsk {in}{required} |
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17 | ; land/sea mask of the input data |
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18 | ; |
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19 | ; @param alonin {in}{required} |
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20 | ; longitude of the output data |
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21 | ; |
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22 | ; @param alat {in}{required} |
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23 | ; latitude of the output data |
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24 | ; |
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25 | ; @param amsk {in}{required} |
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26 | ; land/sea mask of the output data |
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27 | ; |
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28 | ; @param weig {out} |
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29 | ; @param addr {out} |
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30 | ; 2D arrays, weig and addr are the weight and addresses used to |
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31 | ; perform the interpolation: |
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32 | ; dataout = total(weig*datain[addr], 1) |
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33 | ; dataout = reform(dataout, jpia, jpja, /over) |
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34 | ; |
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35 | ; @restrictions |
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36 | ; - the input grid must be an "irregular 2D grid", defined as a grid made |
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37 | ; of quadrilateral cells which corners positions are defined with olonin and olat |
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38 | ; - We supposed the data are located on a sphere, with a periodicity along |
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39 | ; the longitude |
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40 | ; - to perform the bilinear interpolation within quadrilateral cells, we |
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41 | ; first morph the cell into a square cell and then compute the bilinear |
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42 | ; interpolation. |
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43 | ; - if some corners of the cell are land points, their weight is set to 0 |
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44 | ; and the weight is redistributed on the remaining "water" corners |
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45 | ; - points located out of the southern and northern boundaries or in cells |
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46 | ; containing only land points are set the the same value as their closest neighbor l |
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47 | ; |
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48 | ; @history |
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49 | ; June 2006: Sebastien Masson (smasson\@lodyc.jussieu.fr) |
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50 | ; |
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51 | ; @version $Id$ |
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52 | ; |
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53 | ;- |
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54 | ; |
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55 | PRO compute_fromirr_bilinear_weigaddr, olonin, olat, omsk, alonin, alat, amsk, weig, addr |
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56 | ; |
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57 | compile_opt idl2, strictarrsubs |
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58 | ; |
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59 | jpia = (size(alonin, /dimensions))[0] |
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60 | jpja = (size(alonin, /dimensions))[1] |
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61 | ; |
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62 | jpio = (size(olonin, /dimensions))[0] |
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63 | jpjo = (size(olonin, /dimensions))[1] |
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64 | ; |
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65 | ; longitude, between 0 and 360 |
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66 | alon = alonin MOD 360 |
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67 | out = where(alon LT 0) |
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68 | IF out[0] NE -1 THEN alon[out] = alon[out]+360 |
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69 | olon = olonin MOD 360 |
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70 | out = where(olon LT 0) |
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71 | IF out[0] NE -1 THEN olon[out] = olon[out]+360 |
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72 | ; |
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73 | ; we work only on the water points |
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74 | owater = where(omsk EQ 1) |
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75 | nowater = n_elements(owater) |
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76 | awater = where(amsk EQ 1) |
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77 | nawater = n_elements(awater) |
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78 | ; |
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79 | ; define all cells that have corners located at olon, olat |
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80 | ; we define the cell with the address of all corners |
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81 | ; |
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82 | ; 3 2 |
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83 | ; +------+ |
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84 | ; | | |
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85 | ; | | |
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86 | ; | | |
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87 | ; +------+ |
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88 | ; 0 1 |
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89 | ; |
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90 | alladdr = lindgen(jpio, jpjo-1) |
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91 | celladdr = lonarr(4, jpio*(jpjo-1)) |
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92 | celladdr[0, *] = alladdr |
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93 | celladdr[1, *] = shift(alladdr, -1) |
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94 | celladdr[2, *] = shift(alladdr + jpio, -1) |
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95 | celladdr[3, *] = alladdr + jpio |
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96 | ; |
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97 | ; list the cells that have at least 1 ocean point as corner |
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98 | good = where(total(omsk[celladdr], 1) GT 0) |
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99 | ; keep only those cells |
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100 | celladdr = celladdr[*, temporary(good)] |
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101 | ; |
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102 | xcell = olon[celladdr] |
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103 | minxcell = min(xcell, dimension = 1, max = maxxcell) |
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104 | ycell = olat[celladdr] |
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105 | minycell = min(ycell, dimension = 1, max = maxycell) |
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106 | ; foraddr: address of the ocean water cell associated to each atmosphere water point |
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107 | foraddr = lonarr(nawater) |
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108 | ; forweight: x/y position of the atmosphere water point in the ocean water cell |
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109 | forweight = dblarr(nawater, 2) |
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110 | ; |
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111 | ; Loop on all the water point of the atmosphere |
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112 | ; We look for which ocean water cell contains the atmosphere water point |
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113 | ; |
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114 | delta = max([(360./jpio), (180./jpjo)])* 4. |
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115 | FOR n = 0L, nawater-1 DO BEGIN |
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116 | ; control print |
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117 | IF (n MOD 5000) EQ 0 THEN print, n |
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118 | ; longitude and latitude of the atmosphere water point |
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119 | xx = alon[awater[n]] |
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120 | yy = alat[awater[n]] |
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121 | ; 1) we reduce the number of ocean cells for which we will try to know if |
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122 | ; xx,yy is inside. |
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123 | CASE 1 OF |
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124 | ; if we are near the norh pole |
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125 | yy GE (90-delta):BEGIN |
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126 | lat1 = 90-2*delta |
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127 | good = where(maxycell GE lat1) |
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128 | onsphere = 1 |
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129 | END |
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130 | ; if we are near the longitude periodicity area |
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131 | xx LE delta OR xx GE (360-delta):BEGIN |
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132 | lat1 = yy-delta |
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133 | lat2 = yy+delta |
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134 | good = where((minxcell LE 2*delta OR maxxcell GE (360-2*delta)) AND maxycell GE lat1 AND minycell LE lat2) |
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135 | onsphere = 1 |
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136 | END |
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137 | ; other cases |
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138 | ELSE:BEGIN |
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139 | lon1 = xx-delta |
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140 | lon2 = xx+delta |
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141 | lat1 = yy-delta |
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142 | lat2 = yy+delta |
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143 | good = where(maxxcell GE lon1 AND minxcell LE lon2 AND maxycell GE lat1 AND minycell le lat2) |
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144 | ; ORCA cases : orca grid is irregular only northward of 40N |
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145 | CASE 1 OF |
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146 | jpio EQ 92 AND (jpjo EQ 76 OR jpjo EQ 75 OR jpjo EQ 74 ):onsphere = yy GT 40 |
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147 | jpio EQ 180 AND (jpjo EQ 149 OR jpjo EQ 148 OR jpjo EQ 147 ):onsphere = yy GT 40 |
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148 | jpio EQ 720 AND (jpjo EQ 522 OR jpjo EQ 521 OR jpjo EQ 520 ):onsphere = yy GT 40 |
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149 | jpio EQ 1440 AND (jpjo EQ 1021 OR jpjo EQ 1020 OR jpjo EQ 1019):onsphere = yy GT 40 |
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150 | ELSE:onsphere = 1 |
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151 | ENDCASE |
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152 | END |
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153 | ENDCASE |
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154 | ; we found a short list of possible ocean water cells containing the atmosphere water point |
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155 | IF good[0] NE -1 THEN BEGIN |
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156 | ; in which cell is located the atmosphere water point? |
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157 | ; Warning! inquad use clockwise quadrilateral definition |
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158 | ind = inquad(xx, yy $ |
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159 | , xcell[0, good], ycell[0, good] $ |
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160 | , xcell[3, good], ycell[3, good] $ |
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161 | , xcell[2, good], ycell[2, good] $ |
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162 | , xcell[1, good], ycell[1, good] $ |
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163 | , onsphere = onsphere, newcoord = newcoord, /noprint) |
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164 | ; keep only the first cell (if the atmospheric point was located in several ocean cells) |
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165 | ind = ind[0] |
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166 | ; we found one ocean water cell containing the atmosphere water point |
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167 | IF ind NE -1 THEN BEGIN |
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168 | ind = good[ind] |
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169 | ; we keep its address |
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170 | foraddr[n] = ind |
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171 | ; now, we morph the quadrilateral ocean cell into the reference square (0 -> 1) |
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172 | ; in addition we get the corrdinates of the atmospheric point in this new morphed square |
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173 | IF onsphere THEN BEGIN |
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174 | ; Warning! quadrilateral2square use anticlockwise quadrilateral definition |
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175 | xy = quadrilateral2square(newcoord[0, 0], newcoord[1, 0] $ |
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176 | , newcoord[0, 3], newcoord[1, 3] $ |
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177 | , newcoord[0, 2], newcoord[1, 2] $ |
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178 | , newcoord[0, 1], newcoord[1, 1] $ |
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179 | , newcoord[0, 4], newcoord[1, 4]) |
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180 | ENDIF ELSE BEGIN |
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181 | xy = quadrilateral2square(xcell[0, ind], ycell[0, ind] $ |
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182 | , xcell[1, ind], ycell[1, ind] $ |
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183 | , xcell[2, ind], ycell[2, ind] $ |
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184 | , xcell[3, ind], ycell[3, ind], xx, yy) |
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185 | ENDELSE |
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186 | ; take care of rounding errors... |
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187 | zero = where(abs(xy) LT 1e-4) |
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188 | IF zero[0] NE -1 THEN xy[zero] = 0 |
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189 | one = where(abs(1-xy) LT 1e-4) |
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190 | IF one[0] NE -1 THEN xy[one] = 1 |
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191 | ; some (useless) checks... |
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192 | IF xy[0] LT 0 OR xy[0] GT 1 THEN stop |
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193 | IF xy[0] LT 0 OR xy[0] GT 1 THEN stop |
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194 | ; keep the new coordinates |
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195 | forweight[n, 0] = xy[0] |
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196 | forweight[n, 1] = xy[1] |
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197 | ENDIF ELSE foraddr[n] = -1 |
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198 | ENDIF ELSE foraddr[n] = -1 |
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199 | ENDFOR |
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200 | ; do we have some water atmospheric points that are not located in an water oceanic cell? |
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201 | bad = where(foraddr EQ -1) |
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202 | IF bad[0] NE -1 THEN BEGIN |
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203 | ; yes? |
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204 | ; we look for neighbor water atmospheric point located in water oceanic cell |
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205 | badaddr = awater[bad] |
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206 | good = where(foraddr NE -1) |
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207 | ; list the atmospheric points located in water oceanic cell |
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208 | goodaddr = awater[good] |
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209 | ; there longitude and latitude |
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210 | goodlon = alon[goodaddr] |
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211 | goodlat = alat[goodaddr] |
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212 | ; for all the bad points, look for a neighbor |
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213 | neig = lonarr(n_elements(bad)) |
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214 | FOR i = 0, n_elements(bad)-1 DO BEGIN |
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215 | neig[i] = (neighbor(alon[badaddr[i]], alat[badaddr[i]], goodlon, goodlat, /sphere))[0] |
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216 | ENDFOR |
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217 | ; get the address regarding foraddr |
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218 | neig = good[neig] |
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219 | ; associate each bad point with its neighbor (get its address and weight) |
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220 | foraddr[bad] = foraddr[neig] |
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221 | forweight[bad, *] = forweight[neig, *] |
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222 | endif |
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223 | ; transform the address of the ocean cell into the address of its 4 corners |
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224 | newaaddr = celladdr[*, temporary(foraddr)] |
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225 | ; now we compute the weight to give at each corner |
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226 | newaweig = dblarr(4, nawater) |
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227 | a = reform(forweight[*, 0], 1, nawater) |
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228 | b = reform(forweight[*, 1], 1, nawater) |
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229 | forweight = -1 ; free memory |
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230 | newaweig = [(1-a)*(1-b), (1-b)*a, a*b, (1-a)*b] |
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231 | a = -1 & b = -1 ; free memory |
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232 | ; mask the weight to suppress the corner located on land |
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233 | newaweig = newaweig*((omsk)[newaaddr]) |
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234 | totalweig = total(newaweig, 1) |
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235 | ; for cell with some land corner, |
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236 | ; we have to redistribute the weight on the reaining water corners |
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237 | ; weights normalization |
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238 | totalweig = total(newaweig, 1) |
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239 | newaweig = newaweig/(replicate(1., 4)#totalweig) |
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240 | totalweig = total(newaweig, 1) |
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241 | |
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242 | ; weights |
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243 | weig = dblarr(4, jpia*jpja) |
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244 | weig[*, awater] = temporary(newaweig) |
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245 | ; address |
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246 | addr = dblarr(4, jpia*jpja) |
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247 | addr[*, awater] = temporary(newaaddr) |
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248 | ; |
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249 | RETURN |
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250 | END |
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