1 | !*********************************************************************** |
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2 | !* Copyright 2012,2013 * |
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3 | !* Jerome Brioude, Delia Arnold, Andreas Stohl, Wayne Angevine, * |
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4 | !* John Burkhart, Massimo Cassiani, Adam Dingwell, Richard C Easter, Sabine Eckhardt,* |
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5 | !* Stephanie Evan, Jerome D Fast, Don Morton, Ignacio Pisso, * |
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6 | !* Petra Seibert, Gerard Wotawa, Caroline Forster, Harald Sodemann, * |
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7 | !* * |
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8 | !* This file is part of FLEXPART WRF * |
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9 | !* * |
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10 | !* FLEXPART is free software: you can redistribute it and/or modify * |
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11 | !* it under the terms of the GNU General Public License as published by* |
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12 | !* the Free Software Foundation, either version 3 of the License, or * |
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13 | !* (at your option) any later version. * |
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14 | !* * |
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15 | !* FLEXPART is distributed in the hope that it will be useful, * |
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16 | !* but WITHOUT ANY WARRANTY; without even the implied warranty of * |
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17 | !* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * |
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18 | !* GNU General Public License for more details. * |
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19 | !* * |
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20 | !* You should have received a copy of the GNU General Public License * |
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21 | !* along with FLEXPART. If not, see <http://www.gnu.org/licenses/>. * |
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22 | !*********************************************************************** |
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23 | subroutine clustering(xl,yl,zl,n,xclust,yclust,zclust,fclust,rms, & |
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24 | rmsclust,zrms) |
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25 | ! i i i i o o o o o |
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26 | ! o o |
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27 | !******************************************************************************* |
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28 | ! * |
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29 | ! Note: This is the FLEXPART_WRF version of subroutine clustering. * |
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30 | ! The computational grid is the WRF x-y grid rather than lat-lon. * |
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31 | ! * |
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32 | ! This routine clusters the particle position into ncluster custers. * |
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33 | ! Input are the longitudes (xl) and latitudes (yl) of the individual * |
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34 | ! points, output are the cluster mean positions (xclust,yclust). * |
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35 | ! Vertical positions are not directly used for the clustering. * |
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36 | ! * |
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37 | ! For clustering, the procedure described in Dorling et al. (1992) is used. * |
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38 | ! * |
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39 | ! Dorling, S.R., Davies, T.D. and Pierce, C.E. (1992): * |
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40 | ! Cluster analysis: a technique for estimating the synoptic meteorological * |
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41 | ! controls on air and precipitation chemistry - method and applications. * |
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42 | ! Atmospheric Environment 26A, 2575-2581. * |
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43 | ! * |
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44 | ! * |
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45 | ! Author: A. Stohl * |
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46 | ! * |
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47 | ! 1 February 2002 * |
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48 | ! * |
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49 | ! 26 Oct 2005, R. Easter - changes associated with WRF horizontal grid. * |
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50 | ! x and y coordinates are in m, so the clustering * |
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51 | ! calculations are simpler, with no coordinate conversions. * |
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52 | ! 10 Mar 2006, R. Easter - bug fix at (new) lines 131-2 * |
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53 | ! change "yclust(j)" to "yclust(nclust(i))", same for xclust * |
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54 | ! * |
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55 | !******************************************************************************* |
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56 | ! * |
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57 | ! Variables: * |
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58 | ! fclust fraction of particles belonging to each cluster * |
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59 | ! ncluster number of clusters to be used * |
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60 | ! rms total horizontal rms distance after clustering * |
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61 | ! rmsclust horizontal rms distance for each individual cluster * |
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62 | ! zrms total vertical rms distance after clustering * |
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63 | ! xclust,yclust, Cluster centroid positions * |
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64 | ! zclust * |
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65 | ! xl,yl,zl particle positions * |
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66 | ! * |
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67 | ! * |
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68 | !******************************************************************************* |
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69 | |
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70 | |
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71 | use par_mod |
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72 | |
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73 | implicit none |
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74 | |
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75 | integer :: n,i,j,l,numb(ncluster),ncl,stat |
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76 | real :: xl(n),yl(n),zl(n),xclust(ncluster),yclust(ncluster),x,y,z |
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77 | real :: zclust(ncluster),distance2,distances,distancemin,rms,rmsold |
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78 | real :: xav(ncluster),yav(ncluster),zav(ncluster),fclust(ncluster) |
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79 | real :: rmsclust(ncluster) |
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80 | real :: zdist,zrms |
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81 | integer,allocatable, dimension (:) :: nclust |
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82 | |
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83 | allocate(nclust(maxpart) ,stat=stat) |
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84 | |
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85 | if (n.lt.ncluster) return |
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86 | rmsold=-5. |
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87 | |
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88 | ! Convert longitude and latitude from degrees to radians |
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89 | !******************************************************* |
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90 | |
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91 | do i=1,n |
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92 | nclust(i)=i |
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93 | |
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94 | ! for FLEXPART_WRF, x & y coords are in meters |
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95 | ! xl(i)=xl(i)*pi180 |
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96 | !5 yl(i)=yl(i)*pi180 |
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97 | end do |
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98 | |
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99 | ! Generate a seed for each cluster |
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100 | !********************************* |
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101 | |
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102 | do j=1,ncluster |
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103 | zclust(j)=0. |
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104 | xclust(j)=xl(j*n/ncluster) |
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105 | yclust(j)=yl(j*n/ncluster) |
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106 | end do |
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107 | |
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108 | |
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109 | ! Iterative loop to compute the cluster means |
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110 | !******************************************** |
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111 | |
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112 | do l=1,100 |
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113 | |
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114 | ! Assign each particle to a cluster: criterion minimum distance to the |
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115 | ! cluster mean position |
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116 | !********************************************************************* |
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117 | |
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118 | |
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119 | do i=1,n |
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120 | distancemin=10.**10. |
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121 | do j=1,ncluster |
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122 | |
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123 | ! for FLEXPART_WRF, x & y coords are in meters, so calc distance directly |
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124 | ! distances=distance2(yl(i),xl(i),yclust(j),xclust(j)) |
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125 | distances=sqrt( (yl(i)-yclust(j))**2 + & |
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126 | (xl(i)-xclust(j))**2 ) |
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127 | |
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128 | if (distances.lt.distancemin) then |
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129 | distancemin=distances |
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130 | ncl=j |
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131 | endif |
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132 | end do |
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133 | nclust(i)=ncl |
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134 | end do |
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135 | |
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136 | |
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137 | ! Recalculate the cluster centroid position: convert to 3D Cartesian coordinates, |
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138 | ! calculate mean position, and re-project this point onto the Earth's surface |
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139 | !******************************************************************************** |
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140 | |
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141 | do j=1,ncluster |
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142 | xav(j)=0. |
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143 | yav(j)=0. |
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144 | zav(j)=0. |
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145 | rmsclust(j)=0. |
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146 | numb(j)=0 |
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147 | end do |
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148 | |
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149 | rms=0. |
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150 | |
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151 | do i=1,n |
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152 | numb(nclust(i))=numb(nclust(i))+1 |
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153 | |
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154 | ! for FLEXPART_WRF, x & y coords are in meters, so calc distance directly |
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155 | ! distances=distance2(yl(i),xl(i), |
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156 | ! + yclust(nclust(i)),xclust(nclust(i))) |
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157 | ! 10-mar-2006 rce - bug fix - change "yclust(j)" to |
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158 | ! "yclust(nclust(i))", same for xclust |
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159 | distances=sqrt( (yl(i)-yclust(nclust(i)))**2 + & |
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160 | (xl(i)-xclust(nclust(i)))**2 ) |
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161 | |
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162 | ! rms is the total rms of all particles |
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163 | ! rmsclust is the rms for a particular cluster |
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164 | !********************************************* |
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165 | |
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166 | rms=rms+distances*distances |
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167 | rmsclust(nclust(i))=rmsclust(nclust(i))+distances*distances |
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168 | |
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169 | ! Calculate Cartesian 3D coordinates from longitude and latitude |
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170 | !*************************************************************** |
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171 | |
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172 | ! for FLEXPART_WRF, x & y coords are in meters, |
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173 | ! so no conversion is needed |
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174 | ! x = cos(yl(i))*sin(xl(i)) |
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175 | ! y = -1.*cos(yl(i))*cos(xl(i)) |
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176 | ! z = sin(yl(i)) |
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177 | ! xav(nclust(i))=xav(nclust(i))+x |
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178 | ! yav(nclust(i))=yav(nclust(i))+y |
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179 | !50 zav(nclust(i))=zav(nclust(i))+z |
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180 | xav(nclust(i))=xav(nclust(i))+xl(i) |
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181 | yav(nclust(i))=yav(nclust(i))+yl(i) |
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182 | zav(nclust(i))=0.0 |
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183 | end do |
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184 | |
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185 | |
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186 | rms=sqrt(rms/real(n)) |
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187 | |
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188 | |
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189 | ! Find the mean location in Cartesian coordinates |
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190 | !************************************************ |
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191 | |
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192 | do j=1,ncluster |
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193 | if (numb(j).gt.0) then |
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194 | rmsclust(j)=sqrt(rmsclust(j)/real(numb(j))) |
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195 | xav(j)=xav(j)/real(numb(j)) |
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196 | yav(j)=yav(j)/real(numb(j)) |
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197 | zav(j)=zav(j)/real(numb(j)) |
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198 | |
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199 | ! Project the point back onto Earth's surface |
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200 | !******************************************** |
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201 | |
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202 | ! for FLEXPART_WRF, x & y coords are in meters, |
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203 | ! so no conversion is needed |
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204 | ! xclust(j)=atan2(xav(j),-1.*yav(j)) |
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205 | ! yclust(j)=atan2(zav(j),sqrt(xav(j)*xav(j)+yav(j)*yav(j))) |
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206 | xclust(j)=xav(j) |
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207 | yclust(j)=yav(j) |
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208 | endif |
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209 | end do |
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210 | |
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211 | ! Leave the loop if the RMS distance decreases only slightly between 2 iterations |
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212 | !******************************************************************************** |
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213 | |
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214 | if ((l.gt.1).and.(abs(rms-rmsold)/rmsold.lt.0.005)) goto 99 |
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215 | rmsold=rms |
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216 | |
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217 | end do |
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218 | |
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219 | 99 continue |
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220 | |
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221 | ! Convert longitude and latitude from radians to degrees |
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222 | !******************************************************* |
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223 | |
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224 | do i=1,n |
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225 | ! for FLEXPART_WRF, x & y coords are in meters |
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226 | ! xl(i)=xl(i)/pi180 |
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227 | ! yl(i)=yl(i)/pi180 |
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228 | zclust(nclust(i))=zclust(nclust(i))+zl(i) |
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229 | end do |
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230 | |
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231 | do j=1,ncluster |
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232 | ! for FLEXPART_WRF, x & y coords are in meters |
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233 | ! xclust(j)=xclust(j)/pi180 |
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234 | ! yclust(j)=yclust(j)/pi180 |
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235 | if (numb(j).gt.0) zclust(j)=zclust(j)/real(numb(j)) |
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236 | fclust(j)=100.*real(numb(j))/real(n) |
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237 | end do |
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238 | |
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239 | |
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240 | ! Determine total vertical RMS deviation |
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241 | !*************************************** |
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242 | |
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243 | zrms=0. |
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244 | do i=1,n |
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245 | zdist=zl(i)-zclust(nclust(i)) |
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246 | zrms=zrms+zdist*zdist |
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247 | end do |
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248 | |
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249 | if (zrms.gt.0.) zrms=sqrt(zrms/real(n)) |
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250 | |
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251 | end subroutine clustering |
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252 | |
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