[e200b7a] | 1 | !********************************************************************** |
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| 2 | ! Copyright 1998,1999,2000,2001,2002,2005,2007,2008,2009,2010 * |
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| 3 | ! Andreas Stohl, Petra Seibert, A. Frank, Gerhard Wotawa, * |
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| 4 | ! Caroline Forster, Sabine Eckhardt, John Burkhart, Harald Sodemann * |
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| 5 | ! * |
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| 6 | ! This file is part of FLEXPART. * |
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| 7 | ! * |
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| 8 | ! FLEXPART is free software: you can redistribute it and/or modify * |
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| 9 | ! it under the terms of the GNU General Public License as published by* |
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| 10 | ! the Free Software Foundation, either version 3 of the License, or * |
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| 11 | ! (at your option) any later version. * |
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| 12 | ! * |
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| 13 | ! FLEXPART is distributed in the hope that it will be useful, * |
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| 14 | ! but WITHOUT ANY WARRANTY; without even the implied warranty of * |
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| 15 | ! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * |
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| 16 | ! GNU General Public License for more details. * |
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| 17 | ! * |
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| 18 | ! You should have received a copy of the GNU General Public License * |
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| 19 | ! along with FLEXPART. If not, see <http://www.gnu.org/licenses/>. * |
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| 20 | !********************************************************************** |
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| 21 | |
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| 22 | subroutine clustering(xl,yl,zl,n,xclust,yclust,zclust,fclust,rms, & |
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| 23 | rmsclust,zrms) |
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| 24 | ! i i i i o o o o o |
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| 25 | ! o o |
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| 26 | !***************************************************************************** |
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| 27 | ! * |
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| 28 | ! This routine clusters the particle position into ncluster custers. * |
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| 29 | ! Input are the longitudes (xl) and latitudes (yl) of the individual * |
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| 30 | ! points, output are the cluster mean positions (xclust,yclust). * |
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| 31 | ! Vertical positions are not directly used for the clustering. * |
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| 32 | ! * |
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| 33 | ! For clustering, the procedure described in Dorling et al. (1992) is used.* |
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| 34 | ! * |
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| 35 | ! Dorling, S.R., Davies, T.D. and Pierce, C.E. (1992): * |
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| 36 | ! Cluster analysis: a technique for estimating the synoptic meteorological * |
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| 37 | ! controls on air and precipitation chemistry - method and applications. * |
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| 38 | ! Atmospheric Environment 26A, 2575-2581. * |
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| 39 | ! * |
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| 40 | ! * |
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| 41 | ! Author: A. Stohl * |
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| 42 | ! * |
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| 43 | ! 1 February 2002 * |
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| 44 | ! * |
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| 45 | ! Variables: * |
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| 46 | ! fclust fraction of particles belonging to each cluster * |
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| 47 | ! ncluster number of clusters to be used * |
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| 48 | ! rms total horizontal rms distance after clustering * |
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| 49 | ! rmsclust horizontal rms distance for each individual cluster * |
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| 50 | ! zrms total vertical rms distance after clustering * |
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| 51 | ! xclust,yclust, Cluster centroid positions * |
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| 52 | ! zclust * |
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| 53 | ! xl,yl,zl particle positions * |
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| 54 | ! * |
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| 55 | !***************************************************************************** |
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| 56 | |
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| 57 | use par_mod |
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| 58 | |
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| 59 | implicit none |
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| 60 | |
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| 61 | integer :: n,i,j,l,nclust(maxpart),numb(ncluster),ncl |
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| 62 | real :: xl(n),yl(n),zl(n),xclust(ncluster),yclust(ncluster),x,y,z |
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| 63 | real :: zclust(ncluster),distance2,distances,distancemin,rms,rmsold |
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| 64 | real :: xav(ncluster),yav(ncluster),zav(ncluster),fclust(ncluster) |
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| 65 | real :: rmsclust(ncluster) |
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| 66 | real :: zdist,zrms |
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| 67 | |
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| 68 | |
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| 69 | |
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| 70 | if (n.lt.ncluster) return |
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| 71 | rmsold=-5. |
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| 72 | |
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| 73 | ! Convert longitude and latitude from degrees to radians |
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| 74 | !******************************************************* |
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| 75 | |
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| 76 | do i=1,n |
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| 77 | nclust(i)=i |
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| 78 | xl(i)=xl(i)*pi180 |
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| 79 | yl(i)=yl(i)*pi180 |
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| 80 | end do |
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| 81 | |
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| 82 | |
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| 83 | ! Generate a seed for each cluster |
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| 84 | !********************************* |
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| 85 | |
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| 86 | do j=1,ncluster |
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| 87 | zclust(j)=0. |
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| 88 | xclust(j)=xl(j*n/ncluster) |
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| 89 | yclust(j)=yl(j*n/ncluster) |
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| 90 | end do |
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| 91 | |
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| 92 | |
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| 93 | ! Iterative loop to compute the cluster means |
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| 94 | !******************************************** |
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| 95 | |
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| 96 | do l=1,100 |
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| 97 | |
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| 98 | ! Assign each particle to a cluster: criterion minimum distance to the |
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| 99 | ! cluster mean position |
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| 100 | !********************************************************************* |
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| 101 | |
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| 102 | |
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| 103 | do i=1,n |
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| 104 | distancemin=10.**10. |
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| 105 | do j=1,ncluster |
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| 106 | distances=distance2(yl(i),xl(i),yclust(j),xclust(j)) |
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| 107 | if (distances.lt.distancemin) then |
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| 108 | distancemin=distances |
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| 109 | ncl=j |
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| 110 | endif |
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| 111 | end do |
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| 112 | nclust(i)=ncl |
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| 113 | end do |
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| 114 | |
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| 115 | |
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| 116 | ! Recalculate the cluster centroid position: convert to 3D Cartesian coordinates, |
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| 117 | ! calculate mean position, and re-project this point onto the Earth's surface |
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| 118 | !***************************************************************************** |
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| 119 | |
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| 120 | do j=1,ncluster |
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| 121 | xav(j)=0. |
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| 122 | yav(j)=0. |
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| 123 | zav(j)=0. |
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| 124 | rmsclust(j)=0. |
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| 125 | numb(j)=0 |
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| 126 | end do |
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| 127 | rms=0. |
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| 128 | |
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| 129 | do i=1,n |
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| 130 | numb(nclust(i))=numb(nclust(i))+1 |
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| 131 | distances=distance2(yl(i),xl(i), & |
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| 132 | yclust(nclust(i)),xclust(nclust(i))) |
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| 133 | |
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| 134 | ! rms is the total rms of all particles |
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| 135 | ! rmsclust is the rms for a particular cluster |
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| 136 | !********************************************* |
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| 137 | |
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| 138 | rms=rms+distances*distances |
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| 139 | rmsclust(nclust(i))=rmsclust(nclust(i))+distances*distances |
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| 140 | |
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| 141 | ! Calculate Cartesian 3D coordinates from longitude and latitude |
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| 142 | !*************************************************************** |
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| 143 | |
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| 144 | x = cos(yl(i))*sin(xl(i)) |
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| 145 | y = -1.*cos(yl(i))*cos(xl(i)) |
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| 146 | z = sin(yl(i)) |
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| 147 | xav(nclust(i))=xav(nclust(i))+x |
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| 148 | yav(nclust(i))=yav(nclust(i))+y |
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| 149 | zav(nclust(i))=zav(nclust(i))+z |
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| 150 | end do |
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| 151 | |
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| 152 | rms=sqrt(rms/real(n)) |
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| 153 | |
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| 154 | |
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| 155 | ! Find the mean location in Cartesian coordinates |
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| 156 | !************************************************ |
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| 157 | |
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| 158 | do j=1,ncluster |
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| 159 | if (numb(j).gt.0) then |
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| 160 | rmsclust(j)=sqrt(rmsclust(j)/real(numb(j))) |
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| 161 | xav(j)=xav(j)/real(numb(j)) |
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| 162 | yav(j)=yav(j)/real(numb(j)) |
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| 163 | zav(j)=zav(j)/real(numb(j)) |
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| 164 | |
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| 165 | ! Project the point back onto Earth's surface |
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| 166 | !******************************************** |
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| 167 | |
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| 168 | xclust(j)=atan2(xav(j),-1.*yav(j)) |
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| 169 | yclust(j)=atan2(zav(j),sqrt(xav(j)*xav(j)+yav(j)*yav(j))) |
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| 170 | endif |
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| 171 | end do |
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| 172 | |
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| 173 | |
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| 174 | ! Leave the loop if the RMS distance decreases only slightly between 2 iterations |
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| 175 | !***************************************************************************** |
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| 176 | |
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| 177 | if ((l.gt.1).and.(abs(rms-rmsold)/rmsold.lt.0.005)) goto 99 |
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| 178 | rmsold=rms |
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| 179 | |
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| 180 | end do |
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| 181 | |
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| 182 | 99 continue |
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| 183 | |
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| 184 | ! Convert longitude and latitude from radians to degrees |
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| 185 | !******************************************************* |
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| 186 | |
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| 187 | do i=1,n |
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| 188 | xl(i)=xl(i)/pi180 |
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| 189 | yl(i)=yl(i)/pi180 |
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| 190 | zclust(nclust(i))=zclust(nclust(i))+zl(i) |
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| 191 | end do |
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| 192 | |
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| 193 | do j=1,ncluster |
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| 194 | xclust(j)=xclust(j)/pi180 |
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| 195 | yclust(j)=yclust(j)/pi180 |
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| 196 | if (numb(j).gt.0) zclust(j)=zclust(j)/real(numb(j)) |
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| 197 | fclust(j)=100.*real(numb(j))/real(n) |
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| 198 | end do |
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| 199 | |
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| 200 | ! Determine total vertical RMS deviation |
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| 201 | !*************************************** |
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| 202 | |
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| 203 | zrms=0. |
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| 204 | do i=1,n |
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| 205 | zdist=zl(i)-zclust(nclust(i)) |
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| 206 | zrms=zrms+zdist*zdist |
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| 207 | end do |
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| 208 | if (zrms.gt.0.) zrms=sqrt(zrms/real(n)) |
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| 209 | |
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| 210 | end subroutine clustering |
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