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!**********************************************************************
! Copyright 1998,1999,2000,2001,2002,2005,2007,2008,2009,2010 *
! Andreas Stohl, Petra Seibert, A. Frank, Gerhard Wotawa, *
! Caroline Forster, Sabine Eckhardt, John Burkhart, Harald Sodemann *
! *
! This file is part of FLEXPART. *
! *
! FLEXPART is free software: you can redistribute it and/or modify *
! it under the terms of the GNU General Public License as published by*
! the Free Software Foundation, either version 3 of the License, or *
! (at your option) any later version. *
! *
! FLEXPART is distributed in the hope that it will be useful, *
! but WITHOUT ANY WARRANTY; without even the implied warranty of *
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
! GNU General Public License for more details. *
! *
! You should have received a copy of the GNU General Public License *
! along with FLEXPART. If not, see <http://www.gnu.org/licenses/>. *
!**********************************************************************
subroutine clustering(xl,yl,zl,n,xclust,yclust,zclust,fclust,rms, &
rmsclust,zrms)
! i i i i o o o o o
! o o
!*****************************************************************************
! *
! This routine clusters the particle position into ncluster custers. *
! Input are the longitudes (xl) and latitudes (yl) of the individual *
! points, output are the cluster mean positions (xclust,yclust). *
! Vertical positions are not directly used for the clustering. *
! *
! For clustering, the procedure described in Dorling et al. (1992) is used.*
! *
! Dorling, S.R., Davies, T.D. and Pierce, C.E. (1992): *
! Cluster analysis: a technique for estimating the synoptic meteorological *
! controls on air and precipitation chemistry - method and applications. *
! Atmospheric Environment 26A, 2575-2581. *
! *
! *
! Author: A. Stohl *
! *
! 1 February 2002 *
! *
! Variables: *
! fclust fraction of particles belonging to each cluster *
! ncluster number of clusters to be used *
! rms total horizontal rms distance after clustering *
! rmsclust horizontal rms distance for each individual cluster *
! zrms total vertical rms distance after clustering *
! xclust,yclust, Cluster centroid positions *
! zclust *
! xl,yl,zl particle positions *
! *
!*****************************************************************************
use par_mod
implicit none
integer :: n,i,j,l,nclust(maxpart),numb(ncluster),ncl
real :: xl(n),yl(n),zl(n),xclust(ncluster),yclust(ncluster),x,y,z
real :: zclust(ncluster),distance2,distances,distancemin,rms,rmsold
real :: xav(ncluster),yav(ncluster),zav(ncluster),fclust(ncluster)
real :: rmsclust(ncluster)
real :: zdist,zrms
if (n.lt.ncluster) return
rmsold=-5.
! Convert longitude and latitude from degrees to radians
!*******************************************************
do i=1,n
nclust(i)=i
xl(i)=xl(i)*pi180
yl(i)=yl(i)*pi180
end do
! Generate a seed for each cluster
!*********************************
do j=1,ncluster
zclust(j)=0.
xclust(j)=xl(j*n/ncluster)
yclust(j)=yl(j*n/ncluster)
end do
! Iterative loop to compute the cluster means
!********************************************
do l=1,100
! Assign each particle to a cluster: criterion minimum distance to the
! cluster mean position
!*********************************************************************
do i=1,n
distancemin=10.**10.
do j=1,ncluster
distances=distance2(yl(i),xl(i),yclust(j),xclust(j))
if (distances.lt.distancemin) then
distancemin=distances
ncl=j
endif
end do
nclust(i)=ncl
end do
! Recalculate the cluster centroid position: convert to 3D Cartesian coordinates,
! calculate mean position, and re-project this point onto the Earth's surface
!*****************************************************************************
do j=1,ncluster
xav(j)=0.
yav(j)=0.
zav(j)=0.
rmsclust(j)=0.
numb(j)=0
end do
rms=0.
do i=1,n
numb(nclust(i))=numb(nclust(i))+1
distances=distance2(yl(i),xl(i), &
yclust(nclust(i)),xclust(nclust(i)))
! rms is the total rms of all particles
! rmsclust is the rms for a particular cluster
!*********************************************
rms=rms+distances*distances
rmsclust(nclust(i))=rmsclust(nclust(i))+distances*distances
! Calculate Cartesian 3D coordinates from longitude and latitude
!***************************************************************
x = cos(yl(i))*sin(xl(i))
y = -1.*cos(yl(i))*cos(xl(i))
z = sin(yl(i))
xav(nclust(i))=xav(nclust(i))+x
yav(nclust(i))=yav(nclust(i))+y
zav(nclust(i))=zav(nclust(i))+z
end do
rms=sqrt(rms/real(n))
! Find the mean location in Cartesian coordinates
!************************************************
do j=1,ncluster
if (numb(j).gt.0) then
rmsclust(j)=sqrt(rmsclust(j)/real(numb(j)))
xav(j)=xav(j)/real(numb(j))
yav(j)=yav(j)/real(numb(j))
zav(j)=zav(j)/real(numb(j))
! Project the point back onto Earth's surface
!********************************************
xclust(j)=atan2(xav(j),-1.*yav(j))
yclust(j)=atan2(zav(j),sqrt(xav(j)*xav(j)+yav(j)*yav(j)))
endif
end do
! Leave the loop if the RMS distance decreases only slightly between 2 iterations
!*****************************************************************************
if ((l.gt.1).and.(abs(rms-rmsold)/rmsold.lt.0.005)) goto 99
rmsold=rms
end do
99 continue
! Convert longitude and latitude from radians to degrees
!*******************************************************
do i=1,n
xl(i)=xl(i)/pi180
yl(i)=yl(i)/pi180
zclust(nclust(i))=zclust(nclust(i))+zl(i)
end do
do j=1,ncluster
xclust(j)=xclust(j)/pi180
yclust(j)=yclust(j)/pi180
if (numb(j).gt.0) zclust(j)=zclust(j)/real(numb(j))
fclust(j)=100.*real(numb(j))/real(n)
end do
! Determine total vertical RMS deviation
!***************************************
zrms=0.
do i=1,n
zdist=zl(i)-zclust(nclust(i))
zrms=zrms+zdist*zdist
end do
if (zrms.gt.0.) zrms=sqrt(zrms/real(n))
end subroutine clustering
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