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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 interpol_wind(itime,xt,yt,zt)
! i i i i
!*****************************************************************************
! *
! This subroutine interpolates the wind data to current trajectory position.*
! *
! Author: A. Stohl *
! *
! 16 December 1997 *
! *
! Revision March 2005 by AST : all output variables in common block cal- *
! culation of standard deviation done in this *
! routine rather than subroutine call in order *
! to save computation time *
! *
!*****************************************************************************
! *
! Variables: *
! u,v,w wind components *
! itime [s] current temporal position *
! memtime(3) [s] times of the wind fields in memory *
! xt,yt,zt coordinates position for which wind data shall be *
! calculated *
! *
! Constants: *
! *
!*****************************************************************************
use par_mod
use com_mod
use interpol_mod
implicit none
integer :: itime
real :: xt,yt,zt
! Auxiliary variables needed for interpolation
real :: dz1,dz2,dz
real :: u1(2),v1(2),w1(2),uh(2),vh(2),wh(2)
real :: usl,vsl,wsl,usq,vsq,wsq,xaux
integer :: i,m,n,indexh,indzh
real,parameter :: eps=1.0e-30
!********************************************
! Multilinear interpolation in time and space
!********************************************
! Determine the lower left corner and its distance to the current position
!*************************************************************************
ddx=xt-real(ix)
ddy=yt-real(jy)
rddx=1.-ddx
rddy=1.-ddy
p1=rddx*rddy
p2=ddx*rddy
p3=rddx*ddy
p4=ddx*ddy
! Calculate variables for time interpolation
!*******************************************
dt1=real(itime-memtime(1))
dt2=real(memtime(2)-itime)
dtt=1./(dt1+dt2)
! Determine the level below the current position for u,v
!*******************************************************
do i=2,nz
if (height(i).gt.zt) then
indz=i-1
goto 6
endif
end do
6 continue
! Vertical distance to the level below and above current position
!****************************************************************
dz=1./(height(indz+1)-height(indz))
dz1=(zt-height(indz))*dz
dz2=(height(indz+1)-zt)*dz
!**********************************************************************
! 1.) Bilinear horizontal interpolation
! This has to be done separately for 6 fields (Temporal(2)*Vertical(3))
!**********************************************************************
! Loop over 2 time steps and 2 levels
!************************************
usl=0.
vsl=0.
wsl=0.
usq=0.
vsq=0.
wsq=0.
do m=1,2
indexh=memind(m)
do n=1,2
indzh=indz+n-1
if (ngrid.lt.0) then
u1(n)=p1*uupol(ix ,jy ,indzh,indexh) &
+p2*uupol(ixp,jy ,indzh,indexh) &
+p3*uupol(ix ,jyp,indzh,indexh) &
+p4*uupol(ixp,jyp,indzh,indexh)
v1(n)=p1*vvpol(ix ,jy ,indzh,indexh) &
+p2*vvpol(ixp,jy ,indzh,indexh) &
+p3*vvpol(ix ,jyp,indzh,indexh) &
+p4*vvpol(ixp,jyp,indzh,indexh)
usl=usl+uupol(ix ,jy ,indzh,indexh)+ &
uupol(ixp,jy ,indzh,indexh) &
+uupol(ix ,jyp,indzh,indexh)+uupol(ixp,jyp,indzh,indexh)
vsl=vsl+vvpol(ix ,jy ,indzh,indexh)+ &
vvpol(ixp,jy ,indzh,indexh) &
+vvpol(ix ,jyp,indzh,indexh)+vvpol(ixp,jyp,indzh,indexh)
usq=usq+uupol(ix ,jy ,indzh,indexh)* &
uupol(ix ,jy ,indzh,indexh)+ &
uupol(ixp,jy ,indzh,indexh)*uupol(ixp,jy ,indzh,indexh)+ &
uupol(ix ,jyp,indzh,indexh)*uupol(ix ,jyp,indzh,indexh)+ &
uupol(ixp,jyp,indzh,indexh)*uupol(ixp,jyp,indzh,indexh)
vsq=vsq+vvpol(ix ,jy ,indzh,indexh)* &
vvpol(ix ,jy ,indzh,indexh)+ &
vvpol(ixp,jy ,indzh,indexh)*vvpol(ixp,jy ,indzh,indexh)+ &
vvpol(ix ,jyp,indzh,indexh)*vvpol(ix ,jyp,indzh,indexh)+ &
vvpol(ixp,jyp,indzh,indexh)*vvpol(ixp,jyp,indzh,indexh)
else
u1(n)=p1*uu(ix ,jy ,indzh,indexh) &
+p2*uu(ixp,jy ,indzh,indexh) &
+p3*uu(ix ,jyp,indzh,indexh) &
+p4*uu(ixp,jyp,indzh,indexh)
v1(n)=p1*vv(ix ,jy ,indzh,indexh) &
+p2*vv(ixp,jy ,indzh,indexh) &
+p3*vv(ix ,jyp,indzh,indexh) &
+p4*vv(ixp,jyp,indzh,indexh)
usl=usl+uu(ix ,jy ,indzh,indexh)+uu(ixp,jy ,indzh,indexh) &
+uu(ix ,jyp,indzh,indexh)+uu(ixp,jyp,indzh,indexh)
vsl=vsl+vv(ix ,jy ,indzh,indexh)+vv(ixp,jy ,indzh,indexh) &
+vv(ix ,jyp,indzh,indexh)+vv(ixp,jyp,indzh,indexh)
usq=usq+uu(ix ,jy ,indzh,indexh)*uu(ix ,jy ,indzh,indexh)+ &
uu(ixp,jy ,indzh,indexh)*uu(ixp,jy ,indzh,indexh)+ &
uu(ix ,jyp,indzh,indexh)*uu(ix ,jyp,indzh,indexh)+ &
uu(ixp,jyp,indzh,indexh)*uu(ixp,jyp,indzh,indexh)
vsq=vsq+vv(ix ,jy ,indzh,indexh)*vv(ix ,jy ,indzh,indexh)+ &
vv(ixp,jy ,indzh,indexh)*vv(ixp,jy ,indzh,indexh)+ &
vv(ix ,jyp,indzh,indexh)*vv(ix ,jyp,indzh,indexh)+ &
vv(ixp,jyp,indzh,indexh)*vv(ixp,jyp,indzh,indexh)
endif
w1(n)=p1*ww(ix ,jy ,indzh,indexh) &
+p2*ww(ixp,jy ,indzh,indexh) &
+p3*ww(ix ,jyp,indzh,indexh) &
+p4*ww(ixp,jyp,indzh,indexh)
wsl=wsl+ww(ix ,jy ,indzh,indexh)+ww(ixp,jy ,indzh,indexh) &
+ww(ix ,jyp,indzh,indexh)+ww(ixp,jyp,indzh,indexh)
wsq=wsq+ww(ix ,jy ,indzh,indexh)*ww(ix ,jy ,indzh,indexh)+ &
ww(ixp,jy ,indzh,indexh)*ww(ixp,jy ,indzh,indexh)+ &
ww(ix ,jyp,indzh,indexh)*ww(ix ,jyp,indzh,indexh)+ &
ww(ixp,jyp,indzh,indexh)*ww(ixp,jyp,indzh,indexh)
end do
!**********************************
! 2.) Linear vertical interpolation
!**********************************
uh(m)=dz2*u1(1)+dz1*u1(2)
vh(m)=dz2*v1(1)+dz1*v1(2)
wh(m)=dz2*w1(1)+dz1*w1(2)
end do
!************************************
! 3.) Temporal interpolation (linear)
!************************************
u=(uh(1)*dt2+uh(2)*dt1)*dtt
v=(vh(1)*dt2+vh(2)*dt1)*dtt
w=(wh(1)*dt2+wh(2)*dt1)*dtt
! Compute standard deviations
!****************************
xaux=usq-usl*usl/16.
if (xaux.lt.eps) then
usig=0.
else
usig=sqrt(xaux/15.)
endif
xaux=vsq-vsl*vsl/16.
if (xaux.lt.eps) then
vsig=0.
else
vsig=sqrt(xaux/15.)
endif
xaux=wsq-wsl*wsl/16.
if (xaux.lt.eps) then
wsig=0.
else
wsig=sqrt(xaux/15.)
endif
end subroutine interpol_wind
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