| 1 | ! SPDX-FileCopyrightText: FLEXPART 1998-2019, see flexpart_license.txt |
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| 2 | ! SPDX-License-Identifier: GPL-3.0-or-later |
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| 3 | |
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| 4 | subroutine interpol_wind(itime,xt,yt,zt) |
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| 5 | ! i i i i |
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| 6 | !***************************************************************************** |
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| 7 | ! * |
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| 8 | ! This subroutine interpolates the wind data to current trajectory position.* |
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| 9 | ! * |
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| 10 | ! Author: A. Stohl * |
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| 11 | ! * |
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| 12 | ! 16 December 1997 * |
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| 13 | ! * |
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| 14 | ! Revision March 2005 by AST : all output variables in common block cal- * |
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| 15 | ! culation of standard deviation done in this * |
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| 16 | ! routine rather than subroutine call in order * |
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| 17 | ! to save computation time * |
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| 18 | ! * |
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| 19 | !***************************************************************************** |
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| 20 | ! * |
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| 21 | ! Variables: * |
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| 22 | ! u,v,w wind components * |
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| 23 | ! itime [s] current temporal position * |
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| 24 | ! memtime(3) [s] times of the wind fields in memory * |
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| 25 | ! xt,yt,zt coordinates position for which wind data shall be * |
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| 26 | ! calculated * |
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| 27 | ! * |
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| 28 | ! Constants: * |
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| 29 | ! * |
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| 30 | !***************************************************************************** |
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| 31 | |
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| 32 | use par_mod |
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| 33 | use com_mod |
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| 34 | use interpol_mod |
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| 35 | |
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| 36 | implicit none |
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| 37 | |
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| 38 | integer :: itime |
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| 39 | real :: xt,yt,zt |
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| 40 | |
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| 41 | ! Auxiliary variables needed for interpolation |
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| 42 | real :: dz1,dz2,dz |
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| 43 | real :: u1(2),v1(2),w1(2),uh(2),vh(2),wh(2) |
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| 44 | real :: usl,vsl,wsl,usq,vsq,wsq,xaux |
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| 45 | integer :: i,m,n,indexh,indzh |
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| 46 | real,parameter :: eps=1.0e-30 |
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| 47 | |
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| 48 | |
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| 49 | !******************************************** |
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| 50 | ! Multilinear interpolation in time and space |
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| 51 | !******************************************** |
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| 52 | |
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| 53 | ! Determine the lower left corner and its distance to the current position |
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| 54 | !************************************************************************* |
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| 55 | |
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| 56 | ddx=xt-real(ix) |
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| 57 | ddy=yt-real(jy) |
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| 58 | rddx=1.-ddx |
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| 59 | rddy=1.-ddy |
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| 60 | p1=rddx*rddy |
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| 61 | p2=ddx*rddy |
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| 62 | p3=rddx*ddy |
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| 63 | p4=ddx*ddy |
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| 64 | |
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| 65 | ! Calculate variables for time interpolation |
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| 66 | !******************************************* |
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| 67 | |
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| 68 | dt1=real(itime-memtime(1)) |
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| 69 | dt2=real(memtime(2)-itime) |
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| 70 | dtt=1./(dt1+dt2) |
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| 71 | |
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| 72 | ! Determine the level below the current position for u,v |
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| 73 | !******************************************************* |
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| 74 | |
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| 75 | do i=2,nz |
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| 76 | if (height(i).gt.zt) then |
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| 77 | indz=i-1 |
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| 78 | goto 6 |
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| 79 | endif |
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| 80 | end do |
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| 81 | 6 continue |
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| 82 | |
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| 83 | |
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| 84 | ! Vertical distance to the level below and above current position |
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| 85 | !**************************************************************** |
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| 86 | |
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| 87 | dz=1./(height(indz+1)-height(indz)) |
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| 88 | dz1=(zt-height(indz))*dz |
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| 89 | dz2=(height(indz+1)-zt)*dz |
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| 90 | |
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| 91 | !********************************************************************** |
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| 92 | ! 1.) Bilinear horizontal interpolation |
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| 93 | ! This has to be done separately for 6 fields (Temporal(2)*Vertical(3)) |
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| 94 | !********************************************************************** |
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| 95 | |
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| 96 | ! Loop over 2 time steps and 2 levels |
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| 97 | !************************************ |
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| 98 | |
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| 99 | usl=0. |
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| 100 | vsl=0. |
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| 101 | wsl=0. |
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| 102 | usq=0. |
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| 103 | vsq=0. |
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| 104 | wsq=0. |
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| 105 | do m=1,2 |
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| 106 | indexh=memind(m) |
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| 107 | do n=1,2 |
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| 108 | indzh=indz+n-1 |
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| 109 | |
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| 110 | if (ngrid.lt.0) then |
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| 111 | u1(n)=p1*uupol(ix ,jy ,indzh,indexh) & |
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| 112 | +p2*uupol(ixp,jy ,indzh,indexh) & |
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| 113 | +p3*uupol(ix ,jyp,indzh,indexh) & |
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| 114 | +p4*uupol(ixp,jyp,indzh,indexh) |
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| 115 | v1(n)=p1*vvpol(ix ,jy ,indzh,indexh) & |
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| 116 | +p2*vvpol(ixp,jy ,indzh,indexh) & |
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| 117 | +p3*vvpol(ix ,jyp,indzh,indexh) & |
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| 118 | +p4*vvpol(ixp,jyp,indzh,indexh) |
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| 119 | usl=usl+uupol(ix ,jy ,indzh,indexh)+ & |
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| 120 | uupol(ixp,jy ,indzh,indexh) & |
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| 121 | +uupol(ix ,jyp,indzh,indexh)+uupol(ixp,jyp,indzh,indexh) |
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| 122 | vsl=vsl+vvpol(ix ,jy ,indzh,indexh)+ & |
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| 123 | vvpol(ixp,jy ,indzh,indexh) & |
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| 124 | +vvpol(ix ,jyp,indzh,indexh)+vvpol(ixp,jyp,indzh,indexh) |
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| 125 | |
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| 126 | usq=usq+uupol(ix ,jy ,indzh,indexh)* & |
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| 127 | uupol(ix ,jy ,indzh,indexh)+ & |
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| 128 | uupol(ixp,jy ,indzh,indexh)*uupol(ixp,jy ,indzh,indexh)+ & |
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| 129 | uupol(ix ,jyp,indzh,indexh)*uupol(ix ,jyp,indzh,indexh)+ & |
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| 130 | uupol(ixp,jyp,indzh,indexh)*uupol(ixp,jyp,indzh,indexh) |
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| 131 | vsq=vsq+vvpol(ix ,jy ,indzh,indexh)* & |
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| 132 | vvpol(ix ,jy ,indzh,indexh)+ & |
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| 133 | vvpol(ixp,jy ,indzh,indexh)*vvpol(ixp,jy ,indzh,indexh)+ & |
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| 134 | vvpol(ix ,jyp,indzh,indexh)*vvpol(ix ,jyp,indzh,indexh)+ & |
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| 135 | vvpol(ixp,jyp,indzh,indexh)*vvpol(ixp,jyp,indzh,indexh) |
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| 136 | else |
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| 137 | u1(n)=p1*uu(ix ,jy ,indzh,indexh) & |
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| 138 | +p2*uu(ixp,jy ,indzh,indexh) & |
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| 139 | +p3*uu(ix ,jyp,indzh,indexh) & |
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| 140 | +p4*uu(ixp,jyp,indzh,indexh) |
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| 141 | v1(n)=p1*vv(ix ,jy ,indzh,indexh) & |
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| 142 | +p2*vv(ixp,jy ,indzh,indexh) & |
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| 143 | +p3*vv(ix ,jyp,indzh,indexh) & |
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| 144 | +p4*vv(ixp,jyp,indzh,indexh) |
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| 145 | usl=usl+uu(ix ,jy ,indzh,indexh)+uu(ixp,jy ,indzh,indexh) & |
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| 146 | +uu(ix ,jyp,indzh,indexh)+uu(ixp,jyp,indzh,indexh) |
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| 147 | vsl=vsl+vv(ix ,jy ,indzh,indexh)+vv(ixp,jy ,indzh,indexh) & |
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| 148 | +vv(ix ,jyp,indzh,indexh)+vv(ixp,jyp,indzh,indexh) |
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| 149 | |
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| 150 | usq=usq+uu(ix ,jy ,indzh,indexh)*uu(ix ,jy ,indzh,indexh)+ & |
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| 151 | uu(ixp,jy ,indzh,indexh)*uu(ixp,jy ,indzh,indexh)+ & |
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| 152 | uu(ix ,jyp,indzh,indexh)*uu(ix ,jyp,indzh,indexh)+ & |
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| 153 | uu(ixp,jyp,indzh,indexh)*uu(ixp,jyp,indzh,indexh) |
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| 154 | vsq=vsq+vv(ix ,jy ,indzh,indexh)*vv(ix ,jy ,indzh,indexh)+ & |
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| 155 | vv(ixp,jy ,indzh,indexh)*vv(ixp,jy ,indzh,indexh)+ & |
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| 156 | vv(ix ,jyp,indzh,indexh)*vv(ix ,jyp,indzh,indexh)+ & |
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| 157 | vv(ixp,jyp,indzh,indexh)*vv(ixp,jyp,indzh,indexh) |
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| 158 | endif |
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| 159 | w1(n)=p1*ww(ix ,jy ,indzh,indexh) & |
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| 160 | +p2*ww(ixp,jy ,indzh,indexh) & |
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| 161 | +p3*ww(ix ,jyp,indzh,indexh) & |
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| 162 | +p4*ww(ixp,jyp,indzh,indexh) |
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| 163 | wsl=wsl+ww(ix ,jy ,indzh,indexh)+ww(ixp,jy ,indzh,indexh) & |
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| 164 | +ww(ix ,jyp,indzh,indexh)+ww(ixp,jyp,indzh,indexh) |
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| 165 | wsq=wsq+ww(ix ,jy ,indzh,indexh)*ww(ix ,jy ,indzh,indexh)+ & |
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| 166 | ww(ixp,jy ,indzh,indexh)*ww(ixp,jy ,indzh,indexh)+ & |
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| 167 | ww(ix ,jyp,indzh,indexh)*ww(ix ,jyp,indzh,indexh)+ & |
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| 168 | ww(ixp,jyp,indzh,indexh)*ww(ixp,jyp,indzh,indexh) |
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| 169 | end do |
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| 170 | |
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| 171 | |
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| 172 | !********************************** |
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| 173 | ! 2.) Linear vertical interpolation |
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| 174 | !********************************** |
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| 175 | |
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| 176 | uh(m)=dz2*u1(1)+dz1*u1(2) |
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| 177 | vh(m)=dz2*v1(1)+dz1*v1(2) |
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| 178 | wh(m)=dz2*w1(1)+dz1*w1(2) |
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| 179 | end do |
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| 180 | |
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| 181 | |
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| 182 | !************************************ |
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| 183 | ! 3.) Temporal interpolation (linear) |
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| 184 | !************************************ |
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| 185 | |
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| 186 | u=(uh(1)*dt2+uh(2)*dt1)*dtt |
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| 187 | v=(vh(1)*dt2+vh(2)*dt1)*dtt |
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| 188 | w=(wh(1)*dt2+wh(2)*dt1)*dtt |
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| 189 | |
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| 190 | |
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| 191 | ! Compute standard deviations |
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| 192 | !**************************** |
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| 193 | |
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| 194 | xaux=usq-usl*usl/16. |
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| 195 | if (xaux.lt.eps) then |
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| 196 | usig=0. |
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| 197 | else |
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| 198 | usig=sqrt(xaux/15.) |
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| 199 | endif |
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| 200 | |
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| 201 | xaux=vsq-vsl*vsl/16. |
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| 202 | if (xaux.lt.eps) then |
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| 203 | vsig=0. |
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| 204 | else |
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| 205 | vsig=sqrt(xaux/15.) |
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| 206 | endif |
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| 207 | |
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| 208 | |
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| 209 | xaux=wsq-wsl*wsl/16. |
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| 210 | if (xaux.lt.eps) then |
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| 211 | wsig=0. |
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| 212 | else |
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| 213 | wsig=sqrt(xaux/15.) |
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| 214 | endif |
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| 215 | |
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| 216 | end subroutine interpol_wind |
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