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