| 1 | subroutine calcpv(n,uuh,vvh,pvh) |
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| 2 | ! i i i o |
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| 3 | !***************************************************************************** |
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| 4 | ! * |
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| 5 | ! Calculation of potential vorticity on 3-d grid. * |
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| 6 | ! * |
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| 7 | ! Author: P. James * |
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| 8 | ! 3 February 2000 * |
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| 9 | ! * |
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| 10 | ! Adaptation to FLEXPART, A. Stohl, 1 May 2000 * |
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| 11 | ! * |
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| 12 | !***************************************************************************** |
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| 13 | ! * |
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| 14 | ! Variables: * |
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| 15 | ! n temporal index for meteorological fields (1 to 2) * |
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| 16 | ! * |
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| 17 | ! Constants: * |
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| 18 | ! * |
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| 19 | !***************************************************************************** |
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| 20 | |
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| 21 | use par_mod |
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| 22 | use com_mod |
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| 23 | |
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| 24 | implicit none |
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| 25 | |
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| 26 | integer :: n,ix,jy,i,j,k,kl,ii,jj,klvrp,klvrm,klpt,kup,kdn,kch |
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| 27 | integer :: jyvp,jyvm,ixvp,ixvm,jumpx,jumpy,jux,juy,ivrm,ivrp,ivr |
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| 28 | integer :: nlck |
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| 29 | real :: vx(2),uy(2),phi,tanphi,cosphi,dvdx,dudy,f |
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| 30 | real :: theta,thetap,thetam,dthetadp,dt1,dt2,dt |
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| 31 | real :: pvavr,ppml(0:nxmax-1,0:nymax-1,nuvzmax),ppmk(0:nxmax-1,0:nymax-1,nuvzmax) |
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| 32 | real :: thup,thdn |
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| 33 | real,parameter :: eps=1.e-5, p0=101325 |
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| 34 | real :: uuh(0:nxmax-1,0:nymax-1,nuvzmax) |
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| 35 | real :: vvh(0:nxmax-1,0:nymax-1,nuvzmax) |
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| 36 | real :: pvh(0:nxmax-1,0:nymax-1,nuvzmax) |
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| 37 | |
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| 38 | ! Set number of levels to check for adjacent theta |
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| 39 | nlck=nuvz/3 |
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| 40 | ! |
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| 41 | ! Loop over entire grid |
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| 42 | !********************** |
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| 43 | do kl=1,nuvz |
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| 44 | do jy=0,nymin1 |
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| 45 | do ix=0,nxmin1 |
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| 46 | ppml(ix,jy,kl)=akz(kl)+bkz(kl)*ps(ix,jy,1,n) |
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| 47 | enddo |
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| 48 | enddo |
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| 49 | enddo |
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| 50 | |
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| 51 | ! ppmk(:,:,1:nuvz)=(100000./ppml(:,:,1:nuvz))**kappa |
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| 52 | ppmk(0:nxmin1,0:nymin1,1:nuvz)=(100000./ppml(0:nxmin1,0:nymin1,1:nuvz))**kappa |
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| 53 | |
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| 54 | do jy=0,nymin1 |
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| 55 | if (sglobal.and.jy.eq.0) goto 10 |
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| 56 | if (nglobal.and.jy.eq.nymin1) goto 10 |
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| 57 | phi = (ylat0 + jy * dy) * pi / 180. |
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| 58 | f = 0.00014585 * sin(phi) |
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| 59 | tanphi = tan(phi) |
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| 60 | cosphi = cos(phi) |
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| 61 | ! Provide a virtual jy+1 and jy-1 in case we are on domain edge (Lat) |
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| 62 | jyvp=jy+1 |
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| 63 | jyvm=jy-1 |
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| 64 | if (jy.eq.0) jyvm=0 |
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| 65 | if (jy.eq.nymin1) jyvp=nymin1 |
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| 66 | ! Define absolute gap length |
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| 67 | jumpy=2 |
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| 68 | if (jy.eq.0.or.jy.eq.nymin1) jumpy=1 |
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| 69 | if (sglobal.and.jy.eq.1) then |
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| 70 | jyvm=1 |
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| 71 | jumpy=1 |
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| 72 | end if |
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| 73 | if (nglobal.and.jy.eq.ny-2) then |
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| 74 | jyvp=ny-2 |
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| 75 | jumpy=1 |
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| 76 | end if |
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| 77 | juy=jumpy |
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| 78 | ! |
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| 79 | do ix=0,nxmin1 |
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| 80 | ! Provide a virtual ix+1 and ix-1 in case we are on domain edge (Long) |
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| 81 | ixvp=ix+1 |
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| 82 | ixvm=ix-1 |
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| 83 | jumpx=2 |
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| 84 | if (xglobal) then |
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| 85 | ivrp=ixvp |
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| 86 | ivrm=ixvm |
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| 87 | if (ixvm.lt.0) ivrm=ixvm+nxmin1 |
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| 88 | if (ixvp.ge.nx) ivrp=ixvp-nx+1 |
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| 89 | else |
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| 90 | if (ix.eq.0) ixvm=0 |
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| 91 | if (ix.eq.nxmin1) ixvp=nxmin1 |
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| 92 | ivrp=ixvp |
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| 93 | ivrm=ixvm |
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| 94 | ! Define absolute gap length |
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| 95 | if (ix.eq.0.or.ix.eq.nxmin1) jumpx=1 |
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| 96 | end if |
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| 97 | jux=jumpx |
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| 98 | ! |
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| 99 | ! Loop over the vertical |
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| 100 | !*********************** |
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| 101 | |
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| 102 | do kl=1,nuvz |
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| 103 | theta=tth(ix,jy,kl,n)*ppmk(ix,jy,kl) |
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| 104 | klvrp=kl+1 |
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| 105 | klvrm=kl-1 |
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| 106 | klpt=kl |
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| 107 | ! If top or bottom level, dthetadp is evaluated between the current |
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| 108 | ! level and the level inside, otherwise between level+1 and level-1 |
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| 109 | ! |
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| 110 | if (klvrp.gt.nuvz) klvrp=nuvz |
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| 111 | if (klvrm.lt.1) klvrm=1 |
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| 112 | thetap=tth(ix,jy,klvrp,n)*ppmk(ix,jy,klvrp) |
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| 113 | thetam=tth(ix,jy,klvrm,n)*ppmk(ix,jy,klvrm) |
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| 114 | dthetadp=(thetap-thetam)/(ppml(ix,jy,klvrp)-ppml(ix,jy,klvrm)) |
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| 115 | |
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| 116 | ! Compute vertical position at pot. temperature surface on subgrid |
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| 117 | ! and the wind at that position |
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| 118 | !***************************************************************** |
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| 119 | ! a) in x direction |
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| 120 | ii=0 |
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| 121 | do i=ixvm,ixvp,jumpx |
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| 122 | ivr=i |
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| 123 | if (xglobal) then |
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| 124 | if (i.lt.0) ivr=ivr+nxmin1 |
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| 125 | if (i.ge.nx) ivr=ivr-nx+1 |
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| 126 | end if |
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| 127 | ii=ii+1 |
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| 128 | ! Search adjacent levels for current theta value |
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| 129 | ! Spiral out from current level for efficiency |
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| 130 | kup=klpt-1 |
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| 131 | kdn=klpt |
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| 132 | kch=0 |
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| 133 | 40 continue |
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| 134 | ! Upward branch |
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| 135 | kup=kup+1 |
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| 136 | if (kch.ge.nlck) goto 21 ! No more levels to check, |
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| 137 | ! ! and no values found |
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| 138 | if (kup.ge.nuvz) goto 41 |
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| 139 | kch=kch+1 |
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| 140 | k=kup |
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| 141 | thdn=tth(ivr,jy,k,n)*ppmk(ivr,jy,k) |
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| 142 | thup=tth(ivr,jy,k+1,n)*ppmk(ivr,jy,k+1) |
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| 143 | |
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| 144 | |
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| 145 | if (((thdn.ge.theta).and.(thup.le.theta)).or. & |
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| 146 | ((thdn.le.theta).and.(thup.ge.theta))) then |
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| 147 | dt1=abs(theta-thdn) |
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| 148 | dt2=abs(theta-thup) |
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| 149 | dt=dt1+dt2 |
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| 150 | if (dt.lt.eps) then ! Avoid division by zero error |
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| 151 | dt1=0.5 ! G.W., 10.4.1996 |
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| 152 | dt2=0.5 |
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| 153 | dt=1.0 |
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| 154 | endif |
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| 155 | vx(ii)=(vvh(ivr,jy,k)*dt2+vvh(ivr,jy,k+1)*dt1)/dt |
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| 156 | goto 20 |
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| 157 | endif |
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| 158 | 41 continue |
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| 159 | ! Downward branch |
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| 160 | kdn=kdn-1 |
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| 161 | if (kdn.lt.1) goto 40 |
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| 162 | kch=kch+1 |
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| 163 | k=kdn |
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| 164 | thdn=tth(ivr,jy,k,n)*ppmk(ivr,jy,k) |
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| 165 | thup=tth(ivr,jy,k+1,n)*ppmk(ivr,jy,k+1) |
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| 166 | |
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| 167 | if (((thdn.ge.theta).and.(thup.le.theta)).or. & |
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| 168 | ((thdn.le.theta).and.(thup.ge.theta))) then |
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| 169 | dt1=abs(theta-thdn) |
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| 170 | dt2=abs(theta-thup) |
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| 171 | dt=dt1+dt2 |
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| 172 | if (dt.lt.eps) then ! Avoid division by zero error |
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| 173 | dt1=0.5 ! G.W., 10.4.1996 |
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| 174 | dt2=0.5 |
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| 175 | dt=1.0 |
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| 176 | endif |
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| 177 | vx(ii)=(vvh(ivr,jy,k)*dt2+vvh(ivr,jy,k+1)*dt1)/dt |
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| 178 | goto 20 |
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| 179 | endif |
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| 180 | goto 40 |
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| 181 | ! This section used when no values were found |
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| 182 | 21 continue |
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| 183 | ! Must use vv at current level and long. jux becomes smaller by 1 |
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| 184 | vx(ii)=vvh(ix,jy,kl) |
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| 185 | jux=jux-1 |
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| 186 | ! Otherwise OK |
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| 187 | 20 continue |
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| 188 | end do |
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| 189 | if (jux.gt.0) then |
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| 190 | dvdx=(vx(2)-vx(1))/real(jux)/(dx*pi/180.) |
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| 191 | else |
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| 192 | dvdx=vvh(ivrp,jy,kl)-vvh(ivrm,jy,kl) |
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| 193 | dvdx=dvdx/real(jumpx)/(dx*pi/180.) |
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| 194 | ! Only happens if no equivalent theta value |
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| 195 | ! can be found on either side, hence must use values |
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| 196 | ! from either side, same pressure level. |
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| 197 | end if |
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| 198 | |
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| 199 | ! b) in y direction |
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| 200 | |
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| 201 | jj=0 |
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| 202 | do j=jyvm,jyvp,jumpy |
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| 203 | jj=jj+1 |
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| 204 | ! Search adjacent levels for current theta value |
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| 205 | ! Spiral out from current level for efficiency |
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| 206 | kup=klpt-1 |
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| 207 | kdn=klpt |
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| 208 | kch=0 |
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| 209 | 70 continue |
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| 210 | ! Upward branch |
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| 211 | kup=kup+1 |
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| 212 | if (kch.ge.nlck) goto 51 ! No more levels to check, |
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| 213 | ! ! and no values found |
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| 214 | if (kup.ge.nuvz) goto 71 |
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| 215 | kch=kch+1 |
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| 216 | k=kup |
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| 217 | thdn=tth(ix,j,k,n)*ppmk(ix,j,k) |
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| 218 | thup=tth(ix,j,k+1,n)*ppmk(ix,j,k+1) |
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| 219 | if (((thdn.ge.theta).and.(thup.le.theta)).or. & |
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| 220 | ((thdn.le.theta).and.(thup.ge.theta))) then |
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| 221 | dt1=abs(theta-thdn) |
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| 222 | dt2=abs(theta-thup) |
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| 223 | dt=dt1+dt2 |
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| 224 | if (dt.lt.eps) then ! Avoid division by zero error |
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| 225 | dt1=0.5 ! G.W., 10.4.1996 |
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| 226 | dt2=0.5 |
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| 227 | dt=1.0 |
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| 228 | endif |
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| 229 | uy(jj)=(uuh(ix,j,k)*dt2+uuh(ix,j,k+1)*dt1)/dt |
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| 230 | goto 50 |
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| 231 | endif |
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| 232 | 71 continue |
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| 233 | ! Downward branch |
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| 234 | kdn=kdn-1 |
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| 235 | if (kdn.lt.1) goto 70 |
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| 236 | kch=kch+1 |
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| 237 | k=kdn |
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| 238 | thdn=tth(ix,j,k,n)*ppmk(ix,j,k) |
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| 239 | thup=tth(ix,j,k+1,n)*ppmk(ix,j,k+1) |
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| 240 | if (((thdn.ge.theta).and.(thup.le.theta)).or. & |
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| 241 | ((thdn.le.theta).and.(thup.ge.theta))) then |
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| 242 | dt1=abs(theta-thdn) |
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| 243 | dt2=abs(theta-thup) |
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| 244 | dt=dt1+dt2 |
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| 245 | if (dt.lt.eps) then ! Avoid division by zero error |
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| 246 | dt1=0.5 ! G.W., 10.4.1996 |
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| 247 | dt2=0.5 |
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| 248 | dt=1.0 |
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| 249 | endif |
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| 250 | uy(jj)=(uuh(ix,j,k)*dt2+uuh(ix,j,k+1)*dt1)/dt |
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| 251 | goto 50 |
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| 252 | endif |
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| 253 | goto 70 |
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| 254 | ! This section used when no values were found |
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| 255 | 51 continue |
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| 256 | ! Must use uu at current level and lat. juy becomes smaller by 1 |
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| 257 | uy(jj)=uuh(ix,jy,kl) |
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| 258 | juy=juy-1 |
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| 259 | ! Otherwise OK |
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| 260 | 50 continue |
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| 261 | end do |
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| 262 | if (juy.gt.0) then |
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| 263 | dudy=(uy(2)-uy(1))/real(juy)/(dy*pi/180.) |
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| 264 | else |
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| 265 | dudy=uuh(ix,jyvp,kl)-uuh(ix,jyvm,kl) |
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| 266 | dudy=dudy/real(jumpy)/(dy*pi/180.) |
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| 267 | end if |
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| 268 | ! |
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| 269 | pvh(ix,jy,kl)=dthetadp*(f+(dvdx/cosphi-dudy & |
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| 270 | +uuh(ix,jy,kl)*tanphi)/r_earth)*(-1.e6)*9.81 |
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| 271 | |
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| 272 | |
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| 273 | ! |
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| 274 | ! Resest jux and juy |
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| 275 | jux=jumpx |
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| 276 | juy=jumpy |
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| 277 | end do |
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| 278 | end do |
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| 279 | 10 continue |
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| 280 | end do |
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| 281 | ! |
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| 282 | ! Fill in missing PV values on poles, if present |
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| 283 | ! Use mean PV of surrounding latitude ring |
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| 284 | ! |
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| 285 | if (sglobal) then |
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| 286 | do kl=1,nuvz |
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| 287 | pvavr=0. |
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| 288 | do ix=0,nxmin1 |
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| 289 | pvavr=pvavr+pvh(ix,1,kl) |
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| 290 | end do |
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| 291 | pvavr=pvavr/real(nx) |
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| 292 | jy=0 |
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| 293 | do ix=0,nxmin1 |
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| 294 | pvh(ix,jy,kl)=pvavr |
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| 295 | end do |
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| 296 | end do |
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| 297 | end if |
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| 298 | if (nglobal) then |
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| 299 | do kl=1,nuvz |
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| 300 | pvavr=0. |
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| 301 | do ix=0,nxmin1 |
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| 302 | pvavr=pvavr+pvh(ix,ny-2,kl) |
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| 303 | end do |
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| 304 | pvavr=pvavr/real(nx) |
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| 305 | jy=nymin1 |
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| 306 | do ix=0,nxmin1 |
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| 307 | pvh(ix,jy,kl)=pvavr |
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| 308 | end do |
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| 309 | end do |
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| 310 | end if |
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| 311 | |
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| 312 | end subroutine calcpv |
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