| 1 | !********************************************************************** |
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| 2 | ! Copyright 1998,1999,2000,2001,2002,2005,2007,2008,2009,2010 * |
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| 3 | ! Andreas Stohl, Petra Seibert, A. Frank, Gerhard Wotawa, * |
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| 4 | ! Caroline Forster, Sabine Eckhardt, John Burkhart, Harald Sodemann * |
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| 5 | ! * |
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| 6 | ! This file is part of FLEXPART. * |
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| 7 | ! * |
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| 8 | ! FLEXPART is free software: you can redistribute it and/or modify * |
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| 9 | ! it under the terms of the GNU General Public License as published by* |
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| 10 | ! the Free Software Foundation, either version 3 of the License, or * |
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| 11 | ! (at your option) any later version. * |
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| 12 | ! * |
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| 13 | ! FLEXPART is distributed in the hope that it will be useful, * |
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| 14 | ! but WITHOUT ANY WARRANTY; without even the implied warranty of * |
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| 15 | ! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * |
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| 16 | ! GNU General Public License for more details. * |
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| 17 | ! * |
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| 18 | ! You should have received a copy of the GNU General Public License * |
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| 19 | ! along with FLEXPART. If not, see <http://www.gnu.org/licenses/>. * |
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| 20 | !********************************************************************** |
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| 21 | |
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| 22 | subroutine calcpv_nests(l,n,uuhn,vvhn,pvhn) |
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| 23 | ! i i i i o |
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| 24 | !***************************************************************************** |
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| 25 | ! * |
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| 26 | ! Calculation of potential vorticity on 3-d nested grid * |
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| 27 | ! * |
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| 28 | ! Author: P. James * |
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| 29 | ! 22 February 2000 * |
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| 30 | ! * |
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| 31 | !***************************************************************************** |
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| 32 | ! * |
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| 33 | ! Variables: * |
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| 34 | ! n temporal index for meteorological fields (1 to 2) * |
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| 35 | ! l index of current nest * |
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| 36 | ! * |
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| 37 | ! Constants: * |
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| 38 | ! * |
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| 39 | !***************************************************************************** |
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| 40 | |
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| 41 | use par_mod |
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| 42 | use com_mod |
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| 43 | |
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| 44 | implicit none |
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| 45 | |
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| 46 | integer :: n,ix,jy,i,j,k,kl,ii,jj,klvrp,klvrm,klpt,kup,kdn,kch |
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| 47 | integer :: jyvp,jyvm,ixvp,ixvm,jumpx,jumpy,jux,juy,ivrm,ivrp,ivr |
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| 48 | integer :: nlck,l |
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| 49 | real :: vx(2),uy(2),phi,tanphi,cosphi,dvdx,dudy,f |
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| 50 | real :: theta,thetap,thetam,dthetadp,dt1,dt2,dt,ppmk |
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| 51 | real :: ppml(nuvzmax) |
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| 52 | real :: thup,thdn |
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| 53 | real,parameter :: eps=1.e-5,p0=101325 |
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| 54 | real :: uuhn(0:nxmaxn-1,0:nymaxn-1,nuvzmax,maxnests) |
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| 55 | real :: vvhn(0:nxmaxn-1,0:nymaxn-1,nuvzmax,maxnests) |
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| 56 | real :: pvhn(0:nxmaxn-1,0:nymaxn-1,nuvzmax,maxnests) |
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| 57 | |
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| 58 | ! Set number of levels to check for adjacent theta |
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| 59 | nlck=nuvz/3 |
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| 60 | ! |
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| 61 | ! Loop over entire grid |
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| 62 | !********************** |
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| 63 | do jy=0,nyn(l)-1 |
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| 64 | phi = (ylat0n(l) + jy * dyn(l)) * pi / 180. |
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| 65 | f = 0.00014585 * sin(phi) |
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| 66 | tanphi = tan(phi) |
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| 67 | cosphi = cos(phi) |
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| 68 | ! Provide a virtual jy+1 and jy-1 in case we are on domain edge (Lat) |
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| 69 | jyvp=jy+1 |
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| 70 | jyvm=jy-1 |
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| 71 | if (jy.eq.0) jyvm=0 |
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| 72 | if (jy.eq.nyn(l)-1) jyvp=nyn(l)-1 |
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| 73 | ! Define absolute gap length |
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| 74 | jumpy=2 |
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| 75 | if (jy.eq.0.or.jy.eq.nyn(l)-1) jumpy=1 |
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| 76 | juy=jumpy |
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| 77 | ! |
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| 78 | do ix=0,nxn(l)-1 |
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| 79 | ! Provide a virtual ix+1 and ix-1 in case we are on domain edge (Long) |
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| 80 | ixvp=ix+1 |
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| 81 | ixvm=ix-1 |
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| 82 | jumpx=2 |
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| 83 | if (ix.eq.0) ixvm=0 |
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| 84 | if (ix.eq.nxn(l)-1) ixvp=nxn(l)-1 |
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| 85 | ivrp=ixvp |
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| 86 | ivrm=ixvm |
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| 87 | ! Define absolute gap length |
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| 88 | if (ix.eq.0.or.ix.eq.nxn(l)-1) jumpx=1 |
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| 89 | jux=jumpx |
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| 90 | ! Precalculate pressure values for efficiency |
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| 91 | do kl=1,nuvz |
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| 92 | ppml(kl)=akz(kl)+bkz(kl)*psn(ix,jy,1,n,l) |
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| 93 | end do |
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| 94 | ! |
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| 95 | ! Loop over the vertical |
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| 96 | !*********************** |
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| 97 | |
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| 98 | do kl=1,nuvz |
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| 99 | ppmk=akz(kl)+bkz(kl)*psn(ix,jy,1,n,l) |
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| 100 | theta=tthn(ix,jy,kl,n,l)*(100000./ppmk)**kappa |
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| 101 | klvrp=kl+1 |
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| 102 | klvrm=kl-1 |
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| 103 | klpt=kl |
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| 104 | ! If top or bottom level, dthetadp is evaluated between the current |
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| 105 | ! level and the level inside, otherwise between level+1 and level-1 |
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| 106 | ! |
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| 107 | if (klvrp.gt.nuvz) klvrp=nuvz |
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| 108 | if (klvrm.lt.1) klvrm=1 |
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| 109 | ppmk=akz(klvrp)+bkz(klvrp)*psn(ix,jy,1,n,l) |
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| 110 | thetap=tthn(ix,jy,klvrp,n,l)*(100000./ppmk)**kappa |
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| 111 | ppmk=akz(klvrm)+bkz(klvrm)*psn(ix,jy,1,n,l) |
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| 112 | thetam=tthn(ix,jy,klvrm,n,l)*(100000./ppmk)**kappa |
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| 113 | dthetadp=(thetap-thetam)/(ppml(klvrp)-ppml(klvrm)) |
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| 114 | |
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| 115 | ! Compute vertical position at pot. temperature surface on subgrid |
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| 116 | ! and the wind at that position |
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| 117 | !***************************************************************** |
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| 118 | ! a) in x direction |
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| 119 | ii=0 |
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| 120 | do i=ixvm,ixvp,jumpx |
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| 121 | ivr=i |
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| 122 | ii=ii+1 |
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| 123 | ! Search adjacent levels for current theta value |
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| 124 | ! Spiral out from current level for efficiency |
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| 125 | kup=klpt-1 |
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| 126 | kdn=klpt |
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| 127 | kch=0 |
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| 128 | 40 continue |
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| 129 | ! Upward branch |
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| 130 | kup=kup+1 |
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| 131 | if (kch.ge.nlck) goto 21 ! No more levels to check, |
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| 132 | ! ! and no values found |
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| 133 | if (kup.ge.nuvz) goto 41 |
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| 134 | kch=kch+1 |
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| 135 | k=kup |
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| 136 | ppmk=akz(k)+bkz(k)*psn(ivr,jy,1,n,l) |
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| 137 | thdn=tthn(ivr,jy,k,n,l)*(100000./ppmk)**kappa |
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| 138 | ppmk=akz(k+1)+bkz(k+1)*psn(ivr,jy,1,n,l) |
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| 139 | thup=tthn(ivr,jy,k+1,n,l)*(100000./ppmk)**kappa |
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| 140 | |
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| 141 | if (((thdn.ge.theta).and.(thup.le.theta)).or. & |
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| 142 | ((thdn.le.theta).and.(thup.ge.theta))) then |
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| 143 | dt1=abs(theta-thdn) |
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| 144 | dt2=abs(theta-thup) |
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| 145 | dt=dt1+dt2 |
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| 146 | if (dt.lt.eps) then ! Avoid division by zero error |
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| 147 | dt1=0.5 ! G.W., 10.4.1996 |
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| 148 | dt2=0.5 |
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| 149 | dt=1.0 |
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| 150 | endif |
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| 151 | vx(ii)=(vvhn(ivr,jy,k,l)*dt2+vvhn(ivr,jy,k+1,l)*dt1)/dt |
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| 152 | goto 20 |
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| 153 | endif |
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| 154 | 41 continue |
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| 155 | ! Downward branch |
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| 156 | kdn=kdn-1 |
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| 157 | if (kdn.lt.1) goto 40 |
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| 158 | kch=kch+1 |
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| 159 | k=kdn |
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| 160 | ppmk=akz(k)+bkz(k)*psn(ivr,jy,1,n,l) |
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| 161 | thdn=tthn(ivr,jy,k,n,l)*(100000./ppmk)**kappa |
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| 162 | ppmk=akz(k+1)+bkz(k+1)*psn(ivr,jy,1,n,l) |
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| 163 | thup=tthn(ivr,jy,k+1,n,l)*(100000./ppmk)**kappa |
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| 164 | if (((thdn.ge.theta).and.(thup.le.theta)).or. & |
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| 165 | ((thdn.le.theta).and.(thup.ge.theta))) then |
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| 166 | dt1=abs(theta-thdn) |
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| 167 | dt2=abs(theta-thup) |
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| 168 | dt=dt1+dt2 |
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| 169 | if (dt.lt.eps) then ! Avoid division by zero error |
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| 170 | dt1=0.5 ! G.W., 10.4.1996 |
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| 171 | dt2=0.5 |
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| 172 | dt=1.0 |
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| 173 | endif |
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| 174 | vx(ii)=(vvhn(ivr,jy,k,l)*dt2+vvhn(ivr,jy,k+1,l)*dt1)/dt |
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| 175 | goto 20 |
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| 176 | endif |
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| 177 | goto 40 |
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| 178 | ! This section used when no values were found |
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| 179 | 21 continue |
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| 180 | ! Must use vv at current level and long. jux becomes smaller by 1 |
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| 181 | vx(ii)=vvhn(ix,jy,kl,l) |
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| 182 | jux=jux-1 |
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| 183 | ! Otherwise OK |
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| 184 | 20 continue |
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| 185 | end do |
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| 186 | if (jux.gt.0) then |
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| 187 | dvdx=(vx(2)-vx(1))/real(jux)/(dxn(l)*pi/180.) |
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| 188 | else |
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| 189 | dvdx=vvhn(ivrp,jy,kl,l)-vvhn(ivrm,jy,kl,l) |
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| 190 | dvdx=dvdx/real(jumpx)/(dxn(l)*pi/180.) |
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| 191 | ! Only happens if no equivalent theta value |
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| 192 | ! can be found on either side, hence must use values |
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| 193 | ! from either side, same pressure level. |
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| 194 | end if |
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| 195 | |
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| 196 | ! b) in y direction |
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| 197 | |
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| 198 | jj=0 |
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| 199 | do j=jyvm,jyvp,jumpy |
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| 200 | jj=jj+1 |
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| 201 | ! Search adjacent levels for current theta value |
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| 202 | ! Spiral out from current level for efficiency |
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| 203 | kup=klpt-1 |
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| 204 | kdn=klpt |
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| 205 | kch=0 |
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| 206 | 70 continue |
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| 207 | ! Upward branch |
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| 208 | kup=kup+1 |
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| 209 | if (kch.ge.nlck) goto 51 ! No more levels to check, |
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| 210 | ! ! and no values found |
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| 211 | if (kup.ge.nuvz) goto 71 |
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| 212 | kch=kch+1 |
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| 213 | k=kup |
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| 214 | ppmk=akz(k)+bkz(k)*psn(ix,j,1,n,l) |
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| 215 | thdn=tthn(ix,j,k,n,l)*(100000./ppmk)**kappa |
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| 216 | ppmk=akz(k+1)+bkz(k+1)*psn(ix,j,1,n,l) |
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| 217 | thup=tthn(ix,j,k+1,n,l)*(100000./ppmk)**kappa |
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| 218 | if (((thdn.ge.theta).and.(thup.le.theta)).or. & |
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| 219 | ((thdn.le.theta).and.(thup.ge.theta))) then |
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| 220 | dt1=abs(theta-thdn) |
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| 221 | dt2=abs(theta-thup) |
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| 222 | dt=dt1+dt2 |
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| 223 | if (dt.lt.eps) then ! Avoid division by zero error |
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| 224 | dt1=0.5 ! G.W., 10.4.1996 |
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| 225 | dt2=0.5 |
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| 226 | dt=1.0 |
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| 227 | endif |
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| 228 | uy(jj)=(uuhn(ix,j,k,l)*dt2+uuhn(ix,j,k+1,l)*dt1)/dt |
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| 229 | goto 50 |
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| 230 | endif |
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| 231 | 71 continue |
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| 232 | ! Downward branch |
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| 233 | kdn=kdn-1 |
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| 234 | if (kdn.lt.1) goto 70 |
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| 235 | kch=kch+1 |
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| 236 | k=kdn |
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| 237 | ppmk=akz(k)+bkz(k)*psn(ix,j,1,n,l) |
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| 238 | thdn=tthn(ix,j,k,n,l)*(100000./ppmk)**kappa |
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| 239 | ppmk=akz(k+1)+bkz(k+1)*psn(ix,j,1,n,l) |
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| 240 | thup=tthn(ix,j,k+1,n,l)*(100000./ppmk)**kappa |
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| 241 | if (((thdn.ge.theta).and.(thup.le.theta)).or. & |
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| 242 | ((thdn.le.theta).and.(thup.ge.theta))) then |
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| 243 | dt1=abs(theta-thdn) |
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| 244 | dt2=abs(theta-thup) |
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| 245 | dt=dt1+dt2 |
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| 246 | if (dt.lt.eps) then ! Avoid division by zero error |
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| 247 | dt1=0.5 ! G.W., 10.4.1996 |
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| 248 | dt2=0.5 |
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| 249 | dt=1.0 |
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| 250 | endif |
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| 251 | uy(jj)=(uuhn(ix,j,k,l)*dt2+uuhn(ix,j,k+1,l)*dt1)/dt |
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| 252 | goto 50 |
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| 253 | endif |
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| 254 | goto 70 |
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| 255 | ! This section used when no values were found |
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| 256 | 51 continue |
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| 257 | ! Must use uu at current level and lat. juy becomes smaller by 1 |
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| 258 | uy(jj)=uuhn(ix,jy,kl,l) |
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| 259 | juy=juy-1 |
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| 260 | ! Otherwise OK |
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| 261 | 50 continue |
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| 262 | end do |
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| 263 | if (juy.gt.0) then |
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| 264 | dudy=(uy(2)-uy(1))/real(juy)/(dyn(l)*pi/180.) |
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| 265 | else |
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| 266 | dudy=uuhn(ix,jyvp,kl,l)-uuhn(ix,jyvm,kl,l) |
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| 267 | dudy=dudy/real(jumpy)/(dyn(l)*pi/180.) |
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| 268 | end if |
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| 269 | ! |
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| 270 | pvhn(ix,jy,kl,l)=dthetadp*(f+(dvdx/cosphi-dudy & |
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| 271 | +uuhn(ix,jy,kl,l)*tanphi)/r_earth)*(-1.e6)*9.81 |
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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 | end do |
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| 280 | ! |
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| 281 | end subroutine calcpv_nests |
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