| 1 | !********************************************************************** |
|---|
| 2 | ! Copyright 1998,1999,2000,2001,2002,2005,2007,2008,2009,2010 * |
|---|
| 3 | ! Andreas Stohl, Petra Seibert, A. Frank, Gerhard Wotawa, * |
|---|
| 4 | ! Caroline Forster, Sabine Eckhardt, John Burkhart, Harald Sodemann * |
|---|
| 5 | ! * |
|---|
| 6 | ! This file is part of FLEXPART. * |
|---|
| 7 | ! * |
|---|
| 8 | ! FLEXPART is free software: you can redistribute it and/or modify * |
|---|
| 9 | ! it under the terms of the GNU General Public License as published by* |
|---|
| 10 | ! the Free Software Foundation, either version 3 of the License, or * |
|---|
| 11 | ! (at your option) any later version. * |
|---|
| 12 | ! * |
|---|
| 13 | ! FLEXPART is distributed in the hope that it will be useful, * |
|---|
| 14 | ! but WITHOUT ANY WARRANTY; without even the implied warranty of * |
|---|
| 15 | ! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * |
|---|
| 16 | ! GNU General Public License for more details. * |
|---|
| 17 | ! * |
|---|
| 18 | ! You should have received a copy of the GNU General Public License * |
|---|
| 19 | ! along with FLEXPART. If not, see <http://www.gnu.org/licenses/>. * |
|---|
| 20 | !********************************************************************** |
|---|
| 21 | |
|---|
| 22 | subroutine calcpv(n,uuh,vvh,pvh) |
|---|
| 23 | ! i i i o |
|---|
| 24 | !***************************************************************************** |
|---|
| 25 | ! * |
|---|
| 26 | ! Calculation of potential vorticity on 3-d grid. * |
|---|
| 27 | ! * |
|---|
| 28 | ! Author: P. James * |
|---|
| 29 | ! 3 February 2000 * |
|---|
| 30 | ! * |
|---|
| 31 | ! Adaptation to FLEXPART, A. Stohl, 1 May 2000 * |
|---|
| 32 | ! * |
|---|
| 33 | !***************************************************************************** |
|---|
| 34 | ! * |
|---|
| 35 | ! Variables: * |
|---|
| 36 | ! n temporal index for meteorological fields (1 to 2) * |
|---|
| 37 | ! * |
|---|
| 38 | ! Constants: * |
|---|
| 39 | ! * |
|---|
| 40 | !***************************************************************************** |
|---|
| 41 | |
|---|
| 42 | use par_mod |
|---|
| 43 | use com_mod |
|---|
| 44 | |
|---|
| 45 | implicit none |
|---|
| 46 | |
|---|
| 47 | integer :: n,ix,jy,i,j,k,kl,ii,jj,klvrp,klvrm,klpt,kup,kdn,kch |
|---|
| 48 | integer :: jyvp,jyvm,ixvp,ixvm,jumpx,jumpy,jux,juy,ivrm,ivrp,ivr |
|---|
| 49 | integer :: nlck |
|---|
| 50 | real :: vx(2),uy(2),phi,tanphi,cosphi,dvdx,dudy,f |
|---|
| 51 | real :: theta,thetap,thetam,dthetadp,dt1,dt2,dt,ppmk |
|---|
| 52 | real :: pvavr,ppml(nuvzmax) |
|---|
| 53 | real :: thup,thdn |
|---|
| 54 | real,parameter :: eps=1.e-5, p0=101325 |
|---|
| 55 | real :: uuh(0:nxmax-1,0:nymax-1,nuvzmax) |
|---|
| 56 | real :: vvh(0:nxmax-1,0:nymax-1,nuvzmax) |
|---|
| 57 | real :: pvh(0:nxmax-1,0:nymax-1,nuvzmax) |
|---|
| 58 | |
|---|
| 59 | ! Set number of levels to check for adjacent theta |
|---|
| 60 | nlck=nuvz/3 |
|---|
| 61 | ! |
|---|
| 62 | ! Loop over entire grid |
|---|
| 63 | !********************** |
|---|
| 64 | do jy=0,nymin1 |
|---|
| 65 | if (sglobal.and.jy.eq.0) goto 10 |
|---|
| 66 | if (nglobal.and.jy.eq.nymin1) goto 10 |
|---|
| 67 | phi = (ylat0 + jy * dy) * pi / 180. |
|---|
| 68 | f = 0.00014585 * sin(phi) |
|---|
| 69 | tanphi = tan(phi) |
|---|
| 70 | cosphi = cos(phi) |
|---|
| 71 | ! Provide a virtual jy+1 and jy-1 in case we are on domain edge (Lat) |
|---|
| 72 | jyvp=jy+1 |
|---|
| 73 | jyvm=jy-1 |
|---|
| 74 | if (jy.eq.0) jyvm=0 |
|---|
| 75 | if (jy.eq.nymin1) jyvp=nymin1 |
|---|
| 76 | ! Define absolute gap length |
|---|
| 77 | jumpy=2 |
|---|
| 78 | if (jy.eq.0.or.jy.eq.nymin1) jumpy=1 |
|---|
| 79 | if (sglobal.and.jy.eq.1) then |
|---|
| 80 | jyvm=1 |
|---|
| 81 | jumpy=1 |
|---|
| 82 | end if |
|---|
| 83 | if (nglobal.and.jy.eq.ny-2) then |
|---|
| 84 | jyvp=ny-2 |
|---|
| 85 | jumpy=1 |
|---|
| 86 | end if |
|---|
| 87 | juy=jumpy |
|---|
| 88 | ! |
|---|
| 89 | do ix=0,nxmin1 |
|---|
| 90 | ! Provide a virtual ix+1 and ix-1 in case we are on domain edge (Long) |
|---|
| 91 | ixvp=ix+1 |
|---|
| 92 | ixvm=ix-1 |
|---|
| 93 | jumpx=2 |
|---|
| 94 | if (xglobal) then |
|---|
| 95 | ivrp=ixvp |
|---|
| 96 | ivrm=ixvm |
|---|
| 97 | if (ixvm.lt.0) ivrm=ixvm+nxmin1 |
|---|
| 98 | if (ixvp.ge.nx) ivrp=ixvp-nx+1 |
|---|
| 99 | else |
|---|
| 100 | if (ix.eq.0) ixvm=0 |
|---|
| 101 | if (ix.eq.nxmin1) ixvp=nxmin1 |
|---|
| 102 | ivrp=ixvp |
|---|
| 103 | ivrm=ixvm |
|---|
| 104 | ! Define absolute gap length |
|---|
| 105 | if (ix.eq.0.or.ix.eq.nxmin1) jumpx=1 |
|---|
| 106 | end if |
|---|
| 107 | jux=jumpx |
|---|
| 108 | ! Precalculate pressure values for efficiency |
|---|
| 109 | do kl=1,nuvz |
|---|
| 110 | ppml(kl)=akz(kl)+bkz(kl)*ps(ix,jy,1,n) |
|---|
| 111 | end do |
|---|
| 112 | ! |
|---|
| 113 | ! Loop over the vertical |
|---|
| 114 | !*********************** |
|---|
| 115 | |
|---|
| 116 | do kl=1,nuvz |
|---|
| 117 | ppmk=akz(kl)+bkz(kl)*ps(ix,jy,1,n) |
|---|
| 118 | theta=tth(ix,jy,kl,n)*(100000./ppmk)**kappa |
|---|
| 119 | klvrp=kl+1 |
|---|
| 120 | klvrm=kl-1 |
|---|
| 121 | klpt=kl |
|---|
| 122 | ! If top or bottom level, dthetadp is evaluated between the current |
|---|
| 123 | ! level and the level inside, otherwise between level+1 and level-1 |
|---|
| 124 | ! |
|---|
| 125 | if (klvrp.gt.nuvz) klvrp=nuvz |
|---|
| 126 | if (klvrm.lt.1) klvrm=1 |
|---|
| 127 | ppmk=akz(klvrp)+bkz(klvrp)*ps(ix,jy,1,n) |
|---|
| 128 | thetap=tth(ix,jy,klvrp,n)*(100000./ppmk)**kappa |
|---|
| 129 | ppmk=akz(klvrm)+bkz(klvrm)*ps(ix,jy,1,n) |
|---|
| 130 | thetam=tth(ix,jy,klvrm,n)*(100000./ppmk)**kappa |
|---|
| 131 | dthetadp=(thetap-thetam)/(ppml(klvrp)-ppml(klvrm)) |
|---|
| 132 | |
|---|
| 133 | ! Compute vertical position at pot. temperature surface on subgrid |
|---|
| 134 | ! and the wind at that position |
|---|
| 135 | !***************************************************************** |
|---|
| 136 | ! a) in x direction |
|---|
| 137 | ii=0 |
|---|
| 138 | do i=ixvm,ixvp,jumpx |
|---|
| 139 | ivr=i |
|---|
| 140 | if (xglobal) then |
|---|
| 141 | if (i.lt.0) ivr=ivr+nxmin1 |
|---|
| 142 | if (i.ge.nx) ivr=ivr-nx+1 |
|---|
| 143 | end if |
|---|
| 144 | ii=ii+1 |
|---|
| 145 | ! Search adjacent levels for current theta value |
|---|
| 146 | ! Spiral out from current level for efficiency |
|---|
| 147 | kup=klpt-1 |
|---|
| 148 | kdn=klpt |
|---|
| 149 | kch=0 |
|---|
| 150 | 40 continue |
|---|
| 151 | ! Upward branch |
|---|
| 152 | kup=kup+1 |
|---|
| 153 | if (kch.ge.nlck) goto 21 ! No more levels to check, |
|---|
| 154 | ! ! and no values found |
|---|
| 155 | if (kup.ge.nuvz) goto 41 |
|---|
| 156 | kch=kch+1 |
|---|
| 157 | k=kup |
|---|
| 158 | ppmk=akz(k)+bkz(k)*ps(ivr,jy,1,n) |
|---|
| 159 | thdn=tth(ivr,jy,k,n)*(100000./ppmk)**kappa |
|---|
| 160 | ppmk=akz(k+1)+bkz(k+1)*ps(ivr,jy,1,n) |
|---|
| 161 | thup=tth(ivr,jy,k+1,n)*(100000./ppmk)**kappa |
|---|
| 162 | |
|---|
| 163 | |
|---|
| 164 | if (((thdn.ge.theta).and.(thup.le.theta)).or. & |
|---|
| 165 | ((thdn.le.theta).and.(thup.ge.theta))) then |
|---|
| 166 | dt1=abs(theta-thdn) |
|---|
| 167 | dt2=abs(theta-thup) |
|---|
| 168 | dt=dt1+dt2 |
|---|
| 169 | if (dt.lt.eps) then ! Avoid division by zero error |
|---|
| 170 | dt1=0.5 ! G.W., 10.4.1996 |
|---|
| 171 | dt2=0.5 |
|---|
| 172 | dt=1.0 |
|---|
| 173 | endif |
|---|
| 174 | vx(ii)=(vvh(ivr,jy,k)*dt2+vvh(ivr,jy,k+1)*dt1)/dt |
|---|
| 175 | goto 20 |
|---|
| 176 | endif |
|---|
| 177 | 41 continue |
|---|
| 178 | ! Downward branch |
|---|
| 179 | kdn=kdn-1 |
|---|
| 180 | if (kdn.lt.1) goto 40 |
|---|
| 181 | kch=kch+1 |
|---|
| 182 | k=kdn |
|---|
| 183 | ppmk=akz(k)+bkz(k)*ps(ivr,jy,1,n) |
|---|
| 184 | thdn=tth(ivr,jy,k,n)*(100000./ppmk)**kappa |
|---|
| 185 | ppmk=akz(k+1)+bkz(k+1)*ps(ivr,jy,1,n) |
|---|
| 186 | thup=tth(ivr,jy,k+1,n)*(100000./ppmk)**kappa |
|---|
| 187 | |
|---|
| 188 | if (((thdn.ge.theta).and.(thup.le.theta)).or. & |
|---|
| 189 | ((thdn.le.theta).and.(thup.ge.theta))) then |
|---|
| 190 | dt1=abs(theta-thdn) |
|---|
| 191 | dt2=abs(theta-thup) |
|---|
| 192 | dt=dt1+dt2 |
|---|
| 193 | if (dt.lt.eps) then ! Avoid division by zero error |
|---|
| 194 | dt1=0.5 ! G.W., 10.4.1996 |
|---|
| 195 | dt2=0.5 |
|---|
| 196 | dt=1.0 |
|---|
| 197 | endif |
|---|
| 198 | vx(ii)=(vvh(ivr,jy,k)*dt2+vvh(ivr,jy,k+1)*dt1)/dt |
|---|
| 199 | goto 20 |
|---|
| 200 | endif |
|---|
| 201 | goto 40 |
|---|
| 202 | ! This section used when no values were found |
|---|
| 203 | 21 continue |
|---|
| 204 | ! Must use vv at current level and long. jux becomes smaller by 1 |
|---|
| 205 | vx(ii)=vvh(ix,jy,kl) |
|---|
| 206 | jux=jux-1 |
|---|
| 207 | ! Otherwise OK |
|---|
| 208 | 20 continue |
|---|
| 209 | end do |
|---|
| 210 | if (jux.gt.0) then |
|---|
| 211 | dvdx=(vx(2)-vx(1))/real(jux)/(dx*pi/180.) |
|---|
| 212 | else |
|---|
| 213 | dvdx=vvh(ivrp,jy,kl)-vvh(ivrm,jy,kl) |
|---|
| 214 | dvdx=dvdx/real(jumpx)/(dx*pi/180.) |
|---|
| 215 | ! Only happens if no equivalent theta value |
|---|
| 216 | ! can be found on either side, hence must use values |
|---|
| 217 | ! from either side, same pressure level. |
|---|
| 218 | end if |
|---|
| 219 | |
|---|
| 220 | ! b) in y direction |
|---|
| 221 | |
|---|
| 222 | jj=0 |
|---|
| 223 | do j=jyvm,jyvp,jumpy |
|---|
| 224 | jj=jj+1 |
|---|
| 225 | ! Search adjacent levels for current theta value |
|---|
| 226 | ! Spiral out from current level for efficiency |
|---|
| 227 | kup=klpt-1 |
|---|
| 228 | kdn=klpt |
|---|
| 229 | kch=0 |
|---|
| 230 | 70 continue |
|---|
| 231 | ! Upward branch |
|---|
| 232 | kup=kup+1 |
|---|
| 233 | if (kch.ge.nlck) goto 51 ! No more levels to check, |
|---|
| 234 | ! ! and no values found |
|---|
| 235 | if (kup.ge.nuvz) goto 71 |
|---|
| 236 | kch=kch+1 |
|---|
| 237 | k=kup |
|---|
| 238 | ppmk=akz(k)+bkz(k)*ps(ix,j,1,n) |
|---|
| 239 | thdn=tth(ix,j,k,n)*(100000./ppmk)**kappa |
|---|
| 240 | ppmk=akz(k+1)+bkz(k+1)*ps(ix,j,1,n) |
|---|
| 241 | thup=tth(ix,j,k+1,n)*(100000./ppmk)**kappa |
|---|
| 242 | if (((thdn.ge.theta).and.(thup.le.theta)).or. & |
|---|
| 243 | ((thdn.le.theta).and.(thup.ge.theta))) then |
|---|
| 244 | dt1=abs(theta-thdn) |
|---|
| 245 | dt2=abs(theta-thup) |
|---|
| 246 | dt=dt1+dt2 |
|---|
| 247 | if (dt.lt.eps) then ! Avoid division by zero error |
|---|
| 248 | dt1=0.5 ! G.W., 10.4.1996 |
|---|
| 249 | dt2=0.5 |
|---|
| 250 | dt=1.0 |
|---|
| 251 | endif |
|---|
| 252 | uy(jj)=(uuh(ix,j,k)*dt2+uuh(ix,j,k+1)*dt1)/dt |
|---|
| 253 | goto 50 |
|---|
| 254 | endif |
|---|
| 255 | 71 continue |
|---|
| 256 | ! Downward branch |
|---|
| 257 | kdn=kdn-1 |
|---|
| 258 | if (kdn.lt.1) goto 70 |
|---|
| 259 | kch=kch+1 |
|---|
| 260 | k=kdn |
|---|
| 261 | ppmk=akz(k)+bkz(k)*ps(ix,j,1,n) |
|---|
| 262 | thdn=tth(ix,j,k,n)*(100000./ppmk)**kappa |
|---|
| 263 | ppmk=akz(k+1)+bkz(k+1)*ps(ix,j,1,n) |
|---|
| 264 | thup=tth(ix,j,k+1,n)*(100000./ppmk)**kappa |
|---|
| 265 | if (((thdn.ge.theta).and.(thup.le.theta)).or. & |
|---|
| 266 | ((thdn.le.theta).and.(thup.ge.theta))) then |
|---|
| 267 | dt1=abs(theta-thdn) |
|---|
| 268 | dt2=abs(theta-thup) |
|---|
| 269 | dt=dt1+dt2 |
|---|
| 270 | if (dt.lt.eps) then ! Avoid division by zero error |
|---|
| 271 | dt1=0.5 ! G.W., 10.4.1996 |
|---|
| 272 | dt2=0.5 |
|---|
| 273 | dt=1.0 |
|---|
| 274 | endif |
|---|
| 275 | uy(jj)=(uuh(ix,j,k)*dt2+uuh(ix,j,k+1)*dt1)/dt |
|---|
| 276 | goto 50 |
|---|
| 277 | endif |
|---|
| 278 | goto 70 |
|---|
| 279 | ! This section used when no values were found |
|---|
| 280 | 51 continue |
|---|
| 281 | ! Must use uu at current level and lat. juy becomes smaller by 1 |
|---|
| 282 | uy(jj)=uuh(ix,jy,kl) |
|---|
| 283 | juy=juy-1 |
|---|
| 284 | ! Otherwise OK |
|---|
| 285 | 50 continue |
|---|
| 286 | end do |
|---|
| 287 | if (juy.gt.0) then |
|---|
| 288 | dudy=(uy(2)-uy(1))/real(juy)/(dy*pi/180.) |
|---|
| 289 | else |
|---|
| 290 | dudy=uuh(ix,jyvp,kl)-uuh(ix,jyvm,kl) |
|---|
| 291 | dudy=dudy/real(jumpy)/(dy*pi/180.) |
|---|
| 292 | end if |
|---|
| 293 | ! |
|---|
| 294 | pvh(ix,jy,kl)=dthetadp*(f+(dvdx/cosphi-dudy & |
|---|
| 295 | +uuh(ix,jy,kl)*tanphi)/r_earth)*(-1.e6)*9.81 |
|---|
| 296 | |
|---|
| 297 | |
|---|
| 298 | ! |
|---|
| 299 | ! Resest jux and juy |
|---|
| 300 | jux=jumpx |
|---|
| 301 | juy=jumpy |
|---|
| 302 | end do |
|---|
| 303 | end do |
|---|
| 304 | 10 continue |
|---|
| 305 | end do |
|---|
| 306 | ! |
|---|
| 307 | ! Fill in missing PV values on poles, if present |
|---|
| 308 | ! Use mean PV of surrounding latitude ring |
|---|
| 309 | ! |
|---|
| 310 | if (sglobal) then |
|---|
| 311 | do kl=1,nuvz |
|---|
| 312 | pvavr=0. |
|---|
| 313 | do ix=0,nxmin1 |
|---|
| 314 | pvavr=pvavr+pvh(ix,1,kl) |
|---|
| 315 | end do |
|---|
| 316 | pvavr=pvavr/real(nx) |
|---|
| 317 | jy=0 |
|---|
| 318 | do ix=0,nxmin1 |
|---|
| 319 | pvh(ix,jy,kl)=pvavr |
|---|
| 320 | end do |
|---|
| 321 | end do |
|---|
| 322 | end if |
|---|
| 323 | if (nglobal) then |
|---|
| 324 | do kl=1,nuvz |
|---|
| 325 | pvavr=0. |
|---|
| 326 | do ix=0,nxmin1 |
|---|
| 327 | pvavr=pvavr+pvh(ix,ny-2,kl) |
|---|
| 328 | end do |
|---|
| 329 | pvavr=pvavr/real(nx) |
|---|
| 330 | jy=nymin1 |
|---|
| 331 | do ix=0,nxmin1 |
|---|
| 332 | pvh(ix,jy,kl)=pvavr |
|---|
| 333 | end do |
|---|
| 334 | end do |
|---|
| 335 | end if |
|---|
| 336 | |
|---|
| 337 | end subroutine calcpv |
|---|
