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subroutine calcpv(n)
C
********************************************************************************
* *
* Calculation of potential vorticity on 3-d grid. *
* *
* Author: P. James *
* 3 February 2000 *
* *
********************************************************************************
* *
* Variables: *
* n temporal index for meteorological fields (1 to 3) *
* *
* Constants: *
* *
********************************************************************************
include 'includepar'
include 'includecom'
integer n,ix,jy,i,j,k,kl,ii,jj,klvrp,klvrm,klpt,kup,kdn,kch
integer jyvp,jyvm,ixvp,ixvm,jumpx,jumpy,jux,juy,ivrm,ivrp,ivr
integer nlck
real vx(2),uy(2),phi,tanphi,cosphi,dvdx,dudy,f
real theta,thetap,thetam,dthetadp,dt1,dt2,dt,ppmk
real height(nuvzmax),pvavr,ppml(nuvzmax)
real thup,thdn
C Set number of levels to check for adjacent theta
nlck=nuvz/3
do 5 k=1,nuvz
height(k)=akz(k)/p0+bkz(k)
5 continue
C *** Precalculate all theta levels for efficiency
do 9 jy=0,ny-1
do 14 kl=1,nuvz
do 13 ix=0,nx-1
ppmk=akz(kl)+bkz(kl)*ps(ix,jy,1,n)
th(ix,jy,kl,n)=tt(ix,jy,kl,n)*(100000./ppmk)**kappa
13 continue
14 continue
9 continue
C
C Loop over entire grid
***********************
do 10 jy=0,ny-1
if (sglobal.and.jy.eq.0) goto 10
if (nglobal.and.jy.eq.ny-1) goto 10
phi = (ylat0 + jy * dy) * pi / 180.
f = 0.00014585 * sin(phi)
tanphi = tan(phi)
cosphi = cos(phi)
C Provide a virtual jy+1 and jy-1 in case we are on domain edge (Lat)
jyvp=jy+1
jyvm=jy-1
if (jy.eq.0) jyvm=0
if (jy.eq.ny-1) jyvp=ny-1
C Define absolute gap length
jumpy=2
if (jy.eq.0.or.jy.eq.ny-1) jumpy=1
if (sglobal.and.jy.eq.1) then
jyvm=1
jumpy=1
end if
if (nglobal.and.jy.eq.ny-2) then
jyvp=ny-2
jumpy=1
end if
juy=jumpy
C
do 11 ix=0,nx-1
C Provide a virtual ix+1 and ix-1 in case we are on domain edge (Long)
ixvp=ix+1
ixvm=ix-1
jumpx=2
if (xglobal) then
ivrp=ixvp
ivrm=ixvm
if (ixvm.lt.0) ivrm=ixvm+nx-1
if (ixvp.ge.nx) ivrp=ixvp-nx+1
else
if (ix.eq.0) ixvm=0
if (ix.eq.nx-1) ixvp=nx-1
ivrp=ixvp
ivrm=ixvm
C Define absolute gap length
if (ix.eq.0.or.ix.eq.nx-1) jumpx=1
end if
jux=jumpx
C Precalculate pressure values for efficiency
do 8 kl=1,nuvz
ppml(kl)=akz(kl)+bkz(kl)*ps(ix,jy,1,n)
8 continue
C
C Loop over the vertical
************************
do 12 kl=1,nuvz
theta=th(ix,jy,kl,n)
klvrp=kl+1
klvrm=kl-1
klpt=kl
C If top or bottom level, dthetadp is evaluated between the current
C level and the level inside, otherwise between level+1 and level-1
C
if (klvrp.gt.nuvz) klvrp=nuvz
if (klvrm.lt.1) klvrm=1
thetap=th(ix,jy,klvrp,n)
thetam=th(ix,jy,klvrm,n)
dthetadp=(thetap-thetam)/(ppml(klvrp)-ppml(klvrm))
C Compute vertical position at pot. temperature surface on subgrid
C and the wind at that position
******************************************************************
C a) in x direction
ii=0
do 20 i=ixvm,ixvp,jumpx
ivr=i
if (xglobal) then
if (i.lt.0) ivr=ivr+nx-1
if (i.ge.nx) ivr=ivr-nx+1
end if
ii=ii+1
C Search adjacent levels for current theta value
C Spiral out from current level for efficiency
kup=klpt-1
kdn=klpt
kch=0
40 continue
C Upward branch
kup=kup+1
if (kch.ge.nlck) goto 21 ! No more levels to check,
C ! and no values found
if (kup.ge.nuvz) goto 41
kch=kch+1
k=kup
thdn=th(ivr,jy,k,n)
thup=th(ivr,jy,k+1,n)
if (((thdn.ge.theta).and.(thup.le.theta)).or.
+ ((thdn.le.theta).and.(thup.ge.theta))) then
dt1=abs(theta-thdn)
dt2=abs(theta-thup)
dt=dt1+dt2
if (dt.lt.eps) then ! Avoid division by zero error
dt1=0.5 ! G.W., 10.4.1996
dt2=0.5
dt=1.0
endif
vx(ii)=(vv(ivr,jy,k,n)*dt2+vv(ivr,jy,k+1,n)*dt1)/dt
goto 20
endif
41 continue
C Downward branch
kdn=kdn-1
if (kdn.lt.1) goto 40
kch=kch+1
k=kdn
thdn=th(ivr,jy,k,n)
thup=th(ivr,jy,k+1,n)
if (((thdn.ge.theta).and.(thup.le.theta)).or.
+ ((thdn.le.theta).and.(thup.ge.theta))) then
dt1=abs(theta-thdn)
dt2=abs(theta-thup)
dt=dt1+dt2
if (dt.lt.eps) then ! Avoid division by zero error
dt1=0.5 ! G.W., 10.4.1996
dt2=0.5
dt=1.0
endif
vx(ii)=(vv(ivr,jy,k,n)*dt2+vv(ivr,jy,k+1,n)*dt1)/dt
goto 20
endif
goto 40
C This section used when no values were found
21 continue
C Must use vv at current level and long. jux becomes smaller by 1
vx(ii)=vv(ix,jy,kl,n)
jux=jux-1
C Otherwise OK
20 continue
if (jux.gt.0) then
dvdx=(vx(2)-vx(1))/float(jux)/(dx*pi/180.)
else
dvdx=vv(ivrp,jy,kl,n)-vv(ivrm,jy,kl,n)
dvdx=dvdx/float(jumpx)/(dx*pi/180.)
C Only happens if no equivalent theta value
C can be found on either side, hence must use values
C from either side, same pressure level.
end if
C b) in y direction
jj=0
do 50 j=jyvm,jyvp,jumpy
jj=jj+1
C Search adjacent levels for current theta value
C Spiral out from current level for efficiency
kup=klpt-1
kdn=klpt
kch=0
70 continue
C Upward branch
kup=kup+1
if (kch.ge.nlck) goto 51 ! No more levels to check,
C ! and no values found
if (kup.ge.nuvz) goto 71
kch=kch+1
k=kup
thdn=th(ix,j,k,n)
thup=th(ix,j,k+1,n)
if (((thdn.ge.theta).and.(thup.le.theta)).or.
+ ((thdn.le.theta).and.(thup.ge.theta))) then
dt1=abs(theta-thdn)
dt2=abs(theta-thup)
dt=dt1+dt2
if (dt.lt.eps) then ! Avoid division by zero error
dt1=0.5 ! G.W., 10.4.1996
dt2=0.5
dt=1.0
endif
uy(jj)=(uu(ix,j,k,n)*dt2+uu(ix,j,k+1,n)*dt1)/dt
goto 50
endif
71 continue
C Downward branch
kdn=kdn-1
if (kdn.lt.1) goto 70
kch=kch+1
k=kdn
thdn=th(ix,j,k,n)
thup=th(ix,j,k+1,n)
if (((thdn.ge.theta).and.(thup.le.theta)).or.
+ ((thdn.le.theta).and.(thup.ge.theta))) then
dt1=abs(theta-thdn)
dt2=abs(theta-thup)
dt=dt1+dt2
if (dt.lt.eps) then ! Avoid division by zero error
dt1=0.5 ! G.W., 10.4.1996
dt2=0.5
dt=1.0
endif
uy(jj)=(uu(ix,j,k,n)*dt2+uu(ix,j,k+1,n)*dt1)/dt
goto 50
endif
goto 70
C This section used when no values were found
51 continue
C Must use uu at current level and lat. juy becomes smaller by 1
uy(jj)=uu(ix,jy,kl,n)
juy=juy-1
C Otherwise OK
50 continue
if (juy.gt.0) then
dudy=(uy(2)-uy(1))/float(juy)/(dy*pi/180.)
else
dudy=uu(ix,jyvp,kl,n)-uu(ix,jyvm,kl,n)
dudy=dudy/float(jumpy)/(dy*pi/180.)
end if
C
pv(ix,jy,kl,n)=dthetadp*(f+(dvdx/cosphi-dudy
+ +uu(ix,jy,kl,n)*tanphi)/r_earth)*(-1.e6)*9.81
C
C Resest jux and juy
jux=jumpx
juy=jumpy
12 continue
11 continue
10 continue
C
C Fill in missing PV values on poles, if present
C Use mean PV of surrounding latitude ring
C
if (sglobal) then
do 80 kl=1,nuvz
pvavr=0.
do 81 ix=0,nx-1
pvavr=pvavr+pv(ix,1,kl,n)
81 continue
pvavr=pvavr/float(nx)
jy=0
do 82 ix=0,nx-1
pv(ix,jy,kl,n)=pvavr
82 continue
80 continue
end if
if (nglobal) then
do 90 kl=1,nuvz
pvavr=0.
do 91 ix=0,nx-1
pvavr=pvavr+pv(ix,ny-2,kl,n)
91 continue
pvavr=pvavr/float(nx)
jy=ny-1
do 92 ix=0,nx-1
pv(ix,jy,kl,n)=pvavr
92 continue
90 continue
end if
return
end
|
