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