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
|
!**********************************************************************
! 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 interpol_all(itime,xt,yt,zt)
! i i i i
!*****************************************************************************
! *
! This subroutine interpolates everything that is needed for calculating the*
! dispersion. *
! *
! Author: A. Stohl *
! *
! 16 December 1997 *
! *
! Revision March 2005 by AST : all output variables in common block cal- *
! culation of standard deviation done in this *
! routine rather than subroutine call in order *
! to save computation time *
! *
!*****************************************************************************
! *
! Variables: *
! itime [s] current temporal position *
! memtime(3) [s] times of the wind fields in memory *
! xt,yt,zt coordinates position for which wind data shall be *
! culated *
! *
! Constants: *
! *
!*****************************************************************************
use par_mod
use com_mod
use interpol_mod
use hanna_mod
implicit none
integer :: itime
real :: xt,yt,zt
! Auxiliary variables needed for interpolation
real :: ust1(2),wst1(2),oli1(2),oliaux
real :: y1(2),y2(2),y3(2),rho1(2),rhograd1(2)
real :: usl,vsl,wsl,usq,vsq,wsq,xaux
integer :: i,m,n,indexh
real,parameter :: eps=1.0e-30
!********************************************
! Multilinear interpolation in time and space
!********************************************
! Determine the lower left corner and its distance to the current position
!*************************************************************************
ddx=xt-real(ix)
ddy=yt-real(jy)
rddx=1.-ddx
rddy=1.-ddy
p1=rddx*rddy
p2=ddx*rddy
p3=rddx*ddy
p4=ddx*ddy
! Calculate variables for time interpolation
!*******************************************
dt1=real(itime-memtime(1))
dt2=real(memtime(2)-itime)
dtt=1./(dt1+dt2)
!*****************************************
! 1. Interpolate u*, w* and Obukhov length
!*****************************************
! a) Bilinear horizontal interpolation
do m=1,2
indexh=memind(m)
ust1(m)=p1*ustar(ix ,jy ,1,indexh) &
+ p2*ustar(ixp,jy ,1,indexh) &
+ p3*ustar(ix ,jyp,1,indexh) &
+ p4*ustar(ixp,jyp,1,indexh)
wst1(m)=p1*wstar(ix ,jy ,1,indexh) &
+ p2*wstar(ixp,jy ,1,indexh) &
+ p3*wstar(ix ,jyp,1,indexh) &
+ p4*wstar(ixp,jyp,1,indexh)
oli1(m)=p1*oli(ix ,jy ,1,indexh) &
+ p2*oli(ixp,jy ,1,indexh) &
+ p3*oli(ix ,jyp,1,indexh) &
+ p4*oli(ixp,jyp,1,indexh)
end do
! b) Temporal interpolation
ust=(ust1(1)*dt2+ust1(2)*dt1)*dtt
wst=(wst1(1)*dt2+wst1(2)*dt1)*dtt
oliaux=(oli1(1)*dt2+oli1(2)*dt1)*dtt
if (oliaux.ne.0.) then
ol=1./oliaux
else
ol=99999.
endif
!*****************************************************
! 2. Interpolate vertical profiles of u,v,w,rho,drhodz
!*****************************************************
! Determine the level below the current position
!***********************************************
do i=2,nz
if (height(i).gt.zt) then
indz=i-1
indzp=i
goto 6
endif
end do
6 continue
!**************************************
! 1.) Bilinear horizontal interpolation
! 2.) Temporal interpolation (linear)
!**************************************
! Loop over 2 time steps and indz levels
!***************************************
do n=indz,indzp
usl=0.
vsl=0.
wsl=0.
usq=0.
vsq=0.
wsq=0.
do m=1,2
indexh=memind(m)
if (ngrid.lt.0) then
y1(m)=p1*uupol(ix ,jy ,n,indexh) &
+p2*uupol(ixp,jy ,n,indexh) &
+p3*uupol(ix ,jyp,n,indexh) &
+p4*uupol(ixp,jyp,n,indexh)
y2(m)=p1*vvpol(ix ,jy ,n,indexh) &
+p2*vvpol(ixp,jy ,n,indexh) &
+p3*vvpol(ix ,jyp,n,indexh) &
+p4*vvpol(ixp,jyp,n,indexh)
usl=usl+uupol(ix ,jy ,n,indexh)+uupol(ixp,jy ,n,indexh) &
+uupol(ix ,jyp,n,indexh)+uupol(ixp,jyp,n,indexh)
vsl=vsl+vvpol(ix ,jy ,n,indexh)+vvpol(ixp,jy ,n,indexh) &
+vvpol(ix ,jyp,n,indexh)+vvpol(ixp,jyp,n,indexh)
usq=usq+uupol(ix ,jy ,n,indexh)*uupol(ix ,jy ,n,indexh)+ &
uupol(ixp,jy ,n,indexh)*uupol(ixp,jy ,n,indexh)+ &
uupol(ix ,jyp,n,indexh)*uupol(ix ,jyp,n,indexh)+ &
uupol(ixp,jyp,n,indexh)*uupol(ixp,jyp,n,indexh)
vsq=vsq+vvpol(ix ,jy ,n,indexh)*vvpol(ix ,jy ,n,indexh)+ &
vvpol(ixp,jy ,n,indexh)*vvpol(ixp,jy ,n,indexh)+ &
vvpol(ix ,jyp,n,indexh)*vvpol(ix ,jyp,n,indexh)+ &
vvpol(ixp,jyp,n,indexh)*vvpol(ixp,jyp,n,indexh)
else
y1(m)=p1*uu(ix ,jy ,n,indexh) &
+p2*uu(ixp,jy ,n,indexh) &
+p3*uu(ix ,jyp,n,indexh) &
+p4*uu(ixp,jyp,n,indexh)
y2(m)=p1*vv(ix ,jy ,n,indexh) &
+p2*vv(ixp,jy ,n,indexh) &
+p3*vv(ix ,jyp,n,indexh) &
+p4*vv(ixp,jyp,n,indexh)
usl=usl+uu(ix ,jy ,n,indexh)+uu(ixp,jy ,n,indexh) &
+uu(ix ,jyp,n,indexh)+uu(ixp,jyp,n,indexh)
vsl=vsl+vv(ix ,jy ,n,indexh)+vv(ixp,jy ,n,indexh) &
+vv(ix ,jyp,n,indexh)+vv(ixp,jyp,n,indexh)
usq=usq+uu(ix ,jy ,n,indexh)*uu(ix ,jy ,n,indexh)+ &
uu(ixp,jy ,n,indexh)*uu(ixp,jy ,n,indexh)+ &
uu(ix ,jyp,n,indexh)*uu(ix ,jyp,n,indexh)+ &
uu(ixp,jyp,n,indexh)*uu(ixp,jyp,n,indexh)
vsq=vsq+vv(ix ,jy ,n,indexh)*vv(ix ,jy ,n,indexh)+ &
vv(ixp,jy ,n,indexh)*vv(ixp,jy ,n,indexh)+ &
vv(ix ,jyp,n,indexh)*vv(ix ,jyp,n,indexh)+ &
vv(ixp,jyp,n,indexh)*vv(ixp,jyp,n,indexh)
endif
y3(m)=p1*ww(ix ,jy ,n,indexh) &
+p2*ww(ixp,jy ,n,indexh) &
+p3*ww(ix ,jyp,n,indexh) &
+p4*ww(ixp,jyp,n,indexh)
rhograd1(m)=p1*drhodz(ix ,jy ,n,indexh) &
+p2*drhodz(ixp,jy ,n,indexh) &
+p3*drhodz(ix ,jyp,n,indexh) &
+p4*drhodz(ixp,jyp,n,indexh)
rho1(m)=p1*rho(ix ,jy ,n,indexh) &
+p2*rho(ixp,jy ,n,indexh) &
+p3*rho(ix ,jyp,n,indexh) &
+p4*rho(ixp,jyp,n,indexh)
wsl=wsl+ww(ix ,jy ,n,indexh)+ww(ixp,jy ,n,indexh) &
+ww(ix ,jyp,n,indexh)+ww(ixp,jyp,n,indexh)
wsq=wsq+ww(ix ,jy ,n,indexh)*ww(ix ,jy ,n,indexh)+ &
ww(ixp,jy ,n,indexh)*ww(ixp,jy ,n,indexh)+ &
ww(ix ,jyp,n,indexh)*ww(ix ,jyp,n,indexh)+ &
ww(ixp,jyp,n,indexh)*ww(ixp,jyp,n,indexh)
end do
uprof(n)=(y1(1)*dt2+y1(2)*dt1)*dtt
vprof(n)=(y2(1)*dt2+y2(2)*dt1)*dtt
wprof(n)=(y3(1)*dt2+y3(2)*dt1)*dtt
rhoprof(n)=(rho1(1)*dt2+rho1(2)*dt1)*dtt
rhogradprof(n)=(rhograd1(1)*dt2+rhograd1(2)*dt1)*dtt
indzindicator(n)=.false.
! Compute standard deviations
!****************************
xaux=usq-usl*usl/8.
if (xaux.lt.eps) then
usigprof(n)=0.
else
usigprof(n)=sqrt(xaux/7.)
endif
xaux=vsq-vsl*vsl/8.
if (xaux.lt.eps) then
vsigprof(n)=0.
else
vsigprof(n)=sqrt(xaux/7.)
endif
xaux=wsq-wsl*wsl/8.
if (xaux.lt.eps) then
wsigprof(n)=0.
else
wsigprof(n)=sqrt(xaux/7.)
endif
end do
end subroutine interpol_all
|
