source: LMDZ6/trunk/tools/make_sso/make_sso_SpherePack.f90 @ 4484

Last change on this file since 4484 was 4168, checked in by evignon, 2 years ago

deuxieme phase de travail pour l'inclusion de make_sso
Ehouarn, David, Romain , Etienne

File size: 48.3 KB
Line 
1!-------------------------------------------------------------------------------
2!
3PROGRAM make_sso
4!
5!-------------------------------------------------------------------------------
6! Purpose: Project ETOPO file (GMT4 axes conventions) on spherical harmonics.
7!-------------------------------------------------------------------------------
8  USE netcdf
9!  USE sphpack
10  IMPLICIT NONE
11!-------------------------------------------------------------------------------
12! Local variables:
13  REAL,    PARAMETER :: xpi=4.*ATAN(1.),         &    !--- pi
14                        hp=xpi/2., d2r=xpi/180., &    !--- pi, pi/2, pi/180 
15                        REarth=2.E7/xpi,         &    !--- Earth radius
16                        eps=1.E-6                     !--- Tolerance for angles
17  !=== Transition length for spectral filters (to avoid side lobes)
18!  REAL,    PARAMETER :: del=2000./REarth              !--- On unit sphere
19  !=== .TRUE./.FALSE.: Fast/slow routine with heavy O(N^3)/light O(N^2) storage
20  LOGICAL, PARAMETER :: lfast=.TRUE.                  !--- Fast/slow routine
21
22!--- From the input arguments
23  CHARACTER(LEN=256), ALLOCATABLE :: args(:)          !--- All the arguments
24  CHARACTER(LEN=2048):: call_seq                      !--- Calling sequence
25  INTEGER            :: nargs                         !--- Input args number
26  CHARACTER(LEN=256) :: f_in                          !--- Input file name
27  CHARACTER(LEN=256) :: vnam                          !--- Height variable name
28  CHARACTER(LEN=256) :: res_in                        !--- Input resolution
29  CHARACTER(LEN=256) :: fmsk                          !--- Mask file or keyword
30  !=== Filter on output field, of resolution=ffactor*output resolution
31  LOGICAL            :: lfilter=.TRUE.                !--- Filter activation
32  REAL               :: ffactor                       !--- Filter resol. factor
33  REAL               :: tfactor                       !--- Transition factor
34  INTEGER            :: nlon_ou, nlat_ou              !--- Output grid resol.
35
36!--- Quantities related to input field grid
37  CHARACTER(LEN=256) :: lonn, latn                    !--- Axes vars names
38  CHARACTER(LEN=256) :: lonu, latu                    !--- Angular units
39  REAL, ALLOCATABLE  :: lon_in(:), lat_in(:)          !--- Cells centers
40  INTEGER            :: nlon_in,   nlat_in            !--- Input  grid dims
41  INTEGER            :: igrid_in(2)                   !--- Grid identification
42  REAL               :: dlon, dlat                    !--- Domain sizes
43  REAL               :: D1, del1                      !--- Resol. at equator
44  REAL               :: al                            !--- Longitude ratio
45  LOGICAL            :: lcyc                          !--- T: redundant longitude
46  LOGICAL            :: lXdec, lYinc                  !--- T: dec/increasing lon/lat
47  REAL, ALLOCATABLE, DIMENSION(:,:) ::v,h , a , b,mski!--- Heights, coeffs, mask
48  REAL, ALLOCATABLE, DIMENSION(:,:,:) ::hs, as, bs, & !--- Same, filtered
49    dxZ, dyZ, dxZ2, dyZ2, dxyZ, Xk, Xl, Xm, Xp, Xq, dH!--- Grads, correlations
50
51!--- Quantities related to output grid
52  CHARACTER(LEN=256) :: f_ou                          !--- Output file name
53  CHARACTER(LEN=256) :: res_ou                        !--- Output resolution
54  INTEGER(KIND=1), ALLOCATABLE :: mask(:,:)           !--- Boolean out land mask
55  REAL, ALLOCATABLE  :: lon_ou(:), lat_ou(:), tmp1(:) !--- Output grid coords
56  INTEGER            :: igrid_ou(2)                   !--- Grid identification
57  REAL               :: D2, del2                      !--- Resol. at equator
58  REAL, ALLOCATABLE, DIMENSION(:,:) ::   msko, &      !--- Fractional land mask
59                                           h0, &      !--- Large scale orography
60                   Zphi, Zsig, Zthe, Zgam, mu, tmp2   !--- Geopo, SSO parameters
61
62!--- Miscellanous Netcdf-related variables
63  INTEGER :: fID, xID, loID, phiID, sigID, theID, picID, dIDs(4), nn
64  INTEGER :: vID, yID, laID, meaID, gamID, mskID, valID, muID, ix180
65  LOGICAL :: ll
66
67!--- Miscellanous SPHEREPACK-specific quantities
68  INTEGER :: l1, idh, mdab, lsh, la1, la2, lwa, lsvmin, lsave, ierr, intl
69  INTEGER :: l2, jdh, ndab, lvh, lb1, lb2, lwb, lwkmin, lwork, ldwork
70  REAL, ALLOCATABLE :: wsha(:), wsave(:), wvh (:)
71  REAL, ALLOCATABLE :: wshs(:), dwork(:), work(:)
72  INTEGER :: k, n, nt, isym
73
74  CHARACTER(LEN=256) :: sub, fnam, msg, arg
75
76!-------------------------------------------------------------------------------
77  sub='make_sso'
78
79!=== DEAL WITH INPUT ARGUMENTS =================================================
80  call_seq='./'//TRIM(sub)//'.e'
81  nargs=COMMAND_ARGUMENT_COUNT(); ALLOCATE(args(nargs))
82!--- MANUAL DISPLAYED IF NO ARGUMENTS ARE PROVIDED
83  IF(nargs==0) THEN
84    WRITE(*,*)''
85    WRITE(*,*)'General calling sequence:'
86    WRITE(*,*)''
87    WRITE(*,*)TRIM(call_seq)//'  -i <file>  -v <var>  -res <nlon> <nlat>'      &
88      //'  -m <mask>  -f <ffac>  -t <tfac>'
89    WRITE(*,*)''
90    WRITE(*,*)'Where:'
91    WRITE(*,*)''
92    WRITE(*,*)' <file>:   input file name'
93    WRITE(*,*)' <var> :   height variable name'
94    WRITE(*,*)' <nlon>:   number of distinct longitude points of output grid'
95    WRITE(*,*)' <nlat>:   number of distinct latitude  points of output grid'
96    WRITE(*,*)' <mask>:   can be:  1. a mask file (o2a.nc)'
97    WRITE(*,*)'                    2. "noro": computed with grid_noro'
98    WRITE(*,*)'           default: 3. "spec": computed internally'
99    WRITE(*,*)' <ffac>:   filtering  width: ffac*Do         (Do:output resol.)'
100    WRITE(*,*)' <tfac>:   transition width: Di+tfac*(Do-Di) (Di: input resol.)'
101    WRITE(*,*)
102    WRITE(*,*)'Note that latitudes grid contains both poles.'
103    WRITE(*,*)
104    STOP
105  END IF
106!--- ARGUMENTS PARSING
107  DO k=1,nargs
108    CALL GET_COMMAND_ARGUMENT(NUMBER=k,VALUE=args(k))
109    call_seq=TRIM(call_seq)//' '//TRIM(args(k))
110  END DO
111  k=1
112  f_in=''; nlon_ou=0; nlat_ou=0; vnam=''; fmsk=''; ffactor=2.0; tfactor=0.
113  DO
114    k=k+1; ll=.FALSE.; arg=args(k-1)
115    SELECT CASE(arg)
116      CASE('-i');   f_in=args(k); msg='Missing file "'//TRIM(f_in)//'".'
117                    ll=NF90_OPEN(f_in,NF90_NOWRITE,fID)/=NF90_NOERR
118                    IF(.NOT.ll) n=NF90_CLOSE(fID)
119      CASE('-res'); nlon_ou=str2int(args(k)); k=k+1
120                    nlat_ou=str2int(args(k))
121      CASE('-v');   vnam=args(k)
122      CASE('-m');   fmsk=args(k)
123      CASE('-f');   ffactor=str2real(args(k))
124      CASE('-t');   tfactor=str2real(args(k))
125      CASE DEFAULT; msg='Unrecognized argument "'//TRIM(arg)//'".'; ll=.TRUE.
126    END SELECT
127    IF(ll) THEN; WRITE(*,*)msg; STOP; END IF
128    k=k+1
129    IF(k>nargs) EXIT
130  END DO
131!--- CHECK OUTPUT GRID IS DEFINED
132  IF(TRIM(fmsk)=='') fmsk='spec'
133  IF(ALL(['noro','spec']/=fmsk)) THEN
134    msg='Missing or wrong "-m" option ; can be "noro", "spec" or a mask file'
135    CALL err(NF90_OPEN(fmsk,NF90_NOWRITE,fID)/=NF90_NOERR,msg)
136    CALL nc(NF90_INQ_VARID(fID,"MaskOcean",vID),"MaskOcean")    !--- MASK ID
137    CALL nc(NF90_INQUIRE_VARIABLE(fID,vID,dimids=dIDs))         !--- DIMS IDS
138    CALL nc(NF90_INQUIRE_DIMENSION(fID,dIDs(1),len=nlon_ou),'x')!--- NB LONG
139    CALL nc(NF90_INQUIRE_DIMENSION(fID,dIDs(2),len=nlat_ou),'y')!--- NB LAT
140    CALL nc(NF90_CLOSE(fID))
141  END IF
142  IF(nlon_ou<=0.OR.nlat_ou<=0) THEN
143    WRITE(*,*)'Missing or wrong "-res" arguments for output grid'; STOP
144  END IF
145
146!=== READ THE INPUT FIELD =======================================================
147  CALL nc(NF90_OPEN(f_in,NF90_NOWRITE,fID))
148  WRITE(*,*)'>> Reading variable "'//TRIM(vnam)//'" from "'//TRIM(f_in)//'"...'
149
150!--- GET HEIGHT VARIABLE AND ITS DIMENSIONS
151  CALL nc(NF90_INQ_VARID(fID,vnam,vID))
152  CALL nc(NF90_INQUIRE_VARIABLE (fID,vID,dimids=dIDs))
153  CALL nc(NF90_INQUIRE_DIMENSION(fID,dIDs(1),len=nlon_in,name=lonn))
154  CALL nc(NF90_INQUIRE_DIMENSION(fID,dIDs(2),len=nlat_in,name=latn))
155  WRITE(*,*)TRIM(vnam)//' is '//TRIM(lonn)//'('//TRIM(int2str(nlon_in))//')*'   &
156                              //TRIM(latn)//'('//TRIM(int2str(nlat_in))//')'
157  nlon_in=nlon_in-1                                   !--- DISTINCT POINTS NUMBER
158  ALLOCATE(lon_in(nlon_in+1),lat_in(nlat_in),h(nlon_in+1,nlat_in))
159  CALL nc(NF90_INQ_VARID(fID,lonn,loID)        ,lonn)
160  CALL nc(NF90_INQ_VARID(fID,latn,laID)        ,latn)
161  CALL nc(NF90_GET_VAR  (fID,loID,lon_in)      ,lonn)
162  CALL nc(NF90_GET_VAR  (fID,laID,lat_in)      ,latn)
163  CALL nc(NF90_GET_ATT  (fID,loID,'units',lonu),lonn)
164  CALL nc(NF90_GET_ATT  (fID,laID,'units',latu),latn)
165  CALL nc(NF90_GET_VAR  (fID,vID,h(:,:),[1,1],[nlon_in+1,nlat_in]),vnam)
166  CALL nc(NF90_CLOSE(fID))
167
168!--- CHECK WETHER GRID IS CORRECT (GLOBAL DOMAIN, IDENTIFIED UNITS...)
169  dlon=ABS(lon_in(nlon_in+1)-lon_in(1)); dlat=ABS(lat_in(nlat_in)-lat_in(1))
170  CALL err(lonu(1:6)/='degree','Invalid longitudes unit: "'//TRIM(lonu)//'"')
171  CALL err(latu(1:6)/='degree','Invalid latitudes unit: "' //TRIM(latu)//'"')
172  CALL err(ABS(dlon-360.)>eps,'Longitudes domain is not global.')
173  CALL err(ABS(dlat-180.)>eps, 'Latitudes domain is not global.')
174
175!--- ENSURE LONGITUDES ARE INCREASING AND LATITUDES ARE DECREASING
176  lXdec=lon_in(1)>lon_in(nlon_in)
177  lYinc=lat_in(1)<lat_in(nlat_in)
178  IF(lXdec) THEN; lon_in=lon_in(nlon_in+1:1:-1); h(:,:)=h(nlon_in+1:1:-1,:); END IF
179  IF(lYinc) THEN; lat_in=lat_in(nlat_in  :1:-1); h(:,:)=h(:,nlat_in  :1:-1); END IF
180
181!--- ENSURE LONGITUDES ARE BETWEEN -180 and 180deg WITHOUT REDUNDANT END POINT
182  DO ix180=1,nlon_in+1; IF(lon_in(ix180)>=180.) EXIT; END DO
183  IF(ix180>=nlon_in+1) THEN
184    lon_in(:)=[lon_in(ix180:nlon_in)-360.,lon_in(1:ix180)]
185    ALLOCATE(tmp2(nlon_in+1,nlat_in)); nn=nlon_in-ix180+1
186    tmp2(1:nn,:)=h(ix180:nlon_in,:); tmp2(nn+1:nlon_in+1,:)=h(1:ix180,:)
187    DEALLOCATE(tmp2)
188  END IF
189
190!--- REMOVE OCEAN ; FLIP FIELD (SPHEREPACK: LAT FIRST) ; INPUT BOOLEAN MASK
191  WHERE(h(:,:)<0.) h(:,:)=0
192  idh=nlat_in; jdh=nlon_in; CALL flip(h)
193  ALLOCATE(mski(idh,jdh)); mski(:,:)=0.; WHERE(h(:,:)>0.) mski(:,:)=1.
194
195!=== SPHERICAL HARMONICS ANALYSIS ===============================================
196!--- Allocate work vector (min. length depends on used routines)
197  nt=2                                                        ! MAX nt
198  l1=MIN(nlat_in,(nlon_in+2)/2)
199  IF(MODULO(nlon_in,2)==1) l1=MIN(nlat_in,(nlon_in+1)/2)
200  l2=(nlat_in+1)/2
201  IF(lfast) THEN
202    lwork=2*(nlat_in+1)                                       ! shaeci/shseci
203    lwork=MAX(lwork,nlat_in*(nt*nlon_in+MAX(3*l2,nlon_in)))   ! shaec /shaes
204    lwork=MAX(lwork,4*(nlat_in+1))                            ! vhseci
205    lwork=MAX(lwork,nlat_in*(2*nt*nlon_in+MAX(6*l2,nlon_in))+nlat_in*(2*l1*nt+1)) ! gradec
206    lsh=2*nlat_in*l2+3*(  (l1-2  )*(nlat_in+nlat_in-l1-1))/2+nlon_in+15 ! shaec /shsec
207    lvh=4*nlat_in*l2+3*MAX(l1-2,0)*(nlat_in+nlat_in-l1-1)   +nlon_in+15 ! vhseci/gradec
208  ELSE
209    lwork=5*nlat_in*l2+3*((l1-2)*(nlat_in+nlat_in-l1-1))/2    ! shaesi/shsesi
210    lwork=MAX(lwork,(nt+1)*nlat_in*nlon_in)                   ! shaes /shses
211    lwork=MAX(lwork,3*(MAX(l1-2,0)*(nlat_in+nlat_in-l1-1))/2+5*l2*nlat_in)     ! vhsesi
212    lwork=MAX(lwork,nlat_in*((2*nt+1)*nlon_in+2*l1*nt+1))     ! grades
213    lsh=(l1*l2*(nlat_in+nlat_in-l1+1))/2+nlon_in+15           ! shaes /shses
214    lvh= l1*l2*(nlat_in+nlat_in-l1+1)   +nlon_in+15           ! vhsesi/grades
215  END IF
216  ALLOCATE(work(lwork))
217  ALLOCATE(wsha(lsh),wshs(lsh),wvh(lvh))
218
219!--- Allocate spectral coefficients vectors
220  mdab=l1; ndab=nlat_in; IF(.NOT.lfast) mdab=MIN(nlat_in,(nlon_in+2)/2)
221  ALLOCATE(a(mdab,ndab),b(mdab,ndab))
222  isym=0; nt=1                                                !--- Symetries, fields nb
223
224!--- FIELD PROJECTION ON THE SPHERICAL HARMONICS BASE.
225  WRITE(*,*)'>> Projecting fields on the spherical harmonics...'
226  IF(lfast) THEN
227    CALL shaeci(nlat_in,nlon_in,wsha,lsh,work,lwork,ierr)
228    CALL error('shaeci',ierr)
229    CALL shaec(nlat_in,nlon_in,isym,nt,h,idh,jdh,a,b,mdab,ndab,wsha,lsh,work,lwork,ierr)
230    CALL error('shaec',ierr)
231  ELSE
232    CALL shaesi(nlat_in,nlon_in,wsha,lsh,work,lwork,ierr)
233    CALL error('shaesi',ierr)
234    CALL shaes(nlat_in,nlon_in,isym,nt,h,idh,jdh,a,b,mdab,ndab,wsha,lsh,work,lwork,ierr)
235    CALL error('shaes',ierr)
236  END IF
237
238!--- ALIASING DAMPLING FILTER
239!  WRITE(*,*)'>> Bi-Laplacian filtering to avoid Gibbs phenomenon...'
240!  CALL diffusion_filter(a,b)
241
242!=== INPUT/OUTPUT RESOLUTIONS AT EQUATOR (normalized with Earth radius)
243!--- The area of a cell at (lam,phi) of size(dl,dp) is: dl.SIN(dp).COS(phi)
244!--- At equator, Res=SQRT(dl.SIN(dp)) ; with dl=2.pi/nlon and dp=pi/nlat:
245!---             Res=SQRT(2.pi.SIN(pi/nlat)/nlon)~pi*SQRT(2/(nlon*nlat))
246!--- Note: nlat is the slices number = latitude points number -1
247  D1=SQRT(2.*xpi*SIN(xpi/(nlat_in-1))/nlon_in)   !--- Input  grid
248  D2=SQRT(2.*xpi*SIN(xpi/(nlat_ou-1))/nlon_ou)   !--- Output grid
249
250!=== FILTER FACTOR EQUAL TO ZERO => NO FILTERING
251  lfilter=ffactor/=0.
252
253!=== DEFAULT TRANSITION SCALE: INPUT GRID RESOLUTION
254  WRITE(*,*)'tfactor=',tfactor
255  del1=D1; del2=D1+(D2-D1)*tfactor
256  WRITE(*,*)'2*D1,del1,D2,del2=',2*D1,del1,D2,del2
257
258!=== SCALES SEPARATION AT THE OUTPUT GRID RESOLUTION ============================
259  nt=2
260  WRITE(*,*)'>> Scales separation at '//TRIM(real2str(D2/d2r))//' degrees (deta'&
261      //'ils below '//TRIM(real2str(60*D1/d2r))//' minutes removed)...'
262  ALLOCATE(as(mdab,ndab,nt),bs(mdab,ndab,nt))
263  DO n=1,nt; as(:,:,n)=a; bs(:,:,n)=b; END DO
264  CALL  lowpass_filter(as(:,:,1),bs(:,:,1),          D2,del2)   !--- LARGE SCALES
265  CALL bandpass_filter(as(:,:,2),bs(:,:,2),2*D1,del1,D2,del2)   !--- SMALL SCALES
266
267!--- BACKWARD TRANSFORM FOR LARGE AND SUB-CELL SCALES OROGRAPHYS
268  WRITE(*,*)'>> Backward transform of large and sub-cell scales orographies...'
269  ALLOCATE(hs(idh,jdh,nt))
270  IF(lfast) THEN
271    CALL shseci(nlat_in,nlon_in,wshs,lsh,work,lwork,ierr)
272    CALL error('shseci',ierr)
273    CALL shsec(nlat_in,nlon_in,isym,nt,hs,idh,jdh,as,bs,mdab,ndab,wshs,lsh,work,lwork,ierr)
274    CALL error('shsec',ierr)
275  ELSE
276    CALL shsesi(nlat_in,nlon_in,wshs,lsh,work,lwork,ierr)
277    CALL error('shsesi',ierr)
278    CALL shses(nlat_in,nlon_in,isym,nt,hs,idh,jdh,as,bs,mdab,ndab,wshs,lsh,work,lwork,ierr)
279    CALL error('shses',ierr)
280  END IF
281  WHERE(mski==0.); hs(:,:,1)=0.; hs(:,:,2)=0.; END WHERE
282  hs(:,:,2)=hs(:,:,2)**2
283
284!=== COMPUTE GRADIENT ; n=1: large scale ; n=2: sub-cell grid ===================
285  WRITE(*,*)'>> Computing large and sub-cell scales gradients...'
286  ALLOCATE(dxZ(idh,jdh,nt),dyZ(idh,jdh,nt))
287  IF(lfast) THEN
288    CALL vhseci(nlat_in,nlon_in,wvh,lvh,work,lwork,ierr)
289    CALL error('vhseci',ierr)
290    DO n=1,2
291      CALL gradec(nlat_in,nlon_in,isym,1,dyZ(:,:,n),dxZ(:,:,n),idh,jdh,         &
292                           as(:,:,n),bs(:,:,n),mdab,ndab,wvh,lvh,work,lwork,ierr)
293    END DO
294    CALL error('gradec',ierr)
295  ELSE
296    CALL vhsesi(nlat_in,nlon_in,wvh,lvh,work,lwork,ierr)
297    CALL error('vhsesi',ierr)
298    DO n=1,2
299      CALL gradec(nlat_in,nlon_in,isym,1,dyZ(:,:,n),dxZ(:,:,n),idh,jdh,as(:,:,n),&
300                                   bs(:,:,n),mdab,ndab,wvh,lvh,work,lwork,ierr)
301    END DO
302    CALL error('grades',ierr)
303  END IF
304  DEALLOCATE(as,bs)
305  dxZ=dxZ/REarth; dyZ=dyZ/REarth
306  IF(lat_in(nlat_in)>lat_in(1)) dyZ=-dyZ
307  WHERE(mski==0.)
308    dxZ(:,:,1)=0.; dyZ(:,:,1)=0.
309    dxZ(:,:,2)=0.; dyZ(:,:,2)=0.
310  END WHERE
311  ALLOCATE(dH(idh,jdh,6))
312  dH(:,:,1)=dxZ(:,:,1)*dxZ(:,:,1); dH(:,:,4)=dxZ(:,:,2)*dxZ(:,:,2)
313  dH(:,:,2)=dyZ(:,:,1)*dyZ(:,:,1); dH(:,:,5)=dyZ(:,:,2)*dyZ(:,:,2)
314  dH(:,:,3)=dxZ(:,:,1)*dyZ(:,:,1); dH(:,:,6)=dxZ(:,:,2)*dyZ(:,:,2)
315  DEALLOCATE(dxZ,dyZ)
316
317!===============================================================================
318  IF(lfilter) THEN    !=== FILTER TO REMOVE ALIASING ===========================
319!===============================================================================
320    WRITE(*,*)'>> Smoothing large and sub-cell scales fields at '//            &
321             &TRIM(real2str(ffactor*D2/d2r))//' degrees...'
322    CALL spatial_filter_m(dH       ,ffactor*D2,del2)
323    CALL spatial_filter_1(hs(:,:,2),ffactor*D2,del2)
324  END IF
325  DEALLOCATE(work)
326!===============================================================================
327
328!=== DEAL WITH OUTPUT GRID =====================================================
329  intl=0
330!--- OUTPUT GRID (CONTAINS A LONGITUDE REDUNDANT POINT FOR NOW)
331  lon_ou = [(360.*DBLE(n)/DBLE(nlon_ou  ), n = 0, nlon_ou)] + lon_in(1)
332  lat_ou = [(180.*DBLE(n)/DBLE(nlat_ou-1), n = nlat_ou-1, 0, -1)] - 90.
333  la1 = MIN(nlat_in,(nlon_in+1)/2); la2 = (nlat_in+1)/2
334  lb1 = MIN(nlat_ou,(nlon_ou+1)/2); lb2 = (nlat_ou+1)/2
335  lwa = 4*nlat_in*la2+3*MAX(la1-2,0)*(2*nlat_in-la1-1)+la2+nlon_in+15
336  lwb = 4*nlat_ou*lb2+3*MAX(lb1-2,0)*(2*nlat_ou-lb1-1)+    nlon_ou+15
337  lsave=lwa+lwb
338  l1 = MAX(nlat_in,nlat_ou)
339  l2 = MAX(nlon_in,nlon_ou)
340  lwork  = 2*l1*(8*MIN(l1,(l2+2)/2)+4*l2+3)
341  ldwork = 2*l1*(l1+1)+1
342  ALLOCATE(wsave(lsave),work(lwork),dwork(ldwork))
343
344!--- Latitude grid: equally spaced partition of [-pi/2,pi/2]
345  igrid_in(:)=[-1,1]                                  !--- NP->SP, nlat*nlon
346  igrid_ou(:)=[-1,0]                                  !--- NP->SP, nlon*nlat
347
348!--- BUILD FRACTIONAL LAND MASK msko AND GEOPOTENTIAL ('noro' CASE)
349  SELECT CASE(fmsk)
350    CASE('noro')
351      WRITE(*,*)'>> Computing mask & geop (grid_noro compatible)...'
352      ALLOCATE(msko(nlon_ou+1,nlat_ou), Zphi(nlon_ou+1,nlat_ou))
353      CALL flip(h)
354      CALL grid_noro0(lon_in*d2r, lat_in*d2r, h,lon_ou*d2r, lat_ou*d2r, Zphi, msko)
355      msko = msko(1:nlon_ou,:)
356      Zphi = Zphi(1:nlon_ou,:)
357    CASE('spec')
358      WRITE(*,*)'>> Computing mask in spectral space...'
359      ALLOCATE(msko(nlon_ou,nlat_ou))
360      CALL trssph(intl, igrid_in, nlon_in, nlat_in, mski,                      &
361                        igrid_ou, nlon_ou, nlat_ou, msko, wsave, lsave, lsvmin,&
362                                     work, lwork, lwkmin, dwork, ldwork, ierr)
363      intl=1
364    CASE DEFAULT
365      WRITE(*,*)'>> Trying to read mask from "'//TRIM(fmsk)//'" file'
366      ALLOCATE(msko(nlon_ou,nlat_ou))
367      msg='Missing or wrong "-m" option ; can be "noro", "spec" or a mask file'
368      CALL err(NF90_OPEN(fmsk,NF90_NOWRITE,fID)/=NF90_NOERR,msg)
369      CALL nc(NF90_INQ_VARID(fID,"MaskOcean",vID),"MaskOcean")    !--- MASK ID
370      CALL nc(NF90_GET_VAR(fID,vID,msko(:,:)))                    !--- MASK
371      CALL nc(NF90_CLOSE(fID))
372      msko(:,:)=1.0-msko(:,:)
373  END SELECT
374  DEALLOCATE(mski,h)
375
376!--- GET RID OF REDUNDANT LONGITUDE (USELESS FOR SPHEREPACK)
377  lon_ou=lon_ou(1:nlon_ou)
378
379!=== REGRIDDING ON THE TARGET OUTPUT GRID ======================================
380  WRITE(*,*)'>> Regridding on the target grid...'
381
382!--- COMPUTE BOOLEAN OUTPUT MASK
383  ALLOCATE(mask(nlon_ou,nlat_ou)); mask=0_1; WHERE(msko>=0.5) mask=1_1
384
385!--- MEAN OROGRAPHY
386  ALLOCATE(h0(nlon_ou,nlat_ou))
387  CALL trssph(intl, igrid_in, nlon_in, nlat_in, hs(:,:,1),                     &
388                    igrid_ou, nlon_ou, nlat_ou, h0,                            &
389    wsave, lsave, lsvmin, work, lwork, lwkmin, dwork, ldwork, ierr)
390  WHERE(h0<0..OR.mask==0_1) h0(:,:)=0.
391
392!--- STANDARD DEVIATION OF SUB-CELL SCALES OROGRAPHY
393  ALLOCATE(mu(nlon_ou,nlat_ou))
394  CALL trssph(1, igrid_in, nlon_in, nlat_in, hs(:,:,2),                        &
395                 igrid_ou, nlon_ou, nlat_ou, mu,                               &
396    wsave, lsave, lsvmin, work, lwork, lwkmin, dwork, ldwork, ierr)
397  DEALLOCATE(hs)
398  WHERE(mu(:,:)<0..OR.mask==0_1) mu(:,:)=0.; mu=SQRT(mu)
399
400!--- SQUARE OF LARGE AND SUB-CELL SCALES ZONAL SLOPE
401  ALLOCATE(dxZ2(nlon_ou,nlat_ou,2))
402  CALL trssph(1, igrid_in, nlon_in, nlat_in, dH  (:,:,1),                      &
403                 igrid_ou, nlon_ou, nlat_ou, dxZ2(:,:,1),                      &
404    wsave, lsave, lsvmin, work, lwork, lwkmin, dwork, ldwork, ierr)
405  CALL trssph(1, igrid_in, nlon_in, nlat_in, dH  (:,:,4),                      &
406                 igrid_ou, nlon_ou, nlat_ou, dxZ2(:,:,2),                      &
407    wsave, lsave, lsvmin, work, lwork, lwkmin, dwork, ldwork, ierr)
408  WHERE(mask==0_1); dxZ2(:,:,1)=0.; dxZ2(:,:,2)=0.; END WHERE
409
410!--- SQUARE OF LARGE AND SUB-CELL SCALES MERIDIONAL SLOPE
411  ALLOCATE(dyZ2(nlon_ou,nlat_ou,2))
412  CALL trssph(1, igrid_in, nlon_in, nlat_in, dH  (:,:,2),                      &
413                 igrid_ou, nlon_ou, nlat_ou, dyZ2(:,:,1),                      &
414    wsave, lsave, lsvmin, work, lwork, lwkmin, dwork, ldwork, ierr)
415  CALL trssph(1, igrid_in, nlon_in, nlat_in, dH  (:,:,5),                      &
416                 igrid_ou, nlon_ou, nlat_ou, dyZ2(:,:,2),                      &
417    wsave, lsave, lsvmin, work, lwork, lwkmin, dwork, ldwork, ierr)
418  WHERE(mask==0_1); dyZ2(:,:,1)=0.; dyZ2(:,:,2)=0.; END WHERE
419
420!--- PRODUCT OF LARGE AND SUB-CELL SCALES MERIDIONAL AND ZONAL SLOPES
421  ALLOCATE(dxyZ(nlon_ou,nlat_ou,2))
422  CALL trssph(1, igrid_in, nlon_in, nlat_in, dH  (:,:,3),                      &
423                 igrid_ou, nlon_ou, nlat_ou, dxyZ(:,:,1),                      &
424    wsave, lsave, lsvmin, work, lwork, lwkmin, dwork, ldwork, ierr)
425  CALL trssph(1, igrid_in, nlon_in, nlat_in, dH  (:,:,6),                      &
426                 igrid_ou, nlon_ou, nlat_ou, dxyZ(:,:,2),                      &
427    wsave, lsave, lsvmin, work, lwork, lwkmin, dwork, ldwork, ierr)
428  WHERE(mask==0_1); dxyZ(:,:,1)=0.; dxyZ(:,:,2)=0.; END WHERE
429  DEALLOCATE(dH)
430
431!--- COMPUTE LARGE AND SUB-CELL SCALES DERIVED QUANTITIES
432  ALLOCATE(Xk(nlon_ou,nlat_ou,2)); Xk=(dxZ2+dyZ2)/2.
433  ALLOCATE(Xl(nlon_ou,nlat_ou,2)); Xl=(dxZ2-dyZ2)/2.
434  DEALLOCATE(dxZ2,dyZ2)
435  ALLOCATE(Xm(nlon_ou,nlat_ou,2)); Xm=dxyZ
436  DEALLOCATE(dxyZ)
437  ALLOCATE(Xp(nlon_ou,nlat_ou,2),Xq(nlon_ou,nlat_ou,2))
438  Xp=Xk; Xq=Xk; Xk=SQRT(Xl**2+Xm**2); Xp=Xp-Xk; Xq=Xq+Xk
439  DEALLOCATE(Xk)
440  WHERE(ABS(Xm)<=1e-16) Xm=1e-16*SIGN(1.,Xm)
441  ALLOCATE(Zthe(nlon_ou,nlat_ou)); Zthe=0.5*ATAN2(Xm(:,:,1),Xl(:,:,1))/d2r
442  DEALLOCATE(Xm,Xl)
443  ALLOCATE(Zgam(nlon_ou,nlat_ou)); Zgam=0.
444  WHERE(Xq(:,:,1)>0..AND.Xp(:,:,1)>1.E-8) Zgam(:,:)=Xp(:,:,1)/Xq(:,:,1)
445  DEALLOCATE(Xp)
446  ALLOCATE(Zsig(nlon_ou,nlat_ou)); Zsig=SQRT(Xq(:,:,2))
447  WHERE(Xq(:,:,2)<=1.E-16) Zsig(:,:)=1.E-8
448  DEALLOCATE(Xq)
449  WHERE(mask==0_1); Zthe=0.; Zgam=0.; Zsig=0.; END WHERE
450
451!--- Save the data
452  WRITE(*,*)'>> Saving fields in a netcdf file...'
453  res_in=TRIM(int2str(nlon_in))//'x'//TRIM(int2str(nlat_in))
454  res_ou=TRIM(int2str(nlon_ou))//'x'//TRIM(int2str(nlat_ou))
455  f_ou='make_sso_'//TRIM(res_ou)//'_'//TRIM(f_in)
456  fnam=f_ou
457  CALL nc(NF90_CREATE(f_ou,NF90_CLOBBER,fID))
458
459  CALL nc(NF90_DEF_DIM(fID,'x',nlon_ou,xID))
460  CALL nc(NF90_DEF_VAR(fID,'x',NF90_REAL,xID,loID)      ,'x')
461  CALL nc(NF90_PUT_ATT(fID,loID,'long_name','Longitude'),'x')
462  CALL nc(NF90_PUT_ATT(fID,loID,'units','degrees_east') ,'x')
463
464  CALL nc(NF90_DEF_DIM(fID,'y',nlat_ou,yID))
465  CALL nc(NF90_DEF_VAR(fID,'y',NF90_REAL,yID,laID)      ,'y')
466  CALL nc(NF90_PUT_ATT(fID,laID,'long_name','Latitude') ,'y')
467  CALL nc(NF90_PUT_ATT(fID,laID,'units','degrees_north'),'y')
468
469  CALL nc(NF90_DEF_VAR(fID,'mask',NF90_REAL,[xID,yID],mskID),'mask')
470  IF(fmsk=='noro') &
471  CALL nc(NF90_DEF_VAR(fID,'Zphi',NF90_REAL,[xID,yID],phiID),'Zphi')
472  CALL nc(NF90_DEF_VAR(fID,'Zmea',NF90_REAL,[xID,yID],meaID),'Zmea')
473  CALL nc(NF90_DEF_VAR(fID,'mu'  ,NF90_REAL,[xID,yID], muID),'mu'  )
474  CALL nc(NF90_DEF_VAR(fID,'Zsig',NF90_REAL,[xID,yID],sigID),'Zsig')
475  CALL nc(NF90_DEF_VAR(fID,'Zgam',NF90_REAL,[xID,yID],gamID),'Zgam')
476  CALL nc(NF90_DEF_VAR(fID,'Zthe',NF90_REAL,[xID,yID],theID),'Zthe')
477  CALL nc(NF90_DEF_VAR(fID,'Zpic',NF90_REAL,[xID,yID],picID),'Zpic')
478  CALL nc(NF90_DEF_VAR(fID,'Zval',NF90_REAL,[xID,yID],valID),'Zval')
479
480  CALL nc(NF90_PUT_ATT(fID,mskID,'long_name','Fractional land mask'                      ),'mask')
481  IF(fmsk=='noro') &
482  CALL nc(NF90_PUT_ATT(fID,phiID,'long_name','Geopotential'                              ),'Zphi')
483  CALL nc(NF90_PUT_ATT(fID,meaID,'long_name','Mean orography'                            ),'Zmea')
484  CALL nc(NF90_PUT_ATT(fID, muID,'long_name','Std deviation of sub-cell scales orography'),'mu'  )
485  CALL nc(NF90_PUT_ATT(fID,sigID,'long_name','Slope along principal axis'                ),'Zsig')
486  CALL nc(NF90_PUT_ATT(fID,gamID,'long_name','Anisotropy (aspect ratio)'                 ),'Zgam')
487  CALL nc(NF90_PUT_ATT(fID,theID,'long_name','Orientation (principal axis)'              ),'Zthe')
488  CALL nc(NF90_PUT_ATT(fID,picID,'long_name','Maximum height'                            ),'Zpic')
489  CALL nc(NF90_PUT_ATT(fID,valID,'long_name','Minimum height'                            ),'Zval')
490
491  CALL nc(NF90_PUT_ATT(fID,mskID,'units','none'   ),'mask')
492  IF(fmsk=='noro') &
493  CALL nc(NF90_PUT_ATT(fID,phiID,'units','m'      ),'Zphi')
494  CALL nc(NF90_PUT_ATT(fID,meaID,'units','m'      ),'Zmea')
495  CALL nc(NF90_PUT_ATT(fID, muID,'units','m'      ),'mu'  )
496  CALL nc(NF90_PUT_ATT(fID,sigID,'units','m/m'    ),'Zsig')
497  CALL nc(NF90_PUT_ATT(fID,gamID,'units','none'   ),'Zgam')
498  CALL nc(NF90_PUT_ATT(fID,theID,'units','degrees'),'Zthe')
499  CALL nc(NF90_PUT_ATT(fID,picID,'units','m'      ),'Zpic')
500  CALL nc(NF90_PUT_ATT(fID,valID,'units','m'      ),'Zval')
501
502  CALL nc(NF90_PUT_ATT(fID,NF90_GLOBAL,'Conventions','COARDS/CF-1.0'))
503  CALL nc(NF90_PUT_ATT(fID,NF90_GLOBAL,'Initial_Grid',TRIM(res_in)))
504  CALL nc(NF90_PUT_ATT(fID,NF90_GLOBAL,'history',TRIM(call_seq)))
505  CALL nc(NF90_ENDDEF(fID))
506
507  CALL nc(NF90_PUT_VAR(fID, loID,lon_ou),'x' )
508  CALL nc(NF90_PUT_VAR(fID, laID,lat_ou),'y' )
509  CALL nc(NF90_PUT_VAR(fID,mskID,msko),'mask')
510  IF(fmsk=='noro') &
511  CALL nc(NF90_PUT_VAR(fID,phiID,Zphi),'Zphi')
512  CALL nc(NF90_PUT_VAR(fID,meaID,h0  ),'Zmea')
513  CALL nc(NF90_PUT_VAR(fID, muID,mu  ),'mu'  )
514  CALL nc(NF90_PUT_VAR(fID,sigID,Zsig),'Zsig')
515  CALL nc(NF90_PUT_VAR(fID,gamID,Zgam),'Zgam')
516  CALL nc(NF90_PUT_VAR(fID,theID,Zthe),'Zthe')
517  CALL nc(NF90_PUT_VAR(fID,picID,       h0+2*mu ),'Zpic')
518  CALL nc(NF90_PUT_VAR(fID,valID,MAX(0.,h0-2*mu)),'Zval')
519  CALL nc(NF90_CLOSE(fID))
520  WRITE(*,*)'Finished.'
521
522CONTAINS
523
524
525!-------------------------------------------------------------------------------
526!
527SUBROUTINE diffusion_filter(a,b)
528!
529!-------------------------------------------------------------------------------
530! Purpose: ECMWF bi-laplacian diffusion filter to limit aliasing.
531! Note that one third of the frequencies is skipped to allow some accuracy for
532! derived quantities computation.
533!-------------------------------------------------------------------------------
534  IMPLICIT NONE
535!-------------------------------------------------------------------------------
536! Arguments:
537  REAL, INTENT(INOUT) :: a(:,:), b(:,:)
538!-------------------------------------------------------------------------------
539! Local variables:
540  INTEGER :: m
541  REAL, ALLOCATABLE :: fn(:)
542!-------------------------------------------------------------------------------
543  ALLOCATE(fn(ndab)); fn=[(REAL(m*(m-1)),m=1,ndab)]
544  a(1,:)=a(1,:)/(1+4.*fn(:)/fn(ndab))**2
545  b(1,:)=b(1,:)/(1+4.*fn(:)/fn(ndab))**2
546  DO m=1,ndab
547    IF(m<=2*ndab/3) THEN
548      a(m,:)=a(m,:)/(1+5.*fn(:)/fn(ndab))**2
549      b(m,:)=b(m,:)/(1+5.*fn(:)/fn(ndab))**2
550    ELSE
551      a(m,:)=0.
552      b(m,:)=0.
553    END IF
554  END DO
555
556END SUBROUTINE diffusion_filter
557!
558!-------------------------------------------------------------------------------
559
560
561!-------------------------------------------------------------------------------
562!
563SUBROUTINE lowpass_filter(a,b,d,dd)
564!
565!-------------------------------------------------------------------------------
566! Purpose: ECMWF lowpass filter.
567!-------------------------------------------------------------------------------
568  IMPLICIT NONE
569!-------------------------------------------------------------------------------
570! Arguments:
571  REAL, INTENT(INOUT) :: a(:,:), b(:,:)
572  REAL, INTENT(IN)    :: d, dd
573!-------------------------------------------------------------------------------
574! Local variables:
575  INTEGER :: m, na
576  REAL, ALLOCATABLE  :: h(:)
577!-------------------------------------------------------------------------------
578  na=SIZE(a,1)
579  IF(ALLOCATED(h)) THEN; IF(SIZE(h)/=na) DEALLOCATE(h); END IF
580  IF(.NOT.ALLOCATED(h)) ALLOCATE(h(na))
581  CALL lowpass(d,dd,h)
582  DO m=1,SIZE(h); a(m,:)=a(m,:)*h; b(m,:)=b(m,:)*h; END DO
583
584END SUBROUTINE lowpass_filter
585!
586!-------------------------------------------------------------------------------
587
588
589!-------------------------------------------------------------------------------
590!
591SUBROUTINE bandpass_filter(a,b,d1,dd1,d2,dd2)
592!
593!-------------------------------------------------------------------------------
594! Purpose: ECMWF bandpass filter. Calls lowpass filter with 2 different scales.
595!-------------------------------------------------------------------------------
596  IMPLICIT NONE
597!-------------------------------------------------------------------------------
598! Arguments:
599  REAL, INTENT(INOUT) :: a(:,:), b(:,:)
600  REAL, INTENT(IN)    :: d1, dd1, d2, dd2
601!-------------------------------------------------------------------------------
602! Local variables:
603  INTEGER :: m, na
604  REAL, ALLOCATABLE  :: h(:), hh(:)
605!-------------------------------------------------------------------------------
606  na=SIZE(a,1)
607  IF(ALLOCATED(hh)) THEN; IF(SIZE(hh)/=na) DEALLOCATE(hh); END IF
608  IF(ALLOCATED(h )) THEN; IF(SIZE(h )/=na) DEALLOCATE(h ); END IF
609  IF(.NOT.ALLOCATED(hh)) ALLOCATE(hh(na))
610  IF(.NOT.ALLOCATED(h )) ALLOCATE(h (na))
611  CALL lowpass(d1,dd1,hh)
612  CALL lowpass(d2,dd2,h ); hh=hh-h
613  DO m=1,SIZE(h); a(m,:)=a(m,:)*hh; b(m,:)=b(m,:)*hh; END DO
614
615END SUBROUTINE bandpass_filter
616!
617!-------------------------------------------------------------------------------
618
619
620!-------------------------------------------------------------------------------
621!
622SUBROUTINE lowpass(d,dd,h)
623!
624!-------------------------------------------------------------------------------
625  IMPLICIT NONE
626!-------------------------------------------------------------------------------
627! Arguments:
628  REAL, INTENT(IN)    :: d, dd   ! d is DELTA/REarth ; dd is delta/REarth
629  REAL, INTENT(INOUT) :: h(:)
630!-------------------------------------------------------------------------------
631  INTEGER :: m, n
632  REAL    :: hd
633!-------------------------------------------------------------------------------
634  n=SIZE(h); hd=0.5*d
635  h(:)=[((SIN(m*(hd-dd))/m+(COS(hp+m*hd)*SIN(hp+m*dd))/(hp/dd+m)               &
636        + SIN(m*(hd+dd))/m+(COS(hp-m*hd)*SIN(hp-m*dd))/(hp/dd-m))**2/d/d,m=1,n)]
637
638END SUBROUTINE lowpass
639!
640!-------------------------------------------------------------------------------
641
642
643!-------------------------------------------------------------------------------
644!
645SUBROUTINE spatial_filter_1(u,D,dd)
646!
647!-------------------------------------------------------------------------------
648! Purpose: Spatial filter ; using spectral lowpass filter.
649!-------------------------------------------------------------------------------
650  IMPLICIT NONE
651!-------------------------------------------------------------------------------
652! Arguments:
653  REAL, INTENT(INOUT) :: u(:,:)
654  REAL, INTENT(IN)    :: D, dd
655!-------------------------------------------------------------------------------
656! Local variables:
657  REAL, ALLOCATABLE  :: uu(:,:,:)
658!-------------------------------------------------------------------------------
659  ALLOCATE(uu(SIZE(u,1),SIZE(u,2),1)); uu(:,:,1)=u
660  CALL spatial_filter_m(uu,D,dd)
661  u=uu(:,:,1)
662  DEALLOCATE(uu)
663
664END SUBROUTINE spatial_filter_1
665!
666!-------------------------------------------------------------------------------
667
668
669!-------------------------------------------------------------------------------
670!
671SUBROUTINE spatial_filter_m(u,D,dd)
672!
673!-------------------------------------------------------------------------------
674! Purpose: Spatial filter ; using spectral lowpass filter.
675!-------------------------------------------------------------------------------
676  IMPLICIT NONE
677!-------------------------------------------------------------------------------
678! Arguments:
679  REAL, INTENT(INOUT) :: u(:,:,:)
680  REAL, INTENT(IN)    :: D, dd
681!-------------------------------------------------------------------------------
682! Local variables:
683  INTEGER :: ku
684  REAL, ALLOCATABLE  :: aa(:,:,:),bb(:,:,:)
685!-------------------------------------------------------------------------------
686  ku=SIZE(u,3)                                   !--- NUMBER OF FIELDS TO SMOOTH
687  ALLOCATE(aa(mdab,ndab,ku),bb(mdab,ndab,ku))
688
689!--- PROJECTION OF THE SUB-CELL SCALES FIELDS ON THE SPHERICAL HARMONICS BASE.
690  IF(lfast) THEN
691    CALL shaec(nlat_in,nlon_in,0,ku,u,idh,jdh,aa,bb,mdab,ndab,wsha,lsh,work,lwork,ierr)
692    CALL error('shaec',ierr)
693  ELSE
694    CALL shaes(nlat_in,nlon_in,0,ku,u,idh,jdh,aa,bb,mdab,ndab,wsha,lsh,work,lwork,ierr)
695    CALL error('shaes',ierr)
696  END IF
697
698!--- LOW PASS FILTER AT THE OUTPUT GRID RESOLUTION
699  DO n=1,ku; CALL lowpass_filter(aa(:,:,n),bb(:,:,n),D,dd); END DO
700
701!--- BACKWARD TRANSFORM FOR MEAN SUB-CELL SCALES PARAMETERS
702  IF(lfast) THEN
703    CALL shsec(nlat_in,nlon_in,0,ku,u,idh,jdh,aa,bb,mdab,ndab,wshs,lsh,work,lwork,ierr)
704    CALL error('shsec',ierr)
705  ELSE
706    CALL shses(nlat_in,nlon_in,0,ku,u,idh,jdh,aa,bb,mdab,ndab,wshs,lsh,work,lwork,ierr)
707    CALL error('shses',ierr)
708  END IF
709  DEALLOCATE(aa,bb)
710
711END SUBROUTINE spatial_filter_m
712!
713!-------------------------------------------------------------------------------
714
715
716!-------------------------------------------------------------------------------
717!
718SUBROUTINE grid_noro0(xin,yin,zin,xou,you,zphi,mask)
719!
720!-------------------------------------------------------------------------------
721! Purpose: Sub-cell scales orographic parameters coomputation. Angles in radians
722! Notes: Input coordinates contain a longitude periodic redundant point.
723!-------------------------------------------------------------------------------
724  IMPLICIT NONE
725!-------------------------------------------------------------------------------
726! Arguments:
727  REAL, INTENT(IN)  :: xin(:), yin(:)   !--- INPUT  COORDINATES (nxi)   (nyi)
728  REAL, INTENT(IN)  :: zin(:,:)         !--- INPUT  FIELD       (nxi,    nyi)
729  REAL, INTENT(IN)  :: xou(:), you(:)   !--- OUTPUT COORDINATES (nxo+1) (nyo)
730  REAL, INTENT(OUT) :: zphi(:,:)        !--- GEOPOTENTIAL       (nxo+1,  nyo)
731  REAL, INTENT(OUT) :: mask(:,:)        !--- FRACTIONAL MASK    (nxo+1,  nyo)
732!-------------------------------------------------------------------------------
733! Local variables:
734  REAL, ALLOCATABLE :: xi(:), xo_w(:), yo_s(:), zi(:,:), num_tot(:,:)
735  REAL, ALLOCATABLE :: yi(:), xo_e(:), yo_n(:),  w(:,:), num_lan(:,:)
736  REAL    :: dx, dy, wx, wy, zx, zy, ex, ey
737  INTEGER :: nxi, nxo, i, ii, nn
738  INTEGER :: nyi, nyo, j, jj, di
739!-------------------------------------------------------------------------------
740  nxi=SIZE(xin); nxo=SIZE(xou)-1; ex=SIGN(1.,xin(nxi)-xin(1))
741  nyi=SIZE(yin); nyo=SIZE(you);   ey=SIGN(1.,yin(nyi)-yin(1))
742
743!--- MARGIN TO ENSURE OUTPUT CELLS HAVE MATCHING INPUT CELLS
744  di=CEILING(1.+MAXVAL([xou(2:nxo+1)-xou(1:nxo)])/MINVAL([xin(2:nxi)-xin(1:nxi-1)]))
745
746!--- EXTENSION OF THE INPUT DATABASE TO PROCEED COMPUTATIONS AT BOUNDARIES
747  ALLOCATE(xi(nxi+2*di)); xi(:)=[xin(nxi-di:nxi-1)-2.*xpi,xin,xin(2:di+1)+2.*xpi]
748  ALLOCATE(yi(nyi+2));    yi(:)=[2.*yin(1)-yin(2),yin,2.*yin(nyi)-yin(nyi-1)]
749
750  ALLOCATE(zi(nxi+2*di,nyi+2))
751  zi(1      +di:nxi+  di,2:nyi+1)=zin(:,:)
752  zi(1         :      di,2:nyi+1)=zin(nxi-di:nxi-1,:)
753  zi(1+nxi  +di:nxi+2*di,2:nyi+1)=zin(2     :di+1 ,:)
754  zi(1         :nxi/2+di,      1)=zi (1+nxi/2:nxi  +di,    2)
755  zi(1+nxi/2+di:nxi+2*di,      1)=zi (1      :nxi/2+di,    2)
756  zi(1         :nxi/2+di,  nyi+2)=zi (1+nxi/2:nxi  +di,nyi+1)
757  zi(1+nxi/2+di:nxi+2*di,  nyi+2)=zi (1      :nxi/2+di,nyi+1)
758
759!  write(*,'(a,2f10.5,a,2f10.5)')'xin=',xin(1:2),'...',xin(nxi-1:nxi)
760!  write(*,'(a,2f10.5,a,2f10.5)')'yin=',yin(1:2),'...',yin(nyi-1:nyi)
761!  write(*,'(a,2f10.5,a,2f10.5)')'xou=',xou(1:2),'...',xou(nxo:nxo+1)
762!  write(*,'(a,2f10.5,a,2f10.5)')'you=',you(1:2),'...',you(nyo-1:nyo)
763!  write(*,*)'xi=',xi(1:di+1),'...',xi(nxi+di:nxi+2*di)
764!  write(*,'(a,3f10.5,a,3f10.5)')'yi=',yi(1:3),'...',yi(nyi:nyi+2)
765
766!--- COMPUTE LIMITS OF MODEL GRIDPOINT AREA (REGULAR GRID) bdac
767  ALLOCATE(xo_w(nxo+1)); xo_w=(xou+[2.*xou(    1)-xou(  2),xou(1:nxo  )])/2.0
768  ALLOCATE(yo_s(nyo  )); yo_s=(you+[2.*you(    1)-you(  2),you(1:nyo-1)])/2.0
769  ALLOCATE(xo_e(nxo+1)); xo_e=(xou+[xou(2:nxo+1),2.*xou(nxo+1)-xou(nxo)])/2.0
770  ALLOCATE(yo_n(nyo  )); yo_n=(you+[you(2:nyo  ),2.*you(nyo)-you(nyo-1)])/2.0
771
772!--- INITIALIZATIONS:
773  ALLOCATE(w(nxo+1,nyo)); w(:,:)=0.0; zphi(:,:)=0.0
774
775!--- SUMMATION OVER GRIDPOINT AREA
776  zx=2.*xpi/REAL(nxi)                            !--- LON CELL LENGTH (1-SPHERE)
777  dx=zx/2.                                       !--- HALF "
778  ALLOCATE(num_tot(nxo+1,nyo)); num_tot(:,:)=0.
779  ALLOCATE(num_lan(nxo+1,nyo)); num_lan(:,:)=0.
780  DO ii=1,nxo+1
781    DO jj=1,nyo
782      DO j=2,nyi+1
783        zy=xpi/REAL(nyi)*COS(yi(j))              !--- LAT CELL LENGTH (1-SPHERE)
784        dy=zy/2.
785        wy=MAX(0.,MIN(zy,MINVAL(dy+ey*[yo_n(jj)-yi(j),yi(j)-yo_s(jj)])))
786        IF(wy==0.) CYCLE
787        DO i=2,nxi+2*di-1
788          wx=MAX(0.,MIN(zx,MINVAL(dx+ex*[xo_e(ii)-xi(i),xi(i)-xo_w(ii)])*COS(yi(j))))
789          IF(wx==0.) CYCLE
790          num_tot(ii,jj)=num_tot(ii,jj)+1.0
791          IF(zi(i,j)>=1.) num_lan(ii,jj)=num_lan(ii,jj)+1.0
792          w   (ii,jj)=   w(ii,jj)+wx*wy
793          zphi(ii,jj)=zphi(ii,jj)+wx*wy*zi(i,j)
794        END DO
795      END DO
796    END DO
797  END DO
798
799!--- COMPUTE FRACTIONAL MASK AND GEOPOTENTIAL
800  WHERE(w(:,:)/=0.0) mask=num_lan(:,:)/num_tot(:,:)
801  nn=COUNT(w(:,:)==0.0)
802  IF(nn/=0) WRITE(*,*)'Problem with weight ; vanishing occurrences: ',nn
803  WHERE(w/=0.0) zphi=zphi/w
804  WHERE(w==0.0.OR.mask<0.1) zphi=0.0
805  zphi(nxo+1,:)=zphi(1,:)
806  zphi(:,  1)=SUM(w(1:nxo,  1)*zphi(1:nxo,  1))/SUM(w(1:nxo,  1))
807  zphi(:,nyo)=SUM(w(1:nxo,nyo)*zphi(1:nxo,nyo))/SUM(w(1:nxo,nyo))
808
809END SUBROUTINE grid_noro0
810!
811!-------------------------------------------------------------------------------
812
813
814!-------------------------------------------------------------------------------
815!
816SUBROUTINE nc(ncres,var)
817!
818!-------------------------------------------------------------------------------
819! Purpose: NetCDF errors handling.
820!-------------------------------------------------------------------------------
821  IMPLICIT NONE
822!-------------------------------------------------------------------------------
823! Arguments:
824  INTEGER,          INTENT(IN)           :: ncres
825  CHARACTER(LEN=*), OPTIONAL, INTENT(IN) :: var
826!-------------------------------------------------------------------------------
827! Local variables:
828  CHARACTER(LEN=256) :: msg
829!-------------------------------------------------------------------------------
830  IF(ncres/=NF90_NoErr) THEN
831    msg='Error in routine '//TRIM(sub)
832    IF(fnam/='')     msg=TRIM(msg)//' for file "'//TRIM(fnam)//'"'
833    IF(PRESENT(var)) msg=TRIM(msg)//'" and variable "'//TRIM(var)//'"'
834    WRITE(*,*)TRIM(msg)//': '//NF90_STRERROR(ncres); STOP
835  END IF
836
837END SUBROUTINE nc
838!
839!-------------------------------------------------------------------------------
840
841
842!-------------------------------------------------------------------------------
843!
844ELEMENTAL FUNCTION int2str(val)
845!
846!-------------------------------------------------------------------------------
847  IMPLICIT NONE
848!-------------------------------------------------------------------------------
849! Purpose: convert an integer into a string.
850!-------------------------------------------------------------------------------
851! Arguments:
852  CHARACTER(LEN=128)  :: int2str
853  INTEGER, INTENT(IN) :: val
854!-------------------------------------------------------------------------------
855! Local variable:
856  CHARACTER(LEN=128) :: s1
857!-------------------------------------------------------------------------------
858  WRITE(s1,*)val; int2str=TRIM(ADJUSTL(s1))
859
860END FUNCTION int2str
861!-------------------------------------------------------------------------------
862
863
864!-------------------------------------------------------------------------------
865!
866SUBROUTINE err(ierr,str)
867!
868!-------------------------------------------------------------------------------
869  IMPLICIT NONE
870!-------------------------------------------------------------------------------
871! Argument:
872  LOGICAL,          INTENT(IN) :: ierr
873  CHARACTER(LEN=*), INTENT(IN) :: str
874!-------------------------------------------------------------------------------
875  IF(.NOT.ierr) RETURN
876  WRITE(*,*)TRIM(str)
877  STOP
878
879END SUBROUTINE err
880!
881!-------------------------------------------------------------------------------
882
883
884!-------------------------------------------------------------------------------
885!
886SUBROUTINE error(sub,ierr)
887!
888!-------------------------------------------------------------------------------
889  IMPLICIT NONE
890!-------------------------------------------------------------------------------
891! Arguments:
892  CHARACTER(LEN=*), INTENT(IN) :: sub
893  INTEGER,          INTENT(IN) :: ierr
894!-------------------------------------------------------------------------------
895  IF(ierr==0) RETURN
896  WRITE(*,*)'In routine "'//TRIM(sub)//'": error in the specification of argume&
897      &nt nr. '//TRIM(int2str(ierr))
898  STOP
899END SUBROUTINE error
900!
901!-------------------------------------------------------------------------------
902
903
904!-------------------------------------------------------------------------------
905!
906ELEMENTAL FUNCTION real2str(val)
907!
908!-------------------------------------------------------------------------------
909  IMPLICIT NONE
910!-------------------------------------------------------------------------------
911! Purpose: convert an integer into a string.
912!-------------------------------------------------------------------------------
913! Arguments:
914  CHARACTER(LEN=128) :: real2str
915  REAL,   INTENT(IN) :: val
916  INTEGER :: r, s
917!-------------------------------------------------------------------------------
918                s=NINT(val); r=NINT(1000.*(val-REAL(s)))
919  IF(r<0) THEN; s= INT(val); r= INT(1000.*(val-REAL(s))); END IF
920  real2str=TRIM(ADJUSTL(int2str(s)))//'.'//TRIM(ADJUSTL(int2str(r)))
921
922END FUNCTION real2str
923!-------------------------------------------------------------------------------
924
925
926!-------------------------------------------------------------------------------
927!
928SUBROUTINE flip(a)
929!
930!-------------------------------------------------------------------------------
931  IMPLICIT NONE
932!-------------------------------------------------------------------------------
933! Arguments:
934  REAL, ALLOCATABLE, INTENT(INOUT) :: a(:,:)
935!-------------------------------------------------------------------------------
936! Local variables:
937  INTEGER :: k, n
938  REAL, ALLOCATABLE :: tmp(:,:)
939!-------------------------------------------------------------------------------
940  n=SIZE(a,2)
941  ALLOCATE(tmp(n,SIZE(a,1))); DO k=1,n; tmp(k,:)=a(:,k); END DO
942  CALL MOVE_ALLOC(FROM=tmp,TO=a)
943
944END SUBROUTINE flip
945!
946!-------------------------------------------------------------------------------
947
948
949!-------------------------------------------------------------------------------
950ELEMENTAL LOGICAL FUNCTION is_int(str) RESULT(out)
951!-------------------------------------------------------------------------------
952  IMPLICIT NONE
953!-------------------------------------------------------------------------------
954! Purpose: tests if str is a valid integer number
955!-------------------------------------------------------------------------------
956  CHARACTER(LEN=*), INTENT(IN) :: str
957  INTEGER :: k, k0
958!-------------------------------------------------------------------------------
959  out=LEN_TRIM(str)/=0; IF(.NOT.out) RETURN
960  k0=1; IF(INDEX('+-',str(1:1))/=0) k0=2
961  DO k=k0,LEN_TRIM(str); IF(INDEX('0123456789',str(k:k))==0) out=.FALSE.; END DO
962END FUNCTION is_int
963!-------------------------------------------------------------------------------
964
965!-------------------------------------------------------------------------------
966ELEMENTAL LOGICAL FUNCTION is_dec(str) RESULT(out)
967!-------------------------------------------------------------------------------
968  IMPLICIT NONE
969!-------------------------------------------------------------------------------
970! Purpose: tests if str is a valid decimal number or an integer
971!-------------------------------------------------------------------------------
972  CHARACTER(LEN=*), INTENT(IN) :: str
973  INTEGER :: ix
974!-------------------------------------------------------------------------------
975  out=LEN_TRIM(str)/=0; IF(.NOT.out) RETURN
976
977  !--- TEST IF THE NUMBER IS A PURE INTEGER
978  IF(is_int(str)) RETURN
979
980  !--- CHECK FOR POINT SEPARATOR (SHOULD HAVE A STRING INT BEFORE AND/OR AFTER
981  ix=INDEX(str,'.'); out=ix>0.AND.LEN_TRIM(str)/=1; IF(.NOT.out) RETURN
982
983  !--- CHECK SURROUNDING STRINGS ARE INTEGERS
984  out=is_int(str(1:ix-1)); IF(ix==LEN_TRIM(str)) RETURN
985  out=out.AND.is_int(str(ix+1:LEN_TRIM(str)))
986END FUNCTION is_dec
987!-------------------------------------------------------------------------------
988
989!-------------------------------------------------------------------------------
990ELEMENTAL LOGICAL FUNCTION is_num(str) RESULT(out)
991!-------------------------------------------------------------------------------
992  IMPLICIT NONE
993!-------------------------------------------------------------------------------
994! Purpose: test if str is a valid integer/decimal/scientific notation number
995!-------------------------------------------------------------------------------
996  CHARACTER(LEN=*),  INTENT(IN) :: str
997  INTEGER :: ix, ls
998!-------------------------------------------------------------------------------
999  out=LEN_TRIM(str)/=0; IF(.NOT.out) RETURN; ls=LEN_TRIM(str)
1000
1001  !--- TEST IF THE NUMBER IS A PURE INTEGER OR A PURE DECIMAL NUMBER
1002  IF(is_int(str)) RETURN
1003  IF(is_dec(str)) RETURN
1004
1005  !--- CHECK FOR "D" OR "E" SEPARATOR
1006  ix=MAX(INDEX(strLow(str),'d'),INDEX(strLow(str),'e')); out=ix>0
1007  IF(.NOT.out) RETURN
1008
1009  !--- CHECK SURROUNDING STRINGS ARE NUMBERS
1010  out=is_dec(str(1:ix-1)).AND.is_int(str(ix+1:ls))
1011END FUNCTION is_num
1012!-------------------------------------------------------------------------------
1013
1014!-------------------------------------------------------------------------------
1015INTEGER FUNCTION str2int(str) RESULT(out)
1016!-------------------------------------------------------------------------------
1017  IMPLICIT NONE
1018!-------------------------------------------------------------------------------
1019! Purpose: convert a string into an integer
1020!-------------------------------------------------------------------------------
1021  CHARACTER(LEN=*), INTENT(IN) :: str
1022  INTEGER :: k
1023!-------------------------------------------------------------------------------
1024  CALL err(.NOT.is_int(str),'Invalid integer "'//TRIM(str)//'"')
1025  out=0
1026  DO k=1,LEN_TRIM(str); out=10*out+INT(INDEX('0123456789',str(k:k))-1); END DO
1027END FUNCTION str2int
1028!-------------------------------------------------------------------------------
1029
1030!-------------------------------------------------------------------------------
1031REAL FUNCTION str2real(str) RESULT(out)
1032!-------------------------------------------------------------------------------
1033  IMPLICIT NONE
1034!-------------------------------------------------------------------------------
1035! Purpose: Convert a string into an real
1036!-------------------------------------------------------------------------------
1037  CHARACTER(LEN=*), INTENT(IN) :: str
1038  INTEGER :: ix, l
1039!-------------------------------------------------------------------------------
1040  CALL err(.NOT.is_num(str),'Invalid number "'//TRIM(str)//'"')
1041  ix=MAX(INDEX(strLow(str),'d'),INDEX(strLow(str),'e')); l=LEN_TRIM(str)
1042  IF(ix==0) out=dec2real(str)
1043  IF(ix/=0) out=dec2real(str(1:ix-1))*10.**str2int(str(ix+1:l))
1044END FUNCTION str2real
1045!-------------------------------------------------------------------------------
1046
1047!-------------------------------------------------------------------------------
1048ELEMENTAL REAL FUNCTION dec2real(str) RESULT(out)
1049!-------------------------------------------------------------------------------
1050  IMPLICIT NONE
1051!-------------------------------------------------------------------------------
1052! Purpose: convert a valid (already checked) string into an real
1053!-------------------------------------------------------------------------------
1054  CHARACTER(LEN=*), INTENT(IN) :: str
1055  INTEGER :: k, k0, ix
1056!-------------------------------------------------------------------------------
1057  out=0.
1058  k0=1; IF(INDEX('+-',str(1:1))/=0) k0=2; ix=INDEX(str,'.')     !--- CHECK SIGN
1059  DO k=k0,LEN_TRIM(str); IF(k==ix) CYCLE                        !--- SKIP .+-
1060    out=out*10.+REAL(INDEX('0123456789',str(k:k))-1)
1061  END DO
1062  IF(ix/=0) out=out*10.**(ix-LEN_TRIM(str))                     !--- COMA
1063  IF(k0==2) out=-out                                            !--- SIGN
1064END FUNCTION dec2real
1065!-------------------------------------------------------------------------------
1066
1067!-------------------------------------------------------------------------------
1068!
1069ELEMENTAL CHARACTER(LEN=256) FUNCTION strLow(str) RESULT(out)
1070!
1071!-------------------------------------------------------------------------------
1072  IMPLICIT NONE
1073!-------------------------------------------------------------------------------
1074! Purpose: Lower case conversion.
1075!-------------------------------------------------------------------------------
1076! Parameters:
1077  CHARACTER(LEN=*), INTENT(IN) :: str
1078!-------------------------------------------------------------------------------
1079! Local variable:
1080  INTEGER :: k, ix
1081!-------------------------------------------------------------------------------
1082  out=str
1083  DO k=1,LEN(str)
1084    ix=IACHAR(str(k:k)); IF(64<ix.AND.ix<91) out(k:k)=ACHAR(ix+32)
1085  END DO
1086
1087END FUNCTION strLow
1088!
1089!-------------------------------------------------------------------------------
1090
1091END PROGRAM make_sso
1092!
1093!-------------------------------------------------------------------------------
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