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3 michaesp 1
      PROGRAM density
2
 
3
      use netcdf
4
 
5
      implicit none
6
 
7
c     ---------------------------------------------------------------------
8
c     Declaration of variables
9
c     ---------------------------------------------------------------------
10
 
11
c     Parameter and working arrays
12
      real                                    radius
13
      character*80                            runit
14
      integer                                 nx,ny
15
      integer                                 nlonlat
16
      real                                    dlonlat
17
      real                                    xmin,ymin,dx,dy
18
      real                                    clon,clat
19
      integer                                 ntime,nfield,ntra
20
      character*80                            inpfile
21
      character*80                            outfile
22
      character*80                            mode
23
      real                                    param
24
      integer                                 opts,npts
25
      integer                                 step
26
      character*80                            gridtype
27
      character*80                            field
28
      integer                                 crefile,crevar
29
      real,allocatable,    dimension (:,:) :: cnt,res,fld,area
30
      real,allocatable,    dimension (:)   :: traj
31
      real,allocatable,    dimension (:)   :: olon,olat,otim,ofld
32
      real,allocatable,    dimension (:)   :: nlon,nlat,ntim,nfld
33
 
34
c     Output format
35
      character*80                            outformat
36
 
37
c     Physical and mathematical constants
38
      real                                    pi180
39
      parameter                               (pi180=3.14159/180.)
40
      real                                    deltay
41
      parameter                               (deltay=111.)
42
      real                                    eps
43
      parameter                               (eps=0.001)
44
 
45
c     Input trajectories (see iotra.f)
46
      integer                                 inpmode
47
      real,allocatable, dimension (:,:,:) ::  trainp     
48
      integer                                 reftime(6)      
49
      character*80                            varsinp(100)   
50
      integer,allocatable, dimension (:) ::   sel_flag
51
      character*80                            sel_file
52
      character*80                            sel_format
53
 
54
c     Auxiliary variables
55
      character*80                            cdfname,varname
56
      integer                                 i,j,k
57
      integer                                 stat
58
      integer,allocatable, dimension (:,:) :: connect0
59
      integer                                 connectval0
60
      integer,allocatable, dimension (:,:) :: connect1
61
      integer                                 connectval1
62
      integer,allocatable, dimension (:,:) :: connect2
63
      integer                                 connectval2
64
      real                                    slat
65
      integer                                 ipre
66
      real                                    addvalue
67
      real                                    xmax,ymax
68
      real ,allocatable, dimension (:)  ::    odist,ndist
69
      real                                    dt
70
      integer                                 fid
71
      integer                                 dynamic_grid
72
      real                                    ycen,xcen
73
      integer                                 indx,indy
74
      character*80                            unit
75
      real                                    pollon,pollat
76
      real                                    rlon0,rlat0,rlon,rlat
77
      real                                    lon,lat
78
      real                                    crot
79
      integer                                 count
80
      character*80                            longname, varunit
81
      real                                    time
82
      integer                                 ind
83
      integer                                 ifield
84
      real                                    hhmm,frac
85
      integer                                 ierr,ncID
86
 
87
c     External functions
88
      real         lmstolm,lmtolms
89
      real         phstoph,phtophs
90
      external     lmstolm,lmtolms,phstoph,phtophs
91
 
92
      real         sdis
93
      external     sdis
94
 
95
c     ---------------------------------------------------------------------
96
c     Preparations
97
c     ---------------------------------------------------------------------
98
 
99
c     Write start message
100
      print*,'========================================================='
101
      print*,'              *** START OF PROGRAM DENSITY ***'
102
      print*
103
 
104
c     Read input parameters
105
      open(10,file='density.param')
106
       read(10,*) inpfile
107
       read(10,*) outfile
108
       read(10,*) field
109
       read(10,*) ntime,nfield,ntra
110
       read(10,*) gridtype
111
       if ( gridtype.eq.'latlon' ) then 
112
          read(10,*) nx,ny,xmin,ymin,dx,dy
113
       elseif ( gridtype.eq.'rotated') then
114
          read(10,*) clon,clat,nlonlat,dlonlat
115
       else
116
          print*,' ERROR: unsupported grid type ',trim(gridtype)
117
          stop
118
       endif
119
       read(10,*) radius,runit
120
       read(10,*) mode
121
       read(10,*) param
122
       read(10,*) step
123
       read(10,*) sel_file
124
       read(10,*) sel_format
125
       read(10,*) crefile
126
       read(10,*) crevar
127
      close(10)
128
 
129
c     Get the grid parameters if <crefile=0>
130
      if ( crefile.eq.0 ) then
131
 
132
           ierr = nf90_open  (trim(outfile), NF90_NOWRITE  , ncID)
133
 
134
           ierr = nf90_get_att(ncID, NF90_GLOBAL, 'grid'   ,gridtype ) 
135
           ierr = nf90_get_att(ncID, NF90_GLOBAL, 'clon'   ,clon     )
136
           ierr = nf90_get_att(ncID, NF90_GLOBAL, 'clat'   ,clat     )
137
           ierr = nf90_get_att(ncID, NF90_GLOBAL, 'nlonlat',nlonlat  )
138
           ierr = nf90_get_att(ncID, NF90_GLOBAL, 'dlonlat',dlonlat  )
139
           ierr = nf90_get_att(ncID, NF90_GLOBAL, 'nx'     ,nx       )
140
           ierr = nf90_get_att(ncID, NF90_GLOBAL, 'ny'     ,ny       )
141
           ierr = nf90_get_att(ncID, NF90_GLOBAL, 'dx'     ,dx       )
142
           ierr = nf90_get_att(ncID, NF90_GLOBAL, 'dy'     ,dy       )
143
           ierr = nf90_get_att(ncID, NF90_GLOBAL, 'xmin'   ,xmin     )
144
           ierr = nf90_get_att(ncID, NF90_GLOBAL, 'ymin'   ,ymin     )
145
 
146
           ierr = nf90_close(ncID)
147
 
148
           print*,'**** GRID PARAMETERS IMPORTED ',
149
     >            'FROM NETCDF FILE!!!! ****'
150
           print*
151
 
152
      endif
153
 
154
c     Check for consistency
155
      if ( (step.ne.0).and.(mode.ne.'keep') ) then
156
         print*," ERROR: interpolation is only possible for all",
157
     >                   ' time steps... Stop'
158
         stop
159
      endif
160
 
161
c     Set the number of times (just code aesthetics)
162
      opts=ntime
163
 
164
c     Set grid parameters for rotated grid
165
      if ( gridtype.eq.'rotated' ) then
166
         nx   = nlonlat
167
         ny   = nlonlat
168
         dx   = dlonlat
169
         dy   = dlonlat
170
         xmin = - real(nlonlat-1)/2. * dx
171
         xmax = + real(nlonlat-1)/2. * dx
172
         ymin = - real(nlonlat-1)/2. * dy
173
         ymax = + real(nlonlat-1)/2. * dy
174
      endif
175
 
176
c     Set the flag for dynamic grid adjustment
177
      if ( (nx.eq.0).or.(ny.eq.0) ) then
178
         dynamic_grid = 1
179
      else
180
         dynamic_grid = 0
181
      endif
182
 
183
c     Print status information
184
      print*,'---- INPUT PARAMETERS -----------------------------------'
185
      print* 
186
      print*,'Input                : ',trim(inpfile)
187
      print*,'Output               : ',trim(outfile)
188
      print*,'Field                : ',trim(field)
189
      print*,'Trajectory           : ',ntime,nfield,ntra
190
      print*,'Grid type            : ',trim(gridtype)
191
      if ( dynamic_grid.eq.1 ) then
192
         print*,'Grid                 : dynamic (see below)'
193
      elseif ( gridtype.eq.'latlon' ) then
194
         print*,'Grid   nlon,nlat     : ',nx,ny
195
         print*,'       lonmin,latmin : ',xmin,ymin
196
         print*,'       dlon,dlat     : ',dx,dy
197
      elseif ( gridtype.eq.'rotated' ) then
198
         print*,'Grid   clon,clat     : ',clon,clat
199
         print*,'       nlonlat       : ',nlonlat
200
         print*,'       dlonlat       : ',dlonlat
201
      endif
202
      print*,'Filter radius        : ',radius,' ',trim(runit)
203
      print*,'Mode                 : ',trim(mode)
204
      if ( ( mode.eq.'time'  ).or.
205
     >     ( mode.eq.'space' ).or.
206
     >     (mode.eq.'grid' ) ) 
207
     >then
208
         print*,'Parameter            : ',param
209
      endif
210
      if ( step.eq.0 ) then
211
         print*,'Time step            : all'
212
      elseif (step.gt.0) then
213
         print*,'Time step            : ',step
214
      endif
215
      print*,'Selection file       : ',trim(sel_file)
216
      print*,'Selection format     : ',trim(sel_file)
217
      print*,'Flag <crefile>       : ',crefile
218
      print*,'Flag <crevar>        : ',crevar
219
 
220
c     Check whether mode is valid
221
      if ((mode.ne.'keep'  ).and.
222
     >    (mode.ne.'time'  ).and.
223
     >    (mode.ne.'space' ).and.
224
     >    (mode.ne.'grid'  ))  
225
     >then
226
         print*,' ERROR: Invalid mode ',trim(mode)
227
         stop
228
      endif
229
 
230
c     Allocate memory for old and new (reparameterised) trajectory
231
      allocate(olon(ntime),stat=stat)
232
      if (stat.ne.0) print*,'*** error allocating array olon ***'
233
      allocate(olat(ntime),stat=stat)
234
      if (stat.ne.0) print*,'*** error allocating array olat ***'
235
      allocate(otim(ntime),stat=stat)
236
      if (stat.ne.0) print*,'*** error allocating array otim ***'
237
      allocate(nlon(1000*ntime),stat=stat)
238
      if (stat.ne.0) print*,'*** error allocating array nlon ***'
239
      allocate(nlat(1000*ntime),stat=stat)
240
      if (stat.ne.0) print*,'*** error allocating array nlat ***'
241
      allocate(ntim(1000*ntime),stat=stat)
242
      if (stat.ne.0) print*,'*** error allocating array ntim ***'
243
      allocate(odist(ntime),stat=stat)
244
      if (stat.ne.0) print*,'*** error allocating array odist ***'
245
      allocate(ndist(1000*ntime),stat=stat)
246
      if (stat.ne.0) print*,'*** error allocating array ndist ***'
247
      allocate(ofld(ntime),stat=stat)
248
      if (stat.ne.0) print*,'*** error allocating array ofld ***'
249
      allocate(nfld(1000*ntime),stat=stat)
250
      if (stat.ne.0) print*,'*** error allocating array nfld ***'
251
 
252
c     Allocate memory for complete trajectory set
253
      allocate(trainp(ntra,ntime,nfield),stat=stat)
254
      if (stat.ne.0) print*,'*** error allocating array trainp ***'
255
      allocate(sel_flag(ntra),stat=stat)
256
      if (stat.ne.0) print*,'*** error allocating array sel_flag ***'
257
 
258
c     Allocate memory for auxiliary fields
259
      allocate(traj(nfield),stat=stat)
260
      if (stat.ne.0) print*,'*** error allocating array traj ***'
261
 
262
c     Set the format of the input file
263
      call mode_tra(inpmode,inpfile)
264
      if (inpmode.eq.-1) inpmode=1
265
 
266
c     Read the input trajectory file
267
      call ropen_tra(fid,inpfile,ntra,ntime,nfield,
268
     >                   reftime,varsinp,inpmode)
269
      call read_tra (fid,trainp,ntra,ntime,nfield,inpmode)
270
      call close_tra(fid,inpmode)
271
 
272
c     Check that first four columns correspond to time,lon,lat,p
273
      if ( (varsinp(1).ne.'time' ).or.
274
     >     (varsinp(2).ne.'xpos' ).and.(varsinp(2).ne.'lon' ).or.
275
     >     (varsinp(3).ne.'ypos' ).and.(varsinp(3).ne.'lat' ).or.
276
     >     (varsinp(4).ne.'ppos' ).and.(varsinp(4).ne.'p'   ) )
277
     >then
278
         print*,' ERROR: problem with input trajectories ...'
279
         stop
280
      endif
281
      varsinp(1) = 'TIME'
282
      varsinp(2) = 'lon'
283
      varsinp(3) = 'lat'
284
      varsinp(4) = 'p'
285
 
286
c     Get the index of the field (if needed)
287
      if ( field.ne.'nil' ) then
288
         ifield = 0
289
         do i=1,nfield
290
            if ( varsinp(i).eq.field ) ifield = i
291
         enddo
292
         if ( ifield.eq.0 ) then
293
            print*,' ERROR: field ',trim(field),' not found... Stop'
294
            stop
295
         endif
296
      endif
297
 
298
c     Write some status information of the input trajectories
299
      print*
300
      print*,'---- INPUT TRAJECTORIES ---------------------------------'
301
      print*
302
      print*,' Reference time (year)  : ',reftime(1)
303
      print*,'                (month) : ',reftime(2)
304
      print*,'                (day)   : ',reftime(3)
305
      print*,'                (hour)  : ',reftime(4)
306
      print*,'                (min)   : ',reftime(5)
307
      print*,' Time range (min)       : ',reftime(6)
308
      do i=1,nfield
309
         if ( i.ne.ifield ) then
310
            print*,' Var                    :',i,trim(varsinp(i))
311
         else
312
            print*,' Var                    :',i,trim(varsinp(i)),
313
     >                                        '       [ gridding ]'
314
         endif
315
      enddo
316
      print*,' List of selected times'
317
      do i=1,ntime
318
         if ( (step.eq.0).or.(step.eq.i) ) then
319
            print*,'     ',i,'  -> ',trainp(1,i,1)
320
         endif
321
      enddo
322
      print*
323
 
324
c     Select flag: all trajectories are selected
325
      if ( sel_file.eq.'nil' ) then
326
 
327
         do i=1,ntra
328
            sel_flag(i) = 1
329
         enddo
330
 
331
c     Select flag: index file
332
      elseif ( sel_format.eq.'index' ) then
333
 
334
         do i=1,ntra
335
            sel_flag(i) = 0
336
         enddo
337
 
338
         open(10,file=sel_file)
339
 142      read(10,*,end=141) ind
340
          sel_flag(ind) = 1
341
          goto 142 
342
 141     continue
343
         close(10)
344
 
345
c     Select flag: boolean file
346
      elseif ( sel_format.eq.'boolean' ) then
347
 
348
         open(10,file=sel_file)
349
          do i=1,ntra
350
            read(10,*) ind
351
            if ( ind.eq.1 ) sel_flag(i) = ind
352
          enddo
353
         close(10)
354
 
355
      endif
356
 
357
c     Write status information
358
      if ( sel_file.eq.'nil' ) then
359
          print*,' Selected trajectories  : all ',ntra          
360
       else
361
          count = 0
362
          do i=1,ntra
363
             if ( sel_flag(i).eq.1 ) count = count + 1
364
          enddo
365
          print*,' #selected trajectories : ',count,
366
     >            ' [ ',real(count)/real(ntra) * 100.,' % ] '
367
       endif
368
       print*
369
 
370
c     ---------------------------------------------------------------------
371
c     Coordinate transformations and grid adjustment
372
c     ---------------------------------------------------------------------
373
 
374
c     Transform from lat/lon to rotated lat/lon, if requested
375
      if ( gridtype.eq.'rotated') then
376
 
377
         crot = 0.
378
 
379
         pollon=clon-180.
380
         if (pollon.lt.-180.) pollon=pollon+360.
381
         pollat=90.-clat
382
         do i=1,ntra
383
            do j=1,ntime
384
 
385
               if ( sel_flag(i).eq.1 ) then
386
 
387
c                Get lat/lon coordinates for trajectory point
388
                 lon = trainp(i,j,2)
389
                 lat = trainp(i,j,3)
390
 
391
c                First Rotation
392
                 pollon=clon-180.
393
                 if (pollon.lt.-180.) pollon=pollon+360.
394
                 pollat=90.-clat
395
                 rlon0=lmtolms(lat,lon,pollat,pollon)
396
                 rlat0=phtophs(lat,lon,pollat,pollon)            
397
 
398
c                Second rotation
399
                 pollon=-180.
400
                 pollat=90.+crot
401
                 rlon=90.+lmtolms(rlat0,rlon0-90.,pollat,pollon)
402
                 rlat=phtophs(rlat0,rlon0-90.,pollat,pollon)   
403
 
404
c                Get rotated latitude and longitude
405
 100             if (rlon.lt.xmin) then
406
                  rlon=rlon+360.
407
                  goto 100
408
                 endif
409
 102             if (rlon.gt.(xmin+real(nx-1)*dx)) then
410
                  rlon=rlon-360.
411
                  goto 102
412
                 endif
413
 
414
c                Set the new trajectory coordinates
415
                 trainp(i,j,2) = rlon
416
                 trainp(i,j,3) = rlat
417
 
418
              endif
419
 
420
            enddo
421
         enddo
422
 
423
      endif
424
 
425
c     Dynamic grid adjustment
426
      if ( dynamic_grid.eq.1 ) then
427
 
428
c        Get the grid parameters
429
         xmin =  180.
430
         ymin =   90.
431
         xmax = -180.
432
         ymax =  -90.
433
 
434
         do i=1,ntra
435
 
436
            if ( sel_flag(i).eq.1 ) then
437
 
438
              if ( step.eq.0 ) then
439
               do j=1,ntime
440
                  if ( trainp(i,j,2).lt.xmin) xmin =  trainp(i,j,2)
441
                  if ( trainp(i,j,2).gt.xmax) xmax =  trainp(i,j,2)
442
                  if ( trainp(i,j,3).lt.ymin) ymin =  trainp(i,j,3)
443
                  if ( trainp(i,j,3).gt.ymax) ymax =  trainp(i,j,3)
444
               enddo
445
              else
446
                if ( trainp(i,step,2).lt.xmin) xmin =  trainp(i,step,2)
447
                if ( trainp(i,step,2).gt.xmax) xmax =  trainp(i,step,2)
448
                if ( trainp(i,step,3).lt.ymin) ymin =  trainp(i,step,3)
449
                if ( trainp(i,step,3).gt.ymax) ymax =  trainp(i,step,3)
450
              endif
451
 
452
            endif
453
 
454
         enddo
455
 
456
c        Get first guess for "optimal" grid
457
         nx = 400
458
         ny = 400
459
         dx = (xmax - xmin)/real(nx-1)
460
         dy = (ymax - ymin)/real(ny-1)
461
 
462
c        Make the grid spacing equal in zonal and meridional direction
463
         if ( dx.gt.dy ) then
464
 
465
            dy = dx
466
            ny = (ymax - ymin)/dy + 1
467
            if (ny.lt.nx/2)              ny = nx / 2
468
            if ( real(ny)*dy .ge. 180. ) ny = 180./dy + 1
469
            ycen = 0.5* (ymin+ymax)
470
            ymin = ycen - 0.5 * real(ny/2) * dy
471
            if (ymin.le.-90.) ymin = -90.
472
 
473
         else
474
 
475
            dx = dy
476
            nx = (xmax - xmin)/dx + 1
477
            if (nx.lt.ny/2)              nx = ny / 2
478
            if ( real(nx)*dx .ge. 360. ) nx = 360./dx + 1
479
            xcen = 0.5* (xmin+xmax)
480
            xmin = xcen - 0.5 * real(nx/2) * dx
481
            if (xmin.le.-180.) xmin = -180.
482
 
483
         endif
484
 
485
c        Write information
486
         print*
487
         print*,'---- DYNAMIC GRID ADJUSTMENT',
488
     >          ' ----------------------------'  
489
         print*
490
         print*,'Grid   nlon,nlat     : ',nx,ny
491
         print*,'       lonmin,latmin : ',xmin,ymin
492
         print*,'       dlon,dlat     : ',dx,dy
493
         print*
494
 
495
c     Write grid information for rotated grid (if not already done
496
      elseif ( gridtype.eq.'rotated') then
497
 
498
         print*
499
         print*,'---- GRID PARAMETERS -------',
500
     >          ' ----------------------------'  
501
         print*
502
         print*,'Grid   nlon,nlat     : ',nx,ny
503
         print*,'       lonmin,latmin : ',xmin,ymin
504
         print*,'       dlon,dlat     : ',dx,dy
505
         print*
506
 
507
 
508
      endif
509
 
510
c     Set the grid boundaries
511
      xmax=xmin+real(nx-1)*dx
512
      ymax=ymin+real(ny-1)*dy
513
 
514
c     Allocate memory for output array and auxiliary gridding array 
515
      allocate(cnt(nx,ny),stat=stat)
516
      if (stat.ne.0) print*,'*** error allocating array cnt  ***'
517
      allocate(res(nx,ny),stat=stat)
518
      if (stat.ne.0) print*,'*** error allocating array res  ***'
519
      allocate(fld(nx,ny),stat=stat)
520
      if (stat.ne.0) print*,'*** error allocating array fld  ***'
521
      allocate(area(nx,ny),stat=stat)
522
      if (stat.ne.0) print*,'*** error allocating array area ***'
523
 
524
      allocate(connect0(nx,ny),stat=stat)
525
      if (stat.ne.0) print*,'*** error allocating array connect0 ***'
526
      allocate(connect1(nx,ny),stat=stat)
527
      if (stat.ne.0) print*,'*** error allocating array connect1 ***'
528
      allocate(connect2(nx,ny),stat=stat)
529
      if (stat.ne.0) print*,'*** error allocating array connect2 ***'
530
 
531
 
532
c     Init the output array
533
      do i=1,nx
534
         do j=1,ny
535
            connect0(i,j) = 0
536
            connect1(i,j) = 0
537
            connect2(i,j) = 0
538
            cnt(i,j)      = 0.
539
            res(i,j)      = 0.
540
            fld(i,j)      = 0.
541
         enddo
542
      enddo  
543
 
544
c     ---------------------------------------------------------------------
545
c     Gridding
546
c     ---------------------------------------------------------------------
547
 
548
c     Write some status information 
549
      print*,'---- GRIDDING -------------------------------------------'
550
      print*
551
 
552
c     Loop over all entries of sampling table
553
      connectval0 = 0
554
      connectval1 = 0
555
      connectval2 = 0
556
      count       = 0
557
 
558
      do i=1,ntra
559
 
560
         if (mod(i,100).eq.0) print*,i,' of ',ntra
561
 
562
c        Skip all trajectories which are not selected
563
         if ( sel_flag(i).eq.0 ) goto 300
564
 
565
c        ------- Read a complete trajectory ---------------------------
566
         do j=1,ntime
567
            otim(j) = trainp(i,j,1)
568
            olon(j) = trainp(i,j,2)
569
            olat(j) = trainp(i,j,3)
570
            if ( field.ne.'nil' ) then
571
               ofld(j) =trainp(i,j,ifield)
572
            endif
573
         enddo
574
 
575
c        -------- Convert hh.m time into fractional time --------------
576
         do j=1,ntime
577
            hhmm    = otim(j)
578
            call hhmm2frac (hhmm,frac)
579
            otim(j) = frac
580
         enddo
581
 
582
c        -------- Interpolation ---------------------------------------
583
 
584
c        Keep the trajectory points as they are
585
         if ( ( mode.eq.'keep').and.(step.eq.0) ) then
586
            npts=opts
587
            do j=1,opts
588
               ntim(j)=otim(j)
589
               nlon(j)=olon(j)
590
               nlat(j)=olat(j)
591
               if ( field.ne.'nil' ) then
592
                  nfld(j)=ofld(j)
593
               endif
594
            enddo
595
 
596
c        Select a single time step
597
         elseif ( ( mode.eq.'keep').and.(step.gt.0) ) then
598
            npts    = 1
599
            ntim(1) = otim(step)
600
            nlon(1) = olon(step)
601
            nlat(1) = olat(step)
602
            if ( field.ne.'nil' ) then
603
               nfld(1) = ofld(step)
604
            endif
605
 
606
c        Perform a reparameterisation in time
607
         else if ( (mode.eq.'time').and.(step.eq.0) ) then
608
 
609
c           Get the new number of trajectory points
610
            npts=nint(abs(otim(opts)-otim(1))/param)+1
611
 
612
c           Handle date line problem
613
            do j=2,opts
614
               if ( (olon(j-1)-olon(j)).gt.180. ) then
615
                  olon(j) = olon(j) + 360.
616
               else if ( (olon(j-1)-olon(j)).lt.-180. ) then
617
                  olon(j) = olon(j) - 360.
618
               endif
619
            enddo
620
 
621
c           Cubic spline fitting
622
            call curvefit(otim,olon,opts,ntim,nlon,npts)
623
            call curvefit(otim,olat,opts,ntim,nlat,npts)
624
            if ( field.ne.'nil' ) then
625
               call curvefit(otim,ofld,opts,ntim,nfld,npts)
626
            endif
627
 
628
c           Reverse date line handling
629
            do j=1,npts
630
               if ( nlon(j).gt.xmax ) then
631
                  nlon(j) = nlon(j) -360.
632
               else if ( nlon(j).lt.xmin ) then
633
                  nlon(j) = nlon(j) +360.
634
               endif
635
            enddo
636
 
637
c        Perform a reparameterisation with equally spaced gridpoint
638
         elseif ( (mode.eq.'space').and.(step.eq.0) ) then
639
 
640
c           Calculate the distance and spacing
641
            odist(1) = 0.
642
            unit     = 'km'
643
            do j=2,ntime
644
               odist(j)=odist(j-1) + 
645
     >                  sdis(olon(j-1),olat(j-1),olon(j),olat(j),unit)
646
            enddo
647
 
648
c           Determine the new number of trajectory points
649
            npts=nint(odist(ntime)/param)+1
650
            if (npts.eq.0) then
651
               npts=1.
652
            endif
653
 
654
c           Handle date line problem
655
            do j=2,opts
656
               if ( (olon(j-1)-olon(j)).gt.180. ) then
657
                  olon(j) = olon(j) + 360.
658
               else if ( (olon(j-1)-olon(j)).lt.-180. ) then
659
                  olon(j) = olon(j) - 360.
660
               endif
661
            enddo
662
 
663
c           Cubic spline fitting
664
            call curvefit(odist,olon,opts,ndist,nlon,npts)
665
            call curvefit(odist,olat,opts,ndist,nlat,npts)
666
            call curvefit(odist,otim,opts,ndist,ntim,npts)
667
            if ( field.ne.'nil' ) then
668
               call curvefit(odist,ofld,opts,ndist,nfld,npts)
669
            endif
670
 
671
c           Reverse date line handling
672
            do j=1,npts
673
               if ( nlon(j).gt.xmax ) then
674
                  nlon(j) = nlon(j) -360.
675
               else if ( nlon(j).lt.xmin ) then
676
                  nlon(j) = nlon(j) +360.
677
               endif
678
            enddo
679
 
680
c        Perform a reparameterisation with equally spaced gridpoint
681
         elseif ( (mode.eq.'grid').and.(step.eq.0) ) then
682
 
683
c           Calculate the distance and spacing
684
            odist(1) = 0.
685
            unit     = 'deg'
686
            do j=2,ntime
687
               odist(j)=odist(j-1) + 
688
     >                  sdis(olon(j-1),olat(j-1),olon(j),olat(j),unit)
689
            enddo
690
 
691
c           Determine the new number of trajectory points
692
            npts=nint(odist(ntime)/param)+1
693
            if (npts.eq.0) then
694
               npts=1.
695
            endif
696
 
697
c           Handle date line problem
698
            do j=2,opts
699
               if ( (olon(j-1)-olon(j)).gt.180. ) then
700
                  olon(j) = olon(j) + 360.
701
               else if ( (olon(j-1)-olon(j)).lt.-180. ) then
702
                  olon(j) = olon(j) - 360.
703
               endif
704
            enddo
705
 
706
c           Cubic spline fitting
707
            call curvefit(odist,olon,opts,ndist,nlon,npts)
708
            call curvefit(odist,olat,opts,ndist,nlat,npts)
709
            call curvefit(odist,otim,opts,ndist,ntim,npts)
710
            if ( field.ne.'nil' ) then
711
               call curvefit(odist,ofld,opts,ndist,nfld,npts)
712
            endif
713
 
714
c           Reverse date line handling
715
            do j=1,npts
716
               if ( nlon(j).gt.xmax ) then
717
                  nlon(j) = nlon(j) -360.
718
               else if ( nlon(j).lt.xmin ) then
719
                  nlon(j) = nlon(j) +360.
720
               endif
721
            enddo
722
 
723
         endif
724
 
725
c        -------- Do the gridding -------------------------------------
726
 
727
c        Gridding of trajectory
728
         do j=1,npts
729
 
730
c           Check whether point is in data domain
731
	    if ( (nlon(j).gt.xmin).and.(nlon(j).lt.xmax).and.
732
     >           (nlat(j).gt.ymin).and.(nlat(j).lt.ymax))
733
     >      then
734
 
735
c              Increase counter for gridded points
736
               count = count + 1
737
 
738
c              ----------------- Gridding: simple count -----------------
739
               connectval0 = connectval0+1
740
 
741
               addvalue    = 1.
742
 
743
               call  gridding1
744
     >              (nlat(j),nlon(j),addvalue,
745
     >               radius,runit,connect0,connectval0,
746
     >               cnt,nx,ny,xmin,ymin,dx,dy)
747
 
748
c              ----------------- Gridding: residence time ---------------
749
               connectval1 = connectval1+1
750
 
751
               if ( ntime.eq.1 ) then
752
                  addvalue = 0.
753
               elseif ( j.eq.1 )  then
754
                  addvalue=abs(ntim(2)-ntim(1))
755
               else
756
                  addvalue=abs(ntim(j)-ntim(j-1))
757
               endif
758
 
759
               call  gridding1
760
     >              (nlat(j),nlon(j),addvalue,
761
     >               radius,runit,connect1,connectval1,
762
     >               res,nx,ny,xmin,ymin,dx,dy)
763
 
764
 
765
c              --------------- Gridding: field -------------------------
766
               if ( field.ne.'nil' ) then
767
 
768
                   connectval2 = connectval2+1
769
 
770
                   addvalue    = nfld(j)
771
 
772
                   call  gridding1
773
     >                  (nlat(j),nlon(j),addvalue,
774
     >                  radius,runit,connect2,connectval2,
775
     >                  fld,nx,ny,xmin,ymin,dx,dy)
776
 
777
               endif
778
 
779
	    endif
780
 
781
         enddo
782
 
783
c        Exit point for loop over all trajectories
784
 300     continue
785
 
786
      enddo
787
 
788
c     Write status information
789
      print*
790
      print*,' # gridded points       : ',count
791
 
792
c     ---------------------------------------------------------------------
793
c     Unit conversions and output to netCDF file
794
c     ---------------------------------------------------------------------
795
 
796
c     Write some status information 
797
      print*
798
      print*,'---- WRITE OUTPUT ---------------------------------------'
799
      print*
800
 
801
c     Area (in km^2)
802
      do i=1,nx	         
803
         do j=1,ny	
804
            slat=ymin+real(j-1)*dy
805
            if (abs(abs(slat)-90.).gt.eps) then
806
               area(i,j) = dy*dx*cos(pi180*slat)*deltay**2
807
            else
808
               area(i,j) = 0.
809
            endif
810
         enddo
811
      enddo
812
 
813
c     Normalise gridded field
814
      if ( field.ne.'nil' ) then
815
         do i=1,nx
816
            do j=1,ny
817
               if ( cnt(i,j).gt.0. ) then
818
                  fld(i,j) = fld(i,j) / cnt(i,j)
819
               endif
820
            enddo
821
         enddo
822
      endif
823
 
824
c     Set the time for the output netCDF files - if a composite is
825
c     calculatd, then the time is set to 
826
      if ( step.eq.0 ) then
827
         time = -999.
828
         print*,'   ... COMPOSITE OVER ALL TRAJECTORY TIMES (-999)'
829
         print*
830
      else
831
         time = trainp(1,step,1)
832
      endif
833
 
834
c     Write output to CF netCDF
835
      cdfname  = outfile
836
 
837
      varname  = 'COUNT'
838
      longname = 'trajectory counts'
839
      varunit  = 'counts per grid point'
840
      call  writecdf2D_cf (cdfname,varname,longname,varunit,gridtype,
841
     >       clon,clat,nlonlat,dlonlat,cnt,time,dx,dy,xmin,ymin,nx,
842
     >       ny,crefile,crefile,1)
843
      write(*,'(a8,a10,a5,a10,a10,f7.2,a2)') 
844
     >     '    ... ',trim(varname),' -> ',trim(cdfname),
845
     >     ' [ time = ',time,' ]'    
846
 
847
      varname  = 'RESIDENCE'
848
      longname = 'residence time'
849
      varunit  = 'hours per grid point'
850
 
851
      print*,'crefile = ',crefile
852
 
853
      call  writecdf2D_cf (cdfname,varname,longname,varunit,gridtype,
854
     >       clon,clat,nlonlat,dlonlat,res,time,dx,dy,xmin,ymin,nx,
855
     >       ny,0,crefile,1)
856
      write(*,'(a8,a10,a5,a10,a10,f7.2,a2)') 
857
     >     '    ... ',trim(varname),' -> ',trim(cdfname),
858
     >     ' [ time = ',time,' ]'    
859
 
860
      varname  = 'AREA'
861
      longname = 'area corresponding to grid points'
862
      varunit  = 'square kilometers'
863
      call  writecdf2D_cf (cdfname,varname,longname,varunit,gridtype,
864
     >       clon,clat,nlonlat,dlonlat,area,time,dx,dy,xmin,ymin,nx,
865
     >       ny,0,crefile,1)
866
      write(*,'(a8,a10,a5,a10,a10,f7.2,a2)') 
867
     >     '    ... ',trim(varname),' -> ',trim(cdfname),
868
     >     ' [ time = ',time,' ]'    
869
 
870
      if ( field.ne.'nil' ) then
871
         varname  = field
872
         longname = field
873
         varunit  = 'as on trajectory file'
874
         call  writecdf2D_cf (cdfname,varname,longname,varunit,gridtype,
875
     >       clon,clat,nlonlat,dlonlat,fld,time,dx,dy,xmin,ymin,nx,
876
     >       ny,0,crevar,1)
877
 
878
         write(*,'(a8,a10,a5,a10,a10,f7.2,a2)') 
879
     >        '    ... ',trim(varname),' -> ',trim(cdfname),
880
     >        ' [ time = ',time,' ]'    
881
      endif
882
 
883
c     Write status information
884
      print*
885
      print*,'              *** END OF PROGRAM DENSITY **'
886
      print*,'========================================================='
887
 
888
      end
889
 
890
c     ********************************************************************
891
c     * GRIDDING SUBROUTINES                                             *
892
c     ********************************************************************
893
 
894
c     ---------------------------------------------------------------------
895
c     Gridding of one single data point (smoothing in km, deg, gridp)
896
c     ---------------------------------------------------------------------
897
 
898
      subroutine gridding1 (lat,lon,addval,radius,unit,
899
     >                      connect,connectval,
900
     >                      out,nx,ny,xmin,ymin,dx,dy)
901
 
902
      implicit none
903
 
904
c     Declaration of subroutine parameters
905
      real         lat,lon
906
      integer      nx,ny
907
      real         xmin,ymin,dx,dy
908
      real         out(nx,ny)
909
      real         radius
910
      character*80 unit
911
      integer      connectval
912
      integer      connect(nx,ny)
913
      real         addval
914
 
915
c     Auxiliary variables
916
      integer   i,j,k
917
      integer   mu,md,nr,nl,n,m
918
      integer   stackx(nx*ny),stacky(nx*ny)
919
      integer   tab_x(nx*ny),tab_y(nx*ny)
920
      real      tab_r(nx*ny)
921
      integer   sp
922
      real      lat2,lon2
923
      real      dist,sum
924
      real      xmax
925
      integer   periodic
926
      integer   test
927
 
928
c     Numerical epsilon
929
      real      eps
930
      parameter (eps=0.01)
931
 
932
c     Externals
933
      real      sdis,weight
934
      external  sdis,weight
935
 
936
c     Check whether lat/lon point is valid
937
      xmax=xmin+real(nx-1)*dx
938
      if (lon.lt.xmin-eps) lon=lon+360.
939
      if (lon.gt.xmax+eps) lon=lon-360.
940
      if (abs(lat-90).lt.eps) lat=90.
941
      if (abs(lat+90).lt.eps) lat=-90.
942
      if ((abs(lat).gt.(90.+eps)).or.
943
     >    (lon.lt.xmin-eps).or.(lon.gt.xmax+eps)) then
944
         print*,'Invalid lat/lon point ',lat,lon
945
         return
946
      endif
947
 
948
c     Set flag for periodic domain
949
      if (abs(xmax-xmin-360.).lt.eps) then
950
         periodic=1
951
      else if (abs(xmax-xmin-360+dx).lt.eps) then
952
         periodic=2
953
      else
954
         periodic=0
955
      endif
956
 
957
c     Get indices of one coarse grid point within search radius
958
      i=nint((lon-xmin)/dx)+1
959
      if ((i.eq.nx).and.(periodic.eq.1)) i=1
960
      j=nint((lat-ymin)/dy)+1
961
      lat2=ymin+real(j-1)*dy
962
      lon2=xmin+real(i-1)*dx
963
      dist=sdis(lon,lat,lon2,lat2,unit)
964
      if (dist.gt.radius) then
965
         print*,'1: Search radius is too small...'
966
         stop
967
      endif
968
 
969
c     Get connected points
970
      k=0
971
      stackx(1)=i
972
      stacky(1)=j
973
      sp=1
974
      do while (sp.ne.0) 
975
 
976
c        Get an element from stack
977
         n=stackx(sp)
978
         m=stacky(sp)
979
         sp=sp-1
980
 
981
c        Get distance from reference point
982
         lat2=ymin+real(m-1)*dy
983
         lon2=xmin+real(n-1)*dx
984
         dist=sdis(lon,lat,lon2,lat2,unit)
985
 
986
c        Check whether distance is smaller than search radius: connected
987
         if (dist.lt.radius) then
988
 
989
c           Make entry in filter mask
990
            k=k+1
991
            tab_x(k)=n
992
            tab_y(k)=m
993
            tab_r(k)=weight(dist,radius)
994
 
995
c           Mark this point as visited
996
            connect(n,m)=connectval
997
 
998
c           Get coordinates of neighbouring points
999
            nr=n+1
1000
            if ((nr.gt.nx)  .and.(periodic.eq.0)) nr=nx
1001
            if ((nr.gt.nx-1).and.(periodic.eq.1)) nr=1
1002
            if ((nr.gt.nx)  .and.(periodic.eq.2)) nr=1
1003
            nl=n-1
1004
            if ((nl.lt.1).and.(periodic.eq.0)) nl=1
1005
            if ((nl.lt.1).and.(periodic.eq.1)) nl=nx-1
1006
            if ((nl.lt.1).and.(periodic.eq.2)) nl=nx
1007
            mu=m+1
1008
            if (mu.gt.ny) mu=ny
1009
            md=m-1
1010
            if (md.lt.1) md=1
1011
 
1012
c           Update stack
1013
            if (connect(nr,m).ne.connectval) then
1014
               connect(nr,m)=connectval
1015
               sp=sp+1
1016
               stackx(sp)=nr
1017
               stacky(sp)=m
1018
            endif
1019
            if (connect(nl,m).ne.connectval) then
1020
               connect(nl,m)=connectval
1021
               sp=sp+1
1022
               stackx(sp)=nl
1023
               stacky(sp)=m
1024
            endif
1025
            if (connect(n,mu).ne.connectval) then
1026
               connect(n,mu)=connectval
1027
               sp=sp+1
1028
               stackx(sp)=n
1029
               stacky(sp)=mu
1030
            endif
1031
            if (connect(n,md).ne.connectval) then
1032
               connect(n,md)=connectval
1033
               sp=sp+1
1034
               stackx(sp)=n
1035
               stacky(sp)=md
1036
            endif
1037
         endif
1038
 
1039
      end do
1040
 
1041
      if (k.ge.1) then
1042
         sum=0.
1043
         do i=1,k
1044
            sum=sum+tab_r(i)
1045
         enddo
1046
         do i=1,k
1047
            out(tab_x(i),tab_y(i))=out(tab_x(i),tab_y(i))+
1048
     >                             addval*tab_r(i)/sum
1049
 
1050
            if ((tab_x(i).eq.1).and.(periodic.eq.1)) then
1051
               out(nx,tab_y(i))=out(nx,tab_y(i))+
1052
     >                             addval*tab_r(i)/sum
1053
            endif
1054
         enddo
1055
      else
1056
         print*,'2: Search radius is too small...'
1057
         stop
1058
      endif
1059
 
1060
      end
1061
 
1062
 
1063
c     ----------------------------------------------------------------------
1064
c     Get spherical distance between lat/lon points
1065
c     ----------------------------------------------------------------------
1066
 
1067
      real function sdis(xp,yp,xq,yq,unit)
1068
 
1069
c     Calculates spherical distance (in km) between two points given
1070
c     by their spherical coordinates (xp,yp) and (xq,yq), respectively.
1071
 
1072
      real         re
1073
      parameter    (re=6370.)
1074
      real         xp,yp,xq,yq,arg
1075
      character*80 unit
1076
      real         dlon
1077
 
1078
      if ( unit.eq.'km' ) then
1079
 
1080
         arg=sind(yp)*sind(yq)+cosd(yp)*cosd(yq)*cosd(xp-xq)
1081
         if (arg.lt.-1.) arg=-1.
1082
         if (arg.gt.1.) arg=1.
1083
         sdis=re*acos(arg)
1084
 
1085
      elseif ( unit.eq.'deg' ) then
1086
 
1087
         dlon = xp-xq
1088
         if ( dlon.gt. 180. ) dlon = dlon - 360.
1089
         if ( dlon.lt.-180. ) dlon = dlon + 360.
1090
         sdis = sqrt( dlon**2 + (yp-yq)**2 )
1091
 
1092
      endif
1093
 
1094
 
1095
c     Quick and dirty trick to avoid zero distances
1096
      if (sdis.eq.0.) sdis=0.1
1097
 
1098
      end
1099
 
1100
c     ----------------------------------------------------------------------
1101
c     Weight function for the filter mask
1102
c     ----------------------------------------------------------------------
1103
 
1104
      real function weight (r,radius)
1105
 
1106
c     Attribute to each distanc r its corresponding weight in the filter mask
1107
 
1108
      implicit none
1109
 
1110
c     Declaration of subroutine parameters
1111
      real r
1112
      real radius
1113
 
1114
c     Simple 0/1 mask
1115
      if (r.lt.radius) then
1116
         weight=exp(-r/radius)
1117
      else
1118
         weight=0.
1119
      endif
1120
 
1121
      end
1122
 
1123
 
1124
c     ********************************************************************
1125
c     * REPARAMETERIZATION SUBROUTINES                                   *
1126
c     ********************************************************************
1127
 
1128
c     -------------------------------------------------------------
1129
c     Interpolation of the trajectory with a natural cubic spline
1130
c     -------------------------------------------------------------
1131
 
1132
      SUBROUTINE curvefit (time,lon,n,
1133
     >                     sptime,splon,spn)
1134
 
1135
c     Given the curve <time,lon> with <n> data points, fit a
1136
c     cubic spline to this curve. The new curve is returned in 
1137
c     <sptime,splon,spn> with <spn> data points. The parameter
1138
c     <spn> specifies on entry the number of spline interpolated points
1139
c     along the curve.
1140
 
1141
      implicit none
1142
 
1143
c     Declaration of subroutine parameters
1144
      integer n
1145
      real time(n),lon(n)
1146
      integer spn
1147
      real sptime(spn),splon(spn)
1148
 
1149
c     Auxiliary variables
1150
      real y2ax(n)
1151
      real dt
1152
      real s
1153
      integer i
1154
      real order
1155
 
1156
c     Determine whether the input array is ascending or descending
1157
      if (time(1).gt.time(n)) then
1158
         order=-1.
1159
      else
1160
         order= 1.
1161
      endif
1162
 
1163
c     Bring the time array into ascending order
1164
      do i=1,n
1165
         time(i)=order*time(i)
1166
      enddo
1167
 
1168
c     Prepare the (natural) cubic spline interpolation
1169
      call spline (time,lon,n,1.e30,1.e30,y2ax)
1170
      dt=(time(n)-time(1))/real(spn-1)
1171
      do i=1,spn
1172
         sptime(i)=time(1)+real(i-1)*dt
1173
      enddo
1174
 
1175
c     Do the spline interpolation
1176
      do i=1,spn
1177
         call splint(time,lon,y2ax,n,sptime(i),s)
1178
         splon(i)=s
1179
      enddo
1180
 
1181
c     Change the time arrays back
1182
      do i=1,spn
1183
         sptime(i)=order*sptime(i)
1184
      enddo
1185
      do i=1,n
1186
         time(i)=order*time(i)
1187
      enddo
1188
 
1189
      return
1190
      end
1191
 
1192
c     -------------------------------------------------------------
1193
c     Basic routines for spline interpolation (Numerical Recipes)
1194
c     -------------------------------------------------------------
1195
 
1196
      SUBROUTINE spline(x,y,n,yp1,ypn,y2)
1197
      INTEGER n,NMAX
1198
      REAL yp1,ypn,x(n),y(n),y2(n)
1199
      PARAMETER (NMAX=500)
1200
      INTEGER i,k
1201
      REAL p,qn,sig,un,u(NMAX)
1202
      if (yp1.gt..99e30) then
1203
        y2(1)=0.
1204
        u(1)=0.
1205
      else
1206
        y2(1)=-0.5
1207
        u(1)=(3./(x(2)-x(1)))*((y(2)-y(1))/(x(2)-x(1))-yp1)
1208
      endif
1209
      do 11 i=2,n-1
1210
        sig=(x(i)-x(i-1))/(x(i+1)-x(i-1))
1211
        p=sig*y2(i-1)+2.
1212
        y2(i)=(sig-1.)/p
1213
        u(i)=(6.*((y(i+1)-y(i))/(x(i+
1214
     *1)-x(i))-(y(i)-y(i-1))/(x(i)-x(i-1)))/(x(i+1)-x(i-1))-sig*
1215
     *u(i-1))/p
1216
11    continue
1217
      if (ypn.gt..99e30) then
1218
        qn=0.
1219
        un=0.
1220
      else
1221
        qn=0.5
1222
        un=(3./(x(n)-x(n-1)))*(ypn-(y(n)-y(n-1))/(x(n)-x(n-1)))
1223
      endif
1224
      y2(n)=(un-qn*u(n-1))/(qn*y2(n-1)+1.)
1225
      do 12 k=n-1,1,-1
1226
        y2(k)=y2(k)*y2(k+1)+u(k)
1227
12    continue
1228
      return
1229
      END
1230
 
1231
      SUBROUTINE splint(xa,ya,y2a,n,x,y)
1232
      INTEGER n
1233
      REAL x,y,xa(n),y2a(n),ya(n)
1234
      INTEGER k,khi,klo
1235
      REAL a,b,h
1236
      klo=1
1237
      khi=n
1238
1     if (khi-klo.gt.1) then
1239
        k=(khi+klo)/2
1240
        if(xa(k).gt.x)then
1241
          khi=k
1242
        else
1243
          klo=k
1244
        endif
1245
      goto 1
1246
      endif
1247
      h=xa(khi)-xa(klo)
1248
      if (h.eq.0.) then
1249
         print*,'bad xa input in splint'
1250
         stop
1251
      endif
1252
      a=(xa(khi)-x)/h
1253
      b=(x-xa(klo))/h
1254
      y=a*ya(klo)+b*ya(khi)+((a**3-a)*y2a(klo)+(b**3-b)*y2a(khi))*(h**
1255
     *2)/6.
1256
      return
1257
      END
1258
 
1259
c     ********************************************************************
1260
c     * INPUT / OUTPUT SUBROUTINES                                       *
1261
c     ********************************************************************
1262
 
1263
 
1264
c     --------------------------------------------------------------------
1265
c     Subroutines to write the CF netcdf output file
1266
c     --------------------------------------------------------------------
1267
 
1268
      subroutine writecdf2D_cf 
1269
     >          (cdfname,varname,longname,unit,gridtype,clon,clat,
1270
     >           nlonlat,dlonlat,arr,time,dx,dy,xmin,ymin,nx,ny,
1271
     >           crefile,crevar,cretime)
1272
 
1273
c     Create and write to the CF netcdf file <cdfname>. The variable
1274
c     with name <varname> and with time <time> is written. The data
1275
c     are in the two-dimensional array <arr>. The list <dx,dy,xmin,
1276
c     ymin,nx,ny> specifies the output grid. The flags <crefile> and
1277
c     <crevar> determine whether the file and/or the variable should
1278
c     be created; correspondingly for the unlimited dimension <time>
1279
c     with the flag <cretime>.
1280
 
1281
      USE netcdf
1282
 
1283
      IMPLICIT NONE
1284
 
1285
c     Declaration of input parameters
1286
      character*80 cdfname
1287
      character*80 varname,longname,unit
1288
      integer      nx,ny
1289
      real         arr(nx,ny)
1290
      real         dx,dy,xmin,ymin
1291
      real         time
1292
      integer      crefile,crevar,cretime
1293
      character*80 gridtype
1294
      real         clon,clat
1295
      integer      nlonlat
1296
      real         dlonlat
1297
 
1298
c     Local variables
1299
      integer      ierr
1300
      integer      ncID
1301
      integer      LonDimId,    varLonID
1302
      integer      LatDimID,    varLatID
1303
      integer      TimeDimID,   varTimeID
1304
      real         longitude(nx)
1305
      real         latitude (ny)
1306
      real         timeindex
1307
      integer      i
1308
      integer      nvars,varids(100)
1309
      integer      ndims,dimids(100)
1310
      real         timelist(1000)
1311
      integer      ntimes
1312
      integer      ind
1313
      integer      varID
1314
 
1315
c     Quick an dirty solution for fieldname conflict
1316
      if ( varname.eq.'time' ) varname = 'TIME'
1317
 
1318
c     Initially set error to indicate no errors.
1319
      ierr = 0
1320
 
1321
c     ---- Create the netCDF - skip if <crefile=0> ----------------------
1322
      if ( crefile.ne.1 ) goto 100
1323
 
1324
c     Create the file 
1325
      ierr = nf90_create(trim(cdfname), NF90_CLOBBER, ncID)
1326
 
1327
c     Define dimensions 
1328
      ierr=nf90_def_dim(ncID,'longitude',nx            , LonDimID )
1329
      ierr=nf90_def_dim(ncID,'latitude' ,ny            , LatDimID )
1330
      ierr=nf90_def_dim(ncID,'time'     ,nf90_unlimited, TimeDimID)
1331
 
1332
c     Define coordinate Variables 
1333
      ierr = nf90_def_var(ncID,'longitude',NF90_FLOAT,
1334
     >     (/ LonDimID /),varLonID)
1335
      ierr = nf90_put_att(ncID, varLonID, "standard_name","longitude")
1336
      ierr = nf90_put_att(ncID, varLonID, "units"      ,"degree_east")
1337
 
1338
      ierr = nf90_def_var(ncID,'latitude',NF90_FLOAT,
1339
     >     (/ LatDimID /),varLatID)
1340
      ierr = nf90_put_att(ncID, varLatID, "standard_name", "latitude")
1341
      ierr = nf90_put_att(ncID, varLatID, "units"    ,"degree_north")
1342
 
1343
      ierr = nf90_def_var(ncID,'time',NF90_FLOAT, 
1344
     >     (/ TimeDimID /), varTimeID)
1345
      ierr = nf90_put_att(ncID, varTimeID, "axis",            "T")
1346
      ierr = nf90_put_att(ncID, varTimeID, "calendar", "standard")
1347
      ierr = nf90_put_att(ncID, varTimeID, "long_name",    "time")
1348
      ierr = nf90_put_att(ncID, varTimeID, "units",       "hours")
1349
 
1350
c     Write global attributes 
1351
      ierr = nf90_put_att(ncID, NF90_GLOBAL, 'Conventions', 'CF-1.0')
1352
      ierr = nf90_put_att(ncID, NF90_GLOBAL, 'title',  
1353
     >     'Trajectory Densities')
1354
      ierr = nf90_put_att(ncID, NF90_GLOBAL, 'source', 
1355
     >     'Lagranto Trajectories')
1356
      ierr = nf90_put_att(ncID, NF90_GLOBAL, 'institution', 
1357
     >     'ETH Zurich, IACETH')
1358
      ierr = nf90_put_att(ncID, NF90_GLOBAL, 'grid',trim(gridtype) ) 
1359
      ierr = nf90_put_att(ncID, NF90_GLOBAL, 'clon',clon )
1360
      ierr = nf90_put_att(ncID, NF90_GLOBAL, 'clat',clat )
1361
      ierr = nf90_put_att(ncID, NF90_GLOBAL, 'nlonlat',nlonlat )
1362
      ierr = nf90_put_att(ncID, NF90_GLOBAL, 'dlonlat',dlonlat )
1363
      ierr = nf90_put_att(ncID, NF90_GLOBAL, 'nx',nx )
1364
      ierr = nf90_put_att(ncID, NF90_GLOBAL, 'ny',ny )
1365
      ierr = nf90_put_att(ncID, NF90_GLOBAL, 'dx',dx )
1366
      ierr = nf90_put_att(ncID, NF90_GLOBAL, 'dy',dy )
1367
      ierr = nf90_put_att(ncID, NF90_GLOBAL, 'xmin',xmin )
1368
      ierr = nf90_put_att(ncID, NF90_GLOBAL, 'ymin',ymin )
1369
 
1370
c     Write coordinate data 
1371
      do i = 1,nx+1
1372
         longitude(i) = xmin + real(i-1) * dx
1373
      enddo
1374
      do i = 1,ny+1
1375
         latitude(i)  = ymin + real(i-1) * dy
1376
      enddo
1377
 
1378
c     Check whether the definition was successful
1379
      ierr = nf90_enddef(ncID)
1380
      if (ierr.gt.0) then
1381
         print*, 'An error occurred while attempting to ', 
1382
     >        'finish definition mode.'
1383
         stop
1384
      endif
1385
 
1386
c     Write coordinate data  
1387
      ierr = nf90_put_var(ncID,varLonID ,longitude)
1388
      ierr = nf90_put_var(ncID,varLatID ,latitude )
1389
 
1390
c     Close netCDF file 
1391
      ierr = nf90_close(ncID)
1392
 
1393
 100  continue
1394
 
1395
c     ---- Define a new variable - skip if <crevar=0> -----------------------
1396
 
1397
      if ( crevar.ne.1 ) goto 110
1398
 
1399
c     Open the file for read(write access
1400
      ierr = nf90_open  (trim(cdfname), NF90_WRITE  , ncID)
1401
 
1402
c     Get the IDs for dimensions
1403
      ierr = nf90_inq_dimid(ncID,'longitude', LonDimID )
1404
      ierr = nf90_inq_dimid(ncID,'latitude' , LatDimID )
1405
      ierr = nf90_inq_dimid(ncID,'time'     , TimeDimID)
1406
 
1407
c     Enter define mode
1408
      ierr = nf90_redef(ncID)
1409
 
1410
c     Write definition and add attributes
1411
      ierr = nf90_def_var(ncID,varname,NF90_FLOAT,
1412
     >                   (/ LonDimID, LatDimID, TimeDimID /),varID)
1413
      ierr = nf90_put_att(ncID, varID, "long_name" , longname )
1414
      ierr = nf90_put_att(ncID, varID, "units"     , unit     ) 
1415
      ierr = nf90_put_att(ncID, varID, '_FillValue', -999.99  ) 
1416
 
1417
c     Check whether definition was successful
1418
      ierr = nf90_enddef(ncID)
1419
      if (ierr.gt.0) then
1420
         print*, 'An error occurred while attempting to ', 
1421
     >           'finish definition mode.'
1422
         stop
1423
      endif
1424
      print*,trim(varname),' defined on ',trim(cdfname)
1425
 
1426
c     Close netCDF file 
1427
      ierr = nf90_close(ncID)
1428
 
1429
 110  continue
1430
 
1431
c     ---- Create a new time (unlimited dimension) - skip if <cretime=0> ------
1432
 
1433
      if ( cretime.ne.1 ) goto 120
1434
 
1435
c     Open the file for read/write access
1436
      ierr = nf90_open  (trim(cdfname), NF90_WRITE, ncID)
1437
 
1438
c     Get the list of times on the netCDF file
1439
      ierr = nf90_inq_dimid(ncID,'time', TimeDimID)
1440
      if ( ierr.ne.0 ) then
1441
         print*,'Time dimension is not defined on ',trim(cdfname),
1442
     >          ' .... Stop'
1443
         stop
1444
      endif
1445
      ierr = nf90_inquire_dimension(ncID, TimeDimID, len = ntimes)
1446
      ierr = nf90_inq_varid(ncID,'time', varTimeID)
1447
      if ( ierr.ne.0 ) then
1448
         print*,'Variable time is not defined on ',trim(cdfname),
1449
     >          ' ... Stop'
1450
         stop
1451
      endif
1452
      ierr = nf90_get_var(ncID,varTimeID,timelist(1:ntimes))
1453
 
1454
c     Decide whether a new time must be written
1455
      ind = 0
1456
      do i=1,ntimes
1457
         if ( time.eq.timelist(i) ) ind = i
1458
      enddo
1459
 
1460
c     Extend the time list if required 
1461
      if ( ind.eq.0 ) then
1462
         ntimes           = ntimes + 1
1463
         timelist(ntimes) = time
1464
         ierr = nf90_put_var(ncID,varTimeID,timelist(1:ntimes))
1465
      endif
1466
 
1467
c     Close netCDF file 
1468
      ierr = nf90_close(ncID)
1469
 
1470
 120  continue
1471
 
1472
c     ---- Write data --------------------------------------------------
1473
 
1474
c     Open the file for read/write access
1475
      ierr = nf90_open  (trim(cdfname), NF90_WRITE , ncID)
1476
 
1477
c     Get the varID
1478
      ierr = nf90_inq_varid(ncID,varname, varID )
1479
      if (ierr.ne.0) then
1480
         print*,'Variable ',trim(varname),' is not defined on ',
1481
     >          trim(cdfname)
1482
         stop
1483
      endif
1484
 
1485
c     Get the time index
1486
      ierr = nf90_inq_dimid(ncID,'time', TimeDimID)
1487
      if ( ierr.ne.0 ) then
1488
         print*,'Time dimension is not defined on ',trim(cdfname),
1489
     >          ' .... Stop'
1490
         stop
1491
      endif
1492
      ierr = nf90_inquire_dimension(ncID, TimeDimID, len = ntimes)
1493
      ierr = nf90_inq_varid(ncID,'time', varTimeID)
1494
      if ( ierr.ne.0 ) then
1495
         print*,'Variable time is not defined on ',trim(cdfname),
1496
     >          ' ... Stop'
1497
         stop
1498
      endif
1499
      ierr = nf90_get_var(ncID,varTimeID,timelist(1:ntimes))
1500
      ind = 0
1501
      do i=1,ntimes
1502
         if ( time.eq.timelist(i) ) ind = i
1503
      enddo
1504
      if (ind.eq.0) then
1505
         print*,'Time',time,' is not defined on the netCDF file',
1506
     >          trim(cdfname),' ... Stop'
1507
         stop
1508
      endif
1509
 
1510
c     Write data block      
1511
      ierr = nf90_put_var(ncID,varID,arr,
1512
     >                    start = (/ 1, 1, ind /), 
1513
     >                    count = (/ nx, ny, 1 /) )
1514
 
1515
c     Check whether writing was successful 
1516
      ierr = nf90_close(ncID)
1517
      if (ierr.ne.0) then
1518
         write(*,*) trim(nf90_strerror(ierr))
1519
         write(*,*) 'An error occurred while attempting to ', 
1520
     >              'close the netcdf file.'
1521
         write(*,*) 'in clscdf_CF'
1522
      endif
1523
 
1524
      end
1525
 
1526
 
1527
c     ********************************************************************************
1528
c     * Transformation routine: LMSTOLM and PHSTOPH from library gm2em               *
1529
c     ********************************************************************************
1530
 
1531
      REAL FUNCTION LMSTOLM (PHIS, LAMS, POLPHI, POLLAM)
1532
C
1533
C**** LMSTOLM  -   FC:BERECHNUNG DER WAHREN GEOGRAPHISCHEN LAENGE FUER
1534
C****                 EINEN PUNKT MIT DEN KOORDINATEN (PHIS, LAMS)
1535
C****                 IM ROTIERTEN SYSTEM. DER NORDPOL DES SYSTEMS HAT
1536
C****                 DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
1537
C**   AUFRUF   :   LAM = LMSTOLM (PHIS, LAMS, POLPHI, POLLAM)
1538
C**   ENTRIES  :   KEINE
1539
C**   ZWECK    :   BERECHNUNG DER WAHREN GEOGRAPHISCHEN LAENGE FUER
1540
C**                EINEN PUNKT MIT DEN KOORDINATEN (PHIS, LAMS)
1541
C**                IM ROTIERTEN SYSTEM. DER NORDPOL DIESES SYSTEMS HAT
1542
C**                DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
1543
C**   VERSIONS-
1544
C**   DATUM    :   03.05.90
1545
C**
1546
C**   EXTERNALS:   KEINE
1547
C**   EINGABE-
1548
C**   PARAMETER:   PHIS     REAL   GEOGR. BREITE DES PUNKTES IM ROT.SYS.
1549
C**                LAMS     REAL   GEOGR. LAENGE DES PUNKTES IM ROT.SYS.
1550
C**                POLPHI   REAL   WAHRE GEOGR. BREITE DES NORDPOLS
1551
C**                POLLAM   REAL   WAHRE GEOGR. LAENGE DES NORDPOLS
1552
C**   AUSGABE-
1553
C**   PARAMETER:   WAHRE GEOGRAPHISCHE LAENGE ALS WERT DER FUNKTION
1554
C**                ALLE WINKEL IN GRAD (NORDEN>0, OSTEN>0)
1555
C**
1556
C**   COMMON-
1557
C**   BLOECKE  :   KEINE
1558
C**
1559
C**   FEHLERBE-
1560
C**   HANDLUNG :   KEINE
1561
C**   VERFASSER:   D.MAJEWSKI
1562
 
1563
      REAL        LAMS,PHIS,POLPHI,POLLAM
1564
 
1565
      DATA        ZRPI18 , ZPIR18  / 57.2957795 , 0.0174532925 /
1566
 
1567
      ZSINPOL = SIN(ZPIR18*POLPHI)
1568
      ZCOSPOL = COS(ZPIR18*POLPHI)
1569
      ZLAMPOL = ZPIR18*POLLAM
1570
      ZPHIS   = ZPIR18*PHIS
1571
      ZLAMS   = LAMS
1572
      IF(ZLAMS.GT.180.0) ZLAMS = ZLAMS - 360.0
1573
      ZLAMS   = ZPIR18*ZLAMS
1574
 
1575
      ZARG1   = SIN(ZLAMPOL)*(- ZSINPOL*COS(ZLAMS)*COS(ZPHIS)  +
1576
     1                          ZCOSPOL*           SIN(ZPHIS)) -
1577
     2          COS(ZLAMPOL)*           SIN(ZLAMS)*COS(ZPHIS)
1578
      ZARG2   = COS(ZLAMPOL)*(- ZSINPOL*COS(ZLAMS)*COS(ZPHIS)  +
1579
     1                          ZCOSPOL*           SIN(ZPHIS)) +
1580
     2          SIN(ZLAMPOL)*           SIN(ZLAMS)*COS(ZPHIS)
1581
      IF (ABS(ZARG2).LT.1.E-30) THEN
1582
        IF (ABS(ZARG1).LT.1.E-30) THEN
1583
          LMSTOLM =   0.0
1584
        ELSEIF (ZARG1.GT.0.) THEN
1585
              LMSTOLAM =  90.0
1586
            ELSE
1587
              LMSTOLAM = -90.0
1588
            ENDIF
1589
      ELSE
1590
        LMSTOLM = ZRPI18*ATAN2(ZARG1,ZARG2)
1591
      ENDIF
1592
 
1593
      RETURN
1594
      END
1595
 
1596
 
1597
      REAL FUNCTION PHSTOPH (PHIS, LAMS, POLPHI, POLLAM)
1598
C
1599
C**** PHSTOPH  -   FC:BERECHNUNG DER WAHREN GEOGRAPHISCHEN BREITE FUER
1600
C****                 EINEN PUNKT MIT DEN KOORDINATEN (PHIS, LAMS) IM
1601
C****                 ROTIERTEN SYSTEM. DER NORDPOL DIESES SYSTEMS HAT
1602
C****                 DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
1603
C**   AUFRUF   :   PHI = PHSTOPH (PHIS, LAMS, POLPHI, POLLAM)
1604
C**   ENTRIES  :   KEINE
1605
C**   ZWECK    :   BERECHNUNG DER WAHREN GEOGRAPHISCHEN BREITE FUER
1606
C**                EINEN PUNKT MIT DEN KOORDINATEN (PHIS, LAMS) IM
1607
C**                ROTIERTEN SYSTEM. DER NORDPOL DIESES SYSTEMS HAT
1608
C**                DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
1609
C**   VERSIONS-
1610
C**   DATUM    :   03.05.90
1611
C**
1612
C**   EXTERNALS:   KEINE
1613
C**   EINGABE-
1614
C**   PARAMETER:   PHIS     REAL   GEOGR. BREITE DES PUNKTES IM ROT.SYS.
1615
C**                LAMS     REAL   GEOGR. LAENGE DES PUNKTES IM ROT.SYS.
1616
C**                POLPHI   REAL   WAHRE GEOGR. BREITE DES NORDPOLS
1617
C**                POLLAM   REAL   WAHRE GEOGR. LAENGE DES NORDPOLS
1618
C**   AUSGABE-
1619
C**   PARAMETER:   WAHRE GEOGRAPHISCHE BREITE ALS WERT DER FUNKTION
1620
C**                ALLE WINKEL IN GRAD (NORDEN>0, OSTEN>0)
1621
C**
1622
C**   COMMON-
1623
C**   BLOECKE  :   KEINE
1624
C**
1625
C**   FEHLERBE-
1626
C**   HANDLUNG :   KEINE
1627
C**   VERFASSER:   D.MAJEWSKI
1628
 
1629
      REAL        LAMS,PHIS,POLPHI,POLLAM
1630
 
1631
      DATA        ZRPI18 , ZPIR18  / 57.2957795 , 0.0174532925 /
1632
 
1633
      SINPOL = SIN(ZPIR18*POLPHI)
1634
      COSPOL = COS(ZPIR18*POLPHI)
1635
      ZPHIS  = ZPIR18*PHIS
1636
      ZLAMS  = LAMS
1637
      IF(ZLAMS.GT.180.0) ZLAMS = ZLAMS - 360.0
1638
      ZLAMS  = ZPIR18*ZLAMS
1639
      ARG     = COSPOL*COS(ZPHIS)*COS(ZLAMS) + SINPOL*SIN(ZPHIS)
1640
 
1641
      PHSTOPH = ZRPI18*ASIN(ARG)
1642
 
1643
      RETURN
1644
      END
1645
 
1646
 
1647
      REAL FUNCTION LMTOLMS (PHI, LAM, POLPHI, POLLAM)
1648
C
1649
C%Z% Modul %M%, V%I% vom %G%, extrahiert am %H%
1650
C
1651
C**** LMTOLMS  -   FC:UMRECHNUNG DER WAHREN GEOGRAPHISCHEN LAENGE LAM
1652
C****                 AUF EINEM PUNKT MIT DEN KOORDINATEN (PHIS, LAMS)
1653
C****                 IM ROTIERTEN SYSTEM. DER NORDPOL DES SYSTEMS HAT
1654
C****                 DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
1655
C**   AUFRUF   :   LAM = LMTOLMS (PHI, LAM, POLPHI, POLLAM)
1656
C**   ENTRIES  :   KEINE
1657
C**   ZWECK    :   UMRECHNUNG DER WAHREN GEOGRAPHISCHEN LAENGE LAM AUF
1658
C**                EINEM PUNKT MIT DEN KOORDINATEN (PHIS, LAMS) IM
1659
C**                ROTIERTEN SYSTEM. DER NORDPOL DIESES SYSTEMS HAT
1660
C**                DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
1661
C**   VERSIONS-
1662
C**   DATUM    :   03.05.90
1663
C**
1664
C**   EXTERNALS:   KEINE
1665
C**   EINGABE-
1666
C**   PARAMETER:   PHI    REAL BREITE DES PUNKTES IM GEOGR. SYSTEM
1667
C**                LAM    REAL LAENGE DES PUNKTES IM GEOGR. SYSTEM
1668
C**                POLPHI REAL GEOGR.BREITE DES N-POLS DES ROT. SYSTEMS
1669
C**                POLLAM REAL GEOGR.LAENGE DES N-POLS DES ROT. SYSTEMS
1670
C**   AUSGABE-
1671
C**   PARAMETER:   WAHRE GEOGRAPHISCHE LAENGE ALS WERT DER FUNKTION
1672
C**                ALLE WINKEL IN GRAD (NORDEN>0, OSTEN>0)
1673
C**
1674
C**   COMMON-
1675
C**   BLOECKE  :   KEINE
1676
C**
1677
C**   FEHLERBE-
1678
C**   HANDLUNG :   KEINE
1679
C**   VERFASSER:   G. DE MORSIER
1680
 
1681
      REAL        LAM,PHI,POLPHI,POLLAM
1682
 
1683
      DATA        ZRPI18 , ZPIR18  / 57.2957795 , 0.0174532925 /
1684
 
1685
      ZSINPOL = SIN(ZPIR18*POLPHI)
1686
      ZCOSPOL = COS(ZPIR18*POLPHI)
1687
      ZLAMPOL =     ZPIR18*POLLAM
1688
      ZPHI    =     ZPIR18*PHI
1689
      ZLAM    = LAM
1690
      IF(ZLAM.GT.180.0) ZLAM = ZLAM - 360.0
1691
      ZLAM    = ZPIR18*ZLAM
1692
 
1693
      ZARG1   = - SIN(ZLAM-ZLAMPOL)*COS(ZPHI)
1694
      ZARG2   = - ZSINPOL*COS(ZPHI)*COS(ZLAM-ZLAMPOL)+ZCOSPOL*SIN(ZPHI)
1695
      IF (ABS(ZARG2).LT.1.E-30) THEN
1696
        IF (ABS(ZARG1).LT.1.E-30) THEN
1697
          LMTOLMS =   0.0
1698
        ELSEIF (ZARG1.GT.0.) THEN
1699
              LMTOLMS =  90.0
1700
            ELSE
1701
              LMTOLMS = -90.0
1702
            ENDIF
1703
      ELSE
1704
        LMTOLMS = ZRPI18*ATAN2(ZARG1,ZARG2)
1705
      ENDIF
1706
 
1707
      RETURN
1708
      END
1709
 
1710
 
1711
      REAL FUNCTION PHTOPHS (PHI, LAM, POLPHI, POLLAM)
1712
C
1713
C%Z% Modul %M%, V%I% vom %G%, extrahiert am %H%
1714
C
1715
C**** PHTOPHS  -   FC:UMRECHNUNG DER WAHREN GEOGRAPHISCHEN BREITE PHI
1716
C****                 AUF EINEM PUNKT MIT DEN KOORDINATEN (PHIS, LAMS)
1717
C****                 IM ROTIERTEN SYSTEM. DER NORDPOL DES SYSTEMS HAT
1718
C****                 DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
1719
C**   AUFRUF   :   PHI = PHTOPHS (PHI, LAM, POLPHI, POLLAM)
1720
C**   ENTRIES  :   KEINE
1721
C**   ZWECK    :   UMRECHNUNG DER WAHREN GEOGRAPHISCHEN BREITE PHI AUF
1722
C**                EINEM PUNKT MIT DEN KOORDINATEN (PHIS, LAMS) IM
1723
C**                ROTIERTEN SYSTEM. DER NORDPOL DIESES SYSTEMS HAT
1724
C**                DIE WAHREN KOORDINATEN (POLPHI, POLLAM)
1725
C**   VERSIONS-
1726
C**   DATUM    :   03.05.90
1727
C**
1728
C**   EXTERNALS:   KEINE
1729
C**   EINGABE-
1730
C**   PARAMETER:   PHI    REAL BREITE DES PUNKTES IM GEOGR. SYSTEM
1731
C**                LAM    REAL LAENGE DES PUNKTES IM GEOGR. SYSTEM
1732
C**                POLPHI REAL GEOGR.BREITE DES N-POLS DES ROT. SYSTEMS
1733
C**                POLLAM REAL GEOGR.LAENGE DES N-POLS DES ROT. SYSTEMS
1734
C**   AUSGABE-
1735
C**   PARAMETER:   ROTIERTE BREITE PHIS ALS WERT DER FUNKTION
1736
C**                ALLE WINKEL IN GRAD (NORDEN>0, OSTEN>0)
1737
C**
1738
C**   COMMON-
1739
C**   BLOECKE  :   KEINE
1740
C**
1741
C**   FEHLERBE-
1742
C**   HANDLUNG :   KEINE
1743
C**   VERFASSER:   G. DE MORSIER
1744
 
1745
      REAL        LAM,PHI,POLPHI,POLLAM
1746
 
1747
      DATA        ZRPI18 , ZPIR18  / 57.2957795 , 0.0174532925 /
1748
 
1749
      ZSINPOL = SIN(ZPIR18*POLPHI)
1750
      ZCOSPOL = COS(ZPIR18*POLPHI)
1751
      ZLAMPOL = ZPIR18*POLLAM
1752
      ZPHI    = ZPIR18*PHI
1753
      ZLAM    = LAM
1754
      IF(ZLAM.GT.180.0) ZLAM = ZLAM - 360.0
1755
      ZLAM    = ZPIR18*ZLAM
1756
      ZARG    = ZCOSPOL*COS(ZPHI)*COS(ZLAM-ZLAMPOL) + ZSINPOL*SIN(ZPHI)
1757
 
1758
      PHTOPHS = ZRPI18*ASIN(ZARG)
1759
 
1760
      RETURN
1761
      END
1762
 
1763
c     ------------------------------------------------------------------
1764
c     Compute Cos/Sin of an argument in Degree instead of Radian
1765
c     ------------------------------------------------------------------
1766
 
1767
      real function cosd(arg)
1768
 
1769
      real,intent(IN) :: arg
1770
      real,parameter :: grad2rad=3.1415926/360.
1771
      cosd=cos(arg*grad2rad)
1772
      return
1773
      end
1774
 
1775
      real function sind(arg)
1776
 
1777
      real,intent(IN) :: arg
1778
      real,parameter :: grad2rad=3.1415926/360.
1779
      sind=sin(arg*grad2rad)
1780
      return
1781
      end
1782
 
1783