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module_llxy.F @ 2661

Last change on this file since 2661 was 1, checked in by lfita, 10 years ago

-- --- Opening of the WRF+LMDZ coupling repository --- -- -

WRF: version v3.3
LMDZ: version v1818

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File size: 73.3 KB

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1	MODULE module_llxy
2
3	! Module that defines constants, data structures, and
4	! subroutines used to convert grid indices to lat/lon
5	! and vice versa.
6	!
7	! SUPPORTED PROJECTIONS
8	! ---------------------
9	! Cylindrical Lat/Lon (code = PROJ_LATLON)
10	! Mercator (code = PROJ_MERC)
11	! Lambert Conformal (code = PROJ_LC)
12	! Gaussian (code = PROJ_GAUSS)
13	! Polar Stereographic (code = PROJ_PS)
14	! Rotated Lat/Lon (code = PROJ_ROTLL)
15	!
16	! REMARKS
17	! -------
18	! The routines contained within were adapted from routines
19	! obtained from NCEP's w3 library. The original NCEP routines were less
20	! flexible (e.g., polar-stereo routines only supported truelat of 60N/60S)
21	! than what we needed, so modifications based on equations in Hoke, Hayes, and
22	! Renninger (AFGWC/TN/79-003) were added to improve the flexibility.
23	! Additionally, coding was improved to F90 standards and the routines were
24	! combined into this module.
25	!
26	! ASSUMPTIONS
27	! -----------
28	! Grid Definition:
29	! For mercator, lambert conformal, and polar-stereographic projections,
30	! the routines within assume the following:
31	!
32	! 1. Grid is dimensioned (i,j) where i is the East-West direction,
33	! positive toward the east, and j is the north-south direction,
34	! positive toward the north.
35	! 2. Origin is at (1,1) and is located at the southwest corner,
36	! regardless of hemispere.
37	! 3. Grid spacing (dx) is always positive.
38	! 4. Values of true latitudes must be positive for NH domains
39	! and negative for SH domains.
40	!
41	! For the latlon and Gaussian projection, the grid origin may be at any
42	! of the corners, and the deltalat and deltalon values can be signed to
43	! account for this using the following convention:
44	! Origin Location Deltalat Sign Deltalon Sign
45	! --------------- ------------- -------------
46	! SW Corner + +
47	! NE Corner - -
48	! NW Corner - +
49	! SE Corner + -
50	!
51	! Data Definitions:
52	! 1. Any arguments that are a latitude value are expressed in
53	! degrees north with a valid range of -90 -> 90
54	! 2. Any arguments that are a longitude value are expressed in
55	! degrees east with a valid range of -180 -> 180.
56	! 3. Distances are in meters and are always positive.
57	! 4. The standard longitude (stdlon) is defined as the longitude
58	! line which is parallel to the grid's y-axis (j-direction), along
59	! which latitude increases (NOT the absolute value of latitude, but
60	! the actual latitude, such that latitude increases continuously
61	! from the south pole to the north pole) as j increases.
62	! 5. One true latitude value is required for polar-stereographic and
63	! mercator projections, and defines at which latitude the
64	! grid spacing is true. For lambert conformal, two true latitude
65	! values must be specified, but may be set equal to each other to
66	! specify a tangent projection instead of a secant projection.
67	!
68	! USAGE
69	! -----
70	! To use the routines in this module, the calling routines must have the
71	! following statement at the beginning of its declaration block:
72	! USE map_utils
73	!
74	! The use of the module not only provides access to the necessary routines,
75	! but also defines a structure of TYPE (proj_info) that can be used
76	! to declare a variable of the same type to hold your map projection
77	! information. It also defines some integer parameters that contain
78	! the projection codes so one only has to use those variable names rather
79	! than remembering the acutal code when using them. The basic steps are
80	! as follows:
81	!
82	! 1. Ensure the "USE map_utils" is in your declarations.
83	! 2. Declare the projection information structure as type(proj_info):
84	! TYPE(proj_info) :: proj
85	! 3. Populate your structure by calling the map_set routine:
86	! CALL map_set(code,lat1,lon1,knowni,knownj,dx,stdlon,truelat1,truelat2,proj)
87	! where:
88	! code (input) = one of PROJ_LATLON, PROJ_MERC, PROJ_LC, PROJ_PS,
89	! PROJ_GAUSS, or PROJ_ROTLL
90	! lat1 (input) = Latitude of grid origin point (i,j)=(1,1)
91	! (see assumptions!)
92	! lon1 (input) = Longitude of grid origin
93	! knowni (input) = origin point, x-location
94	! knownj (input) = origin point, y-location
95	! dx (input) = grid spacing in meters (ignored for LATLON projections)
96	! stdlon (input) = Standard longitude for PROJ_PS and PROJ_LC,
97	! deltalon (see assumptions) for PROJ_LATLON,
98	! ignored for PROJ_MERC
99	! truelat1 (input) = 1st true latitude for PROJ_PS, PROJ_LC, and
100	! PROJ_MERC, deltalat (see assumptions) for PROJ_LATLON
101	! truelat2 (input) = 2nd true latitude for PROJ_LC,
102	! ignored for all others.
103	! proj (output) = The structure of type (proj_info) that will be fully
104	! populated after this call
105	!
106	! 4. Now that the proj structure is populated, you may call either
107	! of the following routines:
108	!
109	! latlon_to_ij(proj, lat, lon, i, j)
110	! ij_to_latlon(proj, i, j, lat, lon)
111	!
112	! It is incumbent upon the calling routine to determine whether or
113	! not the values returned are within your domain's bounds. All values
114	! of i, j, lat, and lon are REAL values.
115	!
116	!
117	! REFERENCES
118	! ----------
119	! Hoke, Hayes, and Renninger, "Map Preojections and Grid Systems for
120	! Meteorological Applications." AFGWC/TN-79/003(Rev), Air Weather
121	! Service, 1985.
122	!
123	! NCAR MM5v3 Modeling System, REGRIDDER program, module_first_guess_map.F
124	! NCEP routines w3fb06, w3fb07, w3fb08, w3fb09, w3fb11, w3fb12
125	!
126	! HISTORY
127	! -------
128	! 27 Mar 2001 - Original Version
129	! Brent L. Shaw, NOAA/FSL (CSU/CIRA)
130	!
131	!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
132
133	USE module_wrf_error
134
135	INTEGER, PARAMETER :: HH=4, VV=5
136
137	REAL, PARAMETER :: PI = 3.141592653589793
138	REAL, PARAMETER :: OMEGA_E = 7.292e-5
139
140	REAL, PARAMETER :: DEG_PER_RAD = 180./PI
141	REAL, PARAMETER :: RAD_PER_DEG = PI/180.
142
143	REAL, PARAMETER :: A_WGS84 = 6378137.
144	REAL, PARAMETER :: B_WGS84 = 6356752.314
145	REAL, PARAMETER :: RE_WGS84 = A_WGS84
146	REAL, PARAMETER :: E_WGS84 = 0.081819192
147
148	REAL, PARAMETER :: A_NAD83 = 6378137.
149	REAL, PARAMETER :: RE_NAD83 = A_NAD83
150	REAL, PARAMETER :: E_NAD83 = 0.0818187034
151
152	REAL, PARAMETER :: EARTH_RADIUS_M = 6370000.
153	REAL, PARAMETER :: EARTH_CIRC_M = 2.PIEARTH_RADIUS_M
154
155	INTEGER, PUBLIC, PARAMETER :: PROJ_LATLON = 0
156	INTEGER, PUBLIC, PARAMETER :: PROJ_LC = 1
157	INTEGER, PUBLIC, PARAMETER :: PROJ_PS = 2
158	INTEGER, PUBLIC, PARAMETER :: PROJ_PS_WGS84 = 102
159	INTEGER, PUBLIC, PARAMETER :: PROJ_MERC = 3
160	INTEGER, PUBLIC, PARAMETER :: PROJ_GAUSS = 4
161	INTEGER, PUBLIC, PARAMETER :: PROJ_CYL = 5
162	INTEGER, PUBLIC, PARAMETER :: PROJ_CASSINI = 6
163	INTEGER, PUBLIC, PARAMETER :: PROJ_ALBERS_NAD83 = 105
164	INTEGER, PUBLIC, PARAMETER :: PROJ_ROTLL = 203
165
166	! Define some private constants
167	INTEGER, PRIVATE, PARAMETER :: HIGH = 8
168
169	TYPE proj_info
170
171	INTEGER :: code ! Integer code for projection TYPE
172	INTEGER :: nlat ! For Gaussian -- number of latitude points
173	! north of the equator
174	INTEGER :: nlon !
175	!
176	INTEGER :: ixdim ! For Rotated Lat/Lon -- number of mass points
177	! in an odd row
178	INTEGER :: jydim ! For Rotated Lat/Lon -- number of rows
179	INTEGER :: stagger ! For Rotated Lat/Lon -- mass or velocity grid
180	REAL :: phi ! For Rotated Lat/Lon -- domain half-extent in
181	! degrees latitude
182	REAL :: lambda ! For Rotated Lat/Lon -- domain half-extend in
183	! degrees longitude
184	REAL :: lat1 ! SW latitude (1,1) in degrees (-90->90N)
185	REAL :: lon1 ! SW longitude (1,1) in degrees (-180->180E)
186	REAL :: lat0 ! For Cassini, latitude of projection pole
187	REAL :: lon0 ! For Cassini, longitude of projection pole
188	REAL :: dx ! Grid spacing in meters at truelats, used
189	! only for ps, lc, and merc projections
190	REAL :: dy ! Grid spacing in meters at truelats, used
191	! only for ps, lc, and merc projections
192	REAL :: latinc ! Latitude increment for cylindrical lat/lon
193	REAL :: loninc ! Longitude increment for cylindrical lat/lon
194	! also the lon increment for Gaussian grid
195	REAL :: dlat ! Lat increment for lat/lon grids
196	REAL :: dlon ! Lon increment for lat/lon grids
197	REAL :: stdlon ! Longitude parallel to y-axis (-180->180E)
198	REAL :: truelat1 ! First true latitude (all projections)
199	REAL :: truelat2 ! Second true lat (LC only)
200	REAL :: hemi ! 1 for NH, -1 for SH
201	REAL :: cone ! Cone factor for LC projections
202	REAL :: polei ! Computed i-location of pole point
203	REAL :: polej ! Computed j-location of pole point
204	REAL :: rsw ! Computed radius to SW corner
205	REAL :: rebydx ! Earth radius divided by dx
206	REAL :: knowni ! X-location of known lat/lon
207	REAL :: knownj ! Y-location of known lat/lon
208	REAL :: re_m ! Radius of spherical earth, meters
209	REAL :: rho0 ! For Albers equal area
210	REAL :: nc ! For Albers equal area
211	REAL :: bigc ! For Albers equal area
212	LOGICAL :: init ! Flag to indicate if this struct is
213	! ready for use
214	LOGICAL :: wrap ! For Gaussian -- flag to indicate wrapping
215	! around globe?
216	REAL, POINTER, DIMENSION(:) :: gauss_lat ! Latitude array for Gaussian grid
217
218	END TYPE proj_info
219
220	!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
221	CONTAINS
222	!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
223
224	SUBROUTINE map_init(proj)
225	! Initializes the map projection structure to missing values
226
227	IMPLICIT NONE
228	TYPE(proj_info), INTENT(INOUT) :: proj
229
230	proj%lat1 = -999.9
231	proj%lon1 = -999.9
232	proj%lat0 = -999.9
233	proj%lon0 = -999.9
234	proj%dx = -999.9
235	proj%dy = -999.9
236	proj%latinc = -999.9
237	proj%loninc = -999.9
238	proj%stdlon = -999.9
239	proj%truelat1 = -999.9
240	proj%truelat2 = -999.9
241	proj%phi = -999.9
242	proj%lambda = -999.9
243	proj%ixdim = -999
244	proj%jydim = -999
245	proj%stagger = HH
246	proj%nlat = 0
247	proj%nlon = 0
248	proj%hemi = 0.0
249	proj%cone = -999.9
250	proj%polei = -999.9
251	proj%polej = -999.9
252	proj%rsw = -999.9
253	proj%knowni = -999.9
254	proj%knownj = -999.9
255	proj%re_m = EARTH_RADIUS_M
256	proj%init = .FALSE.
257	proj%wrap = .FALSE.
258	proj%rho0 = 0.
259	proj%nc = 0.
260	proj%bigc = 0.
261	nullify(proj%gauss_lat)
262
263	END SUBROUTINE map_init
264
265
266	SUBROUTINE map_set(proj_code, proj, lat1, lon1, lat0, lon0, knowni, knownj, dx, latinc, &
267	loninc, stdlon, truelat1, truelat2, nlat, nlon, ixdim, jydim, &
268	stagger, phi, lambda, r_earth)
269	! Given a partially filled proj_info structure, this routine computes
270	! polei, polej, rsw, and cone (if LC projection) to complete the
271	! structure. This allows us to eliminate redundant calculations when
272	! calling the coordinate conversion routines multiple times for the
273	! same map.
274	! This will generally be the first routine called when a user wants
275	! to be able to use the coordinate conversion routines, and it
276	! will call the appropriate subroutines based on the
277	! proj%code which indicates which projection type this is.
278
279	IMPLICIT NONE
280
281	! Declare arguments
282	INTEGER, INTENT(IN) :: proj_code
283	INTEGER, INTENT(IN), OPTIONAL :: nlat
284	INTEGER, INTENT(IN), OPTIONAL :: nlon
285	INTEGER, INTENT(IN), OPTIONAL :: ixdim
286	INTEGER, INTENT(IN), OPTIONAL :: jydim
287	INTEGER, INTENT(IN), OPTIONAL :: stagger
288	REAL, INTENT(IN), OPTIONAL :: latinc
289	REAL, INTENT(IN), OPTIONAL :: loninc
290	REAL, INTENT(IN), OPTIONAL :: lat1
291	REAL, INTENT(IN), OPTIONAL :: lon1
292	REAL, INTENT(IN), OPTIONAL :: lat0
293	REAL, INTENT(IN), OPTIONAL :: lon0
294	REAL, INTENT(IN), OPTIONAL :: dx
295	REAL, INTENT(IN), OPTIONAL :: stdlon
296	REAL, INTENT(IN), OPTIONAL :: truelat1
297	REAL, INTENT(IN), OPTIONAL :: truelat2
298	REAL, INTENT(IN), OPTIONAL :: knowni
299	REAL, INTENT(IN), OPTIONAL :: knownj
300	REAL, INTENT(IN), OPTIONAL :: phi
301	REAL, INTENT(IN), OPTIONAL :: lambda
302	REAL, INTENT(IN), OPTIONAL :: r_earth
303	TYPE(proj_info), INTENT(OUT) :: proj
304
305	INTEGER :: iter
306	REAL :: dummy_lon1
307	REAL :: dummy_lon0
308	REAL :: dummy_stdlon
309
310	! First, verify that mandatory parameters are present for the specified proj_code
311	IF ( proj_code == PROJ_LC ) THEN
312	IF ( .NOT.PRESENT(truelat1) .OR. &
313	.NOT.PRESENT(truelat2) .OR. &
314	.NOT.PRESENT(lat1) .OR. &
315	.NOT.PRESENT(lon1) .OR. &
316	.NOT.PRESENT(knowni) .OR. &
317	.NOT.PRESENT(knownj) .OR. &
318	.NOT.PRESENT(stdlon) .OR. &
319	.NOT.PRESENT(dx) ) THEN
320	PRINT '(A,I2)', 'The following are mandatory parameters for projection code : ', proj_code
321	PRINT '(A)', ' truelat1, truelat2, lat1, lon1, knowni, knownj, stdlon, dx'
322	CALL wrf_error_fatal ( 'MAP_INIT' )
323	END IF
324	ELSE IF ( proj_code == PROJ_PS ) THEN
325	IF ( .NOT.PRESENT(truelat1) .OR. &
326	.NOT.PRESENT(lat1) .OR. &
327	.NOT.PRESENT(lon1) .OR. &
328	.NOT.PRESENT(knowni) .OR. &
329	.NOT.PRESENT(knownj) .OR. &
330	.NOT.PRESENT(stdlon) .OR. &
331	.NOT.PRESENT(dx) ) THEN
332	PRINT '(A,I2)', 'The following are mandatory parameters for projection code : ', proj_code
333	PRINT '(A)', ' truelat1, lat1, lon1, knonwi, knownj, stdlon, dx'
334	CALL wrf_error_fatal ( 'MAP_INIT' )
335	END IF
336	ELSE IF ( proj_code == PROJ_PS_WGS84 ) THEN
337	IF ( .NOT.PRESENT(truelat1) .OR. &
338	.NOT.PRESENT(lat1) .OR. &
339	.NOT.PRESENT(lon1) .OR. &
340	.NOT.PRESENT(knowni) .OR. &
341	.NOT.PRESENT(knownj) .OR. &
342	.NOT.PRESENT(stdlon) .OR. &
343	.NOT.PRESENT(dx) ) THEN
344	PRINT '(A,I2)', 'The following are mandatory parameters for projection code : ', proj_code
345	PRINT '(A)', ' truelat1, lat1, lon1, knonwi, knownj, stdlon, dx'
346	CALL wrf_error_fatal ( 'MAP_INIT' )
347	END IF
348	ELSE IF ( proj_code == PROJ_ALBERS_NAD83 ) THEN
349	IF ( .NOT.PRESENT(truelat1) .OR. &
350	.NOT.PRESENT(truelat2) .OR. &
351	.NOT.PRESENT(lat1) .OR. &
352	.NOT.PRESENT(lon1) .OR. &
353	.NOT.PRESENT(knowni) .OR. &
354	.NOT.PRESENT(knownj) .OR. &
355	.NOT.PRESENT(stdlon) .OR. &
356	.NOT.PRESENT(dx) ) THEN
357	PRINT '(A,I2)', 'The following are mandatory parameters for projection code : ', proj_code
358	PRINT '(A)', ' truelat1, truelat2, lat1, lon1, knonwi, knownj, stdlon, dx'
359	CALL wrf_error_fatal ( 'MAP_INIT' )
360	END IF
361	ELSE IF ( proj_code == PROJ_MERC ) THEN
362	IF ( .NOT.PRESENT(truelat1) .OR. &
363	.NOT.PRESENT(lat1) .OR. &
364	.NOT.PRESENT(lon1) .OR. &
365	.NOT.PRESENT(knowni) .OR. &
366	.NOT.PRESENT(knownj) .OR. &
367	.NOT.PRESENT(dx) ) THEN
368	PRINT '(A,I2)', 'The following are mandatory parameters for projection code : ', proj_code
369	PRINT '(A)', ' truelat1, lat1, lon1, knowni, knownj, dx'
370	CALL wrf_error_fatal ( 'MAP_INIT' )
371	END IF
372	ELSE IF ( proj_code == PROJ_LATLON ) THEN
373	IF ( .NOT.PRESENT(latinc) .OR. &
374	.NOT.PRESENT(loninc) .OR. &
375	.NOT.PRESENT(knowni) .OR. &
376	.NOT.PRESENT(knownj) .OR. &
377	.NOT.PRESENT(lat1) .OR. &
378	.NOT.PRESENT(lon1) ) THEN
379	PRINT '(A,I2)', 'The following are mandatory parameters for projection code : ', proj_code
380	PRINT '(A)', ' latinc, loninc, knowni, knownj, lat1, lon1'
381	CALL wrf_error_fatal ( 'MAP_INIT' )
382	END IF
383	ELSE IF ( proj_code == PROJ_CYL ) THEN
384	IF ( .NOT.PRESENT(latinc) .OR. &
385	.NOT.PRESENT(loninc) .OR. &
386	.NOT.PRESENT(stdlon) ) THEN
387	PRINT '(A,I2)', 'The following are mandatory parameters for projection code : ', proj_code
388	PRINT '(A)', ' latinc, loninc, stdlon'
389	CALL wrf_error_fatal ( 'MAP_INIT' )
390	END IF
391	ELSE IF ( proj_code == PROJ_CASSINI ) THEN
392	IF ( .NOT.PRESENT(latinc) .OR. &
393	.NOT.PRESENT(loninc) .OR. &
394	.NOT.PRESENT(lat1) .OR. &
395	.NOT.PRESENT(lon1) .OR. &
396	.NOT.PRESENT(lat0) .OR. &
397	.NOT.PRESENT(lon0) .OR. &
398	.NOT.PRESENT(knowni) .OR. &
399	.NOT.PRESENT(knownj) .OR. &
400	.NOT.PRESENT(stdlon) ) THEN
401	PRINT '(A,I2)', 'The following are mandatory parameters for projection code : ', proj_code
402	PRINT '(A)', ' latinc, loninc, lat1, lon1, knowni, knownj, lat0, lon0, stdlon'
403	CALL wrf_error_fatal ( 'MAP_INIT' )
404	END IF
405	ELSE IF ( proj_code == PROJ_GAUSS ) THEN
406	IF ( .NOT.PRESENT(nlat) .OR. &
407	.NOT.PRESENT(lat1) .OR. &
408	.NOT.PRESENT(lon1) .OR. &
409	.NOT.PRESENT(loninc) ) THEN
410	PRINT '(A,I2)', 'The following are mandatory parameters for projection code : ', proj_code
411	PRINT '(A)', ' nlat, lat1, lon1, loninc'
412	CALL wrf_error_fatal ( 'MAP_INIT' )
413	END IF
414	ELSE IF ( proj_code == PROJ_ROTLL ) THEN
415	IF ( .NOT.PRESENT(ixdim) .OR. &
416	.NOT.PRESENT(jydim) .OR. &
417	.NOT.PRESENT(phi) .OR. &
418	.NOT.PRESENT(lambda) .OR. &
419	.NOT.PRESENT(lat1) .OR. &
420	.NOT.PRESENT(lon1) .OR. &
421	.NOT.PRESENT(stagger) ) THEN
422	PRINT '(A,I2)', 'The following are mandatory parameters for projection code : ', proj_code
423	PRINT '(A)', ' ixdim, jydim, phi, lambda, lat1, lon1, stagger'
424	CALL wrf_error_fatal ( 'MAP_INIT' )
425	END IF
426	ELSE
427	PRINT '(A,I2)', 'Unknown projection code: ', proj_code
428	CALL wrf_error_fatal ( 'MAP_INIT' )
429	END IF
430
431	! Check for validity of mandatory variables in proj
432	IF ( PRESENT(lat1) ) THEN
433	IF ( ABS(lat1) .GT. 90. ) THEN
434	PRINT '(A)', 'Latitude of origin corner required as follows:'
435	PRINT '(A)', ' -90N <= lat1 < = 90.N'
436	CALL wrf_error_fatal ( 'MAP_INIT' )
437	ENDIF
438	ENDIF
439
440	IF ( PRESENT(lon1) ) THEN
441	dummy_lon1 = lon1
442	IF ( ABS(dummy_lon1) .GT. 180.) THEN
443	iter = 0
444	DO WHILE (ABS(dummy_lon1) > 180. .AND. iter < 10)
445	IF (dummy_lon1 < -180.) dummy_lon1 = dummy_lon1 + 360.
446	IF (dummy_lon1 > 180.) dummy_lon1 = dummy_lon1 - 360.
447	iter = iter + 1
448	END DO
449	IF (abs(dummy_lon1) > 180.) THEN
450	PRINT '(A)', 'Longitude of origin required as follows:'
451	PRINT '(A)', ' -180E <= lon1 <= 180W'
452	CALL wrf_error_fatal ( 'MAP_INIT' )
453	ENDIF
454	ENDIF
455	ENDIF
456
457	IF ( PRESENT(lon0) ) THEN
458	dummy_lon0 = lon0
459	IF ( ABS(dummy_lon0) .GT. 180.) THEN
460	iter = 0
461	DO WHILE (ABS(dummy_lon0) > 180. .AND. iter < 10)
462	IF (dummy_lon0 < -180.) dummy_lon0 = dummy_lon0 + 360.
463	IF (dummy_lon0 > 180.) dummy_lon0 = dummy_lon0 - 360.
464	iter = iter + 1
465	END DO
466	IF (abs(dummy_lon0) > 180.) THEN
467	PRINT '(A)', 'Longitude of pole required as follows:'
468	PRINT '(A)', ' -180E <= lon0 <= 180W'
469	CALL wrf_error_fatal ( 'MAP_INIT' )
470	ENDIF
471	ENDIF
472	ENDIF
473
474	IF ( PRESENT(dx) ) THEN
475	IF ((dx .LE. 0.).AND.(proj_code .NE. PROJ_LATLON)) THEN
476	PRINT '(A)', 'Require grid spacing (dx) in meters be positive'
477	CALL wrf_error_fatal ( 'MAP_INIT' )
478	ENDIF
479	ENDIF
480
481	IF ( PRESENT(stdlon) ) THEN
482	dummy_stdlon = stdlon
483	IF ((ABS(dummy_stdlon) > 180.).AND.(proj_code /= PROJ_MERC)) THEN
484	iter = 0
485	DO WHILE (ABS(dummy_stdlon) > 180. .AND. iter < 10)
486	IF (dummy_stdlon < -180.) dummy_stdlon = dummy_stdlon + 360.
487	IF (dummy_stdlon > 180.) dummy_stdlon = dummy_stdlon - 360.
488	iter = iter + 1
489	END DO
490	IF (abs(dummy_stdlon) > 180.) THEN
491	PRINT '(A)', 'Need orientation longitude (stdlon) as: '
492	PRINT '(A)', ' -180E <= stdlon <= 180W'
493	CALL wrf_error_fatal ( 'MAP_INIT' )
494	ENDIF
495	ENDIF
496	ENDIF
497
498	IF ( PRESENT(truelat1) ) THEN
499	IF (ABS(truelat1).GT.90.) THEN
500	PRINT '(A)', 'Set true latitude 1 for all projections'
501	CALL wrf_error_fatal ( 'MAP_INIT' )
502	ENDIF
503	ENDIF
504
505	CALL map_init(proj)
506	proj%code = proj_code
507	IF ( PRESENT(lat1) ) proj%lat1 = lat1
508	IF ( PRESENT(lon1) ) proj%lon1 = dummy_lon1
509	IF ( PRESENT(lat0) ) proj%lat0 = lat0
510	IF ( PRESENT(lon0) ) proj%lon0 = dummy_lon0
511	IF ( PRESENT(latinc) ) proj%latinc = latinc
512	IF ( PRESENT(loninc) ) proj%loninc = loninc
513	IF ( PRESENT(knowni) ) proj%knowni = knowni
514	IF ( PRESENT(knownj) ) proj%knownj = knownj
515	IF ( PRESENT(dx) ) proj%dx = dx
516	IF ( PRESENT(stdlon) ) proj%stdlon = dummy_stdlon
517	IF ( PRESENT(truelat1) ) proj%truelat1 = truelat1
518	IF ( PRESENT(truelat2) ) proj%truelat2 = truelat2
519	IF ( PRESENT(nlat) ) proj%nlat = nlat
520	IF ( PRESENT(nlon) ) proj%nlon = nlon
521	IF ( PRESENT(ixdim) ) proj%ixdim = ixdim
522	IF ( PRESENT(jydim) ) proj%jydim = jydim
523	IF ( PRESENT(stagger) ) proj%stagger = stagger
524	IF ( PRESENT(phi) ) proj%phi = phi
525	IF ( PRESENT(lambda) ) proj%lambda = lambda
526	IF ( PRESENT(r_earth) ) proj%re_m = r_earth
527
528	IF ( PRESENT(dx) ) THEN
529	IF ( (proj_code == PROJ_LC) .OR. (proj_code == PROJ_PS) .OR. &
530	(proj_code == PROJ_PS_WGS84) .OR. (proj_code == PROJ_ALBERS_NAD83) .OR. &
531	(proj_code == PROJ_MERC) ) THEN
532	proj%dx = dx
533	IF (truelat1 .LT. 0.) THEN
534	proj%hemi = -1.0
535	ELSE
536	proj%hemi = 1.0
537	ENDIF
538	proj%rebydx = proj%re_m / dx
539	ENDIF
540	ENDIF
541
542	pick_proj: SELECT CASE(proj%code)
543
544	CASE(PROJ_PS)
545	CALL set_ps(proj)
546
547	CASE(PROJ_PS_WGS84)
548	CALL set_ps_wgs84(proj)
549
550	CASE(PROJ_ALBERS_NAD83)
551	CALL set_albers_nad83(proj)
552
553	CASE(PROJ_LC)
554	IF (ABS(proj%truelat2) .GT. 90.) THEN
555	proj%truelat2=proj%truelat1
556	ENDIF
557	CALL set_lc(proj)
558
559	CASE (PROJ_MERC)
560	CALL set_merc(proj)
561
562	CASE (PROJ_LATLON)
563
564	CASE (PROJ_GAUSS)
565	CALL set_gauss(proj)
566
567	CASE (PROJ_CYL)
568	CALL set_cyl(proj)
569
570	CASE (PROJ_CASSINI)
571	CALL set_cassini(proj)
572
573	CASE (PROJ_ROTLL)
574
575	END SELECT pick_proj
576	proj%init = .TRUE.
577
578	RETURN
579
580	END SUBROUTINE map_set
581
582
583	SUBROUTINE latlon_to_ij(proj, lat, lon, i, j)
584	! Converts input lat/lon values to the cartesian (i,j) value
585	! for the given projection.
586
587	IMPLICIT NONE
588	TYPE(proj_info), INTENT(IN) :: proj
589	REAL, INTENT(IN) :: lat
590	REAL, INTENT(IN) :: lon
591	REAL, INTENT(OUT) :: i
592	REAL, INTENT(OUT) :: j
593
594	IF (.NOT.proj%init) THEN
595	PRINT '(A)', 'You have not called map_set for this projection'
596	CALL wrf_error_fatal ( 'LATLON_TO_IJ' )
597	ENDIF
598
599	SELECT CASE(proj%code)
600
601	CASE(PROJ_LATLON)
602	CALL llij_latlon(lat,lon,proj,i,j)
603
604	CASE(PROJ_MERC)
605	CALL llij_merc(lat,lon,proj,i,j)
606
607	CASE(PROJ_PS)
608	CALL llij_ps(lat,lon,proj,i,j)
609
610	CASE(PROJ_PS_WGS84)
611	CALL llij_ps_wgs84(lat,lon,proj,i,j)
612
613	CASE(PROJ_ALBERS_NAD83)
614	CALL llij_albers_nad83(lat,lon,proj,i,j)
615
616	CASE(PROJ_LC)
617	CALL llij_lc(lat,lon,proj,i,j)
618
619	CASE(PROJ_GAUSS)
620	CALL llij_gauss(lat,lon,proj,i,j)
621
622	CASE(PROJ_CYL)
623	CALL llij_cyl(lat,lon,proj,i,j)
624
625	CASE(PROJ_CASSINI)
626	CALL llij_cassini(lat,lon,proj,i,j)
627
628	CASE(PROJ_ROTLL)
629	CALL llij_rotlatlon(lat,lon,proj,i,j)
630
631	CASE DEFAULT
632	PRINT '(A,I2)', 'Unrecognized map projection code: ', proj%code
633	CALL wrf_error_fatal ( 'LATLON_TO_IJ' )
634
635	END SELECT
636
637	RETURN
638
639	END SUBROUTINE latlon_to_ij
640
641
642	SUBROUTINE ij_to_latlon(proj, i, j, lat, lon)
643	! Computes geographical latitude and longitude for a given (i,j) point
644	! in a grid with a projection of proj
645
646	IMPLICIT NONE
647	TYPE(proj_info),INTENT(IN) :: proj
648	REAL, INTENT(IN) :: i
649	REAL, INTENT(IN) :: j
650	REAL, INTENT(OUT) :: lat
651	REAL, INTENT(OUT) :: lon
652
653	IF (.NOT.proj%init) THEN
654	PRINT '(A)', 'You have not called map_set for this projection'
655	CALL wrf_error_fatal ( 'IJ_TO_LATLON' )
656	ENDIF
657	SELECT CASE (proj%code)
658
659	CASE (PROJ_LATLON)
660	CALL ijll_latlon(i, j, proj, lat, lon)
661
662	CASE (PROJ_MERC)
663	CALL ijll_merc(i, j, proj, lat, lon)
664
665	CASE (PROJ_PS)
666	CALL ijll_ps(i, j, proj, lat, lon)
667
668	CASE (PROJ_PS_WGS84)
669	CALL ijll_ps_wgs84(i, j, proj, lat, lon)
670
671	CASE (PROJ_ALBERS_NAD83)
672	CALL ijll_albers_nad83(i, j, proj, lat, lon)
673
674	CASE (PROJ_LC)
675	CALL ijll_lc(i, j, proj, lat, lon)
676
677	CASE (PROJ_CYL)
678	CALL ijll_cyl(i, j, proj, lat, lon)
679
680	CASE (PROJ_CASSINI)
681	CALL ijll_cassini(i, j, proj, lat, lon)
682
683	CASE (PROJ_ROTLL)
684	CALL ijll_rotlatlon(i, j, proj, lat, lon)
685
686	CASE DEFAULT
687	PRINT '(A,I2)', 'Unrecognized map projection code: ', proj%code
688	CALL wrf_error_fatal ( 'IJ_TO_LATLON' )
689
690	END SELECT
691	RETURN
692	END SUBROUTINE ij_to_latlon
693
694
695	SUBROUTINE set_ps(proj)
696	! Initializes a polar-stereographic map projection from the partially
697	! filled proj structure. This routine computes the radius to the
698	! southwest corner and computes the i/j location of the pole for use
699	! in llij_ps and ijll_ps.
700	IMPLICIT NONE
701
702	! Declare args
703	TYPE(proj_info), INTENT(INOUT) :: proj
704
705	! Local vars
706	REAL :: ala1
707	REAL :: alo1
708	REAL :: reflon
709	REAL :: scale_top
710
711	! Executable code
712	reflon = proj%stdlon + 90.
713
714	! Compute numerator term of map scale factor
715	scale_top = 1. + proj%hemi * SIN(proj%truelat1 * rad_per_deg)
716
717	! Compute radius to lower-left (SW) corner
718	ala1 = proj%lat1 * rad_per_deg
719	proj%rsw = proj%rebydxCOS(ala1)scale_top/(1.+proj%hemi*SIN(ala1))
720
721	! Find the pole point
722	alo1 = (proj%lon1 - reflon) * rad_per_deg
723	proj%polei = proj%knowni - proj%rsw * COS(alo1)
724	proj%polej = proj%knownj - proj%hemi * proj%rsw * SIN(alo1)
725
726	RETURN
727
728	END SUBROUTINE set_ps
729
730
731	SUBROUTINE llij_ps(lat,lon,proj,i,j)
732	! Given latitude (-90 to 90), longitude (-180 to 180), and the
733	! standard polar-stereographic projection information via the
734	! public proj structure, this routine returns the i/j indices which
735	! if within the domain range from 1->nx and 1->ny, respectively.
736
737	IMPLICIT NONE
738
739	! Delcare input arguments
740	REAL, INTENT(IN) :: lat
741	REAL, INTENT(IN) :: lon
742	TYPE(proj_info),INTENT(IN) :: proj
743
744	! Declare output arguments
745	REAL, INTENT(OUT) :: i !(x-index)
746	REAL, INTENT(OUT) :: j !(y-index)
747
748	! Declare local variables
749
750	REAL :: reflon
751	REAL :: scale_top
752	REAL :: ala
753	REAL :: alo
754	REAL :: rm
755
756	! BEGIN CODE
757
758	reflon = proj%stdlon + 90.
759
760	! Compute numerator term of map scale factor
761
762	scale_top = 1. + proj%hemi * SIN(proj%truelat1 * rad_per_deg)
763
764	! Find radius to desired point
765	ala = lat * rad_per_deg
766	rm = proj%rebydx * COS(ala) * scale_top/(1. + proj%hemi *SIN(ala))
767	alo = (lon - reflon) * rad_per_deg
768	i = proj%polei + rm * COS(alo)
769	j = proj%polej + proj%hemi * rm * SIN(alo)
770
771	RETURN
772
773	END SUBROUTINE llij_ps
774
775
776	SUBROUTINE ijll_ps(i, j, proj, lat, lon)
777
778	! This is the inverse subroutine of llij_ps. It returns the
779	! latitude and longitude of an i/j point given the projection info
780	! structure.
781
782	IMPLICIT NONE
783
784	! Declare input arguments
785	REAL, INTENT(IN) :: i ! Column
786	REAL, INTENT(IN) :: j ! Row
787	TYPE (proj_info), INTENT(IN) :: proj
788
789	! Declare output arguments
790	REAL, INTENT(OUT) :: lat ! -90 -> 90 north
791	REAL, INTENT(OUT) :: lon ! -180 -> 180 East
792
793	! Local variables
794	REAL :: reflon
795	REAL :: scale_top
796	REAL :: xx,yy
797	REAL :: gi2, r2
798	REAL :: arccos
799
800	! Begin Code
801
802	! Compute the reference longitude by rotating 90 degrees to the east
803	! to find the longitude line parallel to the positive x-axis.
804	reflon = proj%stdlon + 90.
805
806	! Compute numerator term of map scale factor
807	scale_top = 1. + proj%hemi * SIN(proj%truelat1 * rad_per_deg)
808
809	! Compute radius to point of interest
810	xx = i - proj%polei
811	yy = (j - proj%polej) * proj%hemi
812	r2 = xx2 + yy2
813
814	! Now the magic code
815	IF (r2 .EQ. 0.) THEN
816	lat = proj%hemi * 90.
817	lon = reflon
818	ELSE
819	gi2 = (proj%rebydx * scale_top)**2.
820	lat = deg_per_rad * proj%hemi * ASIN((gi2-r2)/(gi2+r2))
821	arccos = ACOS(xx/SQRT(r2))
822	IF (yy .GT. 0) THEN
823	lon = reflon + deg_per_rad * arccos
824	ELSE
825	lon = reflon - deg_per_rad * arccos
826	ENDIF
827	ENDIF
828
829	! Convert to a -180 -> 180 East convention
830	IF (lon .GT. 180.) lon = lon - 360.
831	IF (lon .LT. -180.) lon = lon + 360.
832
833	RETURN
834
835	END SUBROUTINE ijll_ps
836
837
838	SUBROUTINE set_ps_wgs84(proj)
839	! Initializes a polar-stereographic map projection (WGS84 ellipsoid)
840	! from the partially filled proj structure. This routine computes the
841	! radius to the southwest corner and computes the i/j location of the
842	! pole for use in llij_ps and ijll_ps.
843
844	IMPLICIT NONE
845
846	! Arguments
847	TYPE(proj_info), INTENT(INOUT) :: proj
848
849	! Local variables
850	real :: h, mc, tc, t, rho
851
852	h = proj%hemi
853
854	mc = cos(hproj%truelat1rad_per_deg)/sqrt(1.0-(E_WGS84sin(hproj%truelat1rad_per_deg))*2.0)
855	tc = sqrt(((1.0-sin(hproj%truelat1rad_per_deg))/(1.0+sin(hproj%truelat1rad_per_deg)))* &
856	(((1.0+E_WGS84sin(hproj%truelat1rad_per_deg))/(1.0-E_WGS84sin(hproj%truelat1rad_per_deg)))**E_WGS84 ))
857
858	! Find the i/j location of reference lat/lon with respect to the pole of the projection
859	t = sqrt(((1.0-sin(hproj%lat1rad_per_deg))/(1.0+sin(hproj%lat1rad_per_deg)))* &
860	(((1.0+E_WGS84sin(hproj%lat1rad_per_deg))/(1.0-E_WGS84sin(hproj%lat1rad_per_deg)) )**E_WGS84 ) )
861	rho = h * (A_WGS84 / proj%dx) * mc * t / tc
862	proj%polei = rho * sin((hproj%lon1 - hproj%stdlon)*rad_per_deg)
863	proj%polej = -rho * cos((hproj%lon1 - hproj%stdlon)*rad_per_deg)
864
865	RETURN
866
867	END SUBROUTINE set_ps_wgs84
868
869
870	SUBROUTINE llij_ps_wgs84(lat,lon,proj,i,j)
871	! Given latitude (-90 to 90), longitude (-180 to 180), and the
872	! standard polar-stereographic projection information via the
873	! public proj structure, this routine returns the i/j indices which
874	! if within the domain range from 1->nx and 1->ny, respectively.
875
876	IMPLICIT NONE
877
878	! Arguments
879	REAL, INTENT(IN) :: lat
880	REAL, INTENT(IN) :: lon
881	REAL, INTENT(OUT) :: i !(x-index)
882	REAL, INTENT(OUT) :: j !(y-index)
883	TYPE(proj_info),INTENT(IN) :: proj
884
885	! Local variables
886	real :: h, mc, tc, t, rho
887
888	h = proj%hemi
889
890	mc = cos(hproj%truelat1rad_per_deg)/sqrt(1.0-(E_WGS84sin(hproj%truelat1rad_per_deg))*2.0)
891	tc = sqrt(((1.0-sin(hproj%truelat1rad_per_deg))/(1.0+sin(hproj%truelat1rad_per_deg)))* &
892	(((1.0+E_WGS84sin(hproj%truelat1rad_per_deg))/(1.0-E_WGS84sin(hproj%truelat1rad_per_deg)))**E_WGS84 ))
893
894	t = sqrt(((1.0-sin(hlatrad_per_deg))/(1.0+sin(hlatrad_per_deg))) * &
895	(((1.0+E_WGS84sin(hlatrad_per_deg))/(1.0-E_WGS84sin(hlatrad_per_deg)))**E_WGS84))
896
897	! Find the x/y location of the requested lat/lon with respect to the pole of the projection
898	rho = (A_WGS84 / proj%dx) * mc * t / tc
899	i = h * rho * sin((hlon - hproj%stdlon)*rad_per_deg)
900	j = h (-rho) cos((hlon - hproj%stdlon)*rad_per_deg)
901
902	! Get i/j relative to reference i/j
903	i = proj%knowni + (i - proj%polei)
904	j = proj%knownj + (j - proj%polej)
905
906	RETURN
907
908	END SUBROUTINE llij_ps_wgs84
909
910
911	SUBROUTINE ijll_ps_wgs84(i, j, proj, lat, lon)
912
913	! This is the inverse subroutine of llij_ps. It returns the
914	! latitude and longitude of an i/j point given the projection info
915	! structure.
916
917	implicit none
918
919	! Arguments
920	REAL, INTENT(IN) :: i ! Column
921	REAL, INTENT(IN) :: j ! Row
922	REAL, INTENT(OUT) :: lat ! -90 -> 90 north
923	REAL, INTENT(OUT) :: lon ! -180 -> 180 East
924	TYPE (proj_info), INTENT(IN) :: proj
925
926	! Local variables
927	real :: h, mc, tc, t, rho, x, y
928	real :: chi, a, b, c, d
929
930	h = proj%hemi
931	x = (i - proj%knowni + proj%polei)
932	y = (j - proj%knownj + proj%polej)
933
934	mc = cos(hproj%truelat1rad_per_deg)/sqrt(1.0-(E_WGS84sin(hproj%truelat1rad_per_deg))*2.0)
935	tc = sqrt(((1.0-sin(hproj%truelat1rad_per_deg))/(1.0+sin(hproj%truelat1rad_per_deg))) * &
936	(((1.0+E_WGS84sin(hproj%truelat1rad_per_deg))/(1.0-E_WGS84sin(hproj%truelat1rad_per_deg)))**E_WGS84 ))
937
938	rho = sqrt((xproj%dx)2.0 + (yproj%dx)**2.0)
939	t = rho * tc / (A_WGS84 * mc)
940
941	lon = hproj%stdlon + hatan2(hx,h(-y))
942
943	chi = PI/2.0-2.0*atan(t)
944	a = 1./2.E_WGS842. + 5./24.E_WGS84*4. + 1./40.E_WGS84*6. + 73./2016.E_WGS84**8.
945	b = 7./24.E_WGS844. + 29./120.E_WGS84*6. + 54113./40320.E_WGS84**8.
946	c = 7./30.E_WGS846. + 81./280.E_WGS84**8.
947	d = 4279./20160.E_WGS84*8.
948
949	lat = chi + sin(2.chi)(a + cos(2.chi)(b + cos(2.chi)(c + dcos(2.chi))))
950	lat = h * lat
951
952	lat = lat*deg_per_rad
953	lon = lon*deg_per_rad
954
955	RETURN
956
957	END SUBROUTINE ijll_ps_wgs84
958
959
960	SUBROUTINE set_albers_nad83(proj)
961	! Initializes an Albers equal area map projection (NAD83 ellipsoid)
962	! from the partially filled proj structure. This routine computes the
963	! radius to the southwest corner and computes the i/j location of the
964	! pole for use in llij_albers_nad83 and ijll_albers_nad83.
965
966	IMPLICIT NONE
967
968	! Arguments
969	TYPE(proj_info), INTENT(INOUT) :: proj
970
971	! Local variables
972	real :: h, m1, m2, q1, q2, theta, q, sinphi
973
974	h = proj%hemi
975
976	m1 = cos(hproj%truelat1rad_per_deg)/sqrt(1.0-(E_NAD83sin(hproj%truelat1rad_per_deg))*2.0)
977	m2 = cos(hproj%truelat2rad_per_deg)/sqrt(1.0-(E_NAD83sin(hproj%truelat2rad_per_deg))*2.0)
978
979	sinphi = sin(proj%truelat1*rad_per_deg)
980	q1 = (1.0-E_NAD83*2.0) &
981	((sinphi/(1.0-(E_NAD83sinphi)2.0)) - 1.0/(2.0E_NAD83) * log((1.0-E_NAD83sinphi)/(1.0+E_NAD83sinphi)))
982
983	sinphi = sin(proj%truelat2*rad_per_deg)
984	q2 = (1.0-E_NAD83*2.0) &
985	((sinphi/(1.0-(E_NAD83sinphi)2.0)) - 1.0/(2.0E_NAD83) * log((1.0-E_NAD83sinphi)/(1.0+E_NAD83sinphi)))
986
987	if (proj%truelat1 == proj%truelat2) then
988	proj%nc = sin(proj%truelat1*rad_per_deg)
989	else
990	proj%nc = (m12.0 - m22.0) / (q2 - q1)
991	end if
992
993	proj%bigc = m1*2.0 + proj%ncq1
994
995	! Find the i/j location of reference lat/lon with respect to the pole of the projection
996	sinphi = sin(proj%lat1*rad_per_deg)
997	q = (1.0-E_NAD83*2.0) &
998	((sinphi/(1.0-(E_NAD83sinphi)2.0)) - 1.0/(2.0E_NAD83) * log((1.0-E_NAD83sinphi)/(1.0+E_NAD83sinphi)))
999
1000	proj%rho0 = h * (A_NAD83 / proj%dx) * sqrt(proj%bigc - proj%nc * q) / proj%nc
1001	theta = proj%nc(proj%lon1 - proj%stdlon)rad_per_deg
1002
1003	proj%polei = proj%rho0 * sin(h*theta)
1004	proj%polej = proj%rho0 - proj%rho0 * cos(h*theta)
1005
1006	RETURN
1007
1008	END SUBROUTINE set_albers_nad83
1009
1010
1011	SUBROUTINE llij_albers_nad83(lat,lon,proj,i,j)
1012	! Given latitude (-90 to 90), longitude (-180 to 180), and the
1013	! standard projection information via the
1014	! public proj structure, this routine returns the i/j indices which
1015	! if within the domain range from 1->nx and 1->ny, respectively.
1016
1017	IMPLICIT NONE
1018
1019	! Arguments
1020	REAL, INTENT(IN) :: lat
1021	REAL, INTENT(IN) :: lon
1022	REAL, INTENT(OUT) :: i !(x-index)
1023	REAL, INTENT(OUT) :: j !(y-index)
1024	TYPE(proj_info),INTENT(IN) :: proj
1025
1026	! Local variables
1027	real :: h, q, rho, theta, sinphi
1028
1029	h = proj%hemi
1030
1031	sinphi = sin(hlatrad_per_deg)
1032
1033	! Find the x/y location of the requested lat/lon with respect to the pole of the projection
1034	q = (1.0-E_NAD83*2.0) &
1035	((sinphi/(1.0-(E_NAD83sinphi)2.0)) - 1.0/(2.0E_NAD83) * log((1.0-E_NAD83sinphi)/(1.0+E_NAD83sinphi)))
1036
1037	rho = h * (A_NAD83 / proj%dx) * sqrt(proj%bigc - proj%nc * q) / proj%nc
1038	theta = proj%nc * (hlon - hproj%stdlon)*rad_per_deg
1039
1040	i = hrhosin(theta)
1041	j = hproj%rho0 - hrho*cos(theta)
1042
1043	! Get i/j relative to reference i/j
1044	i = proj%knowni + (i - proj%polei)
1045	j = proj%knownj + (j - proj%polej)
1046
1047	RETURN
1048
1049	END SUBROUTINE llij_albers_nad83
1050
1051
1052	SUBROUTINE ijll_albers_nad83(i, j, proj, lat, lon)
1053
1054	! This is the inverse subroutine of llij_albers_nad83. It returns the
1055	! latitude and longitude of an i/j point given the projection info
1056	! structure.
1057
1058	implicit none
1059
1060	! Arguments
1061	REAL, INTENT(IN) :: i ! Column
1062	REAL, INTENT(IN) :: j ! Row
1063	REAL, INTENT(OUT) :: lat ! -90 -> 90 north
1064	REAL, INTENT(OUT) :: lon ! -180 -> 180 East
1065	TYPE (proj_info), INTENT(IN) :: proj
1066
1067	! Local variables
1068	real :: h, q, rho, theta, beta, x, y
1069	real :: a, b, c
1070
1071	h = proj%hemi
1072
1073	x = (i - proj%knowni + proj%polei)
1074	y = (j - proj%knownj + proj%polej)
1075
1076	rho = sqrt(x2.0 + (proj%rho0 - y)2.0)
1077	theta = atan2(x, proj%rho0-y)
1078
1079	q = (proj%bigc - (rhoproj%ncproj%dx/A_NAD83)**2.0) / proj%nc
1080
1081	beta = asin(q/(1.0 - log((1.0-E_NAD83)/(1.0+E_NAD83))(1.0-E_NAD832.0)/(2.0E_NAD83)))
1082	a = 1./3.E_NAD832. + 31./180.E_NAD83*4. + 517./5040.E_NAD83**6.
1083	b = 23./360.E_NAD834. + 251./3780.E_NAD83**6.
1084	c = 761./45360.E_NAD83*6.
1085
1086	lat = beta + asin(2.beta) + bsin(4.beta) + csin(6.beta)
1087
1088	lat = hlatdeg_per_rad
1089	lon = proj%stdlon + theta*deg_per_rad/proj%nc
1090
1091	RETURN
1092
1093	END SUBROUTINE ijll_albers_nad83
1094
1095
1096	SUBROUTINE set_lc(proj)
1097	! Initialize the remaining items in the proj structure for a
1098	! lambert conformal grid.
1099
1100	IMPLICIT NONE
1101
1102	TYPE(proj_info), INTENT(INOUT) :: proj
1103
1104	REAL :: arg
1105	REAL :: deltalon1
1106	REAL :: tl1r
1107	REAL :: ctl1r
1108
1109	! Compute cone factor
1110	CALL lc_cone(proj%truelat1, proj%truelat2, proj%cone)
1111
1112	! Compute longitude differences and ensure we stay out of the
1113	! forbidden "cut zone"
1114	deltalon1 = proj%lon1 - proj%stdlon
1115	IF (deltalon1 .GT. +180.) deltalon1 = deltalon1 - 360.
1116	IF (deltalon1 .LT. -180.) deltalon1 = deltalon1 + 360.
1117
1118	! Convert truelat1 to radian and compute COS for later use
1119	tl1r = proj%truelat1 * rad_per_deg
1120	ctl1r = COS(tl1r)
1121
1122	! Compute the radius to our known lower-left (SW) corner
1123	proj%rsw = proj%rebydx * ctl1r/proj%cone * &
1124	(TAN((90.proj%hemi-proj%lat1)rad_per_deg/2.) / &
1125	TAN((90.proj%hemi-proj%truelat1)rad_per_deg/2.))**proj%cone
1126
1127	! Find pole point
1128	arg = proj%cone(deltalon1rad_per_deg)
1129	proj%polei = proj%hemiproj%knowni - proj%hemi proj%rsw * SIN(arg)
1130	proj%polej = proj%hemiproj%knownj + proj%rsw COS(arg)
1131
1132	RETURN
1133
1134	END SUBROUTINE set_lc
1135
1136
1137	SUBROUTINE lc_cone(truelat1, truelat2, cone)
1138
1139	! Subroutine to compute the cone factor of a Lambert Conformal projection
1140
1141	IMPLICIT NONE
1142
1143	! Input Args
1144	REAL, INTENT(IN) :: truelat1 ! (-90 -> 90 degrees N)
1145	REAL, INTENT(IN) :: truelat2 ! " " " " "
1146
1147	! Output Args
1148	REAL, INTENT(OUT) :: cone
1149
1150	! Locals
1151
1152	! BEGIN CODE
1153
1154	! First, see if this is a secant or tangent projection. For tangent
1155	! projections, truelat1 = truelat2 and the cone is tangent to the
1156	! Earth's surface at this latitude. For secant projections, the cone
1157	! intersects the Earth's surface at each of the distinctly different
1158	! latitudes
1159	IF (ABS(truelat1-truelat2) .GT. 0.1) THEN
1160	cone = ALOG10(COS(truelat1*rad_per_deg)) - &
1161	ALOG10(COS(truelat2*rad_per_deg))
1162	cone = cone /(ALOG10(TAN((45.0 - ABS(truelat1)/2.0) * rad_per_deg)) - &
1163	ALOG10(TAN((45.0 - ABS(truelat2)/2.0) * rad_per_deg)))
1164	ELSE
1165	cone = SIN(ABS(truelat1)*rad_per_deg )
1166	ENDIF
1167
1168	RETURN
1169
1170	END SUBROUTINE lc_cone
1171
1172
1173	SUBROUTINE ijll_lc( i, j, proj, lat, lon)
1174
1175	! Subroutine to convert from the (i,j) cartesian coordinate to the
1176	! geographical latitude and longitude for a Lambert Conformal projection.
1177
1178	! History:
1179	! 25 Jul 01: Corrected by B. Shaw, NOAA/FSL
1180	!
1181	IMPLICIT NONE
1182
1183	! Input Args
1184	REAL, INTENT(IN) :: i ! Cartesian X coordinate
1185	REAL, INTENT(IN) :: j ! Cartesian Y coordinate
1186	TYPE(proj_info),INTENT(IN) :: proj ! Projection info structure
1187
1188	! Output Args
1189	REAL, INTENT(OUT) :: lat ! Latitude (-90->90 deg N)
1190	REAL, INTENT(OUT) :: lon ! Longitude (-180->180 E)
1191
1192	! Locals
1193	REAL :: inew
1194	REAL :: jnew
1195	REAL :: r
1196	REAL :: chi,chi1,chi2
1197	REAL :: r2
1198	REAL :: xx
1199	REAL :: yy
1200
1201	! BEGIN CODE
1202
1203	chi1 = (90. - proj%hemiproj%truelat1)rad_per_deg
1204	chi2 = (90. - proj%hemiproj%truelat2)rad_per_deg
1205
1206	! See if we are in the southern hemispere and flip the indices
1207	! if we are.
1208	inew = proj%hemi * i
1209	jnew = proj%hemi * j
1210
1211	! Compute radius**2 to i/j location
1212	xx = inew - proj%polei
1213	yy = proj%polej - jnew
1214	r2 = (xxxx + yyyy)
1215	r = SQRT(r2)/proj%rebydx
1216
1217	! Convert to lat/lon
1218	IF (r2 .EQ. 0.) THEN
1219	lat = proj%hemi * 90.
1220	lon = proj%stdlon
1221	ELSE
1222
1223	! Longitude
1224	lon = proj%stdlon + deg_per_rad * ATAN2(proj%hemi*xx,yy)/proj%cone
1225	lon = MOD(lon+360., 360.)
1226
1227	! Latitude. Latitude determined by solving an equation adapted
1228	! from:
1229	! Maling, D.H., 1973: Coordinate Systems and Map Projections
1230	! Equations #20 in Appendix I.
1231
1232	IF (chi1 .EQ. chi2) THEN
1233	chi = 2.0ATAN( ( r/TAN(chi1) )(1./proj%cone) TAN(chi1*0.5) )
1234	ELSE
1235	chi = 2.0ATAN( (rproj%cone/SIN(chi1))*(1./proj%cone) TAN(chi1*0.5))
1236	ENDIF
1237	lat = (90.0-chideg_per_rad)proj%hemi
1238
1239	ENDIF
1240
1241	IF (lon .GT. +180.) lon = lon - 360.
1242	IF (lon .LT. -180.) lon = lon + 360.
1243
1244	RETURN
1245
1246	END SUBROUTINE ijll_lc
1247
1248
1249	SUBROUTINE llij_lc( lat, lon, proj, i, j)
1250
1251	! Subroutine to compute the geographical latitude and longitude values
1252	! to the cartesian x/y on a Lambert Conformal projection.
1253
1254	IMPLICIT NONE
1255
1256	! Input Args
1257	REAL, INTENT(IN) :: lat ! Latitude (-90->90 deg N)
1258	REAL, INTENT(IN) :: lon ! Longitude (-180->180 E)
1259	TYPE(proj_info),INTENT(IN) :: proj ! Projection info structure
1260
1261	! Output Args
1262	REAL, INTENT(OUT) :: i ! Cartesian X coordinate
1263	REAL, INTENT(OUT) :: j ! Cartesian Y coordinate
1264
1265	! Locals
1266	REAL :: arg
1267	REAL :: deltalon
1268	REAL :: tl1r
1269	REAL :: rm
1270	REAL :: ctl1r
1271
1272
1273	! BEGIN CODE
1274
1275	! Compute deltalon between known longitude and standard lon and ensure
1276	! it is not in the cut zone
1277	deltalon = lon - proj%stdlon
1278	IF (deltalon .GT. +180.) deltalon = deltalon - 360.
1279	IF (deltalon .LT. -180.) deltalon = deltalon + 360.
1280
1281	! Convert truelat1 to radian and compute COS for later use
1282	tl1r = proj%truelat1 * rad_per_deg
1283	ctl1r = COS(tl1r)
1284
1285	! Radius to desired point
1286	rm = proj%rebydx * ctl1r/proj%cone * &
1287	(TAN((90.proj%hemi-lat)rad_per_deg/2.) / &
1288	TAN((90.proj%hemi-proj%truelat1)rad_per_deg/2.))**proj%cone
1289
1290	arg = proj%cone(deltalonrad_per_deg)
1291	i = proj%polei + proj%hemi * rm * SIN(arg)
1292	j = proj%polej - rm * COS(arg)
1293
1294	! Finally, if we are in the southern hemisphere, flip the i/j
1295	! values to a coordinate system where (1,1) is the SW corner
1296	! (what we assume) which is different than the original NCEP
1297	! algorithms which used the NE corner as the origin in the
1298	! southern hemisphere (left-hand vs. right-hand coordinate?)
1299	i = proj%hemi * i
1300	j = proj%hemi * j
1301
1302	RETURN
1303	END SUBROUTINE llij_lc
1304
1305
1306	SUBROUTINE set_merc(proj)
1307
1308	! Sets up the remaining basic elements for the mercator projection
1309
1310	IMPLICIT NONE
1311	TYPE(proj_info), INTENT(INOUT) :: proj
1312	REAL :: clain
1313
1314
1315	! Preliminary variables
1316
1317	clain = COS(rad_per_deg*proj%truelat1)
1318	proj%dlon = proj%dx / (proj%re_m * clain)
1319
1320	! Compute distance from equator to origin, and store in the
1321	! proj%rsw tag.
1322
1323	proj%rsw = 0.
1324	IF (proj%lat1 .NE. 0.) THEN
1325	proj%rsw = (ALOG(TAN(0.5((proj%lat1+90.)rad_per_deg))))/proj%dlon
1326	ENDIF
1327
1328	RETURN
1329
1330	END SUBROUTINE set_merc
1331
1332
1333	SUBROUTINE llij_merc(lat, lon, proj, i, j)
1334
1335	! Compute i/j coordinate from lat lon for mercator projection
1336
1337	IMPLICIT NONE
1338	REAL, INTENT(IN) :: lat
1339	REAL, INTENT(IN) :: lon
1340	TYPE(proj_info),INTENT(IN) :: proj
1341	REAL,INTENT(OUT) :: i
1342	REAL,INTENT(OUT) :: j
1343	REAL :: deltalon
1344
1345	deltalon = lon - proj%lon1
1346	IF (deltalon .LT. -180.) deltalon = deltalon + 360.
1347	IF (deltalon .GT. 180.) deltalon = deltalon - 360.
1348	i = proj%knowni + (deltalon/(proj%dlon*deg_per_rad))
1349	j = proj%knownj + (ALOG(TAN(0.5((lat + 90.) rad_per_deg)))) / &
1350	proj%dlon - proj%rsw
1351
1352	RETURN
1353
1354	END SUBROUTINE llij_merc
1355
1356
1357	SUBROUTINE ijll_merc(i, j, proj, lat, lon)
1358
1359	! Compute the lat/lon from i/j for mercator projection
1360
1361	IMPLICIT NONE
1362	REAL,INTENT(IN) :: i
1363	REAL,INTENT(IN) :: j
1364	TYPE(proj_info),INTENT(IN) :: proj
1365	REAL, INTENT(OUT) :: lat
1366	REAL, INTENT(OUT) :: lon
1367
1368
1369	lat = 2.0ATAN(EXP(proj%dlon(proj%rsw + j-proj%knownj)))*deg_per_rad - 90.
1370	lon = (i-proj%knowni)proj%dlondeg_per_rad + proj%lon1
1371	IF (lon.GT.180.) lon = lon - 360.
1372	IF (lon.LT.-180.) lon = lon + 360.
1373	RETURN
1374
1375	END SUBROUTINE ijll_merc
1376
1377
1378	SUBROUTINE llij_latlon(lat, lon, proj, i, j)
1379
1380	! Compute the i/j location of a lat/lon on a LATLON grid.
1381	IMPLICIT NONE
1382	REAL, INTENT(IN) :: lat
1383	REAL, INTENT(IN) :: lon
1384	TYPE(proj_info), INTENT(IN) :: proj
1385	REAL, INTENT(OUT) :: i
1386	REAL, INTENT(OUT) :: j
1387
1388	REAL :: deltalat
1389	REAL :: deltalon
1390
1391	! Compute deltalat and deltalon as the difference between the input
1392	! lat/lon and the origin lat/lon
1393	deltalat = lat - proj%lat1
1394	deltalon = lon - proj%lon1
1395
1396	! Compute i/j
1397	i = deltalon/proj%loninc
1398	j = deltalat/proj%latinc
1399
1400	i = i + proj%knowni
1401	j = j + proj%knownj
1402
1403	RETURN
1404
1405	END SUBROUTINE llij_latlon
1406
1407
1408	SUBROUTINE ijll_latlon(i, j, proj, lat, lon)
1409
1410	! Compute the lat/lon location of an i/j on a LATLON grid.
1411	IMPLICIT NONE
1412	REAL, INTENT(IN) :: i
1413	REAL, INTENT(IN) :: j
1414	TYPE(proj_info), INTENT(IN) :: proj
1415	REAL, INTENT(OUT) :: lat
1416	REAL, INTENT(OUT) :: lon
1417
1418	REAL :: i_work, j_work
1419	REAL :: deltalat
1420	REAL :: deltalon
1421
1422	i_work = i - proj%knowni
1423	j_work = j - proj%knownj
1424
1425	! Compute deltalat and deltalon
1426	deltalat = j_work*proj%latinc
1427	deltalon = i_work*proj%loninc
1428
1429	lat = proj%lat1 + deltalat
1430	lon = proj%lon1 + deltalon
1431
1432	RETURN
1433
1434	END SUBROUTINE ijll_latlon
1435
1436
1437	SUBROUTINE set_cyl(proj)
1438
1439	implicit none
1440
1441	! Arguments
1442	type(proj_info), intent(inout) :: proj
1443
1444	proj%hemi = 1.0
1445
1446	END SUBROUTINE set_cyl
1447
1448
1449	SUBROUTINE llij_cyl(lat, lon, proj, i, j)
1450
1451	implicit none
1452
1453	! Arguments
1454	real, intent(in) :: lat, lon
1455	real, intent(out) :: i, j
1456	type(proj_info), intent(in) :: proj
1457
1458	! Local variables
1459	real :: deltalat
1460	real :: deltalon
1461
1462	! Compute deltalat and deltalon as the difference between the input
1463	! lat/lon and the origin lat/lon
1464	deltalat = lat - proj%lat1
1465	! deltalon = lon - proj%stdlon
1466	deltalon = lon - proj%lon1
1467
1468	if (deltalon < 0.) deltalon = deltalon + 360.
1469	if (deltalon > 360.) deltalon = deltalon - 360.
1470
1471	! Compute i/j
1472	i = deltalon/proj%loninc
1473	j = deltalat/proj%latinc
1474
1475	if (i <= 0.) i = i + 360./proj%loninc
1476	if (i > 360./proj%loninc) i = i - 360./proj%loninc
1477
1478	i = i + proj%knowni
1479	j = j + proj%knownj
1480
1481	END SUBROUTINE llij_cyl
1482
1483
1484	SUBROUTINE ijll_cyl(i, j, proj, lat, lon)
1485
1486	implicit none
1487
1488	! Arguments
1489	real, intent(in) :: i, j
1490	real, intent(out) :: lat, lon
1491	type(proj_info), intent(in) :: proj
1492
1493	! Local variables
1494	real :: deltalat
1495	real :: deltalon
1496	real :: i_work, j_work
1497
1498	i_work = i - proj%knowni
1499	j_work = j - proj%knownj
1500
1501	if (i_work < 0.) i_work = i_work + 360./proj%loninc
1502	if (i_work >= 360./proj%loninc) i_work = i_work - 360./proj%loninc
1503
1504	! Compute deltalat and deltalon
1505	deltalat = j_work*proj%latinc
1506	deltalon = i_work*proj%loninc
1507
1508	lat = deltalat + proj%lat1
1509	! lon = deltalon + proj%stdlon
1510	lon = deltalon + proj%lon1
1511
1512	if (lon < -180.) lon = lon + 360.
1513	if (lon > 180.) lon = lon - 360.
1514
1515	END SUBROUTINE ijll_cyl
1516
1517
1518	SUBROUTINE set_cassini(proj)
1519
1520	implicit none
1521
1522	! Arguments
1523	type(proj_info), intent(inout) :: proj
1524
1525	! Local variables
1526	real :: comp_lat, comp_lon
1527	logical :: global_domain
1528
1529	proj%hemi = 1.0
1530
1531	! Try to determine whether this domain has global coverage
1532	if (abs(proj%lat1 - proj%latinc/2. + 90.) < 0.001 .and. &
1533	abs(mod(proj%lon1 - proj%loninc/2. - proj%stdlon,360.)) < 0.001) then
1534	global_domain = .true.
1535	else
1536	global_domain = .false.
1537	end if
1538
1539	if (abs(proj%lat0) /= 90. .and. .not.global_domain) then
1540	call rotate_coords(proj%lat1,proj%lon1,comp_lat,comp_lon,proj%lat0,proj%lon0,proj%stdlon,-1)
1541	proj%lat1 = comp_lat
1542	proj%lon1 = comp_lon
1543	end if
1544
1545	END SUBROUTINE set_cassini
1546
1547
1548	SUBROUTINE llij_cassini(lat, lon, proj, i, j)
1549
1550	implicit none
1551
1552	! Arguments
1553	real, intent(in) :: lat, lon
1554	real, intent(out) :: i, j
1555	type(proj_info), intent(in) :: proj
1556
1557	! Local variables
1558	real :: comp_lat, comp_lon
1559
1560	! Convert geographic to computational lat/lon
1561	if (abs(proj%lat0) /= 90.) then
1562	call rotate_coords(lat,lon,comp_lat,comp_lon,proj%lat0,proj%lon0,proj%stdlon,-1)
1563	else
1564	comp_lat = lat
1565	comp_lon = lon
1566	end if
1567
1568	! Convert computational lat/lon to i/j
1569	call llij_cyl(comp_lat, comp_lon, proj, i, j)
1570
1571	END SUBROUTINE llij_cassini
1572
1573
1574	SUBROUTINE ijll_cassini(i, j, proj, lat, lon)
1575
1576	implicit none
1577
1578	! Arguments
1579	real, intent(in) :: i, j
1580	real, intent(out) :: lat, lon
1581	type(proj_info), intent(in) :: proj
1582
1583	! Local variables
1584	real :: comp_lat, comp_lon
1585
1586	! Convert i/j to computational lat/lon
1587	call ijll_cyl(i, j, proj, comp_lat, comp_lon)
1588
1589	! Convert computational to geographic lat/lon
1590	if (abs(proj%lat0) /= 90.) then
1591	call rotate_coords(comp_lat,comp_lon,lat,lon,proj%lat0,proj%lon0,proj%stdlon,1)
1592	else
1593	lat = comp_lat
1594	lon = comp_lon
1595	end if
1596
1597	END SUBROUTINE ijll_cassini
1598
1599
1600	!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1601	! Purpose: Converts between computational and geographic lat/lon for Cassini
1602	!
1603	! Notes: This routine was provided by Bill Skamarock, 2007-03-27
1604	!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1605	SUBROUTINE rotate_coords(ilat,ilon,olat,olon,lat_np,lon_np,lon_0,direction)
1606
1607	IMPLICIT NONE
1608
1609	REAL, INTENT(IN ) :: ilat, ilon
1610	REAL, INTENT( OUT) :: olat, olon
1611	REAL, INTENT(IN ) :: lat_np, lon_np, lon_0
1612	INTEGER, INTENT(IN ), OPTIONAL :: direction
1613	! >=0, default : computational -> geographical
1614	! < 0 : geographical -> computational
1615
1616	REAL :: rlat, rlon
1617	REAL :: phi_np, lam_np, lam_0, dlam
1618	REAL :: sinphi, cosphi, coslam, sinlam
1619
1620	! Convert all angles to radians
1621	phi_np = lat_np * rad_per_deg
1622	lam_np = lon_np * rad_per_deg
1623	lam_0 = lon_0 * rad_per_deg
1624	rlat = ilat * rad_per_deg
1625	rlon = ilon * rad_per_deg
1626
1627	IF (PRESENT(direction) .AND. (direction < 0)) THEN
1628	! The equations are exactly the same except for one small difference
1629	! with respect to longitude ...
1630	dlam = PI - lam_0
1631	ELSE
1632	dlam = lam_np
1633	END IF
1634	sinphi = COS(phi_np)COS(rlat)COS(rlon-dlam) + SIN(phi_np)*SIN(rlat)
1635	cosphi = SQRT(1.-sinphi*sinphi)
1636	coslam = SIN(phi_np)COS(rlat)COS(rlon-dlam) - COS(phi_np)*SIN(rlat)
1637	sinlam = COS(rlat)*SIN(rlon-dlam)
1638	IF ( cosphi /= 0. ) THEN
1639	coslam = coslam/cosphi
1640	sinlam = sinlam/cosphi
1641	END IF
1642	olat = deg_per_rad*ASIN(sinphi)
1643	olon = deg_per_rad*(ATAN2(sinlam,coslam)-dlam-lam_0+lam_np)
1644	! Both of my F90 text books prefer the DO-EXIT form, and claim it is faster
1645	! when optimization is turned on (as we will always do...)
1646	DO
1647	IF (olon >= -180.) EXIT
1648	olon = olon + 360.
1649	END DO
1650	DO
1651	IF (olon <= 180.) EXIT
1652	olon = olon - 360.
1653	END DO
1654
1655	END SUBROUTINE rotate_coords
1656
1657
1658	SUBROUTINE llij_rotlatlon(lat, lon, proj, i_real, j_real)
1659
1660	IMPLICIT NONE
1661
1662	! Arguments
1663	REAL, INTENT(IN) :: lat, lon
1664	REAL :: i, j
1665	REAL, INTENT(OUT) :: i_real, j_real
1666	TYPE (proj_info), INTENT(IN) :: proj
1667
1668	! Local variables
1669	INTEGER :: ii,imt,jj,jmt,k,krows,ncol,nrow,iri
1670	REAL(KIND=HIGH) :: dphd,dlmd !Grid increments, degrees
1671	REAL(KIND=HIGH) :: glatd !Geographic latitude, positive north
1672	REAL(KIND=HIGH) :: glond !Geographic longitude, positive west
1673	REAL(KIND=HIGH) :: col,d1,d2,d2r,dlm,dlm1,dlm2,dph,glat,glon, &
1674	pi,r2d,row,tlat,tlat1,tlat2, &
1675	tlon,tlon1,tlon2,tph0,tlm0,x,y,z
1676
1677	glatd = lat
1678	glond = -lon
1679
1680	dphd = proj%phi/REAL((proj%jydim-1)/2)
1681	dlmd = proj%lambda/REAL(proj%ixdim-1)
1682
1683	pi = ACOS(-1.0)
1684	d2r = pi/180.
1685	r2d = 1./d2r
1686
1687	imt = 2*proj%ixdim-1
1688	jmt = proj%jydim/2+1
1689
1690	glat = glatd*d2r
1691	glon = glond*d2r
1692	dph = dphd*d2r
1693	dlm = dlmd*d2r
1694	tph0 = proj%lat1*d2r
1695	tlm0 = -proj%lon1*d2r
1696
1697	x = COS(tph0)COS(glat)COS(glon-tlm0)+SIN(tph0)*SIN(glat)
1698	y = -COS(glat)*SIN(glon-tlm0)
1699	z = COS(tph0)SIN(glat)-SIN(tph0)COS(glat)*COS(glon-tlm0)
1700	tlat = r2dATAN(z/SQRT(xx+y*y))
1701	tlon = r2d*ATAN(y/x)
1702
1703	row = tlat/dphd+jmt
1704	col = tlon/dlmd+proj%ixdim
1705
1706	if ( (row - INT(row)) .gt. 0.999) then
1707	row = row + 0.0002
1708	else if ( (col - INT(col)) .gt. 0.999) then
1709	col = col + 0.0002
1710	end if
1711
1712	nrow = INT(row)
1713	ncol = INT(col)
1714
1715	! nrow = NINT(row)
1716	! ncol = NINT(col)
1717
1718	tlat = tlat*d2r
1719	tlon = tlon*d2r
1720
1721
1722	IF (proj%stagger == HH) THEN
1723
1724	IF (mod(nrow,2) .eq. 0) then
1725	i_real = col / 2.0
1726	ELSE
1727	i_real = col / 2.0 + 0.5
1728	ENDIF
1729	j_real=row
1730
1731
1732	IF ((abs(MOD(nrow,2)) == 1 .AND. abs(MOD(ncol,2)) == 1) .OR. &
1733	(MOD(nrow,2) == 0 .AND. MOD(ncol,2) == 0)) THEN
1734
1735	tlat1 = (nrow-jmt)*dph
1736	tlat2 = tlat1+dph
1737	tlon1 = (ncol-proj%ixdim)*dlm
1738	tlon2 = tlon1+dlm
1739
1740	dlm1 = tlon-tlon1
1741	dlm2 = tlon-tlon2
1742	d1 = ACOS(COS(tlat)COS(tlat1)COS(dlm1)+SIN(tlat)*SIN(tlat1))
1743	d2 = ACOS(COS(tlat)COS(tlat2)COS(dlm2)+SIN(tlat)*SIN(tlat2))
1744
1745	IF (d1 > d2) THEN
1746	nrow = nrow+1
1747	ncol = ncol+1
1748	END IF
1749
1750	ELSE
1751	tlat1 = (nrow+1-jmt)*dph
1752	tlat2 = tlat1-dph
1753	tlon1 = (ncol-proj%ixdim)*dlm
1754	tlon2 = tlon1+dlm
1755	dlm1 = tlon-tlon1
1756	dlm2 = tlon-tlon2
1757	d1 = ACOS(COS(tlat)COS(tlat1)COS(dlm1)+SIN(tlat)*SIN(tlat1))
1758	d2 = ACOS(COS(tlat)COS(tlat2)COS(dlm2)+SIN(tlat)*SIN(tlat2))
1759
1760	IF (d1 < d2) THEN
1761	nrow = nrow+1
1762	ELSE
1763	ncol = ncol+1
1764	END IF
1765	END IF
1766
1767	ELSE IF (proj%stagger == VV) THEN
1768
1769	IF (mod(nrow,2) .eq. 0) then
1770	i_real = col / 2.0 + 0.5
1771	ELSE
1772	i_real = col / 2.0
1773	ENDIF
1774	j_real=row
1775
1776	IF ((MOD(nrow,2) == 0 .AND. abs(MOD(ncol,2)) == 1) .OR. &
1777	(abs(MOD(nrow,2)) == 1 .AND. MOD(ncol,2) == 0)) THEN
1778	tlat1 = (nrow-jmt)*dph
1779	tlat2 = tlat1+dph
1780	tlon1 = (ncol-proj%ixdim)*dlm
1781	tlon2 = tlon1+dlm
1782	dlm1 = tlon-tlon1
1783	dlm2 = tlon-tlon2
1784	d1 = ACOS(COS(tlat)COS(tlat1)COS(dlm1)+SIN(tlat)*SIN(tlat1))
1785	d2 = ACOS(COS(tlat)COS(tlat2)COS(dlm2)+SIN(tlat)*SIN(tlat2))
1786
1787	IF (d1 > d2) THEN
1788	nrow = nrow+1
1789	ncol = ncol+1
1790	END IF
1791
1792	ELSE
1793	tlat1 = (nrow+1-jmt)*dph
1794	tlat2 = tlat1-dph
1795	tlon1 = (ncol-proj%ixdim)*dlm
1796	tlon2 = tlon1+dlm
1797	dlm1 = tlon-tlon1
1798	dlm2 = tlon-tlon2
1799	d1 = ACOS(COS(tlat)COS(tlat1)COS(dlm1)+SIN(tlat)*SIN(tlat1))
1800	d2 = ACOS(COS(tlat)COS(tlat2)COS(dlm2)+SIN(tlat)*SIN(tlat2))
1801
1802	IF (d1 < d2) THEN
1803	nrow = nrow+1
1804	ELSE
1805	ncol = ncol+1
1806	END IF
1807	END IF
1808	END IF
1809
1810
1811	!!! Added next line as a Kludge - not yet understood why needed
1812	if (ncol .le. 0) ncol=ncol-1
1813
1814	jj = nrow
1815	ii = ncol/2
1816
1817	IF (proj%stagger == HH) THEN
1818	IF (abs(MOD(jj,2)) == 1) ii = ii+1
1819	ELSE IF (proj%stagger == VV) THEN
1820	IF (MOD(jj,2) == 0) ii=ii+1
1821	END IF
1822
1823	i = REAL(ii)
1824	j = REAL(jj)
1825
1826	END SUBROUTINE llij_rotlatlon
1827
1828
1829	SUBROUTINE ijll_rotlatlon(i, j, proj, lat,lon)
1830
1831	IMPLICIT NONE
1832
1833	! Arguments
1834	REAL, INTENT(IN) :: i, j
1835	REAL, INTENT(OUT) :: lat, lon
1836	TYPE (proj_info), INTENT(IN) :: proj
1837
1838	! Local variables
1839	INTEGER :: ih,jh
1840	INTEGER :: midcol,midrow,ncol,iadd1,iadd2,imt,jh2,knrow,krem,kv,nrow
1841	REAL :: i_work, j_work
1842	REAL :: dphd,dlmd !Grid increments, degrees
1843	REAL(KIND=HIGH) :: arg1,arg2,d2r,fctr,glatr,glatd,glond,pi, &
1844	r2d,tlatd,tlond,tlatr,tlonr,tlm0,tph0
1845	REAL :: col
1846
1847	i_work = i
1848	j_work = j
1849
1850	if ( (j - INT(j)) .gt. 0.999) then
1851	j_work = j + 0.0002
1852	endif
1853
1854	jh = INT(j_work)
1855
1856	dphd = proj%phi/REAL((proj%jydim-1)/2)
1857	dlmd = proj%lambda/REAL(proj%ixdim-1)
1858
1859	pi = ACOS(-1.0)
1860	d2r = pi/180.
1861	r2d = 1./d2r
1862	tph0 = proj%lat1*d2r
1863	tlm0 = -proj%lon1*d2r
1864
1865	midrow = (proj%jydim+1)/2
1866	midcol = proj%ixdim
1867
1868	col = 2*i_work-1+abs(MOD(jh+1,2))
1869	tlatd = (j_work-midrow)*dphd
1870	tlond = (col-midcol)*dlmd
1871
1872	IF (proj%stagger == VV) THEN
1873	if (mod(jh,2) .eq. 0) then
1874	tlond = tlond - DLMD
1875	else
1876	tlond = tlond + DLMD
1877	end if
1878	END IF
1879
1880	tlatr = tlatd*d2r
1881	tlonr = tlond*d2r
1882	arg1 = SIN(tlatr)COS(tph0)+COS(tlatr)SIN(tph0)*COS(tlonr)
1883	glatr = ASIN(arg1)
1884
1885	glatd = glatr*r2d
1886
1887	arg2 = COS(tlatr)COS(tlonr)/(COS(glatr)COS(tph0))-TAN(glatr)*TAN(tph0)
1888	IF (ABS(arg2) > 1.) arg2 = ABS(arg2)/arg2
1889	fctr = 1.
1890	IF (tlond > 0.) fctr = -1.
1891
1892	glond = tlm0r2d+fctrACOS(arg2)*r2d
1893
1894	lat = glatd
1895	lon = -glond
1896
1897	IF (lon .GT. +180.) lon = lon - 360.
1898	IF (lon .LT. -180.) lon = lon + 360.
1899
1900	END SUBROUTINE ijll_rotlatlon
1901
1902
1903	SUBROUTINE set_gauss(proj)
1904
1905	IMPLICIT NONE
1906
1907	! Argument
1908	type (proj_info), intent(inout) :: proj
1909
1910	! Initialize the array that will hold the Gaussian latitudes.
1911
1912	IF ( ASSOCIATED( proj%gauss_lat ) ) THEN
1913	DEALLOCATE ( proj%gauss_lat )
1914	END IF
1915
1916	! Get the needed space for our array.
1917
1918	ALLOCATE ( proj%gauss_lat(proj%nlat*2) )
1919
1920	! Compute the Gaussian latitudes.
1921
1922	CALL gausll( proj%nlat*2 , proj%gauss_lat )
1923
1924	! Now, these could be upside down from what we want, so let's check.
1925	! We take advantage of the equatorial symmetry to remove any sort of
1926	! array re-ordering.
1927
1928	IF ( ABS(proj%gauss_lat(1) - proj%lat1) .GT. 0.01 ) THEN
1929	proj%gauss_lat = -1. * proj%gauss_lat
1930	END IF
1931
1932	! Just a sanity check.
1933
1934	IF ( ABS(proj%gauss_lat(1) - proj%lat1) .GT. 0.01 ) THEN
1935	PRINT '(A)','Oops, something is not right with the Gaussian latitude computation.'
1936	PRINT '(A,F8.3,A)','The input data gave the starting latitude as ',proj%lat1,'.'
1937	PRINT '(A,F8.3,A)','This routine computed the starting latitude as +-',ABS(proj%gauss_lat(1)),'.'
1938	PRINT '(A,F8.3,A)','The difference is larger than 0.01 degrees, which is not expected.'
1939	CALL wrf_error_fatal ( 'Gaussian_latitude_computation' )
1940	END IF
1941
1942	END SUBROUTINE set_gauss
1943
1944
1945	SUBROUTINE gausll ( nlat , lat_sp )
1946
1947	IMPLICIT NONE
1948
1949	INTEGER :: nlat , i
1950	REAL (KIND=HIGH) , PARAMETER :: pi = 3.141592653589793
1951	REAL (KIND=HIGH) , DIMENSION(nlat) :: cosc , gwt , sinc , colat , wos2 , lat
1952	REAL , DIMENSION(nlat) :: lat_sp
1953
1954	CALL lggaus(nlat, cosc, gwt, sinc, colat, wos2)
1955
1956	DO i = 1, nlat
1957	lat(i) = ACOS(sinc(i)) * 180._HIGH / pi
1958	IF (i.gt.nlat/2) lat(i) = -lat(i)
1959	END DO
1960
1961	lat_sp = REAL(lat)
1962
1963	END SUBROUTINE gausll
1964
1965
1966	SUBROUTINE lggaus( nlat, cosc, gwt, sinc, colat, wos2 )
1967
1968	IMPLICIT NONE
1969
1970	! LGGAUS finds the Gaussian latitudes by finding the roots of the
1971	! ordinary Legendre polynomial of degree NLAT using Newton's
1972	! iteration method.
1973
1974	! On entry:
1975	integer NLAT ! the number of latitudes (degree of the polynomial)
1976
1977	! On exit: for each Gaussian latitude
1978	! COSC - cos(colatitude) or sin(latitude)
1979	! GWT - the Gaussian weights
1980	! SINC - sin(colatitude) or cos(latitude)
1981	! COLAT - the colatitudes in radians
1982	! WOS2 - Gaussian weight over sin**2(colatitude)
1983
1984	REAL (KIND=HIGH) , DIMENSION(nlat) :: cosc , gwt , sinc , colat , wos2
1985	REAL (KIND=HIGH) , PARAMETER :: pi = 3.141592653589793
1986
1987	! Convergence criterion for iteration of cos latitude
1988
1989	REAL , PARAMETER :: xlim = 1.0E-14
1990
1991	INTEGER :: nzero, i, j
1992	REAL (KIND=HIGH) :: fi, fi1, a, b, g, gm, gp, gt, delta, c, d
1993
1994	! The number of zeros between pole and equator
1995
1996	nzero = nlat/2
1997
1998	! Set first guess for cos(colat)
1999
2000	DO i=1,nzero
2001	cosc(i) = SIN( (i-0.5)pi/nlat + pi0.5 )
2002	END DO
2003
2004	! Constants for determining the derivative of the polynomial
2005	fi = nlat
2006	fi1 = fi+1.0
2007	a = fifi1 / SQRT(4.0fi1*fi1-1.0)
2008	b = fi1fi / SQRT(4.0fi*fi-1.0)
2009
2010	! Loop over latitudes, iterating the search for each root
2011
2012	DO i=1,nzero
2013	j=0
2014
2015	! Determine the value of the ordinary Legendre polynomial for
2016	! the current guess root
2017
2018	DO
2019	CALL lgord( g, cosc(i), nlat )
2020
2021	! Determine the derivative of the polynomial at this point
2022
2023	CALL lgord( gm, cosc(i), nlat-1 )
2024	CALL lgord( gp, cosc(i), nlat+1 )
2025	gt = (cosc(i)cosc(i)-1.0) / (agp-b*gm)
2026
2027	! Update the estimate of the root
2028
2029	delta = g*gt
2030	cosc(i) = cosc(i) - delta
2031
2032	! If convergence criterion has not been met, keep trying
2033
2034	j = j+1
2035	IF( ABS(delta).GT.xlim ) CYCLE
2036
2037	! Determine the Gaussian weights
2038
2039	c = 2.0 ( 1.0-cosc(i)cosc(i) )
2040	CALL lgord( d, cosc(i), nlat-1 )
2041	d = ddfi*fi
2042	gwt(i) = c *( fi-0.5 ) / d
2043	EXIT
2044
2045	END DO
2046
2047	END DO
2048
2049	! Determine the colatitudes and sin(colat) and weights over sin**2
2050
2051	DO i=1,nzero
2052	colat(i)= ACOS(cosc(i))
2053	sinc(i) = SIN(colat(i))
2054	wos2(i) = gwt(i) /( sinc(i)*sinc(i) )
2055	END DO
2056
2057	! If NLAT is odd, set values at the equator
2058
2059	IF( MOD(nlat,2) .NE. 0 ) THEN
2060	i = nzero+1
2061	cosc(i) = 0.0
2062	c = 2.0
2063	CALL lgord( d, cosc(i), nlat-1 )
2064	d = ddfi*fi
2065	gwt(i) = c *( fi-0.5 ) / d
2066	colat(i)= pi*0.5
2067	sinc(i) = 1.0
2068	wos2(i) = gwt(i)
2069	END IF
2070
2071	! Determine the southern hemisphere values by symmetry
2072
2073	DO i=nlat-nzero+1,nlat
2074	cosc(i) =-cosc(nlat+1-i)
2075	gwt(i) = gwt(nlat+1-i)
2076	colat(i)= pi-colat(nlat+1-i)
2077	sinc(i) = sinc(nlat+1-i)
2078	wos2(i) = wos2(nlat+1-i)
2079	END DO
2080
2081	END SUBROUTINE lggaus
2082
2083
2084	SUBROUTINE lgord( f, cosc, n )
2085
2086	IMPLICIT NONE
2087
2088	! LGORD calculates the value of an ordinary Legendre polynomial at a
2089	! specific latitude.
2090
2091	! On entry:
2092	! cosc - COS(colatitude)
2093	! n - the degree of the polynomial
2094
2095	! On exit:
2096	! f - the value of the Legendre polynomial of degree N at
2097	! latitude ASIN(cosc)
2098
2099	REAL (KIND=HIGH) :: s1, c4, a, b, fk, f, cosc, colat, c1, fn, ang
2100	INTEGER :: n, k
2101
2102	! Determine the colatitude
2103
2104	colat = ACOS(cosc)
2105
2106	c1 = SQRT(2.0_HIGH)
2107	DO k=1,n
2108	c1 = c1 * SQRT( 1.0 - 1.0/(4kk) )
2109	END DO
2110
2111	fn = n
2112	ang= fn * colat
2113	s1 = 0.0
2114	c4 = 1.0
2115	a =-1.0
2116	b = 0.0
2117	DO k=0,n,2
2118	IF (k.eq.n) c4 = 0.5 * c4
2119	s1 = s1 + c4 * COS(ang)
2120	a = a + 2.0
2121	b = b + 1.0
2122	fk = k
2123	ang= colat * (fn-fk-2.0)
2124	c4 = ( a * (fn-b+1.0) / ( b * (fn+fn-a) ) ) * c4
2125	END DO
2126
2127	f = s1 * c1
2128
2129	END SUBROUTINE lgord
2130
2131
2132	SUBROUTINE llij_gauss (lat, lon, proj, i, j)
2133
2134	IMPLICIT NONE
2135
2136	REAL , INTENT(IN) :: lat, lon
2137	REAL , INTENT(OUT) :: i, j
2138	TYPE (proj_info), INTENT(IN) :: proj
2139
2140	INTEGER :: n , n_low
2141	LOGICAL :: found = .FALSE.
2142	REAL :: diff_1 , diff_nlat
2143
2144	! The easy one first, get the x location. The calling routine has already made
2145	! sure that the necessary assumptions concerning the sign of the deltalon and the
2146	! relative east/west'ness of the longitude and the starting longitude are consistent
2147	! to allow this easy computation.
2148
2149	i = ( lon - proj%lon1 ) / proj%loninc + 1.
2150
2151	! Since this is a global data set, we need to be concerned about wrapping the
2152	! fields around the globe.
2153
2154	! IF ( ( proj%loninc .GT. 0 ) .AND. &
2155	! ( FLOOR((lon-proj%lon1)/proj%loninc) + 1 .GE. proj%ixdim ) .AND. &
2156	! ( lon + proj%loninc .GE. proj%lon1 + 360 ) ) THEN
2157	!! BUG: We may need to set proj%wrap, but proj is intent(in)
2158	!! WHAT IS THIS USED FOR?
2159	!! proj%wrap = .TRUE.
2160	! i = proj%ixdim
2161	! ELSE IF ( ( proj%loninc .LT. 0 ) .AND. &
2162	! ( FLOOR((lon-proj%lon1)/proj%loninc) + 1 .GE. proj%ixdim ) .AND. &
2163	! ( lon + proj%loninc .LE. proj%lon1 - 360 ) ) THEN
2164	! ! BUG: We may need to set proj%wrap, but proj is intent(in)
2165	! ! WHAT IS THIS USED FOR?
2166	! ! proj%wrap = .TRUE.
2167	! i = proj%ixdim
2168	! END IF
2169
2170	! Yet another quicky test, can we find bounding values? If not, then we may be
2171	! dealing with putting data to a polar projection, so just give them them maximal
2172	! value for the location. This is an OK assumption for the interpolation across the
2173	! top of the pole, given how close the longitude lines are.
2174
2175	IF ( ABS(lat) .GT. ABS(proj%gauss_lat(1)) ) THEN
2176
2177	diff_1 = lat - proj%gauss_lat(1)
2178	diff_nlat = lat - proj%gauss_lat(proj%nlat*2)
2179
2180	IF ( ABS(diff_1) .LT. ABS(diff_nlat) ) THEN
2181	j = 1
2182	ELSE
2183	j = proj%nlat*2
2184	END IF
2185
2186	! If the latitude is between the two bounding values, we have to search and interpolate.
2187
2188	ELSE
2189
2190	DO n = 1 , proj%nlat*2 -1
2191	IF ( ( proj%gauss_lat(n) - lat ) * ( proj%gauss_lat(n+1) - lat ) .LE. 0 ) THEN
2192	found = .TRUE.
2193	n_low = n
2194	EXIT
2195	END IF
2196	END DO
2197
2198	! Everything still OK?
2199
2200	IF ( .NOT. found ) THEN
2201	PRINT '(A)','Troubles in river city. No bounding values of latitude found in the Gaussian routines.'
2202	CALL wrf_error_fatal ( 'Gee_no_bounding_lats_Gaussian' )
2203	END IF
2204
2205	j = ( ( proj%gauss_lat(n_low) - lat ) * ( n_low + 1 ) + &
2206	( lat - proj%gauss_lat(n_low+1) ) * ( n_low ) ) / &
2207	( proj%gauss_lat(n_low) - proj%gauss_lat(n_low+1) )
2208
2209	END IF
2210
2211	END SUBROUTINE llij_gauss
2212
2213	END MODULE module_llxy

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