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source: palm/trunk/UTIL/inifor/src/inifor_transform.f90 @ 3447

Last change on this file since 3447 was 3447, checked in by eckhard, 5 years ago
inifor: Renamed source files for compatibilty with PALM build system
Property svn:keywords set to `Id`
File size: 46.4 KB

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[3447]	1	!> @file src/inifor_transform.f90
[2696]	2	!------------------------------------------------------------------------------!
[2718]	3	! This file is part of the PALM model system.
[2696]	4	!
[2718]	5	! PALM is free software: you can redistribute it and/or modify it under the
	6	! terms of the GNU General Public License as published by the Free Software
	7	! Foundation, either version 3 of the License, or (at your option) any later
[2696]	8	! version.
	9	!
[2718]	10	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
	11	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	12	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
[2696]	13	!
	14	! You should have received a copy of the GNU General Public License along with
	15	! PALM. If not, see <http://www.gnu.org/licenses/>.
	16	!
[2718]	17	! Copyright 2017-2018 Leibniz Universitaet Hannover
	18	! Copyright 2017-2018 Deutscher Wetterdienst Offenbach
[2696]	19	!------------------------------------------------------------------------------!
	20	!
	21	! Current revisions:
	22	! -----------------
[3183]	23	!
	24	!
	25	! Former revisions:
	26	! -----------------
	27	! $Id: inifor_transform.f90 3447 2018-10-29 15:52:54Z eckhard $
[3447]	28	! Renamed source files for compatibilty with PALM build system
	29	!
	30	!
	31	! 3395 2018-10-22 17:32:49Z eckhard
[3395]	32	! Switched addressing of averaging regions from index bounds to list of columns
	33	! Added routines for the computation of geostrophic winds including:
	34	! - the downward extrapolation of density (linear) and
	35	! - pressure (hydrostatic equation) and
	36	! - rotation of geostrophic wind components to PALM frame of reference
	37	!
	38	! 3183 2018-07-27 14:25:55Z suehring
[3182]	39	! Introduced new PALM grid stretching
	40	! Removed unnecessary subroutine parameters
	41	! Renamed kcur to k_intermediate
[2696]	42	!
	43	!
[3183]	44	! 3182 2018-07-27 13:36:03Z suehring
[2696]	45	! Initial revision
	46	!
	47	!
	48	!
	49	! Authors:
	50	! --------
	51	! @author Eckhard Kadasch
	52	!
	53	! Description:
	54	! ------------
	55	!> The transform module provides INIFOR's low-level transformation and
	56	!> interpolation routines. The rotated-pole transformation routines phirot2phi,
	57	!> phi2phirot, rlarot2rla, rla2rlarot, uv2uvrot, and uvrot2uv are adapted from
	58	!> int2lm's utility routines.
	59	!------------------------------------------------------------------------------!
	60	MODULE transform
	61
	62	USE control
	63	USE defs, &
[3395]	64	ONLY: G, TO_DEGREES, TO_RADIANS, PI, dp
[2696]	65	USE types
	66	USE util, &
	67	ONLY: real_to_str, str
	68
	69	IMPLICIT NONE
	70
	71	CONTAINS
	72
	73	!------------------------------------------------------------------------------!
	74	! Description:
	75	! ------------
	76	!> Interpolates linearly in the vertical direction in very column (i,j) of the
	77	!> output array outvar(i,j,:) using values of the source array invar. In cells
	78	!> that are outside the COSMO-DE domain, indicated by negative interpolation
	79	!> weights, extrapolate constantly from the cell above.
	80	!>
	81	!> Input parameters:
	82	!> -----------------
	83	!> invar : Array of source data
	84	!>
	85	!> outgrid % kk : Array of vertical neighbour indices. kk(i,j,k,:) contain the
	86	!> indices of the two vertical neighbors of PALM-4U point (i,j,k) on the
	87	!> input grid corresponding to the source data invar.
	88	!>
	89	!> outgrid % w_verti : Array of weights for vertical linear interpolation
	90	!> corresponding to neighbour points indexed by kk.
	91	!>
	92	!> Output papameters:
	93	!> ------------------
	94	!> outvar : Array of interpolated data
	95	!------------------------------------------------------------------------------!
	96	SUBROUTINE interpolate_1d(in_arr, out_arr, outgrid)
	97	TYPE(grid_definition), INTENT(IN) :: outgrid
	98	REAL(dp), INTENT(IN) :: in_arr(0:,0:,0:)
[3182]	99	REAL(dp), INTENT(OUT) :: out_arr(0:,0:,:)
[2696]	100
[3182]	101	INTEGER :: i, j, k, l, nz
[2696]	102
	103	nz = UBOUND(out_arr, 3)
	104
[3182]	105	DO j = LBOUND(out_arr, 2), UBOUND(out_arr, 2)
	106	DO i = LBOUND(out_arr, 1), UBOUND(out_arr, 1)
	107	DO k = nz, LBOUND(out_arr, 3), -1
[2696]	108
	109	! TODO: Remove IF clause and extrapolate based on a critical vertical
	110	! TODO: index marking the lower bound of COSMO-DE data coverage.
	111	! Check for negative interpolation weights indicating grid points
	112	! below COSMO-DE domain and extrapolate from the top in such cells.
	113	IF (outgrid % w_verti(i,j,k,1) < -1.0_dp .AND. k < nz) THEN
	114	out_arr(i,j,k) = out_arr(i,j,k+1)
	115	ELSE
	116	out_arr(i,j,k) = 0.0_dp
	117	DO l = 1, 2
[3182]	118	out_arr(i,j,k) = out_arr(i,j,k) + &
	119	outgrid % w_verti(i,j,k,l) * &
[2696]	120	in_arr(i,j,outgrid % kk(i,j,k, l) )
	121	END DO
	122	END IF
	123	END DO
	124	END DO
	125	END DO
	126	END SUBROUTINE interpolate_1d
	127
	128
	129	!------------------------------------------------------------------------------!
	130	! Description:
	131	! ------------
	132	!> Interpolates bi-linearly in horizontal planes on every k level of the output
	133	!> array outvar(:,:,k) using values of the source array invar(:,:,:). The source
	134	!> (invar) and interpolation array (outvar) need to have matching dimensions.
	135	!>
	136	!> Input parameters:
	137	!> -----------------
	138	!> invar : Array of source data
	139	!>
	140	!> outgrid % ii, % jj : Array of neighbour indices in x and y direction.
	141	!> ii(i,j,k,:), and jj(i,j,k,:) contain the four horizontal neighbour points
	142	!> of PALM-4U point (i,j,k) on the input grid corresponding to the source
	143	!> data invar. (The outgrid carries the relationship with the ingrid in the
	144	! form of the interpoaltion weights.)
	145	!>
	146	!> outgrid % w_horiz: Array of weights for horizontal bi-linear interpolation
	147	!> corresponding to neighbour points indexed by ii and jj.
	148	!>
	149	!> Output papameters:
	150	!> ------------------
	151	!> outvar : Array of interpolated data
	152	!------------------------------------------------------------------------------!
	153	SUBROUTINE interpolate_2d(invar, outvar, outgrid, ncvar)
	154	! I index 0-based for the indices of the outvar to be consistent with the
	155	! outgrid indices and interpolation weights.
[3182]	156	TYPE(grid_definition), INTENT(IN) :: outgrid
	157	REAL(dp), INTENT(IN) :: invar(0:,0:,0:)
	158	REAL(dp), INTENT(OUT) :: outvar(0:,0:,0:)
[2696]	159	TYPE(nc_var), INTENT(IN), OPTIONAL :: ncvar
	160
	161	INTEGER :: i, j, k, l
	162
	163	! TODO: check if input dimensions are consistent, i.e. ranges are correct
	164	IF (UBOUND(outvar, 3) .GT. UBOUND(invar, 3)) THEN
	165	message = "Output array for '" // TRIM(ncvar % name) // "' has ' more levels (" // &
	166	TRIM(str(UBOUND(outvar, 3))) // ") than input variable ("//&
	167	TRIM(str(UBOUND(invar, 3))) // ")."
	168	CALL abort('interpolate_2d', message)
	169	END IF
	170
	171	DO k = 0, UBOUND(outvar, 3)
	172	DO j = 0, UBOUND(outvar, 2)
	173	DO i = 0, UBOUND(outvar, 1)
	174	outvar(i,j,k) = 0.0_dp
	175	DO l = 1, 4
	176
	177	outvar(i,j,k) = outvar(i,j,k) + &
	178	outgrid % w_horiz(i,j,l) * invar( outgrid % ii(i,j,l), &
	179	outgrid % jj(i,j,l), &
	180	k )
	181	END DO
	182	END DO
	183	END DO
	184	END DO
	185
	186	END SUBROUTINE interpolate_2d
	187
	188
[3395]	189	SUBROUTINE average_2d(in_arr, out_arr, ii, jj)
	190	REAL(dp), INTENT(IN) :: in_arr(0:,0:,0:)
	191	REAL(dp), INTENT(OUT) :: out_arr(0:)
	192	INTEGER, INTENT(IN), DIMENSION(:) :: ii, jj
[2696]	193
[3395]	194	INTEGER :: i, j, k, l
[2696]	195	REAL(dp) :: ni
	196
[3395]	197	IF (SIZE(ii) .NE. SIZE(jj)) THEN
	198	message = "Length of 'ii' and 'jj' index lists do not match." // &
	199	NEW_LINE(' ') // "ii has " // str(SIZE(ii)) // " elements, " // &
	200	NEW_LINE(' ') // "jj has " // str(SIZE(jj)) // "."
	201	CALL abort('average_2d', message)
	202	END IF
	203
[2696]	204	DO k = 0, UBOUND(out_arr, 1)
	205
	206	out_arr(k) = 0.0_dp
[3395]	207	DO l = 1, UBOUND(ii, 1)
	208	i = ii(l)
	209	j = jj(l)
	210	out_arr(k) = out_arr(k) +&
	211	in_arr(i, j, k)
[2696]	212	END DO
	213
	214	END DO
[3395]	215
	216	ni = 1.0_dp / SIZE(ii)
[2696]	217	out_arr(:) = out_arr(:) * ni
	218
	219	END SUBROUTINE average_2d
	220
	221
	222	SUBROUTINE interpolate_3d(source_array, palm_array, palm_intermediate, palm_grid)
	223	TYPE(grid_definition), INTENT(IN) :: palm_intermediate, palm_grid
	224	REAL(dp), DIMENSION(:,:,:), INTENT(IN) :: source_array
	225	REAL(dp), DIMENSION(:,:,:), INTENT(OUT) :: palm_array
	226	REAL(dp), DIMENSION(:,:,:), ALLOCATABLE :: intermediate_array
[3395]	227	INTEGER :: nx, ny, nlev
[2696]	228
	229	nx = palm_intermediate % nx
	230	ny = palm_intermediate % ny
[3395]	231	nlev = palm_intermediate % nz ! nlev
[2696]	232
	233	! Interpolate from COSMO-DE to intermediate grid. Allocating with one
	234	! less point in the vertical, since scalars like T have 50 instead of 51
	235	! points in COSMO-DE.
[3395]	236	ALLOCATE(intermediate_array(0:nx, 0:ny, 0:nlev-1)) !
[2696]	237
	238	CALL interpolate_2d(source_array, intermediate_array, palm_intermediate)
	239
	240	! Interpolate from intermediate grid to palm_grid grid, includes
	241	! extrapolation for cells below COSMO-DE domain.
	242	CALL interpolate_1d(intermediate_array, palm_array, palm_grid)
	243
	244	DEALLOCATE(intermediate_array)
	245
	246	END SUBROUTINE interpolate_3d
	247
	248
[3395]	249	SUBROUTINE average_profile(source_array, profile_array, avg_grid)
	250	TYPE(grid_definition), INTENT(IN) :: avg_grid
[2696]	251	REAL(dp), DIMENSION(:,:,:), INTENT(IN) :: source_array
[3395]	252	REAL(dp), DIMENSION(:), INTENT(OUT) :: profile_array
[2696]	253
[3395]	254	INTEGER :: i_source, j_source, k_profile, k_source, l, m
[2696]	255
[3395]	256	REAL :: ni_columns
[2696]	257
[3395]	258	profile_array(:) = 0.0_dp
[2696]	259
[3395]	260	DO l = 1, avg_grid % n_columns
	261	i_source = avg_grid % iii(l)
	262	j_source = avg_grid % jjj(l)
[2696]	263
[3395]	264	DO k_profile = avg_grid % k_min, UBOUND(profile_array, 1) ! PALM levels
	265
	266	DO m = 1, 2 ! vertical interpolation neighbours
	267
	268	k_source = avg_grid % kkk(l, k_profile, m)
	269
	270	profile_array(k_profile) = profile_array(k_profile) &
	271	+ avg_grid % w(l, k_profile, m) &
	272	* source_array(i_source, j_source, k_source)
	273
	274	END DO ! m, vertical interpolation neighbours
	275
	276	END DO ! k_profile, PALM levels
	277
	278	END DO ! l, horizontal neighbours
	279
	280	ni_columns = 1.0_dp / avg_grid % n_columns
	281	profile_array(:) = profile_array(:) * ni_columns
	282
	283	! Extrapolate constant to the bottom
	284	profile_array(1:avg_grid % k_min-1) = profile_array(avg_grid % k_min)
	285
[2696]	286	END SUBROUTINE average_profile
	287
	288
[3395]	289	SUBROUTINE extrapolate_density(rho, avg_grid)
	290	REAL(dp), DIMENSION(:), INTENT(INOUT) :: rho
	291	TYPE(grid_definition), INTENT(IN) :: avg_grid
[2696]	292
[3395]	293	REAL(dp) :: drhodz, dz, zk, rhok
	294	INTEGER :: k_min
	295
	296	k_min = avg_grid % k_min
	297	zk = avg_grid % z(k_min)
	298	rhok = rho(k_min)
	299	dz = avg_grid % z(k_min + 1) - avg_grid % z(k_min)
	300	drhodz = (rho(k_min + 1) - rho(k_min)) / dz
	301
	302	rho(1:k_min-1) = rhok + drhodz * (avg_grid % z(1:k_min-1) - zk)
	303
	304	END SUBROUTINE extrapolate_density
	305
	306
	307	SUBROUTINE extrapolate_pressure(p, rho, avg_grid)
	308	REAL(dp), DIMENSION(:), INTENT(IN) :: rho
	309	REAL(dp), DIMENSION(:), INTENT(INOUT) :: p
	310	TYPE(grid_definition), INTENT(IN) :: avg_grid
	311
	312	REAL(dp) :: drhodz, dz, zk, rhok
	313	INTEGER :: k, k_min
	314
	315	k_min = avg_grid % k_min
	316	zk = avg_grid % z(k_min)
	317	rhok = rho(k_min)
	318	dz = avg_grid % z(k_min + 1) - avg_grid % z(k_min)
	319	drhodz = 0.5_dp * (rho(k_min + 1) - rho(k_min)) / dz
	320
	321	DO k = 1, k_min-1
	322	p(k) = constant_density_pressure(p(k_min), zk, rhok, drhodz, &
	323	avg_grid % z(k), G)
	324	END DO
	325
	326	END SUBROUTINE extrapolate_pressure
	327
	328
	329	!------------------------------------------------------------------------------!
	330	! Description:
	331	! ------------
	332	!> Takes the averaged pressure profile <p> and sets the lowest entry to the
	333	!> extrapolated pressure at the surface.
	334	!------------------------------------------------------------------------------!
	335	SUBROUTINE get_surface_pressure(p, rho, avg_grid)
	336	REAL(dp), DIMENSION(:), INTENT(IN) :: rho
	337	REAL(dp), DIMENSION(:), INTENT(INOUT) :: p
	338	TYPE(grid_definition), INTENT(IN) :: avg_grid
	339
	340	REAL(dp) :: drhodz, dz, zk, rhok
	341	INTEGER :: k, k_min
	342
	343	k_min = avg_grid % k_min
	344	zk = avg_grid % z(k_min)
	345	rhok = rho(k_min)
	346	dz = avg_grid % z(k_min + 1) - avg_grid % z(k_min)
	347	drhodz = 0.5_dp * (rho(k_min + 1) - rho(k_min)) / dz
	348
	349	p(1) = constant_density_pressure(p(k_min), zk, rhok, drhodz, &
	350	0.0, G)
	351
	352	END SUBROUTINE get_surface_pressure
	353
	354
	355	FUNCTION constant_density_pressure(pk, zk, rhok, drhodz, z, g) RESULT(p)
	356
	357	REAL(dp), INTENT(IN) :: pk, zk, rhok, drhodz, g, z
	358	REAL(dp) :: p
	359
	360	p = pk + ( zk - z ) * g * ( rhok + 0.5drhodz (zk - z) )
	361
	362	END FUNCTION constant_density_pressure
	363
[2696]	364	!-----------------------------------------------------------------------------!
	365	! Description:
	366	! -----------
[3395]	367	!> This routine computes profiles of the two geostrophic wind components ug and
	368	!> vg.
	369	!-----------------------------------------------------------------------------!
	370	SUBROUTINE geostrophic_winds(p_north, p_south, p_east, p_west, rho, f3, &
	371	Lx, Ly, phi_n, lam_n, phi_g, lam_g, ug, vg)
	372
	373	REAL(dp), DIMENSION(:), INTENT(IN) :: p_north, p_south, p_east, p_west, &
	374	rho
	375	REAL(dp), INTENT(IN) :: f3, Lx, Ly, phi_n, lam_n, phi_g, lam_g
	376	REAL(dp), DIMENSION(:), INTENT(OUT) :: ug, vg
	377	REAL(dp) :: facx, facy
	378
	379	facx = 1.0_dp / (Lx * f3)
	380	facy = 1.0_dp / (Ly * f3)
	381	ug(:) = - facy / rho(:) * (p_north(:) - p_south(:))
	382	vg(:) = facx / rho(:) * (p_east(:) - p_west(:))
	383
	384	CALL rotate_vector_field( &
	385	ug, vg, angle = meridian_convergence_rotated(phi_n, lam_n, phi_g, lam_g)&
	386	)
	387
	388	END SUBROUTINE geostrophic_winds
	389
	390
	391	!-----------------------------------------------------------------------------!
	392	! Description:
	393	! -----------
[2696]	394	!> This routine computes the inverse Plate Carree projection, i.e. in projects
	395	!> Cartesian coordinates (x,y) onto a sphere. It returns the latitude and
	396	!> lngitude of a geographical system centered at x0 and y0.
	397	!-----------------------------------------------------------------------------!
	398	SUBROUTINE inv_plate_carree(x, y, x0, y0, r, lat, lon)
	399	REAL(dp), INTENT(IN) :: x(:), y(:), x0, y0, r
	400	REAL(dp), INTENT(OUT) :: lat(:), lon(:)
	401
	402	REAL(dp) :: ri
	403
	404	! TODO check dimensions of lat/lon and y/x match
	405
	406	ri = 1.0_dp / r
	407
	408	lat(:) = (y(:) - y0) * ri
	409	lon(:) = (x(:) - x0) * ri
	410	END SUBROUTINE
	411
	412
	413	!-----------------------------------------------------------------------------!
	414	! Description:
	415	! ------------
	416	!> Computes the reverse Plate-Carree projection of a x or y position on a
	417	!> Cartesian grid.
	418	!>
	419	!> Input parameters:
	420	!> -----------------
	421	!> xy : x or y coordinate of the Cartasian grid point [m].
	422	!>
	423	!> xy0 : x or y coordinate that coincides with the origin of the underlying
	424	!> sperical system (crossing point of the equator and prime meridian) [m].
	425	!>
	426	!> r : Radius of the of the underlying sphere, e.g. EARTH_RADIUS [m].
	427	!>
	428	!> Returns:
	429	!> --------
	430	!> project : Longitude (in case xy = x) or latitude (xy = y) of the given input
	431	!> coordinate xy.
	432	!------------------------------------------------------------------------------!
	433	ELEMENTAL REAL(dp) FUNCTION project(xy, xy0, r)
	434	REAL(dp), INTENT(IN) :: xy, xy0, r
	435	REAL(dp) :: ri
	436
	437	! If this elemental function is called with a large array as xy, it is
	438	! computationally more efficient to precompute the inverse radius and
	439	! then muliply.
	440	ri = 1.0_dp / r
	441
	442	project = (xy - xy0) * ri
	443
	444	END FUNCTION project
	445
	446
	447	REAL(dp) FUNCTION phic_to_phin(phi_c)
	448	REAL(dp), INTENT(IN) :: phi_c
	449
	450	phic_to_phin = 0.5_dp * PI - ABS(phi_c)
	451
	452	END FUNCTION phic_to_phin
	453
	454
	455	REAL(dp) FUNCTION lamc_to_lamn(phi_c, lam_c)
	456	REAL(dp), INTENT(IN) :: phi_c, lam_c
	457
	458	lamc_to_lamn = lam_c
	459	IF (phi_c > 0.0_dp) THEN
	460	lamc_to_lamn = lam_c - SIGN(PI, lam_c)
	461	END IF
	462
	463	END FUNCTION lamc_to_lamn
	464
	465
	466	REAL(dp) FUNCTION gamma_from_hemisphere(phi_cg, phi_ref)
	467	REAL(dp), INTENT(IN) :: phi_cg, phi_ref
	468	LOGICAL :: palm_centre_is_south_of_cosmo_origin
	469
	470	palm_centre_is_south_of_cosmo_origin = (phi_cg < phi_ref)
	471
	472	IF (palm_centre_is_south_of_cosmo_origin) THEN
	473	gamma_from_hemisphere = PI
	474	ELSE
	475	gamma_from_hemisphere = 0.0_dp
	476	END IF
	477	END FUNCTION gamma_from_hemisphere
	478
	479
	480	!------------------------------------------------------------------------------!
	481	! Description:
	482	! ------------
	483	!> Computes the geographical coordinates corresponding to the given rotated-pole
	484	!> coordinates.
	485	!>
	486	!> In INIFOR, this routine is used to convert coordinates between two
	487	!> rotated-pole systems: COSMO-DE's rotated-pole system, and one centred at the
	488	!> PALM-4U domain centre. In this case, the PALM-4U system is thought of as the
	489	!> rotated-pole system and the routine is used to rotate back to COSMO-DE's
	490	!> system which is thought of as the geographical one.
	491	!>
	492	!> Input parameters:
	493	!> -----------------
	494	!> phir(:), lamr(: ): latitudes and longitudes of the rotated-pole grid
	495	!>
	496	!> phip, lamp: latitude and longitude of the rotated north pole
	497	!>
	498	!> gam: "angle between the north poles. If [gam] is not present, the other
	499	!> system is the real geographical system." (original phiro2rot
	500	!> description)
	501	!>
	502	!> Output parameters:
	503	!> ------------------
	504	!> phi(:,:), lam(:,:): geographical latitudes and logitudes
	505	!------------------------------------------------------------------------------!
	506	SUBROUTINE rotate_to_cosmo(phir, lamr, phip, lamp, phi, lam, gam)
	507	REAL(dp), INTENT(IN) :: phir(0:), lamr(0:), phip, lamp, gam
	508	REAL(dp), INTENT(OUT) :: phi(0:,0:), lam(0:,0:)
	509
	510	INTEGER :: i, j
	511
	512	IF ( SIZE(phi, 1) .NE. SIZE(lam, 1) .OR. &
	513	SIZE(phi, 2) .NE. SIZE(lam, 2) ) THEN
	514	PRINT *, "inifor: rotate_to_cosmo: Dimensions of phi and lambda do not match. Dimensions are:"
	515	PRINT *, "inifor: rotate_to_cosmo: phi: ", SIZE(phi, 1), SIZE(phi, 2)
	516	PRINT *, "inifor: rotate_to_cosmo: lam: ", SIZE(lam, 1), SIZE(lam, 2)
	517	STOP
	518	END IF
	519
	520	IF ( SIZE(phir) .NE. SIZE(phi, 2) .OR. &
	521	SIZE(lamr) .NE. SIZE(phi, 1) ) THEN
	522	PRINT *, "inifor: rotate_to_cosmo: Dimensions of phir and lamr do not match. Dimensions are:"
	523	PRINT *, "inifor: rotate_to_cosmo: phir: ", SIZE(phir), SIZE(phi, 2)
	524	PRINT *, "inifor: rotate_to_cosmo: lamr: ", SIZE(lamr), SIZE(phi, 1)
	525	STOP
	526	END IF
	527
	528	DO j = 0, UBOUND(phir, 1)
	529	DO i = 0, UBOUND(lamr, 1)
	530
	531	phi(i,j) = phirot2phi(phir(j) * TO_DEGREES, &
	532	lamr(i) * TO_DEGREES, &
	533	phip * TO_DEGREES, &
	534	lamp * TO_DEGREES, &
	535	gam * TO_DEGREES) * TO_RADIANS
	536
	537	lam(i,j) = rlarot2rla(phir(j) * TO_DEGREES, &
	538	lamr(i) * TO_DEGREES, &
	539	phip * TO_DEGREES, &
	540	lamp * TO_DEGREES, &
	541	gam * TO_DEGREES) * TO_RADIANS
	542
	543	END DO
	544	END DO
	545
	546	END SUBROUTINE rotate_to_cosmo
[3182]	547
[2696]	548
[3395]	549	SUBROUTINE rotate_vector_field(x, y, angle)
	550	REAL(dp), DIMENSION(:), INTENT(INOUT) :: x, y !< x and y coodrinate in arbitrary units
	551	REAL(dp), INTENT(IN) :: angle !< rotation angle [deg]
[2696]	552
[3395]	553	INTEGER :: i
	554	REAL(dp) :: sine, cosine, v_rot(2), rotation(2,2)
	555
	556	sine = SIN(angle * TO_RADIANS)
	557	cosine = COS(angle * TO_RADIANS)
	558	! RESAHPE() fills columns first, so the rotation matrix becomes
	559	!
	560	! rotation = [ cosine -sine ]
	561	! [ sine cosine ]
	562	rotation = RESHAPE( (/cosine, sine, -sine, cosine/), (/2, 2/) )
	563
	564	DO i = LBOUND(x, 1), UBOUND(x, 1)
	565
	566	v_rot(:) = MATMUL(rotation, (/x(i), y(i)/))
	567
	568	x(i) = v_rot(1)
	569	y(i) = v_rot(2)
	570
	571	END DO
	572
	573	END SUBROUTINE rotate_vector_field
	574
	575
	576
[2696]	577	!------------------------------------------------------------------------------!
	578	! Description:
	579	! ------------
[3395]	580	!> This routine computes the local meridian convergence between a rotated-pole
	581	!> and a geographical system using the Eq. (6) given in the DWD manual
	582	!>
	583	!> Baldauf et al. (2018), Beschreibung des operationelle KuÌrzestfrist-
	584	!> vorhersagemodells COSMO-D2 und COSMO-D2-EPS und seiner Ausgabe in die
	585	!> Datenbanken des DWD.
	586	!> https://www.dwd.de/SharedDocs/downloads/DE/modelldokumentationen/nwv/cosmo_d2/cosmo_d2_dbbeschr_aktuell.pdf?__blob=publicationFile&v=2
	587	!>
	588	FUNCTION meridian_convergence_rotated(phi_n, lam_n, phi_g, lam_g) &
	589	RESULT(delta)
	590
	591	REAL(dp), INTENT(IN) :: phi_n, lam_n, phi_g, lam_g
	592	REAL(dp) :: delta
	593
	594	delta = atan2( COS(phi_n) * SIN(lam_n - lam_g), &
	595	COS(phi_g) * SIN(phi_n) - &
	596	SIN(phi_g) * COS(phi_n) * COS(lam_n - lam_g) )
	597
	598	END FUNCTION meridian_convergence_rotated
	599
	600	!------------------------------------------------------------------------------!
	601	! Description:
	602	! ------------
[2696]	603	!> Compute indices of PALM-4U grid point neighbours in the target
	604	!> system (COSMO-DE) by rounding up and down. (i,j) are the indices of
	605	!> the PALM-4U grid and (ii(i,j,1-4), jj(i,j,1-4)) contain the indices
	606	!> of the its four neigbouring points in the COSMO-DE grid.
	607	!>
	608	!>
	609	!> COSMO-DE grid
	610	!> -------------
	611	!> jj, lat
[3182]	612	!> ^ j
	613	!> \| \ i
[2696]	614	!> jj(i,j,2/3) + ... 2 ---\--------/------ 3
	615	!> \| \| ^ \ / \|
	616	!> \| \| \|wp \ / \|
	617	!> \| \| v \ / \|
	618	!> latpos + ............ o/ (i,j) \|
	619	!> \| \| : \|
	620	!> \| \| :<----wl---->\|
	621	!> jj(i,j,1/4) + ... 1 -------:----------- 4
	622	!> \| : : :
	623	!> \| : : :
	624	!> \| : lonpos :
	625	!> L-----+--------+------------+------> ii, lon
	626	!> ii(i,j,1/2) ii(i,j,3/4)
	627	!>
	628	!>
	629	!> Input parameters:
	630	!> -----------------
	631	!> source_lat, source_lon : (rotated-pole) coordinates of the source grid (e.g.
	632	!> COSMO-DE)
	633	!>
	634	!> source_dxi, source_dyi : inverse grid spacings of the source grid.
	635	!>
	636	!> target_lat, target_lon : (rotated-pole) coordinates of the target grid (e.g.
	637	!> COSMO-DE)
	638	!>
	639	!> Output parameters:
	640	!> ------------------
	641	!> palm_ii, palm_jj : x and y index arrays of horizontal neighbour columns
	642	!>
	643	!------------------------------------------------------------------------------!
[3182]	644	SUBROUTINE find_horizontal_neighbours(cosmo_lat, cosmo_lon, &
	645	palm_clat, palm_clon, &
	646	palm_ii, palm_jj)
[2696]	647
	648	REAL(dp), DIMENSION(0:), INTENT(IN) :: cosmo_lat, cosmo_lon
	649	REAL(dp), DIMENSION(0:,0:), INTENT(IN) :: palm_clat, palm_clon
[3182]	650	REAL(dp) :: cosmo_dxi, cosmo_dyi
[2696]	651	INTEGER, DIMENSION(0:,0:,1:), INTENT(OUT) :: palm_ii, palm_jj
	652
	653	REAL(dp) :: lonpos, latpos, lon0, lat0
	654	INTEGER :: i, j
	655
	656	lon0 = cosmo_lon(0)
	657	lat0 = cosmo_lat(0)
[3182]	658	cosmo_dxi = 1.0_dp / (cosmo_lon(1) - cosmo_lon(0))
	659	cosmo_dyi = 1.0_dp / (cosmo_lat(1) - cosmo_lat(0))
[2696]	660
	661	DO j = 0, UBOUND(palm_clon, 2)!palm_grid % ny
	662	DO i = 0, UBOUND(palm_clon, 1)!palm_grid % nx
	663	! Compute the floating point index corrseponding to PALM-4U grid point
	664	! location along target grid (COSMO-DE) axes.
	665	lonpos = (palm_clon(i,j) - lon0) * cosmo_dxi
	666	latpos = (palm_clat(i,j) - lat0) * cosmo_dyi
	667
	668	IF (lonpos < 0.0 .OR. latpos < 0.0) THEN
	669	PRINT *, " Error while finding neighbours: lonpos or latpos out of bounds!"
	670	PRINT *, " (i,j) = (", i, ",",j,")"
	671	PRINT , " lonpos ", lonposTO_DEGREES, ", latpos ", latpos*TO_DEGREES
	672	PRINT , " lon0 ", lon0 TO_DEGREES, ", lat0 ", lat0*TO_DEGREES
	673	PRINT , " PALM lon ", palm_clon(i,j)TO_DEGREES, ", PALM lat ",palm_clat(i,j)*TO_DEGREES
	674	STOP
	675	END IF
	676
	677	palm_ii(i,j,1) = FLOOR(lonpos)
	678	palm_ii(i,j,2) = FLOOR(lonpos)
	679	palm_ii(i,j,3) = CEILING(lonpos)
	680	palm_ii(i,j,4) = CEILING(lonpos)
	681
	682	palm_jj(i,j,1) = FLOOR(latpos)
	683	palm_jj(i,j,2) = CEILING(latpos)
	684	palm_jj(i,j,3) = CEILING(latpos)
	685	palm_jj(i,j,4) = FLOOR(latpos)
	686	END DO
	687	END DO
	688
	689	END SUBROUTINE find_horizontal_neighbours
	690
	691
[3395]	692	SUBROUTINE find_vertical_neighbours_and_weights_interp( palm_grid, &
	693	palm_intermediate )
[2696]	694	TYPE(grid_definition), INTENT(INOUT) :: palm_grid
	695	TYPE(grid_definition), INTENT(IN) :: palm_intermediate
	696
[3182]	697	INTEGER :: i, j, k, nx, ny, nz, nlev, k_intermediate
[2696]	698	LOGICAL :: point_is_below_grid, point_is_above_grid, &
	699	point_is_in_current_cell
	700	REAL(dp) :: current_height, column_base, column_top, h_top, h_bottom, &
	701	weight
	702
	703	nx = palm_grid % nx
	704	ny = palm_grid % ny
	705	nz = palm_grid % nz
	706	nlev = palm_intermediate % nz
	707
	708	! in each column of the fine grid, find vertical neighbours of every cell
[3395]	709	DO j = 0, ny
[2696]	710	DO i = 0, nx
	711
[3182]	712	k_intermediate = 0
[2696]	713
	714	column_base = palm_intermediate % h(i,j,0)
	715	column_top = palm_intermediate % h(i,j,nlev)
	716
[3395]	717	! scan through palm_grid column and set neighbour indices in
[2696]	718	! case current_height is either below column_base, in the current
	719	! cell, or above column_top. Keep increasing current cell index until
	720	! the current cell overlaps with the current_height.
[3182]	721	DO k = 1, nz
[2696]	722
	723	! Memorize the top and bottom boundaries of the coarse cell and the
	724	! current height within it
	725	current_height = palm_grid % z(k) + palm_grid % z0
[3182]	726	h_top = palm_intermediate % h(i,j,k_intermediate+1)
	727	h_bottom = palm_intermediate % h(i,j,k_intermediate)
[2696]	728
	729	point_is_above_grid = (current_height > column_top) !22000m, very unlikely
	730	point_is_below_grid = (current_height < column_base)
	731
	732	point_is_in_current_cell = ( &
	733	current_height >= h_bottom .AND. &
	734	current_height < h_top &
	735	)
	736
	737	! set default weights
	738	palm_grid % w_verti(i,j,k,1:2) = 0.0_dp
	739
	740	IF (point_is_above_grid) THEN
	741
	742	palm_grid % kk(i,j,k,1:2) = nlev
	743	palm_grid % w_verti(i,j,k,1:2) = - 2.0_dp
	744
[3182]	745	message = "PALM-4U grid extends above COSMO-DE model top."
	746	CALL abort('find_vertical_neighbours_and_weights', message)
	747
[2696]	748	ELSE IF (point_is_below_grid) THEN
	749
	750	palm_grid % kk(i,j,k,1:2) = 0
	751	palm_grid % w_verti(i,j,k,1:2) = - 2.0_dp
	752
	753	ELSE
	754	! cycle through intermediate levels until current
	755	! intermediate-grid cell overlaps with current_height
[3182]	756	DO WHILE (.NOT. point_is_in_current_cell .AND. k_intermediate <= nlev-1)
	757	k_intermediate = k_intermediate + 1
[2696]	758
[3182]	759	h_top = palm_intermediate % h(i,j,k_intermediate+1)
	760	h_bottom = palm_intermediate % h(i,j,k_intermediate)
[2696]	761	point_is_in_current_cell = ( &
	762	current_height >= h_bottom .AND. &
	763	current_height < h_top &
	764	)
	765	END DO
	766
[3182]	767	IF (k_intermediate > nlev-1) THEN
	768	message = "Index " // TRIM(str(k_intermediate)) // &
	769	" is above intermediate grid range."
[2696]	770	CALL abort('find_vertical_neighbours', message)
	771	END IF
	772
[3182]	773	palm_grid % kk(i,j,k,1) = k_intermediate
	774	palm_grid % kk(i,j,k,2) = k_intermediate + 1
[2696]	775
	776	! copmute vertical weights
	777	weight = (h_top - current_height) / (h_top - h_bottom)
	778	palm_grid % w_verti(i,j,k,1) = weight
	779	palm_grid % w_verti(i,j,k,2) = 1.0_dp - weight
	780	END IF
	781
	782	END DO
	783
	784	END DO
	785	END DO
	786
[3395]	787	END SUBROUTINE find_vertical_neighbours_and_weights_interp
[2696]	788
[3395]	789
	790	SUBROUTINE find_vertical_neighbours_and_weights_average( avg_grid )
	791	TYPE(grid_definition), INTENT(INOUT) :: avg_grid
	792
	793	INTEGER :: i, j, k_palm, k_intermediate, l, nlev
	794	LOGICAL :: point_is_below_grid, point_is_above_grid, &
	795	point_is_in_current_cell
	796	REAL(dp) :: current_height, column_base, column_top, h_top, h_bottom, &
	797	weight
	798
	799
	800	avg_grid % k_min = LBOUND(avg_grid % z, 1)
	801
	802	nlev = SIZE(avg_grid % cosmo_h, 3)
	803
	804	! in each column of the fine grid, find vertical neighbours of every cell
	805	DO l = 1, avg_grid % n_columns
	806
	807	i = avg_grid % iii(l)
	808	j = avg_grid % jjj(l)
	809
	810	column_base = avg_grid % cosmo_h(i,j,1)
	811	column_top = avg_grid % cosmo_h(i,j,nlev)
	812
	813	! scan through avg_grid column until and set neighbour indices in
	814	! case current_height is either below column_base, in the current
	815	! cell, or above column_top. Keep increasing current cell index until
	816	! the current cell overlaps with the current_height.
	817	k_intermediate = 1 !avg_grid % cosmo_h is indezed 1-based.
	818	DO k_palm = 1, avg_grid % nz
	819
	820	! Memorize the top and bottom boundaries of the coarse cell and the
	821	! current height within it
	822	current_height = avg_grid % z(k_palm) + avg_grid % z0
	823	h_top = avg_grid % cosmo_h(i,j,k_intermediate+1)
	824	h_bottom = avg_grid % cosmo_h(i,j,k_intermediate)
	825
	826	point_is_above_grid = (current_height > column_top) !22000m, very unlikely
	827	point_is_below_grid = (current_height < column_base)
	828
	829	point_is_in_current_cell = ( &
	830	current_height >= h_bottom .AND. &
	831	current_height < h_top &
	832	)
	833
	834	! set default weights
	835	avg_grid % w(l,k_palm,1:2) = 0.0_dp
	836
	837	IF (point_is_above_grid) THEN
	838
	839	avg_grid % kkk(l,k_palm,1:2) = nlev
	840	avg_grid % w(l,k_palm,1:2) = - 2.0_dp
	841
	842	message = "PALM-4U grid extends above COSMO-DE model top."
	843	CALL abort('find_vertical_neighbours_and_weights_average', message)
	844
	845	ELSE IF (point_is_below_grid) THEN
	846
	847	avg_grid % kkk(l,k_palm,1:2) = 0
	848	avg_grid % w(l,k_palm,1:2) = - 2.0_dp
	849	avg_grid % k_min = MAX(k_palm + 1, avg_grid % k_min)
	850	ELSE
	851	! cycle through intermediate levels until current
	852	! intermediate-grid cell overlaps with current_height
	853	DO WHILE (.NOT. point_is_in_current_cell .AND. k_intermediate <= nlev-1)
	854	k_intermediate = k_intermediate + 1
	855
	856	h_top = avg_grid % cosmo_h(i,j,k_intermediate+1)
	857	h_bottom = avg_grid % cosmo_h(i,j,k_intermediate)
	858	point_is_in_current_cell = ( &
	859	current_height >= h_bottom .AND. &
	860	current_height < h_top &
	861	)
	862	END DO
	863
	864	! k_intermediate = 48 indicates the last section (indices 48 and 49), i.e.
	865	! k_intermediate = 49 is not the beginning of a valid cell.
	866	IF (k_intermediate > nlev-1) THEN
	867	message = "Index " // TRIM(str(k_intermediate)) // &
	868	" is above intermediate grid range."
	869	CALL abort('find_vertical_neighbours', message)
	870	END IF
	871
	872	avg_grid % kkk(l,k_palm,1) = k_intermediate
	873	avg_grid % kkk(l,k_palm,2) = k_intermediate + 1
	874
	875	! copmute vertical weights
	876	weight = (h_top - current_height) / (h_top - h_bottom)
	877	avg_grid % w(l,k_palm,1) = weight
	878	avg_grid % w(l,k_palm,2) = 1.0_dp - weight
	879	END IF
	880
	881	END DO ! k, PALM levels
	882	END DO ! l, averaging columns
	883
	884	END SUBROUTINE find_vertical_neighbours_and_weights_average
	885
[2696]	886	!------------------------------------------------------------------------------!
	887	! Description:
	888	! ------------
	889	!> Compute the four weights for horizontal bilinear interpolation given the
	890	!> coordinates clon(i,j) clat(i,j) of the PALM-4U grid in the COSMO-DE
	891	!> rotated-pole grid and the neightbour indices ii(i,j,1-4) and jj(i,j,1-4).
	892	!>
	893	!> Input parameters:
	894	!> -----------------
	895	!> palm_grid % clon : longitudes of PALM-4U scalars (cell centres) in COSMO-DE's rotated-pole grid [rad]
	896	!>
	897	!> palm_grid % clat : latitudes of PALM-4U cell centres in COSMO-DE's rotated-pole grid [rad]
	898	!>
	899	!> cosmo_grid % lon : rotated-pole longitudes of scalars (cell centres) of the COSMO-DE grid [rad]
	900	!>
	901	!> cosmo_grid % lat : rotated-pole latitudes of scalars (cell centers) of the COSMO-DE grid [rad]
	902	!>
	903	!> cosmo_grid % dxi : inverse grid spacing in the first dimension [m^-1]
	904	!>
	905	!> cosmo_grid % dyi : inverse grid spacing in the second dimension [m^-1]
	906	!>
	907	!> Output parameters:
	908	!> ------------------
	909	!> palm_grid % w_horiz(:,:,1-4) : weights for bilinear horizontal interpolation
	910	!
	911	! COSMO-DE grid
	912	! -------------
	913	! jj, lat
	914	! ^ j
	915	! \| \ i
	916	! jj(i,j,2/3) + ... 2 ---\--------/------ 3
	917	! \| \| ^ \ / \|
	918	! \| \| \|wp \ / \|
	919	! \| \| v \ / \|
	920	! latpos + ............ o/ (i,j) \|
	921	! \| \| : \|
	922	! \| \| :<----wl---->\|
	923	! jj(i,j,1/4) + ... 1 -------:----------- 4
	924	! \| : : :
	925	! \| : : :
	926	! \| : lonpos :
	927	! L-----+--------+------------+------> ii, lon
	928	! ii(i,j,1/2) ii(i,j,3/4)
	929	!
	930	SUBROUTINE compute_horizontal_interp_weights(cosmo_lat, cosmo_lon, &
[3182]	931	palm_clat, palm_clon, palm_ii, palm_jj, palm_w_horiz)
[2696]	932
	933	REAL(dp), DIMENSION(0:), INTENT(IN) :: cosmo_lat, cosmo_lon
[3182]	934	REAL(dp) :: cosmo_dxi, cosmo_dyi
[2696]	935	REAL(dp), DIMENSION(0:,0:), INTENT(IN) :: palm_clat, palm_clon
	936	INTEGER, DIMENSION(0:,0:,1:), INTENT(IN) :: palm_ii, palm_jj
	937
	938	REAL(dp), DIMENSION(0:,0:,1:), INTENT(OUT) :: palm_w_horiz
	939
	940	REAL(dp) :: wl, wp
	941	INTEGER :: i, j
	942
[3182]	943	cosmo_dxi = 1.0_dp / (cosmo_lon(1) - cosmo_lon(0))
	944	cosmo_dyi = 1.0_dp / (cosmo_lat(1) - cosmo_lat(0))
	945
[2696]	946	DO j = 0, UBOUND(palm_clon, 2)
	947	DO i = 0, UBOUND(palm_clon, 1)
	948
	949	! weight in lambda direction
	950	wl = ( cosmo_lon(palm_ii(i,j,4)) - palm_clon(i,j) ) * cosmo_dxi
	951
	952	! weight in phi direction
	953	wp = ( cosmo_lat(palm_jj(i,j,2)) - palm_clat(i,j) ) * cosmo_dyi
	954
	955	IF (wl > 1.0_dp .OR. wl < 0.0_dp) THEN
	956	message = "Horizontal weight wl = " // TRIM(real_to_str(wl)) // &
	957	" is out bounds."
	958	CALL abort('compute_horizontal_interp_weights', message)
	959	END IF
	960	IF (wp > 1.0_dp .OR. wp < 0.0_dp) THEN
	961	message = "Horizontal weight wp = " // TRIM(real_to_str(wp)) // &
	962	" is out bounds."
	963	CALL abort('compute_horizontal_interp_weights', message)
	964	END IF
	965
	966	palm_w_horiz(i,j,1) = wl * wp
	967	palm_w_horiz(i,j,2) = wl * (1.0_dp - wp)
	968	palm_w_horiz(i,j,3) = (1.0_dp - wl) * (1.0_dp - wp)
	969	palm_w_horiz(i,j,4) = 1.0_dp - SUM( palm_w_horiz(i,j,1:3) )
	970
	971	END DO
	972	END DO
	973
	974	END SUBROUTINE compute_horizontal_interp_weights
	975
	976
	977	!------------------------------------------------------------------------------!
	978	! Description:
	979	! ------------
	980	!> Interpolates u and v components of velocities located at cell faces to the
	981	!> cell centres by averaging neighbouring values.
	982	!>
	983	!> This routine is designed to be used with COSMO-DE arrays where there are the
	984	!> same number of grid points for scalars (centres) and velocities (faces). In
	985	!> COSMO-DE the velocity points are staggared one half grid spaceing up-grid
	986	!> which means the first centre point has to be omitted and is set to zero.
	987	SUBROUTINE centre_velocities(u_face, v_face, u_centre, v_centre)
	988	REAL(dp), DIMENSION(0:,0:,0:), INTENT(IN) :: u_face, v_face
	989	REAL(dp), DIMENSION(0:,0:,0:), INTENT(OUT) :: u_centre, v_centre
	990	INTEGER :: nx, ny
	991
	992	nx = UBOUND(u_face, 1)
	993	ny = UBOUND(u_face, 2)
	994
	995	u_centre(0,:,:) = 0.0_dp
	996	u_centre(1:,:,:) = 0.5_dp * ( u_face(0:nx-1,:,:) + u_face(1:,:,:) )
	997
	998	v_centre(:,0,:) = 0.0_dp
	999	v_centre(:,1:,:) = 0.5_dp * ( v_face(:,0:ny-1,:) + v_face(:,1:,:) )
	1000	END SUBROUTINE centre_velocities
	1001
	1002
	1003	FUNCTION phirot2phi (phirot, rlarot, polphi, pollam, polgam)
	1004
	1005	REAL(dp), INTENT (IN) :: polphi !< latitude of the rotated north pole
	1006	REAL(dp), INTENT (IN) :: pollam !< longitude of the rotated north pole
	1007	REAL(dp), INTENT (IN) :: phirot !< latitude in the rotated system
	1008	REAL(dp), INTENT (IN) :: rlarot !< longitude in the rotated system
	1009	REAL(dp), INTENT (IN) :: polgam !< angle between the north poles of the systems
	1010
	1011	REAL(dp) :: phirot2phi !< latitude in the geographical system
	1012
	1013	REAL(dp) :: zsinpol, zcospol, zphis, zrlas, zarg, zgam
	1014
	1015	zsinpol = SIN(polphi * TO_RADIANS)
	1016	zcospol = COS(polphi * TO_RADIANS)
	1017	zphis = phirot * TO_RADIANS
	1018
	1019	IF (rlarot > 180.0_dp) THEN
	1020	zrlas = rlarot - 360.0_dp
	1021	ELSE
	1022	zrlas = rlarot
	1023	END IF
	1024	zrlas = zrlas * TO_RADIANS
	1025
	1026	IF (polgam /= 0.0_dp) THEN
	1027	zgam = polgam * TO_RADIANS
	1028	zarg = zsinpol * SIN (zphis) + &
	1029	zcospol * COS(zphis) * ( COS(zrlas) * COS(zgam) - &
	1030	SIN(zgam) * SIN(zrlas) )
	1031	ELSE
	1032	zarg = zcospol * COS (zphis) * COS (zrlas) + zsinpol * SIN (zphis)
	1033	END IF
	1034
	1035	phirot2phi = ASIN (zarg) * TO_DEGREES
	1036
	1037	END FUNCTION phirot2phi
	1038
	1039
	1040	FUNCTION phi2phirot (phi, rla, polphi, pollam)
	1041
	1042	REAL(dp), INTENT (IN) :: polphi !< latitude of the rotated north pole
	1043	REAL(dp), INTENT (IN) :: pollam !< longitude of the rotated north pole
	1044	REAL(dp), INTENT (IN) :: phi !< latitude in the geographical system
	1045	REAL(dp), INTENT (IN) :: rla !< longitude in the geographical system
	1046
	1047	REAL(dp) :: phi2phirot !< longitude in the rotated system
	1048
	1049	REAL(dp) :: zsinpol, zcospol, zlampol, zphi, zrla, zarg1, zarg2, zrla1
	1050
	1051	zsinpol = SIN(polphi * TO_RADIANS)
	1052	zcospol = COS(polphi * TO_RADIANS)
	1053	zlampol = pollam * TO_RADIANS
	1054	zphi = phi * TO_RADIANS
	1055
	1056	IF (rla > 180.0_dp) THEN
	1057	zrla1 = rla - 360.0_dp
	1058	ELSE
	1059	zrla1 = rla
	1060	END IF
	1061	zrla = zrla1 * TO_RADIANS
	1062
	1063	zarg1 = SIN(zphi) * zsinpol
	1064	zarg2 = COS(zphi) * zcospol * COS(zrla - zlampol)
	1065
	1066	phi2phirot = ASIN(zarg1 + zarg2) * TO_DEGREES
	1067
	1068	END FUNCTION phi2phirot
	1069
	1070
	1071	FUNCTION rlarot2rla(phirot, rlarot, polphi, pollam, polgam)
	1072
	1073	REAL(dp), INTENT (IN) :: polphi !< latitude of the rotated north pole
	1074	REAL(dp), INTENT (IN) :: pollam !< longitude of the rotated north pole
	1075	REAL(dp), INTENT (IN) :: phirot !< latitude in the rotated system
	1076	REAL(dp), INTENT (IN) :: rlarot !< longitude in the rotated system
	1077	REAL(dp), INTENT (IN) :: polgam !< angle between the north poles of the systems
	1078
	1079	REAL(dp) :: rlarot2rla !< latitude in the geographical system
	1080
	1081	REAL(dp) :: zsinpol, zcospol, zlampol, zphis, zrlas, zarg1, zarg2, zgam
	1082
	1083	zsinpol = SIN(TO_RADIANS * polphi)
	1084	zcospol = COS(TO_RADIANS * polphi)
	1085	zlampol = TO_RADIANS * pollam
	1086	zphis = TO_RADIANS * phirot
	1087
	1088	IF (rlarot > 180.0_dp) THEN
	1089	zrlas = rlarot - 360.0_dp
	1090	ELSE
	1091	zrlas = rlarot
	1092	END IF
	1093	zrlas = TO_RADIANS * zrlas
	1094
	1095	IF (polgam /= 0.0_dp) THEN
	1096	zgam = TO_RADIANS * polgam
	1097	zarg1 = SIN(zlampol) * (zcospol * SIN(zphis) - zsinpolCOS(zphis) &
	1098	(COS(zrlas) * COS(zgam) - SIN(zrlas) * SIN(zgam)) ) - &
	1099	COS(zlampol) * COS(zphis) * ( SIN(zrlas) * COS(zgam) + &
	1100	COS(zrlas) * SIN(zgam) )
	1101
	1102	zarg2 = COS (zlampol) * (zcospol * SIN(zphis) - zsinpolCOS(zphis) &
	1103	(COS(zrlas) * COS(zgam) - SIN(zrlas) * SIN(zgam)) ) + &
	1104	SIN(zlampol) * COS(zphis) * ( SIN(zrlas) * COS(zgam) + &
	1105	COS(zrlas) * SIN(zgam) )
	1106	ELSE
	1107	zarg1 = SIN (zlampol) * (-zsinpol * COS(zrlas) * COS(zphis) + &
	1108	zcospol * SIN(zphis)) - &
	1109	COS (zlampol) * SIN(zrlas) * COS(zphis)
	1110	zarg2 = COS (zlampol) * (-zsinpol * COS(zrlas) * COS(zphis) + &
	1111	zcospol * SIN(zphis)) + &
	1112	SIN (zlampol) * SIN(zrlas) * COS(zphis)
	1113	END IF
	1114
	1115	IF (zarg2 == 0.0_dp) zarg2 = 1.0E-20_dp
	1116
	1117	rlarot2rla = ATAN2(zarg1,zarg2) * TO_DEGREES
	1118
	1119	END FUNCTION rlarot2rla
	1120
	1121
	1122	FUNCTION rla2rlarot ( phi, rla, polphi, pollam, polgam )
	1123
	1124	REAL(dp), INTENT (IN) :: polphi !< latitude of the rotated north pole
	1125	REAL(dp), INTENT (IN) :: pollam !< longitude of the rotated north pole
	1126	REAL(dp), INTENT (IN) :: phi !< latitude in geographical system
	1127	REAL(dp), INTENT (IN) :: rla !< longitude in geographical system
	1128	REAL(dp), INTENT (IN) :: polgam !< angle between the north poles of the systems
	1129
	1130	REAL (KIND=dp) :: rla2rlarot !< latitude in the the rotated system
	1131
	1132	REAL (KIND=dp) :: zsinpol, zcospol, zlampol, zphi, zrla, zarg1, zarg2, zrla1
	1133
	1134	zsinpol = SIN(polphi * TO_RADIANS)
	1135	zcospol = COS(polphi * TO_RADIANS)
	1136	zlampol = pollam * TO_RADIANS
	1137	zphi = phi * TO_RADIANS
	1138
	1139	IF (rla > 180.0_dp) THEN
	1140	zrla1 = rla - 360.0_dp
	1141	ELSE
	1142	zrla1 = rla
	1143	END IF
	1144	zrla = zrla1 * TO_RADIANS
	1145
	1146	zarg1 = - SIN (zrla-zlampol) * COS(zphi)
	1147	zarg2 = - zsinpol * COS(zphi) * COS(zrla-zlampol) + zcospol * SIN(zphi)
	1148
	1149	IF (zarg2 == 0.0_dp) zarg2 = 1.0E-20_dp
	1150
	1151	rla2rlarot = ATAN2 (zarg1,zarg2) * TO_DEGREES
	1152
	1153	IF (polgam /= 0.0_dp ) THEN
	1154	rla2rlarot = polgam + rla2rlarot
	1155	IF (rla2rlarot > 180._dp) rla2rlarot = rla2rlarot - 360.0_dp
	1156	END IF
	1157
	1158	END FUNCTION rla2rlarot
	1159
	1160
	1161	SUBROUTINE uv2uvrot(u, v, rlat, rlon, pollat, pollon, urot, vrot)
	1162
	1163	REAL(dp), INTENT (IN) :: u, v !< wind components in the true geographical system
	1164	REAL(dp), INTENT (IN) :: rlat, rlon !< coordinates in the true geographical system
	1165	REAL(dp), INTENT (IN) :: pollat, pollon !< latitude and longitude of the north pole of the rotated grid
	1166
	1167	REAL(dp), INTENT (OUT) :: urot, vrot !< wind components in the rotated grid
	1168
	1169	REAL (dp) :: zsinpol, zcospol, zlonp, zlat, zarg1, zarg2, znorm
	1170
	1171	zsinpol = SIN(pollat * TO_RADIANS)
	1172	zcospol = COS(pollat * TO_RADIANS)
	1173	zlonp = (pollon-rlon) * TO_RADIANS
	1174	zlat = rlat * TO_RADIANS
	1175
	1176	zarg1 = zcospol * SIN(zlonp)
	1177	zarg2 = zsinpol * COS(zlat) - zcospol * SIN(zlat) * COS(zlonp)
	1178	znorm = 1.0_dp / SQRT(zarg1zarg1 + zarg2zarg2)
	1179
	1180	urot = u * zarg2 * znorm - v * zarg1 * znorm
	1181	vrot = u * zarg1 * znorm + v * zarg2 * znorm
	1182
	1183	END SUBROUTINE uv2uvrot
	1184
	1185
	1186	SUBROUTINE uvrot2uv (urot, vrot, rlat, rlon, pollat, pollon, u, v)
	1187
	1188	REAL(dp), INTENT(IN) :: urot, vrot !< wind components in the rotated grid
	1189	REAL(dp), INTENT(IN) :: rlat, rlon !< latitude and longitude in the true geographical system
	1190	REAL(dp), INTENT(IN) :: pollat, pollon !< latitude and longitude of the north pole of the rotated grid
	1191
	1192	REAL(dp), INTENT(OUT) :: u, v !< wind components in the true geographical system
	1193
	1194	REAL(dp) :: zsinpol, zcospol, zlonp, zlat, zarg1, zarg2, znorm
	1195
	1196	zsinpol = SIN(pollat * TO_RADIANS)
	1197	zcospol = COS(pollat * TO_RADIANS)
	1198	zlonp = (pollon-rlon) * TO_RADIANS
	1199	zlat = rlat * TO_RADIANS
	1200
	1201	zarg1 = zcospol * SIN(zlonp)
	1202	zarg2 = zsinpol * COS(zlat) - zcospol * SIN(zlat) * COS(zlonp)
	1203	znorm = 1.0_dp / SQRT(zarg1zarg1 + zarg2zarg2)
	1204
	1205	u = urot * zarg2 * znorm + vrot * zarg1 * znorm
	1206	v = - urot * zarg1 * znorm + vrot * zarg2 * znorm
	1207
	1208	END SUBROUTINE uvrot2uv
	1209
	1210	END MODULE
	1211

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