MODULE module_llxy ! Module that defines constants, data structures, and ! subroutines used to convert grid indices to lat/lon ! and vice versa. ! ! SUPPORTED PROJECTIONS ! --------------------- ! Cylindrical Lat/Lon (code = PROJ_LATLON) ! Mercator (code = PROJ_MERC) ! Lambert Conformal (code = PROJ_LC) ! Gaussian (code = PROJ_GAUSS) ! Polar Stereographic (code = PROJ_PS) ! Rotated Lat/Lon (code = PROJ_ROTLL) ! ! REMARKS ! ------- ! The routines contained within were adapted from routines ! obtained from NCEP's w3 library. The original NCEP routines were less ! flexible (e.g., polar-stereo routines only supported truelat of 60N/60S) ! than what we needed, so modifications based on equations in Hoke, Hayes, and ! Renninger (AFGWC/TN/79-003) were added to improve the flexibility. ! Additionally, coding was improved to F90 standards and the routines were ! combined into this module. ! ! ASSUMPTIONS ! ----------- ! Grid Definition: ! For mercator, lambert conformal, and polar-stereographic projections, ! the routines within assume the following: ! ! 1. Grid is dimensioned (i,j) where i is the East-West direction, ! positive toward the east, and j is the north-south direction, ! positive toward the north. ! 2. Origin is at (1,1) and is located at the southwest corner, ! regardless of hemispere. ! 3. Grid spacing (dx) is always positive. ! 4. Values of true latitudes must be positive for NH domains ! and negative for SH domains. ! ! For the latlon and Gaussian projection, the grid origin may be at any ! of the corners, and the deltalat and deltalon values can be signed to ! account for this using the following convention: ! Origin Location Deltalat Sign Deltalon Sign ! --------------- ------------- ------------- ! SW Corner + + ! NE Corner - - ! NW Corner - + ! SE Corner + - ! ! Data Definitions: ! 1. Any arguments that are a latitude value are expressed in ! degrees north with a valid range of -90 -> 90 ! 2. Any arguments that are a longitude value are expressed in ! degrees east with a valid range of -180 -> 180. ! 3. Distances are in meters and are always positive. ! 4. The standard longitude (stdlon) is defined as the longitude ! line which is parallel to the grid's y-axis (j-direction), along ! which latitude increases (NOT the absolute value of latitude, but ! the actual latitude, such that latitude increases continuously ! from the south pole to the north pole) as j increases. ! 5. One true latitude value is required for polar-stereographic and ! mercator projections, and defines at which latitude the ! grid spacing is true. For lambert conformal, two true latitude ! values must be specified, but may be set equal to each other to ! specify a tangent projection instead of a secant projection. ! ! USAGE ! ----- ! To use the routines in this module, the calling routines must have the ! following statement at the beginning of its declaration block: ! USE map_utils ! ! The use of the module not only provides access to the necessary routines, ! but also defines a structure of TYPE (proj_info) that can be used ! to declare a variable of the same type to hold your map projection ! information. It also defines some integer parameters that contain ! the projection codes so one only has to use those variable names rather ! than remembering the acutal code when using them. The basic steps are ! as follows: ! ! 1. Ensure the "USE map_utils" is in your declarations. ! 2. Declare the projection information structure as type(proj_info): ! TYPE(proj_info) :: proj ! 3. Populate your structure by calling the map_set routine: ! CALL map_set(code,lat1,lon1,knowni,knownj,dx,stdlon,truelat1,truelat2,proj) ! where: ! code (input) = one of PROJ_LATLON, PROJ_MERC, PROJ_LC, PROJ_PS, ! PROJ_GAUSS, or PROJ_ROTLL ! lat1 (input) = Latitude of grid origin point (i,j)=(1,1) ! (see assumptions!) ! lon1 (input) = Longitude of grid origin ! knowni (input) = origin point, x-location ! knownj (input) = origin point, y-location ! dx (input) = grid spacing in meters (ignored for LATLON projections) ! stdlon (input) = Standard longitude for PROJ_PS and PROJ_LC, ! deltalon (see assumptions) for PROJ_LATLON, ! ignored for PROJ_MERC ! truelat1 (input) = 1st true latitude for PROJ_PS, PROJ_LC, and ! PROJ_MERC, deltalat (see assumptions) for PROJ_LATLON ! truelat2 (input) = 2nd true latitude for PROJ_LC, ! ignored for all others. ! proj (output) = The structure of type (proj_info) that will be fully ! populated after this call ! ! 4. Now that the proj structure is populated, you may call either ! of the following routines: ! ! latlon_to_ij(proj, lat, lon, i, j) ! ij_to_latlon(proj, i, j, lat, lon) ! ! It is incumbent upon the calling routine to determine whether or ! not the values returned are within your domain's bounds. All values ! of i, j, lat, and lon are REAL values. ! ! ! REFERENCES ! ---------- ! Hoke, Hayes, and Renninger, "Map Preojections and Grid Systems for ! Meteorological Applications." AFGWC/TN-79/003(Rev), Air Weather ! Service, 1985. ! ! NCAR MM5v3 Modeling System, REGRIDDER program, module_first_guess_map.F ! NCEP routines w3fb06, w3fb07, w3fb08, w3fb09, w3fb11, w3fb12 ! ! HISTORY ! ------- ! 27 Mar 2001 - Original Version ! Brent L. Shaw, NOAA/FSL (CSU/CIRA) ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! USE module_wrf_error INTEGER, PARAMETER :: HH=4, VV=5 REAL, PARAMETER :: PI = 3.141592653589793 REAL, PARAMETER :: OMEGA_E = 7.292e-5 REAL, PARAMETER :: DEG_PER_RAD = 180./PI REAL, PARAMETER :: RAD_PER_DEG = PI/180. REAL, PARAMETER :: A_WGS84 = 6378137. REAL, PARAMETER :: B_WGS84 = 6356752.314 REAL, PARAMETER :: RE_WGS84 = A_WGS84 REAL, PARAMETER :: E_WGS84 = 0.081819192 REAL, PARAMETER :: A_NAD83 = 6378137. REAL, PARAMETER :: RE_NAD83 = A_NAD83 REAL, PARAMETER :: E_NAD83 = 0.0818187034 REAL, PARAMETER :: EARTH_RADIUS_M = 6370000. REAL, PARAMETER :: EARTH_CIRC_M = 2.*PI*EARTH_RADIUS_M INTEGER, PUBLIC, PARAMETER :: PROJ_LATLON = 0 INTEGER, PUBLIC, PARAMETER :: PROJ_LC = 1 INTEGER, PUBLIC, PARAMETER :: PROJ_PS = 2 INTEGER, PUBLIC, PARAMETER :: PROJ_PS_WGS84 = 102 INTEGER, PUBLIC, PARAMETER :: PROJ_MERC = 3 INTEGER, PUBLIC, PARAMETER :: PROJ_GAUSS = 4 INTEGER, PUBLIC, PARAMETER :: PROJ_CYL = 5 INTEGER, PUBLIC, PARAMETER :: PROJ_CASSINI = 6 INTEGER, PUBLIC, PARAMETER :: PROJ_ALBERS_NAD83 = 105 INTEGER, PUBLIC, PARAMETER :: PROJ_ROTLL = 203 ! Define some private constants INTEGER, PRIVATE, PARAMETER :: HIGH = 8 TYPE proj_info INTEGER :: code ! Integer code for projection TYPE INTEGER :: nlat ! For Gaussian -- number of latitude points ! north of the equator INTEGER :: nlon ! ! INTEGER :: ixdim ! For Rotated Lat/Lon -- number of mass points ! in an odd row INTEGER :: jydim ! For Rotated Lat/Lon -- number of rows INTEGER :: stagger ! For Rotated Lat/Lon -- mass or velocity grid REAL :: phi ! For Rotated Lat/Lon -- domain half-extent in ! degrees latitude REAL :: lambda ! For Rotated Lat/Lon -- domain half-extend in ! degrees longitude REAL :: lat1 ! SW latitude (1,1) in degrees (-90->90N) REAL :: lon1 ! SW longitude (1,1) in degrees (-180->180E) REAL :: lat0 ! For Cassini, latitude of projection pole REAL :: lon0 ! For Cassini, longitude of projection pole REAL :: dx ! Grid spacing in meters at truelats, used ! only for ps, lc, and merc projections REAL :: dy ! Grid spacing in meters at truelats, used ! only for ps, lc, and merc projections REAL :: latinc ! Latitude increment for cylindrical lat/lon REAL :: loninc ! Longitude increment for cylindrical lat/lon ! also the lon increment for Gaussian grid REAL :: dlat ! Lat increment for lat/lon grids REAL :: dlon ! Lon increment for lat/lon grids REAL :: stdlon ! Longitude parallel to y-axis (-180->180E) REAL :: truelat1 ! First true latitude (all projections) REAL :: truelat2 ! Second true lat (LC only) REAL :: hemi ! 1 for NH, -1 for SH REAL :: cone ! Cone factor for LC projections REAL :: polei ! Computed i-location of pole point REAL :: polej ! Computed j-location of pole point REAL :: rsw ! Computed radius to SW corner REAL :: rebydx ! Earth radius divided by dx REAL :: knowni ! X-location of known lat/lon REAL :: knownj ! Y-location of known lat/lon REAL :: re_m ! Radius of spherical earth, meters REAL :: rho0 ! For Albers equal area REAL :: nc ! For Albers equal area REAL :: bigc ! For Albers equal area LOGICAL :: init ! Flag to indicate if this struct is ! ready for use LOGICAL :: wrap ! For Gaussian -- flag to indicate wrapping ! around globe? REAL, POINTER, DIMENSION(:) :: gauss_lat ! Latitude array for Gaussian grid END TYPE proj_info !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! CONTAINS !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! SUBROUTINE map_init(proj) ! Initializes the map projection structure to missing values IMPLICIT NONE TYPE(proj_info), INTENT(INOUT) :: proj proj%code = -999 proj%lat1 = -999.9 proj%lon1 = -999.9 proj%lat0 = -999.9 proj%lon0 = -999.9 proj%dx = -999.9 proj%dy = -999.9 proj%latinc = -999.9 proj%loninc = -999.9 proj%stdlon = -999.9 proj%truelat1 = -999.9 proj%truelat2 = -999.9 proj%phi = -999.9 proj%lambda = -999.9 proj%ixdim = -999 proj%jydim = -999 proj%stagger = HH proj%nlat = 0 proj%nlon = 0 proj%hemi = 0.0 proj%cone = -999.9 proj%polei = -999.9 proj%polej = -999.9 proj%rsw = -999.9 proj%knowni = -999.9 proj%knownj = -999.9 proj%re_m = EARTH_RADIUS_M proj%init = .FALSE. proj%wrap = .FALSE. proj%rho0 = 0. proj%nc = 0. proj%bigc = 0. nullify(proj%gauss_lat) END SUBROUTINE map_init SUBROUTINE map_set(proj_code, proj, lat1, lon1, lat0, lon0, knowni, knownj, dx, latinc, & loninc, stdlon, truelat1, truelat2, nlat, nlon, ixdim, jydim, & stagger, phi, lambda, r_earth) ! Given a partially filled proj_info structure, this routine computes ! polei, polej, rsw, and cone (if LC projection) to complete the ! structure. This allows us to eliminate redundant calculations when ! calling the coordinate conversion routines multiple times for the ! same map. ! This will generally be the first routine called when a user wants ! to be able to use the coordinate conversion routines, and it ! will call the appropriate subroutines based on the ! proj%code which indicates which projection type this is. IMPLICIT NONE ! Declare arguments INTEGER, INTENT(IN) :: proj_code INTEGER, INTENT(IN), OPTIONAL :: nlat INTEGER, INTENT(IN), OPTIONAL :: nlon INTEGER, INTENT(IN), OPTIONAL :: ixdim INTEGER, INTENT(IN), OPTIONAL :: jydim INTEGER, INTENT(IN), OPTIONAL :: stagger REAL, INTENT(IN), OPTIONAL :: latinc REAL, INTENT(IN), OPTIONAL :: loninc REAL, INTENT(IN), OPTIONAL :: lat1 REAL, INTENT(IN), OPTIONAL :: lon1 REAL, INTENT(IN), OPTIONAL :: lat0 REAL, INTENT(IN), OPTIONAL :: lon0 REAL, INTENT(IN), OPTIONAL :: dx REAL, INTENT(IN), OPTIONAL :: stdlon REAL, INTENT(IN), OPTIONAL :: truelat1 REAL, INTENT(IN), OPTIONAL :: truelat2 REAL, INTENT(IN), OPTIONAL :: knowni REAL, INTENT(IN), OPTIONAL :: knownj REAL, INTENT(IN), OPTIONAL :: phi REAL, INTENT(IN), OPTIONAL :: lambda REAL, INTENT(IN), OPTIONAL :: r_earth TYPE(proj_info), INTENT(OUT) :: proj INTEGER :: iter REAL :: dummy_lon1 REAL :: dummy_lon0 REAL :: dummy_stdlon ! First, verify that mandatory parameters are present for the specified proj_code IF ( proj_code == PROJ_LC ) THEN IF ( .NOT.PRESENT(truelat1) .OR. & .NOT.PRESENT(truelat2) .OR. & .NOT.PRESENT(lat1) .OR. & .NOT.PRESENT(lon1) .OR. & .NOT.PRESENT(knowni) .OR. & .NOT.PRESENT(knownj) .OR. & .NOT.PRESENT(stdlon) .OR. & .NOT.PRESENT(dx) ) THEN PRINT '(A,I2)', 'The following are mandatory parameters for projection code : ', proj_code PRINT '(A)', ' truelat1, truelat2, lat1, lon1, knowni, knownj, stdlon, dx' CALL wrf_error_fatal ( 'MAP_INIT' ) END IF ELSE IF ( proj_code == PROJ_PS ) THEN IF ( .NOT.PRESENT(truelat1) .OR. & .NOT.PRESENT(lat1) .OR. & .NOT.PRESENT(lon1) .OR. & .NOT.PRESENT(knowni) .OR. & .NOT.PRESENT(knownj) .OR. & .NOT.PRESENT(stdlon) .OR. & .NOT.PRESENT(dx) ) THEN PRINT '(A,I2)', 'The following are mandatory parameters for projection code : ', proj_code PRINT '(A)', ' truelat1, lat1, lon1, knonwi, knownj, stdlon, dx' CALL wrf_error_fatal ( 'MAP_INIT' ) END IF ELSE IF ( proj_code == PROJ_PS_WGS84 ) THEN IF ( .NOT.PRESENT(truelat1) .OR. & .NOT.PRESENT(lat1) .OR. & .NOT.PRESENT(lon1) .OR. & .NOT.PRESENT(knowni) .OR. & .NOT.PRESENT(knownj) .OR. & .NOT.PRESENT(stdlon) .OR. & .NOT.PRESENT(dx) ) THEN PRINT '(A,I2)', 'The following are mandatory parameters for projection code : ', proj_code PRINT '(A)', ' truelat1, lat1, lon1, knonwi, knownj, stdlon, dx' CALL wrf_error_fatal ( 'MAP_INIT' ) END IF ELSE IF ( proj_code == PROJ_ALBERS_NAD83 ) THEN IF ( .NOT.PRESENT(truelat1) .OR. & .NOT.PRESENT(truelat2) .OR. & .NOT.PRESENT(lat1) .OR. & .NOT.PRESENT(lon1) .OR. & .NOT.PRESENT(knowni) .OR. & .NOT.PRESENT(knownj) .OR. & .NOT.PRESENT(stdlon) .OR. & .NOT.PRESENT(dx) ) THEN PRINT '(A,I2)', 'The following are mandatory parameters for projection code : ', proj_code PRINT '(A)', ' truelat1, truelat2, lat1, lon1, knonwi, knownj, stdlon, dx' CALL wrf_error_fatal ( 'MAP_INIT' ) END IF ELSE IF ( proj_code == PROJ_MERC ) THEN IF ( .NOT.PRESENT(truelat1) .OR. & .NOT.PRESENT(lat1) .OR. & .NOT.PRESENT(lon1) .OR. & .NOT.PRESENT(knowni) .OR. & .NOT.PRESENT(knownj) .OR. & .NOT.PRESENT(dx) ) THEN PRINT '(A,I2)', 'The following are mandatory parameters for projection code : ', proj_code PRINT '(A)', ' truelat1, lat1, lon1, knowni, knownj, dx' CALL wrf_error_fatal ( 'MAP_INIT' ) END IF ELSE IF ( proj_code == PROJ_LATLON ) THEN IF ( .NOT.PRESENT(latinc) .OR. & .NOT.PRESENT(loninc) .OR. & .NOT.PRESENT(knowni) .OR. & .NOT.PRESENT(knownj) .OR. & .NOT.PRESENT(lat1) .OR. & .NOT.PRESENT(lon1) ) THEN PRINT '(A,I2)', 'The following are mandatory parameters for projection code : ', proj_code PRINT '(A)', ' latinc, loninc, knowni, knownj, lat1, lon1' CALL wrf_error_fatal ( 'MAP_INIT' ) END IF ELSE IF ( proj_code == PROJ_CYL ) THEN IF ( .NOT.PRESENT(latinc) .OR. & .NOT.PRESENT(loninc) .OR. & .NOT.PRESENT(stdlon) ) THEN PRINT '(A,I2)', 'The following are mandatory parameters for projection code : ', proj_code PRINT '(A)', ' latinc, loninc, stdlon' CALL wrf_error_fatal ( 'MAP_INIT' ) END IF ELSE IF ( proj_code == PROJ_CASSINI ) THEN IF ( .NOT.PRESENT(latinc) .OR. & .NOT.PRESENT(loninc) .OR. & .NOT.PRESENT(lat1) .OR. & .NOT.PRESENT(lon1) .OR. & .NOT.PRESENT(lat0) .OR. & .NOT.PRESENT(lon0) .OR. & .NOT.PRESENT(knowni) .OR. & .NOT.PRESENT(knownj) .OR. & .NOT.PRESENT(stdlon) ) THEN PRINT '(A,I2)', 'The following are mandatory parameters for projection code : ', proj_code PRINT '(A)', ' latinc, loninc, lat1, lon1, knowni, knownj, lat0, lon0, stdlon' CALL wrf_error_fatal ( 'MAP_INIT' ) END IF ELSE IF ( proj_code == PROJ_GAUSS ) THEN IF ( .NOT.PRESENT(nlat) .OR. & .NOT.PRESENT(lat1) .OR. & .NOT.PRESENT(lon1) .OR. & .NOT.PRESENT(loninc) ) THEN PRINT '(A,I2)', 'The following are mandatory parameters for projection code : ', proj_code PRINT '(A)', ' nlat, lat1, lon1, loninc' CALL wrf_error_fatal ( 'MAP_INIT' ) END IF ELSE IF ( proj_code == PROJ_ROTLL ) THEN IF ( .NOT.PRESENT(ixdim) .OR. & .NOT.PRESENT(jydim) .OR. & .NOT.PRESENT(phi) .OR. & .NOT.PRESENT(lambda) .OR. & .NOT.PRESENT(lat1) .OR. & .NOT.PRESENT(lon1) .OR. & .NOT.PRESENT(stagger) ) THEN PRINT '(A,I2)', 'The following are mandatory parameters for projection code : ', proj_code PRINT '(A)', ' ixdim, jydim, phi, lambda, lat1, lon1, stagger' CALL wrf_error_fatal ( 'MAP_INIT' ) END IF ELSE PRINT '(A,I2)', 'Unknown projection code: ', proj_code CALL wrf_error_fatal ( 'MAP_INIT' ) END IF ! Check for validity of mandatory variables in proj IF ( PRESENT(lat1) ) THEN IF ( ABS(lat1) .GT. 90. ) THEN PRINT '(A)', 'Latitude of origin corner required as follows:' PRINT '(A)', ' -90N <= lat1 < = 90.N' CALL wrf_error_fatal ( 'MAP_INIT' ) ENDIF ENDIF IF ( PRESENT(lon1) ) THEN dummy_lon1 = lon1 IF ( ABS(dummy_lon1) .GT. 180.) THEN iter = 0 DO WHILE (ABS(dummy_lon1) > 180. .AND. iter < 10) IF (dummy_lon1 < -180.) dummy_lon1 = dummy_lon1 + 360. IF (dummy_lon1 > 180.) dummy_lon1 = dummy_lon1 - 360. iter = iter + 1 END DO IF (abs(dummy_lon1) > 180.) THEN PRINT '(A)', 'Longitude of origin required as follows:' PRINT '(A)', ' -180E <= lon1 <= 180W' CALL wrf_error_fatal ( 'MAP_INIT' ) ENDIF ENDIF ENDIF IF ( PRESENT(lon0) ) THEN dummy_lon0 = lon0 IF ( ABS(dummy_lon0) .GT. 180.) THEN iter = 0 DO WHILE (ABS(dummy_lon0) > 180. .AND. iter < 10) IF (dummy_lon0 < -180.) dummy_lon0 = dummy_lon0 + 360. IF (dummy_lon0 > 180.) dummy_lon0 = dummy_lon0 - 360. iter = iter + 1 END DO IF (abs(dummy_lon0) > 180.) THEN PRINT '(A)', 'Longitude of pole required as follows:' PRINT '(A)', ' -180E <= lon0 <= 180W' CALL wrf_error_fatal ( 'MAP_INIT' ) ENDIF ENDIF ENDIF IF ( PRESENT(dx) ) THEN IF ((dx .LE. 0.).AND.(proj_code .NE. PROJ_LATLON)) THEN PRINT '(A)', 'Require grid spacing (dx) in meters be positive' CALL wrf_error_fatal ( 'MAP_INIT' ) ENDIF ENDIF IF ( PRESENT(stdlon) ) THEN dummy_stdlon = stdlon IF ((ABS(dummy_stdlon) > 180.).AND.(proj_code /= PROJ_MERC)) THEN iter = 0 DO WHILE (ABS(dummy_stdlon) > 180. .AND. iter < 10) IF (dummy_stdlon < -180.) dummy_stdlon = dummy_stdlon + 360. IF (dummy_stdlon > 180.) dummy_stdlon = dummy_stdlon - 360. iter = iter + 1 END DO IF (abs(dummy_stdlon) > 180.) THEN PRINT '(A)', 'Need orientation longitude (stdlon) as: ' PRINT '(A)', ' -180E <= stdlon <= 180W' CALL wrf_error_fatal ( 'MAP_INIT' ) ENDIF ENDIF ENDIF IF ( PRESENT(truelat1) ) THEN IF (ABS(truelat1).GT.90.) THEN PRINT '(A)', 'Set true latitude 1 for all projections' CALL wrf_error_fatal ( 'MAP_INIT' ) ENDIF ENDIF CALL map_init(proj) proj%code = proj_code IF ( PRESENT(lat1) ) proj%lat1 = lat1 IF ( PRESENT(lon1) ) proj%lon1 = dummy_lon1 IF ( PRESENT(lat0) ) proj%lat0 = lat0 IF ( PRESENT(lon0) ) proj%lon0 = dummy_lon0 IF ( PRESENT(latinc) ) proj%latinc = latinc IF ( PRESENT(loninc) ) proj%loninc = loninc IF ( PRESENT(knowni) ) proj%knowni = knowni IF ( PRESENT(knownj) ) proj%knownj = knownj IF ( PRESENT(dx) ) proj%dx = dx IF ( PRESENT(stdlon) ) proj%stdlon = dummy_stdlon IF ( PRESENT(truelat1) ) proj%truelat1 = truelat1 IF ( PRESENT(truelat2) ) proj%truelat2 = truelat2 IF ( PRESENT(nlat) ) proj%nlat = nlat IF ( PRESENT(nlon) ) proj%nlon = nlon IF ( PRESENT(ixdim) ) proj%ixdim = ixdim IF ( PRESENT(jydim) ) proj%jydim = jydim IF ( PRESENT(stagger) ) proj%stagger = stagger IF ( PRESENT(phi) ) proj%phi = phi IF ( PRESENT(lambda) ) proj%lambda = lambda IF ( PRESENT(r_earth) ) proj%re_m = r_earth IF ( PRESENT(dx) ) THEN IF ( (proj_code == PROJ_LC) .OR. (proj_code == PROJ_PS) .OR. & (proj_code == PROJ_PS_WGS84) .OR. (proj_code == PROJ_ALBERS_NAD83) .OR. & (proj_code == PROJ_MERC) ) THEN proj%dx = dx IF (truelat1 .LT. 0.) THEN proj%hemi = -1.0 ELSE proj%hemi = 1.0 ENDIF proj%rebydx = proj%re_m / dx ENDIF ENDIF pick_proj: SELECT CASE(proj%code) CASE(PROJ_PS) CALL set_ps(proj) CASE(PROJ_PS_WGS84) CALL set_ps_wgs84(proj) CASE(PROJ_ALBERS_NAD83) CALL set_albers_nad83(proj) CASE(PROJ_LC) IF (ABS(proj%truelat2) .GT. 90.) THEN proj%truelat2=proj%truelat1 ENDIF CALL set_lc(proj) CASE (PROJ_MERC) CALL set_merc(proj) CASE (PROJ_LATLON) CASE (PROJ_GAUSS) CALL set_gauss(proj) CASE (PROJ_CYL) CALL set_cyl(proj) CASE (PROJ_CASSINI) CALL set_cassini(proj) CASE (PROJ_ROTLL) END SELECT pick_proj proj%init = .TRUE. RETURN END SUBROUTINE map_set SUBROUTINE latlon_to_ij(proj, lat, lon, i, j) ! Converts input lat/lon values to the cartesian (i,j) value ! for the given projection. IMPLICIT NONE TYPE(proj_info), INTENT(IN) :: proj REAL, INTENT(IN) :: lat REAL, INTENT(IN) :: lon REAL, INTENT(OUT) :: i REAL, INTENT(OUT) :: j IF (.NOT.proj%init) THEN PRINT '(A)', 'You have not called map_set for this projection' CALL wrf_error_fatal ( 'LATLON_TO_IJ' ) ENDIF SELECT CASE(proj%code) CASE(PROJ_LATLON) CALL llij_latlon(lat,lon,proj,i,j) CASE(PROJ_MERC) CALL llij_merc(lat,lon,proj,i,j) CASE(PROJ_PS) CALL llij_ps(lat,lon,proj,i,j) CASE(PROJ_PS_WGS84) CALL llij_ps_wgs84(lat,lon,proj,i,j) CASE(PROJ_ALBERS_NAD83) CALL llij_albers_nad83(lat,lon,proj,i,j) CASE(PROJ_LC) CALL llij_lc(lat,lon,proj,i,j) CASE(PROJ_GAUSS) CALL llij_gauss(lat,lon,proj,i,j) CASE(PROJ_CYL) CALL llij_cyl(lat,lon,proj,i,j) CASE(PROJ_CASSINI) CALL llij_cassini(lat,lon,proj,i,j) CASE(PROJ_ROTLL) CALL llij_rotlatlon(lat,lon,proj,i,j) CASE DEFAULT PRINT '(A,I2)', 'Unrecognized map projection code: ', proj%code CALL wrf_error_fatal ( 'LATLON_TO_IJ' ) END SELECT RETURN END SUBROUTINE latlon_to_ij SUBROUTINE ij_to_latlon(proj, i, j, lat, lon) ! Computes geographical latitude and longitude for a given (i,j) point ! in a grid with a projection of proj IMPLICIT NONE TYPE(proj_info),INTENT(IN) :: proj REAL, INTENT(IN) :: i REAL, INTENT(IN) :: j REAL, INTENT(OUT) :: lat REAL, INTENT(OUT) :: lon IF (.NOT.proj%init) THEN PRINT '(A)', 'You have not called map_set for this projection' CALL wrf_error_fatal ( 'IJ_TO_LATLON' ) ENDIF SELECT CASE (proj%code) CASE (PROJ_LATLON) CALL ijll_latlon(i, j, proj, lat, lon) CASE (PROJ_MERC) CALL ijll_merc(i, j, proj, lat, lon) CASE (PROJ_PS) CALL ijll_ps(i, j, proj, lat, lon) CASE (PROJ_PS_WGS84) CALL ijll_ps_wgs84(i, j, proj, lat, lon) CASE (PROJ_ALBERS_NAD83) CALL ijll_albers_nad83(i, j, proj, lat, lon) CASE (PROJ_LC) CALL ijll_lc(i, j, proj, lat, lon) CASE (PROJ_CYL) CALL ijll_cyl(i, j, proj, lat, lon) CASE (PROJ_CASSINI) CALL ijll_cassini(i, j, proj, lat, lon) CASE (PROJ_ROTLL) CALL ijll_rotlatlon(i, j, proj, lat, lon) CASE DEFAULT PRINT '(A,I2)', 'Unrecognized map projection code: ', proj%code CALL wrf_error_fatal ( 'IJ_TO_LATLON' ) END SELECT RETURN END SUBROUTINE ij_to_latlon SUBROUTINE set_ps(proj) ! Initializes a polar-stereographic map projection from the partially ! filled proj structure. This routine computes the radius to the ! southwest corner and computes the i/j location of the pole for use ! in llij_ps and ijll_ps. IMPLICIT NONE ! Declare args TYPE(proj_info), INTENT(INOUT) :: proj ! Local vars REAL :: ala1 REAL :: alo1 REAL :: reflon REAL :: scale_top ! Executable code reflon = proj%stdlon + 90. ! Compute numerator term of map scale factor scale_top = 1. + proj%hemi * SIN(proj%truelat1 * rad_per_deg) ! Compute radius to lower-left (SW) corner ala1 = proj%lat1 * rad_per_deg proj%rsw = proj%rebydx*COS(ala1)*scale_top/(1.+proj%hemi*SIN(ala1)) ! Find the pole point alo1 = (proj%lon1 - reflon) * rad_per_deg proj%polei = proj%knowni - proj%rsw * COS(alo1) proj%polej = proj%knownj - proj%hemi * proj%rsw * SIN(alo1) RETURN END SUBROUTINE set_ps SUBROUTINE llij_ps(lat,lon,proj,i,j) ! Given latitude (-90 to 90), longitude (-180 to 180), and the ! standard polar-stereographic projection information via the ! public proj structure, this routine returns the i/j indices which ! if within the domain range from 1->nx and 1->ny, respectively. IMPLICIT NONE ! Delcare input arguments REAL, INTENT(IN) :: lat REAL, INTENT(IN) :: lon TYPE(proj_info),INTENT(IN) :: proj ! Declare output arguments REAL, INTENT(OUT) :: i !(x-index) REAL, INTENT(OUT) :: j !(y-index) ! Declare local variables REAL :: reflon REAL :: scale_top REAL :: ala REAL :: alo REAL :: rm ! BEGIN CODE reflon = proj%stdlon + 90. ! Compute numerator term of map scale factor scale_top = 1. + proj%hemi * SIN(proj%truelat1 * rad_per_deg) ! Find radius to desired point ala = lat * rad_per_deg rm = proj%rebydx * COS(ala) * scale_top/(1. + proj%hemi *SIN(ala)) alo = (lon - reflon) * rad_per_deg i = proj%polei + rm * COS(alo) j = proj%polej + proj%hemi * rm * SIN(alo) RETURN END SUBROUTINE llij_ps SUBROUTINE ijll_ps(i, j, proj, lat, lon) ! This is the inverse subroutine of llij_ps. It returns the ! latitude and longitude of an i/j point given the projection info ! structure. IMPLICIT NONE ! Declare input arguments REAL, INTENT(IN) :: i ! Column REAL, INTENT(IN) :: j ! Row TYPE (proj_info), INTENT(IN) :: proj ! Declare output arguments REAL, INTENT(OUT) :: lat ! -90 -> 90 north REAL, INTENT(OUT) :: lon ! -180 -> 180 East ! Local variables REAL :: reflon REAL :: scale_top REAL :: xx,yy REAL :: gi2, r2 REAL :: arccos ! Begin Code ! Compute the reference longitude by rotating 90 degrees to the east ! to find the longitude line parallel to the positive x-axis. reflon = proj%stdlon + 90. ! Compute numerator term of map scale factor scale_top = 1. + proj%hemi * SIN(proj%truelat1 * rad_per_deg) ! Compute radius to point of interest xx = i - proj%polei yy = (j - proj%polej) * proj%hemi r2 = xx**2 + yy**2 ! Now the magic code IF (r2 .EQ. 0.) THEN lat = proj%hemi * 90. lon = reflon ELSE gi2 = (proj%rebydx * scale_top)**2. lat = deg_per_rad * proj%hemi * ASIN((gi2-r2)/(gi2+r2)) arccos = ACOS(xx/SQRT(r2)) IF (yy .GT. 0) THEN lon = reflon + deg_per_rad * arccos ELSE lon = reflon - deg_per_rad * arccos ENDIF ENDIF ! Convert to a -180 -> 180 East convention IF (lon .GT. 180.) lon = lon - 360. IF (lon .LT. -180.) lon = lon + 360. RETURN END SUBROUTINE ijll_ps SUBROUTINE set_ps_wgs84(proj) ! Initializes a polar-stereographic map projection (WGS84 ellipsoid) ! from the partially filled proj structure. This routine computes the ! radius to the southwest corner and computes the i/j location of the ! pole for use in llij_ps and ijll_ps. IMPLICIT NONE ! Arguments TYPE(proj_info), INTENT(INOUT) :: proj ! Local variables real :: h, mc, tc, t, rho h = proj%hemi mc = cos(h*proj%truelat1*rad_per_deg)/sqrt(1.0-(E_WGS84*sin(h*proj%truelat1*rad_per_deg))**2.0) tc = sqrt(((1.0-sin(h*proj%truelat1*rad_per_deg))/(1.0+sin(h*proj%truelat1*rad_per_deg)))* & (((1.0+E_WGS84*sin(h*proj%truelat1*rad_per_deg))/(1.0-E_WGS84*sin(h*proj%truelat1*rad_per_deg)))**E_WGS84 )) ! Find the i/j location of reference lat/lon with respect to the pole of the projection t = sqrt(((1.0-sin(h*proj%lat1*rad_per_deg))/(1.0+sin(h*proj%lat1*rad_per_deg)))* & (((1.0+E_WGS84*sin(h*proj%lat1*rad_per_deg))/(1.0-E_WGS84*sin(h*proj%lat1*rad_per_deg)) )**E_WGS84 ) ) rho = h * (A_WGS84 / proj%dx) * mc * t / tc proj%polei = rho * sin((h*proj%lon1 - h*proj%stdlon)*rad_per_deg) proj%polej = -rho * cos((h*proj%lon1 - h*proj%stdlon)*rad_per_deg) RETURN END SUBROUTINE set_ps_wgs84 SUBROUTINE llij_ps_wgs84(lat,lon,proj,i,j) ! Given latitude (-90 to 90), longitude (-180 to 180), and the ! standard polar-stereographic projection information via the ! public proj structure, this routine returns the i/j indices which ! if within the domain range from 1->nx and 1->ny, respectively. IMPLICIT NONE ! Arguments REAL, INTENT(IN) :: lat REAL, INTENT(IN) :: lon REAL, INTENT(OUT) :: i !(x-index) REAL, INTENT(OUT) :: j !(y-index) TYPE(proj_info),INTENT(IN) :: proj ! Local variables real :: h, mc, tc, t, rho h = proj%hemi mc = cos(h*proj%truelat1*rad_per_deg)/sqrt(1.0-(E_WGS84*sin(h*proj%truelat1*rad_per_deg))**2.0) tc = sqrt(((1.0-sin(h*proj%truelat1*rad_per_deg))/(1.0+sin(h*proj%truelat1*rad_per_deg)))* & (((1.0+E_WGS84*sin(h*proj%truelat1*rad_per_deg))/(1.0-E_WGS84*sin(h*proj%truelat1*rad_per_deg)))**E_WGS84 )) t = sqrt(((1.0-sin(h*lat*rad_per_deg))/(1.0+sin(h*lat*rad_per_deg))) * & (((1.0+E_WGS84*sin(h*lat*rad_per_deg))/(1.0-E_WGS84*sin(h*lat*rad_per_deg)))**E_WGS84)) ! Find the x/y location of the requested lat/lon with respect to the pole of the projection rho = (A_WGS84 / proj%dx) * mc * t / tc i = h * rho * sin((h*lon - h*proj%stdlon)*rad_per_deg) j = h *(-rho)* cos((h*lon - h*proj%stdlon)*rad_per_deg) ! Get i/j relative to reference i/j i = proj%knowni + (i - proj%polei) j = proj%knownj + (j - proj%polej) RETURN END SUBROUTINE llij_ps_wgs84 SUBROUTINE ijll_ps_wgs84(i, j, proj, lat, lon) ! This is the inverse subroutine of llij_ps. It returns the ! latitude and longitude of an i/j point given the projection info ! structure. implicit none ! Arguments REAL, INTENT(IN) :: i ! Column REAL, INTENT(IN) :: j ! Row REAL, INTENT(OUT) :: lat ! -90 -> 90 north REAL, INTENT(OUT) :: lon ! -180 -> 180 East TYPE (proj_info), INTENT(IN) :: proj ! Local variables real :: h, mc, tc, t, rho, x, y real :: chi, a, b, c, d h = proj%hemi x = (i - proj%knowni + proj%polei) y = (j - proj%knownj + proj%polej) mc = cos(h*proj%truelat1*rad_per_deg)/sqrt(1.0-(E_WGS84*sin(h*proj%truelat1*rad_per_deg))**2.0) tc = sqrt(((1.0-sin(h*proj%truelat1*rad_per_deg))/(1.0+sin(h*proj%truelat1*rad_per_deg))) * & (((1.0+E_WGS84*sin(h*proj%truelat1*rad_per_deg))/(1.0-E_WGS84*sin(h*proj%truelat1*rad_per_deg)))**E_WGS84 )) rho = sqrt((x*proj%dx)**2.0 + (y*proj%dx)**2.0) t = rho * tc / (A_WGS84 * mc) lon = h*proj%stdlon*rad_per_deg + h*atan2(h*x,h*(-y)) chi = PI/2.0-2.0*atan(t) a = 1./2.*E_WGS84**2. + 5./24.*E_WGS84**4. + 1./40.*E_WGS84**6. + 73./2016.*E_WGS84**8. b = 7./24.*E_WGS84**4. + 29./120.*E_WGS84**6. + 54113./40320.*E_WGS84**8. c = 7./30.*E_WGS84**6. + 81./280.*E_WGS84**8. d = 4279./20160.*E_WGS84**8. lat = chi + sin(2.*chi)*(a + cos(2.*chi)*(b + cos(2.*chi)*(c + d*cos(2.*chi)))) lat = h * lat lat = lat*deg_per_rad lon = lon*deg_per_rad RETURN END SUBROUTINE ijll_ps_wgs84 SUBROUTINE set_albers_nad83(proj) ! Initializes an Albers equal area map projection (NAD83 ellipsoid) ! from the partially filled proj structure. This routine computes the ! radius to the southwest corner and computes the i/j location of the ! pole for use in llij_albers_nad83 and ijll_albers_nad83. IMPLICIT NONE ! Arguments TYPE(proj_info), INTENT(INOUT) :: proj ! Local variables real :: h, m1, m2, q1, q2, theta, q, sinphi h = proj%hemi m1 = cos(h*proj%truelat1*rad_per_deg)/sqrt(1.0-(E_NAD83*sin(h*proj%truelat1*rad_per_deg))**2.0) m2 = cos(h*proj%truelat2*rad_per_deg)/sqrt(1.0-(E_NAD83*sin(h*proj%truelat2*rad_per_deg))**2.0) sinphi = sin(proj%truelat1*rad_per_deg) q1 = (1.0-E_NAD83**2.0) * & ((sinphi/(1.0-(E_NAD83*sinphi)**2.0)) - 1.0/(2.0*E_NAD83) * log((1.0-E_NAD83*sinphi)/(1.0+E_NAD83*sinphi))) sinphi = sin(proj%truelat2*rad_per_deg) q2 = (1.0-E_NAD83**2.0) * & ((sinphi/(1.0-(E_NAD83*sinphi)**2.0)) - 1.0/(2.0*E_NAD83) * log((1.0-E_NAD83*sinphi)/(1.0+E_NAD83*sinphi))) if (proj%truelat1 == proj%truelat2) then proj%nc = sin(proj%truelat1*rad_per_deg) else proj%nc = (m1**2.0 - m2**2.0) / (q2 - q1) end if proj%bigc = m1**2.0 + proj%nc*q1 ! Find the i/j location of reference lat/lon with respect to the pole of the projection sinphi = sin(proj%lat1*rad_per_deg) q = (1.0-E_NAD83**2.0) * & ((sinphi/(1.0-(E_NAD83*sinphi)**2.0)) - 1.0/(2.0*E_NAD83) * log((1.0-E_NAD83*sinphi)/(1.0+E_NAD83*sinphi))) proj%rho0 = h * (A_NAD83 / proj%dx) * sqrt(proj%bigc - proj%nc * q) / proj%nc theta = proj%nc*(proj%lon1 - proj%stdlon)*rad_per_deg proj%polei = proj%rho0 * sin(h*theta) proj%polej = proj%rho0 - proj%rho0 * cos(h*theta) RETURN END SUBROUTINE set_albers_nad83 SUBROUTINE llij_albers_nad83(lat,lon,proj,i,j) ! Given latitude (-90 to 90), longitude (-180 to 180), and the ! standard projection information via the ! public proj structure, this routine returns the i/j indices which ! if within the domain range from 1->nx and 1->ny, respectively. IMPLICIT NONE ! Arguments REAL, INTENT(IN) :: lat REAL, INTENT(IN) :: lon REAL, INTENT(OUT) :: i !(x-index) REAL, INTENT(OUT) :: j !(y-index) TYPE(proj_info),INTENT(IN) :: proj ! Local variables real :: h, q, rho, theta, sinphi h = proj%hemi sinphi = sin(h*lat*rad_per_deg) ! Find the x/y location of the requested lat/lon with respect to the pole of the projection q = (1.0-E_NAD83**2.0) * & ((sinphi/(1.0-(E_NAD83*sinphi)**2.0)) - 1.0/(2.0*E_NAD83) * log((1.0-E_NAD83*sinphi)/(1.0+E_NAD83*sinphi))) rho = h * (A_NAD83 / proj%dx) * sqrt(proj%bigc - proj%nc * q) / proj%nc theta = proj%nc * (h*lon - h*proj%stdlon)*rad_per_deg i = h*rho*sin(theta) j = h*proj%rho0 - h*rho*cos(theta) ! Get i/j relative to reference i/j i = proj%knowni + (i - proj%polei) j = proj%knownj + (j - proj%polej) RETURN END SUBROUTINE llij_albers_nad83 SUBROUTINE ijll_albers_nad83(i, j, proj, lat, lon) ! This is the inverse subroutine of llij_albers_nad83. It returns the ! latitude and longitude of an i/j point given the projection info ! structure. implicit none ! Arguments REAL, INTENT(IN) :: i ! Column REAL, INTENT(IN) :: j ! Row REAL, INTENT(OUT) :: lat ! -90 -> 90 north REAL, INTENT(OUT) :: lon ! -180 -> 180 East TYPE (proj_info), INTENT(IN) :: proj ! Local variables real :: h, q, rho, theta, beta, x, y real :: a, b, c h = proj%hemi x = (i - proj%knowni + proj%polei) y = (j - proj%knownj + proj%polej) rho = sqrt(x**2.0 + (proj%rho0 - y)**2.0) theta = atan2(x, proj%rho0-y) q = (proj%bigc - (rho*proj%nc*proj%dx/A_NAD83)**2.0) / proj%nc beta = asin(q/(1.0 - log((1.0-E_NAD83)/(1.0+E_NAD83))*(1.0-E_NAD83**2.0)/(2.0*E_NAD83))) a = 1./3.*E_NAD83**2. + 31./180.*E_NAD83**4. + 517./5040.*E_NAD83**6. b = 23./360.*E_NAD83**4. + 251./3780.*E_NAD83**6. c = 761./45360.*E_NAD83**6. lat = beta + a*sin(2.*beta) + b*sin(4.*beta) + c*sin(6.*beta) lat = h*lat*deg_per_rad lon = proj%stdlon + theta*deg_per_rad/proj%nc RETURN END SUBROUTINE ijll_albers_nad83 SUBROUTINE set_lc(proj) ! Initialize the remaining items in the proj structure for a ! lambert conformal grid. IMPLICIT NONE TYPE(proj_info), INTENT(INOUT) :: proj REAL :: arg REAL :: deltalon1 REAL :: tl1r REAL :: ctl1r ! Compute cone factor CALL lc_cone(proj%truelat1, proj%truelat2, proj%cone) ! Compute longitude differences and ensure we stay out of the ! forbidden "cut zone" deltalon1 = proj%lon1 - proj%stdlon IF (deltalon1 .GT. +180.) deltalon1 = deltalon1 - 360. IF (deltalon1 .LT. -180.) deltalon1 = deltalon1 + 360. ! Convert truelat1 to radian and compute COS for later use tl1r = proj%truelat1 * rad_per_deg ctl1r = COS(tl1r) ! Compute the radius to our known lower-left (SW) corner proj%rsw = proj%rebydx * ctl1r/proj%cone * & (TAN((90.*proj%hemi-proj%lat1)*rad_per_deg/2.) / & TAN((90.*proj%hemi-proj%truelat1)*rad_per_deg/2.))**proj%cone ! Find pole point arg = proj%cone*(deltalon1*rad_per_deg) proj%polei = proj%hemi*proj%knowni - proj%hemi * proj%rsw * SIN(arg) proj%polej = proj%hemi*proj%knownj + proj%rsw * COS(arg) RETURN END SUBROUTINE set_lc SUBROUTINE lc_cone(truelat1, truelat2, cone) ! Subroutine to compute the cone factor of a Lambert Conformal projection IMPLICIT NONE ! Input Args REAL, INTENT(IN) :: truelat1 ! (-90 -> 90 degrees N) REAL, INTENT(IN) :: truelat2 ! " " " " " ! Output Args REAL, INTENT(OUT) :: cone ! Locals ! BEGIN CODE ! First, see if this is a secant or tangent projection. For tangent ! projections, truelat1 = truelat2 and the cone is tangent to the ! Earth's surface at this latitude. For secant projections, the cone ! intersects the Earth's surface at each of the distinctly different ! latitudes IF (ABS(truelat1-truelat2) .GT. 0.1) THEN cone = ALOG10(COS(truelat1*rad_per_deg)) - & ALOG10(COS(truelat2*rad_per_deg)) cone = cone /(ALOG10(TAN((45.0 - ABS(truelat1)/2.0) * rad_per_deg)) - & ALOG10(TAN((45.0 - ABS(truelat2)/2.0) * rad_per_deg))) ELSE cone = SIN(ABS(truelat1)*rad_per_deg ) ENDIF RETURN END SUBROUTINE lc_cone SUBROUTINE ijll_lc( i, j, proj, lat, lon) ! Subroutine to convert from the (i,j) cartesian coordinate to the ! geographical latitude and longitude for a Lambert Conformal projection. ! History: ! 25 Jul 01: Corrected by B. Shaw, NOAA/FSL ! IMPLICIT NONE ! Input Args REAL, INTENT(IN) :: i ! Cartesian X coordinate REAL, INTENT(IN) :: j ! Cartesian Y coordinate TYPE(proj_info),INTENT(IN) :: proj ! Projection info structure ! Output Args REAL, INTENT(OUT) :: lat ! Latitude (-90->90 deg N) REAL, INTENT(OUT) :: lon ! Longitude (-180->180 E) ! Locals REAL :: inew REAL :: jnew REAL :: r REAL :: chi,chi1,chi2 REAL :: r2 REAL :: xx REAL :: yy ! BEGIN CODE chi1 = (90. - proj%hemi*proj%truelat1)*rad_per_deg chi2 = (90. - proj%hemi*proj%truelat2)*rad_per_deg ! See if we are in the southern hemispere and flip the indices ! if we are. inew = proj%hemi * i jnew = proj%hemi * j ! Compute radius**2 to i/j location xx = inew - proj%polei yy = proj%polej - jnew r2 = (xx*xx + yy*yy) r = SQRT(r2)/proj%rebydx ! Convert to lat/lon IF (r2 .EQ. 0.) THEN lat = proj%hemi * 90. lon = proj%stdlon ELSE ! Longitude lon = proj%stdlon + deg_per_rad * ATAN2(proj%hemi*xx,yy)/proj%cone lon = MOD(lon+360., 360.) ! Latitude. Latitude determined by solving an equation adapted ! from: ! Maling, D.H., 1973: Coordinate Systems and Map Projections ! Equations #20 in Appendix I. IF (chi1 .EQ. chi2) THEN chi = 2.0*ATAN( ( r/TAN(chi1) )**(1./proj%cone) * TAN(chi1*0.5) ) ELSE chi = 2.0*ATAN( (r*proj%cone/SIN(chi1))**(1./proj%cone) * TAN(chi1*0.5)) ENDIF lat = (90.0-chi*deg_per_rad)*proj%hemi ENDIF IF (lon .GT. +180.) lon = lon - 360. IF (lon .LT. -180.) lon = lon + 360. RETURN END SUBROUTINE ijll_lc SUBROUTINE llij_lc( lat, lon, proj, i, j) ! Subroutine to compute the geographical latitude and longitude values ! to the cartesian x/y on a Lambert Conformal projection. IMPLICIT NONE ! Input Args REAL, INTENT(IN) :: lat ! Latitude (-90->90 deg N) REAL, INTENT(IN) :: lon ! Longitude (-180->180 E) TYPE(proj_info),INTENT(IN) :: proj ! Projection info structure ! Output Args REAL, INTENT(OUT) :: i ! Cartesian X coordinate REAL, INTENT(OUT) :: j ! Cartesian Y coordinate ! Locals REAL :: arg REAL :: deltalon REAL :: tl1r REAL :: rm REAL :: ctl1r ! BEGIN CODE ! Compute deltalon between known longitude and standard lon and ensure ! it is not in the cut zone deltalon = lon - proj%stdlon IF (deltalon .GT. +180.) deltalon = deltalon - 360. IF (deltalon .LT. -180.) deltalon = deltalon + 360. ! Convert truelat1 to radian and compute COS for later use tl1r = proj%truelat1 * rad_per_deg ctl1r = COS(tl1r) ! Radius to desired point rm = proj%rebydx * ctl1r/proj%cone * & (TAN((90.*proj%hemi-lat)*rad_per_deg/2.) / & TAN((90.*proj%hemi-proj%truelat1)*rad_per_deg/2.))**proj%cone arg = proj%cone*(deltalon*rad_per_deg) i = proj%polei + proj%hemi * rm * SIN(arg) j = proj%polej - rm * COS(arg) ! Finally, if we are in the southern hemisphere, flip the i/j ! values to a coordinate system where (1,1) is the SW corner ! (what we assume) which is different than the original NCEP ! algorithms which used the NE corner as the origin in the ! southern hemisphere (left-hand vs. right-hand coordinate?) i = proj%hemi * i j = proj%hemi * j RETURN END SUBROUTINE llij_lc SUBROUTINE set_merc(proj) ! Sets up the remaining basic elements for the mercator projection IMPLICIT NONE TYPE(proj_info), INTENT(INOUT) :: proj REAL :: clain ! Preliminary variables clain = COS(rad_per_deg*proj%truelat1) proj%dlon = proj%dx / (proj%re_m * clain) ! Compute distance from equator to origin, and store in the ! proj%rsw tag. proj%rsw = 0. IF (proj%lat1 .NE. 0.) THEN proj%rsw = (ALOG(TAN(0.5*((proj%lat1+90.)*rad_per_deg))))/proj%dlon ENDIF RETURN END SUBROUTINE set_merc SUBROUTINE llij_merc(lat, lon, proj, i, j) ! Compute i/j coordinate from lat lon for mercator projection IMPLICIT NONE REAL, INTENT(IN) :: lat REAL, INTENT(IN) :: lon TYPE(proj_info),INTENT(IN) :: proj REAL,INTENT(OUT) :: i REAL,INTENT(OUT) :: j REAL :: deltalon deltalon = lon - proj%lon1 IF (deltalon .LT. -180.) deltalon = deltalon + 360. IF (deltalon .GT. 180.) deltalon = deltalon - 360. i = proj%knowni + (deltalon/(proj%dlon*deg_per_rad)) j = proj%knownj + (ALOG(TAN(0.5*((lat + 90.) * rad_per_deg)))) / & proj%dlon - proj%rsw RETURN END SUBROUTINE llij_merc SUBROUTINE ijll_merc(i, j, proj, lat, lon) ! Compute the lat/lon from i/j for mercator projection IMPLICIT NONE REAL,INTENT(IN) :: i REAL,INTENT(IN) :: j TYPE(proj_info),INTENT(IN) :: proj REAL, INTENT(OUT) :: lat REAL, INTENT(OUT) :: lon lat = 2.0*ATAN(EXP(proj%dlon*(proj%rsw + j-proj%knownj)))*deg_per_rad - 90. lon = (i-proj%knowni)*proj%dlon*deg_per_rad + proj%lon1 IF (lon.GT.180.) lon = lon - 360. IF (lon.LT.-180.) lon = lon + 360. RETURN END SUBROUTINE ijll_merc SUBROUTINE llij_latlon(lat, lon, proj, i, j) ! Compute the i/j location of a lat/lon on a LATLON grid. IMPLICIT NONE REAL, INTENT(IN) :: lat REAL, INTENT(IN) :: lon TYPE(proj_info), INTENT(IN) :: proj REAL, INTENT(OUT) :: i REAL, INTENT(OUT) :: j REAL :: deltalat REAL :: deltalon ! Compute deltalat and deltalon as the difference between the input ! lat/lon and the origin lat/lon deltalat = lat - proj%lat1 deltalon = lon - proj%lon1 ! Compute i/j i = deltalon/proj%loninc j = deltalat/proj%latinc i = i + proj%knowni j = j + proj%knownj RETURN END SUBROUTINE llij_latlon SUBROUTINE ijll_latlon(i, j, proj, lat, lon) ! Compute the lat/lon location of an i/j on a LATLON grid. IMPLICIT NONE REAL, INTENT(IN) :: i REAL, INTENT(IN) :: j TYPE(proj_info), INTENT(IN) :: proj REAL, INTENT(OUT) :: lat REAL, INTENT(OUT) :: lon REAL :: i_work, j_work REAL :: deltalat REAL :: deltalon i_work = i - proj%knowni j_work = j - proj%knownj ! Compute deltalat and deltalon deltalat = j_work*proj%latinc deltalon = i_work*proj%loninc lat = proj%lat1 + deltalat lon = proj%lon1 + deltalon RETURN END SUBROUTINE ijll_latlon SUBROUTINE set_cyl(proj) implicit none ! Arguments type(proj_info), intent(inout) :: proj proj%hemi = 1.0 END SUBROUTINE set_cyl SUBROUTINE llij_cyl(lat, lon, proj, i, j) implicit none ! Arguments real, intent(in) :: lat, lon real, intent(out) :: i, j type(proj_info), intent(in) :: proj ! Local variables real :: deltalat real :: deltalon ! Compute deltalat and deltalon as the difference between the input ! lat/lon and the origin lat/lon deltalat = lat - proj%lat1 ! deltalon = lon - proj%stdlon deltalon = lon - proj%lon1 if (deltalon < 0.) deltalon = deltalon + 360. if (deltalon > 360.) deltalon = deltalon - 360. ! Compute i/j i = deltalon/proj%loninc j = deltalat/proj%latinc if (i <= 0.) i = i + 360./proj%loninc if (i > 360./proj%loninc) i = i - 360./proj%loninc i = i + proj%knowni j = j + proj%knownj END SUBROUTINE llij_cyl SUBROUTINE ijll_cyl(i, j, proj, lat, lon) implicit none ! Arguments real, intent(in) :: i, j real, intent(out) :: lat, lon type(proj_info), intent(in) :: proj ! Local variables real :: deltalat real :: deltalon real :: i_work, j_work i_work = i - proj%knowni j_work = j - proj%knownj if (i_work < 0.) i_work = i_work + 360./proj%loninc if (i_work >= 360./proj%loninc) i_work = i_work - 360./proj%loninc ! Compute deltalat and deltalon deltalat = j_work*proj%latinc deltalon = i_work*proj%loninc lat = deltalat + proj%lat1 ! lon = deltalon + proj%stdlon lon = deltalon + proj%lon1 if (lon < -180.) lon = lon + 360. if (lon > 180.) lon = lon - 360. END SUBROUTINE ijll_cyl SUBROUTINE set_cassini(proj) implicit none ! Arguments type(proj_info), intent(inout) :: proj ! Local variables real :: comp_lat, comp_lon logical :: global_domain proj%hemi = 1.0 ! Try to determine whether this domain has global coverage if (abs(proj%lat1 - proj%latinc/2. + 90.) < 0.001 .and. & abs(mod(proj%lon1 - proj%loninc/2. - proj%stdlon,360.)) < 0.001) then global_domain = .true. else global_domain = .false. end if if (abs(proj%lat0) /= 90. .and. .not.global_domain) then call rotate_coords(proj%lat1,proj%lon1,comp_lat,comp_lon,proj%lat0,proj%lon0,proj%stdlon,-1) proj%lat1 = comp_lat proj%lon1 = comp_lon end if END SUBROUTINE set_cassini SUBROUTINE llij_cassini(lat, lon, proj, i, j) implicit none ! Arguments real, intent(in) :: lat, lon real, intent(out) :: i, j type(proj_info), intent(in) :: proj ! Local variables real :: comp_lat, comp_lon ! Convert geographic to computational lat/lon if (abs(proj%lat0) /= 90.) then call rotate_coords(lat,lon,comp_lat,comp_lon,proj%lat0,proj%lon0,proj%stdlon,-1) else comp_lat = lat comp_lon = lon end if ! Convert computational lat/lon to i/j call llij_cyl(comp_lat, comp_lon, proj, i, j) END SUBROUTINE llij_cassini SUBROUTINE ijll_cassini(i, j, proj, lat, lon) implicit none ! Arguments real, intent(in) :: i, j real, intent(out) :: lat, lon type(proj_info), intent(in) :: proj ! Local variables real :: comp_lat, comp_lon ! Convert i/j to computational lat/lon call ijll_cyl(i, j, proj, comp_lat, comp_lon) ! Convert computational to geographic lat/lon if (abs(proj%lat0) /= 90.) then call rotate_coords(comp_lat,comp_lon,lat,lon,proj%lat0,proj%lon0,proj%stdlon,1) else lat = comp_lat lon = comp_lon end if END SUBROUTINE ijll_cassini !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! Purpose: Converts between computational and geographic lat/lon for Cassini ! ! Notes: This routine was provided by Bill Skamarock, 2007-03-27 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! SUBROUTINE rotate_coords(ilat,ilon,olat,olon,lat_np,lon_np,lon_0,direction) IMPLICIT NONE REAL, INTENT(IN ) :: ilat, ilon REAL, INTENT( OUT) :: olat, olon REAL, INTENT(IN ) :: lat_np, lon_np, lon_0 INTEGER, INTENT(IN ), OPTIONAL :: direction ! >=0, default : computational -> geographical ! < 0 : geographical -> computational REAL :: rlat, rlon REAL :: phi_np, lam_np, lam_0, dlam REAL :: sinphi, cosphi, coslam, sinlam ! Convert all angles to radians phi_np = lat_np * rad_per_deg lam_np = lon_np * rad_per_deg lam_0 = lon_0 * rad_per_deg rlat = ilat * rad_per_deg rlon = ilon * rad_per_deg IF ( PRESENT(direction) ) THEN IF (direction < 0) THEN ! The equations are exactly the same except for one small difference ! with respect to longitude ... dlam = PI - lam_0 ELSE dlam = lam_np END IF ELSE dlam = lam_np END IF sinphi = COS(phi_np)*COS(rlat)*COS(rlon-dlam) + SIN(phi_np)*SIN(rlat) cosphi = SQRT(1.-sinphi*sinphi) coslam = SIN(phi_np)*COS(rlat)*COS(rlon-dlam) - COS(phi_np)*SIN(rlat) sinlam = COS(rlat)*SIN(rlon-dlam) IF ( cosphi /= 0. ) THEN coslam = coslam/cosphi sinlam = sinlam/cosphi END IF olat = deg_per_rad*ASIN(sinphi) olon = deg_per_rad*(ATAN2(sinlam,coslam)-dlam-lam_0+lam_np) ! Both of my F90 text books prefer the DO-EXIT form, and claim it is faster ! when optimization is turned on (as we will always do...) DO IF (olon >= -180.) EXIT olon = olon + 360. END DO DO IF (olon <= 180.) EXIT olon = olon - 360. END DO END SUBROUTINE rotate_coords SUBROUTINE llij_rotlatlon(lat, lon, proj, i_real, j_real) IMPLICIT NONE ! Arguments REAL, INTENT(IN) :: lat, lon REAL :: i, j REAL, INTENT(OUT) :: i_real, j_real TYPE (proj_info), INTENT(IN) :: proj ! Local variables INTEGER :: ii,imt,jj,jmt,k,krows,ncol,nrow,iri REAL(KIND=HIGH) :: dphd,dlmd !Grid increments, degrees REAL(KIND=HIGH) :: glatd !Geographic latitude, positive north REAL(KIND=HIGH) :: glond !Geographic longitude, positive west REAL(KIND=HIGH) :: col,d1,d2,d2r,dlm,dlm1,dlm2,dph,glat,glon, & pi,r2d,row,tlat,tlat1,tlat2, & tlon,tlon1,tlon2,tph0,tlm0,x,y,z glatd = lat glond = -lon dphd = proj%phi/REAL((proj%jydim-1)/2) dlmd = proj%lambda/REAL(proj%ixdim-1) pi = ACOS(-1.0) d2r = pi/180. r2d = 1./d2r imt = 2*proj%ixdim-1 jmt = proj%jydim/2+1 glat = glatd*d2r glon = glond*d2r dph = dphd*d2r dlm = dlmd*d2r tph0 = proj%lat1*d2r tlm0 = -proj%lon1*d2r x = COS(tph0)*COS(glat)*COS(glon-tlm0)+SIN(tph0)*SIN(glat) y = -COS(glat)*SIN(glon-tlm0) z = COS(tph0)*SIN(glat)-SIN(tph0)*COS(glat)*COS(glon-tlm0) tlat = r2d*ATAN(z/SQRT(x*x+y*y)) tlon = r2d*ATAN(y/x) row = tlat/dphd+jmt col = tlon/dlmd+proj%ixdim if ( (row - INT(row)) .gt. 0.999) then row = row + 0.0002 else if ( (col - INT(col)) .gt. 0.999) then col = col + 0.0002 end if nrow = INT(row) ncol = INT(col) ! nrow = NINT(row) ! ncol = NINT(col) tlat = tlat*d2r tlon = tlon*d2r IF (proj%stagger == HH) THEN IF (mod(nrow,2) .eq. 0) then i_real = col / 2.0 ELSE i_real = col / 2.0 + 0.5 ENDIF j_real=row IF ((abs(MOD(nrow,2)) == 1 .AND. abs(MOD(ncol,2)) == 1) .OR. & (MOD(nrow,2) == 0 .AND. MOD(ncol,2) == 0)) THEN tlat1 = (nrow-jmt)*dph tlat2 = tlat1+dph tlon1 = (ncol-proj%ixdim)*dlm tlon2 = tlon1+dlm dlm1 = tlon-tlon1 dlm2 = tlon-tlon2 d1 = ACOS(COS(tlat)*COS(tlat1)*COS(dlm1)+SIN(tlat)*SIN(tlat1)) d2 = ACOS(COS(tlat)*COS(tlat2)*COS(dlm2)+SIN(tlat)*SIN(tlat2)) IF (d1 > d2) THEN nrow = nrow+1 ncol = ncol+1 END IF ELSE tlat1 = (nrow+1-jmt)*dph tlat2 = tlat1-dph tlon1 = (ncol-proj%ixdim)*dlm tlon2 = tlon1+dlm dlm1 = tlon-tlon1 dlm2 = tlon-tlon2 d1 = ACOS(COS(tlat)*COS(tlat1)*COS(dlm1)+SIN(tlat)*SIN(tlat1)) d2 = ACOS(COS(tlat)*COS(tlat2)*COS(dlm2)+SIN(tlat)*SIN(tlat2)) IF (d1 < d2) THEN nrow = nrow+1 ELSE ncol = ncol+1 END IF END IF ELSE IF (proj%stagger == VV) THEN IF (mod(nrow,2) .eq. 0) then i_real = col / 2.0 + 0.5 ELSE i_real = col / 2.0 ENDIF j_real=row IF ((MOD(nrow,2) == 0 .AND. abs(MOD(ncol,2)) == 1) .OR. & (abs(MOD(nrow,2)) == 1 .AND. MOD(ncol,2) == 0)) THEN tlat1 = (nrow-jmt)*dph tlat2 = tlat1+dph tlon1 = (ncol-proj%ixdim)*dlm tlon2 = tlon1+dlm dlm1 = tlon-tlon1 dlm2 = tlon-tlon2 d1 = ACOS(COS(tlat)*COS(tlat1)*COS(dlm1)+SIN(tlat)*SIN(tlat1)) d2 = ACOS(COS(tlat)*COS(tlat2)*COS(dlm2)+SIN(tlat)*SIN(tlat2)) IF (d1 > d2) THEN nrow = nrow+1 ncol = ncol+1 END IF ELSE tlat1 = (nrow+1-jmt)*dph tlat2 = tlat1-dph tlon1 = (ncol-proj%ixdim)*dlm tlon2 = tlon1+dlm dlm1 = tlon-tlon1 dlm2 = tlon-tlon2 d1 = ACOS(COS(tlat)*COS(tlat1)*COS(dlm1)+SIN(tlat)*SIN(tlat1)) d2 = ACOS(COS(tlat)*COS(tlat2)*COS(dlm2)+SIN(tlat)*SIN(tlat2)) IF (d1 < d2) THEN nrow = nrow+1 ELSE ncol = ncol+1 END IF END IF END IF !!! Added next line as a Kludge - not yet understood why needed if (ncol .le. 0) ncol=ncol-1 jj = nrow ii = ncol/2 IF (proj%stagger == HH) THEN IF (abs(MOD(jj,2)) == 1) ii = ii+1 ELSE IF (proj%stagger == VV) THEN IF (MOD(jj,2) == 0) ii=ii+1 END IF i = REAL(ii) j = REAL(jj) END SUBROUTINE llij_rotlatlon SUBROUTINE ijll_rotlatlon(i, j, proj, lat,lon) IMPLICIT NONE ! Arguments REAL, INTENT(IN) :: i, j REAL, INTENT(OUT) :: lat, lon TYPE (proj_info), INTENT(IN) :: proj ! Local variables INTEGER :: ih,jh INTEGER :: midcol,midrow,ncol,iadd1,iadd2,imt,jh2,knrow,krem,kv,nrow REAL :: i_work, j_work REAL :: dphd,dlmd !Grid increments, degrees REAL(KIND=HIGH) :: arg1,arg2,d2r,fctr,glatr,glatd,glond,pi, & r2d,tlatd,tlond,tlatr,tlonr,tlm0,tph0 REAL :: col i_work = i j_work = j if ( (j - INT(j)) .gt. 0.999) then j_work = j + 0.0002 endif jh = INT(j_work) dphd = proj%phi/REAL((proj%jydim-1)/2) dlmd = proj%lambda/REAL(proj%ixdim-1) pi = ACOS(-1.0) d2r = pi/180. r2d = 1./d2r tph0 = proj%lat1*d2r tlm0 = -proj%lon1*d2r midrow = (proj%jydim+1)/2 midcol = proj%ixdim col = 2*i_work-1+abs(MOD(jh+1,2)) tlatd = (j_work-midrow)*dphd tlond = (col-midcol)*dlmd IF (proj%stagger == VV) THEN if (mod(jh,2) .eq. 0) then tlond = tlond - DLMD else tlond = tlond + DLMD end if END IF tlatr = tlatd*d2r tlonr = tlond*d2r arg1 = SIN(tlatr)*COS(tph0)+COS(tlatr)*SIN(tph0)*COS(tlonr) glatr = ASIN(arg1) glatd = glatr*r2d arg2 = COS(tlatr)*COS(tlonr)/(COS(glatr)*COS(tph0))-TAN(glatr)*TAN(tph0) IF (ABS(arg2) > 1.) arg2 = ABS(arg2)/arg2 fctr = 1. IF (tlond > 0.) fctr = -1. glond = tlm0*r2d+fctr*ACOS(arg2)*r2d lat = glatd lon = -glond IF (lon .GT. +180.) lon = lon - 360. IF (lon .LT. -180.) lon = lon + 360. END SUBROUTINE ijll_rotlatlon SUBROUTINE set_gauss(proj) IMPLICIT NONE ! Argument type (proj_info), intent(inout) :: proj ! Initialize the array that will hold the Gaussian latitudes. IF ( ASSOCIATED( proj%gauss_lat ) ) THEN DEALLOCATE ( proj%gauss_lat ) END IF ! Get the needed space for our array. ALLOCATE ( proj%gauss_lat(proj%nlat*2) ) ! Compute the Gaussian latitudes. CALL gausll( proj%nlat*2 , proj%gauss_lat ) ! Now, these could be upside down from what we want, so let's check. ! We take advantage of the equatorial symmetry to remove any sort of ! array re-ordering. IF ( ABS(proj%gauss_lat(1) - proj%lat1) .GT. 0.01 ) THEN proj%gauss_lat = -1. * proj%gauss_lat END IF ! Just a sanity check. IF ( ABS(proj%gauss_lat(1) - proj%lat1) .GT. 0.01 ) THEN PRINT '(A)','Oops, something is not right with the Gaussian latitude computation.' PRINT '(A,F8.3,A)','The input data gave the starting latitude as ',proj%lat1,'.' PRINT '(A,F8.3,A)','This routine computed the starting latitude as +-',ABS(proj%gauss_lat(1)),'.' PRINT '(A,F8.3,A)','The difference is larger than 0.01 degrees, which is not expected.' CALL wrf_error_fatal ( 'Gaussian_latitude_computation' ) END IF END SUBROUTINE set_gauss SUBROUTINE gausll ( nlat , lat_sp ) IMPLICIT NONE INTEGER :: nlat , i REAL (KIND=HIGH) , PARAMETER :: pi = 3.141592653589793 REAL (KIND=HIGH) , DIMENSION(nlat) :: cosc , gwt , sinc , colat , wos2 , lat REAL , DIMENSION(nlat) :: lat_sp CALL lggaus(nlat, cosc, gwt, sinc, colat, wos2) DO i = 1, nlat lat(i) = ACOS(sinc(i)) * 180._HIGH / pi IF (i.gt.nlat/2) lat(i) = -lat(i) END DO lat_sp = REAL(lat) END SUBROUTINE gausll SUBROUTINE lggaus( nlat, cosc, gwt, sinc, colat, wos2 ) IMPLICIT NONE ! LGGAUS finds the Gaussian latitudes by finding the roots of the ! ordinary Legendre polynomial of degree NLAT using Newton's ! iteration method. ! On entry: integer NLAT ! the number of latitudes (degree of the polynomial) ! On exit: for each Gaussian latitude ! COSC - cos(colatitude) or sin(latitude) ! GWT - the Gaussian weights ! SINC - sin(colatitude) or cos(latitude) ! COLAT - the colatitudes in radians ! WOS2 - Gaussian weight over sin**2(colatitude) REAL (KIND=HIGH) , DIMENSION(nlat) :: cosc , gwt , sinc , colat , wos2 REAL (KIND=HIGH) , PARAMETER :: pi = 3.141592653589793 ! Convergence criterion for iteration of cos latitude REAL , PARAMETER :: xlim = 1.0E-14 INTEGER :: nzero, i, j REAL (KIND=HIGH) :: fi, fi1, a, b, g, gm, gp, gt, delta, c, d ! The number of zeros between pole and equator nzero = nlat/2 ! Set first guess for cos(colat) DO i=1,nzero cosc(i) = SIN( (i-0.5)*pi/nlat + pi*0.5 ) END DO ! Constants for determining the derivative of the polynomial fi = nlat fi1 = fi+1.0 a = fi*fi1 / SQRT(4.0*fi1*fi1-1.0) b = fi1*fi / SQRT(4.0*fi*fi-1.0) ! Loop over latitudes, iterating the search for each root DO i=1,nzero j=0 ! Determine the value of the ordinary Legendre polynomial for ! the current guess root DO CALL lgord( g, cosc(i), nlat ) ! Determine the derivative of the polynomial at this point CALL lgord( gm, cosc(i), nlat-1 ) CALL lgord( gp, cosc(i), nlat+1 ) gt = (cosc(i)*cosc(i)-1.0) / (a*gp-b*gm) ! Update the estimate of the root delta = g*gt cosc(i) = cosc(i) - delta ! If convergence criterion has not been met, keep trying j = j+1 IF( ABS(delta).GT.xlim ) CYCLE ! Determine the Gaussian weights c = 2.0 *( 1.0-cosc(i)*cosc(i) ) CALL lgord( d, cosc(i), nlat-1 ) d = d*d*fi*fi gwt(i) = c *( fi-0.5 ) / d EXIT END DO END DO ! Determine the colatitudes and sin(colat) and weights over sin**2 DO i=1,nzero colat(i)= ACOS(cosc(i)) sinc(i) = SIN(colat(i)) wos2(i) = gwt(i) /( sinc(i)*sinc(i) ) END DO ! If NLAT is odd, set values at the equator IF( MOD(nlat,2) .NE. 0 ) THEN i = nzero+1 cosc(i) = 0.0 c = 2.0 CALL lgord( d, cosc(i), nlat-1 ) d = d*d*fi*fi gwt(i) = c *( fi-0.5 ) / d colat(i)= pi*0.5 sinc(i) = 1.0 wos2(i) = gwt(i) END IF ! Determine the southern hemisphere values by symmetry DO i=nlat-nzero+1,nlat cosc(i) =-cosc(nlat+1-i) gwt(i) = gwt(nlat+1-i) colat(i)= pi-colat(nlat+1-i) sinc(i) = sinc(nlat+1-i) wos2(i) = wos2(nlat+1-i) END DO END SUBROUTINE lggaus SUBROUTINE lgord( f, cosc, n ) IMPLICIT NONE ! LGORD calculates the value of an ordinary Legendre polynomial at a ! specific latitude. ! On entry: ! cosc - COS(colatitude) ! n - the degree of the polynomial ! On exit: ! f - the value of the Legendre polynomial of degree N at ! latitude ASIN(cosc) REAL (KIND=HIGH) :: s1, c4, a, b, fk, f, cosc, colat, c1, fn, ang INTEGER :: n, k ! Determine the colatitude colat = ACOS(cosc) c1 = SQRT(2.0_HIGH) DO k=1,n c1 = c1 * SQRT( 1.0 - 1.0/(4*k*k) ) END DO fn = n ang= fn * colat s1 = 0.0 c4 = 1.0 a =-1.0 b = 0.0 DO k=0,n,2 IF (k.eq.n) c4 = 0.5 * c4 s1 = s1 + c4 * COS(ang) a = a + 2.0 b = b + 1.0 fk = k ang= colat * (fn-fk-2.0) c4 = ( a * (fn-b+1.0) / ( b * (fn+fn-a) ) ) * c4 END DO f = s1 * c1 END SUBROUTINE lgord SUBROUTINE llij_gauss (lat, lon, proj, i, j) IMPLICIT NONE REAL , INTENT(IN) :: lat, lon REAL , INTENT(OUT) :: i, j TYPE (proj_info), INTENT(IN) :: proj INTEGER :: n , n_low LOGICAL :: found = .FALSE. REAL :: diff_1 , diff_nlat ! The easy one first, get the x location. The calling routine has already made ! sure that the necessary assumptions concerning the sign of the deltalon and the ! relative east/west'ness of the longitude and the starting longitude are consistent ! to allow this easy computation. i = ( lon - proj%lon1 ) / proj%loninc + 1. ! Since this is a global data set, we need to be concerned about wrapping the ! fields around the globe. ! IF ( ( proj%loninc .GT. 0 ) .AND. & ! ( FLOOR((lon-proj%lon1)/proj%loninc) + 1 .GE. proj%ixdim ) .AND. & ! ( lon + proj%loninc .GE. proj%lon1 + 360 ) ) THEN !! BUG: We may need to set proj%wrap, but proj is intent(in) !! WHAT IS THIS USED FOR? !! proj%wrap = .TRUE. ! i = proj%ixdim ! ELSE IF ( ( proj%loninc .LT. 0 ) .AND. & ! ( FLOOR((lon-proj%lon1)/proj%loninc) + 1 .GE. proj%ixdim ) .AND. & ! ( lon + proj%loninc .LE. proj%lon1 - 360 ) ) THEN ! ! BUG: We may need to set proj%wrap, but proj is intent(in) ! ! WHAT IS THIS USED FOR? ! ! proj%wrap = .TRUE. ! i = proj%ixdim ! END IF ! Yet another quicky test, can we find bounding values? If not, then we may be ! dealing with putting data to a polar projection, so just give them them maximal ! value for the location. This is an OK assumption for the interpolation across the ! top of the pole, given how close the longitude lines are. IF ( ABS(lat) .GT. ABS(proj%gauss_lat(1)) ) THEN diff_1 = lat - proj%gauss_lat(1) diff_nlat = lat - proj%gauss_lat(proj%nlat*2) IF ( ABS(diff_1) .LT. ABS(diff_nlat) ) THEN j = 1 ELSE j = proj%nlat*2 END IF ! If the latitude is between the two bounding values, we have to search and interpolate. ELSE DO n = 1 , proj%nlat*2 -1 IF ( ( proj%gauss_lat(n) - lat ) * ( proj%gauss_lat(n+1) - lat ) .LE. 0 ) THEN found = .TRUE. n_low = n EXIT END IF END DO ! Everything still OK? IF ( .NOT. found ) THEN PRINT '(A)','Troubles in river city. No bounding values of latitude found in the Gaussian routines.' CALL wrf_error_fatal ( 'Gee_no_bounding_lats_Gaussian' ) END IF j = ( ( proj%gauss_lat(n_low) - lat ) * ( n_low + 1 ) + & ( lat - proj%gauss_lat(n_low+1) ) * ( n_low ) ) / & ( proj%gauss_lat(n_low) - proj%gauss_lat(n_low+1) ) END IF END SUBROUTINE llij_gauss END MODULE module_llxy