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module_map_utils.F
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MODULE map_utils
! 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 constants_module
use misc_definitions_module
use module_debug
! 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 :: nxmin ! Starting x-coordinate of periodic, regular lat/lon dataset
INTEGER :: nxmax ! Ending x-coordinate of periodic, regular lat/lon dataset
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?
LOGICAL :: comp_ll ! Work in computational lat/lon space for Cassini
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%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%nxmin = 1
proj%nxmax = 43200
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.
proj%comp_ll = .FALSE.
nullify(proj%gauss_lat)
END SUBROUTINE map_init
SUBROUTINE map_set(proj_code, proj, lat1, lon1, lat0, lon0, knowni, knownj, dx, dy, latinc, &
loninc, stdlon, truelat1, truelat2, nlat, nlon, ixdim, jydim, nxmin, nxmax, &
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 :: nxmin
INTEGER, INTENT(IN), OPTIONAL :: nxmax
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 :: dy
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 mprintf(.true.,ERROR,'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 mprintf(.true.,ERROR,'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 mprintf(.true.,ERROR,'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 mprintf(.true.,ERROR,'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 mprintf(.true.,ERROR,'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 mprintf(.true.,ERROR,'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 mprintf(.true.,ERROR,'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 mprintf(.true.,ERROR,'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 mprintf(.true.,ERROR,'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 mprintf(.true.,ERROR,'MAP_INIT')
END IF
ELSE
PRINT '(A,I2)', 'Unknown projection code: ', proj_code
call mprintf(.true.,ERROR,'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 mprintf(.true.,ERROR,'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 mprintf(.true.,ERROR,'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 mprintf(.true.,ERROR,'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 mprintf(.true.,ERROR,'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 mprintf(.true.,ERROR,'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 mprintf(.true.,ERROR,'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(nxmin) ) proj%nxmin = nxmin
IF ( PRESENT(nxmax) ) proj%nxmax = nxmax
IF ( PRESENT(dx) ) proj%dx = dx
IF ( PRESENT(dy) ) THEN
proj%dy = dy
ELSE IF ( PRESENT(dx) ) THEN
proj%dy = dx
END IF
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 mprintf(.true.,ERROR,'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 mprintf(.true.,ERROR,'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 mprintf(.true.,ERROR,'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 mprintf(.true.,ERROR,'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(KIND=HIGH) :: 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(MIN(MAX(xx/SQRT(r2),-1.0_HIGH),1.0_HIGH))
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