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!!----------------------------------------------------------------------
!! NEMO/OCE 4.0 , NEMO Consortium (2018)
!! $Id: obsinter_h2d.h90 10353 2018-11-21 16:04:47Z mathiot $
!! Software governed by the CeCILL license (see ./LICENSE)
!!----------------------------------------------------------------------
SUBROUTINE obs_int_h2d_init( kpk, kpk2, k2dint, plam, pphi, &
& pglam, pgphi, pmask, pweig, pobsmask, &
& iminpoints )
!!-----------------------------------------------------------------------
!!
!! *** ROUTINE obs_int_h2d ***
!!
!! ** Purpose : Computes weights for horizontal interpolation to the
!! observation point.
!!
!! ** Method : Horizontal interpolation to the observation point using
!! model values at the corners of the surrounding grid
!! points.
!!
!! Interpolation Schemes :
!!
!! 1) k2dint = 0: Distance-weighted interpolation scheme 1
!!
!! The interpolation weights are computed as a weighted
!! sum of the distance between the model grid points (A)
!! and the observation point (B). Distance (s) is computed
!! using the great-circle distance formula:
!!
!! s(AB) = arcos( sin( phiA ) x sin( phiB )
!! + cos( phiA ) x cos( phiB )
!! x cos( lamB - lamA ) )
!!
!! 2) k2dint = 1: Distance-weighted interpolation scheme 2
!!
!! As k2dint = 0 but with distance (ds) computed using
!! a small-angle approximation to the great-circle formula:
!!
!! ds(AB) = sqrt( ( phiB - phiA )^{2}
!! + ( ( lamB - lamA ) * cos( phiB ) )^{2} )
!!
!! 3) k2dint = 2: Bilinear interpolation on a geographical grid
!!
!! The interpolation is split into two 1D interpolations in
!! the longitude and latitude directions, respectively.
!!
!! 4) k2dint = 3: General bilinear remapping interpolation
!!
!! An iterative scheme that involves first mapping a
!! quadrilateral cell into a cell with coordinates
!! (0,0), (1,0), (0,1) and (1,1).
!!
!! 5) k2dint = 4: Polynomial interpolation
!!
!! The interpolation weights are computed by fitting a
!! polynomial function of the form
!!
!! P(i) = a1(i) + a2(i) * phi + a3(i) * plam
!! + a4(i) * phi * plam
!!
!! through the model values at the four surrounding grid points.
!!
!! ** Action :
!!
!! References : Jones, P.: A users guide for SCRIP: A Spherical
!! Coordinate Remapping and Interpolation Package.
!! Version 1.4. Los Alomos.
!!
!! http://www.acl.lanl.gov/climate/software/SCRIP/SCRIPmain.html
!!
!! History :
!! ! 97-11 (A. Weaver, N. Daget)
!! ! 06-03 (A. Vidard) NEMOVAR migration
!! ! 06-10 (A. Weaver) Cleanup
!! ! 07-08 (K. Mogensen) Split in two routines for easier adj.
!!-----------------------------------------------------------------------
!! * Modules used
!! * Arguments
INTEGER, INTENT(IN) :: &
& kpk, & ! Parameter values for automatic arrays
& kpk2, &
& k2dint ! Interpolation scheme options
! = 0 distance-weighted (great circle)
! = 1 distance-weighted (small angle)
! = 2 bilinear (geographical grid)
! = 3 bilinear (quadrilateral grid)
! = 4 polynomial (quadrilateral grid)
REAL(KIND=wp), INTENT(INOUT) :: &
& plam, &
& pphi ! Geographical (lat,lon) coordinates of
! observation
REAL(KIND=wp), DIMENSION(2,2), INTENT(IN) :: &
& pglam, & ! Model variable lat
& pgphi ! Model variable lon
REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(IN) :: &
& pmask ! Model variable mask
REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(OUT) :: &
& pweig ! Weights for interpolation
REAL(KIND=wp), DIMENSION(kpk2), INTENT(OUT) :: &
& pobsmask ! Vertical mask for observations
INTEGER, INTENT(IN), OPTIONAL :: &
& iminpoints ! Reject point which is not surrounded
! by at least iminpoints sea points
!! * Local declarations
INTEGER :: &
& jk
INTEGER :: &
& ikmax, &
& iamb1, &
& iamb2
REAL(KIND=wp) :: &
& zphimm, &
& zphimp, &
& zphipm, &
& zphipp, &
& zlammm, &
& zlammp, &
& zlampm, &
& zlampp, &
& zphimin, &
& zphimax, &
& zlammin, &
& zlammax
REAL(KIND=wp), DIMENSION(kpk2) :: &
& z2dmm, &
& z2dmp, &
& z2dpm, &
& z2dpp, &
& z2dmmt, &
& z2dmpt, &
& z2dpmt, &
& z2dppt, &
& zsum
LOGICAL :: &
& ll_ds1, &
& ll_skip, &
& ll_fail
!------------------------------------------------------------------------
! Constants for the 360 degrees ambiguity
!------------------------------------------------------------------------
iamb1 = 10 ! dlam < iamb1 * dphi
iamb2 = 3 ! Special treatment if iamb2 * lam < max(lam)
!------------------------------------------------------------------------
! Initialize number of levels
!------------------------------------------------------------------------
IF ( kpk2 == 1 ) THEN
ikmax = 1
ELSEIF ( kpk2 == kpk) THEN
ikmax = kpk-1
ENDIF
!------------------------------------------------------------------------
! Initialize the cell corners
!------------------------------------------------------------------------
zphimm = pgphi(1,1)
zphimp = pgphi(1,2)
zphipm = pgphi(2,1)
zphipp = pgphi(2,2)
zlammm = pglam(1,1)
zlammp = pglam(1,2)
zlampm = pglam(2,1)
zlampp = pglam(2,2)
!------------------------------------------------------------------------
! Treat the 360 degrees ambiguity
!------------------------------------------------------------------------
DO WHILE ( ( zlammm < 0.0_wp ).OR.( zlammm > 360.0_wp ) &
& .OR.( zlampm < 0.0_wp ).OR.( zlampm > 360.0_wp ) &
& .OR.( zlampp < 0.0_wp ).OR.( zlampp > 360.0_wp ) &
& .OR.( zlammp < 0.0_wp ).OR.( zlammp > 360.0_wp ) )
IF ( zlammm < 0.0_wp ) zlammm = zlammm + 360.0_wp
IF ( zlammm > 360.0_wp ) zlammm = zlammm - 360.0_wp
IF ( zlammp < 0.0_wp ) zlammp = zlammp + 360.0_wp
IF ( zlammp > 360.0_wp ) zlammp = zlammp - 360.0_wp
IF ( zlampm < 0.0_wp ) zlampm = zlampm + 360.0_wp
IF ( zlampm > 360.0_wp ) zlampm = zlampm - 360.0_wp
IF ( zlampp < 0.0_wp ) zlampp = zlampp + 360.0_wp
IF ( zlampp > 360.0_wp ) zlampp = zlampp - 360.0_wp
END DO
DO WHILE ( ( plam < 0.0_wp ) .OR. ( plam > 360.0_wp ) )
IF ( plam < 0.0_wp ) plam = plam + 360.0_wp
IF ( plam > 360.0_wp ) plam = plam - 360.0_wp
END DO
!------------------------------------------------------------------------
! Special case for observation on grid points
!------------------------------------------------------------------------
ll_skip = .FALSE.
IF ( ( ABS( zphimm - pphi ) < 1.0e-6_wp ) .AND. &
& ( ABS( zlammm - plam ) < 1.0e-6_wp ) ) THEN
z2dmm(:) = 1.0_wp
z2dpm(:) = 0.0_wp
z2dmp(:) = 0.0_wp
z2dpp(:) = 0.0_wp
ll_skip = .TRUE.
ENDIF
IF ( ( ABS( zphipm - pphi ) < 1.0e-6_wp ) .AND. &
& ( ABS( zlampm - plam ) < 1.0e-6_wp ) ) THEN
z2dmm(:) = 0.0_wp
z2dpm(:) = 1.0_wp
z2dmp(:) = 0.0_wp
z2dpp(:) = 0.0_wp
ll_skip = .TRUE.
ENDIF
IF ( ( ABS( zphimp - pphi ) < 1.0e-6_wp ) .AND. &
& ( ABS( zlammp - plam ) < 1.0e-6_wp ) ) THEN
z2dmm(:) = 0.0_wp
z2dpm(:) = 0.0_wp
z2dmp(:) = 1.0_wp
z2dpp(:) = 0.0_wp
ll_skip = .TRUE.
ENDIF
IF ( ( ABS( zphipp - pphi ) < 1.0e-6_wp ) .AND. &
& ( ABS( zlampp - plam ) < 1.0e-6_wp ) ) THEN
z2dmm(:) = 0.0_wp
z2dpm(:) = 0.0_wp
z2dmp(:) = 0.0_wp
z2dpp(:) = 1.0_wp
ll_skip = .TRUE.
ENDIF
IF ( .NOT.ll_skip ) THEN
zphimin = MIN( zphimm, zphipm, zphipp, zphimp )
zphimax = MAX( zphimm, zphipm, zphipp, zphimp )
zlammin = MIN( zlammm, zlampm, zlampp, zlammp )
zlammax = MAX( zlammm, zlampm, zlampp, zlammp )
IF ( ( ( zlammax - zlammin ) / ( zphimax - zphimin ) ) > iamb1 ) THEN
IF ( iamb2 * zlammm < zlammax ) zlammm = zlammm + 360.0_wp
IF ( iamb2 * zlammp < zlammax ) zlammp = zlammp + 360.0_wp
IF ( iamb2 * zlampm < zlammax ) zlampm = zlampm + 360.0_wp
IF ( iamb2 * zlampp < zlammax ) zlampp = zlampp + 360.0_wp
ENDIF
zlammin = MIN( zlammm, zlampm, zlampp, zlammp )
IF ( zlammm > ( zlammin + 180.0_wp ) ) zlammm = zlammm - 360.0_wp
IF ( zlammp > ( zlammin + 180.0_wp ) ) zlammp = zlammp - 360.0_wp
IF ( zlampm > ( zlammin + 180.0_wp ) ) zlampm = zlampm - 360.0_wp
IF ( zlampp > ( zlammin + 180.0_wp ) ) zlampp = zlampp - 360.0_wp
IF ( plam < zlammin ) plam = plam + 360.0_wp
z2dmm = 0.0_wp
z2dmp = 0.0_wp
z2dpm = 0.0_wp
z2dpp = 0.0_wp
SELECT CASE (k2dint)
CASE(0)
CALL obs_int_h2d_ds1( kpk2, ikmax, &
& pphi, plam, pmask, &
& zphimm, zlammm, zphimp, zlammp, &
& zphipm, zlampm, zphipp, zlampp, &
& z2dmm, z2dmp, z2dpm, z2dpp )
CASE(1)
CALL obs_int_h2d_ds2( kpk2, ikmax, &
& pphi, plam, pmask, &
& zphimm, zlammm, zphimp, zlammp, &
& zphipm, zlampm, zphipp, zlampp, &
& z2dmm, z2dmp, z2dpm, z2dpp )
CASE(2)
CALL obs_int_h2d_bil( kpk2, ikmax, &
& pphi, plam, pmask, &
& zlammp, &
& zphipm, zphipp, zlampp, &
& z2dmm, z2dmp, z2dpm, z2dpp )
CASE(3)
CALL obs_int_h2d_bir( kpk2, ikmax, &
& pphi, plam, pmask, &
& zphimm, zlammm, zphimp, zlammp, &
& zphipm, zlampm, zphipp, zlampp, &
& z2dmm, z2dmp, z2dpm, z2dpp, ll_fail )
IF (ll_fail) THEN
IF(lwp) THEN
WRITE(numout,*)'Bilinear weight computation failed'
WRITE(numout,*)'Switching to great circle distance'
WRITE(numout,*)
ENDIF
CALL obs_int_h2d_ds1( kpk2, ikmax, &
& pphi, plam, pmask, &
& zphimm, zlammm, zphimp, zlammp, &
& zphipm, zlampm, zphipp, zlampp, &
& z2dmm, z2dmp, z2dpm, z2dpp )
ENDIF
CASE(4)
CALL obs_int_h2d_pol( kpk2, ikmax, &
& pphi, plam, pmask, &
& zphimm, zlammm, zphimp, zlammp, &
& zphipm, zlampm, zphipp, zlampp, &
& z2dmm, z2dmp, z2dpm, z2dpp )
END SELECT
ENDIF
!------------------------------------------------------------------------
! Compute weights for interpolation to the observation point
!------------------------------------------------------------------------
pobsmask(:) = 0.0_wp
pweig(:,:,:) = 0.0_wp
! ll_ds1 is used for failed interpolations
ll_ds1 = .FALSE.
DO jk = 1, ikmax
IF (PRESENT(iminpoints)) THEN
IF (NINT(SUM(pmask(:,:,jk)))<iminpoints) CYCLE
ENDIF
zsum(jk) = z2dmm(jk) + z2dmp(jk) + z2dpm(jk) + z2dpp(jk)
IF ( zsum(jk) /= 0.0_wp ) THEN
pweig(1,1,jk) = z2dmm(jk)
pweig(1,2,jk) = z2dmp(jk)
pweig(2,1,jk) = z2dpm(jk)
pweig(2,2,jk) = z2dpp(jk)
! Set the vertical mask
IF ( ( ( z2dmm(jk) > 0.0_wp ) .AND. &
& ( pmask(1,1,jk) == 1.0_wp ) ) .OR. &
& ( ( z2dmp(jk) > 0.0_wp ) .AND. &
& ( pmask(1,2,jk) == 1.0_wp ) ) .OR. &
& ( ( z2dpm(jk) > 0.0_wp ) .AND. &
& ( pmask(2,1,jk) == 1.0_wp ) ) .OR. &
& ( ( z2dpp(jk) > 0.0_wp ) .AND. &
& ( pmask(2,2,jk) == 1.0_wp ) ) ) pobsmask(jk)=1.0_wp
ELSE
! If the interpolation has failed due to the point
! being on the intersect of two land points retry with
! k2dint = 0
IF ( ( pmask(1,1,jk) /= 0.0_wp ).OR. &
& ( pmask(1,2,jk) /= 0.0_wp ).OR. &
& ( pmask(2,1,jk) /= 0.0_wp ).OR. &
& ( pmask(2,2,jk) /= 0.0_wp ) ) THEN
! If ll_ds1 is false compute k2dint = 0 weights
IF ( .NOT.ll_ds1 ) THEN
CALL obs_int_h2d_ds1( kpk2, ikmax, &
& pphi, plam, pmask, &
& zphimm, zlammm, zphimp, zlammp, &
& zphipm, zlampm, zphipp, zlampp, &
& z2dmmt, z2dmpt, z2dpmt, z2dppt )
ll_ds1 = .TRUE.
ENDIF
zsum(jk) = z2dmmt(jk) + z2dmpt(jk) + z2dpmt(jk) + z2dppt(jk)
IF ( zsum(jk) /= 0.0_wp ) THEN
pweig(1,1,jk) = z2dmmt(jk)
pweig(1,2,jk) = z2dmpt(jk)
pweig(2,1,jk) = z2dpmt(jk)
pweig(2,2,jk) = z2dppt(jk)
! Set the vertical mask
IF ( ( ( z2dmmt(jk) > 0.0_wp ) .AND. &
& ( pmask(1,1,jk) == 1.0_wp ) ) .OR. &
& ( ( z2dmpt(jk) > 0.0_wp ) .AND. &
& ( pmask(1,2,jk) == 1.0_wp ) ) .OR. &
& ( ( z2dpmt(jk) > 0.0_wp) .AND. &
& ( pmask(2,1,jk) == 1.0_wp ) ) .OR. &
& ( ( z2dppt(jk) > 0.0_wp ) .AND. &
& ( pmask(2,2,jk) == 1.0_wp ) ) ) &
& pobsmask(jk)=1.0_wp
ENDIF
ENDIF
ENDIF
END DO
END SUBROUTINE obs_int_h2d_init
SUBROUTINE obs_int_h2d( kpk, kpk2, &
& pweig, pmod, pobsk )
!!-----------------------------------------------------------------------
!!
!! *** ROUTINE obs_int_h2d ***
!!
!! ** Purpose : Horizontal interpolation to the observation point.
!!
!! ** Method : Horizontal interpolation to the observation point using
!! model values at the corners of the surrounding grid
!! points.
!!
!! ** Action :
!!
!! References :
!!
!! History :
!! ! 97-11 (A. Weaver, N. Daget)
!! ! 06-03 (A. Vidard) NEMOVAR migration
!! ! 06-10 (A. Weaver) Cleanup
!! ! 07-08 (K. Mogensen) Split in two routines for easier adj.
!!-----------------------------------------------------------------------
!! * Modules used
!! * Arguments
INTEGER, INTENT(IN) :: &
& kpk, & ! Parameter values for automatic arrays
& kpk2
REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(IN) :: &
& pweig ! Interpolation weights
REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(IN) :: &
& pmod ! Model variable to interpolate
REAL(KIND=wp), DIMENSION(kpk2), INTENT(OUT) :: &
& pobsk ! Model profile interpolated to obs (i,j) pt
!! * Local declarations
INTEGER :: &
& jk
INTEGER :: &
& ikmax
REAL(KIND=wp) :: &
& zsum
!------------------------------------------------------------------------
! Initialize number of levels
!------------------------------------------------------------------------
IF ( kpk2 == 1 ) THEN
ikmax = 1
ELSEIF ( kpk2 == kpk) THEN
ikmax = kpk-1
ENDIF
!------------------------------------------------------------------------
! Interpolate to the observation point
!------------------------------------------------------------------------
pobsk(:) = obfillflt
DO jk = 1, ikmax
zsum = pweig(1,1,jk) + pweig(1,2,jk) + pweig(2,1,jk) + pweig(2,2,jk)
IF ( zsum /= 0.0_wp ) THEN
pobsk(jk) = ( pweig(1,1,jk) * pmod(1,1,jk) &
& + pweig(1,2,jk) * pmod(1,2,jk) &
& + pweig(2,1,jk) * pmod(2,1,jk) &
& + pweig(2,2,jk) * pmod(2,2,jk) &
& ) / zsum
ENDIF
END DO
END SUBROUTINE obs_int_h2d
SUBROUTINE obs_int_h2d_ds1( kpk2, kmax, &
& pphi, plam, pmask, &
& pphimm, plammm, pphimp, plammp, &
& pphipm, plampm, pphipp, plampp, &
& p2dmm, p2dmp, p2dpm, p2dpp )
!!-----------------------------------------------------------------------
!!
!! *** ROUTINE obs_int_h2d_ds1 ***
!!
!! ** Purpose : Distance-weighted interpolation scheme (k2dint = 0)
!!
!! ** Method : The interpolation weights are computed as a weighted
!! sum of the distance between the model grid points (A)
!! and the observation point (B).
!!
!! Distance (s) is computed using the great-circle distance formula:
!!
!! s(AB) = arcos( sin( phiA ) x sin( phiB )
!! + cos( phiA ) x cos( phiB ) x cos( lamB - lamA )
!!
!! ** Action :
!!
!! History :
!! ! 97-11 (A. Weaver, N. Daget)
!! ! 06-10 (A. Weaver) Cleanup
!!-----------------------------------------------------------------------
!! * Modules used
!! * Arguments
INTEGER, INTENT(IN) :: &
& kpk2, & ! Parameter values for automatic arrays
& kmax
REAL(KIND=wp), INTENT(IN) :: &
& pphi, & ! Geographical location of observation
& plam, &
& pphimm, & ! Geographical location of surrounding
& pphimp, & ! model grid points
& pphipm, &
& pphipp, &
& plammm, &
& plammp, &
& plampm, &
& plampp
REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(IN) :: &
& pmask ! Model variable mask
REAL(KIND=wp), DIMENSION(kpk2), INTENT(OUT) :: &
& p2dmm, & ! Interpolation weights
& p2dmp, &
& p2dpm, &
& p2dpp
!! * Local declarations
INTEGER :: &
& jk
REAL(KIND=wp) :: &
& zphi2, &
& zlam2, &
& zcola, &
& za2, &
& zb2, &
& zc2, &
& zphimm2, &
& zphimp2, &
& zphipm2, &
& zphipp2, &
& zlammm2, &
& zlammp2, &
& zlampm2, &
& zlampp2, &
& za1mm, &
& za1mp, &
& za1pm, &
& za1pp, &
& zcomm, &
& zcomp, &
& zcopm, &
& zcopp, &
& zb1mm, &
& zb1mp, &
& zb1pm, &
& zb1pp, &
& zc1mm, &
& zc1mp, &
& zc1pm, &
& zc1pp, &
& zsopmpp, &
& zsommmp, &
& zsomm, &
& zsomp, &
& zsopm, &
& zsopp
!------------------------------------------------------------------------
! Distance-weighted interpolation using the great circle formula
!------------------------------------------------------------------------
zphi2 = pphi * rad
zlam2 = plam * rad
zcola = COS( zphi2 )
za2 = SIN( zphi2 )
zb2 = zcola * COS( zlam2 )
zc2 = zcola * SIN( zlam2 )
zphimm2 = pphimm * rad
zphimp2 = pphimp * rad
zphipm2 = pphipm * rad
zphipp2 = pphipp * rad
zlammm2 = plammm * rad
zlammp2 = plammp * rad
zlampm2 = plampm * rad
zlampp2 = plampp * rad
za1mm = SIN( zphimm2 )
za1mp = SIN( zphimp2 )
za1pm = SIN( zphipm2 )
za1pp = SIN( zphipp2 )
zcomm = COS( zphimm2 )
zcomp = COS( zphimp2 )
zcopm = COS( zphipm2 )
zcopp = COS( zphipp2 )
zb1mm = zcomm * COS( zlammm2 )
zb1mp = zcomp * COS( zlammp2 )
zb1pm = zcopm * COS( zlampm2 )
zb1pp = zcopp * COS( zlampp2 )
zc1mm = zcomm * SIN( zlammm2 )
zc1mp = zcomp * SIN( zlammp2 )
zc1pm = zcopm * SIN( zlampm2 )
zc1pp = zcopp * SIN( zlampp2 )
! Function for arcsin(sqrt(1-x^2) version of great-circle formula
zsomm = grt_cir_dis( za1mm, za2, zb1mm, zb2, zc1mm, zc2 )
zsomp = grt_cir_dis( za1mp, za2, zb1mp, zb2, zc1mp, zc2 )
zsopm = grt_cir_dis( za1pm, za2, zb1pm, zb2, zc1pm, zc2 )
zsopp = grt_cir_dis( za1pp, za2, zb1pp, zb2, zc1pp, zc2 )
zsopmpp = zsopm * zsopp
zsommmp = zsomm * zsomp
DO jk = 1, kmax
p2dmm(jk) = zsomp * zsopmpp * pmask(1,1,jk)
p2dmp(jk) = zsomm * zsopmpp * pmask(1,2,jk)
p2dpm(jk) = zsopp * zsommmp * pmask(2,1,jk)
p2dpp(jk) = zsopm * zsommmp * pmask(2,2,jk)
END DO
END SUBROUTINE obs_int_h2d_ds1
SUBROUTINE obs_int_h2d_ds2( kpk2, kmax, &
& pphi, plam, pmask, &
& pphimm, plammm, pphimp, plammp, &
& pphipm, plampm, pphipp, plampp, &
& p2dmm, p2dmp, p2dpm, p2dpp )
!!-----------------------------------------------------------------------
!!
!! *** ROUTINE obs_int_h2d_ds2 ***
!!
!! ** Purpose : Distance-weighted interpolation scheme (k2dint = 1)
!!
!! ** Method : As k2dint = 0 but with distance (ds) computed using a
!! small-angle approximation to the great-circle distance
!! formula:
!!
!! ds(AB) = sqrt( ( phiB - phiA )^{2}
!! + ( ( lamB - lamA ) * cos( phiB ) )^{2} )
!!
!! ** Action :
!!
!! History :
!! ! 97-11 (A. Weaver, N. Daget)
!! ! 06-10 (A. Weaver) Cleanup
!!-----------------------------------------------------------------------
!!-----------------------------------------------------------------------
!! * Modules used
!!-----------------------------------------------------------------------
!! * Arguments
INTEGER, INTENT(IN) :: &
& kpk2, & ! Parameter values for automatic arrays
& kmax
REAL(KIND=wp), INTENT(IN) :: &
& pphi, & ! Geographical location of observation
& plam, &
& pphimm, & ! Geographical location of surrounding
& pphimp, & ! model grid points
& pphipm, &
& pphipp, &
& plammm, &
& plammp, &
& plampm, &
& plampp
REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(IN) :: &
& pmask ! Model variable mask
REAL(KIND=wp), DIMENSION(kpk2), INTENT(OUT) :: &
& p2dmm, & ! Interpolation weights
& p2dmp, &
& p2dpm, &
& p2dpp
!! * Local declarations
INTEGER :: &
& jk
REAL(KIND=wp) :: &
& zcosp, &
& zdlmm, &
& zdlmp, &
& zdlpm, &
& zdlpp, &
& zdpmm, &
& zdpmp, &
& zdppm, &
& zdppp, &
& zsomm, &
& zsomp, &
& zsopm, &
& zsopp, &
& zsopmpp, &
& zsommmp
!------------------------------------------------------------------------
! Distance-weighted interpolation with a small angle approximation
!------------------------------------------------------------------------
zcosp = COS( pphi * rad )
zdlmm = plammm - plam
zdlmp = plammp - plam
zdlpm = plampm - plam
zdlpp = plampp - plam
zdpmm = pphimm - pphi
zdpmp = pphimp - pphi
zdppm = pphipm - pphi
zdppp = pphipp - pphi
zsomm = grt_cir_dis_saa( zdlmm, zdpmm, zcosp )
zsomp = grt_cir_dis_saa( zdlmp, zdpmp, zcosp )
zsopm = grt_cir_dis_saa( zdlpm, zdppm, zcosp )
zsopp = grt_cir_dis_saa( zdlpp, zdppp, zcosp )
zsopmpp = zsopm * zsopp
zsommmp = zsomm * zsomp
DO jk = 1, kmax
p2dmm(jk) = zsomp * zsopmpp * pmask(1,1,jk)
p2dmp(jk) = zsomm * zsopmpp * pmask(1,2,jk)
p2dpm(jk) = zsopp * zsommmp * pmask(2,1,jk)
p2dpp(jk) = zsopm * zsommmp * pmask(2,2,jk)
END DO
END SUBROUTINE obs_int_h2d_ds2
SUBROUTINE obs_int_h2d_bil( kpk2, kmax, &
& pphi, plam, pmask, &
& plammp, pphipm, pphipp, plampp, &
& p2dmm, p2dmp, p2dpm, p2dpp)
!!-----------------------------------------------------------------------
!!
!! *** ROUTINE obs_int_h2d_bil ***
!!
!! ** Purpose : Bilinear interpolation on a geographical grid (k2dint = 2)
!!
!! ** Method : The interpolation is split into two 1D interpolations in
!! the longitude and latitude directions, respectively.
!!
!! An iterative scheme that involves first mapping a quadrilateral
!! cell into a cell with coordinates (0,0), (1,0), (0,1) and (1,1).
!!
!! ** Action :
!!
!! History :
!! ! 97-11 (A. Weaver, N. Daget)
!! ! 06-10 (A. Weaver) Cleanup
!!-----------------------------------------------------------------------
!! * Arguments
INTEGER, INTENT(IN) :: &
& kpk2, & ! Parameter values for automatic arrays
& kmax
REAL(KIND=wp), INTENT(IN) :: &
& pphi, & ! Geographical location of observation
& plam, &
& pphipm, & ! Geographical location of surrounding
& pphipp, & ! model grid points
& plammp, &
& plampp
REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(IN) :: &
& pmask ! Model variable mask
REAL(KIND=wp), DIMENSION(kpk2), INTENT(OUT) :: &
& p2dmm, & ! Interpolation weights
& p2dmp, &
& p2dpm, &
& p2dpp
!! * Local declarations
INTEGER :: &
& jk
REAL(KIND=wp) :: &
& zdlmp, &
& zdppm, &
& zdlpp, &
& zdppp
!----------------------------------------------------------------------
! Bilinear interpolation for geographical grid
!----------------------------------------------------------------------
zdlmp = ABS(plam - plammp)
zdppm = ABS(pphi - pphipm)
zdlpp = ABS(plampp - plam)
zdppp = ABS(pphipp - pphi)
DO jk = 1, kmax
p2dmm(jk) = zdlpp * zdppp * pmask(1,1,jk)
p2dmp(jk) = zdlpp * zdppm * pmask(1,2,jk)
p2dpm(jk) = zdlmp * zdppp * pmask(2,1,jk)
p2dpp(jk) = zdlmp * zdppm * pmask(2,2,jk)
END DO
END SUBROUTINE obs_int_h2d_bil
SUBROUTINE obs_int_h2d_bir( kpk2, kmax, &
& pphi, plam, pmask, &
& pphimm, plammm, pphimp, plammp, &
& pphipm, plampm, pphipp, plampp, &
& p2dmm, p2dmp, p2dpm, p2dpp, ldfail )
!!-----------------------------------------------------------------------
!!
!! *** ROUTINE obs_int_h2d_bir ***
!!
!! ** Purpose : General bilinear remapping interpolation (k2dint = 3)
!!
!! ** Method : An iterative scheme that involves first mapping a
!! quadrilateral cell into a cell with coordinates
!! (0,0), (1,0), (0,1) and (1,1).
!!
!! ** Action :
!!
!! History :
!! ! 97-11 (A. Weaver, N. Daget)
!! ! 06-10 (A. Weaver) Cleanup
!!-----------------------------------------------------------------------
!! * Arguments
INTEGER, INTENT(IN) :: &
& kpk2, & ! Parameter values for automatic arrays
& kmax
REAL(KIND=wp), INTENT(IN) :: &
& pphi, & ! Geographical location of observation
& plam, &
& pphimm, & ! Geographical location of surrounding
& pphimp, & ! model grid points
& pphipm, &
& pphipp, &
& plammm, &
& plammp, &
& plampm, &
& plampp
REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(IN) :: &
& pmask ! Model variable mask
REAL(KIND=wp), DIMENSION(kpk2), INTENT(OUT) :: &
& p2dmm, & ! Interpolation weights
& p2dmp, &
& p2dpm, &
& p2dpp
LOGICAL, INTENT(OUT) :: &
& ldfail
!! * Local declarations
INTEGER :: &
& jk
REAL(KIND=wp) :: &
& zbiwmm, &
& zbiwmp, &
& zbiwpm, &
& zbiwpp
!----------------------------------------------------------------------
! Bilinear remapping interpolation for general quadrilateral grid
!----------------------------------------------------------------------
CALL bil_wgt( pphimm, pphimp, pphipm, pphipp, &
& plammm, plammp, plampm, plampp, &
& zbiwmm, zbiwmp, zbiwpm, zbiwpp, &
& pphi , plam, ldfail )
IF ( .NOT.ldfail ) THEN
DO jk = 1, kmax
p2dmm(jk) = zbiwmm * pmask(1,1,jk)
p2dmp(jk) = zbiwmp * pmask(1,2,jk)
p2dpm(jk) = zbiwpm * pmask(2,1,jk)
p2dpp(jk) = zbiwpp * pmask(2,2,jk)
END DO
ENDIF
END SUBROUTINE obs_int_h2d_bir
SUBROUTINE obs_int_h2d_pol( kpk2, kmax, &
& pphi, plam, pmask, &
& pphimm, plammm, pphimp, plammp, &
& pphipm, plampm, pphipp, plampp, &
& p2dmm, p2dmp, p2dpm, p2dpp )
!!-----------------------------------------------------------------------
!!
!! *** ROUTINE obs_int_h2d_pol ***
!!
!! ** Purpose : Polynomial interpolation (k2dint = 4)
!!
!! ** Method : The interpolation weights are computed by fitting a
!! polynomial function of the form
!!
!! P(i) = a1(i) + a2(i) * phi + a3(i) * plam + a4(i) * phi * plam
!!
!! through the model values at four surrounding grid pts (i=1,4).
!! As k2dint = 0 but with distance (ds) computed using a small-
!! angle approximation to the great-circle distance formula:
!!
!! ds(AB) = sqrt( ( phiB - phiA )^{2}
!! + ( ( lamB - lamA ) * cos( phiB ) )^{2} )
!!
!! ** Action :
!!
!! History :
!! ! 97-11 (A. Weaver, N. Daget)
!! ! 06-10 (A. Weaver) Cleanup
!!-----------------------------------------------------------------------
!! * Arguments
INTEGER, INTENT(IN) :: &
& kpk2, & ! Parameter values for automatic arrays
& kmax
REAL(KIND=wp), INTENT(IN) :: &
& pphi, & ! Geographical location of observation
& plam, &
& pphimm, & ! Geographical location of surrounding
& pphimp, & ! model grid points
& pphipm, &
& pphipp, &
& plammm, &
& plammp, &
& plampm, &
& plampp
REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(IN) :: &
& pmask ! Model variable mask
REAL(KIND=wp), DIMENSION(kpk2), INTENT(OUT) :: &
& p2dmm, & ! Interpolation weights
& p2dmp, &
& p2dpm, &
& p2dpp
!! * Local declarations
INTEGER :: &
& jk
REAL(KIND=wp) :: &
& zplp
REAL(KIND=wp), DIMENSION(4,4) :: &
& zmat, &
& zmati
!------------------------------------------------------------------------
! Polynomial interpolation
!------------------------------------------------------------------------
zmat(1,1) = 1.0_wp
zmat(1,2) = 1.0_wp
zmat(1,3) = 1.0_wp
zmat(1,4) = 1.0_wp
zmat(2,1) = plammm
zmat(2,2) = plammp
zmat(2,3) = plampm
zmat(2,4) = plampp
zmat(3,1) = pphimm
zmat(3,2) = pphimp
zmat(3,3) = pphipm
zmat(3,4) = pphipp
zmat(4,1) = plammm * pphimm
zmat(4,2) = plammp * pphimp
zmat(4,3) = plampm * pphipm
zmat(4,4) = plampp * pphipp
CALL lu_invmat( zmat, 4, zmati )
zplp = plam * pphi
DO jk = 1, kmax
p2dmm(jk) = ABS( zmati(1,1) + zmati(1,2) * plam &
& + zmati(1,3) * pphi + zmati(1,4) * zplp ) &
& * pmask(1,1,jk)
p2dmp(jk) = ABS( zmati(2,1) + zmati(2,2) * plam &
& + zmati(2,3) * pphi + zmati(2,4) * zplp ) &
& * pmask(1,2,jk)
p2dpm(jk) = ABS( zmati(3,1) + zmati(3,2) * plam &
& + zmati(3,3) * pphi + zmati(3,4) * zplp ) &
& * pmask(2,1,jk)
p2dpp(jk) = ABS( zmati(4,1) + zmati(4,2) * plam &
& + zmati(4,3) * pphi + zmati(4,4) * zplp ) &
& * pmask(2,2,jk)
END DO
END SUBROUTINE obs_int_h2d_pol
SUBROUTINE bil_wgt( pphimm, pphimp, pphipm, pphipp, &
& plammm, plammp, plampm, plampp, &
& pbiwmm, pbiwmp, pbiwpm, pbiwpp, &
& pphi , plam, ldfail )
!!-------------------------------------------------------------------
!!
!! *** ROUTINE bil_wgt ***
!!
!! ** Purpose : Compute the weights for a bilinear remapping
!! interpolation scheme.
!!
!! ** Method : This scheme is appropriate for bilinear interpolation
!! on a general quadrilateral grid.
!! This scheme is also used in OASIS.
!!
!! This routine is a derivative of the SCRIP software.
!! Copyright 1997, 1998 the Regents of the University
!! of California. See SCRIP_Copyright.txt.
!!
!! ** Action :
!!
!! References : Jones, P.: A user's guide for SCRIP: A Spherical
!! Coordinate Remapping and Interpolation Package.
!! Version 1.4. Los Alamos.
!!
!! http://www.acl.lanl.gov/climate/software/SCRIP/SCRIPmain.html
!!
!! History
!! ! 97-11 (A. Weaver, N. Daget)
!! ! 06-03 (A. Vidard)
!! ! 06-10 (A. Weaver) Cleanup
!!-----------------------------------------------------------------------
!! * Arguments
REAL(KIND=wp), INTENT(IN) :: &
& pphi, & ! Geographical location of observation
& plam, &
& pphimm, & ! Geographical location of surrounding
& pphimp, & ! model grid points
& pphipm, &
& pphipp, &
& plammm, &
& plammp, &
& plampm, &
& plampp
REAL(KIND=wp), INTENT(OUT) :: &
& pbiwmm, & ! Interpolation weights
& pbiwmp, &
& pbiwpm, &
& pbiwpp
LOGICAL, INTENT(out) :: &
& ldfail
!! * Local declarations
INTEGER :: &
& jiter
INTEGER :: &
& itermax
REAL(KIND=wp) :: &
& zphi, & ! Geographical location of observation
& zlam, &
& zphimm, & ! Geographical location of surrounding
& zphimp, & ! model grid points
& zphipm, &
& zphipp, &
& zlammm, &
& zlammp, &
& zlampm, &
& zlampp, &
& zdth1, &
& zdth2, &
& zdth3, &
& zdthp, &