MODULE tide_mod
!!======================================================================
!! *** MODULE tide_mod ***
!! Compute nodal modulations corrections and pulsations
!!======================================================================
!! History : 1.0 ! 2007 (O. Le Galloudec) Original code
!! ! 2019 (S. Mueller)
!!----------------------------------------------------------------------
!!
!! ** Reference :
!! S58) Schureman, P. (1958): Manual of Harmonic Analysis and
!! Prediction of Tides (Revised (1940) Edition (Reprinted 1958
!! with corrections). Reprinted June 2001). U.S. Department of
!! Commerce, Coast and Geodetic Survey Special Publication
!! No. 98. Washington DC, United States Government Printing
!! Office. 317 pp. DOI: 10.25607/OBP-155.
!!----------------------------------------------------------------------
USE oce, ONLY : ssh ! sea-surface height
USE par_oce ! ocean parameters
USE phycst, ONLY : rpi, rad, rday
USE daymod, ONLY : ndt05 ! half-length of time step
USE in_out_manager ! I/O units
USE iom ! xIOs server
IMPLICIT NONE
PRIVATE
PUBLIC tide_init
PUBLIC tide_update ! called by stp
PUBLIC tide_init_harmonics ! called internally and by module diaharm
PUBLIC upd_tide ! called in dynspg_... modules
INTEGER, PUBLIC, PARAMETER :: jpmax_harmo = 64 !: maximum number of harmonic components
TYPE :: tide
CHARACTER(LEN=4) :: cname_tide = ''
REAL(wp) :: equitide
INTEGER :: nt, ns, nh, np, np1, shift
INTEGER :: nksi, nnu0, nnu1, nnu2, R
INTEGER :: nformula
END TYPE tide
TYPE(tide), DIMENSION(:), POINTER :: tide_components !: Array of selected tidal component parameters
TYPE, PUBLIC :: tide_harmonic !: Oscillation parameters of harmonic tidal components
CHARACTER(LEN=4) :: cname_tide ! Name of component
REAL(wp) :: equitide ! Amplitude of equilibrium tide
REAL(wp) :: f ! Node factor
REAL(wp) :: omega ! Angular velocity
REAL(wp) :: v0 ! Initial phase at prime meridian
REAL(wp) :: u ! Phase correction
END type tide_harmonic
TYPE(tide_harmonic), PUBLIC, DIMENSION(:), POINTER :: tide_harmonics !: Oscillation parameters of selected tidal components
LOGICAL , PUBLIC :: ln_tide !:
LOGICAL , PUBLIC :: ln_tide_pot !:
INTEGER :: nn_tide_var ! Variant of tidal parameter set and tide-potential computation
LOGICAL :: ln_tide_dia ! Enable tidal diagnostic output
LOGICAL :: ln_read_load !:
LOGICAL , PUBLIC :: ln_scal_load !:
LOGICAL , PUBLIC :: ln_tide_ramp !:
INTEGER , PUBLIC :: nb_harmo !: Number of active tidal components
REAL(wp), PUBLIC :: rn_tide_ramp_dt !:
REAL(wp), PUBLIC :: rn_scal_load !:
CHARACTER(lc), PUBLIC :: cn_tide_load !:
REAL(wp) :: rn_tide_gamma ! Tidal tilt factor
REAL(wp), PUBLIC, ALLOCATABLE, DIMENSION(:,:) :: pot_astro !: tidal potential
REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: pot_astro_comp ! tidal-potential component
REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: amp_pot, phi_pot
REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: amp_load, phi_load
REAL(wp) :: rn_tide_ramp_t ! Elapsed time in seconds
REAL(wp) :: sh_T, sh_s, sh_h, sh_p, sh_p1 ! astronomic angles
REAL(wp) :: sh_xi, sh_nu, sh_nuprim, sh_nusec, sh_R !
REAL(wp) :: sh_I, sh_x1ra, sh_N !
! Longitudes on 1 Jan 1900, 00h and angular velocities (units of deg and
! deg/h, respectively. The values of these module variables have been copied
! from subroutine astronomic_angle of the version of this module used in
! release version 4.0 of NEMO.
REAL(wp) :: rlon00_N = 259.1560564_wp ! Longitude of ascending lunar node
REAL(wp) :: romega_N = -.0022064139_wp
REAL(wp) :: rlon00_T = 180.0_wp ! Mean solar angle (GMT)
REAL(wp) :: romega_T = 15.0_wp
REAL(wp) :: rlon00_h = 280.1895014_wp ! Mean solar Longitude
REAL(wp) :: romega_h = .0410686387_wp
REAL(wp) :: rlon00_s = 277.0256206_wp ! Mean lunar Longitude
REAL(wp) :: romega_s = .549016532_wp
REAL(wp) :: rlon00_p1 = 281.2208569_wp ! Longitude of solar perigee
REAL(wp) :: romega_p1 = .000001961_wp
REAL(wp) :: rlon00_p = 334.3837214_wp ! Longitude of lunar perigee
REAL(wp) :: romega_p = .004641834_wp
! Values of cos(i)*cos(epsilon), rcice, and sin(incl)*sin(epsilon), rsise,
! where i is the inclination of the orbit of the Moon w.r.t. the ecliptic and
! epsilon the obliquity of the ecliptic on 1 January 1900, 00h. The values of
! these module variables have been copied from subroutine astronomic_angle
! (computation of the cosine of inclination of orbit of Moon to the celestial
! equator) of the version of this module used in release version 4.0 of NEMO.
REAL(wp) :: rcice = 0.913694997_wp
REAL(wp) :: rsise = 0.035692561_wp
! Coefficients used to compute sh_xi and sh_nu in subroutine astronomic_angle
! according to two equations given in the explanation of Table 6 of S58
REAL(wp) :: rxinu1, rxinu2
!!----------------------------------------------------------------------
!! NEMO/OCE 4.0 , NEMO Consortium (2018)
!! $Id: tide_mod.F90 13286 2020-07-09 15:48:29Z smasson $
!! Software governed by the CeCILL license (see ./LICENSE)
!!----------------------------------------------------------------------
CONTAINS
SUBROUTINE tide_init
!!----------------------------------------------------------------------
!! *** ROUTINE tide_init ***
!!----------------------------------------------------------------------
INTEGER :: ji, jk
CHARACTER(LEN=4), DIMENSION(jpmax_harmo) :: sn_tide_cnames ! Names of selected tidal components
INTEGER :: ios ! Local integer output status for namelist read
!
NAMELIST/nam_tide/ln_tide, nn_tide_var, ln_tide_dia, ln_tide_pot, rn_tide_gamma, &
& ln_scal_load, ln_read_load, cn_tide_load, &
& ln_tide_ramp, rn_scal_load, rn_tide_ramp_dt, &
& sn_tide_cnames
!!----------------------------------------------------------------------
!
! Initialise all array elements of sn_tide_cnames, as some of them
! typically do not appear in namelist_ref or namelist_cfg
sn_tide_cnames(:) = ''
! Read Namelist nam_tide
READ ( numnam_ref, nam_tide, IOSTAT = ios, ERR = 901)
901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'nam_tide in reference namelist' )
!
READ ( numnam_cfg, nam_tide, IOSTAT = ios, ERR = 902 )
902 IF( ios > 0 ) CALL ctl_nam ( ios , 'nam_tide in configuration namelist' )
IF(lwm) WRITE ( numond, nam_tide )
!
IF( ln_tide ) THEN
IF (lwp) THEN
WRITE(numout,*)
WRITE(numout,*) 'tide_init : Initialization of the tidal components'
WRITE(numout,*) '~~~~~~~~~ '
WRITE(numout,*) ' Namelist nam_tide'
WRITE(numout,*) ' Use tidal components ln_tide = ', ln_tide
WRITE(numout,*) ' Variant (1: default; 0: legacy option) nn_tide_var = ', nn_tide_var
WRITE(numout,*) ' Tidal diagnostic output ln_tide_dia = ', ln_tide_dia
WRITE(numout,*) ' Apply astronomical potential ln_tide_pot = ', ln_tide_pot
WRITE(numout,*) ' Tidal tilt factor rn_tide_gamma = ', rn_tide_gamma
WRITE(numout,*) ' Use scalar approx. for load potential ln_scal_load = ', ln_scal_load
WRITE(numout,*) ' Read load potential from file ln_read_load = ', ln_read_load
WRITE(numout,*) ' Apply ramp on tides at startup ln_tide_ramp = ', ln_tide_ramp
WRITE(numout,*) ' Fraction of SSH used in scal. approx. rn_scal_load = ', rn_scal_load
WRITE(numout,*) ' Duration (days) of ramp rn_tide_ramp_dt = ', rn_tide_ramp_dt
ENDIF
ELSE
rn_scal_load = 0._wp
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*) 'tide_init : tidal components not used (ln_tide = F)'
IF(lwp) WRITE(numout,*) '~~~~~~~~~ '
RETURN
ENDIF
!
IF( ln_read_load.AND.(.NOT.ln_tide_pot) ) &
& CALL ctl_stop('ln_read_load requires ln_tide_pot')
IF( ln_scal_load.AND.(.NOT.ln_tide_pot) ) &
& CALL ctl_stop('ln_scal_load requires ln_tide_pot')
IF( ln_scal_load.AND.ln_read_load ) &
& CALL ctl_stop('Choose between ln_scal_load and ln_read_load')
IF( ln_tide_ramp.AND.((nitend-nit000+1)*rn_Dt/rday < rn_tide_ramp_dt) ) &
& CALL ctl_stop('rn_tide_ramp_dt must be lower than run duration')
IF( ln_tide_ramp.AND.(rn_tide_ramp_dt<0.) ) &
& CALL ctl_stop('rn_tide_ramp_dt must be positive')
!
! Compute coefficients which are used in subroutine astronomic_angle to
! compute sh_xi and sh_nu according to two equations given in the
! explanation of Table 6 of S58
rxinu1 = COS( 0.5_wp * ( ABS( ACOS( rcice + rsise ) ) ) ) / COS( 0.5_wp * ( ACOS( rcice - rsise ) ) )
rxinu2 = SIN( 0.5_wp * ( ABS( ACOS( rcice + rsise ) ) ) ) / SIN( 0.5_wp * ( ACOS( rcice - rsise ) ) )
!
! Initialise array used to store tidal oscillation parameters (frequency,
! amplitude, phase); also retrieve and store array of information about
! selected tidal components
CALL tide_init_harmonics(sn_tide_cnames, tide_harmonics, tide_components)
!
! Number of active tidal components
nb_harmo = size(tide_components)
!
! Ensure that tidal components have been set in namelist_cfg
IF( nb_harmo == 0 ) CALL ctl_stop( 'tide_init : No tidal components set in nam_tide' )
!
IF (.NOT.ln_scal_load ) rn_scal_load = 0._wp
!
ALLOCATE( amp_pot(jpi,jpj,nb_harmo), &
& phi_pot(jpi,jpj,nb_harmo), pot_astro(jpi,jpj) )
IF( ln_tide_dia ) ALLOCATE( pot_astro_comp(jpi,jpj) )
IF( ln_read_load ) THEN
ALLOCATE( amp_load(jpi,jpj,nb_harmo), phi_load(jpi,jpj,nb_harmo) )
CALL tide_init_load
amp_pot(:,:,:) = amp_load(:,:,:)
phi_pot(:,:,:) = phi_load(:,:,:)
ELSE
amp_pot(:,:,:) = 0._wp
phi_pot(:,:,:) = 0._wp
ENDIF
!
END SUBROUTINE tide_init
SUBROUTINE tide_init_components(pcnames, ptide_comp)
!!----------------------------------------------------------------------
!! *** ROUTINE tide_init_components ***
!!
!! Returns pointer to array of variables of type 'tide' that contain
!! information about the selected tidal components
!! ----------------------------------------------------------------------
CHARACTER(LEN=4), DIMENSION(jpmax_harmo), INTENT(in) :: pcnames ! Names of selected components
TYPE(tide), POINTER, DIMENSION(:), INTENT(out) :: ptide_comp ! Selected components
INTEGER, ALLOCATABLE, DIMENSION(:) :: icomppos ! Indices of selected components
INTEGER :: icomp, jk, jj, ji ! Miscellaneous integers
LOGICAL :: llmatch ! Local variables used for
INTEGER :: ic1, ic2 ! string comparison
TYPE(tide), POINTER, DIMENSION(:) :: tide_components ! All available components
! Populate local array with information about all available tidal
! components
!
! Note, here 'tide_components' locally overrides the global module
! variable of the same name to enable the use of the global name in the
! include file that contains the initialisation of elements of array
! 'tide_components'
ALLOCATE(tide_components(jpmax_harmo), icomppos(jpmax_harmo))
! Initialise array of indices of the selected componenents
icomppos(:) = 0
! Include tidal component parameters for all available components
IF (nn_tide_var < 1) THEN
#define TIDE_VAR_0
#include "tide.h90"
#undef TIDE_VAR_0
ELSE
#include "tide.h90"
END IF
! Identify the selected components that are availble
icomp = 0
DO jk = 1, jpmax_harmo
IF (TRIM(pcnames(jk)) /= '') THEN
DO jj = 1, jpmax_harmo
! Find matches between selected and available constituents
! (ignore capitalisation unless legacy variant has been selected)
IF (nn_tide_var < 1) THEN
llmatch = (TRIM(pcnames(jk)) == TRIM(tide_components(jj)%cname_tide))
ELSE
llmatch = .TRUE.
ji = MAX(LEN_TRIM(pcnames(jk)), LEN_TRIM(tide_components(jj)%cname_tide))
DO WHILE (llmatch.AND.(ji > 0))
ic1 = IACHAR(pcnames(jk)(ji:ji))
IF ((ic1 >= 97).AND.(ic1 <= 122)) ic1 = ic1 - 32
ic2 = IACHAR(tide_components(jj)%cname_tide(ji:ji))
IF ((ic2 >= 97).AND.(ic2 <= 122)) ic2 = ic2 - 32
llmatch = (ic1 == ic2)
ji = ji - 1
END DO
END IF
IF (llmatch) THEN
! Count and record the match
icomp = icomp + 1
icomppos(icomp) = jj
! Set the capitalisation of the tidal constituent identifier
! as specified in the namelist
tide_components(jj)%cname_tide = pcnames(jk)
IF (lwp) WRITE(numout, '(10X,"Tidal component #",I2.2,36X,"= ",A4)') icomp, tide_components(jj)%cname_tide
EXIT
END IF
END DO
IF ((lwp).AND.(jj > jpmax_harmo)) WRITE(numout, '(10X,"Tidal component ",A4," is not available!")') pcnames(jk)
END IF
END DO
! Allocate and populate reduced list of components
ALLOCATE(ptide_comp(icomp))
DO jk = 1, icomp
ptide_comp(jk) = tide_components(icomppos(jk))
END DO
! Release local array of available components and list of selected
! components
DEALLOCATE(tide_components, icomppos)
END SUBROUTINE tide_init_components
SUBROUTINE tide_init_harmonics(pcnames, ptide_harmo, ptide_comp)
!!----------------------------------------------------------------------
!! *** ROUTINE tide_init_harmonics ***
!!
!! Returns pointer to array of variables of type 'tide_harmonics' that
!! contain oscillation parameters of the selected harmonic tidal
!! components
!! ----------------------------------------------------------------------
CHARACTER(LEN=4), DIMENSION(jpmax_harmo), INTENT(in) :: pcnames ! Names of selected components
TYPE(tide_harmonic), POINTER, DIMENSION(:) :: ptide_harmo ! Oscillation parameters of tidal components
TYPE(tide), POINTER, DIMENSION(:), OPTIONAL :: ptide_comp ! Selected components
TYPE(tide), POINTER, DIMENSION(:) :: ztcomp ! Selected components
! Retrieve information about selected tidal components
! If requested, prepare tidal component array for returning
IF (PRESENT(ptide_comp)) THEN
CALL tide_init_components(pcnames, ptide_comp)
ztcomp => ptide_comp
ELSE
CALL tide_init_components(pcnames, ztcomp)
END IF
! Allocate and populate array of oscillation parameters
ALLOCATE(ptide_harmo(size(ztcomp)))
ptide_harmo(:)%cname_tide = ztcomp(:)%cname_tide
ptide_harmo(:)%equitide = ztcomp(:)%equitide
CALL tide_harmo(ztcomp, ptide_harmo)
END SUBROUTINE tide_init_harmonics
SUBROUTINE tide_init_potential
!!----------------------------------------------------------------------
!! *** ROUTINE tide_init_potential ***
!!
!! ** Reference :
!! CT71) Cartwright, D. E. and Tayler, R. J. (1971): New computations of
!! the Tide-generating Potential. Geophys. J. R. astr. Soc. 23,
!! pp. 45-74. DOI: 10.1111/j.1365-246X.1971.tb01803.x
!!
!!----------------------------------------------------------------------
INTEGER :: ji, jj, jk ! dummy loop indices
REAL(wp) :: zcons, ztmp1, ztmp2, zlat, zlon, ztmp, zamp, zcs ! local scalar
!!----------------------------------------------------------------------
IF( ln_read_load ) THEN
amp_pot(:,:,:) = amp_load(:,:,:)
phi_pot(:,:,:) = phi_load(:,:,:)
ELSE
amp_pot(:,:,:) = 0._wp
phi_pot(:,:,:) = 0._wp
ENDIF
DO jk = 1, nb_harmo
zcons = rn_tide_gamma * tide_components(jk)%equitide * tide_harmonics(jk)%f
DO ji = 1, jpi
DO jj = 1, jpj
ztmp1 = tide_harmonics(jk)%f * amp_pot(ji,jj,jk) * COS( phi_pot(ji,jj,jk) &
& + tide_harmonics(jk)%v0 + tide_harmonics(jk)%u )
ztmp2 = -tide_harmonics(jk)%f * amp_pot(ji,jj,jk) * SIN( phi_pot(ji,jj,jk) &
& + tide_harmonics(jk)%v0 + tide_harmonics(jk)%u )
zlat = gphit(ji,jj)*rad !! latitude en radian
zlon = glamt(ji,jj)*rad !! longitude en radian
ztmp = tide_harmonics(jk)%v0 + tide_harmonics(jk)%u + tide_components(jk)%nt * zlon
! le potentiel est composé des effets des astres:
SELECT CASE( tide_components(jk)%nt )
CASE( 0 ) ! long-periodic tidal constituents (included unless
zcs = zcons * ( 0.5_wp - 1.5_wp * SIN( zlat )**2 ) ! compatibility with original formulation is requested)
IF ( nn_tide_var < 1 ) zcs = 0.0_wp
CASE( 1 ) ! diurnal tidal constituents
zcs = zcons * SIN( 2.0_wp*zlat )
CASE( 2 ) ! semi-diurnal tidal constituents
zcs = zcons * COS( zlat )**2
CASE( 3 ) ! Terdiurnal tidal constituents; the colatitude-dependent
zcs = zcons * COS( zlat )**3 ! factor is sin(theta)^3 (Table 2 of CT71)
CASE DEFAULT ! constituents of higher frequency are not included
zcs = 0.0_wp
END SELECT
ztmp1 = ztmp1 + zcs * COS( ztmp )
ztmp2 = ztmp2 - zcs * SIN( ztmp )
zamp = SQRT( ztmp1*ztmp1 + ztmp2*ztmp2 )
amp_pot(ji,jj,jk) = zamp
phi_pot(ji,jj,jk) = ATAN2( -ztmp2 / MAX( 1.e-10_wp , zamp ) , &
& ztmp1 / MAX( 1.e-10_wp, zamp ) )
END DO
END DO
END DO
!
END SUBROUTINE tide_init_potential
SUBROUTINE tide_init_load
!!----------------------------------------------------------------------
!! *** ROUTINE tide_init_load ***
!!----------------------------------------------------------------------
INTEGER :: inum ! Logical unit of input file
INTEGER :: ji, jj, itide ! dummy loop indices
REAL(wp), DIMENSION(jpi,jpj) :: ztr, zti !: workspace to read in tidal harmonics data
!!----------------------------------------------------------------------
IF(lwp) THEN
WRITE(numout,*)
WRITE(numout,*) 'tide_init_load : Initialization of load potential from file'
WRITE(numout,*) '~~~~~~~~~~~~~~ '
ENDIF
!
CALL iom_open ( cn_tide_load , inum )
!
DO itide = 1, nb_harmo
CALL iom_get ( inum, jpdom_global,TRIM(tide_components(itide)%cname_tide)//'_z1', ztr(:,:) )
CALL iom_get ( inum, jpdom_global,TRIM(tide_components(itide)%cname_tide)//'_z2', zti(:,:) )
!
DO ji=1,jpi
DO jj=1,jpj
amp_load(ji,jj,itide) = SQRT( ztr(ji,jj)**2. + zti(ji,jj)**2. )
phi_load(ji,jj,itide) = ATAN2(-zti(ji,jj), ztr(ji,jj) )
END DO
END DO
!
END DO
CALL iom_close( inum )
!
END SUBROUTINE tide_init_load
SUBROUTINE tide_update( kt )
!!----------------------------------------------------------------------
!! *** ROUTINE tide_update ***
!!----------------------------------------------------------------------
INTEGER, INTENT( in ) :: kt ! ocean time-step
INTEGER :: jk ! dummy loop index
!!----------------------------------------------------------------------
IF( nsec_day == NINT(0.5_wp * rn_Dt) .OR. kt == nit000 ) THEN ! start a new day
!
CALL tide_harmo(tide_components, tide_harmonics, ndt05) ! Update oscillation parameters of tidal components for start of current day
!
!
IF(lwp) THEN
WRITE(numout,*)
WRITE(numout,*) 'tide_update : Update of the components and (re)Init. the potential at kt=', kt
WRITE(numout,*) '~~~~~~~~~~~ '
DO jk = 1, nb_harmo
WRITE(numout,*) tide_harmonics(jk)%cname_tide, tide_harmonics(jk)%u, &
& tide_harmonics(jk)%f,tide_harmonics(jk)%v0, tide_harmonics(jk)%omega
END DO
ENDIF
!
IF( ln_tide_pot ) CALL tide_init_potential
!
rn_tide_ramp_t = (kt - nit000)*rn_Dt ! Elapsed time in seconds
ENDIF
!
END SUBROUTINE tide_update
SUBROUTINE tide_harmo( ptide_comp, ptide_harmo, psec_day )
!
TYPE(tide), DIMENSION(:), POINTER :: ptide_comp ! Array of selected tidal component parameters
TYPE(tide_harmonic), DIMENSION(:), POINTER :: ptide_harmo ! Oscillation parameters of selected tidal components
INTEGER, OPTIONAL :: psec_day ! Number of seconds since the start of the current day
!
IF (PRESENT(psec_day)) THEN
CALL astronomic_angle(psec_day)
ELSE
CALL astronomic_angle(nsec_day)
END IF
CALL tide_pulse( ptide_comp, ptide_harmo )
CALL tide_vuf( ptide_comp, ptide_harmo )
!
END SUBROUTINE tide_harmo
SUBROUTINE astronomic_angle(psec_day)
!!----------------------------------------------------------------------
!! *** ROUTINE astronomic_angle ***
!!
!! ** Purpose : Compute astronomic angles
!!----------------------------------------------------------------------
INTEGER :: psec_day ! Number of seconds from midnight
REAL(wp) :: zp, zq, zt2, zs2, ztgI2, zP1, ztgn2, zat1, zat2
REAL(wp) :: zqy , zsy, zday, zdj, zhfrac, zt
!!----------------------------------------------------------------------
!
! Computation of the time from 1 Jan 1900, 00h in years
zqy = AINT( (nyear - 1901.0_wp) / 4.0_wp )
zsy = nyear - 1900.0_wp
!
zdj = dayjul( nyear, nmonth, nday )
zday = zdj + zqy - 1.0_wp
!
zhfrac = psec_day / 3600.0_wp
!
zt = zsy * 365.0_wp * 24.0_wp + zday * 24.0_wp + zhfrac
!
! Longitude of ascending lunar node
sh_N = ( rlon00_N + romega_N * zt ) * rad
sh_N = MOD( sh_N, 2*rpi )
! Mean solar angle (Greenwhich time)
sh_T = ( rlon00_T + romega_T * zhfrac ) * rad
! Mean solar Longitude
sh_h = ( rlon00_h + romega_h * zt ) * rad
sh_h = MOD( sh_h, 2*rpi )
! Mean lunar Longitude
sh_s = ( rlon00_s + romega_s * zt ) * rad
sh_s = MOD( sh_s, 2*rpi )
! Longitude of solar perigee
sh_p1 = ( rlon00_p1 + romega_p1 * zt ) * rad
sh_p1= MOD( sh_p1, 2*rpi )
! Longitude of lunar perigee
sh_p = ( rlon00_p + romega_p * zt ) * rad
sh_p = MOD( sh_p, 2*rpi )
!
! Inclination of the orbit of the moon w.r.t. the celestial equator, see
! explanation of Table 6 of S58
sh_I = ACOS( rcice - rsise * COS( sh_N ) )
!
! Computation of sh_xi and sh_nu, see explanation of Table 6 of S58
ztgn2 = TAN( sh_N / 2.0_wp )
zat1 = ATAN( rxinu1 * ztgn2 )
zat2 = ATAN( rxinu2 * ztgn2 )
sh_xi = sh_N - zat1 - zat2
IF( sh_N > rpi ) sh_xi = sh_xi - 2.0_wp * rpi
sh_nu = zat1 - zat2
!
! Computation of sh_x1ra, sh_R, sh_nuprim, and sh_nusec used for tidal
! constituents L2, K1, and K2
!
! Computation of sh_x1ra and sh_R (Equations 204, 213, and 214 of S58)
ztgI2 = tan( sh_I / 2.0_wp )
zP1 = sh_p - sh_xi
zt2 = ztgI2 * ztgI2
sh_x1ra = SQRT( 1.0 - 12.0 * zt2 * COS( 2.0_wp * zP1 ) + 36.0_wp * zt2 * zt2 )
zp = SIN( 2.0_wp * zP1 )
zq = 1.0_wp / ( 6.0_wp * zt2 ) - COS( 2.0_wp * zP1 )
sh_R = ATAN( zp / zq )
!
! Computation of sh_nuprim (Equation 224 of S58)
zp = SIN( 2.0_wp * sh_I ) * SIN( sh_nu )
zq = SIN( 2.0_wp * sh_I ) * COS( sh_nu ) + 0.3347_wp
sh_nuprim = ATAN( zp / zq )
!
! Computation of sh_nusec (Equation 232 of S58)
zs2 = SIN( sh_I ) * SIN( sh_I )
zp = zs2 * SIN( 2.0_wp * sh_nu )
zq = zs2 * COS( 2.0_wp * sh_nu ) + 0.0727_wp
sh_nusec = 0.5_wp * ATAN( zp / zq )
!
END SUBROUTINE astronomic_angle
SUBROUTINE tide_pulse( ptide_comp, ptide_harmo )
!!----------------------------------------------------------------------
!! *** ROUTINE tide_pulse ***
!!
!! ** Purpose : Compute tidal frequencies
!!----------------------------------------------------------------------
TYPE(tide), DIMENSION(:), POINTER :: ptide_comp ! Array of selected tidal component parameters
TYPE(tide_harmonic), DIMENSION(:), POINTER :: ptide_harmo ! Oscillation parameters of selected tidal components
!
INTEGER :: jh
REAL(wp) :: zscale
!!----------------------------------------------------------------------
!
zscale = rad / 3600.0_wp
!
DO jh = 1, size(ptide_harmo)
ptide_harmo(jh)%omega = ( romega_T * ptide_comp( jh )%nT &
& + romega_s * ptide_comp( jh )%ns &
& + romega_h * ptide_comp( jh )%nh &
& + romega_p * ptide_comp( jh )%np &
& + romega_p1* ptide_comp( jh )%np1 ) * zscale
END DO
!
END SUBROUTINE tide_pulse
SUBROUTINE tide_vuf( ptide_comp, ptide_harmo )
!!----------------------------------------------------------------------
!! *** ROUTINE tide_vuf ***
!!
!! ** Purpose : Compute nodal modulation corrections
!!
!! ** Outputs : vt: Phase of tidal potential relative to Greenwich (radians)
!! ut: Phase correction u due to nodal motion (radians)
!! ft: Nodal correction factor
!!----------------------------------------------------------------------
TYPE(tide), DIMENSION(:), POINTER :: ptide_comp ! Array of selected tidal component parameters
TYPE(tide_harmonic), DIMENSION(:), POINTER :: ptide_harmo ! Oscillation parameters of selected tidal components
!
INTEGER :: jh ! dummy loop index
!!----------------------------------------------------------------------
!
DO jh = 1, size(ptide_harmo)
! Phase of the tidal potential relative to the Greenwhich
! meridian (e.g. the position of the fictuous celestial body). Units are radian:
ptide_harmo(jh)%v0 = sh_T * ptide_comp( jh )%nT &
& + sh_s * ptide_comp( jh )%ns &
& + sh_h * ptide_comp( jh )%nh &
& + sh_p * ptide_comp( jh )%np &
& + sh_p1* ptide_comp( jh )%np1 &
& + ptide_comp( jh )%shift * rad
!
! Phase correction u due to nodal motion. Units are radian:
ptide_harmo(jh)%u = sh_xi * ptide_comp( jh )%nksi &
& + sh_nu * ptide_comp( jh )%nnu0 &
& + sh_nuprim * ptide_comp( jh )%nnu1 &
& + sh_nusec * ptide_comp( jh )%nnu2 &
& + sh_R * ptide_comp( jh )%R
! Nodal correction factor:
ptide_harmo(jh)%f = nodal_factort( ptide_comp( jh )%nformula )
END DO
!
END SUBROUTINE tide_vuf
RECURSIVE FUNCTION nodal_factort( kformula ) RESULT( zf )
!!----------------------------------------------------------------------
!! *** FUNCTION nodal_factort ***
!!
!! ** Purpose : Compute amplitude correction factors due to nodal motion
!!----------------------------------------------------------------------
INTEGER, INTENT(in) :: kformula
!
REAL(wp) :: zf
REAL(wp) :: zs, zf1, zf2
CHARACTER(LEN=3) :: clformula
!!----------------------------------------------------------------------
!
SELECT CASE( kformula )
!
CASE( 0 ) ! Formula 0, solar waves
zf = 1.0
!
CASE( 1 ) ! Formula 1, compound waves (78 x 78)
zf=nodal_factort( 78 )
zf = zf * zf
!
CASE ( 4 ) ! Formula 4, compound waves (78 x 235)
zf1 = nodal_factort( 78 )
zf = nodal_factort(235)
zf = zf1 * zf
!
CASE( 18 ) ! Formula 18, compound waves (78 x 78 x 78 )
zf1 = nodal_factort( 78 )
zf = zf1 * zf1 * zf1
!
CASE( 20 ) ! Formula 20, compound waves ( 78 x 78 x 78 x 78 )
zf1 = nodal_factort( 78 )
zf = zf1 * zf1 * zf1 * zf1
!
CASE( 73 ) ! Formula 73 of S58
zs = SIN( sh_I )
zf = ( 2.0_wp / 3.0_wp - zs * zs ) / 0.5021_wp
!
CASE( 74 ) ! Formula 74 of S58
zs = SIN(sh_I)
zf = zs * zs / 0.1578_wp
!
CASE( 75 ) ! Formula 75 of S58
zs = COS( sh_I / 2.0_wp )
zf = SIN( sh_I ) * zs * zs / 0.3800_wp
!
CASE( 76 ) ! Formula 76 of S58
zf = SIN( 2.0_wp * sh_I ) / 0.7214_wp
!
CASE( 78 ) ! Formula 78 of S58
zs = COS( sh_I/2 )
zf = zs * zs * zs * zs / 0.9154_wp
!
CASE( 149 ) ! Formula 149 of S58
zs = COS( sh_I/2 )
zf = zs * zs * zs * zs * zs * zs / 0.8758_wp
!
CASE( 215 ) ! Formula 215 of S58 with typo correction (0.9154 instead of 0.9145)
zs = COS( sh_I/2 )
zf = zs * zs * zs * zs / 0.9154_wp * sh_x1ra
!
CASE( 227 ) ! Formula 227 of S58
zs = SIN( 2.0_wp * sh_I )
zf = SQRT( 0.8965_wp * zs * zs + 0.6001_wp * zs * COS( sh_nu ) + 0.1006_wp )
!
CASE ( 235 ) ! Formula 235 of S58
zs = SIN( sh_I )
zf = SQRT( 19.0444_wp * zs * zs * zs * zs + 2.7702_wp * zs * zs * cos( 2.0_wp * sh_nu ) + 0.0981_wp )
!
CASE DEFAULT
WRITE( clformula, '(I3)' ) kformula
CALL ctl_stop('nodal_factort: formula ' // clformula // ' is not available')
END SELECT
!
END FUNCTION nodal_factort
FUNCTION dayjul( kyr, kmonth, kday )
!!----------------------------------------------------------------------
!! *** FUNCTION dayjul ***
!!
!! Purpose : compute the Julian day
!!----------------------------------------------------------------------
INTEGER,INTENT(in) :: kyr, kmonth, kday
!
INTEGER,DIMENSION(12) :: idayt = (/ 0, 31, 59, 90, 120, 151, 181, 212, 243, 273, 304, 334 /)
INTEGER,DIMENSION(12) :: idays
INTEGER :: inc, ji, zyq
REAL(wp) :: dayjul
!!----------------------------------------------------------------------
!
idays(1) = 0
idays(2) = 31
inc = 0.0_wp
zyq = MOD( kyr - 1900 , 4 )
IF( zyq == 0 ) inc = 1
DO ji = 3, 12
idays(ji) = idayt(ji) + inc
END DO
dayjul = REAL( idays(kmonth) + kday, KIND=wp )
!
END FUNCTION dayjul
SUBROUTINE upd_tide(pdelta, Kmm)
!!----------------------------------------------------------------------
!! *** ROUTINE upd_tide ***
!!
!! ** Purpose : provide at each time step the astronomical potential
!!
!! ** Method : computed from pulsation and amplitude of all tide components
!!
!! ** Action : pot_astro actronomical potential
!!----------------------------------------------------------------------
REAL(wp), INTENT(in) :: pdelta ! Temporal offset in seconds
INTEGER, INTENT(IN) :: Kmm ! Time level index
INTEGER :: jk ! Dummy loop index
REAL(wp) :: zt, zramp ! Local scalars
REAL(wp), DIMENSION(nb_harmo) :: zwt ! Temporary array
!!----------------------------------------------------------------------
!
zwt(:) = tide_harmonics(:)%omega * pdelta
!
IF( ln_tide_ramp ) THEN ! linear increase if asked
zt = rn_tide_ramp_t + pdelta
zramp = MIN( MAX( zt / (rn_tide_ramp_dt*rday) , 0._wp ) , 1._wp )
ENDIF
!
pot_astro(:,:) = 0._wp ! update tidal potential (sum of all harmonics)
DO jk = 1, nb_harmo
IF ( .NOT. ln_tide_dia ) THEN
pot_astro(:,:) = pot_astro(:,:) + amp_pot(:,:,jk) * COS( zwt(jk) + phi_pot(:,:,jk) )
ELSE
pot_astro_comp(:,:) = amp_pot(:,:,jk) * COS( zwt(jk) + phi_pot(:,:,jk) )
pot_astro(:,:) = pot_astro(:,:) + pot_astro_comp(:,:)
IF ( iom_use( "tide_pot_" // TRIM( tide_harmonics(jk)%cname_tide ) ) ) THEN ! Output tidal potential (incl. load potential)
IF ( ln_tide_ramp ) pot_astro_comp(:,:) = zramp * pot_astro_comp(:,:)
CALL iom_put( "tide_pot_" // TRIM( tide_harmonics(jk)%cname_tide ), pot_astro_comp(:,:) )
END IF
END IF
END DO
!
IF ( ln_tide_ramp ) pot_astro(:,:) = zramp * pot_astro(:,:)
!
IF( ln_tide_dia ) THEN ! Output total tidal potential (incl. load potential)
IF ( iom_use( "tide_pot" ) ) CALL iom_put( "tide_pot", pot_astro(:,:) + rn_scal_load * ssh(:,:,Kmm) )
END IF
!
END SUBROUTINE upd_tide
!!======================================================================
END MODULE tide_mod