MODULE tide_mod !!====================================================================== !! *** MODULE tide_mod *** !! Compute nodal modulations corrections and pulsations !!====================================================================== !! History : 1.0 ! 2007 (O. Le Galloudec) Original code !!---------------------------------------------------------------------- USE dom_oce ! ocean space and time domain USE phycst ! physical constant USE daymod ! calendar IMPLICIT NONE PRIVATE PUBLIC tide_harmo ! called by tideini and diaharm modules PUBLIC tide_init_Wave ! called by tideini and diaharm modules INTEGER, PUBLIC, PARAMETER :: jpmax_harmo = 31 !: maximum number of harmonic TYPE, PUBLIC :: tide CHARACTER(LEN=5) :: cname_tide REAL(wp) :: equitide INTEGER :: nutide INTEGER :: nt, ns, nh, np, np1, shift INTEGER :: nksi, nnu0, nnu1, nnu2, R INTEGER :: nformula END TYPE tide TYPE(tide), PUBLIC, DIMENSION(jpmax_harmo) :: Wave !: 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 ! !!---------------------------------------------------------------------- !! NEMO/OPA 3.3 , LOCEAN-IPSL (2010) !! $Id$ !! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE tide_init_Wave # include "tide.h90" END SUBROUTINE tide_init_Wave SUBROUTINE tide_harmo( pomega, pvt, put , pcor, ktide ,kc) !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- INTEGER , DIMENSION(kc), INTENT(in ) :: ktide ! Indice of tidal constituents INTEGER , INTENT(in ) :: kc ! Total number of tidal constituents REAL(wp), DIMENSION(kc), INTENT(out) :: pomega ! pulsation in radians/s REAL(wp), DIMENSION(kc), INTENT(out) :: pvt, put, pcor ! !!---------------------------------------------------------------------- ! CALL astronomic_angle CALL tide_pulse( pomega, ktide ,kc ) CALL tide_vuf ( pvt, put, pcor, ktide ,kc ) ! END SUBROUTINE tide_harmo SUBROUTINE astronomic_angle !!---------------------------------------------------------------------- !! tj is time elapsed since 1st January 1900, 0 hour, counted in julian !! century (e.g. time in days divide by 36525) !!---------------------------------------------------------------------- REAL(wp) :: cosI, p, q, t2, t4, sin2I, s2, tgI2, P1, sh_tgn2, at1, at2 REAL(wp) :: zqy , zsy, zday, zdj, zhfrac !!---------------------------------------------------------------------- ! zqy = AINT( (nyear-1901.)/4. ) zsy = nyear - 1900. ! zdj = dayjul( nyear, nmonth, nday ) zday = zdj + zqy - 1. ! zhfrac = nsec_day / 3600. ! !---------------------------------------------------------------------- ! Sh_n Longitude of ascending lunar node !---------------------------------------------------------------------- sh_N=(259.1560564-19.328185764*zsy-.0529539336*zday-.0022064139*zhfrac)*rad !---------------------------------------------------------------------- ! T mean solar angle (Greenwhich time) !---------------------------------------------------------------------- sh_T=(180.+zhfrac*(360./24.))*rad !---------------------------------------------------------------------- ! h mean solar Longitude !---------------------------------------------------------------------- sh_h=(280.1895014-.238724988*zsy+.9856473288*zday+.0410686387*zhfrac)*rad !---------------------------------------------------------------------- ! s mean lunar Longitude !---------------------------------------------------------------------- sh_s=(277.0256206+129.38482032*zsy+13.176396768*zday+.549016532*zhfrac)*rad !---------------------------------------------------------------------- ! p1 Longitude of solar perigee !---------------------------------------------------------------------- sh_p1=(281.2208569+.01717836*zsy+.000047064*zday+.000001961*zhfrac)*rad !---------------------------------------------------------------------- ! p Longitude of lunar perigee !---------------------------------------------------------------------- sh_p=(334.3837214+40.66246584*zsy+.111404016*zday+.004641834*zhfrac)*rad sh_N = MOD( sh_N ,2*rpi ) sh_s = MOD( sh_s ,2*rpi ) sh_h = MOD( sh_h, 2*rpi ) sh_p = MOD( sh_p, 2*rpi ) sh_p1= MOD( sh_p1,2*rpi ) cosI = 0.913694997 -0.035692561 *cos(sh_N) sh_I = ACOS( cosI ) sin2I = sin(sh_I) sh_tgn2 = tan(sh_N/2.0) at1=atan(1.01883*sh_tgn2) at2=atan(0.64412*sh_tgn2) sh_xi=-at1-at2+sh_N IF( sh_N > rpi ) sh_xi=sh_xi-2.0*rpi sh_nu = at1 - at2 !---------------------------------------------------------------------- ! For constituents l2 k1 k2 !---------------------------------------------------------------------- tgI2 = tan(sh_I/2.0) P1 = sh_p-sh_xi t2 = tgI2*tgI2 t4 = t2*t2 sh_x1ra = sqrt( 1.0-12.0*t2*cos(2.0*P1)+36.0*t4 ) p = sin(2.0*P1) q = 1.0/(6.0*t2)-cos(2.0*P1) sh_R = atan(p/q) p = sin(2.0*sh_I)*sin(sh_nu) q = sin(2.0*sh_I)*cos(sh_nu)+0.3347 sh_nuprim = atan(p/q) s2 = sin(sh_I)*sin(sh_I) p = s2*sin(2.0*sh_nu) q = s2*cos(2.0*sh_nu)+0.0727 sh_nusec = 0.5*atan(p/q) ! END SUBROUTINE astronomic_angle SUBROUTINE tide_pulse( pomega, ktide ,kc ) !!---------------------------------------------------------------------- !! *** ROUTINE tide_pulse *** !! !! ** Purpose : Compute tidal frequencies !!---------------------------------------------------------------------- INTEGER , INTENT(in ) :: kc ! Total number of tidal constituents INTEGER , DIMENSION(kc), INTENT(in ) :: ktide ! Indice of tidal constituents REAL(wp), DIMENSION(kc), INTENT(out) :: pomega ! pulsation in radians/s ! INTEGER :: jh REAL(wp) :: zscale REAL(wp) :: zomega_T = 13149000.0_wp REAL(wp) :: zomega_s = 481267.892_wp REAL(wp) :: zomega_h = 36000.76892_wp REAL(wp) :: zomega_p = 4069.0322056_wp REAL(wp) :: zomega_n = 1934.1423972_wp REAL(wp) :: zomega_p1= 1.719175_wp !!---------------------------------------------------------------------- ! zscale = rad / ( 36525._wp * 86400._wp ) ! DO jh = 1, kc pomega(jh) = ( zomega_T * Wave( ktide(jh) )%nT & & + zomega_s * Wave( ktide(jh) )%ns & & + zomega_h * Wave( ktide(jh) )%nh & & + zomega_p * Wave( ktide(jh) )%np & & + zomega_p1* Wave( ktide(jh) )%np1 ) * zscale END DO ! END SUBROUTINE tide_pulse SUBROUTINE tide_vuf( pvt, put, pcor, ktide ,kc ) !!---------------------------------------------------------------------- !! *** 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 !!---------------------------------------------------------------------- INTEGER , INTENT(in ) :: kc ! Total number of tidal constituents INTEGER , DIMENSION(kc), INTENT(in ) :: ktide ! Indice of tidal constituents REAL(wp), DIMENSION(kc), INTENT(out) :: pvt, put, pcor ! ! INTEGER :: jh ! dummy loop index !!---------------------------------------------------------------------- ! DO jh = 1, kc ! Phase of the tidal potential relative to the Greenwhich ! meridian (e.g. the position of the fictuous celestial body). Units are radian: pvt(jh) = sh_T * Wave( ktide(jh) )%nT & & + sh_s * Wave( ktide(jh) )%ns & & + sh_h * Wave( ktide(jh) )%nh & & + sh_p * Wave( ktide(jh) )%np & & + sh_p1* Wave( ktide(jh) )%np1 & & + Wave( ktide(jh) )%shift * rad ! ! Phase correction u due to nodal motion. Units are radian: put(jh) = sh_xi * Wave( ktide(jh) )%nksi & & + sh_nu * Wave( ktide(jh) )%nnu0 & & + sh_nuprim * Wave( ktide(jh) )%nnu1 & & + sh_nusec * Wave( ktide(jh) )%nnu2 & & + sh_R * Wave( ktide(jh) )%R ! Nodal correction factor: pcor(jh) = nodal_factort( Wave( ktide(jh) )%nformula ) END DO ! END SUBROUTINE tide_vuf RECURSIVE FUNCTION nodal_factort( kformula ) RESULT( zf ) !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- INTEGER, INTENT(in) :: kformula ! REAL(wp) :: zf REAL(wp) :: zs, zf1, zf2 !!---------------------------------------------------------------------- ! SELECT CASE( kformula ) ! CASE( 0 ) !== formule 0, solar waves zf = 1.0 ! CASE( 1 ) !== formule 1, compound waves (78 x 78) zf=nodal_factort(78) zf = zf * zf ! CASE ( 2 ) !== formule 2, compound waves (78 x 0) === (78) zf1= nodal_factort(78) zf = nodal_factort( 0) zf = zf1 * zf ! CASE ( 4 ) !== formule 4, compound waves (78 x 235) zf1 = nodal_factort( 78) zf = nodal_factort(235) zf = zf1 * zf ! CASE ( 5 ) !== formule 5, compound waves (78 *78 x 235) zf1 = nodal_factort( 78) zf = nodal_factort(235) zf = zf * zf1 * zf1 ! CASE ( 6 ) !== formule 6, compound waves (78 *78 x 0) zf1 = nodal_factort(78) zf = nodal_factort( 0) zf = zf * zf1 * zf1 ! CASE( 7 ) !== formule 7, compound waves (75 x 75) zf = nodal_factort(75) zf = zf * zf ! CASE( 8 ) !== formule 8, compound waves (78 x 0 x 235) zf = nodal_factort( 78) zf1 = nodal_factort( 0) zf2 = nodal_factort(235) zf = zf * zf1 * zf2 ! CASE( 9 ) !== formule 9, compound waves (78 x 0 x 227) zf = nodal_factort( 78) zf1 = nodal_factort( 0) zf2 = nodal_factort(227) zf = zf * zf1 * zf2 ! CASE( 10 ) !== formule 10, compound waves (78 x 227) zf = nodal_factort( 78) zf1 = nodal_factort(227) zf = zf * zf1 ! CASE( 11 ) !== formule 11, compound waves (75 x 0) !!gm bug???? zf 2 fois ! zf = nodal_factort(75) zf = nodal_factort( 0) zf = zf * zf1 ! CASE( 12 ) !== formule 12, compound waves (78 x 78 x 78 x 0) zf1 = nodal_factort(78) zf = nodal_factort( 0) zf = zf * zf1 * zf1 * zf1 ! CASE( 13 ) !== formule 13, compound waves (78 x 75) zf1 = nodal_factort(78) zf = nodal_factort(75) zf = zf * zf1 ! CASE( 14 ) !== formule 14, compound waves (235 x 0) === (235) zf = nodal_factort(235) zf1 = nodal_factort( 0) zf = zf * zf1 ! CASE( 15 ) !== formule 15, compound waves (235 x 75) zf = nodal_factort(235) zf1 = nodal_factort( 75) zf = zf * zf1 ! CASE( 16 ) !== formule 16, compound waves (78 x 0 x 0) === (78) zf = nodal_factort(78) zf1 = nodal_factort( 0) zf = zf * zf1 * zf1 ! CASE( 17 ) !== formule 17, compound waves (227 x 0) zf1 = nodal_factort(227) zf = nodal_factort( 0) zf = zf * zf1 ! CASE( 18 ) !== formule 18, compound waves (78 x 78 x 78 ) zf1 = nodal_factort(78) zf = zf1 * zf1 * zf1 ! CASE( 19 ) !== formule 19, compound waves (78 x 0 x 0 x 0) === (78) !!gm bug2 ==>>> here identical to formule 16, a third multiplication by zf1 is missing zf = nodal_factort(78) zf1 = nodal_factort( 0) zf = zf * zf1 * zf1 ! CASE( 73 ) !== formule 73 zs = sin(sh_I) zf = (2./3.-zs*zs)/0.5021 ! CASE( 74 ) !== formule 74 zs = sin(sh_I) zf = zs * zs / 0.1578 ! CASE( 75 ) !== formule 75 zs = cos(sh_I/2) zf = sin(sh_I) * zs * zs / 0.3800 ! CASE( 76 ) !== formule 76 zf = sin(2*sh_I) / 0.7214 ! CASE( 77 ) !== formule 77 zs = sin(sh_I/2) zf = sin(sh_I) * zs * zs / 0.0164 ! CASE( 78 ) !== formule 78 zs = cos(sh_I/2) zf = zs * zs * zs * zs / 0.9154 ! CASE( 79 ) !== formule 79 zs = sin(sh_I) zf = zs * zs / 0.1565 ! CASE( 144 ) !== formule 144 zs = sin(sh_I/2) zf = ( 1-10*zs*zs+15*zs*zs*zs*zs ) * cos(sh_I/2) / 0.5873 ! CASE( 149 ) !== formule 149 zs = cos(sh_I/2) zf = zs*zs*zs*zs*zs*zs / 0.8758 ! CASE( 215 ) !== formule 215 zs = cos(sh_I/2) zf = zs*zs*zs*zs / 0.9154 * sh_x1ra ! CASE( 227 ) !== formule 227 zs = sin(2*sh_I) zf = sqrt( 0.8965*zs*zs+0.6001*zs*cos (sh_nu)+0.1006 ) ! CASE ( 235 ) !== formule 235 zs = sin(sh_I) zf = sqrt( 19.0444*zs*zs*zs*zs + 2.7702*zs*zs*cos(2*sh_nu) + .0981 ) ! END SELECT ! END FUNCTION nodal_factort FUNCTION dayjul( kyr, kmonth, kday ) !!---------------------------------------------------------------------- !! *** THIS ROUTINE COMPUTES THE JULIAN DAY (AS A REAL VARIABLE) !!---------------------------------------------------------------------- INTEGER,INTENT(in) :: kyr, kmonth, kday ! INTEGER,DIMENSION(12) :: idayt, idays INTEGER :: inc, ji REAL(wp) :: dayjul, zyq ! DATA idayt/0.,31.,59.,90.,120.,151.,181.,212.,243.,273.,304.,334./ !!---------------------------------------------------------------------- ! idays(1) = 0. idays(2) = 31. inc = 0. zyq = MOD( kyr-1900. , 4. ) IF( zyq == 0.) inc = 1. DO ji = 3, 12 idays(ji)=idayt(ji)+inc END DO dayjul = idays(kmonth) + kday ! END FUNCTION dayjul !!====================================================================== END MODULE tide_mod