| 1 | MODULE tide_mod |
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| 2 | !!================================================================================= |
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| 3 | !! *** MODULE tide_mod *** |
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| 4 | !! Compute nodal modulations corrections and pulsations |
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| 5 | !!================================================================================= |
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| 6 | !!--------------------------------------------------------------------------------- |
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| 7 | !! OPA 9.0 , LODYC-IPSL (2003) |
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| 8 | !!--------------------------------------------------------------------------------- |
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| 9 | USE dom_oce ! ocean space and time domain |
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| 10 | USE phycst |
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| 11 | USE daymod |
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| 12 | USE in_out_manager ! I/O units |
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| 13 | |
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| 14 | IMPLICIT NONE |
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| 15 | PRIVATE |
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| 16 | |
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| 17 | REAL(wp) :: sh_T, sh_s, sh_h, sh_p, sh_p1, & |
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| 18 | sh_xi, sh_nu, sh_nuprim, sh_nusec, sh_R, & |
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| 19 | sh_I, sh_x1ra, sh_N |
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| 20 | |
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| 21 | INTEGER,PUBLIC, PARAMETER :: & |
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| 22 | jpmax_harmo = 19 ! maximum number of harmonic |
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| 23 | |
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| 24 | TYPE,PUBLIC:: tide |
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| 25 | CHARACTER(LEN=4) :: cname_tide |
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| 26 | REAL(wp) :: equitide |
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| 27 | INTEGER :: nutide |
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| 28 | INTEGER :: nt,ns,nh,np,np1,shift |
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| 29 | INTEGER :: nksi,nnu0,nnu1,nnu2,R |
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| 30 | INTEGER :: nformula |
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| 31 | END TYPE tide |
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| 32 | |
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| 33 | TYPE(tide), PUBLIC, DIMENSION(jpmax_harmo) :: Wave |
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| 34 | |
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| 35 | !! * Accessibility |
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| 36 | PUBLIC tide_harmo |
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| 37 | PUBLIC nodal_factort |
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| 38 | PUBLIC tide_init_Wave |
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| 39 | PUBLIC tide_pulse |
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| 40 | |
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| 41 | CONTAINS |
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| 42 | |
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| 43 | SUBROUTINE tide_init_Wave |
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| 44 | |
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| 45 | # include "tide.h90" |
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| 46 | |
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| 47 | END SUBROUTINE tide_init_Wave |
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| 48 | |
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| 49 | SUBROUTINE tide_harmo( pomega, pvt, put , pcor, ktide ,kc, rdate) |
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| 50 | |
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| 51 | INTEGER, INTENT( in ), OPTIONAL :: & |
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| 52 | rdate ! Reference date for tidal data |
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| 53 | |
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| 54 | INTEGER, DIMENSION(kc), INTENT( in ) :: & |
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| 55 | ktide ! Indice of tidal constituents |
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| 56 | |
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| 57 | INTEGER, INTENT( in ) :: & |
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| 58 | kc ! Total number of tidal constituents |
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| 59 | |
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| 60 | REAL (wp), DIMENSION(kc), INTENT( out ) :: & |
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| 61 | pomega ! pulsation in radians/s |
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| 62 | |
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| 63 | REAL (wp), DIMENSION(kc), INTENT( out ) :: & |
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| 64 | pvt, & ! |
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| 65 | put, & ! |
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| 66 | pcor ! |
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| 67 | |
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| 68 | IF( PRESENT(rdate) ) THEN |
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| 69 | CALL astronomic_angle(rdate) |
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| 70 | ELSE |
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| 71 | CALL astronomic_angle |
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| 72 | ENDIF |
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| 73 | CALL tide_pulse(pomega, ktide ,kc) |
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| 74 | CALL tide_vuf( pvt, put, pcor, ktide ,kc) |
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| 75 | |
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| 76 | END SUBROUTINE tide_harmo |
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| 77 | |
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| 78 | SUBROUTINE astronomic_angle(rdate) |
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| 79 | |
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| 80 | INTEGER, INTENT( in ),OPTIONAL :: & |
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| 81 | rdate ! Reference Year |
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| 82 | |
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| 83 | !!---------------------------------------------------------------------- |
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| 84 | !! |
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| 85 | !! tj is time elapsed since 1st January 1900, 0 hour, counted in julian |
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| 86 | !! century (e.g. time in days divide by 36525) |
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| 87 | !!---------------------------------------------------------------------- |
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| 88 | |
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| 89 | REAL(wp) :: cosI,p,q,t2,t4,sin2I,s2,tgI2,P1,sh_tgn2,at1,at2 |
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| 90 | REAL(wp) :: zqy,zsy,zday,zdj,zhfrac |
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| 91 | INTEGER :: lcl_ryear, lcl_rmonth, lcl_rday |
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| 92 | |
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| 93 | IF( PRESENT(rdate) ) THEN |
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| 94 | lcl_ryear = int(rdate / 10000 ) |
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| 95 | lcl_rmonth = int((rdate - lcl_ryear * 10000 ) / 100 ) |
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| 96 | lcl_rday = int(rdate - lcl_ryear * 10000 - lcl_rmonth * 100) |
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| 97 | ELSE |
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| 98 | lcl_ryear = nyear |
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| 99 | lcl_rmonth = nmonth |
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| 100 | lcl_rday = nday |
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| 101 | ENDIF |
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| 102 | |
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| 103 | zqy=AINT((lcl_ryear-1901.)/4.) |
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| 104 | zsy=lcl_ryear-1900. |
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| 105 | |
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| 106 | zdj=dayjul(lcl_ryear,lcl_rmonth,lcl_rday) |
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| 107 | zday=zdj+zqy-1. |
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| 108 | |
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| 109 | IF( PRESENT(rdate) ) THEN |
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| 110 | zhfrac=0._wp |
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| 111 | ELSE |
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| 112 | zhfrac=nsec_day/3600._wp |
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| 113 | ENDIF |
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| 114 | |
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| 115 | !---------------------------------------------------------------------- |
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| 116 | ! Sh_n Longitude of ascending lunar node |
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| 117 | !---------------------------------------------------------------------- |
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| 118 | |
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| 119 | sh_N=(259.1560564-19.328185764*zsy-.0529539336*zday-.0022064139*zhfrac)*rad |
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| 120 | !---------------------------------------------------------------------- |
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| 121 | ! T mean solar angle (Greenwhich time) |
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| 122 | !---------------------------------------------------------------------- |
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| 123 | sh_T=(180.+zhfrac*(360./24.))*rad |
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| 124 | !---------------------------------------------------------------------- |
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| 125 | ! h mean solar Longitude |
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| 126 | !---------------------------------------------------------------------- |
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| 127 | |
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| 128 | sh_h=(280.1895014-.238724988*zsy+.9856473288*zday+.0410686387*zhfrac)*rad |
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| 129 | !---------------------------------------------------------------------- |
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| 130 | ! s mean lunar Longitude |
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| 131 | !---------------------------------------------------------------------- |
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| 132 | |
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| 133 | sh_s=(277.0256206+129.38482032*zsy+13.176396768*zday+.549016532*zhfrac)*rad |
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| 134 | !---------------------------------------------------------------------- |
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| 135 | ! p1 Longitude of solar perigee |
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| 136 | !---------------------------------------------------------------------- |
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| 137 | |
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| 138 | sh_p1=(281.2208569+.01717836*zsy+.000047064*zday+.000001961*zhfrac)*rad |
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| 139 | !---------------------------------------------------------------------- |
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| 140 | ! p Longitude of lunar perigee |
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| 141 | !---------------------------------------------------------------------- |
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| 142 | |
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| 143 | sh_p=(334.3837214+40.66246584*zsy+.111404016*zday+.004641834*zhfrac)*rad |
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| 144 | |
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| 145 | sh_N =mod(sh_N ,2*rpi) |
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| 146 | sh_s =mod(sh_s ,2*rpi) |
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| 147 | sh_h =mod(sh_h, 2*rpi) |
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| 148 | sh_p =mod(sh_p, 2*rpi) |
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| 149 | sh_p1=mod(sh_p1,2*rpi) |
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| 150 | |
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| 151 | cosI=0.913694997 -0.035692561 *cos(sh_N) |
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| 152 | |
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| 153 | sh_I=acos(cosI) |
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| 154 | |
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| 155 | sin2I=sin(sh_I) |
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| 156 | sh_tgn2=tan(sh_N/2.0) |
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| 157 | |
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| 158 | at1=atan(1.01883*sh_tgn2) |
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| 159 | at2=atan(0.64412*sh_tgn2) |
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| 160 | |
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| 161 | sh_xi=-at1-at2+sh_N |
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| 162 | |
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| 163 | if (sh_N > rpi) sh_xi=sh_xi-2.0*rpi |
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| 164 | |
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| 165 | sh_nu=at1-at2 |
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| 166 | |
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| 167 | !---------------------------------------------------------------------- |
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| 168 | ! For constituents l2 k1 k2 |
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| 169 | !---------------------------------------------------------------------- |
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| 170 | |
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| 171 | tgI2=tan(sh_I/2.0) |
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| 172 | P1=sh_p-sh_xi |
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| 173 | |
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| 174 | t2=tgI2*tgI2 |
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| 175 | t4=t2*t2 |
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| 176 | sh_x1ra=sqrt(1.0-12.0*t2*cos(2.0*P1)+36.0*t4) |
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| 177 | |
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| 178 | p=sin(2.0*P1) |
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| 179 | q=1.0/(6.0*t2)-cos(2.0*P1) |
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| 180 | sh_R=atan(p/q) |
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| 181 | |
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| 182 | p=sin(2.0*sh_I)*sin(sh_nu) |
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| 183 | q=sin(2.0*sh_I)*cos(sh_nu)+0.3347 |
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| 184 | sh_nuprim=atan(p/q) |
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| 185 | |
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| 186 | s2=sin(sh_I)*sin(sh_I) |
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| 187 | p=s2*sin(2.0*sh_nu) |
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| 188 | q=s2*cos(2.0*sh_nu)+0.0727 |
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| 189 | sh_nusec=0.5*atan(p/q) |
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| 190 | |
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| 191 | END SUBROUTINE astronomic_angle |
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| 192 | |
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| 193 | SUBROUTINE tide_pulse( pomega, ktide ,kc) |
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| 194 | !!---------------------------------------------------------------------- |
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| 195 | !! *** ROUTINE tide_pulse *** |
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| 196 | !! |
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| 197 | !! ** Purpose : Compute tidal frequencies |
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| 198 | !! |
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| 199 | !!---------------------------------------------------------------------- |
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| 200 | !! * Arguments |
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| 201 | INTEGER, DIMENSION(kc), INTENT( in ) :: & |
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| 202 | ktide ! Indice of tidal constituents |
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| 203 | |
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| 204 | INTEGER, INTENT( in ) :: & |
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| 205 | kc ! Total number of tidal constituents |
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| 206 | |
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| 207 | REAL (wp), DIMENSION(kc), INTENT( out ) :: & |
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| 208 | pomega ! pulsation in radians/s |
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| 209 | |
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| 210 | !! * Local declarations |
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| 211 | INTEGER :: jh |
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| 212 | REAL(wp) :: zscale = 36525*24.0 |
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| 213 | REAL(wp) :: zomega_T= 13149000.0 |
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| 214 | REAL(wp) :: zomega_s= 481267.892 |
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| 215 | REAL(wp) :: zomega_h= 36000.76892 |
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| 216 | REAL(wp) :: zomega_p= 4069.0322056 |
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| 217 | REAL(wp) :: zomega_n= 1934.1423972 |
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| 218 | REAL(wp) :: zomega_p1= 1.719175 |
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| 219 | !!---------------------------------------------------------------------- |
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| 220 | |
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| 221 | DO jh=1,kc |
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| 222 | pomega(jh) = zomega_T * Wave(ktide(jh))%nT & |
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| 223 | + zomega_s * Wave(ktide(jh))%ns & |
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| 224 | + zomega_h * Wave(ktide(jh))%nh & |
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| 225 | + zomega_p * Wave(ktide(jh))%np & |
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| 226 | + zomega_p1* Wave(ktide(jh))%np1 |
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| 227 | pomega(jh) = (pomega(jh)/zscale)*rad/3600. |
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| 228 | END DO |
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| 229 | |
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| 230 | END SUBROUTINE tide_pulse |
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| 231 | |
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| 232 | SUBROUTINE tide_vuf( pvt, put, pcor, ktide ,kc) |
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| 233 | !!---------------------------------------------------------------------- |
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| 234 | !! *** ROUTINE tide_vuf *** |
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| 235 | !! |
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| 236 | !! ** Purpose : Compute nodal modulation corrections |
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| 237 | !! |
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| 238 | !! ** Outputs : |
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| 239 | !! vt: Pase of tidal potential relative to Greenwich (radians) |
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| 240 | !! ut: Phase correction u due to nodal motion (radians) |
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| 241 | !! ft: Nodal correction factor |
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| 242 | !! |
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| 243 | !! ** Inputs : |
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| 244 | !! tname: array of constituents names (dimension<=nc) |
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| 245 | !! nc: number of constituents |
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| 246 | !! |
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| 247 | !!---------------------------------------------------------------------- |
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| 248 | !! * Arguments |
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| 249 | INTEGER, DIMENSION(kc), INTENT( in ) :: & |
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| 250 | ktide ! Indice of tidal constituents |
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| 251 | INTEGER, INTENT( in ) :: & |
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| 252 | kc ! Total number of tidal constituents |
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| 253 | REAL (wp), DIMENSION(kc), INTENT( out ) :: & |
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| 254 | pvt, & ! |
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| 255 | put, & ! |
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| 256 | pcor ! |
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| 257 | !! * Local declarations |
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| 258 | INTEGER :: jh |
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| 259 | !!---------------------------------------------------------------------- |
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| 260 | |
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| 261 | DO jh =1,kc |
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| 262 | ! Phase of the tidal potential relative to the Greenwhich |
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| 263 | ! meridian (e.g. the position of the fictuous celestial body). Units are |
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| 264 | ! radian: |
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| 265 | pvt(jh) = sh_T *Wave(ktide(jh))%nT & |
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| 266 | +sh_s *Wave(ktide(jh))%ns & |
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| 267 | +sh_h *Wave(ktide(jh))%nh & |
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| 268 | +sh_p *Wave(ktide(jh))%np & |
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| 269 | +sh_p1*Wave(ktide(jh))%np1 & |
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| 270 | +Wave(ktide(jh))%shift*rad |
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| 271 | ! |
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| 272 | ! Phase correction u due to nodal motion. Units are radian: |
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| 273 | put(jh) = sh_xi *Wave(ktide(jh))%nksi & |
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| 274 | +sh_nu *Wave(ktide(jh))%nnu0 & |
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| 275 | +sh_nuprim*Wave(ktide(jh))%nnu1 & |
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| 276 | +sh_nusec *Wave(ktide(jh))%nnu2 & |
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| 277 | +sh_R *Wave(ktide(jh))%R |
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| 278 | |
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| 279 | ! Nodal correction factor: |
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| 280 | pcor(jh) = nodal_factort(Wave(ktide(jh))%nformula) |
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| 281 | END DO |
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| 282 | |
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| 283 | END SUBROUTINE tide_vuf |
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| 284 | |
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| 285 | recursive function nodal_factort(kformula) result (zf) |
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| 286 | !!---------------------------------------------------------------------- |
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| 287 | INTEGER, INTENT(IN) :: kformula |
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| 288 | REAL(wp) :: zf |
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| 289 | REAL(wp) :: zs,zf1,zf2 |
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| 290 | |
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| 291 | SELECT CASE (kformula) |
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| 292 | |
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| 293 | !! formule 0, solar waves |
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| 294 | |
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| 295 | case ( 0 ) |
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| 296 | zf=1.0 |
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| 297 | |
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| 298 | !! formule 1, compound waves (78 x 78) |
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| 299 | |
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| 300 | case ( 1 ) |
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| 301 | zf=nodal_factort(78) |
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| 302 | zf=zf*zf |
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| 303 | |
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| 304 | !! formule 2, compound waves (78 x 0) === (78) |
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| 305 | |
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| 306 | case ( 2 ) |
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| 307 | zf1=nodal_factort(78) |
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| 308 | zf=nodal_factort(0) |
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| 309 | zf=zf1*zf |
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| 310 | |
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| 311 | !! formule 4, compound waves (78 x 235) |
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| 312 | |
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| 313 | case ( 4 ) |
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| 314 | zf1=nodal_factort(78) |
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| 315 | zf=nodal_factort(235) |
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| 316 | zf=zf1*zf |
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| 317 | |
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| 318 | !! formule 5, compound waves (78 *78 x 235) |
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| 319 | |
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| 320 | case ( 5 ) |
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| 321 | zf1=nodal_factort(78) |
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| 322 | zf=nodal_factort(235) |
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| 323 | zf=zf*zf1*zf1 |
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| 324 | |
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| 325 | !! formule 6, compound waves (78 *78 x 0) |
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| 326 | |
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| 327 | case ( 6 ) |
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| 328 | zf1=nodal_factort(78) |
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| 329 | zf=nodal_factort(0) |
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| 330 | zf=zf*zf1*zf1 |
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| 331 | |
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| 332 | !! formule 7, compound waves (75 x 75) |
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| 333 | |
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| 334 | case ( 7 ) |
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| 335 | zf=nodal_factort(75) |
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| 336 | zf=zf*zf |
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| 337 | |
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| 338 | !! formule 8, compound waves (78 x 0 x 235) |
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| 339 | |
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| 340 | case ( 8 ) |
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| 341 | zf=nodal_factort(78) |
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| 342 | zf1=nodal_factort(0) |
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| 343 | zf2=nodal_factort(235) |
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| 344 | zf=zf*zf1*zf2 |
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| 345 | |
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| 346 | !! formule 9, compound waves (78 x 0 x 227) |
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| 347 | |
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| 348 | case ( 9 ) |
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| 349 | zf=nodal_factort(78) |
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| 350 | zf1=nodal_factort(0) |
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| 351 | zf2=nodal_factort(227) |
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| 352 | zf=zf*zf1*zf2 |
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| 353 | |
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| 354 | !! formule 10, compound waves (78 x 227) |
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| 355 | |
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| 356 | case ( 10 ) |
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| 357 | zf=nodal_factort(78) |
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| 358 | zf1=nodal_factort(227) |
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| 359 | zf=zf*zf1 |
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| 360 | |
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| 361 | !! formule 11, compound waves (75 x 0) |
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| 362 | |
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| 363 | case ( 11 ) |
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| 364 | zf=nodal_factort(75) |
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| 365 | zf1=nodal_factort(0) |
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| 366 | zf=zf*zf1 |
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| 367 | |
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| 368 | !! formule 12, compound waves (78 x 78 x 78 x 0) |
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| 369 | |
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| 370 | case ( 12 ) |
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| 371 | zf1=nodal_factort(78) |
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| 372 | zf=nodal_factort(0) |
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| 373 | zf=zf*zf1*zf1*zf1 |
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| 374 | |
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| 375 | !! formule 13, compound waves (78 x 75) |
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| 376 | |
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| 377 | case ( 13 ) |
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| 378 | zf1=nodal_factort(78) |
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| 379 | zf=nodal_factort(75) |
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| 380 | zf=zf*zf1 |
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| 381 | |
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| 382 | !! formule 14, compound waves (235 x 0) === (235) |
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| 383 | |
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| 384 | case ( 14 ) |
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| 385 | zf=nodal_factort(235) |
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| 386 | zf1=nodal_factort(0) |
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| 387 | zf=zf*zf1 |
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| 388 | |
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| 389 | !! formule 15, compound waves (235 x 75) |
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| 390 | |
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| 391 | case ( 15 ) |
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| 392 | zf=nodal_factort(235) |
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| 393 | zf1=nodal_factort(75) |
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| 394 | zf=zf*zf1 |
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| 395 | |
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| 396 | !! formule 16, compound waves (78 x 0 x 0) === (78) |
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| 397 | |
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| 398 | case ( 16 ) |
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| 399 | zf=nodal_factort(78) |
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| 400 | zf1=nodal_factort(0) |
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| 401 | zf=zf*zf1*zf1 |
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| 402 | |
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| 403 | !! formule 17, compound waves (227 x 0) |
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| 404 | |
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| 405 | case ( 17 ) |
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| 406 | zf1=nodal_factort(227) |
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| 407 | zf=nodal_factort(0) |
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| 408 | zf=zf*zf1 |
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| 409 | |
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| 410 | !! formule 18, compound waves (78 x 78 x 78 ) |
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| 411 | |
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| 412 | case ( 18 ) |
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| 413 | zf1=nodal_factort(78) |
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| 414 | zf=zf1*zf1*zf1 |
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| 415 | |
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| 416 | !! formule 19, compound waves (78 x 0 x 0 x 0) === (78) |
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| 417 | |
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| 418 | case ( 19 ) |
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| 419 | zf=nodal_factort(78) |
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| 420 | zf1=nodal_factort(0) |
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| 421 | zf=zf*zf1*zf1 |
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| 422 | |
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| 423 | !! formule 73 |
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| 424 | |
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| 425 | case ( 73 ) |
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| 426 | zs=sin(sh_I) |
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| 427 | zf=(2./3.-zs*zs)/0.5021 |
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| 428 | |
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| 429 | !! formule 74 |
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| 430 | |
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| 431 | case ( 74 ) |
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| 432 | zs=sin(sh_I) |
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| 433 | zf=zs*zs/0.1578 |
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| 434 | |
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| 435 | !! formule 75 |
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| 436 | |
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| 437 | case ( 75 ) |
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| 438 | zs=cos (sh_I/2) |
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| 439 | zf=sin (sh_I)*zs*zs/0.3800 |
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| 440 | |
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| 441 | !! formule 76 |
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| 442 | |
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| 443 | case ( 76 ) |
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| 444 | zf=sin (2*sh_I)/0.7214 |
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| 445 | |
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| 446 | !! formule 77 |
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| 447 | |
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| 448 | case ( 77 ) |
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| 449 | zs=sin (sh_I/2) |
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| 450 | zf=sin (sh_I)*zs*zs/0.0164 |
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| 451 | |
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| 452 | !! formule 78 |
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| 453 | |
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| 454 | case ( 78 ) |
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| 455 | zs=cos (sh_I/2) |
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| 456 | zf=zs*zs*zs*zs/0.9154 |
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| 457 | |
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| 458 | !! formule 79 |
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| 459 | |
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| 460 | case ( 79 ) |
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| 461 | zs=sin(sh_I) |
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| 462 | zf=zs*zs/0.1565 |
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| 463 | |
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| 464 | !! formule 144 |
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| 465 | |
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| 466 | case ( 144 ) |
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| 467 | zs=sin (sh_I/2) |
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| 468 | zf=(1-10*zs*zs+15*zs*zs*zs*zs)*cos(sh_I/2)/0.5873 |
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| 469 | |
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| 470 | !! formule 149 |
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| 471 | |
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| 472 | case ( 149 ) |
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| 473 | zs=cos (sh_I/2) |
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| 474 | zf=zs*zs*zs*zs*zs*zs/0.8758 |
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| 475 | |
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| 476 | !! formule 215 |
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| 477 | |
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| 478 | case ( 215 ) |
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| 479 | zs=cos (sh_I/2) |
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| 480 | zf=zs*zs*zs*zs/0.9154*sh_x1ra |
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| 481 | |
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| 482 | !! formule 227 |
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| 483 | |
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| 484 | case ( 227 ) |
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| 485 | zs=sin (2*sh_I) |
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| 486 | zf=sqrt (0.8965*zs*zs+0.6001*zs*cos (sh_nu)+0.1006) |
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| 487 | |
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| 488 | !! formule 235 |
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| 489 | |
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| 490 | case ( 235 ) |
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| 491 | zs=sin (sh_I) |
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| 492 | zf=sqrt (19.0444*zs*zs*zs*zs+2.7702*zs*zs*cos (2*sh_nu)+.0981) |
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| 493 | |
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| 494 | END SELECT |
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| 495 | |
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| 496 | end function nodal_factort |
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| 497 | |
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| 498 | function dayjul(kyr,kmonth,kday) |
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| 499 | ! |
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| 500 | !*** THIS ROUTINE COMPUTES THE JULIAN DAY (AS A REAL VARIABLE) |
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| 501 | ! |
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| 502 | INTEGER,INTENT(IN) :: kyr,kmonth,kday |
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| 503 | INTEGER,DIMENSION(12) :: idayt,idays |
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| 504 | INTEGER :: inc,ji |
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| 505 | REAL(wp) :: dayjul,zyq |
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| 506 | |
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| 507 | DATA idayt/0.,31.,59.,90.,120.,151.,181.,212.,243.,273.,304.,334./ |
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| 508 | idays(1)=0. |
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| 509 | idays(2)=31. |
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| 510 | inc=0. |
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| 511 | zyq=MOD((kyr-1900.),4.) |
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| 512 | IF(zyq .eq. 0.) inc=1. |
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| 513 | DO ji=3,12 |
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| 514 | idays(ji)=idayt(ji)+inc |
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| 515 | END DO |
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| 516 | dayjul=idays(kmonth)+kday |
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| 517 | |
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| 518 | END FUNCTION dayjul |
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| 519 | |
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| 520 | END MODULE tide_mod |
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