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