1 | MODULE eqn_state_seawater_mod |
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2 | |
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3 | !--------------------------------------------------------------------------------! |
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4 | ! This file is part of PALM. |
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5 | ! |
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6 | ! PALM is free software: you can redistribute it and/or modify it under the terms |
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7 | ! of the GNU General Public License as published by the Free Software Foundation, |
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8 | ! either version 3 of the License, or (at your option) any later version. |
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9 | ! |
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10 | ! PALM is distributed in the hope that it will be useful, but WITHOUT ANY |
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11 | ! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR |
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12 | ! A PARTICULAR PURPOSE. See the GNU General Public License for more details. |
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13 | ! |
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14 | ! You should have received a copy of the GNU General Public License along with |
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15 | ! PALM. If not, see <http://www.gnu.org/licenses/>. |
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16 | ! |
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17 | ! Copyright 1997-2012 Leibniz University Hannover |
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18 | !--------------------------------------------------------------------------------! |
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19 | ! |
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20 | ! Current revisions: |
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21 | ! ----------------- |
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22 | ! |
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23 | ! |
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24 | ! Former revisions: |
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25 | ! ----------------- |
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26 | ! $Id: eqn_state_seawater.f90 1037 2012-10-22 14:10:22Z witha $ |
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27 | ! |
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28 | ! 1036 2012-10-22 13:43:42Z raasch |
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29 | ! code put under GPL (PALM 3.9) |
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30 | ! |
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31 | ! 388 2009-09-23 09:40:33Z raasch |
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32 | ! Potential density is additionally calculated in eqn_state_seawater, |
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33 | ! first constant in array den also defined as type double. |
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34 | ! |
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35 | ! 97 2007-06-21 08:23:15Z raasch |
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36 | ! Initial revision |
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37 | ! |
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38 | ! |
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39 | ! Description: |
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40 | ! ------------ |
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41 | ! Equation of state for seawater as a function of potential temperature, |
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42 | ! salinity, and pressure. |
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43 | ! For coefficients see Jackett et al., 2006: J. Atm. Ocean Tech. |
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44 | ! eqn_state_seawater calculates the potential density referred at hyp(0). |
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45 | ! eqn_state_seawater_func calculates density. |
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46 | !------------------------------------------------------------------------------! |
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47 | |
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48 | IMPLICIT NONE |
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49 | |
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50 | PRIVATE |
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51 | PUBLIC eqn_state_seawater, eqn_state_seawater_func |
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52 | |
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53 | REAL, DIMENSION(12), PARAMETER :: nom = & |
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54 | (/ 9.9984085444849347D2, 7.3471625860981584D0, & |
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55 | -5.3211231792841769D-2, 3.6492439109814549D-4, & |
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56 | 2.5880571023991390D0, -6.7168282786692354D-3, & |
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57 | 1.9203202055760151D-3, 1.1798263740430364D-2, & |
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58 | 9.8920219266399117D-8, 4.6996642771754730D-6, & |
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59 | -2.5862187075154352D-8, -3.2921414007960662D-12 /) |
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60 | |
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61 | REAL, DIMENSION(13), PARAMETER :: den = & |
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62 | (/ 1.0D0, 7.2815210113327091D-3, & |
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63 | -4.4787265461983921D-5, 3.3851002965802430D-7, & |
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64 | 1.3651202389758572D-10, 1.7632126669040377D-3, & |
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65 | -8.8066583251206474D-6, -1.8832689434804897D-10, & |
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66 | 5.7463776745432097D-6, 1.4716275472242334D-9, & |
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67 | 6.7103246285651894D-6, -2.4461698007024582D-17, & |
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68 | -9.1534417604289062D-18 /) |
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69 | |
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70 | INTERFACE eqn_state_seawater |
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71 | MODULE PROCEDURE eqn_state_seawater |
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72 | MODULE PROCEDURE eqn_state_seawater_ij |
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73 | END INTERFACE eqn_state_seawater |
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74 | |
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75 | INTERFACE eqn_state_seawater_func |
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76 | MODULE PROCEDURE eqn_state_seawater_func |
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77 | END INTERFACE eqn_state_seawater_func |
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78 | |
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79 | CONTAINS |
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80 | |
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81 | |
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82 | !------------------------------------------------------------------------------! |
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83 | ! Call for all grid points |
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84 | !------------------------------------------------------------------------------! |
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85 | SUBROUTINE eqn_state_seawater |
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86 | |
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87 | USE arrays_3d |
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88 | USE indices |
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89 | |
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90 | IMPLICIT NONE |
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91 | |
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92 | INTEGER :: i, j, k |
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93 | |
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94 | REAL :: pden, pnom, p1, p2, p3, pt1, pt2, pt3, pt4, sa1, sa15, sa2 |
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95 | |
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96 | DO i = nxl, nxr |
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97 | DO j = nys, nyn |
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98 | DO k = nzb_s_inner(j,i)+1, nzt |
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99 | ! |
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100 | !-- Pressure is needed in dbar |
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101 | p1 = hyp(k) * 1E-4 |
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102 | p2 = p1 * p1 |
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103 | p3 = p2 * p1 |
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104 | |
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105 | ! |
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106 | !-- Temperature needed in degree Celsius |
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107 | pt1 = pt_p(k,j,i) - 273.15 |
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108 | pt2 = pt1 * pt1 |
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109 | pt3 = pt1 * pt2 |
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110 | pt4 = pt2 * pt2 |
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111 | |
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112 | sa1 = sa_p(k,j,i) |
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113 | sa15 = sa1 * SQRT( sa1 ) |
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114 | sa2 = sa1 * sa1 |
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115 | |
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116 | pnom = nom(1) + nom(2)*pt1 + nom(3)*pt2 + & |
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117 | nom(4)*pt3 + nom(5)*sa1 + nom(6)*sa1*pt1 + & |
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118 | nom(7)*sa2 |
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119 | |
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120 | pden = den(1) + den(2)*pt1 + den(3)*pt2 + & |
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121 | den(4)*pt3 + den(5)*pt4 + den(6)*sa1 + & |
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122 | den(7)*sa1*pt1 + den(8)*sa1*pt3 + den(9)*sa15 + & |
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123 | den(10)*sa15*pt2 |
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124 | |
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125 | ! |
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126 | !-- Potential density (without pressure terms) |
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127 | prho(k,j,i) = pnom / pden |
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128 | |
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129 | pnom = pnom + nom(8)*p1 + nom(9)*p1*pt2 + & |
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130 | nom(10)*p1*sa1 + nom(11)*p2 + nom(12)*p2*pt2 |
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131 | |
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132 | pden = pden + den(11)*p1 + den(12)*p2*pt3 + & |
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133 | den(13)*p3*pt1 |
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134 | |
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135 | ! |
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136 | !-- In-situ density |
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137 | rho(k,j,i) = pnom / pden |
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138 | |
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139 | ENDDO |
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140 | ! |
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141 | !-- Neumann conditions are assumed at bottom and top boundary |
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142 | prho(nzt+1,j,i) = prho(nzt,j,i) |
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143 | prho(nzb_s_inner(j,i),j,i) = prho(nzb_s_inner(j,i)+1,j,i) |
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144 | rho(nzt+1,j,i) = rho(nzt,j,i) |
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145 | rho(nzb_s_inner(j,i),j,i) = rho(nzb_s_inner(j,i)+1,j,i) |
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146 | |
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147 | ENDDO |
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148 | ENDDO |
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149 | |
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150 | END SUBROUTINE eqn_state_seawater |
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151 | |
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152 | |
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153 | !------------------------------------------------------------------------------! |
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154 | ! Call for grid point i,j |
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155 | !------------------------------------------------------------------------------! |
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156 | SUBROUTINE eqn_state_seawater_ij( i, j ) |
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157 | |
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158 | USE arrays_3d |
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159 | USE indices |
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160 | |
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161 | IMPLICIT NONE |
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162 | |
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163 | INTEGER :: i, j, k |
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164 | |
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165 | REAL :: pden, pnom, p1, p2, p3, pt1, pt2, pt3, pt4, sa1, sa15, sa2 |
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166 | |
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167 | DO k = nzb_s_inner(j,i)+1, nzt |
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168 | ! |
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169 | !-- Pressure is needed in dbar |
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170 | p1 = hyp(k) * 1E-4 |
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171 | p2 = p1 * p1 |
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172 | p3 = p2 * p1 |
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173 | |
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174 | ! |
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175 | !-- Temperature needed in degree Celsius |
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176 | pt1 = pt_p(k,j,i) - 273.15 |
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177 | pt2 = pt1 * pt1 |
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178 | pt3 = pt1 * pt2 |
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179 | pt4 = pt2 * pt2 |
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180 | |
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181 | sa1 = sa_p(k,j,i) |
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182 | sa15 = sa1 * SQRT( sa1 ) |
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183 | sa2 = sa1 * sa1 |
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184 | |
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185 | pnom = nom(1) + nom(2)*pt1 + nom(3)*pt2 + & |
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186 | nom(4)*pt3 + nom(5)*sa1 + nom(6)*sa1*pt1 + & |
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187 | nom(7)*sa2 |
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188 | |
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189 | pden = den(1) + den(2)*pt1 + den(3)*pt2 + & |
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190 | den(4)*pt3 + den(5)*pt4 + den(6)*sa1 + & |
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191 | den(7)*sa1*pt1 + den(8)*sa1*pt3 + den(9)*sa15 + & |
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192 | den(10)*sa15*pt2 |
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193 | |
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194 | ! |
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195 | !-- Potential density (without pressure terms) |
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196 | prho(k,j,i) = pnom / pden |
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197 | |
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198 | pnom = pnom + nom(8)*p1 + nom(9)*p1*pt2 + & |
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199 | nom(10)*p1*sa1 + nom(11)*p2 + nom(12)*p2*pt2 |
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200 | pden = pden + den(11)*p1 + den(12)*p2*pt3 + & |
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201 | den(13)*p3*pt1 |
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202 | |
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203 | ! |
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204 | !-- In-situ density |
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205 | rho(k,j,i) = pnom / pden |
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206 | |
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207 | |
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208 | ENDDO |
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209 | |
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210 | ! |
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211 | !-- Neumann conditions are assumed at bottom and top boundary |
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212 | prho(nzt+1,j,i) = prho(nzt,j,i) |
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213 | prho(nzb_s_inner(j,i),j,i) = prho(nzb_s_inner(j,i)+1,j,i) |
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214 | rho(nzt+1,j,i) = rho(nzt,j,i) |
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215 | rho(nzb_s_inner(j,i),j,i) = rho(nzb_s_inner(j,i)+1,j,i) |
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216 | |
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217 | END SUBROUTINE eqn_state_seawater_ij |
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218 | |
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219 | |
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220 | !------------------------------------------------------------------------------! |
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221 | ! Equation of state as a function |
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222 | !------------------------------------------------------------------------------! |
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223 | REAL FUNCTION eqn_state_seawater_func( p, pt, sa ) |
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224 | |
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225 | IMPLICIT NONE |
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226 | |
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227 | REAL :: p, p1, p2, p3, pt, pt1, pt2, pt3, pt4, sa, sa15, sa2 |
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228 | |
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229 | ! |
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230 | !-- Pressure is needed in dbar |
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231 | p1 = p * 1E-4 |
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232 | p2 = p1 * p1 |
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233 | p3 = p2 * p1 |
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234 | |
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235 | ! |
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236 | !-- Temperature needed in degree Celsius |
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237 | pt1 = pt - 273.15 |
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238 | pt2 = pt1 * pt1 |
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239 | pt3 = pt1 * pt2 |
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240 | pt4 = pt2 * pt2 |
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241 | |
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242 | sa15 = sa * SQRT( sa ) |
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243 | sa2 = sa * sa |
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244 | |
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245 | |
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246 | eqn_state_seawater_func = & |
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247 | ( nom(1) + nom(2)*pt1 + nom(3)*pt2 + nom(4)*pt3 + & |
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248 | nom(5)*sa + nom(6)*sa*pt1 + nom(7)*sa2 + nom(8)*p1 + & |
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249 | nom(9)*p1*pt2 + nom(10)*p1*sa + nom(11)*p2 + nom(12)*p2*pt2 & |
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250 | ) / & |
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251 | ( den(1) + den(2)*pt1 + den(3)*pt2 + den(4)*pt3 + & |
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252 | den(5)*pt4 + den(6)*sa + den(7)*sa*pt1 + den(8)*sa*pt3 + & |
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253 | den(9)*sa15 + den(10)*sa15*pt2 + den(11)*p1 + den(12)*p2*pt3 + & |
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254 | den(13)*p3*pt1 & |
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255 | ) |
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256 | |
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257 | |
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258 | END FUNCTION eqn_state_seawater_func |
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259 | |
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260 | END MODULE eqn_state_seawater_mod |
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