1 | !> @file eqn_state_seawater.f90 |
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2 | !------------------------------------------------------------------------------! |
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3 | ! This file is part of PALM. |
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4 | ! |
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5 | ! PALM is free software: you can redistribute it and/or modify it under the |
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6 | ! terms of the GNU General Public License as published by the Free Software |
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7 | ! Foundation, either version 3 of the License, or (at your option) any later |
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8 | ! 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 1997-2017 Leibniz Universitaet 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 2369 2017-08-22 15:20:37Z suehring $ |
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27 | ! Bugfix, do not mask topography here, since density becomes zero, leading to |
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28 | ! division by zero in production_e |
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29 | ! |
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30 | ! 2233 2017-05-30 18:08:54Z suehring |
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31 | ! |
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32 | ! 2232 2017-05-30 17:47:52Z suehring |
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33 | ! Adjustments to new topography and surface concept |
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34 | ! |
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35 | ! 2031 2016-10-21 15:11:58Z knoop |
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36 | ! renamed variable rho to rho_ocean |
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37 | ! |
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38 | ! 2000 2016-08-20 18:09:15Z knoop |
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39 | ! Forced header and separation lines into 80 columns |
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40 | ! |
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41 | ! 1873 2016-04-18 14:50:06Z maronga |
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42 | ! Module renamed (removed _mod) |
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43 | ! |
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44 | ! |
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45 | ! 1850 2016-04-08 13:29:27Z maronga |
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46 | ! Module renamed |
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47 | ! |
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48 | ! |
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49 | ! 1682 2015-10-07 23:56:08Z knoop |
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50 | ! Code annotations made doxygen readable |
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51 | ! |
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52 | ! 1353 2014-04-08 15:21:23Z heinze |
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53 | ! REAL constants provided with KIND-attribute |
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54 | ! |
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55 | ! 1320 2014-03-20 08:40:49Z raasch |
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56 | ! ONLY-attribute added to USE-statements, |
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57 | ! kind-parameters added to all INTEGER and REAL declaration statements, |
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58 | ! kinds are defined in new module kinds, |
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59 | ! revision history before 2012 removed, |
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60 | ! comment fields (!:) to be used for variable explanations added to |
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61 | ! all variable declaration statements |
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62 | ! |
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63 | ! 1036 2012-10-22 13:43:42Z raasch |
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64 | ! code put under GPL (PALM 3.9) |
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65 | ! |
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66 | ! 97 2007-06-21 08:23:15Z raasch |
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67 | ! Initial revision |
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68 | ! |
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69 | ! |
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70 | ! Description: |
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71 | ! ------------ |
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72 | !> Equation of state for seawater as a function of potential temperature, |
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73 | !> salinity, and pressure. |
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74 | !> For coefficients see Jackett et al., 2006: J. Atm. Ocean Tech. |
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75 | !> eqn_state_seawater calculates the potential density referred at hyp(0). |
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76 | !> eqn_state_seawater_func calculates density. |
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77 | !------------------------------------------------------------------------------! |
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78 | MODULE eqn_state_seawater_mod |
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79 | |
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80 | |
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81 | USE kinds |
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82 | |
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83 | IMPLICIT NONE |
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84 | |
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85 | PRIVATE |
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86 | PUBLIC eqn_state_seawater, eqn_state_seawater_func |
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87 | |
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88 | REAL(wp), DIMENSION(12), PARAMETER :: nom = & |
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89 | (/ 9.9984085444849347D2, 7.3471625860981584D0, & |
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90 | -5.3211231792841769D-2, 3.6492439109814549D-4, & |
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91 | 2.5880571023991390D0, -6.7168282786692354D-3, & |
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92 | 1.9203202055760151D-3, 1.1798263740430364D-2, & |
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93 | 9.8920219266399117D-8, 4.6996642771754730D-6, & |
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94 | -2.5862187075154352D-8, -3.2921414007960662D-12 /) |
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95 | !< |
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96 | |
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97 | REAL(wp), DIMENSION(13), PARAMETER :: den = & |
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98 | (/ 1.0D0, 7.2815210113327091D-3, & |
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99 | -4.4787265461983921D-5, 3.3851002965802430D-7, & |
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100 | 1.3651202389758572D-10, 1.7632126669040377D-3, & |
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101 | -8.8066583251206474D-6, -1.8832689434804897D-10, & |
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102 | 5.7463776745432097D-6, 1.4716275472242334D-9, & |
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103 | 6.7103246285651894D-6, -2.4461698007024582D-17, & |
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104 | -9.1534417604289062D-18 /) |
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105 | !< |
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106 | |
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107 | INTERFACE eqn_state_seawater |
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108 | MODULE PROCEDURE eqn_state_seawater |
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109 | MODULE PROCEDURE eqn_state_seawater_ij |
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110 | END INTERFACE eqn_state_seawater |
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111 | |
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112 | INTERFACE eqn_state_seawater_func |
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113 | MODULE PROCEDURE eqn_state_seawater_func |
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114 | END INTERFACE eqn_state_seawater_func |
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115 | |
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116 | CONTAINS |
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117 | |
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118 | |
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119 | !------------------------------------------------------------------------------! |
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120 | ! Description: |
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121 | ! ------------ |
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122 | !> Call for all grid points |
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123 | !------------------------------------------------------------------------------! |
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124 | SUBROUTINE eqn_state_seawater |
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125 | |
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126 | USE arrays_3d, & |
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127 | ONLY: hyp, prho, pt_p, rho_ocean, sa_p |
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128 | USE indices, & |
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129 | ONLY: nxl, nxr, nyn, nys, nzb, nzt |
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130 | |
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131 | USE surface_mod, & |
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132 | ONLY : bc_h |
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133 | |
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134 | IMPLICIT NONE |
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135 | |
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136 | INTEGER(iwp) :: i !< running index x direction |
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137 | INTEGER(iwp) :: j !< running index y direction |
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138 | INTEGER(iwp) :: k !< running index z direction |
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139 | INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall |
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140 | INTEGER(iwp) :: m !< running index surface elements |
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141 | INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint |
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142 | INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint |
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143 | |
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144 | REAL(wp) :: pden !< |
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145 | REAL(wp) :: pnom !< |
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146 | REAL(wp) :: p1 !< |
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147 | REAL(wp) :: p2 !< |
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148 | REAL(wp) :: p3 !< |
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149 | REAL(wp) :: pt1 !< |
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150 | REAL(wp) :: pt2 !< |
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151 | REAL(wp) :: pt3 !< |
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152 | REAL(wp) :: pt4 !< |
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153 | REAL(wp) :: sa1 !< |
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154 | REAL(wp) :: sa15 !< |
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155 | REAL(wp) :: sa2 !< |
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156 | |
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157 | |
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158 | |
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159 | DO i = nxl, nxr |
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160 | DO j = nys, nyn |
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161 | DO k = nzb+1, nzt |
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162 | ! |
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163 | !-- Pressure is needed in dbar |
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164 | p1 = hyp(k) * 1E-4_wp |
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165 | p2 = p1 * p1 |
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166 | p3 = p2 * p1 |
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167 | |
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168 | ! |
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169 | !-- Temperature needed in degree Celsius |
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170 | pt1 = pt_p(k,j,i) - 273.15_wp |
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171 | pt2 = pt1 * pt1 |
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172 | pt3 = pt1 * pt2 |
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173 | pt4 = pt2 * pt2 |
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174 | |
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175 | sa1 = sa_p(k,j,i) |
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176 | sa15 = sa1 * SQRT( sa1 ) |
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177 | sa2 = sa1 * sa1 |
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178 | |
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179 | pnom = nom(1) + nom(2)*pt1 + nom(3)*pt2 + & |
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180 | nom(4)*pt3 + nom(5)*sa1 + nom(6)*sa1*pt1 + & |
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181 | nom(7)*sa2 |
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182 | |
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183 | pden = den(1) + den(2)*pt1 + den(3)*pt2 + & |
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184 | den(4)*pt3 + den(5)*pt4 + den(6)*sa1 + & |
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185 | den(7)*sa1*pt1 + den(8)*sa1*pt3 + den(9)*sa15 + & |
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186 | den(10)*sa15*pt2 |
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187 | ! |
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188 | !-- Potential density (without pressure terms) |
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189 | prho(k,j,i) = pnom / pden |
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190 | |
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191 | pnom = pnom + nom(8)*p1 + nom(9)*p1*pt2 + & |
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192 | nom(10)*p1*sa1 + nom(11)*p2 + nom(12)*p2*pt2 |
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193 | |
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194 | pden = pden + den(11)*p1 + den(12)*p2*pt3 + & |
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195 | den(13)*p3*pt1 |
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196 | |
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197 | ! |
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198 | !-- In-situ density |
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199 | rho_ocean(k,j,i) = pnom / pden |
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200 | |
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201 | ENDDO |
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202 | ! |
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203 | !-- Neumann conditions are assumed at top boundary |
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204 | prho(nzt+1,j,i) = prho(nzt,j,i) |
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205 | rho_ocean(nzt+1,j,i) = rho_ocean(nzt,j,i) |
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206 | |
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207 | ENDDO |
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208 | ENDDO |
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209 | ! |
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210 | !-- Neumann conditions at up/downward-facing surfaces |
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211 | !$OMP PARALLEL DO PRIVATE( i, j, k ) |
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212 | DO m = 1, bc_h(0)%ns |
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213 | i = bc_h(0)%i(m) |
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214 | j = bc_h(0)%j(m) |
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215 | k = bc_h(0)%k(m) |
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216 | prho(k-1,j,i) = prho(k,j,i) |
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217 | rho_ocean(k-1,j,i) = rho_ocean(k,j,i) |
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218 | ENDDO |
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219 | ! |
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220 | !-- Downward facing surfaces |
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221 | !$OMP PARALLEL DO PRIVATE( i, j, k ) |
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222 | DO m = 1, bc_h(1)%ns |
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223 | i = bc_h(1)%i(m) |
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224 | j = bc_h(1)%j(m) |
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225 | k = bc_h(1)%k(m) |
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226 | prho(k+1,j,i) = prho(k,j,i) |
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227 | rho_ocean(k+1,j,i) = rho_ocean(k,j,i) |
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228 | ENDDO |
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229 | |
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230 | END SUBROUTINE eqn_state_seawater |
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231 | |
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232 | |
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233 | !------------------------------------------------------------------------------! |
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234 | ! Description: |
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235 | ! ------------ |
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236 | !> Call for grid point i,j |
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237 | !------------------------------------------------------------------------------! |
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238 | SUBROUTINE eqn_state_seawater_ij( i, j ) |
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239 | |
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240 | USE arrays_3d, & |
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241 | ONLY: hyp, prho, pt_p, rho_ocean, sa_p |
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242 | |
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243 | USE indices, & |
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244 | ONLY: nzb, nzt |
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245 | |
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246 | USE surface_mod, & |
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247 | ONLY : bc_h |
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248 | |
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249 | IMPLICIT NONE |
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250 | |
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251 | INTEGER(iwp) :: i !< running index x direction |
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252 | INTEGER(iwp) :: j !< running index y direction |
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253 | INTEGER(iwp) :: k !< running index z direction |
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254 | INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall |
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255 | INTEGER(iwp) :: m !< running index surface elements |
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256 | INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint |
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257 | INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint |
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258 | |
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259 | REAL(wp) :: pden !< |
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260 | REAL(wp) :: pnom !< |
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261 | REAL(wp) :: p1 !< |
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262 | REAL(wp) :: p2 !< |
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263 | REAL(wp) :: p3 !< |
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264 | REAL(wp) :: pt1 !< |
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265 | REAL(wp) :: pt2 !< |
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266 | REAL(wp) :: pt3 !< |
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267 | REAL(wp) :: pt4 !< |
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268 | REAL(wp) :: sa1 !< |
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269 | REAL(wp) :: sa15 !< |
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270 | REAL(wp) :: sa2 !< |
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271 | |
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272 | DO k = nzb+1, nzt |
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273 | ! |
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274 | !-- Pressure is needed in dbar |
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275 | p1 = hyp(k) * 1E-4_wp |
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276 | p2 = p1 * p1 |
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277 | p3 = p2 * p1 |
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278 | |
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279 | ! |
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280 | !-- Temperature needed in degree Celsius |
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281 | pt1 = pt_p(k,j,i) - 273.15_wp |
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282 | pt2 = pt1 * pt1 |
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283 | pt3 = pt1 * pt2 |
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284 | pt4 = pt2 * pt2 |
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285 | |
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286 | sa1 = sa_p(k,j,i) |
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287 | sa15 = sa1 * SQRT( sa1 ) |
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288 | sa2 = sa1 * sa1 |
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289 | |
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290 | pnom = nom(1) + nom(2)*pt1 + nom(3)*pt2 + & |
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291 | nom(4)*pt3 + nom(5)*sa1 + nom(6)*sa1*pt1 + & |
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292 | nom(7)*sa2 |
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293 | |
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294 | pden = den(1) + den(2)*pt1 + den(3)*pt2 + & |
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295 | den(4)*pt3 + den(5)*pt4 + den(6)*sa1 + & |
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296 | den(7)*sa1*pt1 + den(8)*sa1*pt3 + den(9)*sa15 + & |
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297 | den(10)*sa15*pt2 |
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298 | ! |
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299 | !-- Potential density (without pressure terms) |
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300 | prho(k,j,i) = pnom / pden |
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301 | |
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302 | pnom = pnom + nom(8)*p1 + nom(9)*p1*pt2 + & |
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303 | nom(10)*p1*sa1 + nom(11)*p2 + nom(12)*p2*pt2 |
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304 | pden = pden + den(11)*p1 + den(12)*p2*pt3 + & |
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305 | den(13)*p3*pt1 |
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306 | |
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307 | ! |
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308 | !-- In-situ density |
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309 | rho_ocean(k,j,i) = pnom / pden |
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310 | |
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311 | |
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312 | ENDDO |
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313 | ! |
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314 | !-- Neumann conditions at up/downward-facing walls |
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315 | surf_s = bc_h(0)%start_index(j,i) |
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316 | surf_e = bc_h(0)%end_index(j,i) |
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317 | DO m = surf_s, surf_e |
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318 | k = bc_h(0)%k(m) |
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319 | prho(k-1,j,i) = prho(k,j,i) |
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320 | rho_ocean(k-1,j,i) = rho_ocean(k,j,i) |
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321 | ENDDO |
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322 | ! |
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323 | !-- Downward facing surfaces |
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324 | surf_s = bc_h(1)%start_index(j,i) |
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325 | surf_e = bc_h(1)%end_index(j,i) |
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326 | DO m = surf_s, surf_e |
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327 | k = bc_h(1)%k(m) |
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328 | prho(k+1,j,i) = prho(k,j,i) |
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329 | rho_ocean(k+1,j,i) = rho_ocean(k,j,i) |
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330 | ENDDO |
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331 | ! |
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332 | !-- Neumann condition are assumed at top boundary |
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333 | prho(nzt+1,j,i) = prho(nzt,j,i) |
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334 | rho_ocean(nzt+1,j,i) = rho_ocean(nzt,j,i) |
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335 | |
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336 | END SUBROUTINE eqn_state_seawater_ij |
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337 | |
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338 | |
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339 | !------------------------------------------------------------------------------! |
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340 | ! Description: |
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341 | ! ------------ |
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342 | !> Equation of state as a function |
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343 | !------------------------------------------------------------------------------! |
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344 | REAL(wp) FUNCTION eqn_state_seawater_func( p, pt, sa ) |
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345 | |
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346 | IMPLICIT NONE |
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347 | |
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348 | REAL(wp) :: p !< |
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349 | REAL(wp) :: p1 !< |
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350 | REAL(wp) :: p2 !< |
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351 | REAL(wp) :: p3 !< |
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352 | REAL(wp) :: pt !< |
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353 | REAL(wp) :: pt1 !< |
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354 | REAL(wp) :: pt2 !< |
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355 | REAL(wp) :: pt3 !< |
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356 | REAL(wp) :: pt4 !< |
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357 | REAL(wp) :: sa !< |
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358 | REAL(wp) :: sa15 !< |
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359 | REAL(wp) :: sa2 !< |
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360 | |
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361 | ! |
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362 | !-- Pressure is needed in dbar |
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363 | p1 = p * 1E-4_wp |
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364 | p2 = p1 * p1 |
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365 | p3 = p2 * p1 |
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366 | |
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367 | ! |
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368 | !-- Temperature needed in degree Celsius |
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369 | pt1 = pt - 273.15_wp |
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370 | pt2 = pt1 * pt1 |
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371 | pt3 = pt1 * pt2 |
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372 | pt4 = pt2 * pt2 |
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373 | |
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374 | sa15 = sa * SQRT( sa ) |
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375 | sa2 = sa * sa |
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376 | |
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377 | |
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378 | eqn_state_seawater_func = & |
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379 | ( nom(1) + nom(2)*pt1 + nom(3)*pt2 + nom(4)*pt3 + & |
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380 | nom(5)*sa + nom(6)*sa*pt1 + nom(7)*sa2 + nom(8)*p1 + & |
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381 | nom(9)*p1*pt2 + nom(10)*p1*sa + nom(11)*p2 + nom(12)*p2*pt2 & |
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382 | ) / & |
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383 | ( den(1) + den(2)*pt1 + den(3)*pt2 + den(4)*pt3 + & |
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384 | den(5)*pt4 + den(6)*sa + den(7)*sa*pt1 + den(8)*sa*pt3 + & |
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385 | den(9)*sa15 + den(10)*sa15*pt2 + den(11)*p1 + den(12)*p2*pt3 + & |
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386 | den(13)*p3*pt1 & |
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387 | ) |
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388 | |
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389 | |
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390 | END FUNCTION eqn_state_seawater_func |
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391 | |
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392 | END MODULE eqn_state_seawater_mod |
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