[1873] | 1 | !> @file eqn_state_seawater.f90 |
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[1320] | 2 | !------------------------------------------------------------------------------! |
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[1036] | 3 | ! This file is part of PALM. |
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| 4 | ! |
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[2000] | 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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[1036] | 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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[2101] | 17 | ! Copyright 1997-2017 Leibniz Universitaet Hannover |
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[1320] | 18 | !------------------------------------------------------------------------------! |
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[1036] | 19 | ! |
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[484] | 20 | ! Current revisions: |
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[96] | 21 | ! ----------------- |
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[2232] | 22 | ! Adjustments to new topography and surface concept |
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[1354] | 23 | ! |
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[1321] | 24 | ! Former revisions: |
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| 25 | ! ----------------- |
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| 26 | ! $Id: eqn_state_seawater.f90 2232 2017-05-30 17:47:52Z suehring $ |
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| 27 | ! |
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[2032] | 28 | ! 2031 2016-10-21 15:11:58Z knoop |
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| 29 | ! renamed variable rho to rho_ocean |
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| 30 | ! |
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[2001] | 31 | ! 2000 2016-08-20 18:09:15Z knoop |
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| 32 | ! Forced header and separation lines into 80 columns |
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| 33 | ! |
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[1874] | 34 | ! 1873 2016-04-18 14:50:06Z maronga |
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| 35 | ! Module renamed (removed _mod) |
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| 36 | ! |
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| 37 | ! |
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[1851] | 38 | ! 1850 2016-04-08 13:29:27Z maronga |
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| 39 | ! Module renamed |
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| 40 | ! |
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| 41 | ! |
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[1683] | 42 | ! 1682 2015-10-07 23:56:08Z knoop |
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| 43 | ! Code annotations made doxygen readable |
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| 44 | ! |
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[1354] | 45 | ! 1353 2014-04-08 15:21:23Z heinze |
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| 46 | ! REAL constants provided with KIND-attribute |
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| 47 | ! |
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[1321] | 48 | ! 1320 2014-03-20 08:40:49Z raasch |
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[1320] | 49 | ! ONLY-attribute added to USE-statements, |
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| 50 | ! kind-parameters added to all INTEGER and REAL declaration statements, |
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| 51 | ! kinds are defined in new module kinds, |
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| 52 | ! revision history before 2012 removed, |
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| 53 | ! comment fields (!:) to be used for variable explanations added to |
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| 54 | ! all variable declaration statements |
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[96] | 55 | ! |
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[1037] | 56 | ! 1036 2012-10-22 13:43:42Z raasch |
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| 57 | ! code put under GPL (PALM 3.9) |
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| 58 | ! |
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[98] | 59 | ! 97 2007-06-21 08:23:15Z raasch |
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[96] | 60 | ! Initial revision |
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| 61 | ! |
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| 62 | ! |
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| 63 | ! Description: |
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| 64 | ! ------------ |
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[1682] | 65 | !> Equation of state for seawater as a function of potential temperature, |
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| 66 | !> salinity, and pressure. |
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| 67 | !> For coefficients see Jackett et al., 2006: J. Atm. Ocean Tech. |
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| 68 | !> eqn_state_seawater calculates the potential density referred at hyp(0). |
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| 69 | !> eqn_state_seawater_func calculates density. |
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[96] | 70 | !------------------------------------------------------------------------------! |
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[1682] | 71 | MODULE eqn_state_seawater_mod |
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| 72 | |
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[1320] | 73 | |
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| 74 | USE kinds |
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[96] | 75 | |
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| 76 | IMPLICIT NONE |
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| 77 | |
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| 78 | PRIVATE |
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| 79 | PUBLIC eqn_state_seawater, eqn_state_seawater_func |
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| 80 | |
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[1320] | 81 | REAL(wp), DIMENSION(12), PARAMETER :: nom = & |
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| 82 | (/ 9.9984085444849347D2, 7.3471625860981584D0, & |
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| 83 | -5.3211231792841769D-2, 3.6492439109814549D-4, & |
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| 84 | 2.5880571023991390D0, -6.7168282786692354D-3, & |
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| 85 | 1.9203202055760151D-3, 1.1798263740430364D-2, & |
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| 86 | 9.8920219266399117D-8, 4.6996642771754730D-6, & |
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| 87 | -2.5862187075154352D-8, -3.2921414007960662D-12 /) |
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[1682] | 88 | !< |
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[96] | 89 | |
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[1320] | 90 | REAL(wp), DIMENSION(13), PARAMETER :: den = & |
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| 91 | (/ 1.0D0, 7.2815210113327091D-3, & |
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| 92 | -4.4787265461983921D-5, 3.3851002965802430D-7, & |
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| 93 | 1.3651202389758572D-10, 1.7632126669040377D-3, & |
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| 94 | -8.8066583251206474D-6, -1.8832689434804897D-10, & |
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| 95 | 5.7463776745432097D-6, 1.4716275472242334D-9, & |
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| 96 | 6.7103246285651894D-6, -2.4461698007024582D-17, & |
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| 97 | -9.1534417604289062D-18 /) |
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[1682] | 98 | !< |
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[96] | 99 | |
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| 100 | INTERFACE eqn_state_seawater |
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| 101 | MODULE PROCEDURE eqn_state_seawater |
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| 102 | MODULE PROCEDURE eqn_state_seawater_ij |
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| 103 | END INTERFACE eqn_state_seawater |
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| 104 | |
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| 105 | INTERFACE eqn_state_seawater_func |
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| 106 | MODULE PROCEDURE eqn_state_seawater_func |
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| 107 | END INTERFACE eqn_state_seawater_func |
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| 108 | |
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| 109 | CONTAINS |
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| 110 | |
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| 111 | |
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| 112 | !------------------------------------------------------------------------------! |
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[1682] | 113 | ! Description: |
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| 114 | ! ------------ |
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| 115 | !> Call for all grid points |
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[96] | 116 | !------------------------------------------------------------------------------! |
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| 117 | SUBROUTINE eqn_state_seawater |
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| 118 | |
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[1320] | 119 | USE arrays_3d, & |
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[2031] | 120 | ONLY: hyp, prho, pt_p, rho_ocean, sa_p |
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[1320] | 121 | USE indices, & |
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[2232] | 122 | ONLY: nxl, nxr, nyn, nys, nzb, nzt, wall_flags_0 |
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[96] | 123 | |
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[2232] | 124 | USE surface_mod, & |
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| 125 | ONLY : bc_h |
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| 126 | |
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[96] | 127 | IMPLICIT NONE |
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| 128 | |
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[2232] | 129 | INTEGER(iwp) :: i !< running index x direction |
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| 130 | INTEGER(iwp) :: j !< running index y direction |
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| 131 | INTEGER(iwp) :: k !< running index z direction |
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| 132 | INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall |
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| 133 | INTEGER(iwp) :: m !< running index surface elements |
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| 134 | INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint |
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| 135 | INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint |
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[96] | 136 | |
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[2232] | 137 | REAL(wp) :: flag !< flag to mask topography grid points |
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| 138 | REAL(wp) :: pden !< |
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| 139 | REAL(wp) :: pnom !< |
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| 140 | REAL(wp) :: p1 !< |
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| 141 | REAL(wp) :: p2 !< |
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| 142 | REAL(wp) :: p3 !< |
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| 143 | REAL(wp) :: pt1 !< |
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| 144 | REAL(wp) :: pt2 !< |
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| 145 | REAL(wp) :: pt3 !< |
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| 146 | REAL(wp) :: pt4 !< |
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| 147 | REAL(wp) :: sa1 !< |
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| 148 | REAL(wp) :: sa15 !< |
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| 149 | REAL(wp) :: sa2 !< |
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[1320] | 150 | |
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| 151 | |
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[96] | 152 | |
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| 153 | DO i = nxl, nxr |
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| 154 | DO j = nys, nyn |
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[2232] | 155 | DO k = nzb+1, nzt |
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[96] | 156 | ! |
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| 157 | !-- Pressure is needed in dbar |
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[1353] | 158 | p1 = hyp(k) * 1E-4_wp |
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[96] | 159 | p2 = p1 * p1 |
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| 160 | p3 = p2 * p1 |
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| 161 | |
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| 162 | ! |
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| 163 | !-- Temperature needed in degree Celsius |
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[1353] | 164 | pt1 = pt_p(k,j,i) - 273.15_wp |
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[96] | 165 | pt2 = pt1 * pt1 |
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| 166 | pt3 = pt1 * pt2 |
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| 167 | pt4 = pt2 * pt2 |
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| 168 | |
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| 169 | sa1 = sa_p(k,j,i) |
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| 170 | sa15 = sa1 * SQRT( sa1 ) |
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| 171 | sa2 = sa1 * sa1 |
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| 172 | |
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[1320] | 173 | pnom = nom(1) + nom(2)*pt1 + nom(3)*pt2 + & |
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| 174 | nom(4)*pt3 + nom(5)*sa1 + nom(6)*sa1*pt1 + & |
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[388] | 175 | nom(7)*sa2 |
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[96] | 176 | |
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[1320] | 177 | pden = den(1) + den(2)*pt1 + den(3)*pt2 + & |
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| 178 | den(4)*pt3 + den(5)*pt4 + den(6)*sa1 + & |
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| 179 | den(7)*sa1*pt1 + den(8)*sa1*pt3 + den(9)*sa15 + & |
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[388] | 180 | den(10)*sa15*pt2 |
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| 181 | ! |
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[2232] | 182 | !-- Predetermine flag to mask topography |
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| 183 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) ) |
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| 184 | ! |
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[388] | 185 | !-- Potential density (without pressure terms) |
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[2232] | 186 | prho(k,j,i) = pnom / pden * flag |
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[388] | 187 | |
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[1320] | 188 | pnom = pnom + nom(8)*p1 + nom(9)*p1*pt2 + & |
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[388] | 189 | nom(10)*p1*sa1 + nom(11)*p2 + nom(12)*p2*pt2 |
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| 190 | |
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[1320] | 191 | pden = pden + den(11)*p1 + den(12)*p2*pt3 + & |
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[388] | 192 | den(13)*p3*pt1 |
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| 193 | |
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| 194 | ! |
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| 195 | !-- In-situ density |
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[2232] | 196 | rho_ocean(k,j,i) = pnom / pden * flag |
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[388] | 197 | |
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[96] | 198 | ENDDO |
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[97] | 199 | ! |
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[2232] | 200 | !-- Neumann conditions are assumed at top boundary |
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| 201 | prho(nzt+1,j,i) = prho(nzt,j,i) |
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| 202 | rho_ocean(nzt+1,j,i) = rho_ocean(nzt,j,i) |
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[388] | 203 | |
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[96] | 204 | ENDDO |
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| 205 | ENDDO |
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[2232] | 206 | ! |
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| 207 | !-- Neumann conditions at up/downward-facing surfaces |
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| 208 | !$OMP PARALLEL DO PRIVATE( i, j, k ) |
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| 209 | DO m = 1, bc_h(0)%ns |
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| 210 | i = bc_h(0)%i(m) |
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| 211 | j = bc_h(0)%j(m) |
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| 212 | k = bc_h(0)%k(m) |
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| 213 | prho(k-1,j,i) = prho(k,j,i) |
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| 214 | rho_ocean(k-1,j,i) = rho_ocean(k,j,i) |
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| 215 | ENDDO |
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| 216 | ! |
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| 217 | !-- Downward facing surfaces |
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| 218 | !$OMP PARALLEL DO PRIVATE( i, j, k ) |
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| 219 | DO m = 1, bc_h(1)%ns |
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| 220 | i = bc_h(1)%i(m) |
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| 221 | j = bc_h(1)%j(m) |
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| 222 | k = bc_h(1)%k(m) |
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| 223 | prho(k+1,j,i) = prho(k,j,i) |
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| 224 | rho_ocean(k+1,j,i) = rho_ocean(k,j,i) |
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| 225 | ENDDO |
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[96] | 226 | |
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| 227 | END SUBROUTINE eqn_state_seawater |
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| 228 | |
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| 229 | |
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| 230 | !------------------------------------------------------------------------------! |
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[1682] | 231 | ! Description: |
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| 232 | ! ------------ |
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| 233 | !> Call for grid point i,j |
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[96] | 234 | !------------------------------------------------------------------------------! |
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| 235 | SUBROUTINE eqn_state_seawater_ij( i, j ) |
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| 236 | |
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[1320] | 237 | USE arrays_3d, & |
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[2031] | 238 | ONLY: hyp, prho, pt_p, rho_ocean, sa_p |
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[1320] | 239 | |
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| 240 | USE indices, & |
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[2232] | 241 | ONLY: nzb, nzt, wall_flags_0 |
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[96] | 242 | |
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[2232] | 243 | USE surface_mod, & |
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| 244 | ONLY : bc_h |
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| 245 | |
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[96] | 246 | IMPLICIT NONE |
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| 247 | |
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[2232] | 248 | INTEGER(iwp) :: i !< running index x direction |
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| 249 | INTEGER(iwp) :: j !< running index y direction |
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| 250 | INTEGER(iwp) :: k !< running index z direction |
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| 251 | INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall |
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| 252 | INTEGER(iwp) :: m !< running index surface elements |
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| 253 | INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint |
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| 254 | INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint |
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[96] | 255 | |
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[2232] | 256 | REAL(wp) :: flag !< flag to mask topography grid points |
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| 257 | REAL(wp) :: pden !< |
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| 258 | REAL(wp) :: pnom !< |
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| 259 | REAL(wp) :: p1 !< |
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| 260 | REAL(wp) :: p2 !< |
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| 261 | REAL(wp) :: p3 !< |
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| 262 | REAL(wp) :: pt1 !< |
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| 263 | REAL(wp) :: pt2 !< |
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| 264 | REAL(wp) :: pt3 !< |
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| 265 | REAL(wp) :: pt4 !< |
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| 266 | REAL(wp) :: sa1 !< |
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| 267 | REAL(wp) :: sa15 !< |
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| 268 | REAL(wp) :: sa2 !< |
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[96] | 269 | |
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[2232] | 270 | DO k = nzb+1, nzt |
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[96] | 271 | ! |
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| 272 | !-- Pressure is needed in dbar |
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[1353] | 273 | p1 = hyp(k) * 1E-4_wp |
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[96] | 274 | p2 = p1 * p1 |
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| 275 | p3 = p2 * p1 |
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| 276 | |
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| 277 | ! |
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| 278 | !-- Temperature needed in degree Celsius |
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[1353] | 279 | pt1 = pt_p(k,j,i) - 273.15_wp |
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[96] | 280 | pt2 = pt1 * pt1 |
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| 281 | pt3 = pt1 * pt2 |
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| 282 | pt4 = pt2 * pt2 |
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| 283 | |
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| 284 | sa1 = sa_p(k,j,i) |
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| 285 | sa15 = sa1 * SQRT( sa1 ) |
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| 286 | sa2 = sa1 * sa1 |
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| 287 | |
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[1320] | 288 | pnom = nom(1) + nom(2)*pt1 + nom(3)*pt2 + & |
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| 289 | nom(4)*pt3 + nom(5)*sa1 + nom(6)*sa1*pt1 + & |
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[388] | 290 | nom(7)*sa2 |
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| 291 | |
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[1320] | 292 | pden = den(1) + den(2)*pt1 + den(3)*pt2 + & |
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| 293 | den(4)*pt3 + den(5)*pt4 + den(6)*sa1 + & |
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| 294 | den(7)*sa1*pt1 + den(8)*sa1*pt3 + den(9)*sa15 + & |
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[388] | 295 | den(10)*sa15*pt2 |
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| 296 | ! |
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[2232] | 297 | !-- Predetermine flag to mask topography |
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| 298 | flag = MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 0 ) ) |
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| 299 | ! |
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[388] | 300 | !-- Potential density (without pressure terms) |
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[2232] | 301 | prho(k,j,i) = pnom / pden * flag |
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[388] | 302 | |
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[1320] | 303 | pnom = pnom + nom(8)*p1 + nom(9)*p1*pt2 + & |
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[388] | 304 | nom(10)*p1*sa1 + nom(11)*p2 + nom(12)*p2*pt2 |
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[1320] | 305 | pden = pden + den(11)*p1 + den(12)*p2*pt3 + & |
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[388] | 306 | den(13)*p3*pt1 |
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| 307 | |
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| 308 | ! |
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| 309 | !-- In-situ density |
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[2232] | 310 | rho_ocean(k,j,i) = pnom / pden * flag |
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[388] | 311 | |
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| 312 | |
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[96] | 313 | ENDDO |
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[97] | 314 | ! |
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[2232] | 315 | !-- Neumann conditions at up/downward-facing walls |
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| 316 | surf_s = bc_h(0)%start_index(j,i) |
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| 317 | surf_e = bc_h(0)%end_index(j,i) |
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| 318 | DO m = surf_s, surf_e |
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| 319 | k = bc_h(0)%k(m) |
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| 320 | prho(k-1,j,i) = prho(k,j,i) |
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| 321 | rho_ocean(k-1,j,i) = rho_ocean(k,j,i) |
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| 322 | ENDDO |
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| 323 | ! |
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| 324 | !-- Downward facing surfaces |
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| 325 | surf_s = bc_h(1)%start_index(j,i) |
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| 326 | surf_e = bc_h(1)%end_index(j,i) |
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| 327 | DO m = surf_s, surf_e |
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| 328 | k = bc_h(1)%k(m) |
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| 329 | prho(k+1,j,i) = prho(k,j,i) |
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| 330 | rho_ocean(k+1,j,i) = rho_ocean(k,j,i) |
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| 331 | ENDDO |
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| 332 | ! |
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| 333 | !-- Neumann condition are assumed at top boundary |
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| 334 | prho(nzt+1,j,i) = prho(nzt,j,i) |
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| 335 | rho_ocean(nzt+1,j,i) = rho_ocean(nzt,j,i) |
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[96] | 336 | |
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| 337 | END SUBROUTINE eqn_state_seawater_ij |
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| 338 | |
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| 339 | |
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| 340 | !------------------------------------------------------------------------------! |
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[1682] | 341 | ! Description: |
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| 342 | ! ------------ |
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| 343 | !> Equation of state as a function |
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[96] | 344 | !------------------------------------------------------------------------------! |
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[1320] | 345 | REAL(wp) FUNCTION eqn_state_seawater_func( p, pt, sa ) |
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[96] | 346 | |
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| 347 | IMPLICIT NONE |
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| 348 | |
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[1682] | 349 | REAL(wp) :: p !< |
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| 350 | REAL(wp) :: p1 !< |
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| 351 | REAL(wp) :: p2 !< |
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| 352 | REAL(wp) :: p3 !< |
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| 353 | REAL(wp) :: pt !< |
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| 354 | REAL(wp) :: pt1 !< |
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| 355 | REAL(wp) :: pt2 !< |
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| 356 | REAL(wp) :: pt3 !< |
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| 357 | REAL(wp) :: pt4 !< |
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| 358 | REAL(wp) :: sa !< |
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| 359 | REAL(wp) :: sa15 !< |
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| 360 | REAL(wp) :: sa2 !< |
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[96] | 361 | |
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| 362 | ! |
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| 363 | !-- Pressure is needed in dbar |
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[1353] | 364 | p1 = p * 1E-4_wp |
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[96] | 365 | p2 = p1 * p1 |
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| 366 | p3 = p2 * p1 |
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| 367 | |
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| 368 | ! |
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| 369 | !-- Temperature needed in degree Celsius |
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[1353] | 370 | pt1 = pt - 273.15_wp |
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[96] | 371 | pt2 = pt1 * pt1 |
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| 372 | pt3 = pt1 * pt2 |
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| 373 | pt4 = pt2 * pt2 |
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| 374 | |
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| 375 | sa15 = sa * SQRT( sa ) |
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| 376 | sa2 = sa * sa |
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| 377 | |
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| 378 | |
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| 379 | eqn_state_seawater_func = & |
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| 380 | ( nom(1) + nom(2)*pt1 + nom(3)*pt2 + nom(4)*pt3 + & |
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| 381 | nom(5)*sa + nom(6)*sa*pt1 + nom(7)*sa2 + nom(8)*p1 + & |
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| 382 | nom(9)*p1*pt2 + nom(10)*p1*sa + nom(11)*p2 + nom(12)*p2*pt2 & |
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| 383 | ) / & |
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| 384 | ( den(1) + den(2)*pt1 + den(3)*pt2 + den(4)*pt3 + & |
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| 385 | den(5)*pt4 + den(6)*sa + den(7)*sa*pt1 + den(8)*sa*pt3 + & |
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| 386 | den(9)*sa15 + den(10)*sa15*pt2 + den(11)*p1 + den(12)*p2*pt3 + & |
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| 387 | den(13)*p3*pt1 & |
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| 388 | ) |
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| 389 | |
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| 390 | |
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| 391 | END FUNCTION eqn_state_seawater_func |
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| 392 | |
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| 393 | END MODULE eqn_state_seawater_mod |
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