!> @file eqn_state_seawater.f90 !------------------------------------------------------------------------------! ! This file is part of the PALM model system. ! ! PALM is free software: you can redistribute it and/or modify it under the ! terms of the GNU General Public License as published by the Free Software ! Foundation, either version 3 of the License, or (at your option) any later ! version. ! ! PALM is distributed in the hope that it will be useful, but WITHOUT ANY ! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR ! A PARTICULAR PURPOSE. See the GNU General Public License for more details. ! ! You should have received a copy of the GNU General Public License along with ! PALM. If not, see . ! ! Copyright 1997-2018 Leibniz Universitaet Hannover !------------------------------------------------------------------------------! ! ! Current revisions: ! ----------------- ! ! ! Former revisions: ! ----------------- ! $Id: eqn_state_seawater.f90 2718 2018-01-02 08:49:38Z kanani $ ! Corrected "Former revisions" section ! ! 2696 2017-12-14 17:12:51Z kanani ! Change in file header (GPL part) ! ! 2369 2017-08-22 15:20:37Z suehring ! Bugfix, do not mask topography here, since density becomes zero, leading to ! division by zero in production_e ! ! 2233 2017-05-30 18:08:54Z suehring ! ! 2232 2017-05-30 17:47:52Z suehring ! Adjustments to new topography and surface concept ! ! 2031 2016-10-21 15:11:58Z knoop ! renamed variable rho to rho_ocean ! ! 2000 2016-08-20 18:09:15Z knoop ! Forced header and separation lines into 80 columns ! ! 1873 2016-04-18 14:50:06Z maronga ! Module renamed (removed _mod) ! ! ! 1850 2016-04-08 13:29:27Z maronga ! Module renamed ! ! ! 1682 2015-10-07 23:56:08Z knoop ! Code annotations made doxygen readable ! ! 1353 2014-04-08 15:21:23Z heinze ! REAL constants provided with KIND-attribute ! ! 1320 2014-03-20 08:40:49Z raasch ! ONLY-attribute added to USE-statements, ! kind-parameters added to all INTEGER and REAL declaration statements, ! kinds are defined in new module kinds, ! revision history before 2012 removed, ! comment fields (!:) to be used for variable explanations added to ! all variable declaration statements ! ! 1036 2012-10-22 13:43:42Z raasch ! code put under GPL (PALM 3.9) ! ! 97 2007-06-21 08:23:15Z raasch ! Initial revision ! ! ! Description: ! ------------ !> Equation of state for seawater as a function of potential temperature, !> salinity, and pressure. !> For coefficients see Jackett et al., 2006: J. Atm. Ocean Tech. !> eqn_state_seawater calculates the potential density referred at hyp(0). !> eqn_state_seawater_func calculates density. !------------------------------------------------------------------------------! MODULE eqn_state_seawater_mod USE kinds IMPLICIT NONE PRIVATE PUBLIC eqn_state_seawater, eqn_state_seawater_func REAL(wp), DIMENSION(12), PARAMETER :: nom = & (/ 9.9984085444849347D2, 7.3471625860981584D0, & -5.3211231792841769D-2, 3.6492439109814549D-4, & 2.5880571023991390D0, -6.7168282786692354D-3, & 1.9203202055760151D-3, 1.1798263740430364D-2, & 9.8920219266399117D-8, 4.6996642771754730D-6, & -2.5862187075154352D-8, -3.2921414007960662D-12 /) !< REAL(wp), DIMENSION(13), PARAMETER :: den = & (/ 1.0D0, 7.2815210113327091D-3, & -4.4787265461983921D-5, 3.3851002965802430D-7, & 1.3651202389758572D-10, 1.7632126669040377D-3, & -8.8066583251206474D-6, -1.8832689434804897D-10, & 5.7463776745432097D-6, 1.4716275472242334D-9, & 6.7103246285651894D-6, -2.4461698007024582D-17, & -9.1534417604289062D-18 /) !< INTERFACE eqn_state_seawater MODULE PROCEDURE eqn_state_seawater MODULE PROCEDURE eqn_state_seawater_ij END INTERFACE eqn_state_seawater INTERFACE eqn_state_seawater_func MODULE PROCEDURE eqn_state_seawater_func END INTERFACE eqn_state_seawater_func CONTAINS !------------------------------------------------------------------------------! ! Description: ! ------------ !> Call for all grid points !------------------------------------------------------------------------------! SUBROUTINE eqn_state_seawater USE arrays_3d, & ONLY: hyp, prho, pt_p, rho_ocean, sa_p USE indices, & ONLY: nxl, nxr, nyn, nys, nzb, nzt USE surface_mod, & ONLY : bc_h IMPLICIT NONE INTEGER(iwp) :: i !< running index x direction INTEGER(iwp) :: j !< running index y direction INTEGER(iwp) :: k !< running index z direction INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall INTEGER(iwp) :: m !< running index surface elements INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint REAL(wp) :: pden !< REAL(wp) :: pnom !< REAL(wp) :: p1 !< REAL(wp) :: p2 !< REAL(wp) :: p3 !< REAL(wp) :: pt1 !< REAL(wp) :: pt2 !< REAL(wp) :: pt3 !< REAL(wp) :: pt4 !< REAL(wp) :: sa1 !< REAL(wp) :: sa15 !< REAL(wp) :: sa2 !< DO i = nxl, nxr DO j = nys, nyn DO k = nzb+1, nzt ! !-- Pressure is needed in dbar p1 = hyp(k) * 1E-4_wp p2 = p1 * p1 p3 = p2 * p1 ! !-- Temperature needed in degree Celsius pt1 = pt_p(k,j,i) - 273.15_wp pt2 = pt1 * pt1 pt3 = pt1 * pt2 pt4 = pt2 * pt2 sa1 = sa_p(k,j,i) sa15 = sa1 * SQRT( sa1 ) sa2 = sa1 * sa1 pnom = nom(1) + nom(2)*pt1 + nom(3)*pt2 + & nom(4)*pt3 + nom(5)*sa1 + nom(6)*sa1*pt1 + & nom(7)*sa2 pden = den(1) + den(2)*pt1 + den(3)*pt2 + & den(4)*pt3 + den(5)*pt4 + den(6)*sa1 + & den(7)*sa1*pt1 + den(8)*sa1*pt3 + den(9)*sa15 + & den(10)*sa15*pt2 ! !-- Potential density (without pressure terms) prho(k,j,i) = pnom / pden pnom = pnom + nom(8)*p1 + nom(9)*p1*pt2 + & nom(10)*p1*sa1 + nom(11)*p2 + nom(12)*p2*pt2 pden = pden + den(11)*p1 + den(12)*p2*pt3 + & den(13)*p3*pt1 ! !-- In-situ density rho_ocean(k,j,i) = pnom / pden ENDDO ! !-- Neumann conditions are assumed at top boundary prho(nzt+1,j,i) = prho(nzt,j,i) rho_ocean(nzt+1,j,i) = rho_ocean(nzt,j,i) ENDDO ENDDO ! !-- Neumann conditions at up/downward-facing surfaces !$OMP PARALLEL DO PRIVATE( i, j, k ) DO m = 1, bc_h(0)%ns i = bc_h(0)%i(m) j = bc_h(0)%j(m) k = bc_h(0)%k(m) prho(k-1,j,i) = prho(k,j,i) rho_ocean(k-1,j,i) = rho_ocean(k,j,i) ENDDO ! !-- Downward facing surfaces !$OMP PARALLEL DO PRIVATE( i, j, k ) DO m = 1, bc_h(1)%ns i = bc_h(1)%i(m) j = bc_h(1)%j(m) k = bc_h(1)%k(m) prho(k+1,j,i) = prho(k,j,i) rho_ocean(k+1,j,i) = rho_ocean(k,j,i) ENDDO END SUBROUTINE eqn_state_seawater !------------------------------------------------------------------------------! ! Description: ! ------------ !> Call for grid point i,j !------------------------------------------------------------------------------! SUBROUTINE eqn_state_seawater_ij( i, j ) USE arrays_3d, & ONLY: hyp, prho, pt_p, rho_ocean, sa_p USE indices, & ONLY: nzb, nzt USE surface_mod, & ONLY : bc_h IMPLICIT NONE INTEGER(iwp) :: i !< running index x direction INTEGER(iwp) :: j !< running index y direction INTEGER(iwp) :: k !< running index z direction INTEGER(iwp) :: l !< running index of surface type, south- or north-facing wall INTEGER(iwp) :: m !< running index surface elements INTEGER(iwp) :: surf_e !< End index of surface elements at (j,i)-gridpoint INTEGER(iwp) :: surf_s !< Start index of surface elements at (j,i)-gridpoint REAL(wp) :: pden !< REAL(wp) :: pnom !< REAL(wp) :: p1 !< REAL(wp) :: p2 !< REAL(wp) :: p3 !< REAL(wp) :: pt1 !< REAL(wp) :: pt2 !< REAL(wp) :: pt3 !< REAL(wp) :: pt4 !< REAL(wp) :: sa1 !< REAL(wp) :: sa15 !< REAL(wp) :: sa2 !< DO k = nzb+1, nzt ! !-- Pressure is needed in dbar p1 = hyp(k) * 1E-4_wp p2 = p1 * p1 p3 = p2 * p1 ! !-- Temperature needed in degree Celsius pt1 = pt_p(k,j,i) - 273.15_wp pt2 = pt1 * pt1 pt3 = pt1 * pt2 pt4 = pt2 * pt2 sa1 = sa_p(k,j,i) sa15 = sa1 * SQRT( sa1 ) sa2 = sa1 * sa1 pnom = nom(1) + nom(2)*pt1 + nom(3)*pt2 + & nom(4)*pt3 + nom(5)*sa1 + nom(6)*sa1*pt1 + & nom(7)*sa2 pden = den(1) + den(2)*pt1 + den(3)*pt2 + & den(4)*pt3 + den(5)*pt4 + den(6)*sa1 + & den(7)*sa1*pt1 + den(8)*sa1*pt3 + den(9)*sa15 + & den(10)*sa15*pt2 ! !-- Potential density (without pressure terms) prho(k,j,i) = pnom / pden pnom = pnom + nom(8)*p1 + nom(9)*p1*pt2 + & nom(10)*p1*sa1 + nom(11)*p2 + nom(12)*p2*pt2 pden = pden + den(11)*p1 + den(12)*p2*pt3 + & den(13)*p3*pt1 ! !-- In-situ density rho_ocean(k,j,i) = pnom / pden ENDDO ! !-- Neumann conditions at up/downward-facing walls surf_s = bc_h(0)%start_index(j,i) surf_e = bc_h(0)%end_index(j,i) DO m = surf_s, surf_e k = bc_h(0)%k(m) prho(k-1,j,i) = prho(k,j,i) rho_ocean(k-1,j,i) = rho_ocean(k,j,i) ENDDO ! !-- Downward facing surfaces surf_s = bc_h(1)%start_index(j,i) surf_e = bc_h(1)%end_index(j,i) DO m = surf_s, surf_e k = bc_h(1)%k(m) prho(k+1,j,i) = prho(k,j,i) rho_ocean(k+1,j,i) = rho_ocean(k,j,i) ENDDO ! !-- Neumann condition are assumed at top boundary prho(nzt+1,j,i) = prho(nzt,j,i) rho_ocean(nzt+1,j,i) = rho_ocean(nzt,j,i) END SUBROUTINE eqn_state_seawater_ij !------------------------------------------------------------------------------! ! Description: ! ------------ !> Equation of state as a function !------------------------------------------------------------------------------! REAL(wp) FUNCTION eqn_state_seawater_func( p, pt, sa ) IMPLICIT NONE REAL(wp) :: p !< REAL(wp) :: p1 !< REAL(wp) :: p2 !< REAL(wp) :: p3 !< REAL(wp) :: pt !< REAL(wp) :: pt1 !< REAL(wp) :: pt2 !< REAL(wp) :: pt3 !< REAL(wp) :: pt4 !< REAL(wp) :: sa !< REAL(wp) :: sa15 !< REAL(wp) :: sa2 !< ! !-- Pressure is needed in dbar p1 = p * 1E-4_wp p2 = p1 * p1 p3 = p2 * p1 ! !-- Temperature needed in degree Celsius pt1 = pt - 273.15_wp pt2 = pt1 * pt1 pt3 = pt1 * pt2 pt4 = pt2 * pt2 sa15 = sa * SQRT( sa ) sa2 = sa * sa eqn_state_seawater_func = & ( nom(1) + nom(2)*pt1 + nom(3)*pt2 + nom(4)*pt3 + & nom(5)*sa + nom(6)*sa*pt1 + nom(7)*sa2 + nom(8)*p1 + & nom(9)*p1*pt2 + nom(10)*p1*sa + nom(11)*p2 + nom(12)*p2*pt2 & ) / & ( den(1) + den(2)*pt1 + den(3)*pt2 + den(4)*pt3 + & den(5)*pt4 + den(6)*sa + den(7)*sa*pt1 + den(8)*sa*pt3 + & den(9)*sa15 + den(10)*sa15*pt2 + den(11)*p1 + den(12)*p2*pt3 + & den(13)*p3*pt1 & ) END FUNCTION eqn_state_seawater_func END MODULE eqn_state_seawater_mod