| 1 | MODULE eqn_state_seawater_mod |
|---|
| 2 | |
|---|
| 3 | !------------------------------------------------------------------------------! |
|---|
| 4 | ! Actual revisions: |
|---|
| 5 | ! ----------------- |
|---|
| 6 | ! First constant in array den also defined as type double |
|---|
| 7 | ! |
|---|
| 8 | ! Former revisions: |
|---|
| 9 | ! ----------------- |
|---|
| 10 | ! $Id: eqn_state_seawater.f90 336 2009-06-10 11:19:35Z raasch $ |
|---|
| 11 | ! |
|---|
| 12 | ! 97 2007-06-21 08:23:15Z raasch |
|---|
| 13 | ! Initial revision |
|---|
| 14 | ! |
|---|
| 15 | ! |
|---|
| 16 | ! Description: |
|---|
| 17 | ! ------------ |
|---|
| 18 | ! Equation of state for seawater as a function of potential temperature, |
|---|
| 19 | ! salinity, and pressure. |
|---|
| 20 | ! For coefficients see Jackett et al., 2006: J. Atm. Ocean Tech. |
|---|
| 21 | ! eqn_state_seawater calculates the potential density referred at hyp(0). |
|---|
| 22 | ! eqn_state_seawater_func calculates density. |
|---|
| 23 | !------------------------------------------------------------------------------! |
|---|
| 24 | |
|---|
| 25 | IMPLICIT NONE |
|---|
| 26 | |
|---|
| 27 | PRIVATE |
|---|
| 28 | PUBLIC eqn_state_seawater, eqn_state_seawater_func |
|---|
| 29 | |
|---|
| 30 | REAL, DIMENSION(12), PARAMETER :: nom = & |
|---|
| 31 | (/ 9.9984085444849347D2, 7.3471625860981584D0, & |
|---|
| 32 | -5.3211231792841769D-2, 3.6492439109814549D-4, & |
|---|
| 33 | 2.5880571023991390D0, -6.7168282786692354D-3, & |
|---|
| 34 | 1.9203202055760151D-3, 1.1798263740430364D-2, & |
|---|
| 35 | 9.8920219266399117D-8, 4.6996642771754730D-6, & |
|---|
| 36 | -2.5862187075154352D-8, -3.2921414007960662D-12 /) |
|---|
| 37 | |
|---|
| 38 | REAL, DIMENSION(13), PARAMETER :: den = & |
|---|
| 39 | (/ 1.0D0, 7.2815210113327091D-3, & |
|---|
| 40 | -4.4787265461983921D-5, 3.3851002965802430D-7, & |
|---|
| 41 | 1.3651202389758572D-10, 1.7632126669040377D-3, & |
|---|
| 42 | -8.8066583251206474D-6, -1.8832689434804897D-10, & |
|---|
| 43 | 5.7463776745432097D-6, 1.4716275472242334D-9, & |
|---|
| 44 | 6.7103246285651894D-6, -2.4461698007024582D-17, & |
|---|
| 45 | -9.1534417604289062D-18 /) |
|---|
| 46 | |
|---|
| 47 | INTERFACE eqn_state_seawater |
|---|
| 48 | MODULE PROCEDURE eqn_state_seawater |
|---|
| 49 | MODULE PROCEDURE eqn_state_seawater_ij |
|---|
| 50 | END INTERFACE eqn_state_seawater |
|---|
| 51 | |
|---|
| 52 | INTERFACE eqn_state_seawater_func |
|---|
| 53 | MODULE PROCEDURE eqn_state_seawater_func |
|---|
| 54 | END INTERFACE eqn_state_seawater_func |
|---|
| 55 | |
|---|
| 56 | CONTAINS |
|---|
| 57 | |
|---|
| 58 | |
|---|
| 59 | !------------------------------------------------------------------------------! |
|---|
| 60 | ! Call for all grid points |
|---|
| 61 | !------------------------------------------------------------------------------! |
|---|
| 62 | SUBROUTINE eqn_state_seawater |
|---|
| 63 | |
|---|
| 64 | USE arrays_3d |
|---|
| 65 | USE indices |
|---|
| 66 | |
|---|
| 67 | IMPLICIT NONE |
|---|
| 68 | |
|---|
| 69 | INTEGER :: i, j, k |
|---|
| 70 | |
|---|
| 71 | REAL :: p1, p2, p3, pt1, pt2, pt3, pt4, sa1, sa15, sa2 |
|---|
| 72 | |
|---|
| 73 | DO i = nxl, nxr |
|---|
| 74 | DO j = nys, nyn |
|---|
| 75 | DO k = nzb_s_inner(j,i)+1, nzt |
|---|
| 76 | ! |
|---|
| 77 | !-- Pressure is needed in dbar |
|---|
| 78 | ! p1 = hyp(0) * 1E-4 |
|---|
| 79 | ! p1 = 0.0 |
|---|
| 80 | p1 = hyp(k) * 1E-4 |
|---|
| 81 | p2 = p1 * p1 |
|---|
| 82 | p3 = p2 * p1 |
|---|
| 83 | |
|---|
| 84 | ! |
|---|
| 85 | !-- Temperature needed in degree Celsius |
|---|
| 86 | pt1 = pt_p(k,j,i) - 273.15 |
|---|
| 87 | pt2 = pt1 * pt1 |
|---|
| 88 | pt3 = pt1 * pt2 |
|---|
| 89 | pt4 = pt2 * pt2 |
|---|
| 90 | |
|---|
| 91 | sa1 = sa_p(k,j,i) |
|---|
| 92 | sa15 = sa1 * SQRT( sa1 ) |
|---|
| 93 | sa2 = sa1 * sa1 |
|---|
| 94 | |
|---|
| 95 | rho(k,j,i) = & |
|---|
| 96 | ( nom(1) + nom(2)*pt1 + nom(3)*pt2 + & |
|---|
| 97 | nom(4)*pt3 + nom(5)*sa1 + nom(6)*sa1*pt1 + & |
|---|
| 98 | nom(7)*sa2 + nom(8)*p1 + nom(9)*p1*pt2 + & |
|---|
| 99 | nom(10)*p1*sa1 + nom(11)*p2 + nom(12)*p2*pt2 & |
|---|
| 100 | ) / & |
|---|
| 101 | ( den(1) + den(2)*pt1 + den(3)*pt2 + & |
|---|
| 102 | den(4)*pt3 + den(5)*pt4 + den(6)*sa1 + & |
|---|
| 103 | den(7)*sa1*pt1 + den(8)*sa1*pt3 + den(9)*sa15 + & |
|---|
| 104 | den(10)*sa15*pt2 + den(11)*p1 + den(12)*p2*pt3 + & |
|---|
| 105 | den(13)*p3*pt1 & |
|---|
| 106 | ) |
|---|
| 107 | |
|---|
| 108 | ENDDO |
|---|
| 109 | ! |
|---|
| 110 | !-- Neumann conditions are assumed at bottom and top boundary |
|---|
| 111 | rho(nzt+1,j,i) = rho(nzt,j,i) |
|---|
| 112 | rho(nzb_s_inner(j,i),j,i) = rho(nzb_s_inner(j,i)+1,j,i) |
|---|
| 113 | ENDDO |
|---|
| 114 | ENDDO |
|---|
| 115 | |
|---|
| 116 | END SUBROUTINE eqn_state_seawater |
|---|
| 117 | |
|---|
| 118 | |
|---|
| 119 | !------------------------------------------------------------------------------! |
|---|
| 120 | ! Call for grid point i,j |
|---|
| 121 | !------------------------------------------------------------------------------! |
|---|
| 122 | SUBROUTINE eqn_state_seawater_ij( i, j ) |
|---|
| 123 | |
|---|
| 124 | USE arrays_3d |
|---|
| 125 | USE indices |
|---|
| 126 | |
|---|
| 127 | IMPLICIT NONE |
|---|
| 128 | |
|---|
| 129 | INTEGER :: i, j, k |
|---|
| 130 | |
|---|
| 131 | REAL :: p1, p2, p3, pt1, pt2, pt3, pt4, sa1, sa15, sa2 |
|---|
| 132 | |
|---|
| 133 | DO k = nzb_s_inner(j,i)+1, nzt |
|---|
| 134 | ! |
|---|
| 135 | !-- Pressure is needed in dbar |
|---|
| 136 | ! p1 = hyp(0) * 1E-4 |
|---|
| 137 | ! p1 = 0.0 |
|---|
| 138 | p1 = hyp(k) * 1E-4 |
|---|
| 139 | p2 = p1 * p1 |
|---|
| 140 | p3 = p2 * p1 |
|---|
| 141 | |
|---|
| 142 | ! |
|---|
| 143 | !-- Temperature needed in degree Celsius |
|---|
| 144 | pt1 = pt_p(k,j,i) - 273.15 |
|---|
| 145 | pt2 = pt1 * pt1 |
|---|
| 146 | pt3 = pt1 * pt2 |
|---|
| 147 | pt4 = pt2 * pt2 |
|---|
| 148 | |
|---|
| 149 | sa1 = sa_p(k,j,i) |
|---|
| 150 | sa15 = sa1 * SQRT( sa1 ) |
|---|
| 151 | sa2 = sa1 * sa1 |
|---|
| 152 | |
|---|
| 153 | rho(k,j,i) = ( nom(1) + nom(2)*pt1 + nom(3)*pt2 + & |
|---|
| 154 | nom(4)*pt3 + nom(5)*sa1 + nom(6)*sa1*pt1 + & |
|---|
| 155 | nom(7)*sa2 + nom(8)*p1 + nom(9)*p1*pt2 + & |
|---|
| 156 | nom(10)*p1*sa1 + nom(11)*p2 + nom(12)*p2*pt2 & |
|---|
| 157 | ) / & |
|---|
| 158 | ( den(1) + den(2)*pt1 + den(3)*pt2 + & |
|---|
| 159 | den(4)*pt3 + den(5)*pt4 + den(6)*sa1 + & |
|---|
| 160 | den(7)*sa1*pt1 + den(8)*sa1*pt3 + den(9)*sa15 + & |
|---|
| 161 | den(10)*sa15*pt2 + den(11)*p1 + den(12)*p2*pt3 + & |
|---|
| 162 | den(13)*p3*pt1 & |
|---|
| 163 | ) |
|---|
| 164 | ENDDO |
|---|
| 165 | ! |
|---|
| 166 | !-- Neumann conditions are assumed at bottom and top boundary |
|---|
| 167 | rho(nzt+1,j,i) = rho(nzt,j,i) |
|---|
| 168 | rho(nzb_s_inner(j,i),j,i) = rho(nzb_s_inner(j,i)+1,j,i) |
|---|
| 169 | |
|---|
| 170 | END SUBROUTINE eqn_state_seawater_ij |
|---|
| 171 | |
|---|
| 172 | |
|---|
| 173 | !------------------------------------------------------------------------------! |
|---|
| 174 | ! Equation of state as a function |
|---|
| 175 | !------------------------------------------------------------------------------! |
|---|
| 176 | REAL FUNCTION eqn_state_seawater_func( p, pt, sa ) |
|---|
| 177 | |
|---|
| 178 | IMPLICIT NONE |
|---|
| 179 | |
|---|
| 180 | REAL :: p, p1, p2, p3, pt, pt1, pt2, pt3, pt4, sa, sa15, sa2 |
|---|
| 181 | |
|---|
| 182 | ! |
|---|
| 183 | !-- Pressure is needed in dbar |
|---|
| 184 | p1 = p * 1E-4 |
|---|
| 185 | p2 = p1 * p1 |
|---|
| 186 | p3 = p2 * p1 |
|---|
| 187 | |
|---|
| 188 | ! |
|---|
| 189 | !-- Temperature needed in degree Celsius |
|---|
| 190 | pt1 = pt - 273.15 |
|---|
| 191 | pt2 = pt1 * pt1 |
|---|
| 192 | pt3 = pt1 * pt2 |
|---|
| 193 | pt4 = pt2 * pt2 |
|---|
| 194 | |
|---|
| 195 | sa15 = sa * SQRT( sa ) |
|---|
| 196 | sa2 = sa * sa |
|---|
| 197 | |
|---|
| 198 | |
|---|
| 199 | eqn_state_seawater_func = & |
|---|
| 200 | ( nom(1) + nom(2)*pt1 + nom(3)*pt2 + nom(4)*pt3 + & |
|---|
| 201 | nom(5)*sa + nom(6)*sa*pt1 + nom(7)*sa2 + nom(8)*p1 + & |
|---|
| 202 | nom(9)*p1*pt2 + nom(10)*p1*sa + nom(11)*p2 + nom(12)*p2*pt2 & |
|---|
| 203 | ) / & |
|---|
| 204 | ( den(1) + den(2)*pt1 + den(3)*pt2 + den(4)*pt3 + & |
|---|
| 205 | den(5)*pt4 + den(6)*sa + den(7)*sa*pt1 + den(8)*sa*pt3 + & |
|---|
| 206 | den(9)*sa15 + den(10)*sa15*pt2 + den(11)*p1 + den(12)*p2*pt3 + & |
|---|
| 207 | den(13)*p3*pt1 & |
|---|
| 208 | ) |
|---|
| 209 | |
|---|
| 210 | |
|---|
| 211 | END FUNCTION eqn_state_seawater_func |
|---|
| 212 | |
|---|
| 213 | END MODULE eqn_state_seawater_mod |
|---|
