[3] | 1 | MODULE dynhpg |
---|
| 2 | !!====================================================================== |
---|
| 3 | !! *** MODULE dynhpg *** |
---|
| 4 | !! Ocean dynamics: hydrostatic pressure gradient trend |
---|
| 5 | !!====================================================================== |
---|
[2528] | 6 | !! History : OPA ! 1987-09 (P. Andrich, M.-A. Foujols) hpg_zco: Original code |
---|
| 7 | !! 5.0 ! 1991-11 (G. Madec) |
---|
| 8 | !! 7.0 ! 1996-01 (G. Madec) hpg_sco: Original code for s-coordinates |
---|
| 9 | !! 8.0 ! 1997-05 (G. Madec) split dynber into dynkeg and dynhpg |
---|
| 10 | !! 8.5 ! 2002-07 (G. Madec) F90: Free form and module |
---|
| 11 | !! 8.5 ! 2002-08 (A. Bozec) hpg_zps: Original code |
---|
| 12 | !! NEMO 1.0 ! 2005-10 (A. Beckmann, B.W. An) various s-coordinate options |
---|
[3764] | 13 | !! ! Original code for hpg_ctl, hpg_hel hpg_wdj, hpg_djc, hpg_rot |
---|
[2528] | 14 | !! - ! 2005-11 (G. Madec) style & small optimisation |
---|
| 15 | !! 3.3 ! 2010-10 (C. Ethe, G. Madec) reorganisation of initialisation phase |
---|
[3294] | 16 | !! 3.4 ! 2011-11 (H. Liu) hpg_prj: Original code for s-coordinates |
---|
| 17 | !! ! (A. Coward) suppression of hel, wdj and rot options |
---|
[5120] | 18 | !! 3.6 ! 2014-11 (P. Mathiot) hpg_isf: original code for ice shelf cavity |
---|
[503] | 19 | !!---------------------------------------------------------------------- |
---|
[3] | 20 | |
---|
| 21 | !!---------------------------------------------------------------------- |
---|
[455] | 22 | !! dyn_hpg : update the momentum trend with the now horizontal |
---|
[3] | 23 | !! gradient of the hydrostatic pressure |
---|
[2528] | 24 | !! dyn_hpg_init : initialisation and control of options |
---|
[455] | 25 | !! hpg_zco : z-coordinate scheme |
---|
| 26 | !! hpg_zps : z-coordinate plus partial steps (interpolation) |
---|
| 27 | !! hpg_sco : s-coordinate (standard jacobian formulation) |
---|
[5120] | 28 | !! hpg_isf : s-coordinate (sco formulation) adapted to ice shelf |
---|
[455] | 29 | !! hpg_djc : s-coordinate (Density Jacobian with Cubic polynomial) |
---|
[3294] | 30 | !! hpg_prj : s-coordinate (Pressure Jacobian with Cubic polynomial) |
---|
[3] | 31 | !!---------------------------------------------------------------------- |
---|
| 32 | USE oce ! ocean dynamics and tracers |
---|
[4990] | 33 | USE sbc_oce ! surface variable (only for the flag with ice shelf) |
---|
[3] | 34 | USE dom_oce ! ocean space and time domain |
---|
| 35 | USE phycst ! physical constants |
---|
[4990] | 36 | USE trd_oce ! trends: ocean variables |
---|
| 37 | USE trddyn ! trend manager: dynamics |
---|
| 38 | ! |
---|
[2715] | 39 | USE in_out_manager ! I/O manager |
---|
[258] | 40 | USE prtctl ! Print control |
---|
[4990] | 41 | USE lbclnk ! lateral boundary condition |
---|
[2715] | 42 | USE lib_mpp ! MPP library |
---|
[4990] | 43 | USE eosbn2 ! compute density |
---|
[3294] | 44 | USE wrk_nemo ! Memory Allocation |
---|
| 45 | USE timing ! Timing |
---|
[3] | 46 | |
---|
| 47 | IMPLICIT NONE |
---|
| 48 | PRIVATE |
---|
| 49 | |
---|
[2528] | 50 | PUBLIC dyn_hpg ! routine called by step module |
---|
| 51 | PUBLIC dyn_hpg_init ! routine called by opa module |
---|
[3] | 52 | |
---|
[4147] | 53 | ! !!* Namelist namdyn_hpg : hydrostatic pressure gradient |
---|
| 54 | LOGICAL , PUBLIC :: ln_hpg_zco !: z-coordinate - full steps |
---|
| 55 | LOGICAL , PUBLIC :: ln_hpg_zps !: z-coordinate - partial steps (interpolation) |
---|
| 56 | LOGICAL , PUBLIC :: ln_hpg_sco !: s-coordinate (standard jacobian formulation) |
---|
| 57 | LOGICAL , PUBLIC :: ln_hpg_djc !: s-coordinate (Density Jacobian with Cubic polynomial) |
---|
| 58 | LOGICAL , PUBLIC :: ln_hpg_prj !: s-coordinate (Pressure Jacobian scheme) |
---|
[5120] | 59 | LOGICAL , PUBLIC :: ln_hpg_isf !: s-coordinate similar to sco modify for isf |
---|
[4147] | 60 | LOGICAL , PUBLIC :: ln_dynhpg_imp !: semi-implicite hpg flag |
---|
[455] | 61 | |
---|
[3764] | 62 | INTEGER , PUBLIC :: nhpg = 0 ! = 0 to 7, type of pressure gradient scheme used ! (deduced from ln_hpg_... flags) (PUBLIC for TAM) |
---|
[455] | 63 | |
---|
[3] | 64 | !! * Substitutions |
---|
| 65 | # include "domzgr_substitute.h90" |
---|
| 66 | # include "vectopt_loop_substitute.h90" |
---|
| 67 | !!---------------------------------------------------------------------- |
---|
[2528] | 68 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
---|
| 69 | !! $Id$ |
---|
| 70 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
---|
[3] | 71 | !!---------------------------------------------------------------------- |
---|
| 72 | CONTAINS |
---|
| 73 | |
---|
| 74 | SUBROUTINE dyn_hpg( kt ) |
---|
| 75 | !!--------------------------------------------------------------------- |
---|
| 76 | !! *** ROUTINE dyn_hpg *** |
---|
| 77 | !! |
---|
[3764] | 78 | !! ** Method : Call the hydrostatic pressure gradient routine |
---|
[503] | 79 | !! using the scheme defined in the namelist |
---|
[3764] | 80 | !! |
---|
[455] | 81 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
[4990] | 82 | !! - send trends to trd_dyn for futher diagnostics (l_trddyn=T) |
---|
[503] | 83 | !!---------------------------------------------------------------------- |
---|
| 84 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
[3294] | 85 | REAL(wp), POINTER, DIMENSION(:,:,:) :: ztrdu, ztrdv |
---|
[455] | 86 | !!---------------------------------------------------------------------- |
---|
[2528] | 87 | ! |
---|
[3294] | 88 | IF( nn_timing == 1 ) CALL timing_start('dyn_hpg') |
---|
[2715] | 89 | ! |
---|
[503] | 90 | IF( l_trddyn ) THEN ! Temporary saving of ua and va trends (l_trddyn) |
---|
[3294] | 91 | CALL wrk_alloc( jpi,jpj,jpk, ztrdu, ztrdv ) |
---|
[3764] | 92 | ztrdu(:,:,:) = ua(:,:,:) |
---|
| 93 | ztrdv(:,:,:) = va(:,:,:) |
---|
| 94 | ENDIF |
---|
[2528] | 95 | ! |
---|
[3294] | 96 | SELECT CASE ( nhpg ) ! Hydrostatic pressure gradient computation |
---|
[503] | 97 | CASE ( 0 ) ; CALL hpg_zco ( kt ) ! z-coordinate |
---|
| 98 | CASE ( 1 ) ; CALL hpg_zps ( kt ) ! z-coordinate plus partial steps (interpolation) |
---|
| 99 | CASE ( 2 ) ; CALL hpg_sco ( kt ) ! s-coordinate (standard jacobian formulation) |
---|
[3294] | 100 | CASE ( 3 ) ; CALL hpg_djc ( kt ) ! s-coordinate (Density Jacobian with Cubic polynomial) |
---|
| 101 | CASE ( 4 ) ; CALL hpg_prj ( kt ) ! s-coordinate (Pressure Jacobian scheme) |
---|
[5120] | 102 | CASE ( 5 ) ; CALL hpg_isf ( kt ) ! s-coordinate similar to sco modify for ice shelf |
---|
[455] | 103 | END SELECT |
---|
[2528] | 104 | ! |
---|
[503] | 105 | IF( l_trddyn ) THEN ! save the hydrostatic pressure gradient trends for momentum trend diagnostics |
---|
[455] | 106 | ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:) |
---|
| 107 | ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:) |
---|
[4990] | 108 | CALL trd_dyn( ztrdu, ztrdv, jpdyn_hpg, kt ) |
---|
[3294] | 109 | CALL wrk_dealloc( jpi,jpj,jpk, ztrdu, ztrdv ) |
---|
[3764] | 110 | ENDIF |
---|
[503] | 111 | ! |
---|
| 112 | IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' hpg - Ua: ', mask1=umask, & |
---|
| 113 | & tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) |
---|
| 114 | ! |
---|
[3294] | 115 | IF( nn_timing == 1 ) CALL timing_stop('dyn_hpg') |
---|
[2715] | 116 | ! |
---|
[455] | 117 | END SUBROUTINE dyn_hpg |
---|
| 118 | |
---|
| 119 | |
---|
[2528] | 120 | SUBROUTINE dyn_hpg_init |
---|
[455] | 121 | !!---------------------------------------------------------------------- |
---|
[2528] | 122 | !! *** ROUTINE dyn_hpg_init *** |
---|
[455] | 123 | !! |
---|
| 124 | !! ** Purpose : initializations for the hydrostatic pressure gradient |
---|
| 125 | !! computation and consistency control |
---|
| 126 | !! |
---|
[1601] | 127 | !! ** Action : Read the namelist namdyn_hpg and check the consistency |
---|
[455] | 128 | !! with the type of vertical coordinate used (zco, zps, sco) |
---|
| 129 | !!---------------------------------------------------------------------- |
---|
| 130 | INTEGER :: ioptio = 0 ! temporary integer |
---|
[4147] | 131 | INTEGER :: ios ! Local integer output status for namelist read |
---|
[1601] | 132 | !! |
---|
[3294] | 133 | NAMELIST/namdyn_hpg/ ln_hpg_zco, ln_hpg_zps, ln_hpg_sco, & |
---|
[5120] | 134 | & ln_hpg_djc, ln_hpg_prj, ln_hpg_isf, ln_dynhpg_imp |
---|
[455] | 135 | !!---------------------------------------------------------------------- |
---|
[2528] | 136 | ! |
---|
[4147] | 137 | REWIND( numnam_ref ) ! Namelist namdyn_hpg in reference namelist : Hydrostatic pressure gradient |
---|
| 138 | READ ( numnam_ref, namdyn_hpg, IOSTAT = ios, ERR = 901) |
---|
| 139 | 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in reference namelist', lwp ) |
---|
| 140 | |
---|
| 141 | REWIND( numnam_cfg ) ! Namelist namdyn_hpg in configuration namelist : Hydrostatic pressure gradient |
---|
| 142 | READ ( numnam_cfg, namdyn_hpg, IOSTAT = ios, ERR = 902 ) |
---|
| 143 | 902 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_hpg in configuration namelist', lwp ) |
---|
[4624] | 144 | IF(lwm) WRITE ( numond, namdyn_hpg ) |
---|
[2528] | 145 | ! |
---|
| 146 | IF(lwp) THEN ! Control print |
---|
[455] | 147 | WRITE(numout,*) |
---|
[2528] | 148 | WRITE(numout,*) 'dyn_hpg_init : hydrostatic pressure gradient initialisation' |
---|
| 149 | WRITE(numout,*) '~~~~~~~~~~~~' |
---|
[1601] | 150 | WRITE(numout,*) ' Namelist namdyn_hpg : choice of hpg scheme' |
---|
| 151 | WRITE(numout,*) ' z-coord. - full steps ln_hpg_zco = ', ln_hpg_zco |
---|
| 152 | WRITE(numout,*) ' z-coord. - partial steps (interpolation) ln_hpg_zps = ', ln_hpg_zps |
---|
| 153 | WRITE(numout,*) ' s-coord. (standard jacobian formulation) ln_hpg_sco = ', ln_hpg_sco |
---|
[5120] | 154 | WRITE(numout,*) ' s-coord. (standard jacobian formulation) for isf ln_hpg_isf = ', ln_hpg_isf |
---|
[1601] | 155 | WRITE(numout,*) ' s-coord. (Density Jacobian: Cubic polynomial) ln_hpg_djc = ', ln_hpg_djc |
---|
[3294] | 156 | WRITE(numout,*) ' s-coord. (Pressure Jacobian: Cubic polynomial) ln_hpg_prj = ', ln_hpg_prj |
---|
[1601] | 157 | WRITE(numout,*) ' time stepping: centered (F) or semi-implicit (T) ln_dynhpg_imp = ', ln_dynhpg_imp |
---|
[455] | 158 | ENDIF |
---|
[2528] | 159 | ! |
---|
[3294] | 160 | IF( ln_hpg_djc ) & |
---|
| 161 | & CALL ctl_stop('dyn_hpg_init : Density Jacobian: Cubic polynominal method & |
---|
| 162 | & currently disabled (bugs under investigation). Please select & |
---|
| 163 | & either ln_hpg_sco or ln_hpg_prj instead') |
---|
[2528] | 164 | ! |
---|
[5120] | 165 | IF( lk_vvl .AND. .NOT. (ln_hpg_sco.OR.ln_hpg_prj.OR.ln_hpg_isf) ) & |
---|
[3294] | 166 | & CALL ctl_stop('dyn_hpg_init : variable volume key_vvl requires:& |
---|
| 167 | & the standard jacobian formulation hpg_sco or & |
---|
| 168 | & the pressure jacobian formulation hpg_prj') |
---|
[5120] | 169 | |
---|
| 170 | IF( ln_hpg_isf .AND. .NOT. ln_isfcav ) & |
---|
| 171 | & CALL ctl_stop( ' hpg_isf not available if ln_isfcav = false ' ) |
---|
| 172 | IF( .NOT. ln_hpg_isf .AND. ln_isfcav ) & |
---|
| 173 | & CALL ctl_stop( 'Only hpg_isf has been corrected to work with ice shelf cavity.' ) |
---|
[3294] | 174 | ! |
---|
[503] | 175 | ! ! Set nhpg from ln_hpg_... flags |
---|
[455] | 176 | IF( ln_hpg_zco ) nhpg = 0 |
---|
| 177 | IF( ln_hpg_zps ) nhpg = 1 |
---|
| 178 | IF( ln_hpg_sco ) nhpg = 2 |
---|
[3294] | 179 | IF( ln_hpg_djc ) nhpg = 3 |
---|
| 180 | IF( ln_hpg_prj ) nhpg = 4 |
---|
[5120] | 181 | IF( ln_hpg_isf ) nhpg = 5 |
---|
[2528] | 182 | ! |
---|
[3294] | 183 | ! ! Consistency check |
---|
[3764] | 184 | ioptio = 0 |
---|
[455] | 185 | IF( ln_hpg_zco ) ioptio = ioptio + 1 |
---|
| 186 | IF( ln_hpg_zps ) ioptio = ioptio + 1 |
---|
| 187 | IF( ln_hpg_sco ) ioptio = ioptio + 1 |
---|
| 188 | IF( ln_hpg_djc ) ioptio = ioptio + 1 |
---|
[3294] | 189 | IF( ln_hpg_prj ) ioptio = ioptio + 1 |
---|
[5120] | 190 | IF( ln_hpg_isf ) ioptio = ioptio + 1 |
---|
[2715] | 191 | IF( ioptio /= 1 ) CALL ctl_stop( 'NO or several hydrostatic pressure gradient options used' ) |
---|
[5120] | 192 | ! |
---|
| 193 | ! initialisation of ice load |
---|
| 194 | riceload(:,:)=0.0 |
---|
[503] | 195 | ! |
---|
[2528] | 196 | END SUBROUTINE dyn_hpg_init |
---|
[455] | 197 | |
---|
| 198 | |
---|
| 199 | SUBROUTINE hpg_zco( kt ) |
---|
| 200 | !!--------------------------------------------------------------------- |
---|
| 201 | !! *** ROUTINE hpg_zco *** |
---|
| 202 | !! |
---|
| 203 | !! ** Method : z-coordinate case, levels are horizontal surfaces. |
---|
| 204 | !! The now hydrostatic pressure gradient at a given level, jk, |
---|
| 205 | !! is computed by taking the vertical integral of the in-situ |
---|
| 206 | !! density gradient along the model level from the suface to that |
---|
| 207 | !! level: zhpi = grav ..... |
---|
| 208 | !! zhpj = grav ..... |
---|
[3] | 209 | !! add it to the general momentum trend (ua,va). |
---|
[455] | 210 | !! ua = ua - 1/e1u * zhpi |
---|
| 211 | !! va = va - 1/e2v * zhpj |
---|
[3764] | 212 | !! |
---|
[3] | 213 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
[503] | 214 | !!---------------------------------------------------------------------- |
---|
| 215 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 216 | !! |
---|
| 217 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 218 | REAL(wp) :: zcoef0, zcoef1 ! temporary scalars |
---|
[3764] | 219 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
---|
[3] | 220 | !!---------------------------------------------------------------------- |
---|
[3764] | 221 | ! |
---|
[3294] | 222 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
| 223 | ! |
---|
[3] | 224 | IF( kt == nit000 ) THEN |
---|
| 225 | IF(lwp) WRITE(numout,*) |
---|
[455] | 226 | IF(lwp) WRITE(numout,*) 'dyn:hpg_zco : hydrostatic pressure gradient trend' |
---|
| 227 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate case ' |
---|
[3] | 228 | ENDIF |
---|
| 229 | |
---|
[3764] | 230 | zcoef0 = - grav * 0.5_wp ! Local constant initialization |
---|
| 231 | |
---|
[455] | 232 | ! Surface value |
---|
[3] | 233 | DO jj = 2, jpjm1 |
---|
| 234 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[455] | 235 | zcoef1 = zcoef0 * fse3w(ji,jj,1) |
---|
| 236 | ! hydrostatic pressure gradient |
---|
| 237 | zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj,1) - rhd(ji,jj,1) ) / e1u(ji,jj) |
---|
| 238 | zhpj(ji,jj,1) = zcoef1 * ( rhd(ji,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj) |
---|
[3] | 239 | ! add to the general momentum trend |
---|
[455] | 240 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
---|
| 241 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
---|
| 242 | END DO |
---|
| 243 | END DO |
---|
[3294] | 244 | |
---|
[503] | 245 | ! |
---|
[455] | 246 | ! interior value (2=<jk=<jpkm1) |
---|
[3] | 247 | DO jk = 2, jpkm1 |
---|
[455] | 248 | DO jj = 2, jpjm1 |
---|
[3] | 249 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[455] | 250 | zcoef1 = zcoef0 * fse3w(ji,jj,jk) |
---|
| 251 | ! hydrostatic pressure gradient |
---|
| 252 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
---|
| 253 | & + zcoef1 * ( ( rhd(ji+1,jj,jk)+rhd(ji+1,jj,jk-1) ) & |
---|
| 254 | & - ( rhd(ji ,jj,jk)+rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj) |
---|
| 255 | |
---|
| 256 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
---|
| 257 | & + zcoef1 * ( ( rhd(ji,jj+1,jk)+rhd(ji,jj+1,jk-1) ) & |
---|
| 258 | & - ( rhd(ji,jj, jk)+rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj) |
---|
[3] | 259 | ! add to the general momentum trend |
---|
[455] | 260 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
---|
| 261 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
---|
[3] | 262 | END DO |
---|
| 263 | END DO |
---|
| 264 | END DO |
---|
[503] | 265 | ! |
---|
[3294] | 266 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
| 267 | ! |
---|
[455] | 268 | END SUBROUTINE hpg_zco |
---|
[216] | 269 | |
---|
[3] | 270 | |
---|
[455] | 271 | SUBROUTINE hpg_zps( kt ) |
---|
[3] | 272 | !!--------------------------------------------------------------------- |
---|
[455] | 273 | !! *** ROUTINE hpg_zps *** |
---|
[3764] | 274 | !! |
---|
[455] | 275 | !! ** Method : z-coordinate plus partial steps case. blahblah... |
---|
[3764] | 276 | !! |
---|
[3] | 277 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
[3764] | 278 | !!---------------------------------------------------------------------- |
---|
[503] | 279 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 280 | !! |
---|
| 281 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 282 | INTEGER :: iku, ikv ! temporary integers |
---|
| 283 | REAL(wp) :: zcoef0, zcoef1, zcoef2, zcoef3 ! temporary scalars |
---|
[3764] | 284 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
---|
[3] | 285 | !!---------------------------------------------------------------------- |
---|
[3294] | 286 | ! |
---|
| 287 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
| 288 | ! |
---|
[3] | 289 | IF( kt == nit000 ) THEN |
---|
| 290 | IF(lwp) WRITE(numout,*) |
---|
[455] | 291 | IF(lwp) WRITE(numout,*) 'dyn:hpg_zps : hydrostatic pressure gradient trend' |
---|
[503] | 292 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ z-coordinate with partial steps - vector optimization' |
---|
[3] | 293 | ENDIF |
---|
| 294 | |
---|
[3294] | 295 | |
---|
[503] | 296 | ! Local constant initialization |
---|
[2528] | 297 | zcoef0 = - grav * 0.5_wp |
---|
[3] | 298 | |
---|
[2528] | 299 | ! Surface value (also valid in partial step case) |
---|
[3] | 300 | DO jj = 2, jpjm1 |
---|
| 301 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[170] | 302 | zcoef1 = zcoef0 * fse3w(ji,jj,1) |
---|
[3] | 303 | ! hydrostatic pressure gradient |
---|
[455] | 304 | zhpi(ji,jj,1) = zcoef1 * ( rhd(ji+1,jj ,1) - rhd(ji,jj,1) ) / e1u(ji,jj) |
---|
| 305 | zhpj(ji,jj,1) = zcoef1 * ( rhd(ji ,jj+1,1) - rhd(ji,jj,1) ) / e2v(ji,jj) |
---|
[3] | 306 | ! add to the general momentum trend |
---|
| 307 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
---|
| 308 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
---|
| 309 | END DO |
---|
| 310 | END DO |
---|
| 311 | |
---|
[3294] | 312 | |
---|
[503] | 313 | ! interior value (2=<jk=<jpkm1) |
---|
[3] | 314 | DO jk = 2, jpkm1 |
---|
| 315 | DO jj = 2, jpjm1 |
---|
| 316 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[170] | 317 | zcoef1 = zcoef0 * fse3w(ji,jj,jk) |
---|
[3] | 318 | ! hydrostatic pressure gradient |
---|
| 319 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
---|
[455] | 320 | & + zcoef1 * ( ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) ) & |
---|
| 321 | & - ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) ) ) / e1u(ji,jj) |
---|
[3] | 322 | |
---|
| 323 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
---|
[455] | 324 | & + zcoef1 * ( ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) ) & |
---|
| 325 | & - ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) ) ) / e2v(ji,jj) |
---|
[3] | 326 | ! add to the general momentum trend |
---|
| 327 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
---|
| 328 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
---|
[455] | 329 | END DO |
---|
[3] | 330 | END DO |
---|
| 331 | END DO |
---|
| 332 | |
---|
[3294] | 333 | |
---|
[2528] | 334 | ! partial steps correction at the last level (use gru & grv computed in zpshde.F90) |
---|
[3] | 335 | DO jj = 2, jpjm1 |
---|
| 336 | DO ji = 2, jpim1 |
---|
[2528] | 337 | iku = mbku(ji,jj) |
---|
| 338 | ikv = mbkv(ji,jj) |
---|
[3] | 339 | zcoef2 = zcoef0 * MIN( fse3w(ji,jj,iku), fse3w(ji+1,jj ,iku) ) |
---|
| 340 | zcoef3 = zcoef0 * MIN( fse3w(ji,jj,ikv), fse3w(ji ,jj+1,ikv) ) |
---|
[2528] | 341 | IF( iku > 1 ) THEN ! on i-direction (level 2 or more) |
---|
| 342 | ua (ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) ! subtract old value |
---|
| 343 | zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) & ! compute the new one |
---|
| 344 | & + zcoef2 * ( rhd(ji+1,jj,iku-1) - rhd(ji,jj,iku-1) + gru(ji,jj) ) / e1u(ji,jj) |
---|
| 345 | ua (ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) ! add the new one to the general momentum trend |
---|
[3] | 346 | ENDIF |
---|
[2528] | 347 | IF( ikv > 1 ) THEN ! on j-direction (level 2 or more) |
---|
| 348 | va (ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) ! subtract old value |
---|
| 349 | zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) & ! compute the new one |
---|
| 350 | & + zcoef3 * ( rhd(ji,jj+1,ikv-1) - rhd(ji,jj,ikv-1) + grv(ji,jj) ) / e2v(ji,jj) |
---|
| 351 | va (ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) ! add the new one to the general momentum trend |
---|
[3] | 352 | ENDIF |
---|
| 353 | END DO |
---|
| 354 | END DO |
---|
[503] | 355 | ! |
---|
[3294] | 356 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
| 357 | ! |
---|
[455] | 358 | END SUBROUTINE hpg_zps |
---|
[216] | 359 | |
---|
[455] | 360 | SUBROUTINE hpg_sco( kt ) |
---|
[3] | 361 | !!--------------------------------------------------------------------- |
---|
[455] | 362 | !! *** ROUTINE hpg_sco *** |
---|
[3] | 363 | !! |
---|
[455] | 364 | !! ** Method : s-coordinate case. Jacobian scheme. |
---|
| 365 | !! The now hydrostatic pressure gradient at a given level, jk, |
---|
| 366 | !! is computed by taking the vertical integral of the in-situ |
---|
[3] | 367 | !! density gradient along the model level from the suface to that |
---|
[455] | 368 | !! level. s-coordinates (ln_sco): a corrective term is added |
---|
| 369 | !! to the horizontal pressure gradient : |
---|
| 370 | !! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ] |
---|
| 371 | !! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ] |
---|
[3] | 372 | !! add it to the general momentum trend (ua,va). |
---|
[455] | 373 | !! ua = ua - 1/e1u * zhpi |
---|
| 374 | !! va = va - 1/e2v * zhpj |
---|
[3] | 375 | !! |
---|
| 376 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
[503] | 377 | !!---------------------------------------------------------------------- |
---|
| 378 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 379 | !! |
---|
[5120] | 380 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 381 | REAL(wp) :: zcoef0, zuap, zvap, znad ! temporary scalars |
---|
| 382 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
---|
| 383 | !!---------------------------------------------------------------------- |
---|
| 384 | ! |
---|
| 385 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
| 386 | ! |
---|
| 387 | IF( kt == nit000 ) THEN |
---|
| 388 | IF(lwp) WRITE(numout,*) |
---|
| 389 | IF(lwp) WRITE(numout,*) 'dyn:hpg_sco : hydrostatic pressure gradient trend' |
---|
| 390 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used' |
---|
| 391 | ENDIF |
---|
| 392 | |
---|
| 393 | ! Local constant initialization |
---|
| 394 | zcoef0 = - grav * 0.5_wp |
---|
| 395 | ! To use density and not density anomaly |
---|
| 396 | IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume |
---|
| 397 | ELSE ; znad = 0._wp ! Fixed volume |
---|
| 398 | ENDIF |
---|
| 399 | |
---|
| 400 | ! Surface value |
---|
| 401 | DO jj = 2, jpjm1 |
---|
| 402 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 403 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 404 | zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( fse3w(ji+1,jj ,1) * ( znad + rhd(ji+1,jj ,1) ) & |
---|
| 405 | & - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) |
---|
| 406 | zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( fse3w(ji ,jj+1,1) * ( znad + rhd(ji ,jj+1,1) ) & |
---|
| 407 | & - fse3w(ji ,jj ,1) * ( znad + rhd(ji ,jj ,1) ) ) |
---|
| 408 | ! s-coordinate pressure gradient correction |
---|
| 409 | zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
| 410 | & * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj) |
---|
| 411 | zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
| 412 | & * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj) |
---|
| 413 | ! add to the general momentum trend |
---|
| 414 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) + zuap |
---|
| 415 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) + zvap |
---|
| 416 | END DO |
---|
| 417 | END DO |
---|
| 418 | |
---|
| 419 | ! interior value (2=<jk=<jpkm1) |
---|
| 420 | DO jk = 2, jpkm1 |
---|
| 421 | DO jj = 2, jpjm1 |
---|
| 422 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 423 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 424 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + zcoef0 / e1u(ji,jj) & |
---|
| 425 | & * ( fse3w(ji+1,jj,jk) * ( rhd(ji+1,jj,jk) + rhd(ji+1,jj,jk-1) + 2*znad ) & |
---|
| 426 | & - fse3w(ji ,jj,jk) * ( rhd(ji ,jj,jk) + rhd(ji ,jj,jk-1) + 2*znad ) ) |
---|
| 427 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) + zcoef0 / e2v(ji,jj) & |
---|
| 428 | & * ( fse3w(ji,jj+1,jk) * ( rhd(ji,jj+1,jk) + rhd(ji,jj+1,jk-1) + 2*znad ) & |
---|
| 429 | & - fse3w(ji,jj ,jk) * ( rhd(ji,jj, jk) + rhd(ji,jj ,jk-1) + 2*znad ) ) |
---|
| 430 | ! s-coordinate pressure gradient correction |
---|
| 431 | zuap = -zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 432 | & * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) |
---|
| 433 | zvap = -zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 434 | & * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) |
---|
| 435 | ! add to the general momentum trend |
---|
| 436 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) + zuap |
---|
| 437 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) + zvap |
---|
| 438 | END DO |
---|
| 439 | END DO |
---|
| 440 | END DO |
---|
| 441 | ! |
---|
| 442 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj ) |
---|
| 443 | ! |
---|
| 444 | END SUBROUTINE hpg_sco |
---|
| 445 | |
---|
| 446 | SUBROUTINE hpg_isf( kt ) |
---|
| 447 | !!--------------------------------------------------------------------- |
---|
| 448 | !! *** ROUTINE hpg_sco *** |
---|
| 449 | !! |
---|
| 450 | !! ** Method : s-coordinate case. Jacobian scheme. |
---|
| 451 | !! The now hydrostatic pressure gradient at a given level, jk, |
---|
| 452 | !! is computed by taking the vertical integral of the in-situ |
---|
| 453 | !! density gradient along the model level from the suface to that |
---|
| 454 | !! level. s-coordinates (ln_sco): a corrective term is added |
---|
| 455 | !! to the horizontal pressure gradient : |
---|
| 456 | !! zhpi = grav ..... + 1/e1u mi(rhd) di[ grav dep3w ] |
---|
| 457 | !! zhpj = grav ..... + 1/e2v mj(rhd) dj[ grav dep3w ] |
---|
| 458 | !! add it to the general momentum trend (ua,va). |
---|
| 459 | !! ua = ua - 1/e1u * zhpi |
---|
| 460 | !! va = va - 1/e2v * zhpj |
---|
| 461 | !! iceload is added and partial cell case are added to the top and bottom |
---|
| 462 | !! |
---|
| 463 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
| 464 | !!---------------------------------------------------------------------- |
---|
| 465 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 466 | !! |
---|
[4990] | 467 | INTEGER :: ji, jj, jk, iku, ikv, ikt, iktp1i, iktp1j ! dummy loop indices |
---|
| 468 | REAL(wp) :: zcoef0, zuap, zvap, znad, ze3wu, ze3wv, zuapint, zvapint, zhpjint, zhpiint, zdzwt, zdzwtjp1, zdzwtip1 ! temporary scalars |
---|
| 469 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj, zrhd |
---|
| 470 | REAL(wp), POINTER, DIMENSION(:,:,:) :: ztstop |
---|
| 471 | REAL(wp), POINTER, DIMENSION(:,:) :: ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj |
---|
[3] | 472 | !!---------------------------------------------------------------------- |
---|
[3294] | 473 | ! |
---|
[4990] | 474 | CALL wrk_alloc( jpi,jpj, 2, ztstop) |
---|
| 475 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zhpj, zrhd) |
---|
| 476 | CALL wrk_alloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj) |
---|
[3294] | 477 | ! |
---|
[4990] | 478 | IF( kt == nit000 ) THEN |
---|
[3] | 479 | IF(lwp) WRITE(numout,*) |
---|
[5120] | 480 | IF(lwp) WRITE(numout,*) 'dyn:hpg_isf : hydrostatic pressure gradient trend for ice shelf' |
---|
[455] | 481 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, OPA original scheme used' |
---|
[3] | 482 | ENDIF |
---|
| 483 | |
---|
[503] | 484 | ! Local constant initialization |
---|
[2528] | 485 | zcoef0 = - grav * 0.5_wp |
---|
[592] | 486 | ! To use density and not density anomaly |
---|
[4990] | 487 | ! IF ( lk_vvl ) THEN ; znad = 1._wp ! Variable volume |
---|
| 488 | ! ELSE ; znad = 0._wp ! Fixed volume |
---|
| 489 | ! ENDIF |
---|
| 490 | znad=1._wp |
---|
| 491 | ! iniitialised to 0. zhpi zhpi |
---|
| 492 | zhpi(:,:,:)=0._wp ; zhpj(:,:,:)=0._wp |
---|
[455] | 493 | |
---|
[4990] | 494 | !================================================================================== |
---|
| 495 | !=====Compute iceload and contribution of the half first wet layer ================= |
---|
| 496 | !=================================================================================== |
---|
| 497 | |
---|
| 498 | ! assume water displaced by the ice shelf is at T=-1.9 and S=34.4 (rude) |
---|
| 499 | ztstop(:,:,1)=-1.9_wp ; ztstop(:,:,2)=34.4_wp |
---|
| 500 | |
---|
| 501 | ! compute density of the water displaced by the ice shelf |
---|
| 502 | zrhd = rhd ! save rhd |
---|
| 503 | DO jk = 1, jpk |
---|
| 504 | zdept(:,:)=gdept_1d(jk) |
---|
| 505 | CALL eos(ztstop(:,:,:),zdept(:,:),rhd(:,:,jk)) |
---|
| 506 | END DO |
---|
| 507 | WHERE ( tmask(:,:,:) == 1._wp) |
---|
| 508 | rhd(:,:,:) = zrhd(:,:,:) ! replace wet cell by the saved rhd |
---|
| 509 | END WHERE |
---|
| 510 | |
---|
| 511 | ! compute rhd at the ice/oce interface (ice shelf side) |
---|
| 512 | CALL eos(ztstop,risfdep,zrhdtop_isf) |
---|
| 513 | |
---|
| 514 | ! compute rhd at the ice/oce interface (ocean side) |
---|
| 515 | DO ji=1,jpi |
---|
| 516 | DO jj=1,jpj |
---|
| 517 | ikt=mikt(ji,jj) |
---|
| 518 | ztstop(ji,jj,1)=tsn(ji,jj,ikt,1) |
---|
| 519 | ztstop(ji,jj,2)=tsn(ji,jj,ikt,2) |
---|
| 520 | END DO |
---|
| 521 | END DO |
---|
| 522 | CALL eos(ztstop,risfdep,zrhdtop_oce) |
---|
| 523 | ! |
---|
| 524 | ! Surface value + ice shelf gradient |
---|
| 525 | ! compute pressure due to ice shelf load (used to compute hpgi/j for all the level from 1 to miku/v) |
---|
| 526 | ziceload = 0._wp |
---|
| 527 | DO jj = 1, jpj |
---|
| 528 | DO ji = 1, jpi ! vector opt. |
---|
| 529 | ikt=mikt(ji,jj) |
---|
| 530 | ziceload(ji,jj) = ziceload(ji,jj) + (znad + rhd(ji,jj,1) ) * fse3w(ji,jj,1) * (1._wp - tmask(ji,jj,1)) |
---|
| 531 | DO jk=2,ikt-1 |
---|
| 532 | ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + rhd(ji,jj,jk-1) + rhd(ji,jj,jk)) * fse3w(ji,jj,jk) & |
---|
| 533 | & * (1._wp - tmask(ji,jj,jk)) |
---|
| 534 | END DO |
---|
| 535 | IF (ikt .GE. 2) ziceload(ji,jj) = ziceload(ji,jj) + (2._wp * znad + zrhdtop_isf(ji,jj) + rhd(ji,jj,ikt-1)) & |
---|
| 536 | & * ( risfdep(ji,jj) - gdept_1d(ikt-1) ) |
---|
| 537 | END DO |
---|
| 538 | END DO |
---|
| 539 | riceload(:,:) = 0.0_wp ; riceload(:,:)=ziceload(:,:) ! need to be saved for diaar5 |
---|
| 540 | ! compute zp from z=0 to first T wet point (correction due to zps not yet applied) |
---|
[455] | 541 | DO jj = 2, jpjm1 |
---|
[3764] | 542 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[4990] | 543 | ikt=mikt(ji,jj) ; iktp1i=mikt(ji+1,jj); iktp1j=mikt(ji,jj+1) |
---|
| 544 | ! hydrostatic pressure gradient along s-surfaces and ice shelf pressure |
---|
| 545 | ! we assume ISF is in isostatic equilibrium |
---|
| 546 | zhpi(ji,jj,1) = zcoef0 / e1u(ji,jj) * ( 0.5_wp * fse3w(ji+1,jj ,iktp1i) & |
---|
| 547 | & * ( 2._wp * znad + rhd(ji+1,jj ,iktp1i) + zrhdtop_oce(ji+1,jj ) ) & |
---|
| 548 | & - 0.5_wp * fse3w(ji ,jj ,ikt ) & |
---|
| 549 | & * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) & |
---|
| 550 | & + ( ziceload(ji+1,jj) - ziceload(ji,jj)) ) |
---|
| 551 | zhpj(ji,jj,1) = zcoef0 / e2v(ji,jj) * ( 0.5_wp * fse3w(ji ,jj+1,iktp1j) & |
---|
| 552 | & * ( 2._wp * znad + rhd(ji ,jj+1,iktp1j) + zrhdtop_oce(ji ,jj+1) ) & |
---|
| 553 | & - 0.5_wp * fse3w(ji ,jj ,ikt ) & |
---|
| 554 | & * ( 2._wp * znad + rhd(ji ,jj ,ikt ) + zrhdtop_oce(ji ,jj ) ) & |
---|
| 555 | & + ( ziceload(ji,jj+1) - ziceload(ji,jj) ) ) |
---|
| 556 | ! s-coordinate pressure gradient correction (=0 if z coordinate) |
---|
[2528] | 557 | zuap = -zcoef0 * ( rhd (ji+1,jj,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
[455] | 558 | & * ( fsde3w(ji+1,jj,1) - fsde3w(ji,jj,1) ) / e1u(ji,jj) |
---|
[2528] | 559 | zvap = -zcoef0 * ( rhd (ji,jj+1,1) + rhd (ji,jj,1) + 2._wp * znad ) & |
---|
[455] | 560 | & * ( fsde3w(ji,jj+1,1) - fsde3w(ji,jj,1) ) / e2v(ji,jj) |
---|
| 561 | ! add to the general momentum trend |
---|
[4990] | 562 | ua(ji,jj,1) = ua(ji,jj,1) + (zhpi(ji,jj,1) + zuap) * umask(ji,jj,1) |
---|
| 563 | va(ji,jj,1) = va(ji,jj,1) + (zhpj(ji,jj,1) + zvap) * vmask(ji,jj,1) |
---|
[3764] | 564 | END DO |
---|
| 565 | END DO |
---|
[4990] | 566 | !================================================================================== |
---|
| 567 | !===== Compute partial cell contribution for the top cell ========================= |
---|
| 568 | !================================================================================== |
---|
| 569 | DO jj = 2, jpjm1 |
---|
| 570 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 571 | iku = miku(ji,jj) ; |
---|
| 572 | zpshpi(ji,jj)=0.0_wp ; zpshpj(ji,jj)=0.0_wp |
---|
| 573 | ze3wu = (gdepw_0(ji+1,jj,iku+1) - gdept_0(ji+1,jj,iku)) - (gdepw_0(ji,jj,iku+1) - gdept_0(ji,jj,iku)) |
---|
| 574 | ! u direction |
---|
| 575 | IF ( iku .GT. 1 ) THEN |
---|
| 576 | ! case iku |
---|
| 577 | zhpi(ji,jj,iku) = zcoef0 / e1u(ji,jj) * ze3wu & |
---|
| 578 | & * ( rhd (ji+1,jj,iku) + rhd (ji,jj,iku) & |
---|
| 579 | & + SIGN(1._wp,ze3wu) * grui(ji,jj) + 2._wp * znad ) |
---|
| 580 | ! corrective term ( = 0 if z coordinate ) |
---|
| 581 | zuap = -zcoef0 * ( arui(ji,jj) + 2._wp * znad ) * gzui(ji,jj) / e1u(ji,jj) |
---|
| 582 | ! zhpi will be added in interior loop |
---|
| 583 | ua(ji,jj,iku) = ua(ji,jj,iku) + zuap |
---|
| 584 | ! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure |
---|
| 585 | IF (mbku(ji,jj) == iku + 1) zpshpi(ji,jj) = zhpi(ji,jj,iku) |
---|
[3764] | 586 | |
---|
[4990] | 587 | ! case iku + 1 (remove the zphi term added in the interior loop and compute the one corrected for zps) |
---|
| 588 | zhpiint = zcoef0 / e1u(ji,jj) & |
---|
| 589 | & * ( fse3w(ji+1,jj ,iku+1) * ( (rhd(ji+1,jj,iku+1) + znad) & |
---|
| 590 | & + (rhd(ji+1,jj,iku ) + znad) ) * tmask(ji+1,jj,iku) & |
---|
| 591 | & - fse3w(ji ,jj ,iku+1) * ( (rhd(ji ,jj,iku+1) + znad) & |
---|
| 592 | & + (rhd(ji ,jj,iku ) + znad) ) * tmask(ji ,jj,iku) ) |
---|
| 593 | zhpi(ji,jj,iku+1) = zcoef0 / e1u(ji,jj) * ge3rui(ji,jj) - zhpiint |
---|
| 594 | END IF |
---|
| 595 | |
---|
| 596 | ! v direction |
---|
| 597 | ikv = mikv(ji,jj) |
---|
| 598 | ze3wv = (gdepw_0(ji,jj+1,ikv+1) - gdept_0(ji,jj+1,ikv)) - (gdepw_0(ji,jj,ikv+1) - gdept_0(ji,jj,ikv)) |
---|
| 599 | IF ( ikv .GT. 1 ) THEN |
---|
| 600 | ! case ikv |
---|
| 601 | zhpj(ji,jj,ikv) = zcoef0 / e2v(ji,jj) * ze3wv & |
---|
| 602 | & * ( rhd(ji,jj+1,ikv) + rhd (ji,jj,ikv) & |
---|
| 603 | & + SIGN(1._wp,ze3wv) * grvi(ji,jj) + 2._wp * znad ) |
---|
| 604 | ! corrective term ( = 0 if z coordinate ) |
---|
| 605 | zvap = -zcoef0 * ( arvi(ji,jj) + 2._wp * znad ) * gzvi(ji,jj) / e2v(ji,jj) |
---|
| 606 | ! zhpi will be added in interior loop |
---|
| 607 | va(ji,jj,ikv) = va(ji,jj,ikv) + zvap |
---|
| 608 | ! in case of 2 cell water column, need to save the pressure gradient to compute the bottom pressure |
---|
| 609 | IF (mbkv(ji,jj) == ikv + 1) zpshpj(ji,jj) = zhpj(ji,jj,ikv) |
---|
| 610 | |
---|
| 611 | ! case ikv + 1 (remove the zphj term added in the interior loop and compute the one corrected for zps) |
---|
| 612 | zhpjint = zcoef0 / e2v(ji,jj) & |
---|
| 613 | & * ( fse3w(ji ,jj+1,ikv+1) * ( (rhd(ji,jj+1,ikv+1) + znad) & |
---|
| 614 | & + (rhd(ji,jj+1,ikv ) + znad) ) * tmask(ji,jj+1,ikv) & |
---|
| 615 | & - fse3w(ji ,jj ,ikv+1) * ( (rhd(ji,jj ,ikv+1) + znad) & |
---|
| 616 | & + (rhd(ji,jj ,ikv ) + znad) ) * tmask(ji,jj ,ikv) ) |
---|
| 617 | zhpj(ji,jj,ikv+1) = zcoef0 / e2v(ji,jj) * ge3rvi(ji,jj) - zhpjint |
---|
| 618 | END IF |
---|
| 619 | END DO |
---|
| 620 | END DO |
---|
| 621 | |
---|
| 622 | !================================================================================== |
---|
| 623 | !===== Compute interior value ===================================================== |
---|
| 624 | !================================================================================== |
---|
| 625 | |
---|
| 626 | DO jj = 2, jpjm1 |
---|
| 627 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 628 | iku=miku(ji,jj); ikv=mikv(ji,jj) |
---|
| 629 | DO jk = 2, jpkm1 |
---|
[455] | 630 | ! hydrostatic pressure gradient along s-surfaces |
---|
[4990] | 631 | ! zhpi is masked for the first wet cell (contribution already done in the upper bloc) |
---|
| 632 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk) + zhpi(ji,jj,jk-1) & |
---|
| 633 | & + zcoef0 / e1u(ji,jj) & |
---|
| 634 | & * ( fse3w(ji+1,jj ,jk) * ( (rhd(ji+1,jj,jk ) + znad) & |
---|
| 635 | & + (rhd(ji+1,jj,jk-1) + znad) ) * tmask(ji+1,jj,jk-1) & |
---|
| 636 | & - fse3w(ji ,jj ,jk) * ( (rhd(ji ,jj,jk ) + znad) & |
---|
| 637 | & + (rhd(ji ,jj,jk-1) + znad) ) * tmask(ji ,jj,jk-1) ) |
---|
[455] | 638 | ! s-coordinate pressure gradient correction |
---|
[4990] | 639 | ! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc) |
---|
| 640 | zuap = - zcoef0 * ( rhd (ji+1,jj ,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 641 | & * ( fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk) ) / e1u(ji,jj) * umask(ji,jj,jk-1) |
---|
| 642 | ua(ji,jj,jk) = ua(ji,jj,jk) + ( zhpi(ji,jj,jk) + zuap) * umask(ji,jj,jk) |
---|
| 643 | |
---|
| 644 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 645 | ! zhpi is masked for the first wet cell (contribution already done in the upper bloc) |
---|
| 646 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk) + zhpj(ji,jj,jk-1) & |
---|
| 647 | & + zcoef0 / e2v(ji,jj) & |
---|
| 648 | & * ( fse3w(ji ,jj+1,jk) * ( (rhd(ji,jj+1,jk ) + znad) & |
---|
| 649 | & + (rhd(ji,jj+1,jk-1) + znad) ) * tmask(ji,jj+1,jk-1) & |
---|
| 650 | & - fse3w(ji ,jj ,jk) * ( (rhd(ji,jj ,jk ) + znad) & |
---|
| 651 | & + (rhd(ji,jj ,jk-1) + znad) ) * tmask(ji,jj ,jk-1) ) |
---|
| 652 | ! s-coordinate pressure gradient correction |
---|
| 653 | ! corrective term, we mask this term for the first wet level beneath the ice shelf (contribution done in the upper bloc) |
---|
| 654 | zvap = - zcoef0 * ( rhd (ji ,jj+1,jk) + rhd (ji,jj,jk) + 2._wp * znad ) & |
---|
| 655 | & * ( fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk) ) / e2v(ji,jj) * vmask(ji,jj,jk-1) |
---|
[455] | 656 | ! add to the general momentum trend |
---|
[4990] | 657 | va(ji,jj,jk) = va(ji,jj,jk) + ( zhpj(ji,jj,jk) + zvap ) * vmask(ji,jj,jk) |
---|
[455] | 658 | END DO |
---|
| 659 | END DO |
---|
| 660 | END DO |
---|
[4990] | 661 | |
---|
| 662 | !================================================================================== |
---|
| 663 | !===== Compute bottom cell contribution (partial cell) ============================ |
---|
| 664 | !================================================================================== |
---|
| 665 | |
---|
| 666 | DO jj = 2, jpjm1 |
---|
| 667 | DO ji = 2, jpim1 |
---|
| 668 | iku = mbku(ji,jj) |
---|
| 669 | ikv = mbkv(ji,jj) |
---|
| 670 | |
---|
| 671 | IF (iku .GT. 1) THEN |
---|
| 672 | ! remove old value (interior case) |
---|
| 673 | zuap = -zcoef0 * ( rhd (ji+1,jj ,iku) + rhd (ji,jj,iku) + 2._wp * znad ) & |
---|
| 674 | & * ( fsde3w(ji+1,jj ,iku) - fsde3w(ji,jj,iku) ) / e1u(ji,jj) |
---|
| 675 | ua(ji,jj,iku) = ua(ji,jj,iku) - zhpi(ji,jj,iku) - zuap |
---|
| 676 | ! put new value |
---|
| 677 | ! -zpshpi to avoid double contribution of the partial step in the top layer |
---|
| 678 | zuap = -zcoef0 * ( aru(ji,jj) + 2._wp * znad ) * gzu(ji,jj) / e1u(ji,jj) |
---|
| 679 | zhpi(ji,jj,iku) = zhpi(ji,jj,iku-1) + zcoef0 / e1u(ji,jj) * ge3ru(ji,jj) - zpshpi(ji,jj) |
---|
| 680 | ua(ji,jj,iku) = ua(ji,jj,iku) + zhpi(ji,jj,iku) + zuap |
---|
| 681 | END IF |
---|
| 682 | ! v direction |
---|
| 683 | IF (ikv .GT. 1) THEN |
---|
| 684 | ! remove old value (interior case) |
---|
| 685 | zvap = -zcoef0 * ( rhd (ji ,jj+1,ikv) + rhd (ji,jj,ikv) + 2._wp * znad ) & |
---|
| 686 | & * ( fsde3w(ji ,jj+1,ikv) - fsde3w(ji,jj,ikv) ) / e2v(ji,jj) |
---|
| 687 | va(ji,jj,ikv) = va(ji,jj,ikv) - zhpj(ji,jj,ikv) - zvap |
---|
| 688 | ! put new value |
---|
| 689 | ! -zpshpj to avoid double contribution of the partial step in the top layer |
---|
| 690 | zvap = -zcoef0 * ( arv(ji,jj) + 2._wp * znad ) * gzv(ji,jj) / e2v(ji,jj) |
---|
| 691 | zhpj(ji,jj,ikv) = zhpj(ji,jj,ikv-1) + zcoef0 / e2v(ji,jj) * ge3rv(ji,jj) - zpshpj(ji,jj) |
---|
| 692 | va(ji,jj,ikv) = va(ji,jj,ikv) + zhpj(ji,jj,ikv) + zvap |
---|
| 693 | END IF |
---|
| 694 | END DO |
---|
| 695 | END DO |
---|
| 696 | |
---|
| 697 | ! set back to original density value into the ice shelf cell (maybe useless because it is masked) |
---|
| 698 | rhd = zrhd |
---|
[503] | 699 | ! |
---|
[4990] | 700 | CALL wrk_dealloc( jpi,jpj,2, ztstop) |
---|
| 701 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zhpj, zrhd) |
---|
| 702 | CALL wrk_dealloc( jpi,jpj, ze3w, zp, zrhdtop_isf, zrhdtop_oce, ziceload, zdept, zpshpi, zpshpj) |
---|
[3294] | 703 | ! |
---|
[5120] | 704 | END SUBROUTINE hpg_isf |
---|
[455] | 705 | |
---|
[4990] | 706 | |
---|
[455] | 707 | SUBROUTINE hpg_djc( kt ) |
---|
| 708 | !!--------------------------------------------------------------------- |
---|
| 709 | !! *** ROUTINE hpg_djc *** |
---|
| 710 | !! |
---|
| 711 | !! ** Method : Density Jacobian with Cubic polynomial scheme |
---|
[3764] | 712 | !! |
---|
[503] | 713 | !! Reference: Shchepetkin and McWilliams, J. Geophys. Res., 108(C3), 3090, 2003 |
---|
[455] | 714 | !!---------------------------------------------------------------------- |
---|
[503] | 715 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
| 716 | !! |
---|
| 717 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 718 | REAL(wp) :: zcoef0, zep, cffw ! temporary scalars |
---|
| 719 | REAL(wp) :: z1_10, cffu, cffx ! " " |
---|
| 720 | REAL(wp) :: z1_12, cffv, cffy ! " " |
---|
[3764] | 721 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zhpj |
---|
[3294] | 722 | REAL(wp), POINTER, DIMENSION(:,:,:) :: dzx, dzy, dzz, dzu, dzv, dzw |
---|
| 723 | REAL(wp), POINTER, DIMENSION(:,:,:) :: drhox, drhoy, drhoz, drhou, drhov, drhow |
---|
| 724 | REAL(wp), POINTER, DIMENSION(:,:,:) :: rho_i, rho_j, rho_k |
---|
[455] | 725 | !!---------------------------------------------------------------------- |
---|
[3294] | 726 | ! |
---|
[3764] | 727 | CALL wrk_alloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw ) |
---|
| 728 | CALL wrk_alloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow ) |
---|
| 729 | CALL wrk_alloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj ) |
---|
[3294] | 730 | ! |
---|
[455] | 731 | |
---|
| 732 | IF( kt == nit000 ) THEN |
---|
| 733 | IF(lwp) WRITE(numout,*) |
---|
| 734 | IF(lwp) WRITE(numout,*) 'dyn:hpg_djc : hydrostatic pressure gradient trend' |
---|
| 735 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, density Jacobian with cubic polynomial scheme' |
---|
[216] | 736 | ENDIF |
---|
| 737 | |
---|
[503] | 738 | ! Local constant initialization |
---|
[2528] | 739 | zcoef0 = - grav * 0.5_wp |
---|
| 740 | z1_10 = 1._wp / 10._wp |
---|
| 741 | z1_12 = 1._wp / 12._wp |
---|
[455] | 742 | |
---|
| 743 | !---------------------------------------------------------------------------------------- |
---|
| 744 | ! compute and store in provisional arrays elementary vertical and horizontal differences |
---|
| 745 | !---------------------------------------------------------------------------------------- |
---|
| 746 | |
---|
| 747 | !!bug gm Not a true bug, but... dzz=e3w for dzx, dzy verify what it is really |
---|
| 748 | |
---|
| 749 | DO jk = 2, jpkm1 |
---|
| 750 | DO jj = 2, jpjm1 |
---|
| 751 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 752 | drhoz(ji,jj,jk) = rhd (ji ,jj ,jk) - rhd (ji,jj,jk-1) |
---|
| 753 | dzz (ji,jj,jk) = fsde3w(ji ,jj ,jk) - fsde3w(ji,jj,jk-1) |
---|
| 754 | drhox(ji,jj,jk) = rhd (ji+1,jj ,jk) - rhd (ji,jj,jk ) |
---|
| 755 | dzx (ji,jj,jk) = fsde3w(ji+1,jj ,jk) - fsde3w(ji,jj,jk ) |
---|
| 756 | drhoy(ji,jj,jk) = rhd (ji ,jj+1,jk) - rhd (ji,jj,jk ) |
---|
| 757 | dzy (ji,jj,jk) = fsde3w(ji ,jj+1,jk) - fsde3w(ji,jj,jk ) |
---|
| 758 | END DO |
---|
| 759 | END DO |
---|
| 760 | END DO |
---|
| 761 | |
---|
| 762 | !------------------------------------------------------------------------- |
---|
| 763 | ! compute harmonic averages using eq. 5.18 |
---|
| 764 | !------------------------------------------------------------------------- |
---|
| 765 | zep = 1.e-15 |
---|
| 766 | |
---|
[503] | 767 | !!bug gm drhoz not defined at level 1 and used (jk-1 with jk=2) |
---|
| 768 | !!bug gm idem for drhox, drhoy et ji=jpi and jj=jpj |
---|
[455] | 769 | |
---|
| 770 | DO jk = 2, jpkm1 |
---|
| 771 | DO jj = 2, jpjm1 |
---|
| 772 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[2528] | 773 | cffw = 2._wp * drhoz(ji ,jj ,jk) * drhoz(ji,jj,jk-1) |
---|
[455] | 774 | |
---|
[2528] | 775 | cffu = 2._wp * drhox(ji+1,jj ,jk) * drhox(ji,jj,jk ) |
---|
| 776 | cffx = 2._wp * dzx (ji+1,jj ,jk) * dzx (ji,jj,jk ) |
---|
[3764] | 777 | |
---|
[2528] | 778 | cffv = 2._wp * drhoy(ji ,jj+1,jk) * drhoy(ji,jj,jk ) |
---|
| 779 | cffy = 2._wp * dzy (ji ,jj+1,jk) * dzy (ji,jj,jk ) |
---|
[455] | 780 | |
---|
| 781 | IF( cffw > zep) THEN |
---|
[2528] | 782 | drhow(ji,jj,jk) = 2._wp * drhoz(ji,jj,jk) * drhoz(ji,jj,jk-1) & |
---|
| 783 | & / ( drhoz(ji,jj,jk) + drhoz(ji,jj,jk-1) ) |
---|
[455] | 784 | ELSE |
---|
[2528] | 785 | drhow(ji,jj,jk) = 0._wp |
---|
[455] | 786 | ENDIF |
---|
| 787 | |
---|
[2528] | 788 | dzw(ji,jj,jk) = 2._wp * dzz(ji,jj,jk) * dzz(ji,jj,jk-1) & |
---|
| 789 | & / ( dzz(ji,jj,jk) + dzz(ji,jj,jk-1) ) |
---|
[455] | 790 | |
---|
| 791 | IF( cffu > zep ) THEN |
---|
[2528] | 792 | drhou(ji,jj,jk) = 2._wp * drhox(ji+1,jj,jk) * drhox(ji,jj,jk) & |
---|
| 793 | & / ( drhox(ji+1,jj,jk) + drhox(ji,jj,jk) ) |
---|
[455] | 794 | ELSE |
---|
[2528] | 795 | drhou(ji,jj,jk ) = 0._wp |
---|
[455] | 796 | ENDIF |
---|
| 797 | |
---|
| 798 | IF( cffx > zep ) THEN |
---|
[2528] | 799 | dzu(ji,jj,jk) = 2._wp * dzx(ji+1,jj,jk) * dzx(ji,jj,jk) & |
---|
| 800 | & / ( dzx(ji+1,jj,jk) + dzx(ji,jj,jk) ) |
---|
[455] | 801 | ELSE |
---|
[2528] | 802 | dzu(ji,jj,jk) = 0._wp |
---|
[455] | 803 | ENDIF |
---|
| 804 | |
---|
| 805 | IF( cffv > zep ) THEN |
---|
[2528] | 806 | drhov(ji,jj,jk) = 2._wp * drhoy(ji,jj+1,jk) * drhoy(ji,jj,jk) & |
---|
| 807 | & / ( drhoy(ji,jj+1,jk) + drhoy(ji,jj,jk) ) |
---|
[455] | 808 | ELSE |
---|
[2528] | 809 | drhov(ji,jj,jk) = 0._wp |
---|
[455] | 810 | ENDIF |
---|
| 811 | |
---|
| 812 | IF( cffy > zep ) THEN |
---|
[2528] | 813 | dzv(ji,jj,jk) = 2._wp * dzy(ji,jj+1,jk) * dzy(ji,jj,jk) & |
---|
| 814 | & / ( dzy(ji,jj+1,jk) + dzy(ji,jj,jk) ) |
---|
[455] | 815 | ELSE |
---|
[2528] | 816 | dzv(ji,jj,jk) = 0._wp |
---|
[455] | 817 | ENDIF |
---|
| 818 | |
---|
| 819 | END DO |
---|
| 820 | END DO |
---|
| 821 | END DO |
---|
| 822 | |
---|
| 823 | !---------------------------------------------------------------------------------- |
---|
| 824 | ! apply boundary conditions at top and bottom using 5.36-5.37 |
---|
| 825 | !---------------------------------------------------------------------------------- |
---|
[2528] | 826 | drhow(:,:, 1 ) = 1.5_wp * ( drhoz(:,:, 2 ) - drhoz(:,:, 1 ) ) - 0.5_wp * drhow(:,:, 2 ) |
---|
| 827 | drhou(:,:, 1 ) = 1.5_wp * ( drhox(:,:, 2 ) - drhox(:,:, 1 ) ) - 0.5_wp * drhou(:,:, 2 ) |
---|
| 828 | drhov(:,:, 1 ) = 1.5_wp * ( drhoy(:,:, 2 ) - drhoy(:,:, 1 ) ) - 0.5_wp * drhov(:,:, 2 ) |
---|
[455] | 829 | |
---|
[2528] | 830 | drhow(:,:,jpk) = 1.5_wp * ( drhoz(:,:,jpk) - drhoz(:,:,jpkm1) ) - 0.5_wp * drhow(:,:,jpkm1) |
---|
| 831 | drhou(:,:,jpk) = 1.5_wp * ( drhox(:,:,jpk) - drhox(:,:,jpkm1) ) - 0.5_wp * drhou(:,:,jpkm1) |
---|
| 832 | drhov(:,:,jpk) = 1.5_wp * ( drhoy(:,:,jpk) - drhoy(:,:,jpkm1) ) - 0.5_wp * drhov(:,:,jpkm1) |
---|
[455] | 833 | |
---|
| 834 | |
---|
| 835 | !-------------------------------------------------------------- |
---|
| 836 | ! Upper half of top-most grid box, compute and store |
---|
| 837 | !------------------------------------------------------------- |
---|
| 838 | |
---|
| 839 | !!bug gm : e3w-de3w = 0.5*e3w .... and de3w(2)-de3w(1)=e3w(2) .... to be verified |
---|
| 840 | ! true if de3w is really defined as the sum of the e3w scale factors as, it seems to me, it should be |
---|
| 841 | |
---|
| 842 | DO jj = 2, jpjm1 |
---|
| 843 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
[2528] | 844 | rho_k(ji,jj,1) = -grav * ( fse3w(ji,jj,1) - fsde3w(ji,jj,1) ) & |
---|
| 845 | & * ( rhd(ji,jj,1) & |
---|
| 846 | & + 0.5_wp * ( rhd(ji,jj,2) - rhd(ji,jj,1) ) & |
---|
| 847 | & * ( fse3w (ji,jj,1) - fsde3w(ji,jj,1) ) & |
---|
[3764] | 848 | & / ( fsde3w(ji,jj,2) - fsde3w(ji,jj,1) ) ) |
---|
[455] | 849 | END DO |
---|
| 850 | END DO |
---|
| 851 | |
---|
| 852 | !!bug gm : here also, simplification is possible |
---|
| 853 | !!bug gm : optimisation: 1/10 and 1/12 the division should be done before the loop |
---|
| 854 | |
---|
| 855 | DO jk = 2, jpkm1 |
---|
| 856 | DO jj = 2, jpjm1 |
---|
| 857 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 858 | |
---|
| 859 | rho_k(ji,jj,jk) = zcoef0 * ( rhd (ji,jj,jk) + rhd (ji,jj,jk-1) ) & |
---|
| 860 | & * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) ) & |
---|
| 861 | & - grav * z1_10 * ( & |
---|
| 862 | & ( drhow (ji,jj,jk) - drhow (ji,jj,jk-1) ) & |
---|
| 863 | & * ( fsde3w(ji,jj,jk) - fsde3w(ji,jj,jk-1) - z1_12 * ( dzw (ji,jj,jk) + dzw (ji,jj,jk-1) ) ) & |
---|
| 864 | & - ( dzw (ji,jj,jk) - dzw (ji,jj,jk-1) ) & |
---|
| 865 | & * ( rhd (ji,jj,jk) - rhd (ji,jj,jk-1) - z1_12 * ( drhow(ji,jj,jk) + drhow(ji,jj,jk-1) ) ) & |
---|
| 866 | & ) |
---|
| 867 | |
---|
| 868 | rho_i(ji,jj,jk) = zcoef0 * ( rhd (ji+1,jj,jk) + rhd (ji,jj,jk) ) & |
---|
| 869 | & * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) ) & |
---|
| 870 | & - grav* z1_10 * ( & |
---|
| 871 | & ( drhou (ji+1,jj,jk) - drhou (ji,jj,jk) ) & |
---|
| 872 | & * ( fsde3w(ji+1,jj,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzu (ji+1,jj,jk) + dzu (ji,jj,jk) ) ) & |
---|
| 873 | & - ( dzu (ji+1,jj,jk) - dzu (ji,jj,jk) ) & |
---|
| 874 | & * ( rhd (ji+1,jj,jk) - rhd (ji,jj,jk) - z1_12 * ( drhou(ji+1,jj,jk) + drhou(ji,jj,jk) ) ) & |
---|
| 875 | & ) |
---|
| 876 | |
---|
| 877 | rho_j(ji,jj,jk) = zcoef0 * ( rhd (ji,jj+1,jk) + rhd (ji,jj,jk) ) & |
---|
| 878 | & * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) ) & |
---|
| 879 | & - grav* z1_10 * ( & |
---|
| 880 | & ( drhov (ji,jj+1,jk) - drhov (ji,jj,jk) ) & |
---|
| 881 | & * ( fsde3w(ji,jj+1,jk) - fsde3w(ji,jj,jk) - z1_12 * ( dzv (ji,jj+1,jk) + dzv (ji,jj,jk) ) ) & |
---|
| 882 | & - ( dzv (ji,jj+1,jk) - dzv (ji,jj,jk) ) & |
---|
| 883 | & * ( rhd (ji,jj+1,jk) - rhd (ji,jj,jk) - z1_12 * ( drhov(ji,jj+1,jk) + drhov(ji,jj,jk) ) ) & |
---|
| 884 | & ) |
---|
| 885 | |
---|
| 886 | END DO |
---|
| 887 | END DO |
---|
| 888 | END DO |
---|
| 889 | CALL lbc_lnk(rho_k,'W',1.) |
---|
| 890 | CALL lbc_lnk(rho_i,'U',1.) |
---|
| 891 | CALL lbc_lnk(rho_j,'V',1.) |
---|
| 892 | |
---|
| 893 | |
---|
| 894 | ! --------------- |
---|
| 895 | ! Surface value |
---|
| 896 | ! --------------- |
---|
| 897 | DO jj = 2, jpjm1 |
---|
| 898 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 899 | zhpi(ji,jj,1) = ( rho_k(ji+1,jj ,1) - rho_k(ji,jj,1) - rho_i(ji,jj,1) ) / e1u(ji,jj) |
---|
| 900 | zhpj(ji,jj,1) = ( rho_k(ji ,jj+1,1) - rho_k(ji,jj,1) - rho_j(ji,jj,1) ) / e2v(ji,jj) |
---|
| 901 | ! add to the general momentum trend |
---|
| 902 | ua(ji,jj,1) = ua(ji,jj,1) + zhpi(ji,jj,1) |
---|
| 903 | va(ji,jj,1) = va(ji,jj,1) + zhpj(ji,jj,1) |
---|
| 904 | END DO |
---|
| 905 | END DO |
---|
| 906 | |
---|
| 907 | ! ---------------- |
---|
| 908 | ! interior value (2=<jk=<jpkm1) |
---|
| 909 | ! ---------------- |
---|
| 910 | DO jk = 2, jpkm1 |
---|
[3764] | 911 | DO jj = 2, jpjm1 |
---|
[455] | 912 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
| 913 | ! hydrostatic pressure gradient along s-surfaces |
---|
| 914 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) & |
---|
| 915 | & + ( ( rho_k(ji+1,jj,jk) - rho_k(ji,jj,jk ) ) & |
---|
| 916 | & - ( rho_i(ji ,jj,jk) - rho_i(ji,jj,jk-1) ) ) / e1u(ji,jj) |
---|
| 917 | zhpj(ji,jj,jk) = zhpj(ji,jj,jk-1) & |
---|
| 918 | & + ( ( rho_k(ji,jj+1,jk) - rho_k(ji,jj,jk ) ) & |
---|
| 919 | & -( rho_j(ji,jj ,jk) - rho_j(ji,jj,jk-1) ) ) / e2v(ji,jj) |
---|
| 920 | ! add to the general momentum trend |
---|
| 921 | ua(ji,jj,jk) = ua(ji,jj,jk) + zhpi(ji,jj,jk) |
---|
| 922 | va(ji,jj,jk) = va(ji,jj,jk) + zhpj(ji,jj,jk) |
---|
| 923 | END DO |
---|
| 924 | END DO |
---|
| 925 | END DO |
---|
[503] | 926 | ! |
---|
[3764] | 927 | CALL wrk_dealloc( jpi, jpj, jpk, dzx , dzy , dzz , dzu , dzv , dzw ) |
---|
| 928 | CALL wrk_dealloc( jpi, jpj, jpk, drhox, drhoy, drhoz, drhou, drhov, drhow ) |
---|
| 929 | CALL wrk_dealloc( jpi, jpj, jpk, rho_i, rho_j, rho_k, zhpi, zhpj ) |
---|
[2715] | 930 | ! |
---|
[455] | 931 | END SUBROUTINE hpg_djc |
---|
| 932 | |
---|
| 933 | |
---|
[3294] | 934 | SUBROUTINE hpg_prj( kt ) |
---|
[455] | 935 | !!--------------------------------------------------------------------- |
---|
[3294] | 936 | !! *** ROUTINE hpg_prj *** |
---|
[455] | 937 | !! |
---|
[3294] | 938 | !! ** Method : s-coordinate case. |
---|
| 939 | !! A Pressure-Jacobian horizontal pressure gradient method |
---|
| 940 | !! based on the constrained cubic-spline interpolation for |
---|
| 941 | !! all vertical coordinate systems |
---|
[455] | 942 | !! |
---|
[3294] | 943 | !! ** Action : - Update (ua,va) with the now hydrastatic pressure trend |
---|
[455] | 944 | !!---------------------------------------------------------------------- |
---|
[3294] | 945 | INTEGER, PARAMETER :: polynomial_type = 1 ! 1: cubic spline, 2: linear |
---|
| 946 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
---|
[503] | 947 | !! |
---|
[3294] | 948 | INTEGER :: ji, jj, jk, jkk ! dummy loop indices |
---|
| 949 | REAL(wp) :: zcoef0, znad ! temporary scalars |
---|
[503] | 950 | !! |
---|
[3294] | 951 | !! The local variables for the correction term |
---|
| 952 | INTEGER :: jk1, jis, jid, jjs, jjd |
---|
| 953 | REAL(wp) :: zuijk, zvijk, zpwes, zpwed, zpnss, zpnsd, zdeps |
---|
[3764] | 954 | REAL(wp) :: zrhdt1 |
---|
[3294] | 955 | REAL(wp) :: zdpdx1, zdpdx2, zdpdy1, zdpdy2 |
---|
[3764] | 956 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zdept, zrhh |
---|
[3294] | 957 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp |
---|
[5224] | 958 | REAL(wp), POINTER, DIMENSION(:,:) :: zsshu_n, zsshv_n |
---|
[455] | 959 | !!---------------------------------------------------------------------- |
---|
[3294] | 960 | ! |
---|
[3764] | 961 | CALL wrk_alloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp ) |
---|
| 962 | CALL wrk_alloc( jpi,jpj,jpk, zdept, zrhh ) |
---|
[5224] | 963 | CALL wrk_alloc( jpi,jpj, zsshu_n, zsshv_n ) |
---|
[3294] | 964 | ! |
---|
[455] | 965 | IF( kt == nit000 ) THEN |
---|
| 966 | IF(lwp) WRITE(numout,*) |
---|
[3294] | 967 | IF(lwp) WRITE(numout,*) 'dyn:hpg_prj : hydrostatic pressure gradient trend' |
---|
| 968 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ s-coordinate case, cubic spline pressure Jacobian' |
---|
[3] | 969 | ENDIF |
---|
| 970 | |
---|
[3294] | 971 | !!---------------------------------------------------------------------- |
---|
| 972 | ! Local constant initialization |
---|
[3764] | 973 | zcoef0 = - grav |
---|
[3294] | 974 | znad = 0.0_wp |
---|
| 975 | IF( lk_vvl ) znad = 1._wp |
---|
[3] | 976 | |
---|
[3294] | 977 | ! Clean 3-D work arrays |
---|
| 978 | zhpi(:,:,:) = 0._wp |
---|
| 979 | zrhh(:,:,:) = rhd(:,:,:) |
---|
[3764] | 980 | |
---|
[3294] | 981 | ! Preparing vertical density profile "zrhh(:,:,:)" for hybrid-sco coordinate |
---|
| 982 | DO jj = 1, jpj |
---|
[3764] | 983 | DO ji = 1, jpi |
---|
[3294] | 984 | jk = mbathy(ji,jj) |
---|
| 985 | IF( jk <= 0 ) THEN; zrhh(ji,jj,:) = 0._wp |
---|
| 986 | ELSE IF(jk == 1) THEN; zrhh(ji,jj, jk+1:jpk) = rhd(ji,jj,jk) |
---|
| 987 | ELSE IF(jk < jpkm1) THEN |
---|
| 988 | DO jkk = jk+1, jpk |
---|
| 989 | zrhh(ji,jj,jkk) = interp1(fsde3w(ji,jj,jkk), fsde3w(ji,jj,jkk-1), & |
---|
| 990 | fsde3w(ji,jj,jkk-2), rhd(ji,jj,jkk-1), rhd(ji,jj,jkk-2)) |
---|
[3764] | 991 | END DO |
---|
[3294] | 992 | ENDIF |
---|
| 993 | END DO |
---|
| 994 | END DO |
---|
[3] | 995 | |
---|
[3632] | 996 | ! Transfer the depth of "T(:,:,:)" to vertical coordinate "zdept(:,:,:)" |
---|
[4990] | 997 | DO jj = 1, jpj |
---|
| 998 | DO ji = 1, jpi |
---|
| 999 | zdept(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) - sshn(ji,jj) * znad |
---|
| 1000 | END DO |
---|
| 1001 | END DO |
---|
[455] | 1002 | |
---|
[4990] | 1003 | DO jk = 2, jpk |
---|
| 1004 | DO jj = 1, jpj |
---|
| 1005 | DO ji = 1, jpi |
---|
| 1006 | zdept(ji,jj,jk) = zdept(ji,jj,jk-1) + fse3w(ji,jj,jk) |
---|
| 1007 | END DO |
---|
| 1008 | END DO |
---|
| 1009 | END DO |
---|
[455] | 1010 | |
---|
[4990] | 1011 | fsp(:,:,:) = zrhh (:,:,:) |
---|
[3632] | 1012 | xsp(:,:,:) = zdept(:,:,:) |
---|
| 1013 | |
---|
[3764] | 1014 | ! Construct the vertical density profile with the |
---|
[3294] | 1015 | ! constrained cubic spline interpolation |
---|
| 1016 | ! rho(z) = asp + bsp*z + csp*z^2 + dsp*z^3 |
---|
[3764] | 1017 | CALL cspline(fsp,xsp,asp,bsp,csp,dsp,polynomial_type) |
---|
[3294] | 1018 | |
---|
| 1019 | ! Integrate the hydrostatic pressure "zhpi(:,:,:)" at "T(ji,jj,1)" |
---|
| 1020 | DO jj = 2, jpj |
---|
[3764] | 1021 | DO ji = 2, jpi |
---|
[3632] | 1022 | zrhdt1 = zrhh(ji,jj,1) - interp3(zdept(ji,jj,1),asp(ji,jj,1), & |
---|
[3294] | 1023 | bsp(ji,jj,1), csp(ji,jj,1), & |
---|
[3632] | 1024 | dsp(ji,jj,1) ) * 0.25_wp * fse3w(ji,jj,1) |
---|
[3294] | 1025 | |
---|
| 1026 | ! assuming linear profile across the top half surface layer |
---|
[3764] | 1027 | zhpi(ji,jj,1) = 0.5_wp * fse3w(ji,jj,1) * zrhdt1 |
---|
[3294] | 1028 | END DO |
---|
[455] | 1029 | END DO |
---|
| 1030 | |
---|
[3294] | 1031 | ! Calculate the pressure "zhpi(:,:,:)" at "T(ji,jj,2:jpkm1)" |
---|
[3764] | 1032 | DO jk = 2, jpkm1 |
---|
| 1033 | DO jj = 2, jpj |
---|
[3294] | 1034 | DO ji = 2, jpi |
---|
| 1035 | zhpi(ji,jj,jk) = zhpi(ji,jj,jk-1) + & |
---|
[3632] | 1036 | integ_spline(zdept(ji,jj,jk-1), zdept(ji,jj,jk),& |
---|
[3294] | 1037 | asp(ji,jj,jk-1), bsp(ji,jj,jk-1), & |
---|
| 1038 | csp(ji,jj,jk-1), dsp(ji,jj,jk-1)) |
---|
| 1039 | END DO |
---|
| 1040 | END DO |
---|
[455] | 1041 | END DO |
---|
| 1042 | |
---|
[3294] | 1043 | ! Z coordinate of U(ji,jj,1:jpkm1) and V(ji,jj,1:jpkm1) |
---|
[5224] | 1044 | |
---|
| 1045 | ! Prepare zsshu_n and zsshv_n |
---|
[3764] | 1046 | DO jj = 2, jpjm1 |
---|
| 1047 | DO ji = 2, jpim1 |
---|
[5224] | 1048 | zsshu_n(ji,jj) = (e12u(ji,jj) * sshn(ji,jj) + e12u(ji+1, jj) * sshn(ji+1,jj)) * & |
---|
| 1049 | & r1_e12u(ji,jj) * umask(ji,jj,1) * 0.5_wp |
---|
| 1050 | zsshv_n(ji,jj) = (e12v(ji,jj) * sshn(ji,jj) + e12v(ji+1, jj) * sshn(ji,jj+1)) * & |
---|
| 1051 | & r1_e12v(ji,jj) * vmask(ji,jj,1) * 0.5_wp |
---|
[3294] | 1052 | END DO |
---|
[455] | 1053 | END DO |
---|
| 1054 | |
---|
[5224] | 1055 | DO jj = 2, jpjm1 |
---|
| 1056 | DO ji = 2, jpim1 |
---|
| 1057 | zu(ji,jj,1) = - ( fse3u(ji,jj,1) - zsshu_n(ji,jj) * znad) |
---|
| 1058 | zv(ji,jj,1) = - ( fse3v(ji,jj,1) - zsshv_n(ji,jj) * znad) |
---|
| 1059 | END DO |
---|
| 1060 | END DO |
---|
| 1061 | |
---|
[3764] | 1062 | DO jk = 2, jpkm1 |
---|
| 1063 | DO jj = 2, jpjm1 |
---|
| 1064 | DO ji = 2, jpim1 |
---|
[3294] | 1065 | zu(ji,jj,jk) = zu(ji,jj,jk-1)- fse3u(ji,jj,jk) |
---|
| 1066 | zv(ji,jj,jk) = zv(ji,jj,jk-1)- fse3v(ji,jj,jk) |
---|
| 1067 | END DO |
---|
| 1068 | END DO |
---|
[455] | 1069 | END DO |
---|
[3764] | 1070 | |
---|
| 1071 | DO jk = 1, jpkm1 |
---|
| 1072 | DO jj = 2, jpjm1 |
---|
| 1073 | DO ji = 2, jpim1 |
---|
[3294] | 1074 | zu(ji,jj,jk) = zu(ji,jj,jk) + 0.5_wp * fse3u(ji,jj,jk) |
---|
| 1075 | zv(ji,jj,jk) = zv(ji,jj,jk) + 0.5_wp * fse3v(ji,jj,jk) |
---|
| 1076 | END DO |
---|
| 1077 | END DO |
---|
| 1078 | END DO |
---|
[455] | 1079 | |
---|
[3632] | 1080 | DO jk = 1, jpkm1 |
---|
| 1081 | DO jj = 2, jpjm1 |
---|
| 1082 | DO ji = 2, jpim1 |
---|
| 1083 | zu(ji,jj,jk) = min(zu(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk))) |
---|
| 1084 | zu(ji,jj,jk) = max(zu(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji+1,jj,jk))) |
---|
| 1085 | zv(ji,jj,jk) = min(zv(ji,jj,jk), max(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk))) |
---|
| 1086 | zv(ji,jj,jk) = max(zv(ji,jj,jk), min(-zdept(ji,jj,jk), -zdept(ji,jj+1,jk))) |
---|
| 1087 | END DO |
---|
| 1088 | END DO |
---|
| 1089 | END DO |
---|
| 1090 | |
---|
| 1091 | |
---|
[3764] | 1092 | DO jk = 1, jpkm1 |
---|
| 1093 | DO jj = 2, jpjm1 |
---|
| 1094 | DO ji = 2, jpim1 |
---|
[3294] | 1095 | zpwes = 0._wp; zpwed = 0._wp |
---|
| 1096 | zpnss = 0._wp; zpnsd = 0._wp |
---|
| 1097 | zuijk = zu(ji,jj,jk) |
---|
| 1098 | zvijk = zv(ji,jj,jk) |
---|
| 1099 | |
---|
| 1100 | !!!!! for u equation |
---|
| 1101 | IF( jk <= mbku(ji,jj) ) THEN |
---|
[3632] | 1102 | IF( -zdept(ji+1,jj,jk) >= -zdept(ji,jj,jk) ) THEN |
---|
[3294] | 1103 | jis = ji + 1; jid = ji |
---|
| 1104 | ELSE |
---|
| 1105 | jis = ji; jid = ji +1 |
---|
| 1106 | ENDIF |
---|
| 1107 | |
---|
| 1108 | ! integrate the pressure on the shallow side |
---|
[3764] | 1109 | jk1 = jk |
---|
[3632] | 1110 | DO WHILE ( -zdept(jis,jj,jk1) > zuijk ) |
---|
[3294] | 1111 | IF( jk1 == mbku(ji,jj) ) THEN |
---|
[3632] | 1112 | zuijk = -zdept(jis,jj,jk1) |
---|
[3294] | 1113 | EXIT |
---|
| 1114 | ENDIF |
---|
[3632] | 1115 | zdeps = MIN(zdept(jis,jj,jk1+1), -zuijk) |
---|
[3764] | 1116 | zpwes = zpwes + & |
---|
[3632] | 1117 | integ_spline(zdept(jis,jj,jk1), zdeps, & |
---|
[3294] | 1118 | asp(jis,jj,jk1), bsp(jis,jj,jk1), & |
---|
| 1119 | csp(jis,jj,jk1), dsp(jis,jj,jk1)) |
---|
| 1120 | jk1 = jk1 + 1 |
---|
| 1121 | END DO |
---|
[3764] | 1122 | |
---|
[3294] | 1123 | ! integrate the pressure on the deep side |
---|
[3764] | 1124 | jk1 = jk |
---|
[3632] | 1125 | DO WHILE ( -zdept(jid,jj,jk1) < zuijk ) |
---|
[3294] | 1126 | IF( jk1 == 1 ) THEN |
---|
[3632] | 1127 | zdeps = zdept(jid,jj,1) + MIN(zuijk, sshn(jid,jj)*znad) |
---|
| 1128 | zrhdt1 = zrhh(jid,jj,1) - interp3(zdept(jid,jj,1), asp(jid,jj,1), & |
---|
| 1129 | bsp(jid,jj,1), csp(jid,jj,1), & |
---|
| 1130 | dsp(jid,jj,1)) * zdeps |
---|
| 1131 | zpwed = zpwed + 0.5_wp * (zrhh(jid,jj,1) + zrhdt1) * zdeps |
---|
[3294] | 1132 | EXIT |
---|
| 1133 | ENDIF |
---|
[3632] | 1134 | zdeps = MAX(zdept(jid,jj,jk1-1), -zuijk) |
---|
[3764] | 1135 | zpwed = zpwed + & |
---|
[3632] | 1136 | integ_spline(zdeps, zdept(jid,jj,jk1), & |
---|
[3294] | 1137 | asp(jid,jj,jk1-1), bsp(jid,jj,jk1-1), & |
---|
| 1138 | csp(jid,jj,jk1-1), dsp(jid,jj,jk1-1) ) |
---|
| 1139 | jk1 = jk1 - 1 |
---|
| 1140 | END DO |
---|
[3764] | 1141 | |
---|
[3294] | 1142 | ! update the momentum trends in u direction |
---|
| 1143 | |
---|
| 1144 | zdpdx1 = zcoef0 / e1u(ji,jj) * (zhpi(ji+1,jj,jk) - zhpi(ji,jj,jk)) |
---|
| 1145 | IF( lk_vvl ) THEN |
---|
[3764] | 1146 | zdpdx2 = zcoef0 / e1u(ji,jj) * & |
---|
| 1147 | ( REAL(jis-jid, wp) * (zpwes + zpwed) + (sshn(ji+1,jj)-sshn(ji,jj)) ) |
---|
[3294] | 1148 | ELSE |
---|
[3764] | 1149 | zdpdx2 = zcoef0 / e1u(ji,jj) * REAL(jis-jid, wp) * (zpwes + zpwed) |
---|
[3294] | 1150 | ENDIF |
---|
| 1151 | |
---|
| 1152 | ua(ji,jj,jk) = ua(ji,jj,jk) + (zdpdx1 + zdpdx2) * & |
---|
| 1153 | & umask(ji,jj,jk) * tmask(ji,jj,jk) * tmask(ji+1,jj,jk) |
---|
| 1154 | ENDIF |
---|
[3764] | 1155 | |
---|
[3294] | 1156 | !!!!! for v equation |
---|
| 1157 | IF( jk <= mbkv(ji,jj) ) THEN |
---|
[3632] | 1158 | IF( -zdept(ji,jj+1,jk) >= -zdept(ji,jj,jk) ) THEN |
---|
[3294] | 1159 | jjs = jj + 1; jjd = jj |
---|
| 1160 | ELSE |
---|
| 1161 | jjs = jj ; jjd = jj + 1 |
---|
| 1162 | ENDIF |
---|
| 1163 | |
---|
| 1164 | ! integrate the pressure on the shallow side |
---|
[3764] | 1165 | jk1 = jk |
---|
[3632] | 1166 | DO WHILE ( -zdept(ji,jjs,jk1) > zvijk ) |
---|
[3294] | 1167 | IF( jk1 == mbkv(ji,jj) ) THEN |
---|
[3632] | 1168 | zvijk = -zdept(ji,jjs,jk1) |
---|
[3294] | 1169 | EXIT |
---|
| 1170 | ENDIF |
---|
[3632] | 1171 | zdeps = MIN(zdept(ji,jjs,jk1+1), -zvijk) |
---|
[3764] | 1172 | zpnss = zpnss + & |
---|
[3632] | 1173 | integ_spline(zdept(ji,jjs,jk1), zdeps, & |
---|
[3294] | 1174 | asp(ji,jjs,jk1), bsp(ji,jjs,jk1), & |
---|
| 1175 | csp(ji,jjs,jk1), dsp(ji,jjs,jk1) ) |
---|
| 1176 | jk1 = jk1 + 1 |
---|
| 1177 | END DO |
---|
[3764] | 1178 | |
---|
[3294] | 1179 | ! integrate the pressure on the deep side |
---|
[3764] | 1180 | jk1 = jk |
---|
[3632] | 1181 | DO WHILE ( -zdept(ji,jjd,jk1) < zvijk ) |
---|
[3294] | 1182 | IF( jk1 == 1 ) THEN |
---|
[3632] | 1183 | zdeps = zdept(ji,jjd,1) + MIN(zvijk, sshn(ji,jjd)*znad) |
---|
| 1184 | zrhdt1 = zrhh(ji,jjd,1) - interp3(zdept(ji,jjd,1), asp(ji,jjd,1), & |
---|
| 1185 | bsp(ji,jjd,1), csp(ji,jjd,1), & |
---|
| 1186 | dsp(ji,jjd,1) ) * zdeps |
---|
| 1187 | zpnsd = zpnsd + 0.5_wp * (zrhh(ji,jjd,1) + zrhdt1) * zdeps |
---|
[3294] | 1188 | EXIT |
---|
| 1189 | ENDIF |
---|
[3632] | 1190 | zdeps = MAX(zdept(ji,jjd,jk1-1), -zvijk) |
---|
[3764] | 1191 | zpnsd = zpnsd + & |
---|
[3632] | 1192 | integ_spline(zdeps, zdept(ji,jjd,jk1), & |
---|
[3294] | 1193 | asp(ji,jjd,jk1-1), bsp(ji,jjd,jk1-1), & |
---|
| 1194 | csp(ji,jjd,jk1-1), dsp(ji,jjd,jk1-1) ) |
---|
| 1195 | jk1 = jk1 - 1 |
---|
| 1196 | END DO |
---|
| 1197 | |
---|
[3764] | 1198 | |
---|
[3294] | 1199 | ! update the momentum trends in v direction |
---|
| 1200 | |
---|
| 1201 | zdpdy1 = zcoef0 / e2v(ji,jj) * (zhpi(ji,jj+1,jk) - zhpi(ji,jj,jk)) |
---|
| 1202 | IF( lk_vvl ) THEN |
---|
| 1203 | zdpdy2 = zcoef0 / e2v(ji,jj) * & |
---|
[3764] | 1204 | ( REAL(jjs-jjd, wp) * (zpnss + zpnsd) + (sshn(ji,jj+1)-sshn(ji,jj)) ) |
---|
[3294] | 1205 | ELSE |
---|
[3764] | 1206 | zdpdy2 = zcoef0 / e2v(ji,jj) * REAL(jjs-jjd, wp) * (zpnss + zpnsd ) |
---|
[3294] | 1207 | ENDIF |
---|
| 1208 | |
---|
| 1209 | va(ji,jj,jk) = va(ji,jj,jk) + (zdpdy1 + zdpdy2)*& |
---|
| 1210 | & vmask(ji,jj,jk)*tmask(ji,jj,jk)*tmask(ji,jj+1,jk) |
---|
| 1211 | ENDIF |
---|
| 1212 | |
---|
[3764] | 1213 | |
---|
[3294] | 1214 | END DO |
---|
| 1215 | END DO |
---|
[455] | 1216 | END DO |
---|
[503] | 1217 | ! |
---|
[3764] | 1218 | CALL wrk_dealloc( jpi,jpj,jpk, zhpi, zu, zv, fsp, xsp, asp, bsp, csp, dsp ) |
---|
| 1219 | CALL wrk_dealloc( jpi,jpj,jpk, zdept, zrhh ) |
---|
[5224] | 1220 | CALL wrk_dealloc( jpi,jpj, zsshu_n, zsshv_n ) |
---|
[2715] | 1221 | ! |
---|
[3294] | 1222 | END SUBROUTINE hpg_prj |
---|
[455] | 1223 | |
---|
[4990] | 1224 | |
---|
[3294] | 1225 | SUBROUTINE cspline(fsp, xsp, asp, bsp, csp, dsp, polynomial_type) |
---|
| 1226 | !!---------------------------------------------------------------------- |
---|
| 1227 | !! *** ROUTINE cspline *** |
---|
[3764] | 1228 | !! |
---|
[3294] | 1229 | !! ** Purpose : constrained cubic spline interpolation |
---|
[3764] | 1230 | !! |
---|
| 1231 | !! ** Method : f(x) = asp + bsp*x + csp*x^2 + dsp*x^3 |
---|
[4990] | 1232 | !! |
---|
[3294] | 1233 | !! Reference: CJC Kruger, Constrained Cubic Spline Interpoltation |
---|
| 1234 | !!---------------------------------------------------------------------- |
---|
| 1235 | IMPLICIT NONE |
---|
| 1236 | REAL(wp), DIMENSION(:,:,:), INTENT(in) :: fsp, xsp ! value and coordinate |
---|
[3764] | 1237 | REAL(wp), DIMENSION(:,:,:), INTENT(out) :: asp, bsp, csp, dsp ! coefficients of |
---|
[3294] | 1238 | ! the interpoated function |
---|
[3764] | 1239 | INTEGER, INTENT(in) :: polynomial_type ! 1: cubic spline |
---|
[3294] | 1240 | ! 2: Linear |
---|
[4990] | 1241 | ! |
---|
[3294] | 1242 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
| 1243 | INTEGER :: jpi, jpj, jpkm1 |
---|
| 1244 | REAL(wp) :: zdf1, zdf2, zddf1, zddf2, ztmp1, ztmp2, zdxtmp |
---|
| 1245 | REAL(wp) :: zdxtmp1, zdxtmp2, zalpha |
---|
| 1246 | REAL(wp) :: zdf(size(fsp,3)) |
---|
| 1247 | !!---------------------------------------------------------------------- |
---|
| 1248 | |
---|
| 1249 | jpi = size(fsp,1) |
---|
| 1250 | jpj = size(fsp,2) |
---|
| 1251 | jpkm1 = size(fsp,3) - 1 |
---|
| 1252 | |
---|
[3764] | 1253 | |
---|
[3294] | 1254 | IF (polynomial_type == 1) THEN ! Constrained Cubic Spline |
---|
| 1255 | DO ji = 1, jpi |
---|
| 1256 | DO jj = 1, jpj |
---|
[3764] | 1257 | !!Fritsch&Butland's method, 1984 (preferred, but more computation) |
---|
[3294] | 1258 | ! DO jk = 2, jpkm1-1 |
---|
[3764] | 1259 | ! zdxtmp1 = xsp(ji,jj,jk) - xsp(ji,jj,jk-1) |
---|
| 1260 | ! zdxtmp2 = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
[3294] | 1261 | ! zdf1 = ( fsp(ji,jj,jk) - fsp(ji,jj,jk-1) ) / zdxtmp1 |
---|
| 1262 | ! zdf2 = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp2 |
---|
| 1263 | ! |
---|
| 1264 | ! zalpha = ( zdxtmp1 + 2._wp * zdxtmp2 ) / ( zdxtmp1 + zdxtmp2 ) / 3._wp |
---|
[3764] | 1265 | ! |
---|
[3294] | 1266 | ! IF(zdf1 * zdf2 <= 0._wp) THEN |
---|
| 1267 | ! zdf(jk) = 0._wp |
---|
| 1268 | ! ELSE |
---|
| 1269 | ! zdf(jk) = zdf1 * zdf2 / ( ( 1._wp - zalpha ) * zdf1 + zalpha * zdf2 ) |
---|
| 1270 | ! ENDIF |
---|
| 1271 | ! END DO |
---|
[3764] | 1272 | |
---|
[3294] | 1273 | !!Simply geometric average |
---|
| 1274 | DO jk = 2, jpkm1-1 |
---|
| 1275 | zdf1 = (fsp(ji,jj,jk) - fsp(ji,jj,jk-1)) / (xsp(ji,jj,jk) - xsp(ji,jj,jk-1)) |
---|
| 1276 | zdf2 = (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / (xsp(ji,jj,jk+1) - xsp(ji,jj,jk)) |
---|
[3764] | 1277 | |
---|
[3294] | 1278 | IF(zdf1 * zdf2 <= 0._wp) THEN |
---|
| 1279 | zdf(jk) = 0._wp |
---|
| 1280 | ELSE |
---|
| 1281 | zdf(jk) = 2._wp * zdf1 * zdf2 / (zdf1 + zdf2) |
---|
| 1282 | ENDIF |
---|
| 1283 | END DO |
---|
[3764] | 1284 | |
---|
[3294] | 1285 | zdf(1) = 1.5_wp * ( fsp(ji,jj,2) - fsp(ji,jj,1) ) / & |
---|
| 1286 | & ( xsp(ji,jj,2) - xsp(ji,jj,1) ) - 0.5_wp * zdf(2) |
---|
| 1287 | zdf(jpkm1) = 1.5_wp * ( fsp(ji,jj,jpkm1) - fsp(ji,jj,jpkm1-1) ) / & |
---|
| 1288 | & ( xsp(ji,jj,jpkm1) - xsp(ji,jj,jpkm1-1) ) - & |
---|
| 1289 | & 0.5_wp * zdf(jpkm1 - 1) |
---|
[3764] | 1290 | |
---|
[3294] | 1291 | DO jk = 1, jpkm1 - 1 |
---|
[3764] | 1292 | zdxtmp = xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
[3294] | 1293 | ztmp1 = (zdf(jk+1) + 2._wp * zdf(jk)) / zdxtmp |
---|
| 1294 | ztmp2 = 6._wp * (fsp(ji,jj,jk+1) - fsp(ji,jj,jk)) / zdxtmp / zdxtmp |
---|
[3764] | 1295 | zddf1 = -2._wp * ztmp1 + ztmp2 |
---|
[3294] | 1296 | ztmp1 = (2._wp * zdf(jk+1) + zdf(jk)) / zdxtmp |
---|
[3764] | 1297 | zddf2 = 2._wp * ztmp1 - ztmp2 |
---|
| 1298 | |
---|
[3294] | 1299 | dsp(ji,jj,jk) = (zddf2 - zddf1) / 6._wp / zdxtmp |
---|
| 1300 | csp(ji,jj,jk) = ( xsp(ji,jj,jk+1) * zddf1 - xsp(ji,jj,jk)*zddf2 ) / 2._wp / zdxtmp |
---|
[3764] | 1301 | bsp(ji,jj,jk) = ( fsp(ji,jj,jk+1) - fsp(ji,jj,jk) ) / zdxtmp - & |
---|
[3294] | 1302 | & csp(ji,jj,jk) * ( xsp(ji,jj,jk+1) + xsp(ji,jj,jk) ) - & |
---|
| 1303 | & dsp(ji,jj,jk) * ((xsp(ji,jj,jk+1) + xsp(ji,jj,jk))**2 - & |
---|
| 1304 | & xsp(ji,jj,jk+1) * xsp(ji,jj,jk)) |
---|
| 1305 | asp(ji,jj,jk) = fsp(ji,jj,jk) - xsp(ji,jj,jk) * (bsp(ji,jj,jk) + & |
---|
| 1306 | & (xsp(ji,jj,jk) * (csp(ji,jj,jk) + & |
---|
| 1307 | & dsp(ji,jj,jk) * xsp(ji,jj,jk)))) |
---|
| 1308 | END DO |
---|
| 1309 | END DO |
---|
| 1310 | END DO |
---|
[3764] | 1311 | |
---|
[3294] | 1312 | ELSE IF (polynomial_type == 2) THEN ! Linear |
---|
| 1313 | DO ji = 1, jpi |
---|
| 1314 | DO jj = 1, jpj |
---|
| 1315 | DO jk = 1, jpkm1-1 |
---|
[3764] | 1316 | zdxtmp =xsp(ji,jj,jk+1) - xsp(ji,jj,jk) |
---|
[3294] | 1317 | ztmp1 = fsp(ji,jj,jk+1) - fsp(ji,jj,jk) |
---|
[3764] | 1318 | |
---|
[3294] | 1319 | dsp(ji,jj,jk) = 0._wp |
---|
| 1320 | csp(ji,jj,jk) = 0._wp |
---|
| 1321 | bsp(ji,jj,jk) = ztmp1 / zdxtmp |
---|
| 1322 | asp(ji,jj,jk) = fsp(ji,jj,jk) - bsp(ji,jj,jk) * xsp(ji,jj,jk) |
---|
| 1323 | END DO |
---|
| 1324 | END DO |
---|
| 1325 | END DO |
---|
| 1326 | |
---|
| 1327 | ELSE |
---|
| 1328 | CALL ctl_stop( 'invalid polynomial type in cspline' ) |
---|
| 1329 | ENDIF |
---|
| 1330 | |
---|
| 1331 | END SUBROUTINE cspline |
---|
| 1332 | |
---|
| 1333 | |
---|
[3764] | 1334 | FUNCTION interp1(x, xl, xr, fl, fr) RESULT(f) |
---|
[3294] | 1335 | !!---------------------------------------------------------------------- |
---|
| 1336 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1337 | !! |
---|
[3294] | 1338 | !! ** Purpose : 1-d linear interpolation |
---|
[3764] | 1339 | !! |
---|
[4990] | 1340 | !! ** Method : interpolation is straight forward |
---|
[3764] | 1341 | !! extrapolation is also permitted (no value limit) |
---|
[3294] | 1342 | !!---------------------------------------------------------------------- |
---|
| 1343 | IMPLICIT NONE |
---|
[3764] | 1344 | REAL(wp), INTENT(in) :: x, xl, xr, fl, fr |
---|
[3294] | 1345 | REAL(wp) :: f ! result of the interpolation (extrapolation) |
---|
| 1346 | REAL(wp) :: zdeltx |
---|
| 1347 | !!---------------------------------------------------------------------- |
---|
| 1348 | |
---|
| 1349 | zdeltx = xr - xl |
---|
| 1350 | IF(abs(zdeltx) <= 10._wp * EPSILON(x)) THEN |
---|
| 1351 | f = 0.5_wp * (fl + fr) |
---|
| 1352 | ELSE |
---|
| 1353 | f = ( (x - xl ) * fr - ( x - xr ) * fl ) / zdeltx |
---|
| 1354 | ENDIF |
---|
[3764] | 1355 | |
---|
[3294] | 1356 | END FUNCTION interp1 |
---|
| 1357 | |
---|
[4990] | 1358 | |
---|
[3764] | 1359 | FUNCTION interp2(x, a, b, c, d) RESULT(f) |
---|
[3294] | 1360 | !!---------------------------------------------------------------------- |
---|
| 1361 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1362 | !! |
---|
[3294] | 1363 | !! ** Purpose : 1-d constrained cubic spline interpolation |
---|
[3764] | 1364 | !! |
---|
[3294] | 1365 | !! ** Method : cubic spline interpolation |
---|
| 1366 | !! |
---|
| 1367 | !!---------------------------------------------------------------------- |
---|
| 1368 | IMPLICIT NONE |
---|
[3764] | 1369 | REAL(wp), INTENT(in) :: x, a, b, c, d |
---|
[3294] | 1370 | REAL(wp) :: f ! value from the interpolation |
---|
| 1371 | !!---------------------------------------------------------------------- |
---|
| 1372 | |
---|
[3764] | 1373 | f = a + x* ( b + x * ( c + d * x ) ) |
---|
[3294] | 1374 | |
---|
| 1375 | END FUNCTION interp2 |
---|
| 1376 | |
---|
| 1377 | |
---|
[3764] | 1378 | FUNCTION interp3(x, a, b, c, d) RESULT(f) |
---|
[3294] | 1379 | !!---------------------------------------------------------------------- |
---|
| 1380 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1381 | !! |
---|
[3294] | 1382 | !! ** Purpose : Calculate the first order of deriavtive of |
---|
| 1383 | !! a cubic spline function y=a+b*x+c*x^2+d*x^3 |
---|
[3764] | 1384 | !! |
---|
[3294] | 1385 | !! ** Method : f=dy/dx=b+2*c*x+3*d*x^2 |
---|
| 1386 | !! |
---|
| 1387 | !!---------------------------------------------------------------------- |
---|
| 1388 | IMPLICIT NONE |
---|
[3764] | 1389 | REAL(wp), INTENT(in) :: x, a, b, c, d |
---|
[3294] | 1390 | REAL(wp) :: f ! value from the interpolation |
---|
| 1391 | !!---------------------------------------------------------------------- |
---|
| 1392 | |
---|
| 1393 | f = b + x * ( 2._wp * c + 3._wp * d * x) |
---|
| 1394 | |
---|
| 1395 | END FUNCTION interp3 |
---|
| 1396 | |
---|
[3764] | 1397 | |
---|
| 1398 | FUNCTION integ_spline(xl, xr, a, b, c, d) RESULT(f) |
---|
[3294] | 1399 | !!---------------------------------------------------------------------- |
---|
| 1400 | !! *** ROUTINE interp1 *** |
---|
[3764] | 1401 | !! |
---|
[3294] | 1402 | !! ** Purpose : 1-d constrained cubic spline integration |
---|
| 1403 | !! |
---|
[3764] | 1404 | !! ** Method : integrate polynomial a+bx+cx^2+dx^3 from xl to xr |
---|
| 1405 | !! |
---|
[3294] | 1406 | !!---------------------------------------------------------------------- |
---|
| 1407 | IMPLICIT NONE |
---|
[3764] | 1408 | REAL(wp), INTENT(in) :: xl, xr, a, b, c, d |
---|
| 1409 | REAL(wp) :: za1, za2, za3 |
---|
[3294] | 1410 | REAL(wp) :: f ! integration result |
---|
| 1411 | !!---------------------------------------------------------------------- |
---|
| 1412 | |
---|
[3764] | 1413 | za1 = 0.5_wp * b |
---|
| 1414 | za2 = c / 3.0_wp |
---|
| 1415 | za3 = 0.25_wp * d |
---|
[3294] | 1416 | |
---|
| 1417 | f = xr * ( a + xr * ( za1 + xr * ( za2 + za3 * xr ) ) ) - & |
---|
| 1418 | & xl * ( a + xl * ( za1 + xl * ( za2 + za3 * xl ) ) ) |
---|
| 1419 | |
---|
[3632] | 1420 | END FUNCTION integ_spline |
---|
[3294] | 1421 | |
---|
[3] | 1422 | !!====================================================================== |
---|
| 1423 | END MODULE dynhpg |
---|
[3632] | 1424 | |
---|