1 | MODULE zpshde |
---|
2 | !!====================================================================== |
---|
3 | !! *** MODULE zpshde *** |
---|
4 | !! z-coordinate + partial step : Horizontal Derivative at ocean bottom level |
---|
5 | !!====================================================================== |
---|
6 | !! History : OPA ! 2002-04 (A. Bozec) Original code |
---|
7 | !! NEMO 1.0 ! 2002-08 (G. Madec E. Durand) Optimization and Free form |
---|
8 | !! - ! 2004-03 (C. Ethe) adapted for passive tracers |
---|
9 | !! 3.3 ! 2010-05 (C. Ethe, G. Madec) merge TRC-TRA |
---|
10 | !!====================================================================== |
---|
11 | |
---|
12 | !!---------------------------------------------------------------------- |
---|
13 | !! zps_hde : Horizontal DErivative of T, S and rd at the last |
---|
14 | !! ocean level (Z-coord. with Partial Steps) |
---|
15 | !!---------------------------------------------------------------------- |
---|
16 | USE oce ! ocean: dynamics and tracers variables |
---|
17 | USE dom_oce ! domain: ocean variables |
---|
18 | USE phycst ! physical constants |
---|
19 | USE eosbn2 ! ocean equation of state |
---|
20 | USE in_out_manager ! I/O manager |
---|
21 | USE lbclnk ! lateral boundary conditions (or mpp link) |
---|
22 | USE lib_mpp ! MPP library |
---|
23 | USE wrk_nemo ! Memory allocation |
---|
24 | USE timing ! Timing |
---|
25 | |
---|
26 | IMPLICIT NONE |
---|
27 | PRIVATE |
---|
28 | |
---|
29 | PUBLIC zps_hde ! routine called by step.F90 |
---|
30 | |
---|
31 | !! * Substitutions |
---|
32 | # include "domzgr_substitute.h90" |
---|
33 | # include "vectopt_loop_substitute.h90" |
---|
34 | !!---------------------------------------------------------------------- |
---|
35 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
---|
36 | !! $Id$ |
---|
37 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
---|
38 | !!---------------------------------------------------------------------- |
---|
39 | CONTAINS |
---|
40 | |
---|
41 | SUBROUTINE zps_hde( kt, kjpt, pta, pgtu, pgtv, & |
---|
42 | prd, pgru, pgrv ) |
---|
43 | !!---------------------------------------------------------------------- |
---|
44 | !! *** ROUTINE zps_hde *** |
---|
45 | !! |
---|
46 | !! ** Purpose : Compute the horizontal derivative of T, S and rho |
---|
47 | !! at u- and v-points with a linear interpolation for z-coordinate |
---|
48 | !! with partial steps. |
---|
49 | !! |
---|
50 | !! ** Method : In z-coord with partial steps, scale factors on last |
---|
51 | !! levels are different for each grid point, so that T, S and rd |
---|
52 | !! points are not at the same depth as in z-coord. To have horizontal |
---|
53 | !! gradients again, we interpolate T and S at the good depth : |
---|
54 | !! Linear interpolation of T, S |
---|
55 | !! Computation of di(tb) and dj(tb) by vertical interpolation: |
---|
56 | !! di(t) = t~ - t(i,j,k) or t(i+1,j,k) - t~ |
---|
57 | !! dj(t) = t~ - t(i,j,k) or t(i,j+1,k) - t~ |
---|
58 | !! This formulation computes the two cases: |
---|
59 | !! CASE 1 CASE 2 |
---|
60 | !! k-1 ___ ___________ k-1 ___ ___________ |
---|
61 | !! Ti T~ T~ Ti+1 |
---|
62 | !! _____ _____ |
---|
63 | !! k | |Ti+1 k Ti | | |
---|
64 | !! | |____ ____| | |
---|
65 | !! ___ | | | ___ | | | |
---|
66 | !! |
---|
67 | !! case 1-> e3w(i+1) >= e3w(i) ( and e3w(j+1) >= e3w(j) ) then |
---|
68 | !! t~ = t(i+1,j ,k) + (e3w(i+1) - e3w(i)) * dk(Ti+1)/e3w(i+1) |
---|
69 | !! ( t~ = t(i ,j+1,k) + (e3w(j+1) - e3w(j)) * dk(Tj+1)/e3w(j+1) ) |
---|
70 | !! or |
---|
71 | !! case 2-> e3w(i+1) <= e3w(i) ( and e3w(j+1) <= e3w(j) ) then |
---|
72 | !! t~ = t(i,j,k) + (e3w(i) - e3w(i+1)) * dk(Ti)/e3w(i ) |
---|
73 | !! ( t~ = t(i,j,k) + (e3w(j) - e3w(j+1)) * dk(Tj)/e3w(j ) ) |
---|
74 | !! Idem for di(s) and dj(s) |
---|
75 | !! |
---|
76 | !! For rho, we call eos_insitu_2d which will compute rd~(t~,s~) at |
---|
77 | !! the good depth zh from interpolated T and S for the different |
---|
78 | !! formulation of the equation of state (eos). |
---|
79 | !! Gradient formulation for rho : |
---|
80 | !! di(rho) = rd~ - rd(i,j,k) or rd(i+1,j,k) - rd~ |
---|
81 | !! |
---|
82 | !! ** Action : - pgtu, pgtv: horizontal gradient of tracer at u- & v-points |
---|
83 | !! - pgru, pgrv: horizontal gradient of rho (if present) at u- & v-points |
---|
84 | !!---------------------------------------------------------------------- |
---|
85 | ! |
---|
86 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
---|
87 | INTEGER , INTENT(in ) :: kjpt ! number of tracers |
---|
88 | REAL(wp), DIMENSION(jpi,jpj,jpk,kjpt), INTENT(in ) :: pta ! 4D tracers fields |
---|
89 | REAL(wp), DIMENSION(jpi,jpj, kjpt), INTENT( out) :: pgtu, pgtv ! hor. grad. of ptra at u- & v-pts |
---|
90 | REAL(wp), DIMENSION(jpi,jpj,jpk ), INTENT(in ), OPTIONAL :: prd ! 3D density anomaly fields |
---|
91 | REAL(wp), DIMENSION(jpi,jpj ), INTENT( out), OPTIONAL :: pgru, pgrv ! hor. grad. of prd at u- & v-pts |
---|
92 | ! |
---|
93 | INTEGER :: ji, jj, jn ! Dummy loop indices |
---|
94 | INTEGER :: iku, ikv, ikum1, ikvm1 ! partial step level (ocean bottom level) at u- and v-points |
---|
95 | REAL(wp) :: ze3wu, ze3wv, zmaxu, zmaxv ! temporary scalars |
---|
96 | REAL(wp), POINTER, DIMENSION(:,: ) :: zri, zrj, zhi, zhj |
---|
97 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zti, ztj ! interpolated value of tracer |
---|
98 | !!---------------------------------------------------------------------- |
---|
99 | ! |
---|
100 | IF( nn_timing == 1 ) CALL timing_start( 'zps_hde') |
---|
101 | ! |
---|
102 | CALL wrk_alloc( jpi, jpj, zri, zrj, zhi, zhj ) |
---|
103 | CALL wrk_alloc( jpi, jpj, kjpt, zti, ztj ) |
---|
104 | ! |
---|
105 | DO jn = 1, kjpt !== Interpolation of tracers at the last ocean level ==! |
---|
106 | ! |
---|
107 | # if defined key_vectopt_loop |
---|
108 | jj = 1 |
---|
109 | DO ji = 1, jpij-jpi ! vector opt. (forced unrolled) |
---|
110 | # else |
---|
111 | DO jj = 1, jpjm1 |
---|
112 | DO ji = 1, jpim1 |
---|
113 | # endif |
---|
114 | iku = mbku(ji,jj) ; ikum1 = MAX( iku - 1 , 1 ) ! last and before last ocean level at u- & v-points |
---|
115 | ikv = mbkv(ji,jj) ; ikvm1 = MAX( ikv - 1 , 1 ) ! if level first is a p-step, ik.m1=1 |
---|
116 | ze3wu = fse3w(ji+1,jj ,iku) - fse3w(ji,jj,iku) |
---|
117 | ze3wv = fse3w(ji ,jj+1,ikv) - fse3w(ji,jj,ikv) |
---|
118 | ! |
---|
119 | ! i- direction |
---|
120 | IF( ze3wu >= 0._wp ) THEN ! case 1 |
---|
121 | zmaxu = ze3wu / fse3w(ji+1,jj,iku) |
---|
122 | ! interpolated values of tracers |
---|
123 | zti(ji,jj,jn) = pta(ji+1,jj,iku,jn) + zmaxu * ( pta(ji+1,jj,ikum1,jn) - pta(ji+1,jj,iku,jn) ) |
---|
124 | ! gradient of tracers |
---|
125 | pgtu(ji,jj,jn) = umask(ji,jj,1) * ( zti(ji,jj,jn) - pta(ji,jj,iku,jn) ) |
---|
126 | ELSE ! case 2 |
---|
127 | zmaxu = -ze3wu / fse3w(ji,jj,iku) |
---|
128 | ! interpolated values of tracers |
---|
129 | zti(ji,jj,jn) = pta(ji,jj,iku,jn) + zmaxu * ( pta(ji,jj,ikum1,jn) - pta(ji,jj,iku,jn) ) |
---|
130 | ! gradient of tracers |
---|
131 | pgtu(ji,jj,jn) = umask(ji,jj,1) * ( pta(ji+1,jj,iku,jn) - zti(ji,jj,jn) ) |
---|
132 | ENDIF |
---|
133 | ! |
---|
134 | ! j- direction |
---|
135 | IF( ze3wv >= 0._wp ) THEN ! case 1 |
---|
136 | zmaxv = ze3wv / fse3w(ji,jj+1,ikv) |
---|
137 | ! interpolated values of tracers |
---|
138 | ztj(ji,jj,jn) = pta(ji,jj+1,ikv,jn) + zmaxv * ( pta(ji,jj+1,ikvm1,jn) - pta(ji,jj+1,ikv,jn) ) |
---|
139 | ! gradient of tracers |
---|
140 | pgtv(ji,jj,jn) = vmask(ji,jj,1) * ( ztj(ji,jj,jn) - pta(ji,jj,ikv,jn) ) |
---|
141 | ELSE ! case 2 |
---|
142 | zmaxv = -ze3wv / fse3w(ji,jj,ikv) |
---|
143 | ! interpolated values of tracers |
---|
144 | ztj(ji,jj,jn) = pta(ji,jj,ikv,jn) + zmaxv * ( pta(ji,jj,ikvm1,jn) - pta(ji,jj,ikv,jn) ) |
---|
145 | ! gradient of tracers |
---|
146 | pgtv(ji,jj,jn) = vmask(ji,jj,1) * ( pta(ji,jj+1,ikv,jn) - ztj(ji,jj,jn) ) |
---|
147 | ENDIF |
---|
148 | # if ! defined key_vectopt_loop |
---|
149 | END DO |
---|
150 | # endif |
---|
151 | END DO |
---|
152 | CALL lbc_lnk( pgtu(:,:,jn), 'U', -1. ) ; CALL lbc_lnk( pgtv(:,:,jn), 'V', -1. ) ! Lateral boundary cond. |
---|
153 | ! |
---|
154 | END DO |
---|
155 | |
---|
156 | ! horizontal derivative of density anomalies (rd) |
---|
157 | IF( PRESENT( prd ) ) THEN ! depth of the partial step level |
---|
158 | # if defined key_vectopt_loop |
---|
159 | jj = 1 |
---|
160 | DO ji = 1, jpij-jpi ! vector opt. (forced unrolled) |
---|
161 | # else |
---|
162 | DO jj = 1, jpjm1 |
---|
163 | DO ji = 1, jpim1 |
---|
164 | # endif |
---|
165 | iku = mbku(ji,jj) |
---|
166 | ikv = mbkv(ji,jj) |
---|
167 | ze3wu = fse3w(ji+1,jj ,iku) - fse3w(ji,jj,iku) |
---|
168 | ze3wv = fse3w(ji ,jj+1,ikv) - fse3w(ji,jj,ikv) |
---|
169 | IF( ze3wu >= 0._wp ) THEN ; zhi(ji,jj) = fsdept(ji ,jj,iku) ! i-direction: case 1 |
---|
170 | ELSE ; zhi(ji,jj) = fsdept(ji+1,jj,iku) ! - - case 2 |
---|
171 | ENDIF |
---|
172 | IF( ze3wv >= 0._wp ) THEN ; zhj(ji,jj) = fsdept(ji,jj ,ikv) ! j-direction: case 1 |
---|
173 | ELSE ; zhj(ji,jj) = fsdept(ji,jj+1,ikv) ! - - case 2 |
---|
174 | ENDIF |
---|
175 | # if ! defined key_vectopt_loop |
---|
176 | END DO |
---|
177 | # endif |
---|
178 | END DO |
---|
179 | |
---|
180 | ! Compute interpolated rd from zti, ztj for the 2 cases at the depth of the partial |
---|
181 | ! step and store it in zri, zrj for each case |
---|
182 | CALL eos( zti, zhi, zri ) |
---|
183 | CALL eos( ztj, zhj, zrj ) |
---|
184 | |
---|
185 | ! Gradient of density at the last level |
---|
186 | # if defined key_vectopt_loop |
---|
187 | jj = 1 |
---|
188 | DO ji = 1, jpij-jpi ! vector opt. (forced unrolled) |
---|
189 | # else |
---|
190 | DO jj = 1, jpjm1 |
---|
191 | DO ji = 1, jpim1 |
---|
192 | # endif |
---|
193 | iku = mbku(ji,jj) |
---|
194 | ikv = mbkv(ji,jj) |
---|
195 | ze3wu = fse3w(ji+1,jj ,iku) - fse3w(ji,jj,iku) |
---|
196 | ze3wv = fse3w(ji ,jj+1,ikv) - fse3w(ji,jj,ikv) |
---|
197 | IF( ze3wu >= 0._wp ) THEN ; pgru(ji,jj) = umask(ji,jj,1) * ( zri(ji ,jj) - prd(ji,jj,iku) ) ! i: 1 |
---|
198 | ELSE ; pgru(ji,jj) = umask(ji,jj,1) * ( prd(ji+1,jj,iku) - zri(ji,jj) ) ! i: 2 |
---|
199 | ENDIF |
---|
200 | IF( ze3wv >= 0._wp ) THEN ; pgrv(ji,jj) = vmask(ji,jj,1) * ( zrj(ji,jj ) - prd(ji,jj,ikv) ) ! j: 1 |
---|
201 | ELSE ; pgrv(ji,jj) = vmask(ji,jj,1) * ( prd(ji,jj+1,ikv) - zrj(ji,jj) ) ! j: 2 |
---|
202 | ENDIF |
---|
203 | # if ! defined key_vectopt_loop |
---|
204 | END DO |
---|
205 | # endif |
---|
206 | END DO |
---|
207 | CALL lbc_lnk( pgru , 'U', -1. ) ; CALL lbc_lnk( pgrv , 'V', -1. ) ! Lateral boundary conditions |
---|
208 | ! |
---|
209 | END IF |
---|
210 | ! |
---|
211 | CALL wrk_dealloc( jpi, jpj, zri, zrj, zhi, zhj ) |
---|
212 | CALL wrk_dealloc( jpi, jpj, kjpt, zti, ztj ) |
---|
213 | ! |
---|
214 | IF( nn_timing == 1 ) CALL timing_stop( 'zps_hde') |
---|
215 | ! |
---|
216 | END SUBROUTINE zps_hde |
---|
217 | |
---|
218 | !!====================================================================== |
---|
219 | END MODULE zpshde |
---|