1 | MODULE zpshde |
---|
2 | !!============================================================================== |
---|
3 | !! *** MODULE zpshde *** |
---|
4 | !! z-coordinate - partial step : Horizontal Derivative |
---|
5 | !!============================================================================== |
---|
6 | |
---|
7 | !!---------------------------------------------------------------------- |
---|
8 | !! zps_hde : Horizontal DErivative of T, S and rd at the last |
---|
9 | !! ocean level (Z-coord. with Partial Steps) |
---|
10 | !!---------------------------------------------------------------------- |
---|
11 | !! * Modules used |
---|
12 | USE dom_oce ! ocean space domain variables |
---|
13 | USE oce ! ocean dynamics and tracers variables |
---|
14 | USE phycst ! physical constants |
---|
15 | USE in_out_manager ! I/O manager |
---|
16 | USE eosbn2 ! ocean equation of state |
---|
17 | USE lbclnk ! lateral boundary conditions (or mpp link) |
---|
18 | |
---|
19 | IMPLICIT NONE |
---|
20 | PRIVATE |
---|
21 | |
---|
22 | !! * Routine accessibility |
---|
23 | PUBLIC zps_hde ! routine called by step.F90 |
---|
24 | |
---|
25 | !! * module variables |
---|
26 | INTEGER, DIMENSION(jpi,jpj) :: & |
---|
27 | mbatu, mbatv ! bottom ocean level index at U- and V-points |
---|
28 | |
---|
29 | !! * Substitutions |
---|
30 | # include "domzgr_substitute.h90" |
---|
31 | # include "vectopt_loop_substitute.h90" |
---|
32 | !!---------------------------------------------------------------------- |
---|
33 | !!---------------------------------------------------------------------- |
---|
34 | !! OPA 9.0 , LOCEAN-IPSL (2005) |
---|
35 | !! $Id$ |
---|
36 | !! This software is governed by the CeCILL licence see modipsl/doc/NEMO_CeCILL.txt |
---|
37 | !!---------------------------------------------------------------------- |
---|
38 | CONTAINS |
---|
39 | |
---|
40 | SUBROUTINE zps_hde ( kt, ptem, psal, prd , & |
---|
41 | pgtu, pgsu, pgru, & |
---|
42 | pgtv, pgsv, pgrv ) |
---|
43 | !!---------------------------------------------------------------------- |
---|
44 | !! *** ROUTINE zps_hde *** |
---|
45 | !! |
---|
46 | !! ** Purpose : Compute the horizontal derivative of T, S and rd |
---|
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, pgsu, pgru: horizontal gradient of T, S |
---|
83 | !! and rd at U-points |
---|
84 | !! - pgtv, pgsv, pgrv: horizontal gradient of T, S |
---|
85 | !! and rd at V-points |
---|
86 | !! |
---|
87 | !! History : |
---|
88 | !! 8.5 ! 02-04 (A. Bozec) Original code |
---|
89 | !! 8.5 ! 02-08 (G. Madec E. Durand) Optimization and Free form |
---|
90 | !!---------------------------------------------------------------------- |
---|
91 | !! * Arguments |
---|
92 | INTEGER, INTENT( in ) :: kt ! ocean time-step index |
---|
93 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT( in ) :: & |
---|
94 | ptem, psal, prd ! 3D T, S and rd fields |
---|
95 | REAL(wp), DIMENSION(jpi,jpj), INTENT( out ) :: & |
---|
96 | pgtu, pgsu, pgru, & ! horizontal grad. of T, S and rd at u- |
---|
97 | pgtv, pgsv, pgrv ! and v-points of the partial step level |
---|
98 | |
---|
99 | !! * Local declarations |
---|
100 | INTEGER :: ji, jj, & ! Dummy loop indices |
---|
101 | iku,ikv ! partial step level at u- and v-points |
---|
102 | REAL(wp), DIMENSION(jpi,jpj) :: & |
---|
103 | zti, ztj, zsi, zsj, & ! interpolated value of T, S |
---|
104 | zri, zrj, & ! and rd |
---|
105 | zhgi, zhgj ! depth of interpolation for eos2d |
---|
106 | REAL(wp) :: & |
---|
107 | ze3wu, ze3wv, & ! temporary scalars |
---|
108 | zmaxu1, zmaxu2, & ! " " |
---|
109 | zmaxv1, zmaxv2 ! " " |
---|
110 | |
---|
111 | ! Initialization (first time-step only): compute mbatu and mbatv |
---|
112 | IF( kt == nit000 ) THEN |
---|
113 | mbatu(:,:) = 0 |
---|
114 | mbatv(:,:) = 0 |
---|
115 | DO jj = 1, jpjm1 |
---|
116 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
117 | mbatu(ji,jj) = MAX( MIN( mbathy(ji,jj), mbathy(ji+1,jj ) ) - 1, 2 ) |
---|
118 | mbatv(ji,jj) = MAX( MIN( mbathy(ji,jj), mbathy(ji ,jj+1) ) - 1, 2 ) |
---|
119 | END DO |
---|
120 | END DO |
---|
121 | zti(:,:) = FLOAT( mbatu(:,:) ) |
---|
122 | ztj(:,:) = FLOAT( mbatv(:,:) ) |
---|
123 | ! lateral boundary conditions: T-point, sign unchanged |
---|
124 | CALL lbc_lnk( zti , 'U', 1. ) |
---|
125 | CALL lbc_lnk( ztj , 'V', 1. ) |
---|
126 | mbatu(:,:) = MAX( INT( zti(:,:) ), 2 ) |
---|
127 | mbatv(:,:) = MAX( INT( ztj(:,:) ), 2 ) |
---|
128 | ENDIF |
---|
129 | |
---|
130 | |
---|
131 | ! Interpolation of T and S at the last ocean level |
---|
132 | # if defined key_vectopt_loop |
---|
133 | jj = 1 |
---|
134 | DO ji = 1, jpij-jpi ! vector opt. (forced unrolled) |
---|
135 | # else |
---|
136 | DO jj = 1, jpjm1 |
---|
137 | DO ji = 1, jpim1 |
---|
138 | # endif |
---|
139 | ! last level |
---|
140 | iku = mbatu(ji,jj) |
---|
141 | ikv = mbatv(ji,jj) |
---|
142 | |
---|
143 | ze3wu = fse3w(ji+1,jj ,iku) - fse3w(ji,jj,iku) |
---|
144 | ze3wv = fse3w(ji ,jj+1,ikv) - fse3w(ji,jj,ikv) |
---|
145 | zmaxu1 = ze3wu / fse3w(ji+1,jj ,iku) |
---|
146 | zmaxu2 = -ze3wu / fse3w(ji ,jj ,iku) |
---|
147 | zmaxv1 = ze3wv / fse3w(ji ,jj+1,ikv) |
---|
148 | zmaxv2 = -ze3wv / fse3w(ji ,jj ,ikv) |
---|
149 | |
---|
150 | ! i- direction |
---|
151 | |
---|
152 | IF( ze3wu >= 0. ) THEN ! case 1 |
---|
153 | ! interpolated values of T and S |
---|
154 | zti(ji,jj) = ptem(ji+1,jj,iku) + zmaxu1 * ( ptem(ji+1,jj,iku-1) - ptem(ji+1,jj,iku) ) |
---|
155 | zsi(ji,jj) = psal(ji+1,jj,iku) + zmaxu1 * ( psal(ji+1,jj,iku-1) - psal(ji+1,jj,iku) ) |
---|
156 | ! depth of the partial step level |
---|
157 | zhgi(ji,jj) = fsdept(ji,jj,iku) |
---|
158 | ! gradient of T and S |
---|
159 | pgtu(ji,jj) = umask(ji,jj,1) * ( zti(ji,jj) - ptem(ji,jj,iku) ) |
---|
160 | pgsu(ji,jj) = umask(ji,jj,1) * ( zsi(ji,jj) - psal(ji,jj,iku) ) |
---|
161 | |
---|
162 | ELSE ! case 2 |
---|
163 | ! interpolated values of T and S |
---|
164 | zti(ji,jj) = ptem(ji,jj,iku) + zmaxu2 * ( ptem(ji,jj,iku-1) - ptem(ji,jj,iku) ) |
---|
165 | zsi(ji,jj) = psal(ji,jj,iku) + zmaxu2 * ( psal(ji,jj,iku-1) - psal(ji,jj,iku) ) |
---|
166 | ! depth of the partial step level |
---|
167 | zhgi(ji,jj) = fsdept(ji+1,jj,iku) |
---|
168 | ! gradient of T and S |
---|
169 | pgtu(ji,jj) = umask(ji,jj,1) * ( ptem(ji+1,jj,iku) - zti (ji,jj) ) |
---|
170 | pgsu(ji,jj) = umask(ji,jj,1) * ( psal(ji+1,jj,iku) - zsi (ji,jj) ) |
---|
171 | ENDIF |
---|
172 | |
---|
173 | ! j- direction |
---|
174 | |
---|
175 | IF( ze3wv >= 0. ) THEN ! case 1 |
---|
176 | ! interpolated values of T and S |
---|
177 | ztj(ji,jj) = ptem(ji,jj+1,ikv) + zmaxv1 * ( ptem(ji,jj+1,ikv-1) - ptem(ji,jj+1,ikv) ) |
---|
178 | zsj(ji,jj) = psal(ji,jj+1,ikv) + zmaxv1 * ( psal(ji,jj+1,ikv-1) - psal(ji,jj+1,ikv) ) |
---|
179 | ! depth of the partial step level |
---|
180 | zhgj(ji,jj) = fsdept(ji,jj,ikv) |
---|
181 | ! gradient of T and S |
---|
182 | pgtv(ji,jj) = vmask(ji,jj,1) * ( ztj(ji,jj) - ptem(ji,jj,ikv) ) |
---|
183 | pgsv(ji,jj) = vmask(ji,jj,1) * ( zsj(ji,jj) - psal(ji,jj,ikv) ) |
---|
184 | |
---|
185 | ELSE ! case 2 |
---|
186 | ! interpolated values of T and S |
---|
187 | ztj(ji,jj) = ptem(ji,jj,ikv) + zmaxv2 * ( ptem(ji,jj,ikv-1) - ptem(ji,jj,ikv) ) |
---|
188 | zsj(ji,jj) = psal(ji,jj,ikv) + zmaxv2 * ( psal(ji,jj,ikv-1) - psal(ji,jj,ikv) ) |
---|
189 | ! depth of the partial step level |
---|
190 | zhgj(ji,jj) = fsdept(ji,jj+1,ikv) |
---|
191 | ! gradient of T and S |
---|
192 | pgtv(ji,jj) = vmask(ji,jj,1) * ( ptem(ji,jj+1,ikv) - ztj(ji,jj) ) |
---|
193 | pgsv(ji,jj) = vmask(ji,jj,1) * ( psal(ji,jj+1,ikv) - zsj(ji,jj) ) |
---|
194 | ENDIF |
---|
195 | # if ! defined key_vectopt_loop |
---|
196 | END DO |
---|
197 | # endif |
---|
198 | END DO |
---|
199 | |
---|
200 | ! Compute interpolated rd from zti, zsi, ztj, zsj for the 2 cases at the depth of the partial |
---|
201 | ! step and store it in zri, zrj for each case |
---|
202 | CALL eos( zti, zsi, zhgi, zri ) |
---|
203 | CALL eos( ztj, zsj, zhgj, zrj ) |
---|
204 | |
---|
205 | |
---|
206 | ! Gradient of density at the last level |
---|
207 | # if defined key_vectopt_loop |
---|
208 | jj = 1 |
---|
209 | DO ji = 1, jpij-jpi ! vector opt. (forced unrolled) |
---|
210 | # else |
---|
211 | DO jj = 1, jpjm1 |
---|
212 | DO ji = 1, jpim1 |
---|
213 | # endif |
---|
214 | iku = mbatu(ji,jj) |
---|
215 | ikv = mbatv(ji,jj) |
---|
216 | ze3wu = fse3w(ji+1,jj ,iku) - fse3w(ji,jj,iku) |
---|
217 | ze3wv = fse3w(ji ,jj+1,ikv) - fse3w(ji,jj,ikv) |
---|
218 | IF( ze3wu >= 0. ) THEN ! i-direction: case 1 |
---|
219 | pgru(ji,jj) = umask(ji,jj,1) * ( zri(ji,jj) - prd(ji,jj,iku) ) |
---|
220 | ELSE ! i-direction: case 2 |
---|
221 | pgru(ji,jj) = umask(ji,jj,1) * ( prd(ji+1,jj,iku) - zri(ji,jj) ) |
---|
222 | ENDIF |
---|
223 | IF( ze3wv >= 0. ) THEN ! j-direction: case 1 |
---|
224 | pgrv(ji,jj) = vmask(ji,jj,1) * ( zrj(ji,jj) - prd(ji,jj,ikv) ) |
---|
225 | ELSE ! j-direction: case 2 |
---|
226 | pgrv(ji,jj) = vmask(ji,jj,1) * ( prd(ji,jj+1,ikv) - zrj(ji,jj) ) |
---|
227 | ENDIF |
---|
228 | # if ! defined key_vectopt_loop |
---|
229 | END DO |
---|
230 | # endif |
---|
231 | END DO |
---|
232 | |
---|
233 | ! Lateral boundary conditions on each gradient |
---|
234 | CALL lbc_lnk( pgtu , 'U', -1. ) ; CALL lbc_lnk( pgtv , 'V', -1. ) |
---|
235 | CALL lbc_lnk( pgsu , 'U', -1. ) ; CALL lbc_lnk( pgsv , 'V', -1. ) |
---|
236 | CALL lbc_lnk( pgru , 'U', -1. ) ; CALL lbc_lnk( pgrv , 'V', -1. ) |
---|
237 | |
---|
238 | END SUBROUTINE zps_hde |
---|
239 | |
---|
240 | !!====================================================================== |
---|
241 | END MODULE zpshde |
---|