Newer
Older
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
MODULE ablmod
!!======================================================================
!! *** MODULE ablmod ***
!! Surface module : ABL computation to provide atmospheric data
!! for surface fluxes computation
!!======================================================================
!! History : 3.6 ! 2019-03 (F. Lemarié & G. Samson) Original code
!!----------------------------------------------------------------------
!!----------------------------------------------------------------------
!! abl_stp : ABL single column model
!! abl_zdf_tke : atmospheric vertical closure
!!----------------------------------------------------------------------
USE abl ! ABL dynamics and tracers
USE par_abl ! ABL constants
USE phycst ! physical constants
USE dom_oce, ONLY : tmask
USE sbc_oce, ONLY : ght_abl, ghw_abl, e3t_abl, e3w_abl, jpka, jpkam1, rhoa
USE sbcblk ! use rn_efac
USE sbc_phy ! Catalog of functions for physical/meteorological parameters in the marine boundary layer
!
USE prtctl ! Print control (prt_ctl routine)
USE iom ! IOM library
USE in_out_manager ! I/O manager
USE lib_mpp ! MPP library
USE timing ! Timing
IMPLICIT NONE
PUBLIC abl_stp ! called by sbcabl.F90
REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:) :: ustar2, zrough
!! * Substitutions
# include "do_loop_substitute.h90"
CONTAINS
!===================================================================================================
SUBROUTINE abl_stp( kt, psst, pssu, pssv, pssq, & ! in
& pu_dta, pv_dta, pt_dta, pq_dta, &
& pslp_dta, pgu_dta, pgv_dta, &
& pcd_du, psen, pevp, plat, & ! in/out
& pwndm, ptaui, ptauj, ptaum &
#if defined key_si3
& , ptm_su, pssu_ice, pssv_ice &
& , pssq_ice, pcd_du_ice, psen_ice &
& , pevp_ice, pwndm_ice, pfrac_oce &
& , ptaui_ice, ptauj_ice &
#endif
& )
!---------------------------------------------------------------------------------------------------
!!---------------------------------------------------------------------
!! *** ROUTINE abl_stp ***
!!
!! ** Purpose : Time-integration of the ABL model
!!
!! ** Method : Compute atmospheric variables : vertical turbulence
!! + Coriolis term + newtonian relaxation
!!
!! ** Action : - Advance TKE to time n+1 and compute Avm_abl, Avt_abl, PBLh
!! - Advance tracers to time n+1 (Euler backward scheme)
!! - Compute Coriolis term with forward-backward scheme (possibly with geostrophic guide)
!! - Advance u,v to time n+1 (Euler backward scheme)
!! - Apply newtonian relaxation on the dynamics and the tracers
!! - Finalize flux computation in psen, pevp, pwndm, ptaui, ptauj, ptaum
!!
!!----------------------------------------------------------------------
INTEGER , INTENT(in ) :: kt ! time step index
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: psst ! sea-surface temperature [Celsius]
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: pssu ! sea-surface u (U-point)
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: pssv ! sea-surface v (V-point)
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: pssq ! sea-surface humidity
REAL(wp) , INTENT(in ), DIMENSION(:,:,:) :: pu_dta ! large-scale windi
REAL(wp) , INTENT(in ), DIMENSION(:,:,:) :: pv_dta ! large-scale windj
REAL(wp) , INTENT(in ), DIMENSION(:,:,:) :: pgu_dta ! large-scale hpgi
REAL(wp) , INTENT(in ), DIMENSION(:,:,:) :: pgv_dta ! large-scale hpgj
REAL(wp) , INTENT(in ), DIMENSION(:,:,:) :: pt_dta ! large-scale pot. temp.
REAL(wp) , INTENT(in ), DIMENSION(:,:,:) :: pq_dta ! large-scale humidity
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: pslp_dta ! sea-level pressure
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: pcd_du ! Cd x Du (T-point)
REAL(wp) , INTENT(inout), DIMENSION(:,: ) :: psen ! Ch x Du
REAL(wp) , INTENT(inout), DIMENSION(:,: ) :: pevp ! Ce x Du
Guillaume Samson
committed
REAL(wp) , INTENT(inout), DIMENSION(:,: ) :: pwndm ! ||uwnd - uoce||
REAL(wp) , INTENT( out), DIMENSION(:,: ) :: plat ! latent heat flux
REAL(wp) , INTENT( out), DIMENSION(:,: ) :: ptaui ! taux
REAL(wp) , INTENT( out), DIMENSION(:,: ) :: ptauj ! tauy
REAL(wp) , INTENT( out), DIMENSION(:,: ) :: ptaum ! ||tau||
!
#if defined key_si3
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: ptm_su ! ice-surface temperature [K]
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: pssu_ice ! ice-surface u (U-point)
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: pssv_ice ! ice-surface v (V-point)
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: pssq_ice ! ice-surface humidity
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: pcd_du_ice ! Cd x Du over ice (T-point)
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: psen_ice ! Ch x Du over ice (T-point)
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: pevp_ice ! Ce x Du over ice (T-point)
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: pwndm_ice ! ||uwnd - uice||
REAL(wp) , INTENT(in ), DIMENSION(:,: ) :: pfrac_oce ! ocean fraction
REAL(wp) , INTENT( out), DIMENSION(:,: ) :: ptaui_ice ! ice-surface taux stress (T-point)
REAL(wp) , INTENT( out), DIMENSION(:,: ) :: ptauj_ice ! ice-surface tauy stress (T-point)
#endif
!
REAL(wp), DIMENSION(1:jpi,1:jpj ) :: zwnd_i, zwnd_j
Guillaume Samson
committed
REAL(wp), DIMENSION(1:jpi,1:jpj ) :: zsspt
REAL(wp), DIMENSION(1:jpi,1:jpj ) :: ztabs, zpre
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
REAL(wp), DIMENSION(1:jpi ,2:jpka) :: zCF
!
REAL(wp), DIMENSION(1:jpi ,1:jpka) :: z_elem_a
REAL(wp), DIMENSION(1:jpi ,1:jpka) :: z_elem_b
REAL(wp), DIMENSION(1:jpi ,1:jpka) :: z_elem_c
!
INTEGER :: ji, jj, jk, jtra, jbak ! dummy loop indices
REAL(wp) :: zztmp, zcff, ztemp, zhumi, zcff1, zztmp1, zztmp2
REAL(wp) :: zcff2, zfcor, zmsk, zsig, zcffu, zcffv, zzice,zzoce
LOGICAL :: SemiImp_Cor = .TRUE.
!
!!---------------------------------------------------------------------
!
IF(lwp .AND. kt == nit000) THEN ! control print
WRITE(numout,*)
WRITE(numout,*) 'abl_stp : ABL time stepping'
WRITE(numout,*) '~~~~~~'
ENDIF
!
IF( kt == nit000 ) ALLOCATE ( ustar2( 1:jpi, 1:jpj ) )
IF( kt == nit000 ) ALLOCATE ( zrough( 1:jpi, 1:jpj ) )
!! Compute ustar squared as Cd || Uatm-Uoce ||^2
!! needed for surface boundary condition of TKE
!! pwndm contains | U10m - U_oce | (see blk_oce_1 in sbcblk)
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
zzoce = pCd_du (ji,jj) * pwndm (ji,jj)
#if defined key_si3
zzice = pCd_du_ice(ji,jj) * pwndm_ice(ji,jj)
ustar2(ji,jj) = zzoce * pfrac_oce(ji,jj) + (1._wp - pfrac_oce(ji,jj)) * zzice
#else
ustar2(ji,jj) = zzoce
#endif
!#LB: sorry Cdn_oce is gone:
!zrough(ji,jj) = ght_abl(2) * EXP( - vkarmn / SQRT( MAX( Cdn_oce(ji,jj), 1.e-4 ) ) ) !<-- recover the value of z0 from Cdn_oce
END_2D
zrough(:,:) = z0_from_Cd( ght_abl(2), pCd_du(:,:) / MAX( pwndm(:,:), 0.5_wp ) ) ! #LB: z0_from_Cd is define in sbc_phy.F90...
Guillaume Samson
committed
! sea surface potential temperature [K]
zsspt(:,:) = theta_exner( psst(:,:)+rt0, pslp_dta(:,:) )
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
!
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
! ! 1 *** Advance TKE to time n+1 and compute Avm_abl, Avt_abl, PBLh
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
CALL abl_zdf_tke( ) !--> Avm_abl, Avt_abl, pblh defined on (1,jpi) x (1,jpj)
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
! ! 2 *** Advance tracers to time n+1
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
!-------------
DO jj = 1, jpj ! outer loop !--> tq_abl computed on (1:jpi) x (1:jpj)
!-------------
! Compute matrix elements for interior points
DO jk = 3, jpkam1
DO ji = 1, jpi ! vector opt.
z_elem_a( ji, jk ) = - rDt_abl * Avt_abl( ji, jj, jk-1 ) / e3w_abl( jk-1 ) ! lower-diagonal
z_elem_c( ji, jk ) = - rDt_abl * Avt_abl( ji, jj, jk ) / e3w_abl( jk ) ! upper-diagonal
z_elem_b( ji, jk ) = e3t_abl(jk) - z_elem_a( ji, jk ) - z_elem_c( ji, jk ) ! diagonal
END DO
END DO
! Boundary conditions
DO ji = 1, jpi ! vector opt.
! Neumann at the bottom
z_elem_a( ji, 2 ) = 0._wp
z_elem_c( ji, 2 ) = - rDt_abl * Avt_abl( ji, jj, 2 ) / e3w_abl( 2 )
! Homogeneous Neumann at the top
z_elem_a( ji, jpka ) = - rDt_abl * Avt_abl( ji, jj, jpka ) / e3w_abl( jpka )
z_elem_c( ji, jpka ) = 0._wp
z_elem_b( ji, jpka ) = e3t_abl( jpka ) - z_elem_a( ji, jpka )
END DO
DO jtra = 1,jptq ! loop on active tracers
DO jk = 3, jpkam1
!DO ji = 2, jpim1
DO ji = 1,jpi !!GS: to be checked if needed
tq_abl( ji, jj, jk, nt_a, jtra ) = e3t_abl(jk) * tq_abl( ji, jj, jk, nt_n, jtra ) ! initialize right-hand-side
END DO
END DO
IF(jtra == jp_ta) THEN
DO ji = 1,jpi ! surface boundary condition for temperature
zztmp1 = psen(ji, jj)
Guillaume Samson
committed
zztmp2 = psen(ji, jj) * zsspt(ji, jj)
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
#if defined key_si3
zztmp1 = zztmp1 * pfrac_oce(ji,jj) + (1._wp - pfrac_oce(ji,jj)) * psen_ice(ji,jj)
zztmp2 = zztmp2 * pfrac_oce(ji,jj) + (1._wp - pfrac_oce(ji,jj)) * psen_ice(ji,jj) * ptm_su(ji,jj)
#endif
z_elem_b( ji, 2 ) = e3t_abl( 2 ) - z_elem_c( ji, 2 ) + rDt_abl * zztmp1
tq_abl ( ji, jj, 2, nt_a, jtra ) = e3t_abl( 2 ) * tq_abl ( ji, jj, 2, nt_n, jtra ) + rDt_abl * zztmp2
tq_abl ( ji, jj, jpka, nt_a, jtra ) = e3t_abl( jpka ) * tq_abl ( ji, jj, jpka, nt_n, jtra )
END DO
ELSE ! jp_qa
DO ji = 1,jpi ! surface boundary condition for humidity
zztmp1 = pevp(ji, jj)
zztmp2 = pevp(ji, jj) * pssq(ji, jj)
#if defined key_si3
zztmp1 = zztmp1 * pfrac_oce(ji,jj) + (1._wp - pfrac_oce(ji,jj)) * pevp_ice(ji,jj)
zztmp2 = zztmp2 * pfrac_oce(ji,jj) + (1._wp - pfrac_oce(ji,jj)) * pevp_ice(ji, jj) * pssq_ice(ji, jj)
#endif
z_elem_b( ji, 2 ) = e3t_abl( 2 ) - z_elem_c( ji, 2 ) + rDt_abl * zztmp1
tq_abl ( ji, jj, 2 , nt_a, jtra ) = e3t_abl( 2 ) * tq_abl ( ji, jj, 2, nt_n, jtra ) + rDt_abl * zztmp2
tq_abl ( ji, jj, jpka, nt_a, jtra ) = e3t_abl( jpka ) * tq_abl ( ji, jj, jpka, nt_n, jtra )
END DO
END IF
!!
!! Matrix inversion
!! ----------------------------------------------------------
DO ji = 1,jpi
zcff = 1._wp / z_elem_b( ji, 2 )
zCF ( ji, 2 ) = - zcff * z_elem_c( ji, 2 )
tq_abl( ji, jj, 2, nt_a, jtra ) = zcff * tq_abl( ji, jj, 2, nt_a, jtra )
END DO
DO jk = 3, jpka
DO ji = 1,jpi
zcff = 1._wp / ( z_elem_b( ji, jk ) + z_elem_a( ji, jk ) * zCF( ji, jk-1 ) )
zCF(ji,jk) = - zcff * z_elem_c( ji, jk )
tq_abl(ji,jj,jk,nt_a,jtra) = zcff * ( tq_abl(ji,jj,jk ,nt_a,jtra) &
& - z_elem_a(ji, jk) * tq_abl(ji,jj,jk-1,nt_a,jtra) )
END DO
END DO
!!FL at this point we could check positivity of tq_abl(:,:,:,nt_a,jp_qa) ... test to do ...
DO jk = jpkam1,2,-1
DO ji = 1,jpi
tq_abl(ji,jj,jk,nt_a,jtra) = tq_abl(ji,jj,jk,nt_a,jtra) + &
& zCF(ji,jk) * tq_abl(ji,jj,jk+1,nt_a,jtra)
END DO
END DO
END DO !<-- loop on tracers
!!
!-------------
END DO ! end outer loop
!-------------
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
! ! 3 *** Compute Coriolis term with geostrophic guide
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
IF( SemiImp_Cor ) THEN
!-------------
DO jk = 2, jpka ! outer loop
!-------------
!
! Advance u_abl & v_abl to time n+1
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
zcff = ( fft_abl(ji,jj) * rDt_abl )*( fft_abl(ji,jj) * rDt_abl ) ! (f dt)**2
u_abl( ji, jj, jk, nt_a ) = e3t_abl(jk) *( &
& (1._wp-gamma_Cor*(1._wp-gamma_Cor)*zcff) * u_abl( ji, jj, jk, nt_n ) &
& + rDt_abl * fft_abl(ji, jj) * v_abl( ji, jj, jk, nt_n ) ) &
& / (1._wp + gamma_Cor*gamma_Cor*zcff)
v_abl( ji, jj, jk, nt_a ) = e3t_abl(jk) *( &
& (1._wp-gamma_Cor*(1._wp-gamma_Cor)*zcff) * v_abl( ji, jj, jk, nt_n ) &
& - rDt_abl * fft_abl(ji, jj) * u_abl( ji, jj, jk, nt_n ) ) &
& / (1._wp + gamma_Cor*gamma_Cor*zcff)
END_2D
!
!-------------
END DO ! end outer loop !<-- u_abl and v_abl are properly updated on (1:jpi) x (1:jpj)
!-------------
!
IF( ln_geos_winds ) THEN
DO jj = 1, jpj ! outer loop
DO jk = 1, jpka
DO ji = 1, jpi
u_abl( ji, jj, jk, nt_a ) = u_abl( ji, jj, jk, nt_a ) &
& - rDt_abl * e3t_abl(jk) * fft_abl(ji , jj) * pgv_dta(ji ,jj ,jk)
v_abl( ji, jj, jk, nt_a ) = v_abl( ji, jj, jk, nt_a ) &
& + rDt_abl * e3t_abl(jk) * fft_abl(ji, jj ) * pgu_dta(ji ,jj ,jk)
END DO
END DO
END DO
END IF
!
IF( ln_hpgls_frc ) THEN
DO jj = 1, jpj ! outer loop
DO jk = 1, jpka
DO ji = 1, jpi
u_abl( ji, jj, jk, nt_a ) = u_abl( ji, jj, jk, nt_a ) - rDt_abl * e3t_abl(jk) * pgu_dta(ji,jj,jk)
v_abl( ji, jj, jk, nt_a ) = v_abl( ji, jj, jk, nt_a ) - rDt_abl * e3t_abl(jk) * pgv_dta(ji,jj,jk)
ENDDO
ENDDO
ENDDO
END IF
ELSE ! SemiImp_Cor = .FALSE.
IF( ln_geos_winds ) THEN
!-------------
DO jk = 2, jpka ! outer loop
!-------------
!
IF( MOD( kt, 2 ) == 0 ) then
! Advance u_abl & v_abl to time n+1
DO jj = 1, jpj
DO ji = 1, jpi
zcff = fft_abl(ji,jj) * ( v_abl ( ji , jj , jk, nt_n ) - pgv_dta(ji ,jj ,jk) )
u_abl( ji, jj, jk, nt_a ) = u_abl( ji, jj, jk, nt_n ) + rDt_abl * zcff
zcff = fft_abl(ji,jj) * ( u_abl ( ji , jj , jk, nt_a ) - pgu_dta(ji ,jj ,jk) )
v_abl( ji, jj, jk, nt_a ) = e3t_abl(jk) *( v_abl( ji, jj, jk, nt_n ) - rDt_abl * zcff )
u_abl( ji, jj, jk, nt_a ) = e3t_abl(jk) * u_abl( ji, jj, jk, nt_a )
END DO
END DO
ELSE
DO jj = 1, jpj
DO ji = 1, jpi
zcff = fft_abl(ji,jj) * ( u_abl ( ji , jj , jk, nt_n ) - pgu_dta(ji ,jj ,jk) )
v_abl( ji, jj, jk, nt_a ) = v_abl( ji, jj, jk, nt_n ) - rDt_abl * zcff
zcff = fft_abl(ji,jj) * ( v_abl ( ji , jj , jk, nt_a ) - pgv_dta(ji ,jj ,jk) )
u_abl( ji, jj, jk, nt_a ) = e3t_abl(jk) *( u_abl( ji, jj, jk, nt_n ) + rDt_abl * zcff )
v_abl( ji, jj, jk, nt_a ) = e3t_abl(jk) * v_abl( ji, jj, jk, nt_a )
END DO
END DO
END IF
!
!-------------
END DO ! end outer loop !<-- u_abl and v_abl are properly updated on (1:jpi) x (1:jpj)
!-------------
ENDIF ! ln_geos_winds
ENDIF ! SemiImp_Cor
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
! ! 4 *** Advance u,v to time n+1
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
!
! Vertical diffusion for u_abl
!-------------
DO jj = 1, jpj ! outer loop
!-------------
DO jk = 3, jpkam1
DO ji = 1, jpi
Guillaume Samson
committed
z_elem_a( ji, jk ) = - rDt_abl * Avm_abl( ji, jj, jk-1 ) / e3w_abl( jk-1 ) ! lower-diagonal
z_elem_c( ji, jk ) = - rDt_abl * Avm_abl( ji, jj, jk ) / e3w_abl( jk ) ! upper-diagonal
z_elem_b( ji, jk ) = e3t_abl(jk) - z_elem_a( ji, jk ) - z_elem_c( ji, jk ) ! diagonal
Guillaume Samson
committed
DO ji = 2, jpi ! boundary conditions (Avm_abl and pcd_du must be available at ji=jpi)
!++ Surface boundary condition
z_elem_a( ji, 2 ) = 0._wp
z_elem_c( ji, 2 ) = - rDt_abl * Avm_abl( ji, jj, 2 ) / e3w_abl( 2 )
!
Guillaume Samson
committed
zztmp1 = pcd_du(ji, jj)
zztmp2 = 0.5_wp * pcd_du(ji, jj) * ( pssu(ji-1, jj) + pssu(ji, jj ) ) * rn_vfac
#if defined key_si3
zztmp1 = zztmp1 * pfrac_oce(ji,jj) + (1._wp - pfrac_oce(ji,jj)) * pcd_du_ice(ji, jj)
Guillaume Samson
committed
zzice = 0.5_wp * ( pssu_ice(ji-1, jj) + pssu_ice(ji, jj ) ) * rn_vfac
zztmp2 = zztmp2 * pfrac_oce(ji,jj) + (1._wp - pfrac_oce(ji,jj)) * pcd_du_ice(ji, jj) * zzice
#endif
z_elem_b( ji, 2 ) = e3t_abl( 2 ) - z_elem_c( ji, 2 ) + rDt_abl * zztmp1
Guillaume Samson
committed
u_abl( ji, jj, 2, nt_a ) = u_abl( ji, jj, 2, nt_a ) + rDt_abl * zztmp2
! idealized test cases only
!IF( ln_topbc_neumann ) THEN
! !++ Top Neumann B.C.
! z_elem_a( ji, jpka ) = - rDt_abl * Avm_abl( ji, jj, jpka ) / e3w_abl( jpka )
! z_elem_c( ji, jpka ) = 0._wp
! z_elem_b( ji, jpka ) = e3t_abl( jpka ) - z_elem_a( ji, jpka )
! !u_abl ( ji, jj, jpka, nt_a ) = e3t_abl( jpka ) * u_abl ( ji, jj, jpka, nt_a )
!ELSE
!++ Top Dirichlet B.C.
z_elem_a( ji, jpka ) = 0._wp
z_elem_c( ji, jpka ) = 0._wp
z_elem_b( ji, jpka ) = e3t_abl( jpka )
u_abl ( ji, jj, jpka, nt_a ) = e3t_abl( jpka ) * pu_dta(ji,jj,jk)
!ENDIF
END DO
!!
!! Matrix inversion
!! ----------------------------------------------------------
Guillaume Samson
committed
DO ji = 1, jpi !DO ji = 2, jpi !!GS: TBI
Guillaume Samson
committed
zCF (ji, 2 ) = - zcff * z_elem_c( ji, 2 )
u_abl (ji,jj,2,nt_a) = zcff * u_abl ( ji, jj, 2, nt_a )
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
END DO
DO jk = 3, jpka
DO ji = 2, jpi
zcff = 1._wp / ( z_elem_b( ji, jk ) + z_elem_a( ji, jk ) * zCF (ji, jk-1 ) )
zCF(ji,jk) = - zcff * z_elem_c( ji, jk )
u_abl(ji,jj,jk,nt_a) = zcff * ( u_abl(ji,jj,jk ,nt_a) &
& - z_elem_a(ji, jk) * u_abl(ji,jj,jk-1,nt_a) )
END DO
END DO
DO jk = jpkam1,2,-1
DO ji = 2, jpi
u_abl(ji,jj,jk,nt_a) = u_abl(ji,jj,jk,nt_a) + zCF(ji,jk) * u_abl(ji,jj,jk+1,nt_a)
END DO
END DO
!-------------
END DO ! end outer loop
!-------------
!
! Vertical diffusion for v_abl
!-------------
DO jj = 2, jpj ! outer loop
!-------------
!
DO jk = 3, jpkam1
DO ji = 1, jpi
Guillaume Samson
committed
z_elem_a( ji, jk ) = - rDt_abl * Avm_abl( ji, jj, jk-1 ) / e3w_abl( jk-1 ) ! lower-diagonal
z_elem_c( ji, jk ) = - rDt_abl * Avm_abl( ji, jj, jk ) / e3w_abl( jk ) ! upper-diagonal
z_elem_b( ji, jk ) = e3t_abl(jk) - z_elem_a( ji, jk ) - z_elem_c( ji, jk ) ! diagonal
END DO
END DO
DO ji = 1, jpi ! boundary conditions (Avm_abl and pcd_du must be available at jj=jpj)
!++ Surface boundary condition
z_elem_a( ji, 2 ) = 0._wp
z_elem_c( ji, 2 ) = - rDt_abl * Avm_abl( ji, jj, 2 ) / e3w_abl( 2 )
!
zztmp1 = pcd_du(ji, jj)
Guillaume Samson
committed
zztmp2 = 0.5_wp * pcd_du(ji, jj) * ( pssv(ji, jj) + pssv(ji, jj-1) ) * rn_vfac
#if defined key_si3
zztmp1 = zztmp1 * pfrac_oce(ji,jj) + (1._wp - pfrac_oce(ji,jj)) * pcd_du_ice(ji, jj)
Guillaume Samson
committed
zzice = 0.5_wp * ( pssv_ice(ji, jj) + pssv_ice(ji, jj-1) ) * rn_vfac
zztmp2 = zztmp2 * pfrac_oce(ji,jj) + (1._wp - pfrac_oce(ji,jj)) * pcd_du_ice(ji, jj) * zzice
#endif
z_elem_b( ji, 2 ) = e3t_abl( 2 ) - z_elem_c( ji, 2 ) + rDt_abl * zztmp1
v_abl( ji, jj, 2, nt_a ) = v_abl( ji, jj, 2, nt_a ) + rDt_abl * zztmp2
! idealized test cases only
!IF( ln_topbc_neumann ) THEN
! !++ Top Neumann B.C.
! z_elem_a( ji, jpka ) = - rDt_abl * Avm_abl( ji, jj, jpka ) / e3w_abl( jpka )
! z_elem_c( ji, jpka ) = 0._wp
! z_elem_b( ji, jpka ) = e3t_abl( jpka ) - z_elem_a( ji, jpka )
! !v_abl ( ji, jj, jpka, nt_a ) = e3t_abl( jpka ) * v_abl ( ji, jj, jpka, nt_a )
!ELSE
!++ Top Dirichlet B.C.
z_elem_a( ji, jpka ) = 0._wp
z_elem_c( ji, jpka ) = 0._wp
z_elem_b( ji, jpka ) = e3t_abl( jpka )
v_abl ( ji, jj, jpka, nt_a ) = e3t_abl( jpka ) * pv_dta(ji,jj,jk)
!ENDIF
END DO
!!
!! Matrix inversion
!! ----------------------------------------------------------
DO ji = 1, jpi
Guillaume Samson
committed
zcff = 1._wp / z_elem_b( ji, 2 )
zCF (ji, 2 ) = - zcff * z_elem_c( ji, 2 )
v_abl (ji,jj,2,nt_a) = zcff * v_abl ( ji, jj, 2, nt_a )
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
END DO
DO jk = 3, jpka
DO ji = 1, jpi
zcff = 1._wp / ( z_elem_b( ji, jk ) + z_elem_a( ji, jk ) * zCF (ji, jk-1 ) )
zCF(ji,jk) = - zcff * z_elem_c( ji, jk )
v_abl(ji,jj,jk,nt_a) = zcff * ( v_abl(ji,jj,jk ,nt_a) &
& - z_elem_a(ji, jk) * v_abl(ji,jj,jk-1,nt_a) )
END DO
END DO
DO jk = jpkam1,2,-1
DO ji = 1, jpi
v_abl(ji,jj,jk,nt_a) = v_abl(ji,jj,jk,nt_a) + zCF(ji,jk) * v_abl(ji,jj,jk+1,nt_a)
END DO
END DO
!
!-------------
END DO ! end outer loop
!-------------
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
! ! 5 *** Apply nudging on the dynamics and the tracers
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
IF( nn_dyn_restore > 0 ) THEN
!-------------
DO jk = 2, jpka ! outer loop
!-------------
DO_2D( nn_hls-1, nn_hls, nn_hls-1, nn_hls )
zcff1 = pblh( ji, jj )
zsig = ght_abl(jk) / MAX( jp_pblh_min, MIN( jp_pblh_max, zcff1 ) )
zsig = MIN( jp_bmax , MAX( zsig, jp_bmin) )
zmsk = msk_abl(ji,jj)
zcff2 = jp_alp3_dyn * zsig**3 + jp_alp2_dyn * zsig**2 &
& + jp_alp1_dyn * zsig + jp_alp0_dyn
Guillaume Samson
committed
zcff = (1._wp-zmsk) + zmsk * zcff2 * rDt_abl ! zcff = 1 for masked points
! rn_Dt = rDt_abl / nn_fsbc
zcff = zcff * rest_eq(ji,jj)
u_abl( ji, jj, jk, nt_a ) = (1._wp - zcff ) * u_abl( ji, jj, jk, nt_a ) &
& + zcff * pu_dta( ji, jj, jk )
v_abl( ji, jj, jk, nt_a ) = (1._wp - zcff ) * v_abl( ji, jj, jk, nt_a ) &
& + zcff * pv_dta( ji, jj, jk )
END_2D
!-------------
END DO ! end outer loop
!-------------
END IF
!-------------
DO jk = 2, jpka ! outer loop
!-------------
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
zcff1 = pblh( ji, jj )
zsig = ght_abl(jk) / MAX( jp_pblh_min, MIN( jp_pblh_max, zcff1 ) )
zsig = MIN( jp_bmax , MAX( zsig, jp_bmin) )
zmsk = msk_abl(ji,jj)
zcff2 = jp_alp3_tra * zsig**3 + jp_alp2_tra * zsig**2 &
& + jp_alp1_tra * zsig + jp_alp0_tra
Guillaume Samson
committed
zcff = (1._wp-zmsk) + zmsk * zcff2 * rDt_abl ! zcff = 1 for masked points
! rn_Dt = rDt_abl / nn_fsbc
tq_abl( ji, jj, jk, nt_a, jp_ta ) = (1._wp - zcff ) * tq_abl( ji, jj, jk, nt_a, jp_ta ) &
& + zcff * pt_dta( ji, jj, jk )
tq_abl( ji, jj, jk, nt_a, jp_qa ) = (1._wp - zcff ) * tq_abl( ji, jj, jk, nt_a, jp_qa ) &
& + zcff * pq_dta( ji, jj, jk )
END_2D
!-------------
END DO ! end outer loop
!-------------
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
! ! 6 *** MPI exchanges & IOM outputs
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
!
CALL lbc_lnk( 'ablmod', u_abl(:,:,:,nt_a ), 'T', -1._wp, v_abl(:,:,:,nt_a) , 'T', -1._wp )
Guillaume Samson
committed
!CALL lbc_lnk( 'ablmod', tq_abl(:,:,:,nt_a,jp_ta), 'T', 1._wp, tq_abl(:,:,:,nt_a,jp_qa), 'T', 1._wp, kfillmode = jpfillnothing ) ! ++++ this should not be needed...
!
#if defined key_xios
! 2D & first ABL level
IF ( iom_use("pblh" ) ) CALL iom_put ( "pblh", pblh(:,: ) )
IF ( iom_use("uz1_abl") ) CALL iom_put ( "uz1_abl", u_abl(:,:,2,nt_a ) )
IF ( iom_use("vz1_abl") ) CALL iom_put ( "vz1_abl", v_abl(:,:,2,nt_a ) )
IF ( iom_use("tz1_abl") ) CALL iom_put ( "tz1_abl", tq_abl(:,:,2,nt_a,jp_ta) )
IF ( iom_use("qz1_abl") ) CALL iom_put ( "qz1_abl", tq_abl(:,:,2,nt_a,jp_qa) )
IF ( iom_use("uz1_dta") ) CALL iom_put ( "uz1_dta", pu_dta(:,:,2 ) )
IF ( iom_use("vz1_dta") ) CALL iom_put ( "vz1_dta", pv_dta(:,:,2 ) )
IF ( iom_use("tz1_dta") ) CALL iom_put ( "tz1_dta", pt_dta(:,:,2 ) )
IF ( iom_use("qz1_dta") ) CALL iom_put ( "qz1_dta", pq_dta(:,:,2 ) )
! debug 2D
IF( ln_geos_winds ) THEN
IF ( iom_use("uz1_geo") ) CALL iom_put ( "uz1_geo", pgu_dta(:,:,2) )
IF ( iom_use("vz1_geo") ) CALL iom_put ( "vz1_geo", pgv_dta(:,:,2) )
END IF
IF( ln_hpgls_frc ) THEN
Guillaume Samson
committed
IF ( iom_use("uz1_geo") ) CALL iom_put ( "uz1_geo", -pgv_dta(:,:,2)/MAX( ABS( fft_abl(:,:)), 2.5e-5_wp)*fft_abl(:,:)/ABS(fft_abl(:,:)) )
IF ( iom_use("vz1_geo") ) CALL iom_put ( "vz1_geo", pgu_dta(:,:,2)/MAX( ABS( fft_abl(:,:)), 2.5e-5_wp)*fft_abl(:,:)/ABS(fft_abl(:,:)) )
END IF
! 3D (all ABL levels)
IF ( iom_use("u_abl" ) ) CALL iom_put ( "u_abl" , u_abl(:,:,2:jpka,nt_a ) )
IF ( iom_use("v_abl" ) ) CALL iom_put ( "v_abl" , v_abl(:,:,2:jpka,nt_a ) )
IF ( iom_use("t_abl" ) ) CALL iom_put ( "t_abl" , tq_abl(:,:,2:jpka,nt_a,jp_ta) )
IF ( iom_use("q_abl" ) ) CALL iom_put ( "q_abl" , tq_abl(:,:,2:jpka,nt_a,jp_qa) )
IF ( iom_use("tke_abl" ) ) CALL iom_put ( "tke_abl" , tke_abl(:,:,2:jpka,nt_a ) )
IF ( iom_use("avm_abl" ) ) CALL iom_put ( "avm_abl" , avm_abl(:,:,2:jpka ) )
IF ( iom_use("avt_abl" ) ) CALL iom_put ( "avt_abl" , avt_abl(:,:,2:jpka ) )
IF ( iom_use("mxlm_abl") ) CALL iom_put ( "mxlm_abl", mxlm_abl(:,:,2:jpka ) )
IF ( iom_use("mxld_abl") ) CALL iom_put ( "mxld_abl", mxld_abl(:,:,2:jpka ) )
! debug 3D
IF ( iom_use("u_dta") ) CALL iom_put ( "u_dta", pu_dta(:,:,2:jpka) )
IF ( iom_use("v_dta") ) CALL iom_put ( "v_dta", pv_dta(:,:,2:jpka) )
IF ( iom_use("t_dta") ) CALL iom_put ( "t_dta", pt_dta(:,:,2:jpka) )
IF ( iom_use("q_dta") ) CALL iom_put ( "q_dta", pq_dta(:,:,2:jpka) )
IF( ln_geos_winds ) THEN
IF ( iom_use("u_geo") ) CALL iom_put ( "u_geo", pgu_dta(:,:,2:jpka) )
IF ( iom_use("v_geo") ) CALL iom_put ( "v_geo", pgv_dta(:,:,2:jpka) )
END IF
IF( ln_hpgls_frc ) THEN
Guillaume Samson
committed
IF ( iom_use("u_geo") ) CALL iom_put ( "u_geo", -pgv_dta(:,:,2:jpka)/MAX( ABS( RESHAPE( fft_abl(:,:), (/jpi,jpj,jpka-1/), fft_abl(:,:))), 2.5e-5_wp) * RESHAPE( fft_abl(:,:)/ABS(fft_abl(:,:)), (/jpi,jpj,jpka-1/), fft_abl(:,:)/ABS(fft_abl(:,:))) )
IF ( iom_use("v_geo") ) CALL iom_put ( "v_geo", pgu_dta(:,:,2:jpka)/MAX( ABS( RESHAPE( fft_abl(:,:), (/jpi,jpj,jpka-1/), fft_abl(:,:))), 2.5e-5_wp) * RESHAPE( fft_abl(:,:)/ABS(fft_abl(:,:)), (/jpi,jpj,jpka-1/), fft_abl(:,:)/ABS(fft_abl(:,:))) )
END IF
#endif
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
! ! 7 *** Finalize flux computation
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
!
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
Guillaume Samson
committed
ztemp = tq_abl( ji, jj, 2, nt_a, jp_ta )
zhumi = tq_abl( ji, jj, 2, nt_a, jp_qa )
zpre( ji, jj ) = pres_temp( zhumi, pslp_dta(ji,jj), ght_abl(2), ptpot=ztemp, pta=ztabs( ji, jj ) )
zcff = rho_air( ztabs( ji, jj ), zhumi, zpre( ji, jj ) )
psen( ji, jj ) = - cp_air(zhumi) * zcff * psen(ji,jj) * ( zsspt(ji,jj) - ztemp ) !GS: negative sign to respect aerobulk convention
pevp( ji, jj ) = rn_efac*MAX( 0._wp, zcff * pevp(ji,jj) * ( pssq(ji,jj) - zhumi ) )
plat( ji, jj ) = - L_vap( psst(ji,jj) ) * pevp( ji, jj )
rhoa( ji, jj ) = zcff
END_2D
DO_2D( nn_hls-1, nn_hls, nn_hls-1, nn_hls )
Guillaume Samson
committed
zwnd_i(ji,jj) = u_abl(ji ,jj,2,nt_a) - 0.5_wp * ( pssu(ji ,jj) + pssu(ji-1,jj) ) * rn_vfac
zwnd_j(ji,jj) = v_abl(ji,jj ,2,nt_a) - 0.5_wp * ( pssv(ji,jj ) + pssv(ji,jj-1) ) * rn_vfac
END_2D
!
CALL lbc_lnk( 'ablmod', zwnd_i(:,:) , 'T', -1.0_wp, zwnd_j(:,:) , 'T', -1.0_wp )
!
! ... scalar wind ( = | U10m - U_oce | ) at T-point (masked)
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
zcff = SQRT( zwnd_i(ji,jj) * zwnd_i(ji,jj) &
& + zwnd_j(ji,jj) * zwnd_j(ji,jj) ) ! * msk_abl(ji,jj)
zztmp = rhoa(ji,jj) * pcd_du(ji,jj)
pwndm (ji,jj) = zcff
ptaum (ji,jj) = zztmp * zcff
zwnd_i(ji,jj) = zztmp * zwnd_i(ji,jj)
zwnd_j(ji,jj) = zztmp * zwnd_j(ji,jj)
END_2D
! ... utau, vtau at T-points
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
ptaui(ji,jj) = zwnd_i(ji,jj) * msk_abl(ji,jj) !!clem tau: check
ptauj(ji,jj) = zwnd_j(ji,jj) * msk_abl(ji,jj) !!clem tau: check
END_2D
CALL iom_put( "taum_oce", ptaum )
IF(sn_cfctl%l_prtctl) THEN
CALL prt_ctl( tab2d_1=ptaui , clinfo1=' abl_stp: utau : ', mask1=tmask, &
& tab2d_2=ptauj , clinfo2=' vtau : ', mask2=tmask )
CALL prt_ctl( tab2d_1=pwndm , clinfo1=' abl_stp: wndm : ' )
ENDIF
#if defined key_si3
! ------------------------------------------------------------ !
! Wind stress relative to the moving ice ( U10m - U_ice ) !
! ------------------------------------------------------------ !
Guillaume Samson
committed
!DO_2D( 0, 0, 0, 0 )
! ptaui_ice(ji,jj) = 0.5_wp * ( rhoa(ji+1,jj) * pCd_du_ice(ji+1,jj) + rhoa(ji,jj) * pCd_du_ice(ji,jj) ) &
! & * ( 0.5_wp * ( u_abl(ji+1,jj,2,nt_a) + u_abl(ji,jj,2,nt_a) ) - pssu_ice(ji,jj) )
! ptauj_ice(ji,jj) = 0.5_wp * ( rhoa(ji,jj+1) * pCd_du_ice(ji,jj+1) + rhoa(ji,jj) * pCd_du_ice(ji,jj) ) &
! & * ( 0.5_wp * ( v_abl(ji,jj+1,2,nt_a) + v_abl(ji,jj,2,nt_a) ) - pssv_ice(ji,jj) )
!END_2D
!CALL lbc_lnk( 'ablmod', ptaui_ice, 'U', -1.0_wp, ptauj_ice, 'V', -1.0_wp )
!!
!IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab2d_1=ptaui_ice , clinfo1=' abl_stp: putaui : ' &
! & , tab2d_2=ptauj_ice , clinfo2=' pvtaui : ' )
! ------------------------------------------------------------ !
! Wind stress relative to the moving ice ( U10m - U_ice ) !
! ------------------------------------------------------------ !
DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
ptaui_ice(ji,jj) = rhoa(ji,jj) * pCd_du_ice(ji,jj) * ( u_abl(ji,jj,2,nt_a) - pssu_ice(ji,jj) * rn_vfac )
ptauj_ice(ji,jj) = rhoa(ji,jj) * pCd_du_ice(ji,jj) * ( v_abl(ji,jj,2,nt_a) - pssv_ice(ji,jj) * rn_vfac )
CALL prt_ctl( tab2d_1=ptaui_ice , clinfo1=' abl_stp: utau_ice : ', mask1=tmask, &
& tab2d_2=ptauj_ice , clinfo2=' vtau_ice : ', mask2=tmask )
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
END IF
#endif
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
! ! 8 *** Swap time indices for the next timestep
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
nt_n = 1 + MOD( nt_n, 2)
nt_a = 1 + MOD( nt_a, 2)
!
!---------------------------------------------------------------------------------------------------
END SUBROUTINE abl_stp
!===================================================================================================
!===================================================================================================
SUBROUTINE abl_zdf_tke( )
!---------------------------------------------------------------------------------------------------
!!----------------------------------------------------------------------
!! *** ROUTINE abl_zdf_tke ***
!!
!! ** Purpose : Time-step Turbulente Kinetic Energy (TKE) equation
!!
!! ** Method : - source term due to shear
!! - source term due to stratification
!! - resolution of the TKE equation by inverting
!! a tridiagonal linear system
!!
!! ** Action : - en : now turbulent kinetic energy)
!! - avmu, avmv : production of TKE by shear at u and v-points
!! (= Kz dz[Ub] * dz[Un] )
!! ---------------------------------------------------------------------
INTEGER :: ji, jj, jk, tind, jbak, jkup, jkdwn
INTEGER, DIMENSION(1:jpi ) :: ikbl
REAL(wp) :: zcff, zcff2, ztken, zesrf, zetop, ziRic, ztv
REAL(wp) :: zdU , zdV , zcff1, zshear, zbuoy, zsig, zustar2
REAL(wp) :: zdU2, zdV2, zbuoy1, zbuoy2 ! zbuoy for BL89
REAL(wp) :: zwndi, zwndj
REAL(wp), DIMENSION(1:jpi, 1:jpka) :: zsh2
REAL(wp), DIMENSION(1:jpi,1:jpj,1:jpka) :: zbn2
REAL(wp), DIMENSION(1:jpi,1:jpka ) :: zFC, zRH, zCF
REAL(wp), DIMENSION(1:jpi,1:jpka ) :: z_elem_a
REAL(wp), DIMENSION(1:jpi,1:jpka ) :: z_elem_b
REAL(wp), DIMENSION(1:jpi,1:jpka ) :: z_elem_c
LOGICAL :: ln_Patankar = .FALSE.
LOGICAL :: ln_dumpvar = .FALSE.
LOGICAL , DIMENSION(1:jpi ) :: ln_foundl
!
tind = nt_n
ziRic = 1._wp / rn_Ric
! if tind = nt_a it is required to apply lbc_lnk on u_abl(nt_a) and v_abl(nt_a)
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
! ! Advance TKE equation to time n+1
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
!-------------
DO jj = 1, jpj ! outer loop
!-------------
!
! Compute vertical shear
DO jk = 2, jpkam1
DO ji = 1, jpi
zcff = 1.0_wp / e3w_abl( jk )**2
zdU = zcff* Avm_abl(ji,jj,jk) * (u_abl( ji, jj, jk+1, tind)-u_abl( ji, jj, jk , tind) )**2
zdV = zcff* Avm_abl(ji,jj,jk) * (v_abl( ji, jj, jk+1, tind)-v_abl( ji, jj, jk , tind) )**2
zsh2(ji,jk) = zdU+zdV !<-- zsh2 = Km ( ( du/dz )^2 + ( dv/dz )^2 )
END DO
END DO
!
! Compute brunt-vaisala frequency
DO jk = 2, jpkam1
DO ji = 1,jpi
zcff = grav * itvref / e3w_abl( jk )
zcff1 = tq_abl( ji, jj, jk+1, tind, jp_ta) - tq_abl( ji, jj, jk , tind, jp_ta)
zcff2 = tq_abl( ji, jj, jk+1, tind, jp_ta) * tq_abl( ji, jj, jk+1, tind, jp_qa) &
& - tq_abl( ji, jj, jk , tind, jp_ta) * tq_abl( ji, jj, jk , tind, jp_qa)
zbn2(ji,jj,jk) = zcff * ( zcff1 + rctv0 * zcff2 ) !<-- zbn2 defined on (2,jpi)
END DO
END DO
!
! Terms for the tridiagonal problem
DO jk = 2, jpkam1
DO ji = 1, jpi
zshear = zsh2( ji, jk ) ! zsh2 is already multiplied by Avm_abl at this point
zsh2(ji,jk) = zsh2( ji, jk ) / Avm_abl( ji, jj, jk ) ! reformulate zsh2 as a 'true' vertical shear for PBLH computation
zbuoy = - Avt_abl( ji, jj, jk ) * zbn2( ji, jj, jk )
z_elem_a( ji, jk ) = - 0.5_wp * rDt_abl * rn_Sch * ( Avm_abl( ji, jj, jk ) + Avm_abl( ji, jj, jk-1 ) ) / e3t_abl( jk ) ! lower-diagonal
z_elem_c( ji, jk ) = - 0.5_wp * rDt_abl * rn_Sch * ( Avm_abl( ji, jj, jk ) + Avm_abl( ji, jj, jk+1 ) ) / e3t_abl( jk+1 ) ! upper-diagonal
IF( (zbuoy + zshear) .gt. 0.) THEN ! Patankar trick to avoid negative values of TKE
z_elem_b( ji, jk ) = e3w_abl(jk) - z_elem_a( ji, jk ) - z_elem_c( ji, jk ) &
& + e3w_abl(jk) * rDt_abl * rn_Ceps * sqrt(tke_abl( ji, jj, jk, nt_n )) / mxld_abl(ji,jj,jk) ! diagonal
tke_abl( ji, jj, jk, nt_a ) = e3w_abl(jk) * ( tke_abl( ji, jj, jk, nt_n ) + rDt_abl * ( zbuoy + zshear ) ) ! right-hand-side
ELSE
z_elem_b( ji, jk ) = e3w_abl(jk) - z_elem_a( ji, jk ) - z_elem_c( ji, jk ) &
& + e3w_abl(jk) * rDt_abl * rn_Ceps * sqrt(tke_abl( ji, jj, jk, nt_n )) / mxld_abl(ji,jj,jk) & ! diagonal
& - e3w_abl(jk) * rDt_abl * zbuoy
tke_abl( ji, jj, jk, nt_a ) = e3w_abl(jk) * ( tke_abl( ji, jj, jk, nt_n ) + rDt_abl * zshear ) ! right-hand-side
END IF
END DO
END DO
DO ji = 1,jpi ! vector opt.
zesrf = MAX( rn_Esfc * ustar2(ji,jj), tke_min )
zetop = tke_min
z_elem_a ( ji, 1 ) = 0._wp
z_elem_c ( ji, 1 ) = 0._wp
z_elem_b ( ji, 1 ) = 1._wp
tke_abl ( ji, jj, 1, nt_a ) = zesrf
!++ Top Neumann B.C.
!z_elem_a ( ji, jpka ) = - 0.5 * rDt_abl * rn_Sch * (Avm_abl(ji,jj, jpka-1 )+Avm_abl(ji,jj, jpka )) / e3t_abl( jpka )
!z_elem_c ( ji, jpka ) = 0._wp
!z_elem_b ( ji, jpka ) = e3w_abl(jpka) - z_elem_a(ji, jpka )
!tke_abl ( ji, jj, jpka, nt_a ) = e3w_abl(jpka) * tke_abl( ji,jj, jpka, nt_n )
!++ Top Dirichlet B.C.
z_elem_a ( ji, jpka ) = 0._wp
z_elem_c ( ji, jpka ) = 0._wp
z_elem_b ( ji, jpka ) = 1._wp
tke_abl ( ji, jj, jpka, nt_a ) = zetop
zbn2 ( ji, jj, 1 ) = zbn2 ( ji, jj, 2 )
zsh2 ( ji, 1 ) = zsh2 ( ji, 2 )
zbn2 ( ji, jj, jpka ) = zbn2 ( ji, jj, jpkam1 )
zsh2 ( ji, jpka ) = zsh2 ( ji , jpkam1 )
END DO
!!
!! Matrix inversion
!! ----------------------------------------------------------
DO ji = 1,jpi
zcff = 1._wp / z_elem_b( ji, 1 )
zCF (ji, 1 ) = - zcff * z_elem_c( ji, 1 )
tke_abl(ji,jj,1,nt_a) = zcff * tke_abl ( ji, jj, 1, nt_a )
END DO
DO jk = 2, jpka
DO ji = 1,jpi
zcff = 1._wp / ( z_elem_b( ji, jk ) + z_elem_a( ji, jk ) * zCF(ji, jk-1 ) )
zCF(ji,jk) = - zcff * z_elem_c( ji, jk )
tke_abl(ji,jj,jk,nt_a) = zcff * ( tke_abl(ji,jj,jk ,nt_a) &
& - z_elem_a(ji, jk) * tke_abl(ji,jj,jk-1,nt_a) )
END DO
END DO
DO jk = jpkam1,1,-1
DO ji = 1,jpi
tke_abl(ji,jj,jk,nt_a) = tke_abl(ji,jj,jk,nt_a) + zCF(ji,jk) * tke_abl(ji,jj,jk+1,nt_a)
END DO
END DO
!!FL should not be needed because of Patankar procedure
tke_abl(2:jpi,jj,1:jpka,nt_a) = MAX( tke_abl(2:jpi,jj,1:jpka,nt_a), tke_min )
!!
!! Diagnose PBL height
!! ----------------------------------------------------------
!
! arrays zRH, zFC and zCF are available at this point
! and zFC(:, 1 ) = 0.
! diagnose PBL height based on zsh2 and zbn2
zFC ( : ,1) = 0._wp
ikbl( 1:jpi ) = 0
DO jk = 2,jpka
DO ji = 1, jpi
zcff = ghw_abl( jk-1 )
zcff1 = zcff / ( zcff + rn_epssfc * pblh ( ji, jj ) )
zcff = ghw_abl( jk )
zcff2 = zcff / ( zcff + rn_epssfc * pblh ( ji, jj ) )
zFC( ji, jk ) = zFC( ji, jk-1) + 0.5_wp * e3t_abl( jk )*( &
zcff2 * ( zsh2( ji, jk ) - ziRic * zbn2( ji, jj, jk ) &
- rn_Cek * ( fft_abl( ji, jj ) * fft_abl( ji, jj ) ) ) &
+ zcff1 * ( zsh2( ji, jk-1) - ziRic * zbn2( ji, jj, jk-1 ) &
- rn_Cek * ( fft_abl( ji, jj ) * fft_abl( ji, jj ) ) ) &
& )
IF( ikbl(ji) == 0 .and. zFC( ji, jk ).lt.0._wp ) ikbl(ji)=jk
END DO
END DO
!
! finalize the computation of the PBL height
DO ji = 1, jpi
jk = ikbl(ji)
IF( jk > 2 ) THEN ! linear interpolation to get subgrid value of pblh
pblh( ji, jj ) = ( ghw_abl( jk-1 ) * zFC( ji, jk ) &
& - ghw_abl( jk ) * zFC( ji, jk-1 ) &
& ) / ( zFC( ji, jk ) - zFC( ji, jk-1 ) )
ELSE IF( jk==2 ) THEN
pblh( ji, jj ) = ghw_abl(2 )
ELSE
pblh( ji, jj ) = ghw_abl(jpka)
END IF
END DO
!-------------
END DO
!-------------
!
! Optional : could add pblh smoothing if pblh is noisy horizontally ...
IF(ln_smth_pblh) THEN
CALL lbc_lnk( 'ablmod', pblh, 'T', 1.0_wp) !, kfillmode = jpfillnothing)
CALL smooth_pblh( pblh, msk_abl )
CALL lbc_lnk( 'ablmod', pblh, 'T', 1.0_wp) !, kfillmode = jpfillnothing)
ENDIF
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
! ! Diagnostic mixing length computation
! !<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
!
SELECT CASE ( nn_amxl )
!
CASE ( 0 ) ! Deardroff 80 length-scale bounded by the distance to surface and bottom
# define zlup zRH
# define zldw zFC
DO jj = 1, jpj ! outer loop
!
DO ji = 1, jpi
mxld_abl( ji, jj, 1 ) = mxl_min
mxld_abl( ji, jj, jpka ) = mxl_min
mxlm_abl( ji, jj, 1 ) = mxl_min
mxlm_abl( ji, jj, jpka ) = mxl_min
zldw ( ji, 1 ) = zrough(ji,jj) * rn_Lsfc
zlup ( ji, jpka ) = mxl_min
END DO
!
DO jk = 2, jpkam1
DO ji = 1, jpi
zbuoy = MAX( zbn2(ji, jj, jk), rsmall )
mxlm_abl( ji, jj, jk ) = MAX( mxl_min, &
& SQRT( 2._wp * tke_abl( ji, jj, jk, nt_a ) / zbuoy ) )
END DO
END DO
!
! Limit mxl
DO jk = jpkam1,1,-1
DO ji = 1, jpi
zlup(ji,jk) = MIN( zlup(ji,jk+1) + (ghw_abl(jk+1)-ghw_abl(jk)) , mxlm_abl(ji, jj, jk) )
END DO
END DO
!
DO jk = 2, jpka
DO ji = 1, jpi
zldw(ji,jk) = MIN( zldw(ji,jk-1) + (ghw_abl(jk)-ghw_abl(jk-1)) , mxlm_abl(ji, jj, jk) )
END DO
END DO
!
! DO jk = 1, jpka
! DO ji = 1, jpi
! mxlm_abl( ji, jj, jk ) = SQRT( zldw( ji, jk ) * zlup( ji, jk ) )
! mxld_abl( ji, jj, jk ) = MIN ( zldw( ji, jk ), zlup( ji, jk ) )
! END DO
! END DO
!
DO jk = 1, jpka
DO ji = 1, jpi
! zcff = 2.*SQRT(2.)*( zldw( ji, jk )**(-2._wp/3._wp) + zlup( ji, jk )**(-2._wp/3._wp) )**(-3._wp/2._wp)
zcff = SQRT( zldw( ji, jk ) * zlup( ji, jk ) )
mxlm_abl( ji, jj, jk ) = MAX( zcff, mxl_min )
mxld_abl( ji, jj, jk ) = MAX( MIN( zldw( ji, jk ), zlup( ji, jk ) ), mxl_min )
END DO
END DO
!
END DO
# undef zlup
# undef zldw
!
!
CASE ( 1 ) ! Modified Deardroff 80 length-scale bounded by the distance to surface and bottom
# define zlup zRH
# define zldw zFC
DO jj = 1, jpj ! outer loop
!
DO jk = 2, jpkam1
DO ji = 1,jpi
zcff = 1.0_wp / e3w_abl( jk )**2
zdU = zcff* (u_abl( ji, jj, jk+1, tind)-u_abl( ji, jj, jk , tind) )**2
zdV = zcff* (v_abl( ji, jj, jk+1, tind)-v_abl( ji, jj, jk , tind) )**2
zsh2(ji,jk) = SQRT(zdU+zdV) !<-- zsh2 = SQRT ( ( du/dz )^2 + ( dv/dz )^2 )
ENDDO
ENDDO
!
DO ji = 1, jpi
zcff = zrough(ji,jj) * rn_Lsfc
mxld_abl ( ji, jj, 1 ) = zcff
mxld_abl ( ji, jj, jpka ) = mxl_min
mxlm_abl ( ji, jj, 1 ) = zcff
mxlm_abl ( ji, jj, jpka ) = mxl_min
zldw ( ji, 1 ) = zcff
zlup ( ji, jpka ) = mxl_min
END DO
!
DO jk = 2, jpkam1
DO ji = 1, jpi
zbuoy = MAX( zbn2(ji, jj, jk), rsmall )
zcff = 2.0_wp*SQRT(tke_abl( ji, jj, jk, nt_a )) / ( rn_Rod*zsh2(ji,jk) &
& + SQRT(rn_Rod*rn_Rod*zsh2(ji,jk)*zsh2(ji,jk)+2.0_wp*zbuoy ) )
mxlm_abl( ji, jj, jk ) = MAX( mxl_min, zcff )
END DO
END DO
!
! Limit mxl
DO jk = jpkam1,1,-1
DO ji = 1, jpi
zlup(ji,jk) = MIN( zlup(ji,jk+1) + (ghw_abl(jk+1)-ghw_abl(jk)) , mxlm_abl(ji, jj, jk) )
END DO
END DO
!
DO jk = 2, jpka
DO ji = 1, jpi
zldw(ji,jk) = MIN( zldw(ji,jk-1) + (ghw_abl(jk)-ghw_abl(jk-1)) , mxlm_abl(ji, jj, jk) )
END DO
END DO
!
DO jk = 1, jpka
DO ji = 1, jpi
!mxlm_abl( ji, jj, jk ) = SQRT( zldw( ji, jk ) * zlup( ji, jk ) )
!zcff = 2.*SQRT(2.)*( zldw( ji, jk )**(-2._wp/3._wp) + zlup( ji, jk )**(-2._wp/3._wp) )**(-3._wp/2._wp)
zcff = SQRT( zldw( ji, jk ) * zlup( ji, jk ) )
mxlm_abl( ji, jj, jk ) = MAX( zcff, mxl_min )
!mxld_abl( ji, jj, jk ) = MIN( zldw( ji, jk ), zlup( ji, jk ) )
mxld_abl( ji, jj, jk ) = MAX( MIN( zldw( ji, jk ), zlup( ji, jk ) ), mxl_min )
END DO
END DO
!
END DO
# undef zlup
# undef zldw
!
CASE ( 2 ) ! Bougeault & Lacarrere 89 length-scale
!
# define zlup zRH
# define zldw zFC
! zCF is used for matrix inversion
!
DO jj = 1, jpj ! outer loop
DO ji = 1, jpi
zcff = zrough(ji,jj) * rn_Lsfc
zlup( ji, 1 ) = zcff
zldw( ji, 1 ) = zcff