source: LMDZ6/branches/LMDZ-QUEST/libf/phylmd/acama_gwd_rando_m.F90 @ 5407

Last change on this file since 5407 was 3200, checked in by Laurent Fairhead, 7 years ago

Inclusion of r3198 from trunk
Retour vers l'insensibilite au decoupage en sous domaine.
Les routines gwd_rando incluait le calcul de niveaux de reference
sur la base d'un profile pris au milieu du domaine (en klon/2).
Rempace par un test en presnivs.

Une autre intercation entre routines concernant la tke a fait apparaitre
que la tke n'?\195?\169tait pas passee correctement au niveau klev+1 au moment
du regroupement des mailles sous les sous surface.

Ces changements garantissent la convergence numerique si
addtkeoro=0
iflag_pbl<12
et
ok_gwd_rando=n
La convergence n'est pas garantie pour les dernieres versions des physiq.def
mais les differences devraient etre mineures.

FH
File size: 18.5 KB
Line 
1module ACAMA_GWD_rando_m
2
3  implicit none
4
5contains
6
7  SUBROUTINE ACAMA_GWD_rando(DTIME, pp, plat, tt, uu, vv, rot, &
8       zustr, zvstr, d_u, d_v,east_gwstress,west_gwstress)
9
10    ! Parametrization of the momentum flux deposition due to a discrete
11    ! number of gravity waves.
12    ! Author: F. Lott, A. de la Camara
13    ! July, 24th, 2014
14    ! Gaussian distribution of the source, source is vorticity squared
15    ! Reference: de la Camara and Lott (GRL, 2015, vol 42, 2071-2078 )
16    ! Lott et al (JAS, 2010, vol 67, page 157-170)
17    ! Lott et al (JAS, 2012, vol 69, page 2134-2151)
18
19!  ONLINE:
20    use dimphy, only: klon, klev
21    use assert_m, only: assert
22    USE ioipsl_getin_p_mod, ONLY : getin_p
23    USE vertical_layers_mod, ONLY : presnivs
24
25    include "YOMCST.h"
26    include "clesphys.h"
27!  OFFLINE:
28!   include "dimensions.h"
29!   include "dimphy.h"
30!END DIFFERENCE
31    include "YOEGWD.h"
32
33    ! 0. DECLARATIONS:
34
35    ! 0.1 INPUTS
36    REAL, intent(in)::DTIME ! Time step of the Physics
37    REAL, intent(in):: PP(:, :) ! (KLON, KLEV) Pressure at full levels
38    REAL, intent(in):: ROT(:,:) ! Relative vorticity             
39    REAL, intent(in):: TT(:, :) ! (KLON, KLEV) Temp at full levels
40    REAL, intent(in):: UU(:, :) ! (KLON, KLEV) Zonal wind at full levels
41    REAL, intent(in):: VV(:, :) ! (KLON, KLEV) Merid wind at full levels
42    REAL, intent(in):: PLAT(:) ! (KLON) LATITUDE                   
43
44    ! 0.2 OUTPUTS
45    REAL, intent(out):: zustr(:), zvstr(:) ! (KLON) Surface Stresses
46
47    REAL, intent(inout):: d_u(:, :), d_v(:, :)
48    REAL, intent(inout):: east_gwstress(:, :) !  Profile of eastward stress
49    REAL, intent(inout):: west_gwstress(:, :) !  Profile of westward stress
50    ! (KLON, KLEV) tendencies on winds
51
52    ! O.3 INTERNAL ARRAYS
53    REAL BVLOW(klon)  !  LOW LEVEL BV FREQUENCY
54    REAL ROTBA(KLON),CORIO(KLON)  !  BAROTROPIC REL. VORTICITY AND PLANETARY
55    REAL UZ(KLON, KLEV + 1)
56
57    INTEGER II, JJ, LL
58
59    ! 0.3.0 TIME SCALE OF THE LIFE CYCLE OF THE WAVES PARAMETERIZED
60
61    REAL DELTAT
62
63    ! 0.3.1 GRAVITY-WAVES SPECIFICATIONS
64
65    INTEGER, PARAMETER:: NK = 2, NP = 2, NO = 2, NW = NK * NP * NO
66    INTEGER JK, JP, JO, JW
67    INTEGER, PARAMETER:: NA = 5  !number of realizations to get the phase speed
68    REAL KMIN, KMAX ! Min and Max horizontal wavenumbers
69    REAL CMIN, CMAX ! Min and Max absolute ph. vel.
70    REAL CPHA ! absolute PHASE VELOCITY frequency
71    REAL ZK(NW, KLON) ! Horizontal wavenumber amplitude
72    REAL ZP(NW, KLON) ! Horizontal wavenumber angle
73    REAL ZO(NW, KLON) ! Absolute frequency !
74
75    ! Waves Intr. freq. at the 1/2 lev surrounding the full level
76    REAL ZOM(NW, KLON), ZOP(NW, KLON)
77
78    ! Wave EP-fluxes at the 2 semi levels surrounding the full level
79    REAL WWM(NW, KLON), WWP(NW, KLON)
80
81    REAL RUW0(NW, KLON) ! Fluxes at launching level
82
83    REAL RUWP(NW, KLON), RVWP(NW, KLON)
84    ! Fluxes X and Y for each waves at 1/2 Levels
85
86    INTEGER LAUNCH, LTROP ! Launching altitude and tropo altitude
87
88    REAL XLAUNCH ! Controle the launching altitude
89    REAL XTROP ! SORT of Tropopause altitude
90    REAL RUW(KLON, KLEV + 1) ! Flux x at semi levels
91    REAL RVW(KLON, KLEV + 1) ! Flux y at semi levels
92
93    REAL PRMAX ! Maximum value of PREC, and for which our linear formula
94    ! for GWs parameterisation apply
95
96    ! 0.3.2 PARAMETERS OF WAVES DISSIPATIONS
97
98    REAL RDISS, ZOISEC ! COEFF DE DISSIPATION, SECURITY FOR INTRINSIC FREQ
99    REAL CORSEC ! SECURITY FOR INTRINSIC CORIOLIS
100    REAL RUWFRT,SATFRT
101
102    ! 0.3.3 BACKGROUND FLOW AT 1/2 LEVELS AND VERTICAL COORDINATE
103
104    REAL H0 ! Characteristic Height of the atmosphere
105    REAL DZ ! Characteristic depth of the source!
106    REAL PR, TR ! Reference Pressure and Temperature
107
108    REAL ZH(KLON, KLEV + 1) ! Log-pressure altitude
109
110    REAL UH(KLON, KLEV + 1), VH(KLON, KLEV + 1) ! Winds at 1/2 levels
111    REAL PH(KLON, KLEV + 1) ! Pressure at 1/2 levels
112    REAL PSEC ! Security to avoid division by 0 pressure
113    REAL PHM1(KLON, KLEV + 1) ! 1/Press at 1/2 levels
114    REAL BV(KLON, KLEV + 1) ! Brunt Vaisala freq. (BVF) at 1/2 levels
115    REAL BVSEC ! Security to avoid negative BVF
116
117    REAL, DIMENSION(klev+1) ::HREF
118    LOGICAL, SAVE :: gwd_reproductibilite_mpiomp=.true.
119    LOGICAL, SAVE :: firstcall = .TRUE.
120  !$OMP THREADPRIVATE(firstcall,gwd_reproductibilite_mpiomp)
121
122    CHARACTER (LEN=20) :: modname='flott_gwd_rando'
123    CHARACTER (LEN=80) :: abort_message
124
125
126
127  IF (firstcall) THEN
128    ! Cle introduite pour resoudre un probleme de non reproductibilite
129    ! Le but est de pouvoir tester de revenir a la version precedenete
130    ! A eliminer rapidement
131    CALL getin_p('gwd_reproductibilite_mpiomp',gwd_reproductibilite_mpiomp)
132    IF (NW+4*(NA-1)+NA>=KLEV) THEN
133       abort_message = 'NW+3*NA>=KLEV Probleme pour generation des ondes'
134       CALL abort_physic (modname,abort_message,1)
135    ENDIF
136    firstcall=.false.
137!    CALL iophys_ini
138  ENDIF
139
140    !-----------------------------------------------------------------
141
142    ! 1. INITIALISATIONS
143
144    ! 1.1 Basic parameter
145
146    ! Are provided from elsewhere (latent heat of vaporization, dry
147    ! gaz constant for air, gravity constant, heat capacity of dry air
148    ! at constant pressure, earth rotation rate, pi).
149
150    ! 1.2 Tuning parameters of V14
151
152! Values for linear in rot (recommended):
153!   RUWFRT=0.005 ! As RUWMAX but for frontal waves
154!   SATFRT=1.00  ! As SAT    but for frontal waves
155! Values when rot^2 is used                         
156!    RUWFRT=0.02  ! As RUWMAX but for frontal waves
157!    SATFRT=1.00  ! As SAT    but for frontal waves
158!    CMAX = 30.   ! Characteristic phase speed
159! Values when rot^2*EXP(-pi*sqrt(J)) is used                         
160!   RUWFRT=2.5   ! As RUWMAX but for frontal waves ~ N0*F0/4*DZ
161!   SATFRT=0.60   ! As SAT    but for frontal waves
162    RUWFRT=gwd_front_ruwmax 
163    SATFRT=gwd_front_sat
164    CMAX = 50.    ! Characteristic phase speed
165! Phase speed test
166!   RUWFRT=0.01
167!   CMAX = 50.   ! Characteristic phase speed (TEST)
168! Values when rot^2 and exp(-m^2*dz^2) are used     
169!   RUWFRT=0.03  ! As RUWMAX but for frontal waves
170!   SATFRT=1.00  ! As SAT    but for frontal waves
171! CRUCIAL PARAMETERS FOR THE WIND FILTERING
172    XLAUNCH=0.95 ! Parameter that control launching altitude
173    RDISS = 0.5  ! Diffusion parameter
174
175    ! maximum of rain for which our theory applies (in kg/m^2/s)
176
177    DZ = 1000. ! Characteristic depth of the source
178    XTROP=0.2 ! Parameter that control tropopause altitude
179    DELTAT=24.*3600. ! Time scale of the waves (first introduced in 9b)
180!   DELTAT=DTIME     ! No AR-1 Accumulation, OR OFFLINE             
181
182    KMIN = 2.E-5
183    ! minimum horizontal wavenumber (inverse of the subgrid scale resolution)
184
185    KMAX = 1.E-3  ! Max horizontal wavenumber
186    CMIN = 1.     ! Min phase velocity
187
188    TR = 240. ! Reference Temperature
189    PR = 101300. ! Reference pressure
190    H0 = RD * TR / RG ! Characteristic vertical scale height
191
192    BVSEC = 5.E-3 ! Security to avoid negative BVF
193    PSEC = 1.E-6 ! Security to avoid division by 0 pressure
194    ZOISEC = 1.E-6 ! Security FOR 0 INTRINSIC FREQ
195    CORSEC = ROMEGA*2.*SIN(2.*RPI/180.)! Security for CORIO
196
197!  ONLINE
198    call assert(klon == (/size(pp, 1), size(tt, 1), size(uu, 1), &
199         size(vv, 1), size(rot,1), size(zustr), size(zvstr), size(d_u, 1), &
200         size(d_v, 1), &
201        size(east_gwstress,1), size(west_gwstress,1) /), &
202        "ACAMA_GWD_RANDO klon")
203    call assert(klev == (/size(pp, 2), size(tt, 2), size(uu, 2), &
204         size(vv, 2), size(d_u, 2), size(d_v, 2), &
205         size(east_gwstress,2), size(west_gwstress,2) /), &
206         "ACAMA_GWD_RANDO klev")
207!  END ONLINE
208
209    IF(DELTAT < DTIME)THEN
210       PRINT *, 'flott_gwd_rando: deltat < dtime!'
211       STOP 1
212    ENDIF
213
214    IF (KLEV < NW) THEN
215       PRINT *, 'flott_gwd_rando: you will have problem with random numbers'
216       STOP 1
217    ENDIF
218
219    ! 2. EVALUATION OF THE BACKGROUND FLOW AT SEMI-LEVELS
220
221    ! Pressure and Inv of pressure
222    DO LL = 2, KLEV
223       PH(:, LL) = EXP((LOG(PP(:, LL)) + LOG(PP(:, LL - 1))) / 2.)
224       PHM1(:, LL) = 1. / PH(:, LL)
225    end DO
226
227    PH(:, KLEV + 1) = 0.
228    PHM1(:, KLEV + 1) = 1. / PSEC
229    PH(:, 1) = 2. * PP(:, 1) - PH(:, 2)
230
231    ! Launching altitude
232
233    IF (gwd_reproductibilite_mpiomp) THEN
234       ! Reprend la formule qui calcule PH en fonction de PP=play
235       DO LL = 2, KLEV
236          HREF(LL) = EXP((LOG(presnivs(LL)) + LOG(presnivs(LL - 1))) / 2.)
237       end DO
238       HREF(KLEV + 1) = 0.
239       HREF(1) = 2. * presnivs(1) - HREF(2)
240    ELSE
241       HREF(1:KLEV)=PH(KLON/2,1:KLEV)
242    ENDIF
243
244    LAUNCH=0
245    LTROP =0
246    DO LL = 1, KLEV
247       IF (HREF(LL) / HREF(1) > XLAUNCH) LAUNCH = LL
248    ENDDO
249    DO LL = 1, KLEV
250       IF (HREF(LL) / HREF(1) > XTROP) LTROP = LL
251    ENDDO
252
253!   PRINT *,'LAUNCH IN ACAMARA:',LAUNCH
254
255    ! Log pressure vert. coordinate
256    DO LL = 1, KLEV + 1
257       ZH(:, LL) = H0 * LOG(PR / (PH(:, LL) + PSEC))
258    end DO
259
260    ! BV frequency
261    DO LL = 2, KLEV
262       ! BVSEC: BV Frequency (UH USED IS AS A TEMPORARY ARRAY DOWN TO WINDS)
263       UH(:, LL) = 0.5 * (TT(:, LL) + TT(:, LL - 1)) &
264            * RD**2 / RCPD / H0**2 + (TT(:, LL) &
265            - TT(:, LL - 1)) / (ZH(:, LL) - ZH(:, LL - 1)) * RD / H0
266    end DO
267    BVLOW = 0.5 * (TT(:, LTROP )+ TT(:, LAUNCH)) &
268         * RD**2 / RCPD / H0**2 + (TT(:, LTROP ) &
269         - TT(:, LAUNCH))/(ZH(:, LTROP )- ZH(:, LAUNCH)) * RD / H0
270
271    UH(:, 1) = UH(:, 2)
272    UH(:, KLEV + 1) = UH(:, KLEV)
273    BV(:, 1) = UH(:, 2)
274    BV(:, KLEV + 1) = UH(:, KLEV)
275    ! SMOOTHING THE BV HELPS
276    DO LL = 2, KLEV
277       BV(:, LL)=(UH(:, LL+1)+2.*UH(:, LL)+UH(:, LL-1))/4.
278    end DO
279
280    BV=MAX(SQRT(MAX(BV, 0.)), BVSEC)
281    BVLOW=MAX(SQRT(MAX(BVLOW, 0.)), BVSEC)
282
283    ! WINDS
284    DO LL = 2, KLEV
285       UH(:, LL) = 0.5 * (UU(:, LL) + UU(:, LL - 1)) ! Zonal wind
286       VH(:, LL) = 0.5 * (VV(:, LL) + VV(:, LL - 1)) ! Meridional wind
287       UZ(:, LL) = ABS((SQRT(UU(:, LL)**2+VV(:, LL)**2) &
288          - SQRT(UU(:,LL-1)**2+VV(:, LL-1)**2)) &
289          /(ZH(:, LL)-ZH(:, LL-1)) )
290    end DO
291    UH(:, 1) = 0.
292    VH(:, 1) = 0.
293    UH(:, KLEV + 1) = UU(:, KLEV)
294    VH(:, KLEV + 1) = VV(:, KLEV)
295
296    UZ(:, 1) = UZ(:, 2)
297    UZ(:, KLEV + 1) = UZ(:, KLEV)
298    UZ(:, :) = MAX(UZ(:,:), PSEC)
299
300   ! BAROTROPIC VORTICITY AND INTEGRATED CORIOLIS PARAMETER
301   
302    CORIO(:) = MAX(ROMEGA*2.*ABS(SIN(PLAT(:)*RPI/180.)),CORSEC)
303    ROTBA(:)=0.
304    DO LL = 1,KLEV-1
305        !ROTBA(:) = ROTBA(:) + (ROT(:,LL)+ROT(:,LL+1))/2./RG*(PP(:,LL)-PP(:,LL+1))
306        ! Introducing the complete formula (exp of Richardson number):
307        ROTBA(:) = ROTBA(:) + &
308                !((ROT(:,LL)+ROT(:,LL+1))/2.)**2 &
309                (CORIO(:)*TANH(ABS(ROT(:,LL)+ROT(:,LL+1))/2./CORIO(:)))**2 &
310                /RG*(PP(:,LL)-PP(:,LL+1)) &
311                * EXP(-RPI*BV(:,LL+1)/UZ(:,LL+1)) &
312!               * DZ*BV(:,LL+1)/4./ABS(CORIO(:))
313                * DZ*BV(:,LL+1)/4./1.E-4           !  Changes after 1991
314!ARRET
315    ENDDO
316    !   PRINT *,'MAX ROTBA:',MAXVAL(ROTBA)
317    !   ROTBA(:)=(1.*ROTBA(:)  & ! Testing zone
318    !           +0.15*CORIO(:)**2                &
319    !           /(COS(PLAT(:)*RPI/180.)+0.02)  &
320    !           )*DZ*0.01/0.0001/4. ! & ! Testing zone
321    !   MODIF GWD4 AFTER 1985
322    !            *(1.25+SIN(PLAT(:)*RPI/180.))/(1.05+SIN(PLAT(:)*RPI/180.))/1.25
323    !          *1./(COS(PLAT(:)*RPI/180.)+0.02)
324    !    CORIO(:) = MAX(ROMEGA*2.*ABS(SIN(PLAT(:)*RPI/180.)),ZOISEC)/RG*PP(:,1)
325
326    ! 3 WAVES CHARACTERISTICS CHOSEN RANDOMLY AT THE LAUNCH ALTITUDE
327
328    ! The mod functions of weird arguments are used to produce the
329    ! waves characteristics in an almost stochastic way
330
331    JW = 0
332    DO JW = 1, NW
333             ! Angle
334             DO II = 1, KLON
335                ! Angle (0 or PI so far)
336                ! ZP(JW, II) = (SIGN(1., 0.5 - MOD(TT(II, JW) * 10., 1.)) + 1.) &
337                !      * RPI / 2.
338                ! Angle between 0 and pi
339                  ZP(JW, II) = MOD(TT(II, JW) * 10., 1.) * RPI
340! TEST WITH POSITIVE WAVES ONLY (Part I/II)
341!               ZP(JW, II) = 0.
342                ! Horizontal wavenumber amplitude
343                ZK(JW, II) = KMIN + (KMAX - KMIN) * MOD(TT(II, JW) * 100., 1.)
344                ! Horizontal phase speed
345                CPHA = 0.
346                DO JJ = 1, NA
347                    CPHA = CPHA + &
348         CMAX*2.*(MOD(TT(II, JW+4*(JJ-1)+JJ)**2, 1.)-0.5)*SQRT(3.)/SQRT(NA*1.)
349                END DO
350                IF (CPHA.LT.0.)  THEN
351                   CPHA = -1.*CPHA
352                   ZP(JW,II) = ZP(JW,II) + RPI
353! TEST WITH POSITIVE WAVES ONLY (Part II/II)
354!               ZP(JW, II) = 0.
355                ENDIF
356                CPHA = CPHA + CMIN !we dont allow |c|<1m/s
357                ! Absolute frequency is imposed
358                ZO(JW, II) = CPHA * ZK(JW, II)
359                ! Intrinsic frequency is imposed
360                ZO(JW, II) = ZO(JW, II) &
361                     + ZK(JW, II) * COS(ZP(JW, II)) * UH(II, LAUNCH) &
362                     + ZK(JW, II) * SIN(ZP(JW, II)) * VH(II, LAUNCH)
363                ! Momentum flux at launch lev
364                ! LAUNCHED RANDOM WAVES WITH LOG-NORMAL AMPLITUDE
365                !  RIGHT IN THE SH (GWD4 after 1990)
366                  RUW0(JW, II) = 0.
367                 DO JJ = 1, NA
368                    RUW0(JW, II) = RUW0(JW,II) + &
369         2.*(MOD(TT(II, JW+4*(JJ-1)+JJ)**2, 1.)-0.5)*SQRT(3.)/SQRT(NA*1.)
370                END DO
371                RUW0(JW, II) = RUWFRT &
372                          * EXP(RUW0(JW,II))/1250. &  ! 2 mpa at south pole
373       *((1.05+SIN(PLAT(II)*RPI/180.))/(1.01+SIN(PLAT(II)*RPI/180.))-2.05/2.01)
374                ! RUW0(JW, II) = RUWFRT
375             ENDDO
376    end DO
377
378    ! 4. COMPUTE THE FLUXES
379
380    ! 4.0
381
382    ! 4.1 Vertical velocity at launching altitude to ensure
383    ! the correct value to the imposed fluxes.
384
385    DO JW = 1, NW
386
387       ! Evaluate intrinsic frequency at launching altitude:
388       ZOP(JW, :) = ZO(JW, :) &
389            - ZK(JW, :) * COS(ZP(JW, :)) * UH(:, LAUNCH) &
390            - ZK(JW, :) * SIN(ZP(JW, :)) * VH(:, LAUNCH)
391
392       ! VERSION WITH FRONTAL SOURCES
393
394       ! Momentum flux at launch level imposed by vorticity sources
395
396       ! tanh limitation for values above CORIO (inertial instability).
397       ! WWP(JW, :) = RUW0(JW, :) &
398       WWP(JW, :) = RUWFRT      &
399       !     * (CORIO(:)*TANH(ROTBA(:)/CORIO(:)))**2 &
400       !    * ABS((CORIO(:)*TANH(ROTBA(:)/CORIO(:)))*CORIO(:)) &
401       !  CONSTANT FLUX
402       !    * (CORIO(:)*CORIO(:)) &
403       ! MODERATION BY THE DEPTH OF THE SOURCE (DZ HERE)
404       !      *EXP(-BVLOW(:)**2/MAX(ABS(ZOP(JW, :)),ZOISEC)**2 &
405       !      *ZK(JW, :)**2*DZ**2) &
406       ! COMPLETE FORMULA:
407            !* CORIO(:)**2*TANH(ROTBA(:)/CORIO(:)**2) &
408            * ROTBA(:) &
409       !  RESTORE DIMENSION OF A FLUX
410       !     *RD*TR/PR
411       !     *1. + RUW0(JW, :)
412             *1.
413
414       ! Factor related to the characteristics of the waves: NONE
415
416       ! Moderation by the depth of the source (dz here): NONE
417
418       ! Put the stress in the right direction:
419
420        RUWP(JW, :) = SIGN(1., ZOP(JW, :))*COS(ZP(JW, :)) * WWP(JW, :)
421        RVWP(JW, :) = SIGN(1., ZOP(JW, :))*SIN(ZP(JW, :)) * WWP(JW, :)
422
423    end DO
424
425    ! 4.2 Uniform values below the launching altitude
426
427    DO LL = 1, LAUNCH
428       RUW(:, LL) = 0
429       RVW(:, LL) = 0
430       DO JW = 1, NW
431          RUW(:, LL) = RUW(:, LL) + RUWP(JW, :)
432          RVW(:, LL) = RVW(:, LL) + RVWP(JW, :)
433       end DO
434    end DO
435
436    ! 4.3 Loop over altitudes, with passage from one level to the next
437    ! done by i) conserving the EP flux, ii) dissipating a little,
438    ! iii) testing critical levels, and vi) testing the breaking.
439
440    DO LL = LAUNCH, KLEV - 1
441       ! Warning: all the physics is here (passage from one level
442       ! to the next)
443       DO JW = 1, NW
444          ZOM(JW, :) = ZOP(JW, :)
445          WWM(JW, :) = WWP(JW, :)
446          ! Intrinsic Frequency
447          ZOP(JW, :) = ZO(JW, :) - ZK(JW, :) * COS(ZP(JW, :)) * UH(:, LL + 1) &
448               - ZK(JW, :) * SIN(ZP(JW, :)) * VH(:, LL + 1)
449
450          ! No breaking (Eq.6)
451          ! Dissipation (Eq. 8)
452          WWP(JW, :) = WWM(JW, :) * EXP(- 4. * RDISS * PR / (PH(:, LL + 1) &
453               + PH(:, LL)) * ((BV(:, LL + 1) + BV(:, LL)) / 2.)**3 &
454               / MAX(ABS(ZOP(JW, :) + ZOM(JW, :)) / 2., ZOISEC)**4 &
455               * ZK(JW, :)**3 * (ZH(:, LL + 1) - ZH(:, LL)))
456
457          ! Critical levels (forced to zero if intrinsic frequency changes sign)
458          ! Saturation (Eq. 12)
459          WWP(JW, :) = min(WWP(JW, :), MAX(0., &
460               SIGN(1., ZOP(JW, :) * ZOM(JW, :))) * ABS(ZOP(JW, :))**3 &
461          !    / BV(:, LL + 1) * EXP(- ZH(:, LL + 1) / H0) * SATFRT**2 * KMIN**2 &
462               / BV(:, LL + 1) * EXP(- ZH(:, LL + 1) / H0) * KMIN**2 &
463!              *(SATFRT*(2.5+1.5*TANH((ZH(:,LL+1)/H0-8.)/2.)))**2 &
464               *SATFRT**2       &
465               / ZK(JW, :)**4)
466       end DO
467
468       ! Evaluate EP-flux from Eq. 7 and give the right orientation to
469       ! the stress
470
471       DO JW = 1, NW
472          RUWP(JW, :) = SIGN(1., ZOP(JW, :))*COS(ZP(JW, :)) * WWP(JW, :)
473          RVWP(JW, :) = SIGN(1., ZOP(JW, :))*SIN(ZP(JW, :)) * WWP(JW, :)
474       end DO
475
476       RUW(:, LL + 1) = 0.
477       RVW(:, LL + 1) = 0.
478
479       DO JW = 1, NW
480          RUW(:, LL + 1) = RUW(:, LL + 1) + RUWP(JW, :)
481          RVW(:, LL + 1) = RVW(:, LL + 1) + RVWP(JW, :)
482          EAST_GWSTRESS(:, LL)=EAST_GWSTRESS(:, LL)+MAX(0.,RUWP(JW,:))/FLOAT(NW)
483          WEST_GWSTRESS(:, LL)=WEST_GWSTRESS(:, LL)+MIN(0.,RUWP(JW,:))/FLOAT(NW)
484       end DO
485    end DO
486
487    ! 5 CALCUL DES TENDANCES:
488
489    ! 5.1 Rectification des flux au sommet et dans les basses couches
490
491    RUW(:, KLEV + 1) = 0.
492    RVW(:, KLEV + 1) = 0.
493    RUW(:, 1) = RUW(:, LAUNCH)
494    RVW(:, 1) = RVW(:, LAUNCH)
495    DO LL = 1, LAUNCH
496       RUW(:, LL) = RUW(:, LAUNCH+1)
497       RVW(:, LL) = RVW(:, LAUNCH+1)
498       EAST_GWSTRESS(:, LL)=EAST_GWSTRESS(:, LAUNCH)
499       WEST_GWSTRESS(:, LL)=WEST_GWSTRESS(:, LAUNCH)
500    end DO
501
502    ! AR-1 RECURSIVE FORMULA (13) IN VERSION 4
503    DO LL = 1, KLEV
504       D_U(:, LL) = (1.-DTIME/DELTAT) * D_U(:, LL) + DTIME/DELTAT/REAL(NW) * &
505            RG * (RUW(:, LL + 1) - RUW(:, LL)) &
506            / (PH(:, LL + 1) - PH(:, LL)) * DTIME
507!  NO AR1 FOR MERIDIONAL TENDENCIES
508!      D_V(:, LL) = (1.-DTIME/DELTAT) * D_V(:, LL) + DTIME/DELTAT/REAL(NW) * &
509       D_V(:, LL) =                                            1./REAL(NW) * &
510            RG * (RVW(:, LL + 1) - RVW(:, LL)) &
511            / (PH(:, LL + 1) - PH(:, LL)) * DTIME
512    ENDDO
513
514    ! Cosmetic: evaluation of the cumulated stress
515    ZUSTR = 0.
516    ZVSTR = 0.
517    DO LL = 1, KLEV
518       ZUSTR = ZUSTR + D_U(:, LL) / RG * (PH(:, LL + 1) - PH(:, LL))/DTIME
519!      ZVSTR = ZVSTR + D_V(:, LL) / RG * (PH(:, LL + 1) - PH(:, LL))/DTIME
520    ENDDO
521! COSMETICS TO VISUALIZE ROTBA
522    ZVSTR = ROTBA
523
524  END SUBROUTINE ACAMA_GWD_RANDO
525
526end module ACAMA_GWD_rando_m
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