source: LMDZ6/trunk/libf/phylmd/acama_gwd_rando_m.F90 @ 3825

Last change on this file since 3825 was 3531, checked in by Laurent Fairhead, 5 years ago

Replaced STOP statements by a call to abort_physic in phylmd as per ticket #86
Still some work to be done in phylmd subdirectories
  • Property svn:keywords set to Id
File size: 18.8 KB
RevLine 
[3531]1!
2! $Id: acama_gwd_rando_m.F90 3531 2019-06-06 15:08:45Z musat $
3!
[2333]4module ACAMA_GWD_rando_m
5
6  implicit none
7
8contains
9
10  SUBROUTINE ACAMA_GWD_rando(DTIME, pp, plat, tt, uu, vv, rot, &
11       zustr, zvstr, d_u, d_v,east_gwstress,west_gwstress)
12
13    ! Parametrization of the momentum flux deposition due to a discrete
14    ! number of gravity waves.
15    ! Author: F. Lott, A. de la Camara
16    ! July, 24th, 2014
17    ! Gaussian distribution of the source, source is vorticity squared
18    ! Reference: de la Camara and Lott (GRL, 2015, vol 42, 2071-2078 )
19    ! Lott et al (JAS, 2010, vol 67, page 157-170)
20    ! Lott et al (JAS, 2012, vol 69, page 2134-2151)
21
22!  ONLINE:
23    use dimphy, only: klon, klev
24    use assert_m, only: assert
[3198]25    USE ioipsl_getin_p_mod, ONLY : getin_p
26    USE vertical_layers_mod, ONLY : presnivs
27
[2333]28    include "YOMCST.h"
29    include "clesphys.h"
30!  OFFLINE:
31!   include "dimensions.h"
32!   include "dimphy.h"
33!END DIFFERENCE
34    include "YOEGWD.h"
35
36    ! 0. DECLARATIONS:
37
38    ! 0.1 INPUTS
39    REAL, intent(in)::DTIME ! Time step of the Physics
40    REAL, intent(in):: PP(:, :) ! (KLON, KLEV) Pressure at full levels
41    REAL, intent(in):: ROT(:,:) ! Relative vorticity             
42    REAL, intent(in):: TT(:, :) ! (KLON, KLEV) Temp at full levels
43    REAL, intent(in):: UU(:, :) ! (KLON, KLEV) Zonal wind at full levels
44    REAL, intent(in):: VV(:, :) ! (KLON, KLEV) Merid wind at full levels
45    REAL, intent(in):: PLAT(:) ! (KLON) LATITUDE                   
46
47    ! 0.2 OUTPUTS
48    REAL, intent(out):: zustr(:), zvstr(:) ! (KLON) Surface Stresses
49
50    REAL, intent(inout):: d_u(:, :), d_v(:, :)
51    REAL, intent(inout):: east_gwstress(:, :) !  Profile of eastward stress
52    REAL, intent(inout):: west_gwstress(:, :) !  Profile of westward stress
53    ! (KLON, KLEV) tendencies on winds
54
55    ! O.3 INTERNAL ARRAYS
56    REAL BVLOW(klon)  !  LOW LEVEL BV FREQUENCY
57    REAL ROTBA(KLON),CORIO(KLON)  !  BAROTROPIC REL. VORTICITY AND PLANETARY
58    REAL UZ(KLON, KLEV + 1)
59
60    INTEGER II, JJ, LL
61
62    ! 0.3.0 TIME SCALE OF THE LIFE CYCLE OF THE WAVES PARAMETERIZED
63
64    REAL DELTAT
65
66    ! 0.3.1 GRAVITY-WAVES SPECIFICATIONS
67
68    INTEGER, PARAMETER:: NK = 2, NP = 2, NO = 2, NW = NK * NP * NO
69    INTEGER JK, JP, JO, JW
70    INTEGER, PARAMETER:: NA = 5  !number of realizations to get the phase speed
71    REAL KMIN, KMAX ! Min and Max horizontal wavenumbers
72    REAL CMIN, CMAX ! Min and Max absolute ph. vel.
73    REAL CPHA ! absolute PHASE VELOCITY frequency
74    REAL ZK(NW, KLON) ! Horizontal wavenumber amplitude
75    REAL ZP(NW, KLON) ! Horizontal wavenumber angle
76    REAL ZO(NW, KLON) ! Absolute frequency !
77
78    ! Waves Intr. freq. at the 1/2 lev surrounding the full level
79    REAL ZOM(NW, KLON), ZOP(NW, KLON)
80
81    ! Wave EP-fluxes at the 2 semi levels surrounding the full level
82    REAL WWM(NW, KLON), WWP(NW, KLON)
83
84    REAL RUW0(NW, KLON) ! Fluxes at launching level
85
86    REAL RUWP(NW, KLON), RVWP(NW, KLON)
87    ! Fluxes X and Y for each waves at 1/2 Levels
88
89    INTEGER LAUNCH, LTROP ! Launching altitude and tropo altitude
90
91    REAL XLAUNCH ! Controle the launching altitude
92    REAL XTROP ! SORT of Tropopause altitude
93    REAL RUW(KLON, KLEV + 1) ! Flux x at semi levels
94    REAL RVW(KLON, KLEV + 1) ! Flux y at semi levels
95
96    REAL PRMAX ! Maximum value of PREC, and for which our linear formula
97    ! for GWs parameterisation apply
98
99    ! 0.3.2 PARAMETERS OF WAVES DISSIPATIONS
100
101    REAL RDISS, ZOISEC ! COEFF DE DISSIPATION, SECURITY FOR INTRINSIC FREQ
102    REAL CORSEC ! SECURITY FOR INTRINSIC CORIOLIS
103    REAL RUWFRT,SATFRT
104
105    ! 0.3.3 BACKGROUND FLOW AT 1/2 LEVELS AND VERTICAL COORDINATE
106
107    REAL H0 ! Characteristic Height of the atmosphere
108    REAL DZ ! Characteristic depth of the source!
109    REAL PR, TR ! Reference Pressure and Temperature
110
111    REAL ZH(KLON, KLEV + 1) ! Log-pressure altitude
112
113    REAL UH(KLON, KLEV + 1), VH(KLON, KLEV + 1) ! Winds at 1/2 levels
114    REAL PH(KLON, KLEV + 1) ! Pressure at 1/2 levels
115    REAL PSEC ! Security to avoid division by 0 pressure
116    REAL PHM1(KLON, KLEV + 1) ! 1/Press at 1/2 levels
117    REAL BV(KLON, KLEV + 1) ! Brunt Vaisala freq. (BVF) at 1/2 levels
118    REAL BVSEC ! Security to avoid negative BVF
119
[3198]120    REAL, DIMENSION(klev+1) ::HREF
121    LOGICAL, SAVE :: gwd_reproductibilite_mpiomp=.true.
122    LOGICAL, SAVE :: firstcall = .TRUE.
123  !$OMP THREADPRIVATE(firstcall,gwd_reproductibilite_mpiomp)
124
[3531]125    CHARACTER (LEN=20) :: modname='acama_gwd_rando_m'
[3198]126    CHARACTER (LEN=80) :: abort_message
127
128
129
130  IF (firstcall) THEN
131    ! Cle introduite pour resoudre un probleme de non reproductibilite
132    ! Le but est de pouvoir tester de revenir a la version precedenete
133    ! A eliminer rapidement
134    CALL getin_p('gwd_reproductibilite_mpiomp',gwd_reproductibilite_mpiomp)
135    IF (NW+4*(NA-1)+NA>=KLEV) THEN
136       abort_message = 'NW+3*NA>=KLEV Probleme pour generation des ondes'
137       CALL abort_physic (modname,abort_message,1)
138    ENDIF
139    firstcall=.false.
140!    CALL iophys_ini
141  ENDIF
142
[2333]143    !-----------------------------------------------------------------
144
145    ! 1. INITIALISATIONS
146
147    ! 1.1 Basic parameter
148
149    ! Are provided from elsewhere (latent heat of vaporization, dry
150    ! gaz constant for air, gravity constant, heat capacity of dry air
151    ! at constant pressure, earth rotation rate, pi).
152
153    ! 1.2 Tuning parameters of V14
154
155! Values for linear in rot (recommended):
156!   RUWFRT=0.005 ! As RUWMAX but for frontal waves
157!   SATFRT=1.00  ! As SAT    but for frontal waves
158! Values when rot^2 is used                         
159!    RUWFRT=0.02  ! As RUWMAX but for frontal waves
160!    SATFRT=1.00  ! As SAT    but for frontal waves
161!    CMAX = 30.   ! Characteristic phase speed
162! Values when rot^2*EXP(-pi*sqrt(J)) is used                         
[2357]163!   RUWFRT=2.5   ! As RUWMAX but for frontal waves ~ N0*F0/4*DZ
164!   SATFRT=0.60   ! As SAT    but for frontal waves
165    RUWFRT=gwd_front_ruwmax 
166    SATFRT=gwd_front_sat
[2665]167    CMAX = 50.    ! Characteristic phase speed
[2333]168! Phase speed test
169!   RUWFRT=0.01
170!   CMAX = 50.   ! Characteristic phase speed (TEST)
171! Values when rot^2 and exp(-m^2*dz^2) are used     
172!   RUWFRT=0.03  ! As RUWMAX but for frontal waves
173!   SATFRT=1.00  ! As SAT    but for frontal waves
174! CRUCIAL PARAMETERS FOR THE WIND FILTERING
175    XLAUNCH=0.95 ! Parameter that control launching altitude
[2665]176    RDISS = 0.5  ! Diffusion parameter
[2333]177
178    ! maximum of rain for which our theory applies (in kg/m^2/s)
179
180    DZ = 1000. ! Characteristic depth of the source
181    XTROP=0.2 ! Parameter that control tropopause altitude
182    DELTAT=24.*3600. ! Time scale of the waves (first introduced in 9b)
183!   DELTAT=DTIME     ! No AR-1 Accumulation, OR OFFLINE             
184
185    KMIN = 2.E-5
186    ! minimum horizontal wavenumber (inverse of the subgrid scale resolution)
187
188    KMAX = 1.E-3  ! Max horizontal wavenumber
189    CMIN = 1.     ! Min phase velocity
190
191    TR = 240. ! Reference Temperature
192    PR = 101300. ! Reference pressure
193    H0 = RD * TR / RG ! Characteristic vertical scale height
194
195    BVSEC = 5.E-3 ! Security to avoid negative BVF
196    PSEC = 1.E-6 ! Security to avoid division by 0 pressure
197    ZOISEC = 1.E-6 ! Security FOR 0 INTRINSIC FREQ
198    CORSEC = ROMEGA*2.*SIN(2.*RPI/180.)! Security for CORIO
199
200!  ONLINE
201    call assert(klon == (/size(pp, 1), size(tt, 1), size(uu, 1), &
202         size(vv, 1), size(rot,1), size(zustr), size(zvstr), size(d_u, 1), &
203         size(d_v, 1), &
204        size(east_gwstress,1), size(west_gwstress,1) /), &
205        "ACAMA_GWD_RANDO klon")
206    call assert(klev == (/size(pp, 2), size(tt, 2), size(uu, 2), &
207         size(vv, 2), size(d_u, 2), size(d_v, 2), &
208         size(east_gwstress,2), size(west_gwstress,2) /), &
209         "ACAMA_GWD_RANDO klev")
210!  END ONLINE
211
212    IF(DELTAT < DTIME)THEN
[3531]213!       PRINT *, 'flott_gwd_rando: deltat < dtime!'
214!       STOP 1
215       abort_message=' deltat < dtime! '
216       CALL abort_physic(modname,abort_message,1)
[2333]217    ENDIF
218
219    IF (KLEV < NW) THEN
[3531]220!       PRINT *, 'flott_gwd_rando: you will have problem with random numbers'
221!       STOP 1
222       abort_message=' you will have problem with random numbers'
223       CALL abort_physic(modname,abort_message,1)
[2333]224    ENDIF
225
226    ! 2. EVALUATION OF THE BACKGROUND FLOW AT SEMI-LEVELS
227
228    ! Pressure and Inv of pressure
229    DO LL = 2, KLEV
230       PH(:, LL) = EXP((LOG(PP(:, LL)) + LOG(PP(:, LL - 1))) / 2.)
231       PHM1(:, LL) = 1. / PH(:, LL)
232    end DO
233
234    PH(:, KLEV + 1) = 0.
235    PHM1(:, KLEV + 1) = 1. / PSEC
236    PH(:, 1) = 2. * PP(:, 1) - PH(:, 2)
237
238    ! Launching altitude
239
[3198]240    IF (gwd_reproductibilite_mpiomp) THEN
241       ! Reprend la formule qui calcule PH en fonction de PP=play
242       DO LL = 2, KLEV
243          HREF(LL) = EXP((LOG(presnivs(LL)) + LOG(presnivs(LL - 1))) / 2.)
244       end DO
245       HREF(KLEV + 1) = 0.
246       HREF(1) = 2. * presnivs(1) - HREF(2)
247    ELSE
248       HREF(1:KLEV)=PH(KLON/2,1:KLEV)
249    ENDIF
250
[2333]251    LAUNCH=0
252    LTROP =0
253    DO LL = 1, KLEV
[3198]254       IF (HREF(LL) / HREF(1) > XLAUNCH) LAUNCH = LL
[2333]255    ENDDO
256    DO LL = 1, KLEV
[3198]257       IF (HREF(LL) / HREF(1) > XTROP) LTROP = LL
[2333]258    ENDDO
[3198]259    !LAUNCH=22 ; LTROP=33
260!   print*,'LAUNCH=',LAUNCH,'LTROP=',LTROP
[2333]261
[3198]262
[2333]263!   PRINT *,'LAUNCH IN ACAMARA:',LAUNCH
264
265    ! Log pressure vert. coordinate
266    DO LL = 1, KLEV + 1
267       ZH(:, LL) = H0 * LOG(PR / (PH(:, LL) + PSEC))
268    end DO
269
270    ! BV frequency
271    DO LL = 2, KLEV
272       ! BVSEC: BV Frequency (UH USED IS AS A TEMPORARY ARRAY DOWN TO WINDS)
273       UH(:, LL) = 0.5 * (TT(:, LL) + TT(:, LL - 1)) &
274            * RD**2 / RCPD / H0**2 + (TT(:, LL) &
275            - TT(:, LL - 1)) / (ZH(:, LL) - ZH(:, LL - 1)) * RD / H0
276    end DO
277    BVLOW = 0.5 * (TT(:, LTROP )+ TT(:, LAUNCH)) &
278         * RD**2 / RCPD / H0**2 + (TT(:, LTROP ) &
279         - TT(:, LAUNCH))/(ZH(:, LTROP )- ZH(:, LAUNCH)) * RD / H0
280
281    UH(:, 1) = UH(:, 2)
282    UH(:, KLEV + 1) = UH(:, KLEV)
283    BV(:, 1) = UH(:, 2)
284    BV(:, KLEV + 1) = UH(:, KLEV)
285    ! SMOOTHING THE BV HELPS
286    DO LL = 2, KLEV
287       BV(:, LL)=(UH(:, LL+1)+2.*UH(:, LL)+UH(:, LL-1))/4.
288    end DO
289
290    BV=MAX(SQRT(MAX(BV, 0.)), BVSEC)
291    BVLOW=MAX(SQRT(MAX(BVLOW, 0.)), BVSEC)
292
293    ! WINDS
294    DO LL = 2, KLEV
295       UH(:, LL) = 0.5 * (UU(:, LL) + UU(:, LL - 1)) ! Zonal wind
296       VH(:, LL) = 0.5 * (VV(:, LL) + VV(:, LL - 1)) ! Meridional wind
297       UZ(:, LL) = ABS((SQRT(UU(:, LL)**2+VV(:, LL)**2) &
298          - SQRT(UU(:,LL-1)**2+VV(:, LL-1)**2)) &
299          /(ZH(:, LL)-ZH(:, LL-1)) )
300    end DO
301    UH(:, 1) = 0.
302    VH(:, 1) = 0.
303    UH(:, KLEV + 1) = UU(:, KLEV)
304    VH(:, KLEV + 1) = VV(:, KLEV)
305
306    UZ(:, 1) = UZ(:, 2)
307    UZ(:, KLEV + 1) = UZ(:, KLEV)
308    UZ(:, :) = MAX(UZ(:,:), PSEC)
309
310   ! BAROTROPIC VORTICITY AND INTEGRATED CORIOLIS PARAMETER
311   
312    CORIO(:) = MAX(ROMEGA*2.*ABS(SIN(PLAT(:)*RPI/180.)),CORSEC)
313    ROTBA(:)=0.
314    DO LL = 1,KLEV-1
315        !ROTBA(:) = ROTBA(:) + (ROT(:,LL)+ROT(:,LL+1))/2./RG*(PP(:,LL)-PP(:,LL+1))
316        ! Introducing the complete formula (exp of Richardson number):
317        ROTBA(:) = ROTBA(:) + &
318                !((ROT(:,LL)+ROT(:,LL+1))/2.)**2 &
319                (CORIO(:)*TANH(ABS(ROT(:,LL)+ROT(:,LL+1))/2./CORIO(:)))**2 &
320                /RG*(PP(:,LL)-PP(:,LL+1)) &
321                * EXP(-RPI*BV(:,LL+1)/UZ(:,LL+1)) &
322!               * DZ*BV(:,LL+1)/4./ABS(CORIO(:))
323                * DZ*BV(:,LL+1)/4./1.E-4           !  Changes after 1991
324!ARRET
325    ENDDO
326    !   PRINT *,'MAX ROTBA:',MAXVAL(ROTBA)
327    !   ROTBA(:)=(1.*ROTBA(:)  & ! Testing zone
328    !           +0.15*CORIO(:)**2                &
329    !           /(COS(PLAT(:)*RPI/180.)+0.02)  &
330    !           )*DZ*0.01/0.0001/4. ! & ! Testing zone
331    !   MODIF GWD4 AFTER 1985
332    !            *(1.25+SIN(PLAT(:)*RPI/180.))/(1.05+SIN(PLAT(:)*RPI/180.))/1.25
333    !          *1./(COS(PLAT(:)*RPI/180.)+0.02)
334    !    CORIO(:) = MAX(ROMEGA*2.*ABS(SIN(PLAT(:)*RPI/180.)),ZOISEC)/RG*PP(:,1)
335
336    ! 3 WAVES CHARACTERISTICS CHOSEN RANDOMLY AT THE LAUNCH ALTITUDE
337
338    ! The mod functions of weird arguments are used to produce the
339    ! waves characteristics in an almost stochastic way
340
341    JW = 0
[3198]342    DO JW = 1, NW
[2333]343             ! Angle
344             DO II = 1, KLON
345                ! Angle (0 or PI so far)
346                ! ZP(JW, II) = (SIGN(1., 0.5 - MOD(TT(II, JW) * 10., 1.)) + 1.) &
347                !      * RPI / 2.
348                ! Angle between 0 and pi
349                  ZP(JW, II) = MOD(TT(II, JW) * 10., 1.) * RPI
350! TEST WITH POSITIVE WAVES ONLY (Part I/II)
351!               ZP(JW, II) = 0.
352                ! Horizontal wavenumber amplitude
353                ZK(JW, II) = KMIN + (KMAX - KMIN) * MOD(TT(II, JW) * 100., 1.)
354                ! Horizontal phase speed
355                CPHA = 0.
356                DO JJ = 1, NA
357                    CPHA = CPHA + &
358         CMAX*2.*(MOD(TT(II, JW+4*(JJ-1)+JJ)**2, 1.)-0.5)*SQRT(3.)/SQRT(NA*1.)
359                END DO
360                IF (CPHA.LT.0.)  THEN
361                   CPHA = -1.*CPHA
362                   ZP(JW,II) = ZP(JW,II) + RPI
363! TEST WITH POSITIVE WAVES ONLY (Part II/II)
364!               ZP(JW, II) = 0.
365                ENDIF
366                CPHA = CPHA + CMIN !we dont allow |c|<1m/s
367                ! Absolute frequency is imposed
368                ZO(JW, II) = CPHA * ZK(JW, II)
369                ! Intrinsic frequency is imposed
370                ZO(JW, II) = ZO(JW, II) &
371                     + ZK(JW, II) * COS(ZP(JW, II)) * UH(II, LAUNCH) &
372                     + ZK(JW, II) * SIN(ZP(JW, II)) * VH(II, LAUNCH)
373                ! Momentum flux at launch lev
374                ! LAUNCHED RANDOM WAVES WITH LOG-NORMAL AMPLITUDE
375                !  RIGHT IN THE SH (GWD4 after 1990)
376                  RUW0(JW, II) = 0.
377                 DO JJ = 1, NA
378                    RUW0(JW, II) = RUW0(JW,II) + &
379         2.*(MOD(TT(II, JW+4*(JJ-1)+JJ)**2, 1.)-0.5)*SQRT(3.)/SQRT(NA*1.)
380                END DO
381                RUW0(JW, II) = RUWFRT &
382                          * EXP(RUW0(JW,II))/1250. &  ! 2 mpa at south pole
383       *((1.05+SIN(PLAT(II)*RPI/180.))/(1.01+SIN(PLAT(II)*RPI/180.))-2.05/2.01)
384                ! RUW0(JW, II) = RUWFRT
385             ENDDO
386    end DO
387
388    ! 4. COMPUTE THE FLUXES
389
390    ! 4.0
391
392    ! 4.1 Vertical velocity at launching altitude to ensure
393    ! the correct value to the imposed fluxes.
394
395    DO JW = 1, NW
396
397       ! Evaluate intrinsic frequency at launching altitude:
398       ZOP(JW, :) = ZO(JW, :) &
399            - ZK(JW, :) * COS(ZP(JW, :)) * UH(:, LAUNCH) &
400            - ZK(JW, :) * SIN(ZP(JW, :)) * VH(:, LAUNCH)
401
402       ! VERSION WITH FRONTAL SOURCES
403
404       ! Momentum flux at launch level imposed by vorticity sources
405
406       ! tanh limitation for values above CORIO (inertial instability).
407       ! WWP(JW, :) = RUW0(JW, :) &
408       WWP(JW, :) = RUWFRT      &
409       !     * (CORIO(:)*TANH(ROTBA(:)/CORIO(:)))**2 &
410       !    * ABS((CORIO(:)*TANH(ROTBA(:)/CORIO(:)))*CORIO(:)) &
411       !  CONSTANT FLUX
412       !    * (CORIO(:)*CORIO(:)) &
413       ! MODERATION BY THE DEPTH OF THE SOURCE (DZ HERE)
414       !      *EXP(-BVLOW(:)**2/MAX(ABS(ZOP(JW, :)),ZOISEC)**2 &
415       !      *ZK(JW, :)**2*DZ**2) &
416       ! COMPLETE FORMULA:
417            !* CORIO(:)**2*TANH(ROTBA(:)/CORIO(:)**2) &
418            * ROTBA(:) &
419       !  RESTORE DIMENSION OF A FLUX
420       !     *RD*TR/PR
[2665]421       !     *1. + RUW0(JW, :)
422             *1.
[2333]423
424       ! Factor related to the characteristics of the waves: NONE
425
426       ! Moderation by the depth of the source (dz here): NONE
427
428       ! Put the stress in the right direction:
429
430        RUWP(JW, :) = SIGN(1., ZOP(JW, :))*COS(ZP(JW, :)) * WWP(JW, :)
431        RVWP(JW, :) = SIGN(1., ZOP(JW, :))*SIN(ZP(JW, :)) * WWP(JW, :)
432
433    end DO
434
435    ! 4.2 Uniform values below the launching altitude
436
437    DO LL = 1, LAUNCH
438       RUW(:, LL) = 0
439       RVW(:, LL) = 0
440       DO JW = 1, NW
441          RUW(:, LL) = RUW(:, LL) + RUWP(JW, :)
442          RVW(:, LL) = RVW(:, LL) + RVWP(JW, :)
443       end DO
444    end DO
445
446    ! 4.3 Loop over altitudes, with passage from one level to the next
447    ! done by i) conserving the EP flux, ii) dissipating a little,
448    ! iii) testing critical levels, and vi) testing the breaking.
449
450    DO LL = LAUNCH, KLEV - 1
451       ! Warning: all the physics is here (passage from one level
452       ! to the next)
453       DO JW = 1, NW
454          ZOM(JW, :) = ZOP(JW, :)
455          WWM(JW, :) = WWP(JW, :)
456          ! Intrinsic Frequency
457          ZOP(JW, :) = ZO(JW, :) - ZK(JW, :) * COS(ZP(JW, :)) * UH(:, LL + 1) &
458               - ZK(JW, :) * SIN(ZP(JW, :)) * VH(:, LL + 1)
459
460          ! No breaking (Eq.6)
461          ! Dissipation (Eq. 8)
[2665]462          WWP(JW, :) = WWM(JW, :) * EXP(- 4. * RDISS * PR / (PH(:, LL + 1) &
[2333]463               + PH(:, LL)) * ((BV(:, LL + 1) + BV(:, LL)) / 2.)**3 &
464               / MAX(ABS(ZOP(JW, :) + ZOM(JW, :)) / 2., ZOISEC)**4 &
465               * ZK(JW, :)**3 * (ZH(:, LL + 1) - ZH(:, LL)))
466
467          ! Critical levels (forced to zero if intrinsic frequency changes sign)
468          ! Saturation (Eq. 12)
469          WWP(JW, :) = min(WWP(JW, :), MAX(0., &
470               SIGN(1., ZOP(JW, :) * ZOM(JW, :))) * ABS(ZOP(JW, :))**3 &
471          !    / BV(:, LL + 1) * EXP(- ZH(:, LL + 1) / H0) * SATFRT**2 * KMIN**2 &
472               / BV(:, LL + 1) * EXP(- ZH(:, LL + 1) / H0) * KMIN**2 &
473!              *(SATFRT*(2.5+1.5*TANH((ZH(:,LL+1)/H0-8.)/2.)))**2 &
474               *SATFRT**2       &
475               / ZK(JW, :)**4)
476       end DO
477
478       ! Evaluate EP-flux from Eq. 7 and give the right orientation to
479       ! the stress
480
481       DO JW = 1, NW
482          RUWP(JW, :) = SIGN(1., ZOP(JW, :))*COS(ZP(JW, :)) * WWP(JW, :)
483          RVWP(JW, :) = SIGN(1., ZOP(JW, :))*SIN(ZP(JW, :)) * WWP(JW, :)
484       end DO
485
486       RUW(:, LL + 1) = 0.
487       RVW(:, LL + 1) = 0.
488
489       DO JW = 1, NW
490          RUW(:, LL + 1) = RUW(:, LL + 1) + RUWP(JW, :)
491          RVW(:, LL + 1) = RVW(:, LL + 1) + RVWP(JW, :)
492          EAST_GWSTRESS(:, LL)=EAST_GWSTRESS(:, LL)+MAX(0.,RUWP(JW,:))/FLOAT(NW)
493          WEST_GWSTRESS(:, LL)=WEST_GWSTRESS(:, LL)+MIN(0.,RUWP(JW,:))/FLOAT(NW)
494       end DO
495    end DO
496
497    ! 5 CALCUL DES TENDANCES:
498
499    ! 5.1 Rectification des flux au sommet et dans les basses couches
500
501    RUW(:, KLEV + 1) = 0.
502    RVW(:, KLEV + 1) = 0.
503    RUW(:, 1) = RUW(:, LAUNCH)
504    RVW(:, 1) = RVW(:, LAUNCH)
505    DO LL = 1, LAUNCH
506       RUW(:, LL) = RUW(:, LAUNCH+1)
507       RVW(:, LL) = RVW(:, LAUNCH+1)
508       EAST_GWSTRESS(:, LL)=EAST_GWSTRESS(:, LAUNCH)
509       WEST_GWSTRESS(:, LL)=WEST_GWSTRESS(:, LAUNCH)
510    end DO
511
512    ! AR-1 RECURSIVE FORMULA (13) IN VERSION 4
513    DO LL = 1, KLEV
514       D_U(:, LL) = (1.-DTIME/DELTAT) * D_U(:, LL) + DTIME/DELTAT/REAL(NW) * &
515            RG * (RUW(:, LL + 1) - RUW(:, LL)) &
516            / (PH(:, LL + 1) - PH(:, LL)) * DTIME
517!  NO AR1 FOR MERIDIONAL TENDENCIES
518!      D_V(:, LL) = (1.-DTIME/DELTAT) * D_V(:, LL) + DTIME/DELTAT/REAL(NW) * &
519       D_V(:, LL) =                                            1./REAL(NW) * &
520            RG * (RVW(:, LL + 1) - RVW(:, LL)) &
521            / (PH(:, LL + 1) - PH(:, LL)) * DTIME
522    ENDDO
523
524    ! Cosmetic: evaluation of the cumulated stress
525    ZUSTR = 0.
526    ZVSTR = 0.
527    DO LL = 1, KLEV
528       ZUSTR = ZUSTR + D_U(:, LL) / RG * (PH(:, LL + 1) - PH(:, LL))/DTIME
529!      ZVSTR = ZVSTR + D_V(:, LL) / RG * (PH(:, LL + 1) - PH(:, LL))/DTIME
530    ENDDO
531! COSMETICS TO VISUALIZE ROTBA
532    ZVSTR = ROTBA
533
534  END SUBROUTINE ACAMA_GWD_RANDO
535
536end module ACAMA_GWD_rando_m
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