source: trunk/LMDZ.GENERIC/libf/phystd/nonoro_gwd_ran_mod.F90 @ 2299

Last change on this file since 2299 was 2299, checked in by dbardet, 5 years ago

27/04/2017 (r2299) == DB

Add non-orographic gravity waves drag parameterization (Flott scheme adpated from the Earth GCM)

It can be called using 'calllott_nonoro=.true.' in callphys.def, and set the maximum value of the Eliassen-Plam flux 'epflux_max'.
Cumulated output fields are du_nonoro, dv_nonoro (winds tendency due to GW drag), east_gwstress and west_gwstress (stress profile in esatward and westward direction due to GW drag)
These variables are added in Xhisitns and start files.

File size: 22.0 KB
Line 
1MODULE nonoro_gwd_ran_mod
2
3IMPLICIT NONE
4
5      REAL, allocatable, save :: du_nonoro_gwd(:, :) ! Zonal wind tendency due to GWD
6      REAL, allocatable, save :: dv_nonoro_gwd(:, :) ! Meridional wind tendency due to GWD
7      REAL, allocatable, save :: east_gwstress(:, :) ! Eastward stress profile
8      REAL, allocatable, save :: west_gwstress(:, :) ! Westward stress profile
9
10CONTAINS
11
12      SUBROUTINE nonoro_gwd_ran(ngrid, nlayer, dtime, pp, &
13                   zmax_therm, pt, pu, pv, pdt, pdu, pdv, &
14                   zustr, zvstr, d_t, d_u, d_v)
15
16!--------------------------------------------------------------------------------
17! Parametrization of the momentum flux deposition due to a discrete
18! number of gravity waves.
19! F. Lott
20! Version 14, Gaussian distribution of the source
21! LMDz model online version     
22! ADAPTED FOR VENUS /  F. LOTT + S. LEBONNOIS
23! Version adapted on 03/04/2013:
24!      - input flux compensated in the deepest layers
25!                           
26! ADAPTED FOR MARS     G.GILLI     02/2016
27!        Revision with F.Forget    06/2016  Variable EP-flux
28!        according to
29!                                           PBL variation (max
30!                                           velocity thermals)
31!                      D.BARDET    01/2020  - reproductibility of
32!                                           the launching altitude
33!                                           calculation
34!                                           - wave characteristic
35!                                           calculation using MOD
36!                                           - adding east_gwstress
37!                                           and west_gwstress variables   
38!
39! ADAPTED FOR GENERIC  D.BARDET    01/2020
40!---------------------------------------------------------------------------------
41
42
43
44     use comcstfi_mod, only: g, pi, cpp, r
45     USE ioipsl_getin_p_mod, ONLY : getin_p
46     use assert_m, only : assert
47     use vertical_layers_mod, only : presnivs
48     use callkeys_mod, only : epflux_max, & ! Max EP flux value at launching altitude (previous name: RUWMAX)
49                              gwd_convective_source
50     use inifis_mod
51     use xios_output_mod, only: send_xios_field
52 implicit none
53
54! 0. DECLARATIONS:
55
56     ! 0.1 INPUTS
57
58     INTEGER, intent(in):: ngrid, nlayer
59     REAL, intent(in):: dtime              ! Time step of the Physics
60     REAL, intent(in):: zmax_therm(ngrid)  ! Altitude of max velocity thermals (m)
61     REAL, intent(in):: pp(ngrid, nlayer)  ! Pressure at full levels
62     REAL, intent(in):: pt(ngrid, nlayer)  ! Temperature at full levels
63     REAL, intent(in):: pu(ngrid, nlayer)  ! Zonal wind at full levels
64     REAL, intent(in):: pv(ngrid, nlayer)  ! Meridional wind at full levels
65     REAL, intent(in):: pdt(ngrid, nlayer) ! Tendency on temperature
66     REAL, intent(in):: pdu(ngrid, nlayer) ! Tendency on zonal wind
67     REAL, intent(in):: pdv(ngrid, nlayer) ! Tendency on meridional wind
68     
69     ! 0.2 OUTPUTS
70
71     REAL, intent(out):: zustr(ngrid)         ! Zonal surface stress
72     REAL, intent(out):: zvstr(ngrid)         ! Meridional surface stress
73     REAL, intent(out):: d_t(ngrid, nlayer)   ! Tendency on temperature
74     REAL, intent(out):: d_u(ngrid, nlayer)   ! Tendency on zonal wind
75     REAL, intent(out):: d_v(ngrid, nlayer)   ! Tendency on meridional wind
76
77     ! 0.3 INTERNAL ARRAYS
78
79     REAL :: tt(ngrid, nlayer) ! Temperature at full levels
80     REAL :: uu(ngrid, nlayer) ! Zonal wind at full levels
81     REAL :: vv(ngrid, nlayer) ! Meridional wind at full levels
82     REAL :: bvlow(ngrid)      ! Qu est-ce ?
83     REAL :: dz
84
85     INTEGER ii, jj, ll
86
87     ! 0.3.0 Time scale of the like cycle of the waves parametrized
88     REAL, parameter:: deltat = 24. * 3600.
89
90     ! 0.3.1 Gravity waves specifications
91     INTEGER, parameter:: nk = 2 ! number of horizontal wavenumbers
92     INTEGER, parameter:: np = 2 ! directions (eastward and westward) phase speed
93     INTEGER, parameter:: no = 2 ! absolute values of phase speed
94     INTEGER, parameter:: na = 5 ! Number of realizations to get the phase speed
95     INTEGER, parameter:: nw = nk * np *no ! Total numbers of gravity waves
96     INTEGER jk, jp, jo, jw
97     REAL, parameter:: kmax = 7.e-4 ! Max horizontal wavenumber
98     REAL, parameter:: kmin = 2.e-5 ! Min horizontal wavenumber
99     !REAL, parameter:: cmax = 30.   ! Max horizontal absolute phase velocity
100     REAL, parameter:: cmax = 100.  ! Test for Saturn: Max horizontal absolute phase velocity
101     REAL, parameter:: cmin = 1.    ! Min horizontal absolute phase velocity
102     REAL cpha                      ! absolute phase velocity frequency
103     REAL zk(nw, ngrid)             ! horizontal wavenumber amplitude
104     REAL zp(nw, ngrid)             ! horizontal wavenumber angle
105     REAL zo(nw, ngrid)             ! absolute frequency
106
107     REAL intr_freq_m(nw, ngrid)          ! Waves Intr. freq. at the 1/2 lev below the full level (previous name: ZOM)
108     REAL intr_freq_p(nw, ngrid)          ! Waves Intr. freq. at the 1/2 lev above the full level (previous name: ZOP)
109     REAL wwm(nw, ngrid)                  ! Wave EP-fluxes at the 1/2 level below the full level
110     REAL wwp(nw, ngrid)                  ! Wave EP-fluxes at the 1/2 level above the full level
111     REAL u_epflux_p(nw, ngrid)           ! Partial zonal flux (=for each wave) at the 1/2 level above the full level (previous name: RUWP)
112     REAL v_epflux_p(nw, ngrid)           ! Partial meridional flux (=for each wave) at the 1/2 level above the full level (previous name: RVWP)
113     REAL u_epflux_tot(ngrid, nlayer + 1) ! Total zonal flux (=for all waves (nw)) at the 1/2 level above the full level (3D) (previous name: RUW) 
114     REAL v_epflux_tot(ngrid, nlayer + 1) ! Total meridional flux (=for all waves (nw)) at the 1/2 level above the full level (3D) (previous name: RVW)
115     REAL epflux_0(nw, ngrid)             ! Fluxes at launching level (previous name: RUW0)
116     INTEGER launch                       ! Launching altitude
117     REAL, parameter:: xlaunch = 0.4      ! Control the launching altitude
118     REAL, parameter:: zmaxth_top = 8000. ! Top of convective layer (approx.)
119
120     REAL prec(ngrid)     ! precipitations
121     REAL prmax           ! Max value of precipitation
122
123     ! 0.3.2 Parameters of waves dissipations
124     REAL, parameter:: sat   = 1.     ! saturation parameter
125     REAL, parameter:: rdiss = 1.     ! coefficient of dissipation
126     REAL, parameter:: zoisec = 1.e-6 ! security for intrinsic freguency
127
128     ! 0.3.3 Background flow at 1/2 levels and vertical coordinate
129     REAL H0bis(ngrid, nlayer)       ! characteristic height of the atmosphere
130     REAL, save::  H0                ! characteristic height of the atmosphere
131     REAL, parameter:: pr = 250      ! Reference pressure [Pa]
132     REAL, parameter:: tr = 220.     ! Reference temperature [K]
133     REAL zh(ngrid, nlayer + 1)      ! Log-pressure altitude (constant H0)
134     REAL zhbis(ngrid, nlayer + 1)   ! Log-pressure altitude (varying H)
135     REAL uh(ngrid, nlayer + 1)      ! Zonal wind at 1/2 levels
136     REAL vh(ngrid, nlayer + 1)      ! Meridional wind at 1/2 levels
137     REAL ph(ngrid, nlayer + 1)      ! Pressure at 1/2 levels
138     REAL, parameter:: psec = 1.e-6  ! Security to avoid division by 0 pressure
139     REAL bv(ngrid, nlayer + 1)      ! Brunt Vaisala freq. at 1/2 levels
140     REAL, parameter:: bvsec = 1.e-5 ! Security to avoid negative BV
141     REAL href(nlayer + 1)           ! Reference altitude for launching altitude
142
143
144
145     REAL ran_num_1, ran_num_2, ran_num_3
146   
147
148     LOGICAL, save :: firstcall = .true.
149
150!-------------------------------------------------------------------------------------------------- 
151! 1. INITIALISATION
152!------------------
153     IF (firstcall) THEN
154        write(*,*) "nonoro_gwd_ran: FLott non-oro GW scheme is active!"
155        ! Characteristic vertical scale height
156        H0 = r * tr / g
157        ! Control
158        if (deltat .LT. dtime) THEN
159             call abort_physic("nonoro_gwd_ran","gwd random: deltat lower than dtime!",1)
160        endif
161        if (nlayer .LT. nw) THEN
162             call abort_physic("nonoro_gwd_ran","gwd random: nlayer lower than nw!",1)
163        endif
164        firstcall = .false.
165     ENDIF
166     gwd_convective_source = .false.
167
168     ! Compute subroutine's current values of temperature and winds
169     tt(:,:) = pt(:,:) + dtime * pdt(:,:)
170     uu(:,:) = pu(:,:) + dtime * pdu(:,:)
171     vv(:,:) = pv(:,:) + dtime * pdv(:,:)
172!    print*,'epflux_max just after firstcall:', epflux_max
173
174
175! 2. EVALUATION OF THE BACKGROUND FLOW AT SEMI-LEVELS
176!----------------------------------------------------
177     ! Pressure and Inv of pressure, temperature at 1/2 level
178     DO ll = 2, nlayer
179        ph(:, ll) = exp((log(pp(:, ll)) + log(pp(:, ll - 1))) / 2.)
180     end DO
181
182     ph(:, nlayer + 1) = 0.
183     ph(:, 1) = 2. * pp(:, 1) - ph(:, 2)
184   
185     ! Launching altitude for reproductible case
186     DO ll = 2, nlayer
187        href(ll) = exp((log(presnivs(ll)) + log(presnivs(ll - 1))) / 2.)
188     end DO
189     href(nlayer + 1) = 0.
190     href(1) = 2. * presnivs(1) - href(2)
191
192     launch = 0.
193     DO ll =1, nlayer
194        IF (href (ll) / href(1) > xlaunch) launch = ll
195     end DO
196   
197     ! Log-pressure vertical coordinate
198     DO ll = 1, nlayer + 1
199        zh(:,ll) = H0 * log(pr / (ph(:,ll) + psec))
200     end DO
201     
202     ! Winds and Brunt Vaisala frequency
203     DO ll = 2, nlayer
204        uh(:, ll) = 0.5 * (uu(:, ll) + uu(:, ll - 1)) ! Zonal wind
205        vh(:, ll) = 0.5 * (vv(:, ll) + vv(:, ll - 1)) ! Meridional wind
206
207        bv(:, ll) = 0.5 * (tt(:, ll) + tt(:, ll - 1)) &
208                    * r**2 / cpp / H0**2              &
209                    + (tt(:, ll) - tt(:, ll - 1))     &
210                    / (zh(:, ll) - zh(:, ll - 1))     &
211                    * r / H0
212        bv(:, ll) = sqrt(max(bvsec, bv(:,ll)))
213     end DO
214
215     bv(:, 1) = bv(:, 2)
216     uh(:, 1) = 0.
217     vh(:, 1) = 0.
218     bv(:, nlayer + 1) = bv(:, nlayer)
219     uh(:, nlayer + 1) = uu(:, nlayer)
220     vh(:, nlayer + 1) = vv(:, nlayer)
221
222! 3. WAVES CHARACTERISTICS CHOSEN RANDOMLY
223!-----------------------------------------
224! The mod function of here a weird arguments
225! are used to produce the waves characteristics
226! in a stochastic way
227     DO jw = 1, nw
228        DO ii = 1, ngrid
229           
230           ran_num_1 = mod(tt(ii, jw) * 10., 1.)
231           ran_num_2 = mod(tt(ii, jw) * 100., 1.)
232
233           ! angle (0 or pi so far)
234           zp(jw, ii) = (sign(1., 0.5 - ran_num_1) &
235                        + 1.) * pi / 2.
236           ! horizontal wavenumber amplitude
237           zk(jw, ii) = kmin + (kmax - kmin) * ran_num_2
238           ! horizontal phase speed
239           cpha = 0.
240           DO jj = 1, na
241              ran_num_3 = mod(tt(ii, jw + 3 * jj)**2, 1.)
242              cpha = cpha + 2. * cmax *            &
243                     (ran_num_3 - 0.5) *           &
244                     sqrt(3.) / sqrt(na * 1.)
245           end DO
246           IF (cpha < 0.) THEN
247              cpha = - 1. * cpha
248              zp (jw, ii) = zp(jw, ii) + pi
249           ENDIF
250           ! Intrinsic frequency
251           zo(jw, ii) = cpha * zk(jw, ii)
252           ! Intrinsic frequency is imposed
253           zo(jw, ii) = zo(jw, ii)                                    &
254                      + zk(jw, ii) * cos(zp(jw, ii)) * uh(ii, launch) &
255                      + zk(jw, ii) * sin(zp(jw, ii)) * vh(ii, launch)
256           ! Momentum flux at launch level
257           epflux_0(jw, ii) = epflux_max                              &
258                        * mod(100. * (uu(ii, jw)**2 + vv(ii, jw)**2), 1.)
259
260        end DO
261     end DO
262
263!    print*,'epflux_max just after waves charac. ramdon:', epflux_max
264!    print*,'epflux_0 just after waves charac. ramdon:', epflux_0
265! 4. COMPUTE THE FLUXES
266!----------------------
267     ! 4.1 Vertical velocity at launching altitude to ensure
268     !     the correct value to the imposed fluxes.
269     !------------------------------------------------------
270     DO jw = 1, nw
271        ! Evaluate intrinsic frequency at launching altutide:
272        intr_freq_p(jw, :) = zo(jw, :)                                &
273                   - zk(jw, :) * cos(zp(jw, :)) * uh(:, launch)       &
274                   - zk(jw, :) * sin(zp(jw, :)) * vh(:, launch)
275     end DO
276 
277     IF (gwd_convective_source) THEN
278        DO jw = 1, nw
279       ! VERSION WITH CONVECTIVE SOURCE ! designed for Earth
280
281       ! Vertical velocity at launch level, value to ensure the
282       ! imposed mmt flux factor related to the convective forcing:
283       ! precipitations.
284
285       ! tanh limitation to values above prmax:
286!       WWP(JW, :) = epflux_0(JW, :) &
287!            * (r / cpp / H0 * RLVTT * PRMAX * TANH(PREC(:) / PRMAX))**2
288!       Here, we neglected the kinetic energy providing of the thermodynamic
289!       phase change
290
291!
292
293       ! Factor related to the characteristics of the waves:
294            wwp(jw, :) = wwp(jw, :) * zk(jw, :)**3 / kmin / bvlow(:)  &
295                       / MAX(ABS(intr_freq_p(jw, :)), zoisec)**3
296
297      ! Moderation by the depth of the source (dz here):
298            wwp(jw, :) = wwp(jw, :)                                          &
299                       * exp(- bvlow(:)**2 / max(abs(intr_freq_p(jw, :)), zoisec)**2 &
300                       * zk(jw, :)**2 * dz**2)
301
302      ! Put the stress in the right direction:
303            u_epflux_p(jw, :) = intr_freq_p(jw, :) / max(abs(intr_freq_p(jw, :)), zoisec)**2       &
304                        * bv(:, launch) * cos(zp(jw, :)) * wwp(jw, :)**2
305            v_epflux_p(JW, :) = intr_freq_p(jw, :) / max(abs(intr_freq_p(jw, :)), zoisec)**2       &
306                        * bv(:, launch) * sin(zp(jw, :)) * wwp(jw, :)**2
307        end DO
308     ELSE ! VERSION WITHOUT CONVECTIVE SOURCE
309       ! Vertical velocity at launch level, value to ensure the imposed
310       ! mom flux:
311        DO jw = 1, nw
312       ! WW is directly a flux, here, not vertical velocity anymore
313            wwp(jw, :) = epflux_0(JW,:)
314            u_epflux_p(jw, :) = cos(zp(jw, :)) * sign(1., intr_freq_p(jw, :)) * epflux_0(jw, :)
315            v_epflux_p(jw, :) = sin(zp(jw, :)) * sign(1., intr_freq_p(jw, :)) * epflux_0(jw, :)
316
317        end DO
318     ENDIF
319     
320     ! 4.2 Initial flux at launching altitude
321     !---------------------------------------
322     u_epflux_tot(:, launch) = 0.
323     v_epflux_tot(:, launch) = 0.
324     DO jw = 1, nw
325        u_epflux_tot(:, launch) = u_epflux_tot(:, launch) + u_epflux_p(jw, :)
326        v_epflux_tot(:, launch) = v_epflux_tot(:, launch) + v_epflux_p(jw, :)
327     end DO
328
329     ! 4.3 Loop over altitudes, with passage from one level to the next done by:
330     !--------------------------------------------------------------------------
331     !     i) conserving the EP flux,
332     !     ii) dissipating a little,
333     !     iii) testing critical levels,
334     !     iv) testing the breaking.
335     !--------------------------------------------------------------------------
336     DO ll = launch, nlayer - 1
337        ! Warning! all the physics is here (passage from one level to the next
338        DO jw = 1, nw
339           intr_freq_m(jw, :) = intr_freq_p(jw, :)
340           wwm(jw, :) = wwp(jw, :)
341           ! Intrinsic frequency
342           intr_freq_p(jw, :) = zo(jw, :) - zk(jw, :) * cos(zp(jw, :)) * uh(:, ll + 1)    &
343                      - zk(jw, :) * sin(zp(jw, :)) * vh(:, ll + 1)
344           ! Vertical velocity in flux formulation
345           wwp(jw, :) = min(                                                              &
346                      ! No breaking (Eq. 6):
347                      wwm(jw, :)                                                          &
348                      ! Dissipation (Eq. 8):
349                      * exp(-rdiss * pr / (ph(:, ll + 1) + ph (:, ll))                    &
350                      * ((bv(:, ll + 1) + bv (:, ll)) / 2.)**3                            &
351                      / max(abs(intr_freq_p(jw, :) + intr_freq_m(jw, :)) / 2., zoisec)**4 &
352                      * zk(jw, :)**3 * (zh(:, ll + 1) - zh(:, ll))) ,                     &
353                      ! Critical levels (forced to zero if intrinsic frequency
354                      ! changes sign)
355                      max(0., sign(1., intr_freq_p(jw, :) * intr_freq_m(jw, :)))          &
356                      ! Saturation (Eq. 12)
357                      * abs(intr_freq_p(jw, :))**3 / bv(:, ll + 1)                        &
358                      * exp(-zh(:, ll + 1) / H0)                                          &
359                      * sat**2 * kmin**2 / zk(jw, :)**4)
360        end DO
361
362     ! Evaluate EP-flux from Eq. 7 and give the right orientation to the stress
363        DO jw = 1, nw
364           u_epflux_p(jw, :) = sign(1., intr_freq_p(jw, :)) * cos(zp(jw, :)) * wwp(jw, :)
365           v_epflux_p(jw, :) = sign(1., intr_freq_p(jw, :)) * sin(zp(jw, :)) * wwp(jw, :)
366        end DO
367
368        u_epflux_tot(:, ll + 1) = 0.
369        v_epflux_tot(:, ll + 1) = 0.
370        DO jw = 1, nw
371           u_epflux_tot(:, ll + 1) = u_epflux_tot(:, ll + 1) + u_epflux_p(jw, :)
372           v_epflux_tot(:, ll + 1) = v_epflux_tot(:, ll + 1) + v_epflux_p(jw, :)
373           east_gwstress(:, ll) = east_gwstress(:, ll)                         & 
374                                + max(0., u_epflux_p(jw, :)) / float(nw)
375           west_gwstress(:, ll) = west_gwstress(:, ll)                         &
376                                + min(0., u_epflux_p(jw, ll)) / float(nw)
377        end DO
378     end DO ! DO LL = LAUNCH, nlayer - 1
379
380!    print*,'u_epflux_tot just after launching:', u_epflux_tot
381!    print*,'v_epflux_tot just after launching:', v_epflux_tot
382!    print*,'u_epflux_p just after launching:', maxval(u_epflux_p), minval(u_epflux_p)
383!    print*,'v_epflux_p just after launching:', maxval(v_epflux_p), minval(v_epflux_p)
384
385! 5. TENDENCY CALCULATIONS
386!-------------------------
387     ! 5.1 Flow rectification at the top and in the low layers
388     ! --------------------------------------------------------
389     ! Warning, this is the total on all GW...
390
391     u_epflux_tot(:, nlayer + 1) = 0.
392     v_epflux_tot(:, nlayer + 1) = 0.
393
394     ! Here, big change compared to FLott version:
395     ! We compensate (u_epflux_(:, LAUNCH), ie total emitted upward flux
396     ! over the layers max(1,LAUNCH-3) to LAUNCH-1
397     DO LL = 1, max(1,LAUNCH-3)
398        u_epflux_tot(:, LL) = 0.
399        v_epflux_tot(:, LL) = 0.
400     end DO
401     DO LL = max(2,LAUNCH-2), LAUNCH-1
402        u_epflux_tot(:, LL) = u_epflux_tot(:, LL - 1)                          &
403                            + u_epflux_tot(:, LAUNCH) * (PH(:,LL)-PH(:,LL-1))  &
404                            / (PH(:,LAUNCH)-PH(:,max(1,LAUNCH-3)))
405        v_epflux_tot(:, LL) = v_epflux_tot(:, LL - 1)                          &
406                            + v_epflux_tot(:, LAUNCH) * (PH(:,LL)-PH(:,LL-1))  &
407                            / (PH(:,LAUNCH)-PH(:,max(1,LAUNCH-3)))
408        east_gwstress(:,LL) = east_gwstress(:, LL - 1)                         &
409                            + east_gwstress(:, LAUNCH) * (PH(:,LL)-PH(:,LL-1)) &
410                            / (PH(:,LAUNCH)-PH(:,max(1,LAUNCH-3)))
411        west_gwstress(:,LL) = west_gwstress(:, LL - 1)                         &
412                            + west_gwstress(:, LAUNCH) * (PH(:,LL)-PH(:,LL-1)) &
413                            / (PH(:,LAUNCH)-PH(:,max(1,LAUNCH-3)))
414     end DO
415     ! This way, the total flux from GW is zero, but there is a net transport
416     ! (upward) that should be compensated by circulation
417     ! and induce additional friction at the surface
418
419     ! 5.2 AR-1 RECURSIVE FORMULA (13) IN VERSION 4
420     !---------------------------------------------
421     DO LL = 1, nlayer
422       d_u(:, LL) = (u_epflux_tot(:, LL + 1) - u_epflux_tot(:, LL))! &
423       !d_u(:, LL) = G * (u_epflux_tot(:, LL + 1) - u_epflux_tot(:, LL))! &
424        !          / (PH(:, LL + 1) - PH(:, LL)) * DTIME
425       d_v(:, LL) = (v_epflux_tot(:, LL + 1) - v_epflux_tot(:, LL))! &
426       !d_v(:, LL) = G * (v_epflux_tot(:, LL + 1) - v_epflux_tot(:, LL))! &
427         !         / (PH(:, LL + 1) - PH(:, LL)) * DTIME
428     ENDDO
429     d_t(:,:) = 0.
430
431     ! 5.3 Update tendency of wind with the previous (and saved) values
432     !-----------------------------------------------------------------
433     d_u(:,:) = DTIME/DELTAT/REAL(NW) * d_u(:,:)                       &
434              + (1.-DTIME/DELTAT) * du_nonoro_gwd(:,:)
435     d_v(:,:) = DTIME/DELTAT/REAL(NW) * d_v(:,:)                       &
436              + (1.-DTIME/DELTAT) * dv_nonoro_gwd(:,:)
437     du_nonoro_gwd(:,:) = d_u(:,:)
438     dv_nonoro_gwd(:,:) = d_v(:,:)
439
440!    print*,'u_epflux_tot just after tendency:', u_epflux_tot
441!    print*,'v_epflux_tot just after tendency:', v_epflux_tot
442!    print*,'d_u just after tendency:', maxval(d_u(:,:)), minval(d_u)
443!    print*,'d_v just after tendency:', maxval(d_v(:,:)), minval(d_v)
444     ! Cosmetic: evaluation of the cumulated stress
445
446     ZUSTR(:) = 0.
447     ZVSTR(:) = 0.
448     DO LL = 1, nlayer
449        ZUSTR(:) = ZUSTR(:) + D_U(:, LL) !/ g * (PH(:, LL + 1) - PH(:, LL))
450        ZVSTR(:) = ZVSTR(:) + D_V(:, LL) !/ g * (PH(:, LL + 1) - PH(:, LL))
451     ENDDO
452
453     call send_xios_field("du_nonoro", d_u)
454     call send_xios_field("dv_nonoro", d_v)
455     call send_xios_field("east_gwstress", east_gwstress)
456     call send_xios_field("west_gwstress", west_gwstress)
457
458
459      END SUBROUTINE nonoro_gwd_ran
460
461! ===================================================================
462! Subroutines used to write variables of memory in start files       
463! ===================================================================
464
465      SUBROUTINE ini_nonoro_gwd_ran(ngrid,nlayer)
466
467      IMPLICIT NONE
468
469      INTEGER, INTENT (in) :: ngrid  ! number of atmospheric columns
470      INTEGER, INTENT (in) :: nlayer ! number of atmospheric layers
471
472         allocate(du_nonoro_gwd(ngrid, nlayer))
473         allocate(dv_nonoro_gwd(ngrid, nlayer))
474         allocate(east_gwstress(ngrid, nlayer))
475         allocate(west_gwstress(ngrid, nlayer))
476
477      END SUBROUTINE ini_nonoro_gwd_ran
478! ----------------------------------
479      SUBROUTINE end_nonoro_gwd_ran
480
481      IMPLICIT NONE
482
483         if (allocated(du_nonoro_gwd)) deallocate(du_nonoro_gwd)
484         if (allocated(dv_nonoro_gwd)) deallocate(dv_nonoro_gwd)
485         if (allocated(east_gwstress)) deallocate(east_gwstress)
486         if (allocated(west_gwstress)) deallocate(west_gwstress)
487
488      END SUBROUTINE end_nonoro_gwd_ran
489
490END MODULE nonoro_gwd_ran_mod
491
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