source: LMDZ6/trunk/libf/phylmd/lmdz_atke_exchange_coeff.F90 @ 4831

Last change on this file since 4831 was 4804, checked in by evignon, 9 months ago

travail de documentation et commentaire des routines ATKE par Clement Dehondt
File size: 20.0 KB
RevLine 
[4687]1module lmdz_atke_exchange_coeff
[4449]2
3implicit none
4
5contains
6
[4631]7subroutine atke_compute_km_kh(ngrid,nlay,dtime, &
[4653]8                        wind_u,wind_v,temp,qvap,play,pinterf,cdrag_uv, &
[4478]9                        tke,Km_out,Kh_out)
[4449]10
11!========================================================================
12! Routine that computes turbulent Km / Kh coefficients with a
13! 1.5 order closure scheme (TKE) with or without stationarity assumption
14!
15! This parameterization has been constructed in the framework of a
16! collective and collaborative workshop,
17! the so-called 'Atelier TKE (ATKE)' with
[4478]18! K. Arjdal, L. Raillard, C. Dehondt, P. Tiengou, A. Spiga, F. Cheruy, T Dubos,
[4449]19! M. Coulon-Decorzens, S. Fromang, G. Riviere, A. Sima, F. Hourdin, E. Vignon
20!
21! Main assumptions of the model :
[4714]22! (1) horizontal homogeneity (Dx=Dy=0.)
[4449]23!=======================================================================
24
[4780]25USE lmdz_atke_turbulence_ini, ONLY : iflag_atke, kappa, l0, ric, cinf, rpi, rcpd, atke_ok_virtual, ri0, ri1
[4745]26USE lmdz_atke_turbulence_ini, ONLY : cepsilon, pr_slope, pr_asym, pr_neut, ctkes, rg, rd, rv, atke_ok_vdiff
[4780]27USE lmdz_atke_turbulence_ini, ONLY : viscom, viscoh, clmix, clmixshear, iflag_atke_lmix, lmin, smmin, cn
[4449]28
[4804]29!!-------------------------------------------------------------------------------------------------------------
30! integer :: iflag_atke        ! flag that controls options in atke_compute_km_kh
31! integer :: iflag_atke_lmix   ! flag that controls the calculation of mixing length in atke
32! integer :: iflag_num_atke    ! flag that controls the numerical treatment of diffusion coeffiient calculation
33
34! logical :: atke_ok_vdiff    ! activate vertical diffusion of TKE or not
35! logical :: atke_ok_virtual  ! account for vapor for flottability
36
37! real :: kappa = 0.4         ! Von Karman constant
38! real :: cn                  ! Sm value at Ri=0
39! real :: cinf                ! Sm value at Ri=-Inf
40! real :: ri0                 ! Richardson number near zero to guarantee continuity in slope of Sm (stability function) at Ri=0
41! real :: ri1                 ! Richardson number near zero to guarantee continuity in slope of Pr (Prandlt's number) at Ri=0
42! real :: lmin                ! minimum mixing length corresponding to the Kolmogov dissipation scale  in planetary atmospheres (Chen et al 2016, JGR Atmos)
43! real :: ctkes               ! coefficient for surface TKE
44! real :: clmixshear          ! coefficient for mixing length depending on local wind shear
45
46! Tunable parameters for the ATKE scheme and their range of values
47!!-------------------------------------------------------------------------------------------------------------
48! real :: cepsilon            ! controls the value of the dissipation length scale, range [1.2 - 10]
49! real :: cke                 ! controls the value of the diffusion coefficient of TKE, range [1 - 5]
50! real :: l0                  ! asymptotic mixing length far from the ground [m] (Sun et al 2011, JAMC), range [15 - 75]
51! real :: clmix               ! controls the value of the mixing length in stratified conditions, range [0.1 - 2]
52! real :: ric                 ! critical Richardson number controlling the slope of Sm in stable conditions, range [0.19 - 0.25]
53! real :: smmin               ! minimum value of Sm in very stable conditions (defined here as minsqrt(Ez/Ek)) at large Ri, range [0.025 - 0.1]
54! real :: pr_neut             ! neutral value of the Prandtl number (Ri=0), range [0.7 - 1]
55! real :: pr_slope            ! linear slope of Pr with Ri in the very stable regime, range [3 - 5]
56! real :: cinffac             ! ratio between cinf and cn controlling the convective limit of Sm, range [1.2 - 5.0]
57! real :: pr_asym             ! value of Prandlt in the convective limit(Ri=-Inf), range [0.3 - 0.5]
58!!-------------------------------------------------------------------------------------------------------------
59
[4449]60implicit none
61
62
63! Declarations:
64!=============
65
66INTEGER, INTENT(IN) :: ngrid ! number of horizontal index (flat grid)
[4631]67INTEGER, INTENT(IN) :: nlay  ! number of vertical index 
[4449]68
[4631]69REAL, INTENT(IN)    :: dtime ! physics time step (s)
[4449]70REAL, DIMENSION(ngrid,nlay), INTENT(IN)       :: wind_u   ! zonal velocity (m/s)
71REAL, DIMENSION(ngrid,nlay), INTENT(IN)       :: wind_v   ! meridional velocity (m/s)
72REAL, DIMENSION(ngrid,nlay), INTENT(IN)       :: temp   ! temperature (K)
[4653]73REAL, DIMENSION(ngrid,nlay), INTENT(IN)       :: qvap   ! specific humidity (kg/kg)
[4449]74REAL, DIMENSION(ngrid,nlay), INTENT(IN)       :: play   ! pressure (Pa)
75REAL, DIMENSION(ngrid,nlay+1), INTENT(IN)     :: pinterf   ! pressure at interfaces(Pa)
[4644]76REAL, DIMENSION(ngrid), INTENT(IN)            :: cdrag_uv   ! surface drag coefficient for momentum
[4449]77
78REAL, DIMENSION(ngrid,nlay+1), INTENT(INOUT)  :: tke  ! turbulent kinetic energy at interface between layers
79
[4478]80REAL, DIMENSION(ngrid,nlay), INTENT(OUT)      :: Km_out   ! output: Exchange coefficient for momentum at interface between layers
81REAL, DIMENSION(ngrid,nlay), INTENT(OUT)      :: Kh_out   ! output: Exchange coefficient for heat flux at interface between layers
[4449]82
83! Local variables
[4478]84REAL, DIMENSION(ngrid,nlay+1) :: Km          ! Exchange coefficient for momentum at interface between layers
85REAL, DIMENSION(ngrid,nlay+1) :: Kh          ! Exchange coefficient for heat flux at interface between layers
86REAL, DIMENSION(ngrid,nlay)   :: theta       ! Potential temperature
87REAL, DIMENSION(ngrid,nlay+1) :: l_exchange  ! Length of exchange (at interface)
88REAL, DIMENSION(ngrid,nlay+1) :: z_interf    ! Altitude at the interface
89REAL, DIMENSION(ngrid,nlay)   :: z_lay       ! Altitude of layers
90REAL, DIMENSION(ngrid,nlay)   :: dz_interf   ! distance between two consecutive interfaces
91REAL, DIMENSION(ngrid,nlay)   :: dz_lay      ! distance between two layer middles (NB: first and last are half layers)
[4631]92REAL, DIMENSION(ngrid,nlay+1) :: N2          ! square of Brunt Vaisala pulsation (at interface)
93REAL, DIMENSION(ngrid,nlay+1) :: shear2      ! square of wind shear (at interface)
[4478]94REAL, DIMENSION(ngrid,nlay+1) :: Ri          ! Richardson's number (at interface)
95REAL, DIMENSION(ngrid,nlay+1) :: Prandtl     ! Turbulent Prandtl's number (at interface)
96REAL, DIMENSION(ngrid,nlay+1) :: Sm          ! Stability function for momentum (at interface)
97REAL, DIMENSION(ngrid,nlay+1) :: Sh          ! Stability function for heat (at interface)
[4449]98
99INTEGER :: igrid,ilay ! horizontal,vertical index (flat grid)
[4478]100REAL    :: preff      ! reference pressure for potential temperature calculations
101REAL    :: thetam     ! mean potential temperature at interface
[4631]102REAL    :: delta      ! discriminant of the second order polynomial
103REAL    :: qq         ! tke=qq**2/2
104REAL    :: shear      ! wind shear
105REAL    :: lstrat     ! mixing length depending on local stratification
106REAL    :: taustrat   ! caracteristic timescale for turbulence in very stable conditions
[4644]107REAL    :: netloss    ! net loss term of tke
108REAL    :: netsource  ! net source term of tke
109REAL    :: ustar      ! friction velocity estimation
[4653]110REAL    :: invtau     
111REAL    :: rvap
[4449]112
113! Initializations:
114!================
115
116DO igrid=1,ngrid
[4478]117    dz_interf(igrid,1) = 0.0
[4449]118    z_interf(igrid,1) = 0.0
119END DO
120
[4653]121! Calculation of potential temperature: (if vapor -> virtual potential temperature)
[4478]122!=====================================
[4449]123
[4478]124preff=100000.
[4653]125! results should not depend on the choice of preff
[4478]126DO ilay=1,nlay
[4804]127    DO igrid = 1, ngrid
[4478]128        theta(igrid,ilay)=temp(igrid,ilay)*(preff/play(igrid,ilay))**(rd/rcpd)
[4804]129    END DO
[4478]130END DO
[4449]131
[4653]132! account for water vapor mass for buoyancy calculation
133IF (atke_ok_virtual) THEN
[4804]134    DO ilay=1,nlay
135        DO igrid = 1, ngrid
136            rvap=max(0.,qvap(igrid,ilay)/(1.-qvap(igrid,ilay)))
137            theta(igrid,ilay)=theta(igrid,ilay)*(1.+rvap/(RD/RV))/(1.+rvap)
138        END DO
139    END DO
[4653]140ENDIF
[4449]141
[4478]142
143! Calculation of altitude of layers' middle and bottom interfaces:
144!=================================================================
145
[4449]146DO ilay=2,nlay+1
147    DO igrid=1,ngrid
[4478]148        dz_interf(igrid,ilay-1) = rd*temp(igrid,ilay-1)/rg/play(igrid,ilay-1)*(pinterf(igrid,ilay-1)-pinterf(igrid,ilay))
149        z_interf(igrid,ilay) = z_interf(igrid,ilay-1) + dz_interf(igrid,ilay-1)
[4449]150    ENDDO
151ENDDO
152
[4478]153DO ilay=1,nlay
[4804]154    DO igrid=1,ngrid
155        z_lay(igrid,ilay)=0.5*(z_interf(igrid, ilay+1) + z_interf(igrid, ilay))
156    ENDDO
[4478]157ENDDO
[4449]158
[4478]159
[4449]160! Computes the gradient Richardson's number and stability functions:
161!===================================================================
162
[4478]163DO ilay=2,nlay
[4449]164    DO igrid=1,ngrid
[4478]165        dz_lay(igrid,ilay)=z_lay(igrid,ilay)-z_lay(igrid,ilay-1)
166        thetam=0.5*(theta(igrid,ilay) + theta(igrid,ilay-1))
[4631]167        N2(igrid,ilay) = rg * (theta(igrid,ilay) - theta(igrid,ilay-1))/thetam / dz_lay(igrid,ilay)
168        shear2(igrid,ilay)= (((wind_u(igrid,ilay) - wind_u(igrid,ilay-1)) / dz_lay(igrid,ilay))**2 + &
169            ((wind_v(igrid,ilay) - wind_v(igrid,ilay-1)) / dz_lay(igrid,ilay))**2 )
170        Ri(igrid,ilay) = N2(igrid,ilay) / MAX(shear2(igrid,ilay),1E-10)
[4481]171       
172        IF (Ri(igrid,ilay) < 0.) THEN ! unstable cases
[4478]173            Sm(igrid,ilay) = 2./rpi * (cinf-cn) * atan(-Ri(igrid,ilay)/Ri0) + cn
174            Prandtl(igrid,ilay) = -2./rpi * (pr_asym - pr_neut) * atan(Ri(igrid,ilay)/Ri1) + pr_neut
[4481]175        ELSE ! stable cases
[4644]176            Sm(igrid,ilay) = max(smmin,cn*(1.-Ri(igrid,ilay)/Ric))
[4688]177            ! prandlt expression from venayagamoorthy and stretch 2010, Li et al 2019
178            Prandtl(igrid,ilay) = pr_neut*exp(-pr_slope/pr_neut*Ri(igrid,ilay)+Ri(igrid,ilay)/pr_neut) &
179                                + Ri(igrid,ilay) * pr_slope
[4481]180            IF (Ri(igrid,ilay) .GE. Prandtl(igrid,ilay)) THEN
[4804]181                call abort_physic("atke_compute_km_kh", &
182                'Ri>=Pr in stable conditions -> violates energy conservation principles, change pr_neut or slope', 1)
[4481]183            ENDIF
[4449]184        END IF
185       
186        Sh(igrid,ilay) = Sm(igrid,ilay) / Prandtl(igrid,ilay)
187
188    ENDDO
189ENDDO
190
[4631]191
192! Computing the mixing length:
193!==============================================================
194
195
196IF (iflag_atke_lmix .EQ. 1 ) THEN
[4804]197    ! Blackadar formulation (~kappa l) + buoyancy length scale (Deardoff 1980) for very stable conditions
198        DO ilay=2,nlay
199            DO igrid=1,ngrid
200                l_exchange(igrid,ilay) = kappa*l0*z_interf(igrid,ilay) / (kappa*z_interf(igrid,ilay) + l0)
201                IF (N2(igrid,ilay) .GT. 0.) THEN
202                    lstrat=clmix*sqrt(tke(igrid,ilay))/sqrt(N2(igrid,ilay))
203                    lstrat=max(lstrat,lmin)
204                    !Inverse interpolation, Van de Wiel et al. 2010
205                    l_exchange(igrid,ilay)=(1./(l_exchange(igrid,ilay))+1./(lstrat))**(-1.0)
206                ENDIF
207            ENDDO
208        ENDDO
[4631]209
[4804]210    ELSE IF (iflag_atke_lmix .EQ. 2 ) THEN
211    ! add effect of wind shear on lstrat following grisogono and belusic 2008, qjrms
212    ! implies 2 tuning coefficients clmix and clmixshear
213    DO ilay=2,nlay
214        DO igrid=1,ngrid
215            l_exchange(igrid,ilay) = kappa*l0*z_interf(igrid,ilay) / (kappa*z_interf(igrid,ilay) + l0)
216            IF (N2(igrid,ilay) .GT. 0. .AND. shear2(igrid,ilay) .GT. 0.) THEN
217                lstrat=min(clmix*sqrt(tke(igrid,ilay))/sqrt(N2(igrid,ilay)), &
[4663]218                    clmixshear*sqrt(tke(igrid,ilay))/sqrt(shear2(igrid,ilay)))
[4804]219                lstrat=max(lstrat,lmin)
220                !Inverse interpolation, Van de Wiel et al. 2010   
221                l_exchange(igrid,ilay)=(1./(l_exchange(igrid,ilay))+1./(lstrat))**(-1.0)
222            ENDIF
223        ENDDO
224    ENDDO
[4632]225
[4804]226    ELSE IF (iflag_atke_lmix .EQ. 3 ) THEN
227    ! add effect of wind shear on lstrat following grisogono 2010, qjrms
228    ! keeping a single tuning coefficient clmix
229    DO ilay=2,nlay
230        DO igrid=1,ngrid
231            l_exchange(igrid,ilay) = kappa*l0*z_interf(igrid,ilay) / (kappa*z_interf(igrid,ilay) + l0)
232            IF (N2(igrid,ilay) .GT. 0. .AND. shear2(igrid,ilay) .GT. 0.) THEN
233                lstrat=clmix*sqrt(tke(igrid,ilay))/sqrt(shear2(igrid,ilay))*(1.0+Ri(igrid,ilay)/(2.*Prandtl(igrid,ilay)))
234                lstrat=max(lstrat,lmin)
235                !Inverse interpolation, Van de Wiel et al. 2010   
236                l_exchange(igrid,ilay)=(1./(l_exchange(igrid,ilay))+1./(lstrat))**(-1.0)
237            ENDIF
238        ENDDO
239    ENDDO
[4632]240
[4631]241ELSE
[4804]242    ! default Blackadar formulation: neglect effect of local stratification and shear
243    DO ilay=2,nlay+1
244        DO igrid=1,ngrid
245            l_exchange(igrid,ilay) = kappa*l0*z_interf(igrid,ilay) / (kappa*z_interf(igrid,ilay) + l0)
246        ENDDO
247    ENDDO
[4631]248ENDIF
249
250
[4644]251! Computing the TKE k>=2:
252!========================
[4449]253IF (iflag_atke == 0) THEN
254
[4804]255    ! stationary solution (dtke/dt=0)
[4644]256
[4804]257    DO ilay=2,nlay
258            DO igrid=1,ngrid
259                tke(igrid,ilay) = cepsilon * l_exchange(igrid,ilay)**2 * Sm(igrid,ilay) * &
260                shear2(igrid,ilay) * (1. - Ri(igrid,ilay) / Prandtl(igrid,ilay))
261            ENDDO
[4449]262        ENDDO
263
[4631]264ELSE IF (iflag_atke == 1) THEN
265
[4804]266    ! full implicit scheme resolved with a second order polynomial equation
267    ! default solution which shows fair convergence properties
268        DO ilay=2,nlay
269            DO igrid=1,ngrid
270            qq=max(sqrt(2.*tke(igrid,ilay)),1.e-10)
271            delta=(2.*sqrt(2.)*cepsilon*l_exchange(igrid,ilay)/dtime)**2. &
272                    +4.*(2.*sqrt(2.)*cepsilon*l_exchange(igrid,ilay)/dtime*qq + &
273                    2.*l_exchange(igrid,ilay)*l_exchange(igrid,ilay)*cepsilon*Sm(igrid,ilay) &
274                    *shear2(igrid,ilay) * (1. - Ri(igrid,ilay) / Prandtl(igrid,ilay)))
275            qq=(-2.*sqrt(2.)*cepsilon*l_exchange(igrid,ilay)/dtime + sqrt(delta))/2.
276            qq=max(0.,qq)
277            tke(igrid,ilay)=0.5*(qq**2)
278            ENDDO
[4631]279        ENDDO
280
[4644]281
[4631]282ELSE IF (iflag_atke == 2) THEN
283
[4804]284    ! semi implicit scheme when l does not depend on tke
285    ! positive-guaranteed if pr slope in stable condition >1
[4644]286
[4804]287    DO ilay=2,nlay
288            DO igrid=1,ngrid
289            qq=max(sqrt(2.*tke(igrid,ilay)),1.e-10)
290            qq=(qq+l_exchange(igrid,ilay)*Sm(igrid,ilay)*dtime/sqrt(2.)      &
291                *shear2(igrid,ilay)*(1.-Ri(igrid,ilay)/Prandtl(igrid,ilay))) &
292                /(1.+qq*dtime/(cepsilon*l_exchange(igrid,ilay)*2.*sqrt(2.)))
293            tke(igrid,ilay)=0.5*(qq**2)
294            ENDDO
[4644]295        ENDDO
296
297
298ELSE IF (iflag_atke == 3) THEN
[4804]299    ! numerical resolution adapted from that in MAR (Deleersnijder 1992)
300    ! positively defined by construction
[4644]301
[4804]302        DO ilay=2,nlay
303            DO igrid=1,ngrid
304            qq=max(sqrt(2.*tke(igrid,ilay)),1.e-10)
305            IF (Ri(igrid,ilay) .LT. 0.) THEN
306                netloss=qq/(2.*sqrt(2.)*cepsilon*l_exchange(igrid,ilay))
307                netsource=l_exchange(igrid,ilay)*Sm(igrid,ilay)/sqrt(2.)*shear2(igrid,ilay)*(1.-Ri(igrid,ilay)/Prandtl(igrid,ilay))
308            ELSE
309                netloss=qq/(2.*sqrt(2.)*cepsilon*l_exchange(igrid,ilay))+ &
310                        l_exchange(igrid,ilay)*Sm(igrid,ilay)/sqrt(2.)*N2(igrid,ilay)/Prandtl(igrid,ilay)
311                netsource=l_exchange(igrid,ilay)*Sm(igrid,ilay)/sqrt(2.)*shear2(igrid,ilay)
312            ENDIF
313            qq=((qq**2)/dtime+qq*netsource)/(qq/dtime+netloss)
314            tke(igrid,ilay)=0.5*(qq**2)
315            ENDDO
[4631]316        ENDDO
317
[4644]318ELSE IF (iflag_atke == 4) THEN
[4804]319    ! semi implicit scheme from Arpege (V. Masson methodology with
320    ! Taylor expansion of the dissipation term)
321        DO ilay=2,nlay
322            DO igrid=1,ngrid
323            qq=max(sqrt(2.*tke(igrid,ilay)),1.e-10)
324            qq=(l_exchange(igrid,ilay)*Sm(igrid,ilay)/sqrt(2.)*shear2(igrid,ilay)*(1.-Ri(igrid,ilay)/Prandtl(igrid,ilay)) &
325                +qq*(1.+dtime*qq/(cepsilon*l_exchange(igrid,ilay)*2.*sqrt(2.)))) &
326                /(1.+2.*qq*dtime/(cepsilon*l_exchange(igrid,ilay)*2.*sqrt(2.)))
327            qq=max(0.,qq)
328            tke(igrid,ilay)=0.5*(qq**2)
329            ENDDO
[4631]330        ENDDO
331
332
333ELSE
[4804]334    call abort_physic("atke_compute_km_kh", &
[4631]335        'numerical treatment of TKE not possible yet', 1)
[4449]336
337END IF
338
[4644]339! We impose a 0 tke at nlay+1
340!==============================
[4449]341
[4644]342DO igrid=1,ngrid
[4804]343    tke(igrid,nlay+1)=0.
[4644]344END DO
345
346
347! Calculation of surface TKE (k=1)
348!=================================
349! surface TKE calculation inspired from what is done in Arpege (see E. Bazile note)
350DO igrid=1,ngrid
[4804]351    ustar=sqrt(cdrag_uv(igrid)*(wind_u(igrid,1)**2+wind_v(igrid,1)**2))
352    tke(igrid,1)=ctkes*(ustar**2)
[4644]353END DO
354
355
356! vertical diffusion of TKE
357!==========================
[4653]358IF (atke_ok_vdiff) THEN
[4804]359    CALL atke_vdiff_tke(ngrid,nlay,dtime,z_lay,z_interf,temp,play,l_exchange,Sm,tke)
[4644]360ENDIF
361
362
[4449]363! Computing eddy diffusivity coefficients:
364!========================================
[4478]365DO ilay=2,nlay ! TODO: also calculate for nlay+1 ?
[4449]366    DO igrid=1,ngrid
[4478]367        ! we add the molecular viscosity to Km,h
368        Km(igrid,ilay) = viscom + l_exchange(igrid,ilay) * Sm(igrid,ilay) * tke(igrid,ilay)**0.5
369        Kh(igrid,ilay) = viscoh + l_exchange(igrid,ilay) * Sh(igrid,ilay) * tke(igrid,ilay)**0.5
[4449]370    END DO
371END DO
372
[4478]373! for output:
374!===========
375Km_out(1:ngrid,2:nlay)=Km(1:ngrid,2:nlay)
376Kh_out(1:ngrid,2:nlay)=Kh(1:ngrid,2:nlay)
[4449]377
378end subroutine atke_compute_km_kh
379
[4644]380!===============================================================================================
381subroutine atke_vdiff_tke(ngrid,nlay,dtime,z_lay,z_interf,temp,play,l_exchange,Sm,tke)
[4449]382
[4644]383! routine that computes the vertical diffusion of TKE by the turbulence
[4653]384! using an implicit resolution (See note by Dufresne and Ghattas (2009))
[4644]385! E Vignon, July 2023
386
[4687]387USE lmdz_atke_turbulence_ini, ONLY : rd, cke, viscom
[4644]388
389
390INTEGER, INTENT(IN) :: ngrid ! number of horizontal index (flat grid)
391INTEGER, INTENT(IN) :: nlay  ! number of vertical index 
392
393REAL, INTENT(IN)    :: dtime ! physics time step (s)
394REAL, DIMENSION(ngrid,nlay), INTENT(IN)       :: z_lay   ! altitude of mid-layers (m)
395REAL, DIMENSION(ngrid,nlay+1), INTENT(IN)       :: z_interf   ! altitude of bottom interfaces (m)
396REAL, DIMENSION(ngrid,nlay), INTENT(IN)       :: temp   ! temperature (K)
397REAL, DIMENSION(ngrid,nlay), INTENT(IN)       :: play   ! pressure (Pa)
398REAL, DIMENSION(ngrid,nlay+1), INTENT(IN)     :: l_exchange     ! mixing length at interfaces between layers
399REAL, DIMENSION(ngrid,nlay+1), INTENT(IN)     :: Sm     ! stability function for eddy diffusivity for momentum at interface between layers
400
401REAL, DIMENSION(ngrid,nlay+1), INTENT(INOUT)  :: tke    ! turbulent kinetic energy at interface between layers
402
403
404
405INTEGER                                       :: igrid,ilay
406REAL, DIMENSION(ngrid,nlay+1)                 :: Ke     ! eddy diffusivity for TKE
407REAL, DIMENSION(ngrid,nlay+1)                 :: dtke
408REAL, DIMENSION(ngrid,nlay+1)                 :: ak, bk, ck, CCK, DDK
409REAL                                          :: gammak,Kem,KKb,KKt
410
411
412! Few initialisations
413CCK(:,:)=0.
414DDK(:,:)=0.
415dtke(:,:)=0.
416
417
418! Eddy diffusivity for TKE
419
420DO ilay=2,nlay
421    DO igrid=1,ngrid
[4804]422        Ke(igrid,ilay)=(viscom+l_exchange(igrid,ilay)*Sm(igrid,ilay)*sqrt(tke(igrid,ilay)))*cke
[4644]423    ENDDO
424ENDDO
425! at the top of the atmosphere set to 0
426Ke(:,nlay+1)=0.
427! at the surface, set it equal to that at the first model level
428Ke(:,1)=Ke(:,2)
429
430
431! calculate intermediary variables
432
433DO ilay=2,nlay
434    DO igrid=1,ngrid
435    Kem=0.5*(Ke(igrid,ilay+1)+Ke(igrid,ilay))   
436    KKt=Kem*play(igrid,ilay)/rd/temp(igrid,ilay)/(z_interf(igrid,ilay+1)-z_interf(igrid,ilay))
437    Kem=0.5*(Ke(igrid,ilay)+Ke(igrid,ilay-1))
438    KKb=Kem*play(igrid,ilay-1)/rd/temp(igrid,ilay-1)/(z_interf(igrid,ilay)-z_interf(igrid,ilay-1))
439    gammak=1./(z_lay(igrid,ilay)-z_lay(igrid,ilay-1))
440    ak(igrid,ilay)=-gammak*dtime*KKb
441    ck(igrid,ilay)=-gammak*dtime*KKt
442    bk(igrid,ilay)=1.+gammak*dtime*(KKt+KKb)
443    ENDDO
444ENDDO
445
446! calculate CCK and DDK coefficients
447! downhill phase
448
449DO igrid=1,ngrid
[4804]450    CCK(igrid,nlay)=tke(igrid,nlay)/bk(igrid,nlay)
451    DDK(igrid,nlay)=-ak(igrid,nlay)/bk(igrid,nlay)
[4644]452ENDDO
453
454
455DO ilay=nlay-1,2,-1
456    DO igrid=1,ngrid
457        CCK(igrid,ilay)=(tke(igrid,ilay)/bk(igrid,ilay)-ck(igrid,ilay)/bk(igrid,ilay)*CCK(igrid,ilay+1)) &
[4804]458                        / (1.+ck(igrid,ilay)/bk(igrid,ilay)*DDK(igrid,ilay+1))
[4644]459        DDK(igrid,ilay)=-ak(igrid,ilay)/bk(igrid,ilay)/(1+ck(igrid,ilay)/bk(igrid,ilay)*DDK(igrid,ilay+1))
460    ENDDO
461ENDDO
462
463! calculate TKE
464! uphill phase
465
466DO ilay=2,nlay+1
467    DO igrid=1,ngrid
468        dtke(igrid,ilay)=CCK(igrid,ilay)+DDK(igrid,ilay)*tke(igrid,ilay-1)-tke(igrid,ilay)
469    ENDDO
470ENDDO
471
472! update TKE
473tke(:,:)=tke(:,:)+dtke(:,:)
474
475
476end subroutine atke_vdiff_tke
477
478
479
[4687]480end module lmdz_atke_exchange_coeff
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