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lmdz_ratqs_multi.F90 @ 4799

Last change on this file since 4799 was 4664, checked in by fhourdin, 17 months ago

standardisatio des noms pour lscp et fisrtilp

fisrtilp passe dans le module lmdz_lscp_old.F90
Prepartation de la replaysation de fisrtilp (deja fait pour lscp)

File size: 16.9 KB

Rev	Line
[4613]	1	MODULE lmdz_ratqs_multi
[4009]	2
	3	!=============================================
[4613]	4	! A FAIRE :
[4664]	5	! Traiter le probleme de USE lmdz_lscp_tools, ONLY: CALC_QSAT_ECMWF
[4613]	6	!=============================================
	7
	8	!=============================================
[4009]	9	! module containing subroutines that take
	10	! into account the effect of convection, orography,
	11	! surface heterogeneities and subgrid-scale
	12	! turbulence on ratqs, i.e. on the width of the
	13	! total water subgrid distribution.
	14	!=============================================
	15
	16	IMPLICIT NONE
	17
	18	! Include
	19	!=============================================
	20	INCLUDE "YOETHF.h"
	21
	22
	23	CONTAINS
	24
	25
	26	!========================================================================
[4613]	27	SUBROUTINE ratqs_inter(klon,klev,iflag_ratqs,pdtphys,paprs, &
[4009]	28	ratqsbas, wake_deltaq, wake_s, q_seri,qtc_cv, sigt_cv, &
[4613]	29	fm_therm,entr_therm,detr_therm,detrain_cv,fm_cv,fqd,fqcomp,sigd, &
	30	ratqs_inter_)
	31
	32	USE lmdz_ratqs_ini, ONLY : a_ratqs_cv,tau_var,fac_tau,tau_cumul,a_ratqs_wake, dqimpl
	33	USE lmdz_ratqs_ini, ONLY : RG
	34	USE lmdz_ratqs_ini, ONLY : povariance, var_conv
	35	USE lmdz_thermcell_dq, ONLY : thermcell_dq
	36
[4009]	37	implicit none
	38
	39	!========================================================================
	40	! L. d'Alençon, 25/02/2021
[4613]	41	! Cette subroutine calcule une valeur de ratqsbas interactive
	42	! Elle est appelée par la subroutine ratqs lorsque iflag_ratqs = 11.
[4009]	43	!========================================================================
	44
	45	! Declarations
	46	! Input
	47	integer,intent(in) :: klon,klev,iflag_ratqs
	48	real,intent(in) :: pdtphys,ratqsbas
[4613]	49	real, dimension(klon,klev+1),intent(in) :: paprs
[4009]	50	real, dimension(klon,klev),intent(in) :: wake_deltaq, q_seri,qtc_cv, sigt_cv
	51	real, dimension(klon),intent(in) :: wake_s
[4613]	52	real, dimension(klon,klev+1),intent(in) :: fm_therm
	53	real, dimension(klon,klev),intent(in) :: entr_therm,detr_therm,detrain_cv,fm_cv,fqd,fqcomp
	54	real, dimension(klon),intent(in) :: sigd
[4009]	55
	56	! Output
[4613]	57	real, dimension(klon,klev),intent(inout) :: ratqs_inter_
[4009]	58
	59	! local
[4613]	60	LOGICAL :: klein = .false.
	61	LOGICAL :: klein_conv = .true.
	62	REAL :: taup0 = 70000
	63	REAL :: taudp = 500
	64	integer :: lev_out=10
	65	REAL, DIMENSION (klon,klev) :: zmasse,entr0,detr0,detraincv,dqp,detrain_p,q0,qd0,tau_diss
	66	REAL, DIMENSION (klon,klev+1) :: fm0
[4009]	67	integer i,k
	68	real, dimension(klon,klev) :: wake_dq
[4613]	69
	70
	71	real, dimension(klon) :: max_sigd, max_dqconv,max_sigt
	72	real, dimension(klon,klev) :: zoa,zocarrea,pdocarreadj,pocarre,po,pdoadj,varq_therm
	73
	74
	75	lev_out=0.
	76
	77	print*,'ratqs_inter'
	78
	79	!-----------------------------------------------------------------------
	80	! Calcul des masses
	81	!-----------------------------------------------------------------------
	82
	83	do k=1,klev
	84	zmasse(:,k)=(paprs(:,k)-paprs(:,k+1))/RG
	85	enddo
[4009]	86	!-------------------------------------------------------------------------
[4613]	87	! Caclul du terme de détrainement de la variance pour les thermiques
[4009]	88	!-------------------------------------------------------------------------
	89
[4613]	90	! initialisations
	91
	92
	93	do k=1,klev
	94	do i=1,klon
	95	tau_diss(i,k)=tau_var +0.5fac_tautau_var*(tanh((taup0-paprs(i,k))/taudp) + 1.)
	96	enddo
	97	enddo
	98
	99
[4009]	100
[4613]	101	entr0(:,:) = entr_therm(:,:)
	102	fm0(:,:) = fm_therm(:,:)
	103	detr0(:,:) = detr_therm(:,:)
	104
	105	! calcul du carré de l'humidité spécifique
	106	po(:,:) = q_seri(:,:)
	107	call thermcell_dq(klon,klev,dqimpl,pdtphys,fm0,entr0,zmasse, &
	108	& po,pdoadj,zoa,lev_out)
	109	do k=1,klev
	110	do i=1,klon
	111	pocarre(i,k)=po(i,k)*po(i,k) + povariance(i,k)
	112	enddo
	113	enddo
	114	call thermcell_dq(klon,klev,dqimpl,pdtphys,fm0,entr0,zmasse, &
	115	& pocarre,pdocarreadj,zocarrea,lev_out)
	116
	117
	118	do k=1,klev
	119	do i=1,klon
	120	varq_therm(i,k)=zocarrea(i,k)-zoa(i,k)*zoa(i,k)
	121	enddo
	122	enddo
	123
	124
	125	if (klein) then
	126	do k=1,klev-1
	127	do i=1,klon
	128	qd0(:,:) = 0.0
	129	if (sigd(i).ne.0) then
	130	qd0(i,k) = fqd(i,k)*tau_cumul/sigd(i)
	131	endif
	132	enddo
	133	enddo
	134	do k=1,klev-1
	135	do i=1,klon
	136	povariance(i,k)= (detr0(i,k)((zoa(i,k)-po(i,k))2 + (varq_therm(i,k)-povariance(i,k)))/zmasse(i,k) + fm0(i,k+1)povariance(i,k+1)/zmasse(i,k) - &
	137	fm0(i,k)*povariance(i,k)/zmasse(i,k) + &
	138	a_ratqs_cv(detrain_cv(i,k)/zmasse(i,k)) + sigd(i)(1-sigd(i))qd0(i,k)*2/tau_cumul &
	139	+ ((povariance(i,k+1)-povariance(i,k))(fm_cv(i,k)/zmasse(i,k))))pdtphys + povariance(i,k)
	140	povariance(i,k)= povariance(i,k)*exp(-pdtphys/tau_diss(i,k))
	141	enddo
	142	enddo
	143	povariance(:,klev) = povariance(:,klev-1)
	144
	145	else ! calcul direct
	146	qd0(:,:) = 0.0
	147	q0(:,:) = 0.0
	148	do k=1,klev-1
	149	do i=1,klon
	150	if (sigd(i).ne.0) then
	151	qd0(i,k) = fqd(i,k)*tau_cumul/sigd(i)
	152	endif
	153	if (sigt_cv(i,k).ne.0) then
	154	q0(i,k) = fqcomp(i,k)*tau_cumul/sigt_cv(i,k)
	155	endif
	156	enddo
	157	enddo
	158	do k=1,klev-1
	159	do i=1,klon
	160	povariance(i,k)= (pdocarreadj(i,k)-2.po(i,k)pdoadj(i,k) + &
	161	a_ratqs_cv(sigt_cv(i,k)(1-sigt_cv(i,k))q0(i,k)2/tau_cumul + sigd(i)(1-sigd(i))qd0(i,k)*2/tau_cumul) + &
	162	((povariance(i,k+1)-povariance(i,k))(fm_cv(i,k)/zmasse(i,k))))pdtphys + povariance(i,k)
	163	povariance(i,k)=povariance(i,k)*exp(-pdtphys/tau_diss(i,k))
	164	enddo
	165	enddo
	166	povariance(:,klev) = povariance(:,klev-1)
	167	! fqd(:,:)=sigt_cv(:,:)(1-sigt_cv(:,:))q0(:,:)**2/tau_cumul
[4009]	168	endif
[4613]	169
	170	!-------------------------------------------------------------------------
	171	! Caclul du terme de détrainement de la variance pour la convection (version fausse avec deux calculs de variance indépendants)
	172	!-------------------------------------------------------------------------
[4009]	173
[4613]	174	! if (klein_conv) then
	175	! detrain_p(:,:) = 0.
	176	! detraincv(:,:) = 0.
	177	! dqp(:,:) = 0.
	178
	179	! do k=1,klev-1
	180	! do i=1,klon
	181	! dqp(i,k) = q_seri(i,k) - qp(i,k)
	182	! detraincv(i,k) = abs(detrain_cv(i,k))
	183
	184	! if ((mp(i,k)-mp(i,k+1)).le.0) then
	185	! detrain_p(i,k) = (mp(i,k+1)-mp(i,k))
	186	! endif
	187	! enddo
	188	! enddo
	189
	190	! do k=1,klev-1
	191	! do i=1,klon
	192	! qd0(:,:) = 0.0
	193	! if (sigd(i).ne.0) then
	194	! qd0(i,k) = fqd(i,k)*tau_cumul/sigd(i)
	195	! endif
	196	! enddo
	197	! enddo
	198
	199	! do k=1,klev-1
	200	! do i=1,klon
	201	! var_conv(i,k)= var_conv(i,k)*exp(-pdtphys/tau_conv) + &
	202	! (a_ratqs_cv(detraincv(i,k)/zmasse(i,k)) + sigd(i)(1-sigd(i))qd0(i,k)*2/tau_cumul &
	203	! + ((var_conv(i,k+1)-var_conv(i,k))(fm_cv(i,k)/zmasse(i,k)))) &
	204	! ((dqp(i,k)*2)(detrain_p(i,k)/zmasse(i,k))))* & ! les termes de descentes précipitantes qui seront traités autrement
	205	! (((mp(i,k)-mp(i,k+1))/zmasse(i,k))dqp(i,k)2) + (2mp(i,k)dqp(i,k)(qp(i,k+1)-qp(i,k))/zmasse(i,k)))* &
	206	! (1.-exp(-pdtphys/tau_conv))/(1/tau_conv)
	207	! enddo
	208	! enddo
	209	! var_conv(:,klev) = var_conv(:,klev-1)
	210	! fqd(:,:) = var_conv(:,:)
	211	! else
	212
	213
	214	! do k=1,klev-1
	215	! do i=1,klon
	216	! var_conv(i,k)= var_conv(i,k)*exp(-pdtphys/tau_conv) + &
	217	! (a_ratqs_cv(sigt_cv(i,k)(1-sigt_cv(i,k))q0(i,k)2/pdtphys + sigd(i)(1-sigd(i))qd0(i,k)*2/tau_cumul) + & ! somme des contributions des descentes précipitantes et des flux mélangés
	218	! + ((var_conv(i,k+1)-var_conv(i,k))(fm_cv(i,k)/zmasse(i,k)))) & ! flux compensatoires dans l'environnement
	219	! (1.-exp(-pdtphys/tau_conv))/(1/tau_conv)
	220	! ((var_conv(i,k+1)-var_conv(i,k))*(fm_cv(i,k)/zmasse(i,k)))
	221	! enddo
	222	! enddo
	223	! var_conv(:,klev) = var_conv(:,klev-1)
	224	! endif
	225
	226	!-------------------------------------------------------------------------
	227	! Caclul du ratqs_inter_
	228	!-------------------------------------------------------------------------
	229
	230	do k=1,klev
	231	do i=1,klon
	232	if(q_seri(i,k).ge.1E-7) then
	233	ratqs_inter_(i,k) = abs(povariance(i,k))**0.5/q_seri(i,k)
	234	else
	235	ratqs_inter_(i,k) = 0.
	236	endif
[4009]	237	enddo
[4613]	238	enddo
[4009]	239
	240	return
[4613]	241	end
[4009]	242
	243	!------------------------------------------------------------------
[4613]	244	SUBROUTINE ratqs_oro(klon,klev,pctsrf,zstd,qsat,temp,pplay,paprs,ratqs_oro_)
[4009]	245
	246	! Etienne Vignon, November 2021: effect of subgrid orography on ratqs
	247
[4613]	248	USE lmdz_ratqs_ini, ONLY : RG,RV,RD,RLSTT,RLVTT,RTT,nbsrf,is_lic,is_ter
[4009]	249
	250	IMPLICIT NONE
	251
	252	! Declarations
	253	!--------------
	254
	255	! INPUTS
	256
	257	INTEGER, INTENT(IN) :: klon ! number of horizontal grid points
	258	INTEGER, INTENT(IN) :: klev ! number of vertical layers
[4613]	259	REAL, DIMENSION(klon,nbsrf) :: pctsrf
[4009]	260	REAL, DIMENSION(klon,klev), INTENT(IN) :: qsat ! saturation specific humidity [kg/kg]
[4613]	261	REAL, DIMENSION(klon), INTENT(IN) :: zstd ! sub grid orography standard deviation
[4009]	262	REAL, DIMENSION(klon,klev), INTENT(IN) :: temp ! air temperature [K]
	263	REAL, DIMENSION(klon,klev), INTENT(IN) :: pplay ! air pressure, layer's center [Pa]
	264	REAL, DIMENSION(klon,klev+1), INTENT(IN) :: paprs ! air pressure, lower inteface [Pa]
	265
	266	! OUTPUTS
	267
[4613]	268	REAL, DIMENSION(klon,klev), INTENT(out) :: ratqs_oro_ ! ratqs profile due to subgrid orography
[4009]	269
	270
	271	! LOCAL
	272
	273	INTEGER :: i,k
	274	REAL, DIMENSION(klon) :: orogradT,xsi0
	275	REAL, DIMENSION (klon,klev) :: zlay
	276	REAL :: Lvs, temp0
	277
	278
	279	! Calculation of the near-surface temperature gradient along the topography
	280	!--------------------------------------------------------------------------
	281
	282	! at the moment, we fix it at a constant value (moist adiab. lapse rate)
	283
	284	orogradT(:)=-6.5/1000. ! K/m
	285
	286	! Calculation of near-surface surface ratqs
	287	!-------------------------------------------
	288
	289	DO i=1,klon
	290	temp0=temp(i,1)
	291	IF (temp0 .LT. RTT) THEN
	292	Lvs=RLSTT
	293	ELSE
	294	Lvs=RLVTT
	295	ENDIF
	296	xsi0(i)=zstd(i)ABS(orogradT(i))Lvs/temp0/temp0/RV
[4613]	297	ratqs_oro_(i,1)=xsi0(i)
[4009]	298	END DO
	299
	300	! Vertical profile of ratqs assuming an exponential decrease with height
	301	!------------------------------------------------------------------------
	302
	303	! calculation of geop. height AGL
	304	zlay(:,1)= RDtemp(:,1)/(0.5(paprs(:,1)+pplay(:,1))) &
	305	*(paprs(:,1)-pplay(:,1))/RG
	306
	307	DO k=2,klev
	308	DO i = 1, klon
	309	zlay(i,k)= zlay(i,k-1)+RD0.5(temp(i,k-1)+temp(i,k)) &
	310	/paprs(i,k)*(pplay(i,k-1)-pplay(i,k))/RG
	311
[4613]	312	ratqs_oro_(i,k)=MAX(0.0,pctsrf(i,is_ter)xsi0(i)exp(-zlay(i,k)/MAX(zstd(i),1.)))
[4009]	313	END DO
	314	END DO
	315
	316
	317
	318
[4613]	319	END SUBROUTINE ratqs_oro
[4009]	320
	321	!=============================================
	322
[4613]	323	SUBROUTINE ratqs_hetero(klon,klev,pctsrf,s_pblh,t2m,q2m,temp,q,pplay,paprs,ratqs_hetero_)
[4009]	324
	325	! Etienne Vignon, November 2021
	326	! Effect of subgrid surface heterogeneities on ratqs
	327
[4664]	328	USE lmdz_lscp_tools, ONLY: CALC_QSAT_ECMWF
[4009]	329
[4613]	330	USE lmdz_ratqs_ini, ONLY : RG,RD,RTT,nbsrf
	331
[4009]	332	IMPLICIT NONE
	333
	334	! INPUTS
	335
	336
	337	INTEGER, INTENT(IN) :: klon ! number of horizontal grid points
	338	INTEGER, INTENT(IN) :: klev ! number of vertical layers
[4613]	339	REAL, DIMENSION(klon) :: s_pblh ! height of the planetary boundary layer(HPBL)
	340	REAL, DIMENSION(klon,nbsrf) :: pctsrf ! Fractional cover of subsurfaces
[4009]	341	REAL, DIMENSION(klon,nbsrf), INTENT(IN) :: t2m ! 2m temperature for each tile [K]
	342	REAL, DIMENSION(klon,nbsrf), INTENT(IN) :: q2m ! 2m specific humidity for each tile [kg/kg]
	343	REAL, DIMENSION(klon,klev), INTENT(IN) :: temp ! air temperature [K]
	344	REAL, DIMENSION(klon,klev), INTENT(IN) :: q ! specific humidity [kg/kg]
	345	REAL, DIMENSION(klon,klev), INTENT(IN) :: pplay ! air pressure, layer's center [Pa]
	346	REAL, DIMENSION(klon,klev+1), INTENT(IN) :: paprs ! air pressure, lower inteface [Pa]
	347
	348	! OUTPUTS
	349
[4613]	350	REAL, DIMENSION(klon,klev), INTENT(out) :: ratqs_hetero_ ! ratsq profile due to surface heterogeneities
[4009]	351
	352
	353	INTEGER :: i,k,nsrf
[4072]	354	REAL, DIMENSION(klon) :: xsi0, ratiom, qsat2m, dqsatdT
[4009]	355	REAL, DIMENSION (klon,klev) :: zlay
	356
	357
	358
	359	! Calculation of near-surface surface ratqs
	360	!-------------------------------------------
	361
	362
[4072]	363	ratiom(:)=0.
	364	xsi0(:)=0.
[4009]	365
	366	DO nsrf=1,nbsrf
[4072]	367	CALL CALC_QSAT_ECMWF(klon,t2m(:,nsrf),q2m(:,nsrf),paprs(:,1),RTT,0,.false.,qsat2m,dqsatdT)
	368	ratiom(:)=ratiom(:)+pctsrf(:,nsrf)*(q2m(:,nsrf)/qsat2m(:))
	369	xsi0(:)=xsi0(:)+pctsrf(:,nsrf)((q2m(:,nsrf)/qsat2m(:)-ratiom(:))*2)
[4009]	370	END DO
	371
[4072]	372	xsi0(:)=sqrt(xsi0(:))/(ratiom(:)+1E-6)
[4009]	373
	374
	375
	376	! Vertical profile of ratqs assuming an exponential decrease with height
	377	!------------------------------------------------------------------------
	378
	379	! calculation of geop. height AGL
	380
	381	zlay(:,1)= RDtemp(:,1)/(0.5(paprs(:,1)+pplay(:,1))) &
	382	*(paprs(:,1)-pplay(:,1))/RG
[4613]	383	ratqs_hetero_(:,1)=xsi0(:)
[4009]	384
	385	DO k=2,klev
	386	DO i = 1, klon
	387	zlay(i,k)= zlay(i,k-1)+RD0.5(temp(i,k-1)+temp(i,k)) &
	388	/paprs(i,k)*(pplay(i,k-1)-pplay(i,k))/RG
	389
[4613]	390	ratqs_hetero_(i,k)=MAX(xsi0(i)*exp(-zlay(i,k)/(s_pblh(i)+1.0)),0.0)
[4009]	391	END DO
	392	END DO
	393
[4613]	394	END SUBROUTINE ratqs_hetero
[4009]	395
	396	!=============================================
	397
[4613]	398	SUBROUTINE ratqs_tke(klon,klev,pdtphys,temp,q,qsat,pplay,paprs,omega,tke,tke_dissip,lmix,wprime,ratqs_tke_)
[4009]	399
	400	! References:
	401	!
	402	! Etienne Vignon: effect of subgrid turbulence on ratqs
	403	!
	404	! Field, P.R., Hill, A., Furtado, K., Korolev, A., 2014b. Mixed-phase clouds in a turbulent environment. Part
	405	! 2: analytic treatment. Q. J. R. Meteorol. Soc. 21, 2651–2663. https://doi.org/10.1002/qj.2175.
	406	!
	407	! Furtado, K., Field, P.R., Boutle, I.A., Morcrette, C.R., Wilkinson, J., 2016. A physically-based, subgrid
	408	! parametrization for the production and maintenance of mixed-phase clouds in a general circulation
	409	! model. J. Atmos. Sci. 73, 279–291. https://doi.org/10.1175/JAS-D-15-0021.
	410
[4613]	411	USE lmdz_ratqs_ini, ONLY : RG,RV,RD,RCPD,RLSTT,RLVTT,RTT
[4009]	412
	413	IMPLICIT NONE
	414
	415	! INPUTS
	416
	417	INTEGER, INTENT(IN) :: klon ! number of horizontal grid points
	418	INTEGER, INTENT(IN) :: klev ! number of vertical layers
	419	REAL, INTENT(IN) :: pdtphys ! physics time step [s]
	420	REAL, DIMENSION(klon,klev), INTENT(IN) :: temp ! air temperature [K]
	421	REAL, DIMENSION(klon,klev), INTENT(IN) :: q ! specific humidity [kg/kg]
	422	REAL, DIMENSION(klon,klev), INTENT(IN) :: qsat ! saturation specific humidity [kg/kg]
	423	REAL, DIMENSION(klon,klev), INTENT(IN) :: pplay ! air pressure, layer's center [Pa]
	424	REAL, DIMENSION(klon,klev+1), INTENT(IN) :: paprs ! air pressure, lower inteface [Pa]
[4613]	425	REAL, DIMENSION(klon,klev), INTENT(IN) :: omega ! air pressure, lower inteface [Pa]
[4009]	426	REAL, DIMENSION(klon,klev+1), INTENT(IN) :: tke ! Turbulent Kinetic Energy [m2/s2]
	427	REAL, DIMENSION(klon,klev+1), INTENT(IN) :: tke_dissip ! Turbulent Kinetic Energy Dissipation rate [m2/s3]
	428	REAL, DIMENSION(klon,klev+1), INTENT(IN) :: lmix ! Turbulent mixing length
	429	REAL, DIMENSION(klon,klev+1), INTENT(IN) :: wprime ! Turbulent vertical velocity scale [m/s]
	430
	431	! OUTPUTS
	432
[4613]	433	REAL, DIMENSION(klon,klev), INTENT(out) :: ratqs_tke_ ! ratsq profile due to subgrid TKE
[4009]	434
	435	! LOCAL
	436	INTEGER :: i, k
	437	REAL :: AA, DD, NW, AAprime, VARLOG,rho,Lvs,taue,lhomo,dissmin,maxvarlog
	438	REAL, DIMENSION(klon,klev) :: sigmaw,w
	439	REAL, PARAMETER :: C0=10.0
	440	REAL, PARAMETER :: lmin=0.001
	441	REAL, PARAMETER :: ratqsmin=1E-6
	442	REAL, PARAMETER :: ratqsmax=0.5
	443
	444
	445	! Calculation of large scale and turbulent vertical velocities
	446	!---------------------------------------------------------------
	447
	448	DO k=1,klev
	449	DO i=1,klon
	450	rho=pplay(i,k)/temp(i,k)/RD
	451	w(i,k)=-rhoRGomega(i,k)
	452	sigmaw(i,k)=0.5*(wprime(i,k+1)+wprime(i,k)) ! turbulent vertical velocity at the middle of model layers.
	453	END DO
	454	END DO
	455
	456	! Calculation of ratqs
	457	!---------------------------------------------------------------
[4613]	458	ratqs_tke_(:,1)=ratqsmin ! set to a very low value to avoid division by 0 in order parts
[4009]	459	! of the code
	460	DO k=2,klev ! we start from second model level since TKE is not defined at k=1
	461	DO i=1,klon
	462
	463	IF (temp(i,k) .LT. RTT) THEN
	464	Lvs=RLSTT
	465	ELSE
	466	Lvs=RLVTT
	467	ENDIF
	468	dissmin=0.01(0.5(tke(i,k)+tke(i,k+1))/pdtphys)
	469	maxvarlog=LOG(1.0+ratqsmax**2)! to prevent ratqs from exceeding an arbitrary threshold value
	470	AA=RG(Lvs/(RCPDtemp(i,k)temp(i,k)RV) - 1./(RD*temp(i,k)))
	471	lhomo=MAX(0.5*(lmix(i,k)+lmix(i,k+1)),lmin)
	472	taue=(lhomolhomo/MAX(0.5(tke_dissip(i,k)+tke_dissip(i,k+1)),dissmin))**(1./3) ! Fields et al. 2014
	473	DD=1.0/taue
	474	NW=(sigmaw(i,k)*2)SQRT(2./(C0MAX(0.5(tke_dissip(i,k)+tke_dissip(i,k+1)),dissmin)))
	475	AAprime=AA*NW
	476	VARLOG=AAprime/2./DD
	477	VARLOG=MIN(VARLOG,maxvarlog)
[4613]	478	ratqs_tke_(i,k)=SQRT(MAX(EXP(VARLOG)-1.0,ratqsmin))
[4009]	479	END DO
	480	END DO
[4613]	481	END SUBROUTINE ratqs_tke
[4009]	482
[4613]	483	END MODULE lmdz_ratqs_multi

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