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!MNH_LIC Copyright 1994-2014 CNRS, Meteo-France and Universite Paul Sabatier
!MNH_LIC This is part of the Meso-NH software governed by the CeCILL-C licence
!MNH_LIC version 1. See LICENSE, CeCILL-C_V1-en.txt and CeCILL-C_V1-fr.txt
!MNH_LIC for details. version 1.
!-----------------------------------------------------------------
!--------------- special set of characters for RCS information
!-----------------------------------------------------------------
! $Source$ $Revision$
! MASDEV4_7 mode 2006/05/18 13:07:25
!-----------------------------------------------------------------
! ####################
MODULE MODE_PRANDTL
! ####################
!
!* modification 08/2010 V. Masson smoothing of the discontinuity in functions
! used for implicitation of exchange coefficients
RODIER Quentin
committed
! 05/2020 V. Masson and C. Lac : bug in D_PHI3DTDZ2_O_DDTDZ
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!
USE MODD_CTURB, ONLY : XCTV, XCSHF, XCTD, XPHI_LIM, XCPR3, XCPR4, XCPR5
USE MODD_PARAMETERS, ONLY : JPVEXT_TURB
!
USE MODI_SHUMAN
IMPLICIT NONE
!----------------------------------------------------------------------------
CONTAINS
!----------------------------------------------------------------------------
SUBROUTINE SMOOTH_TURB_FUNCT(PPHI3,PF_LIM,PF)
!
REAL, DIMENSION(:,:,:), INTENT(IN) :: PPHI3 ! Phi3
REAL, DIMENSION(:,:,:), INTENT(IN) :: PF_LIM ! Value of F when Phi3 is
! ! larger than Phi_lim
REAL, DIMENSION(:,:,:), INTENT(INOUT) :: PF ! function F to smooth
!
REAL, DIMENSION(SIZE(PF,1),SIZE(PF,2),SIZE(PF,3)) :: ZCOEF
!
!* adds a artificial correction to smooth the function near the discontinuity
! point at Phi3 = Phi_lim
! This smoothing is applied between 0.9*phi_lim (=2.7) and Phi_lim (=3)
! Note that in the Boundary layer, phi is usually between 0.8 and 1
!
!
ZCOEF = MAX(MIN(( 10.*(1.-PPHI3/XPHI_LIM)) ,1.), 0.)
!
PF(:,:,:) = ZCOEF(:,:,:) * PF &
+ (1.-ZCOEF(:,:,:)) * PF_LIM
!
END SUBROUTINE SMOOTH_TURB_FUNCT
!----------------------------------------------------------------------------
FUNCTION PHI3(PREDTH1,PREDR1,PRED2TH3,PRED2R3,PRED2THR3,HTURBDIM,OUSERV)
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDTH1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PRED2TH3
REAL, DIMENSION(:,:,:), INTENT(IN) :: PRED2R3
REAL, DIMENSION(:,:,:), INTENT(IN) :: PRED2THR3
CHARACTER(len=4), INTENT(IN) :: HTURBDIM ! 1DIM or 3DIM turb. scheme
LOGICAL, INTENT(IN) :: OUSERV ! flag to use vapor
REAL, DIMENSION(SIZE(PREDTH1,1),SIZE(PREDTH1,2),SIZE(PREDTH1,3)) :: PHI3
!
REAL, DIMENSION(SIZE(PREDTH1,1),SIZE(PREDTH1,2),SIZE(PREDTH1,3)) :: ZW1, ZW2
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PREDTH1,3)-JPVEXT_TURB
!
IF (HTURBDIM=='3DIM') THEN
!* 3DIM case
IF (OUSERV) THEN
ZW1(:,:,:) = 1. + 1.5* (PREDTH1(:,:,:)+PREDR1(:,:,:)) + &
( 0.5 * (PREDTH1(:,:,:)**2+PREDR1(:,:,:)**2) &
+ PREDTH1(:,:,:) * PREDR1(:,:,:) &
)
ZW2(:,:,:) = 0.5 * (PRED2TH3(:,:,:)-PRED2R3(:,:,:))
PHI3(:,:,:)= 1. - &
( ( (1.+PREDR1(:,:,:)) * &
(PRED2THR3(:,:,:) + PRED2TH3(:,:,:)) / PREDTH1(:,:,:) &
) + ZW2(:,:,:) &
) / ZW1(:,:,:)
ELSE
ZW1(:,:,:) = 1. + 1.5* PREDTH1(:,:,:) + &
0.5* PREDTH1(:,:,:)**2
ZW2(:,:,:) = 0.5* PRED2TH3(:,:,:)
PHI3(:,:,:)= 1. - &
(PRED2TH3(:,:,:) / PREDTH1(:,:,:) + ZW2(:,:,:)) / ZW1(:,:,:)
END IF
WHERE( PHI3 <= 0. .OR. PHI3 > XPHI_LIM )
PHI3 = XPHI_LIM
END WHERE
ELSE
!* 1DIM case
IF (OUSERV) THEN
PHI3(:,:,:)= 1./(1.+PREDTH1(:,:,:)+PREDR1(:,:,:))
ELSE
PHI3(:,:,:)= 1./(1.+PREDTH1(:,:,:))
END IF
END IF
!
PHI3(:,:,IKB-1)=PHI3(:,:,IKB)
PHI3(:,:,IKE+1)=PHI3(:,:,IKE)
!
END FUNCTION PHI3
!----------------------------------------------------------------------------
FUNCTION PSI_SV(PREDTH1,PREDR1,PREDS1,PRED2THS,PRED2RS,PPHI3,PPSI3)
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDTH1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:,:), INTENT(IN) :: PREDS1
REAL, DIMENSION(:,:,:,:), INTENT(IN) :: PRED2THS
REAL, DIMENSION(:,:,:,:), INTENT(IN) :: PRED2RS
REAL, DIMENSION(:,:,:), INTENT(IN) :: PPHI3
REAL, DIMENSION(:,:,:), INTENT(IN) :: PPSI3
REAL, DIMENSION(SIZE(PRED2THS,1),SIZE(PRED2THS,2),SIZE(PRED2THS,3),SIZE(PRED2THS,4)) :: PSI_SV
!
INTEGER :: IKB, IKE
INTEGER :: JSV
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PREDTH1,3)-JPVEXT_TURB
!
DO JSV=1,SIZE(PSI_SV,4)
PSI_SV(:,:,:,JSV) = ( 1. &
- (XCPR3+XCPR5) * (PRED2THS(:,:,:,JSV)/PREDS1(:,:,:,JSV)-PREDTH1) &
- (XCPR4+XCPR5) * (PRED2RS (:,:,:,JSV)/PREDS1(:,:,:,JSV)-PREDR1 ) &
- XCPR3 * PREDTH1 * PPHI3 - XCPR4 * PREDR1 * PPSI3 &
) / ( 1. + XCPR5 * ( PREDTH1 + PREDR1 ) )
! control of the PSI_SV positivity
WHERE ( (PSI_SV(:,:,:,JSV) <=0.).AND. (PREDTH1+PREDR1) <= 0. )
PSI_SV(:,:,:,JSV)=XPHI_LIM
END WHERE
PSI_SV(:,:,:,JSV) = MAX( 1.E-4, MIN(XPHI_LIM,PSI_SV(:,:,:,JSV)) )
!
PSI_SV(:,:,IKB-1,JSV)=PSI_SV(:,:,IKB,JSV)
PSI_SV(:,:,IKE+1,JSV)=PSI_SV(:,:,IKE,JSV)
END DO
!
END FUNCTION PSI_SV
!----------------------------------------------------------------------------
FUNCTION D_PHI3DTDZ_O_DDTDZ(PPHI3,PREDTH1,PREDR1,PRED2TH3,PRED2THR3,HTURBDIM,OUSERV)
REAL, DIMENSION(:,:,:), INTENT(IN) :: PPHI3
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDTH1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PRED2TH3
REAL, DIMENSION(:,:,:), INTENT(IN) :: PRED2THR3
CHARACTER(len=4), INTENT(IN) :: HTURBDIM ! 1DIM or 3DIM turb. scheme
LOGICAL, INTENT(IN) :: OUSERV ! flag to use vapor
REAL, DIMENSION(SIZE(PREDTH1,1),SIZE(PREDTH1,2),SIZE(PREDTH1,3)) :: D_PHI3DTDZ_O_DDTDZ
INTEGER :: IKB, IKE,JL,JK,JJ
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PREDTH1,3)-JPVEXT_TURB
!
IF (HTURBDIM=='3DIM') THEN
!* 3DIM case
IF (OUSERV) THEN
WHERE (PPHI3(:,:,:)<=XPHI_LIM)
D_PHI3DTDZ_O_DDTDZ(:,:,:) = PPHI3(:,:,:) &
* (1. - PREDTH1(:,:,:) * (3./2.+PREDTH1+PREDR1) &
/((1.+PREDTH1+PREDR1)*(1.+1./2.*(PREDTH1+PREDR1)))) &
+ (1.+PREDR1)*(PRED2THR3+PRED2TH3) &
/ (PREDTH1*(1.+PREDTH1+PREDR1)*(1.+1./2.*(PREDTH1+PREDR1))) &
- (1./2.*PREDTH1+PREDR1 * (1.+PREDTH1+PREDR1)) &
/ ((1.+PREDTH1+PREDR1)*(1.+1./2.*(PREDTH1+PREDR1)))
ELSEWHERE
D_PHI3DTDZ_O_DDTDZ(:,:,:) = PPHI3(:,:,:)
ENDWHERE
!
ELSE
WHERE (PPHI3(:,:,:)<=XPHI_LIM)
D_PHI3DTDZ_O_DDTDZ(:,:,:) = PPHI3(:,:,:) &
* (1. - PREDTH1(:,:,:) * (3./2.+PREDTH1) &
/((1.+PREDTH1)*(1.+1./2.*PREDTH1))) &
+ PRED2TH3 / (PREDTH1*(1.+PREDTH1)*(1.+1./2.*PREDTH1)) &
- 1./2.*PREDTH1 / ((1.+PREDTH1)*(1.+1./2.*PREDTH1))
ELSEWHERE
D_PHI3DTDZ_O_DDTDZ(:,:,:) = PPHI3(:,:,:)
ENDWHERE
!
END IF
ELSE
!* 1DIM case
! WHERE (PPHI3(:,:,:)<=XPHI_LIM)
! D_PHI3DTDZ_O_DDTDZ(:,:,:) = PPHI3(:,:,:) &
! * (1. - PREDTH1(:,:,:)*PPHI3(:,:,:))
! ELSEWHERE
! D_PHI3DTDZ_O_DDTDZ(:,:,:) = PPHI3(:,:,:)
! ENDWHERE
DO JJ=1,SIZE(PPHI3,2)
DO JL=1,SIZE(PPHI3,1)
DO JK=1,SIZE(PPHI3,3)
IF ( ABS(PPHI3(JL,JJ,JK)-XPHI_LIM) < 1.E-12 ) THEN
D_PHI3DTDZ_O_DDTDZ(JL,JJ,JK)=PPHI3(JL,JJ,JK)*&
& (1. - PREDTH1(JL,JJ,JK)*PPHI3(JL,JJ,JK))
ELSE
D_PHI3DTDZ_O_DDTDZ(JL,JJ,JK)=PPHI3(JL,JJ,JK)
ENDIF
ENDDO
ENDDO
ENDDO
END IF
!
!* smoothing
CALL SMOOTH_TURB_FUNCT(PPHI3,PPHI3,D_PHI3DTDZ_O_DDTDZ)
!
D_PHI3DTDZ_O_DDTDZ(:,:,IKB-1)=D_PHI3DTDZ_O_DDTDZ(:,:,IKB)
D_PHI3DTDZ_O_DDTDZ(:,:,IKE+1)=D_PHI3DTDZ_O_DDTDZ(:,:,IKE)
!
END FUNCTION D_PHI3DTDZ_O_DDTDZ
!----------------------------------------------------------------------------
FUNCTION D_PHI3DRDZ_O_DDRDZ(PPHI3,PREDTH1,PREDR1,PRED2TH3,PRED2THR3,HTURBDIM,OUSERV)
REAL, DIMENSION(:,:,:), INTENT(IN) :: PPHI3
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDTH1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PRED2TH3
REAL, DIMENSION(:,:,:), INTENT(IN) :: PRED2THR3
CHARACTER(len=4), INTENT(IN) :: HTURBDIM ! 1DIM or 3DIM turb. scheme
LOGICAL, INTENT(IN) :: OUSERV ! flag to use vapor
REAL, DIMENSION(SIZE(PREDTH1,1),SIZE(PREDTH1,2),SIZE(PREDTH1,3)) :: D_PHI3DRDZ_O_DDRDZ
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PREDTH1,3)-JPVEXT_TURB
!
!
IF (HTURBDIM=='3DIM') THEN
!* 3DIM case
IF (OUSERV) THEN
WHERE (PPHI3(:,:,:)<=XPHI_LIM)
D_PHI3DRDZ_O_DDRDZ(:,:,:) = &
PPHI3(:,:,:) * (1.-PREDR1(:,:,:)*(3./2.+PREDTH1+PREDR1) &
/ ((1.+PREDTH1+PREDR1)*(1.+1./2.*(PREDTH1+PREDR1)))) &
- PREDR1(:,:,:) * (PRED2THR3+PRED2TH3) / (PREDTH1 &
* (1.+PREDTH1+PREDR1)*(1.+1./2.*(PREDTH1+PREDR1))) &
+ PREDR1(:,:,:) * (1./2.+PREDTH1+PREDR1) &
/ ((1.+PREDTH1+PREDR1)*(1.+1./2.*(PREDTH1+PREDR1)))
ELSEWHERE
D_PHI3DRDZ_O_DDRDZ(:,:,:) = PPHI3(:,:,:)
END WHERE
ELSE
D_PHI3DRDZ_O_DDRDZ(:,:,:) = PPHI3(:,:,:)
END IF
ELSE
!* 1DIM case
WHERE (PPHI3(:,:,:)<=XPHI_LIM)
D_PHI3DRDZ_O_DDRDZ(:,:,:) = PPHI3(:,:,:) &
* (1. - PREDR1(:,:,:)*PPHI3(:,:,:))
ELSEWHERE
D_PHI3DRDZ_O_DDRDZ(:,:,:) = PPHI3(:,:,:)
END WHERE
END IF
!
!* smoothing
CALL SMOOTH_TURB_FUNCT(PPHI3,PPHI3,D_PHI3DRDZ_O_DDRDZ)
!
D_PHI3DRDZ_O_DDRDZ(:,:,IKB-1)=D_PHI3DRDZ_O_DDRDZ(:,:,IKB)
D_PHI3DRDZ_O_DDRDZ(:,:,IKE+1)=D_PHI3DRDZ_O_DDRDZ(:,:,IKE)
!
END FUNCTION D_PHI3DRDZ_O_DDRDZ
!----------------------------------------------------------------------------
FUNCTION D_PHI3DTDZ2_O_DDTDZ(PPHI3,PREDTH1,PREDR1,PRED2TH3,PRED2THR3,PDTDZ,HTURBDIM,OUSERV)
REAL, DIMENSION(:,:,:), INTENT(IN) :: PPHI3
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDTH1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PRED2TH3
REAL, DIMENSION(:,:,:), INTENT(IN) :: PRED2THR3
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDTDZ
CHARACTER(len=4), INTENT(IN) :: HTURBDIM ! 1DIM or 3DIM turb. scheme
LOGICAL, INTENT(IN) :: OUSERV ! flag to use vapor
REAL, DIMENSION(SIZE(PREDTH1,1),SIZE(PREDTH1,2),SIZE(PREDTH1,3)) :: D_PHI3DTDZ2_O_DDTDZ
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PREDTH1,3)-JPVEXT_TURB
!
!
IF (HTURBDIM=='3DIM') THEN
RODIER Quentin
committed
! by derivation of (phi3 dtdz) * dtdz according to dtdz we obtain:
D_PHI3DTDZ2_O_DDTDZ(:,:,:) = PDTDZ * (PPHI3 + &
D_PHI3DTDZ_O_DDTDZ(PPHI3,PREDTH1,PREDR1,PRED2TH3,PRED2THR3,HTURBDIM,OUSERV) )
RODIER Quentin
committed
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! !* 3DIM case
! IF (OUSERV) THEN
! WHERE (PPHI3(:,:,:)<=XPHI_LIM)
! D_PHI3DTDZ2_O_DDTDZ(:,:,:) = PPHI3(:,:,:) &
! * PDTDZ(:,:,:)*(2.-PREDTH1(:,:,:)*(3./2.+PREDTH1+PREDR1) &
! /((1.+PREDTH1+PREDR1)*(1.+1./2.*(PREDTH1+PREDR1)))) &
! + (1.+PREDR1)*(PRED2THR3+PRED2TH3) &
! / (PREDTH1*(1.+PREDTH1+PREDR1)*(1.+1./2.*(PREDTH1+PREDR1))) &
! - (1./2.*PREDTH1+PREDR1 * (1.+PREDTH1+PREDR1)) &
! / ((1.+PREDTH1+PREDR1)*(1.+1./2.*(PREDTH1+PREDR1)))
! ELSEWHERE
! D_PHI3DTDZ2_O_DDTDZ(:,:,:) = PPHI3(:,:,:) * 2. * PDTDZ(:,:,:)
! ENDWHERE
!
!!
! ELSE
! WHERE (PPHI3(:,:,:)<=XPHI_LIM)
! D_PHI3DTDZ2_O_DDTDZ(:,:,:) = PPHI3(:,:,:) &
! * PDTDZ(:,:,:)*(2.-PREDTH1(:,:,:)*(3./2.+PREDTH1) &
! /((1.+PREDTH1)*(1.+1./2.*PREDTH1))) &
! + PRED2TH3 / (PREDTH1*(1.+PREDTH1)*(1.+1./2.*PREDTH1)) &
! - 1./2.*PREDTH1 / ((1.+PREDTH1)*(1.+1./2.*PREDTH1))
! ELSEWHERE
! D_PHI3DTDZ2_O_DDTDZ(:,:,:) = PPHI3(:,:,:) * 2. * PDTDZ(:,:,:)
! ENDWHERE
! END IF
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ELSE
!* 1DIM case
WHERE (PPHI3(:,:,:)<=XPHI_LIM)
D_PHI3DTDZ2_O_DDTDZ(:,:,:) = PPHI3(:,:,:)*PDTDZ(:,:,:) &
* (2. - PREDTH1(:,:,:)*PPHI3(:,:,:))
ELSEWHERE
D_PHI3DTDZ2_O_DDTDZ(:,:,:) = PPHI3(:,:,:) * 2. * PDTDZ(:,:,:)
END WHERE
END IF
!
!* smoothing
CALL SMOOTH_TURB_FUNCT(PPHI3,PPHI3*2.*PDTDZ,D_PHI3DTDZ2_O_DDTDZ)
!
!
D_PHI3DTDZ2_O_DDTDZ(:,:,IKB-1)=D_PHI3DTDZ2_O_DDTDZ(:,:,IKB)
D_PHI3DTDZ2_O_DDTDZ(:,:,IKE+1)=D_PHI3DTDZ2_O_DDTDZ(:,:,IKE)
!
END FUNCTION D_PHI3DTDZ2_O_DDTDZ
!----------------------------------------------------------------------------
FUNCTION M3_WTH_WTH2(PREDTH1,PREDR1,PD,PBLL_O_E,PETHETA)
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDTH1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PBLL_O_E
REAL, DIMENSION(:,:,:), INTENT(IN) :: PETHETA
REAL, DIMENSION(SIZE(PD,1),SIZE(PD,2),SIZE(PD,3)) :: M3_WTH_WTH2
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
M3_WTH_WTH2(:,:,:) = XCSHF*PBLL_O_E*PETHETA*0.5/XCTD &
* (1.+0.5*PREDTH1+PREDR1) / PD
M3_WTH_WTH2(:,:,IKB-1)=M3_WTH_WTH2(:,:,IKB)
M3_WTH_WTH2(:,:,IKE+1)=M3_WTH_WTH2(:,:,IKE)
!
END FUNCTION M3_WTH_WTH2
!----------------------------------------------------------------------------
FUNCTION D_M3_WTH_WTH2_O_DDTDZ(PM3_WTH_WTH2,PREDTH1,PREDR1,PD,PBLL_O_E,PETHETA)
REAL, DIMENSION(:,:,:), INTENT(IN) :: PM3_WTH_WTH2
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDTH1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PBLL_O_E
REAL, DIMENSION(:,:,:), INTENT(IN) :: PETHETA
REAL, DIMENSION(SIZE(PD,1),SIZE(PD,2),SIZE(PD,3)) :: D_M3_WTH_WTH2_O_DDTDZ
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
D_M3_WTH_WTH2_O_DDTDZ(:,:,:) = ( 0.5*XCSHF*PBLL_O_E*PETHETA*0.5/XCTD/PD &
- PM3_WTH_WTH2/PD*(1.5+PREDTH1+PREDR1) )&
* PBLL_O_E * PETHETA * XCTV
!
D_M3_WTH_WTH2_O_DDTDZ(:,:,IKB-1)=D_M3_WTH_WTH2_O_DDTDZ(:,:,IKB)
D_M3_WTH_WTH2_O_DDTDZ(:,:,IKE+1)=D_M3_WTH_WTH2_O_DDTDZ(:,:,IKE)
!
END FUNCTION D_M3_WTH_WTH2_O_DDTDZ
!----------------------------------------------------------------------------
FUNCTION M3_WTH_W2TH(KKA,KKU,KKL,PREDTH1,PREDR1,PD,PKEFF,PTKE)
INTEGER, INTENT(IN) :: KKA
INTEGER, INTENT(IN) :: KKU
INTEGER, INTENT(IN) :: KKL
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDTH1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PKEFF
REAL, DIMENSION(:,:,:), INTENT(IN) :: PTKE
REAL, DIMENSION(SIZE(PD,1),SIZE(PD,2),SIZE(PD,3)) :: M3_WTH_W2TH
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
M3_WTH_W2TH(:,:,:) = XCSHF*PKEFF*1.5/MZM(KKA,KKU,KKL,PTKE) &
* (1. - 0.5*PREDR1*(1.+PREDR1)/PD ) / (1.+PREDTH1)
!
M3_WTH_W2TH(:,:,IKB-1)=M3_WTH_W2TH(:,:,IKB)
M3_WTH_W2TH(:,:,IKE+1)=M3_WTH_W2TH(:,:,IKE)
!
END FUNCTION M3_WTH_W2TH
!----------------------------------------------------------------------------
FUNCTION D_M3_WTH_W2TH_O_DDTDZ(KKA,KKU,KKL,PREDTH1,PREDR1,PD,PBLL_O_E,PETHETA,PKEFF,PTKE)
INTEGER, INTENT(IN) :: KKA
INTEGER, INTENT(IN) :: KKU
INTEGER, INTENT(IN) :: KKL
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDTH1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PBLL_O_E
REAL, DIMENSION(:,:,:), INTENT(IN) :: PETHETA
REAL, DIMENSION(:,:,:), INTENT(IN) :: PKEFF
REAL, DIMENSION(:,:,:), INTENT(IN) :: PTKE
REAL, DIMENSION(SIZE(PD,1),SIZE(PD,2),SIZE(PD,3)) :: D_M3_WTH_W2TH_O_DDTDZ
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
D_M3_WTH_W2TH_O_DDTDZ(:,:,:) = &
- XCSHF*PKEFF*1.5/MZM(KKA,KKU,KKL,PTKE)/(1.+PREDTH1)**2*XCTV*PBLL_O_E*PETHETA &
* (1. - 0.5*PREDR1*(1.+PREDR1)/PD*( 1.+(1.+PREDTH1)*(1.5+PREDR1+PREDTH1)/PD) )
!
D_M3_WTH_W2TH_O_DDTDZ(:,:,IKB-1)=D_M3_WTH_W2TH_O_DDTDZ(:,:,IKB)
D_M3_WTH_W2TH_O_DDTDZ(:,:,IKE+1)=D_M3_WTH_W2TH_O_DDTDZ(:,:,IKE)
!
END FUNCTION D_M3_WTH_W2TH_O_DDTDZ
!----------------------------------------------------------------------------
FUNCTION M3_WTH_W2R(KKA,KKU,KKL,PREDTH1,PREDR1,PD,PKEFF,PTKE,PBLL_O_E,PEMOIST,PDTDZ)
INTEGER, INTENT(IN) :: KKA
INTEGER, INTENT(IN) :: KKU
INTEGER, INTENT(IN) :: KKL
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDTH1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PKEFF
REAL, DIMENSION(:,:,:), INTENT(IN) :: PTKE
REAL, DIMENSION(:,:,:), INTENT(IN) :: PBLL_O_E
REAL, DIMENSION(:,:,:), INTENT(IN) :: PEMOIST
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDTDZ
REAL, DIMENSION(SIZE(PD,1),SIZE(PD,2),SIZE(PD,3)) :: M3_WTH_W2R
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
M3_WTH_W2R(:,:,:) = - XCSHF*PKEFF*0.75*XCTV*PBLL_O_E/MZM(KKA,KKU,KKL,PTKE)*PEMOIST*PDTDZ/PD
!
M3_WTH_W2R(:,:,IKB-1)=M3_WTH_W2R(:,:,IKB)
M3_WTH_W2R(:,:,IKE+1)=M3_WTH_W2R(:,:,IKE)
!
END FUNCTION M3_WTH_W2R
!----------------------------------------------------------------------------
FUNCTION D_M3_WTH_W2R_O_DDTDZ(KKA,KKU,KKL,PREDTH1,PREDR1,PD,PKEFF,PTKE,PBLL_O_E,PEMOIST)
INTEGER, INTENT(IN) :: KKA
INTEGER, INTENT(IN) :: KKU
INTEGER, INTENT(IN) :: KKL
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDTH1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PKEFF
REAL, DIMENSION(:,:,:), INTENT(IN) :: PTKE
REAL, DIMENSION(:,:,:), INTENT(IN) :: PBLL_O_E
REAL, DIMENSION(:,:,:), INTENT(IN) :: PEMOIST
REAL, DIMENSION(SIZE(PD,1),SIZE(PD,2),SIZE(PD,3)) :: D_M3_WTH_W2R_O_DDTDZ
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
D_M3_WTH_W2R_O_DDTDZ(:,:,:) = - XCSHF*PKEFF*0.75*XCTV*PBLL_O_E/MZM(KKA,KKU,KKL,PTKE)*PEMOIST/PD &
* (1. - PREDTH1*(1.5+PREDTH1+PREDR1)/PD)
!
D_M3_WTH_W2R_O_DDTDZ(:,:,IKB-1)=D_M3_WTH_W2R_O_DDTDZ(:,:,IKB)
D_M3_WTH_W2R_O_DDTDZ(:,:,IKE+1)=D_M3_WTH_W2R_O_DDTDZ(:,:,IKE)
!
END FUNCTION D_M3_WTH_W2R_O_DDTDZ
!----------------------------------------------------------------------------
FUNCTION M3_WTH_WR2(KKA,KKU,KKL,PREDTH1,PREDR1,PD,PKEFF,PTKE,PSQRT_TKE,PBLL_O_E,PBETA,PLEPS,PEMOIST,PDTDZ)
INTEGER, INTENT(IN) :: KKA
INTEGER, INTENT(IN) :: KKU
INTEGER, INTENT(IN) :: KKL
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDTH1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PKEFF
REAL, DIMENSION(:,:,:), INTENT(IN) :: PTKE
REAL, DIMENSION(:,:,:), INTENT(IN) :: PSQRT_TKE
REAL, DIMENSION(:,:,:), INTENT(IN) :: PBLL_O_E
REAL, DIMENSION(:,:,:), INTENT(IN) :: PBETA
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLEPS
REAL, DIMENSION(:,:,:), INTENT(IN) :: PEMOIST
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDTDZ
REAL, DIMENSION(SIZE(PD,1),SIZE(PD,2),SIZE(PD,3)) :: M3_WTH_WR2
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
M3_WTH_WR2(:,:,:) = - XCSHF*PKEFF*0.25*PBLL_O_E*XCTV*PEMOIST**2 &
*MZM(KKA,KKU,KKL,PBETA*PLEPS/(PSQRT_TKE*PTKE))/XCTD*PDTDZ/PD
!
M3_WTH_WR2(:,:,IKB-1)=M3_WTH_WR2(:,:,IKB)
M3_WTH_WR2(:,:,IKE+1)=M3_WTH_WR2(:,:,IKE)
!
END FUNCTION M3_WTH_WR2
!----------------------------------------------------------------------------
FUNCTION D_M3_WTH_WR2_O_DDTDZ(KKA,KKU,KKL,PREDTH1,PREDR1,PD,PKEFF,PTKE,PSQRT_TKE,PBLL_O_E,PBETA,PLEPS,PEMOIST)
INTEGER, INTENT(IN) :: KKA
INTEGER, INTENT(IN) :: KKU
INTEGER, INTENT(IN) :: KKL
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDTH1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PKEFF
REAL, DIMENSION(:,:,:), INTENT(IN) :: PTKE
REAL, DIMENSION(:,:,:), INTENT(IN) :: PSQRT_TKE
REAL, DIMENSION(:,:,:), INTENT(IN) :: PBLL_O_E
REAL, DIMENSION(:,:,:), INTENT(IN) :: PBETA
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLEPS
REAL, DIMENSION(:,:,:), INTENT(IN) :: PEMOIST
REAL, DIMENSION(SIZE(PD,1),SIZE(PD,2),SIZE(PD,3)) :: D_M3_WTH_WR2_O_DDTDZ
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
D_M3_WTH_WR2_O_DDTDZ(:,:,:) = - XCSHF*PKEFF*0.25*PBLL_O_E*XCTV*PEMOIST**2 &
*MZM(KKA,KKU,KKL,PBETA*PLEPS/(PSQRT_TKE*PTKE))/XCTD/PD &
* (1. - PREDTH1*(1.5+PREDTH1+PREDR1)/PD)
!
D_M3_WTH_WR2_O_DDTDZ(:,:,IKB-1)=D_M3_WTH_WR2_O_DDTDZ(:,:,IKB)
D_M3_WTH_WR2_O_DDTDZ(:,:,IKE+1)=D_M3_WTH_WR2_O_DDTDZ(:,:,IKE)
!
END FUNCTION D_M3_WTH_WR2_O_DDTDZ
!----------------------------------------------------------------------------
FUNCTION M3_WTH_WTHR(KKA,KKU,KKL,PREDR1,PD,PKEFF,PTKE,PSQRT_TKE,PBETA,PLEPS,PEMOIST)
INTEGER, INTENT(IN) :: KKA
INTEGER, INTENT(IN) :: KKU
INTEGER, INTENT(IN) :: KKL
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PKEFF
REAL, DIMENSION(:,:,:), INTENT(IN) :: PTKE
REAL, DIMENSION(:,:,:), INTENT(IN) :: PSQRT_TKE
REAL, DIMENSION(:,:,:), INTENT(IN) :: PBETA
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLEPS
REAL, DIMENSION(:,:,:), INTENT(IN) :: PEMOIST
REAL, DIMENSION(SIZE(PREDR1,1),SIZE(PREDR1,2),SIZE(PREDR1,3)) :: M3_WTH_WTHR
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
!M3_WTH_WTHR(:,:,:) = XCSHF*PKEFF*PEMOIST/MZM(KKA,KKU,KKL,PBETA*PTKE*PSQRT_TKE) &
! *0.5*PLEPS/XCTD*(1+PREDR1)/PD
M3_WTH_WTHR(:,:,:) = XCSHF*PKEFF*PEMOIST*MZM(KKA,KKU,KKL,PBETA/PTKE*PSQRT_TKE) &
*0.5*PLEPS/XCTD*(1+PREDR1)/PD
!
M3_WTH_WTHR(:,:,IKB-1)=M3_WTH_WTHR(:,:,IKB)
M3_WTH_WTHR(:,:,IKE+1)=M3_WTH_WTHR(:,:,IKE)
!
END FUNCTION M3_WTH_WTHR
!----------------------------------------------------------------------------
FUNCTION D_M3_WTH_WTHR_O_DDTDZ(PM3_WTH_WTHR,PREDTH1,PREDR1,PD,PBLL_O_E,PETHETA)
REAL, DIMENSION(:,:,:), INTENT(IN) :: PM3_WTH_WTHR
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDTH1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PBLL_O_E
REAL, DIMENSION(:,:,:), INTENT(IN) :: PETHETA
REAL, DIMENSION(SIZE(PD,1),SIZE(PD,2),SIZE(PD,3)) :: D_M3_WTH_WTHR_O_DDTDZ
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
D_M3_WTH_WTHR_O_DDTDZ(:,:,:) = - PM3_WTH_WTHR * (1.5+PREDTH1+PREDR1)/PD*XCTV*PBLL_O_E*PETHETA
!
D_M3_WTH_WTHR_O_DDTDZ(:,:,IKB-1)=D_M3_WTH_WTHR_O_DDTDZ(:,:,IKB)
D_M3_WTH_WTHR_O_DDTDZ(:,:,IKE+1)=D_M3_WTH_WTHR_O_DDTDZ(:,:,IKE)
!
END FUNCTION D_M3_WTH_WTHR_O_DDTDZ
!----------------------------------------------------------------------------
FUNCTION M3_TH2_W2TH(KKA,KKU,KKL,PREDTH1,PREDR1,PD,PDTDZ,PLM,PLEPS,PTKE)
INTEGER, INTENT(IN) :: KKA
INTEGER, INTENT(IN) :: KKU
INTEGER, INTENT(IN) :: KKL
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDTH1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDTDZ
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLM
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLEPS
REAL, DIMENSION(:,:,:), INTENT(IN) :: PTKE
REAL, DIMENSION(SIZE(PD,1),SIZE(PD,2),SIZE(PD,3)) :: M3_TH2_W2TH
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
M3_TH2_W2TH(:,:,:) = - MZF(KKA,KKU,KKL,(1.-0.5*PREDR1*(1.+PREDR1)/PD)/(1.+PREDTH1)*PDTDZ) &
* 1.5*PLM*PLEPS/PTKE*XCTV
!
M3_TH2_W2TH(:,:,IKB-1)=M3_TH2_W2TH(:,:,IKB)
M3_TH2_W2TH(:,:,IKE+1)=M3_TH2_W2TH(:,:,IKE)
!
END FUNCTION M3_TH2_W2TH
!----------------------------------------------------------------------------
FUNCTION D_M3_TH2_W2TH_O_DDTDZ(KKA,KKU,KKL,PREDTH1,PREDR1,PD,PLM,PLEPS,PTKE,OUSERV)
INTEGER, INTENT(IN) :: KKA
INTEGER, INTENT(IN) :: KKU
INTEGER, INTENT(IN) :: KKL
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDTH1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLM
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLEPS
REAL, DIMENSION(:,:,:), INTENT(IN) :: PTKE
LOGICAL, INTENT(IN) :: OUSERV
REAL, DIMENSION(SIZE(PD,1),SIZE(PD,2),SIZE(PD,3)) :: D_M3_TH2_W2TH_O_DDTDZ
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
IF (OUSERV) THEN
! D_M3_TH2_W2TH_O_DDTDZ(:,:,:) = - 1.5*PLM*PLEPS/PTKE*XCTV * MZF(KKA,KKU,KKL, &
! (1.-0.5*PREDR1*(1.+PREDR1)/PD)*(1.-(1.5+PREDTH1+PREDR1)*(1.+PREDTH1)/PD ) &
! / (1.+PREDTH1)**2 )
D_M3_TH2_W2TH_O_DDTDZ(:,:,:) = - 1.5*PLM*PLEPS/PTKE*XCTV * MZF(KKA,KKU,KKL, &
(1.-0.5*PREDR1*(1.+PREDR1)/PD)*(1.-(1.5+PREDTH1+PREDR1)* &
PREDTH1*(1.+PREDTH1)/PD ) / (1.+PREDTH1)**2 )
ELSE
D_M3_TH2_W2TH_O_DDTDZ(:,:,:) = - 1.5*PLM*PLEPS/PTKE*XCTV * MZF(KKA,KKU,KKL,1./(1.+PREDTH1)**2)
END IF
!
D_M3_TH2_W2TH_O_DDTDZ(:,:,IKB-1)=D_M3_TH2_W2TH_O_DDTDZ(:,:,IKB)
D_M3_TH2_W2TH_O_DDTDZ(:,:,IKE+1)=D_M3_TH2_W2TH_O_DDTDZ(:,:,IKE)
!
END FUNCTION D_M3_TH2_W2TH_O_DDTDZ
!----------------------------------------------------------------------------
FUNCTION M3_TH2_WTH2(KKA,KKU,KKL,PREDTH1,PREDR1,PD,PLEPS,PSQRT_TKE)
INTEGER, INTENT(IN) :: KKA
INTEGER, INTENT(IN) :: KKU
INTEGER, INTENT(IN) :: KKL
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDTH1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLEPS
REAL, DIMENSION(:,:,:), INTENT(IN) :: PSQRT_TKE
REAL, DIMENSION(SIZE(PD,1),SIZE(PD,2),SIZE(PD,3)) :: M3_TH2_WTH2
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
M3_TH2_WTH2(:,:,:) = PLEPS*0.5/XCTD/PSQRT_TKE &
* MZF(KKA,KKU,KKL, (1.+0.5*PREDTH1+1.5*PREDR1+0.5*PREDR1**2)/PD )
!
M3_TH2_WTH2(:,:,IKB-1)=M3_TH2_WTH2(:,:,IKB)
M3_TH2_WTH2(:,:,IKE+1)=M3_TH2_WTH2(:,:,IKE)
!
END FUNCTION M3_TH2_WTH2
!----------------------------------------------------------------------------
FUNCTION D_M3_TH2_WTH2_O_DDTDZ(KKA,KKU,KKL,PREDTH1,PREDR1,PD,PLEPS,PSQRT_TKE,PBLL_O_E,PETHETA)
INTEGER, INTENT(IN) :: KKA
INTEGER, INTENT(IN) :: KKU
INTEGER, INTENT(IN) :: KKL
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDTH1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLEPS
REAL, DIMENSION(:,:,:), INTENT(IN) :: PSQRT_TKE
REAL, DIMENSION(:,:,:), INTENT(IN) :: PBLL_O_E
REAL, DIMENSION(:,:,:), INTENT(IN) :: PETHETA
REAL, DIMENSION(SIZE(PD,1),SIZE(PD,2),SIZE(PD,3)) :: D_M3_TH2_WTH2_O_DDTDZ
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
D_M3_TH2_WTH2_O_DDTDZ(:,:,:) = PLEPS*0.5/XCTD/PSQRT_TKE*XCTV &
* MZF(KKA,KKU,KKL, PBLL_O_E*PETHETA* (0.5/PD &
- (1.5+PREDTH1+PREDR1)*(1.+0.5*PREDTH1+1.5*PREDR1+0.5*PREDR1**2)/PD**2 &
) )
!
D_M3_TH2_WTH2_O_DDTDZ(:,:,IKB-1)=D_M3_TH2_WTH2_O_DDTDZ(:,:,IKB)
D_M3_TH2_WTH2_O_DDTDZ(:,:,IKE+1)=D_M3_TH2_WTH2_O_DDTDZ(:,:,IKE)
!
END FUNCTION D_M3_TH2_WTH2_O_DDTDZ
!----------------------------------------------------------------------------
FUNCTION M3_TH2_W2R(KKA,KKU,KKL,PD,PLM,PLEPS,PTKE,PBLL_O_E,PEMOIST,PDTDZ)
INTEGER, INTENT(IN) :: KKA
INTEGER, INTENT(IN) :: KKU
INTEGER, INTENT(IN) :: KKL
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLM
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLEPS
REAL, DIMENSION(:,:,:), INTENT(IN) :: PTKE
REAL, DIMENSION(:,:,:), INTENT(IN) :: PBLL_O_E
REAL, DIMENSION(:,:,:), INTENT(IN) :: PEMOIST
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDTDZ
REAL, DIMENSION(SIZE(PD,1),SIZE(PD,2),SIZE(PD,3)) :: M3_TH2_W2R
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
M3_TH2_W2R(:,:,:) = 0.75*XCTV**2*MZF(KKA,KKU,KKL,PBLL_O_E*PEMOIST/PD*PDTDZ**2)*PLM*PLEPS/PTKE
!
M3_TH2_W2R(:,:,IKB-1)=M3_TH2_W2R(:,:,IKB)
M3_TH2_W2R(:,:,IKE+1)=M3_TH2_W2R(:,:,IKE)
!
END FUNCTION M3_TH2_W2R
!----------------------------------------------------------------------------
FUNCTION D_M3_TH2_W2R_O_DDTDZ(KKA,KKU,KKL,PREDTH1,PREDR1,PD,PLM,PLEPS,PTKE,PBLL_O_E,PEMOIST,PDTDZ)
INTEGER, INTENT(IN) :: KKA
INTEGER, INTENT(IN) :: KKU
INTEGER, INTENT(IN) :: KKL
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDTH1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLM
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLEPS
REAL, DIMENSION(:,:,:), INTENT(IN) :: PTKE
REAL, DIMENSION(:,:,:), INTENT(IN) :: PBLL_O_E
REAL, DIMENSION(:,:,:), INTENT(IN) :: PEMOIST
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDTDZ
REAL, DIMENSION(SIZE(PD,1),SIZE(PD,2),SIZE(PD,3)) :: D_M3_TH2_W2R_O_DDTDZ
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
D_M3_TH2_W2R_O_DDTDZ(:,:,:) = 0.75*XCTV**2*PLM*PLEPS/PTKE &
* MZF(KKA,KKU,KKL, PBLL_O_E*PEMOIST/PD*PDTDZ*(2.-PREDTH1*(1.5+PREDTH1+PREDR1)/PD) )
!
D_M3_TH2_W2R_O_DDTDZ(:,:,IKB-1)=D_M3_TH2_W2R_O_DDTDZ(:,:,IKB)
D_M3_TH2_W2R_O_DDTDZ(:,:,IKE+1)=D_M3_TH2_W2R_O_DDTDZ(:,:,IKE)
!
END FUNCTION D_M3_TH2_W2R_O_DDTDZ
!----------------------------------------------------------------------------
FUNCTION M3_TH2_WR2(KKA,KKU,KKL,PD,PLEPS,PSQRT_TKE,PBLL_O_E,PEMOIST,PDTDZ)
INTEGER, INTENT(IN) :: KKA
INTEGER, INTENT(IN) :: KKU
INTEGER, INTENT(IN) :: KKL
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLEPS
REAL, DIMENSION(:,:,:), INTENT(IN) :: PSQRT_TKE
REAL, DIMENSION(:,:,:), INTENT(IN) :: PBLL_O_E
REAL, DIMENSION(:,:,:), INTENT(IN) :: PEMOIST
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDTDZ
REAL, DIMENSION(SIZE(PD,1),SIZE(PD,2),SIZE(PD,3)) :: M3_TH2_WR2
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
M3_TH2_WR2(:,:,:) = 0.25*XCTV**2*MZF(KKA,KKU,KKL,(PBLL_O_E*PEMOIST*PDTDZ)**2/PD)*PLEPS/PSQRT_TKE/XCTD
!
M3_TH2_WR2(:,:,IKB-1)=M3_TH2_WR2(:,:,IKB)
M3_TH2_WR2(:,:,IKE+1)=M3_TH2_WR2(:,:,IKE)
!
END FUNCTION M3_TH2_WR2
!----------------------------------------------------------------------------
FUNCTION D_M3_TH2_WR2_O_DDTDZ(KKA,KKU,KKL,PREDTH1,PREDR1,PD,PLEPS,PSQRT_TKE,PBLL_O_E,PEMOIST,PDTDZ)
INTEGER, INTENT(IN) :: KKA
INTEGER, INTENT(IN) :: KKU
INTEGER, INTENT(IN) :: KKL
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDTH1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLEPS
REAL, DIMENSION(:,:,:), INTENT(IN) :: PSQRT_TKE
REAL, DIMENSION(:,:,:), INTENT(IN) :: PBLL_O_E
REAL, DIMENSION(:,:,:), INTENT(IN) :: PEMOIST
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDTDZ
REAL, DIMENSION(SIZE(PD,1),SIZE(PD,2),SIZE(PD,3)) :: D_M3_TH2_WR2_O_DDTDZ
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
D_M3_TH2_WR2_O_DDTDZ(:,:,:) = 0.25*XCTV**2*PLEPS/PSQRT_TKE/XCTD &
* MZF(KKA,KKU,KKL, (PBLL_O_E*PEMOIST)**2*PDTDZ/PD*(2.-PREDTH1*(1.5+PREDTH1+PREDR1)/PD) )
!
D_M3_TH2_WR2_O_DDTDZ(:,:,IKB-1)=D_M3_TH2_WR2_O_DDTDZ(:,:,IKB)
D_M3_TH2_WR2_O_DDTDZ(:,:,IKE+1)=D_M3_TH2_WR2_O_DDTDZ(:,:,IKE)
!
END FUNCTION D_M3_TH2_WR2_O_DDTDZ
!----------------------------------------------------------------------------
FUNCTION M3_TH2_WTHR(KKA,KKU,KKL,PREDR1,PD,PLEPS,PSQRT_TKE,PBLL_O_E,PEMOIST,PDTDZ)
INTEGER, INTENT(IN) :: KKA
INTEGER, INTENT(IN) :: KKU
INTEGER, INTENT(IN) :: KKL
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLEPS
REAL, DIMENSION(:,:,:), INTENT(IN) :: PSQRT_TKE
REAL, DIMENSION(:,:,:), INTENT(IN) :: PBLL_O_E
REAL, DIMENSION(:,:,:), INTENT(IN) :: PEMOIST
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDTDZ
REAL, DIMENSION(SIZE(PD,1),SIZE(PD,2),SIZE(PD,3)) :: M3_TH2_WTHR
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
M3_TH2_WTHR(:,:,:) = - 0.5*XCTV*PLEPS/PSQRT_TKE/XCTD &
* MZF(KKA,KKU,KKL, PBLL_O_E*PEMOIST*PDTDZ*(1.+PREDR1)/PD )
!
M3_TH2_WTHR(:,:,IKB-1)=M3_TH2_WTHR(:,:,IKB)
M3_TH2_WTHR(:,:,IKE+1)=M3_TH2_WTHR(:,:,IKE)
!
END FUNCTION M3_TH2_WTHR
!----------------------------------------------------------------------------
FUNCTION D_M3_TH2_WTHR_O_DDTDZ(KKA,KKU,KKL,PREDTH1,PREDR1,PD,PLEPS,PSQRT_TKE,PBLL_O_E,PEMOIST,PDTDZ)
INTEGER, INTENT(IN) :: KKA
INTEGER, INTENT(IN) :: KKU
INTEGER, INTENT(IN) :: KKL
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDTH1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLEPS
REAL, DIMENSION(:,:,:), INTENT(IN) :: PSQRT_TKE
REAL, DIMENSION(:,:,:), INTENT(IN) :: PBLL_O_E
REAL, DIMENSION(:,:,:), INTENT(IN) :: PEMOIST
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDTDZ
REAL, DIMENSION(SIZE(PD,1),SIZE(PD,2),SIZE(PD,3)) :: D_M3_TH2_WTHR_O_DDTDZ
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
D_M3_TH2_WTHR_O_DDTDZ(:,:,:) = - 0.5*XCTV*PLEPS/PSQRT_TKE/XCTD &
* MZF(KKA,KKU,KKL, PBLL_O_E*PEMOIST*(1.+PREDR1)/PD * (1. -PREDTH1*(1.5+PREDTH1+PREDR1)/PD) )
!
D_M3_TH2_WTHR_O_DDTDZ(:,:,IKB-1)=D_M3_TH2_WTHR_O_DDTDZ(:,:,IKB)
D_M3_TH2_WTHR_O_DDTDZ(:,:,IKE+1)=D_M3_TH2_WTHR_O_DDTDZ(:,:,IKE)
!
END FUNCTION D_M3_TH2_WTHR_O_DDTDZ
!----------------------------------------------------------------------------
FUNCTION M3_THR_WTHR(KKA,KKU,KKL,PREDTH1,PREDR1,PD,PLEPS,PSQRT_TKE)
INTEGER, INTENT(IN) :: KKA
INTEGER, INTENT(IN) :: KKU
INTEGER, INTENT(IN) :: KKL
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDTH1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLEPS
REAL, DIMENSION(:,:,:), INTENT(IN) :: PSQRT_TKE
REAL, DIMENSION(SIZE(PD,1),SIZE(PD,2),SIZE(PD,3)) :: M3_THR_WTHR
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
M3_THR_WTHR(:,:,:) = 0.5*PLEPS/PSQRT_TKE/XCTD &
* MZF(KKA,KKU,KKL, (1.+PREDTH1)*(1.+PREDR1)/PD )
!
M3_THR_WTHR(:,:,IKB-1)=M3_THR_WTHR(:,:,IKB)
M3_THR_WTHR(:,:,IKE+1)=M3_THR_WTHR(:,:,IKE)
!
END FUNCTION M3_THR_WTHR
!----------------------------------------------------------------------------
FUNCTION D_M3_THR_WTHR_O_DDTDZ(KKA,KKU,KKL,PREDTH1,PREDR1,PD,PLEPS,PSQRT_TKE,PBLL_O_E,PETHETA)
INTEGER, INTENT(IN) :: KKA
INTEGER, INTENT(IN) :: KKU
INTEGER, INTENT(IN) :: KKL
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDTH1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLEPS
REAL, DIMENSION(:,:,:), INTENT(IN) :: PSQRT_TKE
REAL, DIMENSION(:,:,:), INTENT(IN) :: PBLL_O_E
REAL, DIMENSION(:,:,:), INTENT(IN) :: PETHETA
REAL, DIMENSION(SIZE(PD,1),SIZE(PD,2),SIZE(PD,3)) :: D_M3_THR_WTHR_O_DDTDZ
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
D_M3_THR_WTHR_O_DDTDZ(:,:,:) = 0.5*PLEPS/PSQRT_TKE/XCTD * XCTV &
* MZF(KKA,KKU,KKL, PETHETA*PBLL_O_E/PD*(1.+PREDR1)*(1.-(1.+PREDTH1)*(1.5+PREDTH1+PREDR1)/PD) )
!
D_M3_THR_WTHR_O_DDTDZ(:,:,IKB-1)=D_M3_THR_WTHR_O_DDTDZ(:,:,IKB)
D_M3_THR_WTHR_O_DDTDZ(:,:,IKE+1)=D_M3_THR_WTHR_O_DDTDZ(:,:,IKE)
!
END FUNCTION D_M3_THR_WTHR_O_DDTDZ
!----------------------------------------------------------------------------
FUNCTION M3_THR_WTH2(KKA,KKU,KKL,PREDR1,PD,PLEPS,PSQRT_TKE,PBLL_O_E,PETHETA,PDRDZ)
INTEGER, INTENT(IN) :: KKA
INTEGER, INTENT(IN) :: KKU
INTEGER, INTENT(IN) :: KKL
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLEPS
REAL, DIMENSION(:,:,:), INTENT(IN) :: PSQRT_TKE
REAL, DIMENSION(:,:,:), INTENT(IN) :: PBLL_O_E
REAL, DIMENSION(:,:,:), INTENT(IN) :: PETHETA
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDRDZ
REAL, DIMENSION(SIZE(PD,1),SIZE(PD,2),SIZE(PD,3)) :: M3_THR_WTH2
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
M3_THR_WTH2(:,:,:) = - 0.25*PLEPS/PSQRT_TKE/XCTD*XCTV &
* MZF(KKA,KKU,KKL, (1.+PREDR1)*PBLL_O_E*PETHETA*PDRDZ/PD )
!
M3_THR_WTH2(:,:,IKB-1)=M3_THR_WTH2(:,:,IKB)
M3_THR_WTH2(:,:,IKE+1)=M3_THR_WTH2(:,:,IKE)
!
END FUNCTION M3_THR_WTH2
!----------------------------------------------------------------------------
FUNCTION D_M3_THR_WTH2_O_DDTDZ(KKA,KKU,KKL,PREDTH1,PREDR1,PD,PLEPS,PSQRT_TKE,PBLL_O_E,PETHETA,PDRDZ)
INTEGER, INTENT(IN) :: KKA
INTEGER, INTENT(IN) :: KKU
INTEGER, INTENT(IN) :: KKL
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDTH1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLEPS
REAL, DIMENSION(:,:,:), INTENT(IN) :: PSQRT_TKE
REAL, DIMENSION(:,:,:), INTENT(IN) :: PBLL_O_E
REAL, DIMENSION(:,:,:), INTENT(IN) :: PETHETA
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDRDZ
REAL, DIMENSION(SIZE(PD,1),SIZE(PD,2),SIZE(PD,3)) :: D_M3_THR_WTH2_O_DDTDZ
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
D_M3_THR_WTH2_O_DDTDZ(:,:,:) = - 0.25*PLEPS/PSQRT_TKE/XCTD*XCTV**2 &
* MZF(KKA,KKU,KKL, -(1.+PREDR1)*(PBLL_O_E*PETHETA/PD)**2*PDRDZ*(1.5+PREDTH1+PREDR1) )
!
D_M3_THR_WTH2_O_DDTDZ(:,:,IKB-1)=D_M3_THR_WTH2_O_DDTDZ(:,:,IKB)
D_M3_THR_WTH2_O_DDTDZ(:,:,IKE+1)=D_M3_THR_WTH2_O_DDTDZ(:,:,IKE)
!
END FUNCTION D_M3_THR_WTH2_O_DDTDZ
!----------------------------------------------------------------------------
FUNCTION D_M3_THR_WTH2_O_DDRDZ(KKA,KKU,KKL,PREDTH1,PREDR1,PD,PLEPS,PSQRT_TKE,PBLL_O_E,PETHETA)
INTEGER, INTENT(IN) :: KKA
INTEGER, INTENT(IN) :: KKU
INTEGER, INTENT(IN) :: KKL
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDTH1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLEPS
REAL, DIMENSION(:,:,:), INTENT(IN) :: PSQRT_TKE
REAL, DIMENSION(:,:,:), INTENT(IN) :: PBLL_O_E
REAL, DIMENSION(:,:,:), INTENT(IN) :: PETHETA
REAL, DIMENSION(SIZE(PD,1),SIZE(PD,2),SIZE(PD,3)) :: D_M3_THR_WTH2_O_DDRDZ
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
D_M3_THR_WTH2_O_DDRDZ(:,:,:) = - 0.25*PLEPS/PSQRT_TKE/XCTD*XCTV &
* MZF(KKA,KKU,KKL, PBLL_O_E*PETHETA/PD &
*(-(1.+PREDR1)*PREDR1/PD*(1.5+PREDTH1+PREDR1)+(1.+2.*PREDR1)) &
)
!
D_M3_THR_WTH2_O_DDRDZ(:,:,IKB-1)=D_M3_THR_WTH2_O_DDRDZ(:,:,IKB)
D_M3_THR_WTH2_O_DDRDZ(:,:,IKE+1)=D_M3_THR_WTH2_O_DDRDZ(:,:,IKE)
!
END FUNCTION D_M3_THR_WTH2_O_DDRDZ
!----------------------------------------------------------------------------
FUNCTION M3_THR_W2TH(KKA,KKU,KKL,PREDR1,PD,PLM,PLEPS,PTKE,PDRDZ)
INTEGER, INTENT(IN) :: KKA
INTEGER, INTENT(IN) :: KKU
INTEGER, INTENT(IN) :: KKL
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLM
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLEPS
REAL, DIMENSION(:,:,:), INTENT(IN) :: PTKE
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDRDZ
REAL, DIMENSION(SIZE(PD,1),SIZE(PD,2),SIZE(PD,3)) :: M3_THR_W2TH
INTEGER :: IKB, IKE
!
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
M3_THR_W2TH(:,:,:) = - 0.75*PLM*PLEPS/PTKE * XCTV &
* MZF(KKA,KKU,KKL, (1.+PREDR1)*PDRDZ/PD )
!
M3_THR_W2TH(:,:,IKB-1)=M3_THR_W2TH(:,:,IKB)
M3_THR_W2TH(:,:,IKE+1)=M3_THR_W2TH(:,:,IKE)
!
END FUNCTION M3_THR_W2TH
!----------------------------------------------------------------------------
FUNCTION D_M3_THR_W2TH_O_DDTDZ(KKA,KKU,KKL,PREDTH1,PREDR1,PD,PLM,PLEPS,PTKE,PBLL_O_E,PDRDZ,PETHETA)
INTEGER, INTENT(IN) :: KKA
INTEGER, INTENT(IN) :: KKU
INTEGER, INTENT(IN) :: KKL
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDTH1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PREDR1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PD
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLM
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLEPS
REAL, DIMENSION(:,:,:), INTENT(IN) :: PTKE
REAL, DIMENSION(:,:,:), INTENT(IN) :: PBLL_O_E
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDRDZ
REAL, DIMENSION(:,:,:), INTENT(IN) :: PETHETA
REAL, DIMENSION(SIZE(PD,1),SIZE(PD,2),SIZE(PD,3)) :: D_M3_THR_W2TH_O_DDTDZ
INTEGER :: IKB, IKE