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!MNH_LIC Copyright 1994-2020 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.
!-----------------------------------------------------------------
! ####################
MODULE MODE_PRANDTL
USE PARKIND1, ONLY : JPRB
USE YOMHOOK , ONLY : LHOOK, DR_HOOK
! ####################
!
!* modification 08/2010 V. Masson smoothing of the discontinuity in functions
! used for implicitation of exchange coefficients
! 05/2020 V. Masson and C. Lac : bug in D_PHI3DTDZ2_O_DDTDZ
!
USE MODD_CTURB, ONLY : XCTV, XCSHF, XCTD, XPHI_LIM, XCPR3, XCPR4, XCPR5
USE MODD_PARAMETERS, ONLY : JPVEXT_TURB
!
IMPLICIT NONE
!----------------------------------------------------------------------------
CONTAINS
!----------------------------------------------------------------------------
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SUBROUTINE PRANDTL(KKA,KKU,KKL,KRR,KRRI,OTURB_DIAG, &
HTURBDIM, &
TPFILE, &
PDXX,PDYY,PDZZ,PDZX,PDZY, &
PTHVREF,PLOCPEXNM,PATHETA,PAMOIST, &
PLM,PLEPS,PTKEM,PTHLM,PRM,PSVM,PSRCM, &
PREDTH1,PREDR1, &
PRED2TH3, PRED2R3, PRED2THR3, &
PREDS1,PRED2THS3, PRED2RS3, &
PBLL_O_E, &
PETHETA, PEMOIST )
! ###########################################################
!
!
!!**** *PRANDTL* - routine to compute the Prandtl turbulent numbers
!!
!! PURPOSE
!! -------
! The purpose of this routine is to compute the Redelsperger
! numbers and then get the turbulent Prandtl and Schmidt numbers:
! * for the heat fluxes - PHI3 = 1/ Prandtl
! * for the moisture fluxes - PSI3 = 1/ Schmidt
!
!!** METHOD
!! ------
!! The following steps are performed:
!!
!! 1 - default values of 1 are taken for phi3 and psi3 and different masks
!! are defined depending on the presence of turbulence, stratification and
!! humidity. The 1D Redelsperger numbers are computed
!! * ZREDTH1 : (g / THVREF ) (LT**2 / TKE ) ETHETA (D Theta / Dz)
!! * ZREDR1 : (g / THVREF ) (LT**2 / TKE ) EMOIST (D TW / Dz)
!! 2 - 3D Redelsperger numbers are computed only for turbulent
!! grid points where ZREDTH1 or ZREDR1 are > 0.
!! 3 - PHI3 is computed only for turbulent grid points where ZREDTH1 > 0
!! (turbulent thermally stratified points)
!! 4 - PSI3 is computed only for turbulent grid points where ZREDR1 > 0
!! (turbulent moist points)
!!
!!
!! EXTERNAL
!! --------
!! FUNCTIONs ETHETA and EMOIST :
!! allows to compute the coefficients
!! for the turbulent correlation between any variable
!! and the virtual potential temperature, of its correlations
!! with the conservative potential temperature and the humidity
!! conservative variable:
!! ------- ------- -------
!! A' Thv' = ETHETA A' Thl' + EMOIST A' Rnp'
!!
!! GX_M_M, GY_M_M, GZ_M_M : Cartesian gradient operators
!! MZM : Shuman function (mean operator in the z direction)
!! Module MODI_ETHETA : interface module for ETHETA
!! Module MODI_EMOIST : interface module for EMOIST
!! Module MODI_SHUMAN : interface module for Shuman operators
!!
!! IMPLICIT ARGUMENTS
!! ------------------
!! Module MODD_CST : contains physical constants
!! XG : gravity constant
!!
!! Module MODD_CTURB: contains the set of constants for
!! the turbulence scheme
!! XCTV,XCPR2 : constants for the turbulent prandtl numbers
!! XTKEMIN : minimum value allowed for the TKE
!!
!! Module MODD_PARAMETERS
!! JPVEXT_TURB : number of vertical marginal points
!!
!! REFERENCE
!! ---------
!! Book 2 of documentation (routine PRANDTL)
!! Book 1 of documentation (Chapter: Turbulence)
!!
!! AUTHOR
!! ------
!! Joan Cuxart * INM and Meteo-France *
!!
!! MODIFICATIONS
!! -------------
!! Original 18/10/94
!! Modifications: Feb 14, 1995 (J.Cuxart and J.Stein)
!! Doctorization and Optimization
!! Modifications: March 21, 1995 (J.M. Carriere)
!! Introduction of cloud water
!! Modifications: March 21, 1995 (J. Cuxart and J.Stein)
!! Phi3 and Psi3 at w point + cleaning
!! Modifications: July 2, 1995 (J.Cuxart and Ph.Bougeault)
!! change the value of Phi3 and Psi3 if negative
!! Modifications: Sept 20, 1995 (J. Stein, J. Cuxart, J.L. Redelsperger)
!! remove the Where + use REDTH1+REDR1 for the tests
!! Modifications: October 10, 1995 (J. Cuxart and J.Stein)
!! Psi3 for tPREDS1he scalar variables
!! Modifications: February 27, 1996 (J.Stein) optimization
!! Modifications: June 15, 1996 (P.Jabouille) return to the previous
!! computation of Phi3 and Psi3
!! Modifications: October 10, 1996 (J. Stein) change the temporal
!! discretization
!! Modifications: May 23, 1997 (J. Stein) bug in 3D Redels number at ground
!! with orography
!! Modifications: Feb 20, 1998 (J. Stein) bug in all the 3D cases due to
!! the use of ZW1 instead of ZW2
!! Feb 20, 2003 (JP Pinty) Add PFRAC_ICE
!! July 2005 (Tomas, Masson) implicitation of PHI3 and PSI3
!! October 2009 (G. Tanguy) add ILENCH=LEN(YCOMMENT) after
!! change of YCOMMENT
!! 2012-02 Y. Seity, add possibility to run with reversed
!! vertical levels
!! Modifications: July 2015 (Wim de Rooy) LHARAT (Racmo turbulence) switch
!! 2017-09 J.Escobar, use epsilon XMNH_TINY_12 for R*4
!! Philippe Wautelet: 05/2016-04/2018: new data structures and calls for I/O
!! JL Redelsperger 03/2021 : adding Ocean case for temperature only
!! --------------------------------------------------------------------------
!
!* 0. DECLARATIONS
! ------------
!
USE PARKIND1, ONLY : JPRB
USE YOMHOOK , ONLY : LHOOK, DR_HOOK
!
USE MODD_CST
USE MODD_CONF
USE MODD_CTURB
USE MODD_DYN_n, ONLY: LOCEAN
USE MODD_FIELD, ONLY: TFIELDDATA, TYPEREAL
USE MODD_IO, ONLY: TFILEDATA
USE MODD_PARAMETERS
!
USE MODI_GRADIENT_M
USE MODE_EMOIST, ONLY: EMOIST
USE MODE_ETHETA, ONLY: ETHETA
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USE MODI_SHUMAN, ONLY: MZM
USE MODE_IO_FIELD_WRITE, ONLY: IO_FIELD_WRITE
!
IMPLICIT NONE
!
!
!* 0.1 declarations of arguments
!
INTEGER, INTENT(IN) :: KKA !near ground array index
INTEGER, INTENT(IN) :: KKU !uppest atmosphere array index
INTEGER, INTENT(IN) :: KKL !vert. levels type 1=MNH -1=ARO
INTEGER, INTENT(IN) :: KRR ! number of moist var.
INTEGER, INTENT(IN) :: KRRI ! number of ice var.
!
LOGICAL, INTENT(IN) :: OTURB_DIAG ! switch to write some
! diagnostic fields in the syncronous FM-file
CHARACTER(LEN=4), INTENT(IN) :: HTURBDIM ! Kind of turbulence param.
TYPE(TFILEDATA), INTENT(IN) :: TPFILE ! Output file
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDXX,PDYY,PDZZ,PDZX,PDZY
! metric coefficients
!
REAL, DIMENSION(:,:,:), INTENT(IN) :: PTHVREF ! Virtual Potential Temp.
! of the reference state
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLOCPEXNM ! Lv(T)/Cp/Exner at t-1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PATHETA ! coefficients between
REAL, DIMENSION(:,:,:), INTENT(IN) :: PAMOIST ! s and Thetal and Rnp
!
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLM ! Turbulent Mixing length
REAL, DIMENSION(:,:,:), INTENT(IN) :: PLEPS ! Dissipative length
REAL, DIMENSION(:,:,:), INTENT(IN) :: PTHLM,PTKEM! Conservative Potential
! Temperature and TKE at t-1
REAL, DIMENSION(:,:,:,:), INTENT(IN) :: PRM ! Mixing ratios at t-1
! with PRM(:,:,:,1) = cons.
! mixing ratio
REAL, DIMENSION(:,:,:,:), INTENT(IN) :: PSVM ! Scalars at t-1
REAL, DIMENSION(:,:,:), INTENT(IN) :: PSRCM
! s'r'c/2Sigma_s2 at t-1 multiplied by Lambda_3
!
!
REAL, DIMENSION(:,:,:), INTENT(OUT) :: PREDTH1 ! Redelsperger number R_theta
REAL, DIMENSION(:,:,:), INTENT(OUT) :: PREDR1 ! Redelsperger number R_q
REAL, DIMENSION(:,:,:), INTENT(OUT) :: PRED2TH3 ! Redelsperger number R*2_theta
REAL, DIMENSION(:,:,:), INTENT(OUT) :: PRED2R3 ! Redelsperger number R*2_q
REAL, DIMENSION(:,:,:), INTENT(OUT) :: PRED2THR3! Redelsperger number R*2_thq
REAL, DIMENSION(:,:,:,:), INTENT(OUT):: PREDS1 ! Redelsperger number R_s
REAL, DIMENSION(:,:,:,:), INTENT(OUT):: PRED2THS3! Redelsperger number R*2_thsv
REAL, DIMENSION(:,:,:,:), INTENT(OUT):: PRED2RS3 ! Redelsperger number R*2_qsv
REAL, DIMENSION(:,:,:), INTENT(OUT) :: PBLL_O_E! beta*Lk*Leps/tke
REAL, DIMENSION(:,:,:), INTENT(OUT) :: PETHETA ! coefficient E_theta
REAL, DIMENSION(:,:,:), INTENT(OUT) :: PEMOIST ! coefficient E_moist
!
!
! 0.2 declaration of local variables
!
REAL, DIMENSION(SIZE(PTHLM,1),SIZE(PTHLM,2),SIZE(PTHLM,3)) :: &
ZW1, ZW2, ZW3
! working variables
!
INTEGER :: IKB ! vertical index value for the first inner mass point
INTEGER :: IKE ! vertical index value for the last inner mass point
INTEGER :: IRESP ! Return code of FM routines
INTEGER :: ILENG ! Length of the data field in LFIFM file
INTEGER :: IGRID ! C-grid indicator in LFIFM file
INTEGER :: ILENCH ! Length of comment string in LFIFM file
CHARACTER (LEN=100) :: YCOMMENT ! comment string in LFIFM file
CHARACTER (LEN=16) :: YRECFM ! Name of the desired field in LFIFM file
INTEGER:: ISV ! number of scalar variables
INTEGER:: JSV ! loop index for the scalar variables
INTEGER :: JLOOP
REAL :: ZMINVAL
TYPE(TFIELDDATA) :: TZFIELD
! ---------------------------------------------------------------------------
!
!* 1. DEFAULT VALUES, 1D REDELSPERGER NUMBERS
! ----------------------------------------
!
REAL(KIND=JPRB) :: ZHOOK_HANDLE
IF (LHOOK) CALL DR_HOOK('PRANDTL',0,ZHOOK_HANDLE)
IF (LHARAT) THEN
PREDTH1(:,:,:)=0.
PREDR1(:,:,:)=0.
PRED2TH3(:,:,:)=0.
PRED2R3(:,:,:)=0.
PRED2THR3(:,:,:)=0.
PREDS1(:,:,:,:)=0.
PRED2THS3(:,:,:,:)=0.
PRED2RS3(:,:,:,:)=0.
PBLL_O_E(:,:,:)=0.
ENDIF
!
IKB = KKA+JPVEXT_TURB*KKL
IKE = KKU-JPVEXT_TURB*KKL
ILENG=SIZE(PTHLM,1)*SIZE(PTHLM,2)*SIZE(PTHLM,3)
ISV =SIZE(PSVM,4)
!
PETHETA(:,:,:) = MZM(ETHETA(KRR,KRRI,PTHLM,PRM,PLOCPEXNM,PATHETA,PSRCM), KKA, KKU, KKL)
PEMOIST(:,:,:) = MZM(EMOIST(KRR,KRRI,PTHLM,PRM,PLOCPEXNM,PAMOIST,PSRCM), KKA, KKU, KKL)
PETHETA(:,:,KKA) = 2.*PETHETA(:,:,IKB) - PETHETA(:,:,IKB+KKL)
PEMOIST(:,:,KKA) = 2.*PEMOIST(:,:,IKB) - PEMOIST(:,:,IKB+KKL)
!
!---------------------------------------------------------------------------
IF (.NOT. LHARAT) THEN
!
! 1.3 1D Redelsperger numbers
!
PBLL_O_E(:,:,:) = MZM(XG / PTHVREF(:,:,:) * PLM(:,:,:) * PLEPS(:,:,:) / PTKEM(:,:,:), KKA, KKU, KKL)
IF (KRR /= 0) THEN ! moist case
PREDTH1(:,:,:)= XCTV*PBLL_O_E(:,:,:) * PETHETA(:,:,:) * &
RODIER Quentin
committed
& GZ_M_W(KKA, KKU, KKL,PTHLM,PDZZ)
PREDR1(:,:,:) = XCTV*PBLL_O_E(:,:,:) * PEMOIST(:,:,:) * &
RODIER Quentin
committed
& GZ_M_W(KKA, KKU, KKL,PRM(:,:,:,1),PDZZ)
ELSE ! dry case
RODIER Quentin
committed
PREDTH1(:,:,:)= XCTV*PBLL_O_E(:,:,:) * GZ_M_W(KKA, KKU, KKL,PTHLM,PDZZ)
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PREDR1(:,:,:) = 0.
END IF
!
! 3. Limits on 1D Redelperger numbers
! --------------------------------
!
ZMINVAL = (1.-1./XPHI_LIM)
!
ZW1 = 1.
ZW2 = 1.
!
WHERE (PREDTH1+PREDR1<-ZMINVAL)
ZW1 = (-ZMINVAL) / (PREDTH1+PREDR1)
END WHERE
!
WHERE (PREDTH1<-ZMINVAL)
ZW2 = (-ZMINVAL) / (PREDTH1)
END WHERE
ZW2 = MIN(ZW1,ZW2)
!
ZW1 = 1.
WHERE (PREDR1<-ZMINVAL)
ZW1 = (-ZMINVAL) / (PREDR1)
END WHERE
ZW1 = MIN(ZW2,ZW1)
!
!
! 3. Modification of Mixing length and dissipative length
! ----------------------------------------------------
!
PBLL_O_E(:,:,:) = PBLL_O_E(:,:,:) * ZW1(:,:,:)
PREDTH1 (:,:,:) = PREDTH1 (:,:,:) * ZW1(:,:,:)
PREDR1 (:,:,:) = PREDR1 (:,:,:) * ZW1(:,:,:)
!
! 4. Threshold for very small (in absolute value) Redelperger numbers
! ----------------------------------------------------------------
!
ZW2=SIGN(1.,PREDTH1(:,:,:))
PREDTH1(:,:,:)= ZW2(:,:,:) * MAX(1.E-30, ZW2(:,:,:)*PREDTH1(:,:,:))
!
IF (KRR /= 0) THEN ! dry case
ZW2=SIGN(1.,PREDR1(:,:,:))
PREDR1(:,:,:)= ZW2(:,:,:) * MAX(1.E-30, ZW2(:,:,:)*PREDR1(:,:,:))
END IF
!
!
!---------------------------------------------------------------------------
!
! For the scalar variables
DO JSV=1,ISV
RODIER Quentin
committed
PREDS1(:,:,:,JSV)=XCTV*PBLL_O_E(:,:,:)*GZ_M_W(KKA, KKU, KKL,PSVM(:,:,:,JSV),PDZZ)
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END DO
!
DO JSV=1,ISV
ZW2=SIGN(1.,PREDS1(:,:,:,JSV))
PREDS1(:,:,:,JSV)= ZW2(:,:,:) * MAX(1.E-30, ZW2(:,:,:)*PREDS1(:,:,:,JSV))
END DO
!
!---------------------------------------------------------------------------
!
!* 2. 3D REDELSPERGER NUMBERS
! ------------------------
!
IF(HTURBDIM=='1DIM') THEN ! 1D case
!
!
PRED2TH3(:,:,:) = PREDTH1(:,:,:)**2
!
PRED2R3(:,:,:) = PREDR1(:,:,:) **2
!
PRED2THR3(:,:,:) = PREDTH1(:,:,:) * PREDR1(:,:,:)
!
ELSE IF (L2D) THEN ! 3D case in a 2D model
!
IF (KRR /= 0) THEN ! moist 3D case
PRED2TH3(:,:,:)= PREDTH1(:,:,:)**2+(XCTV*PBLL_O_E(:,:,:)*PETHETA(:,:,:) )**2 * &
MZM(GX_M_M(PTHLM,PDXX,PDZZ,PDZX, KKA, KKU, KKL)**2, KKA, KKU, KKL)
PRED2TH3(:,:,IKB)=PRED2TH3(:,:,IKB+KKL)
!
PRED2R3(:,:,:)= PREDR1(:,:,:)**2 + (XCTV*PBLL_O_E(:,:,:)*PEMOIST(:,:,:))**2 * &
MZM(GX_M_M(PRM(:,:,:,1),PDXX,PDZZ,PDZX, KKA, KKU, KKL)**2, KKA, KKU, KKL)
PRED2R3(:,:,IKB)=PRED2R3(:,:,IKB+KKL)
!
PRED2THR3(:,:,:)= PREDR1(:,:,:) * PREDTH1(:,:,:) + XCTV**2*PBLL_O_E(:,:,:)**2 * &
PEMOIST(:,:,:) * PETHETA(:,:,:) * &
MZM(GX_M_M(PRM(:,:,:,1),PDXX,PDZZ,PDZX, KKA, KKU, KKL)* &
GX_M_M(PTHLM,PDXX,PDZZ,PDZX, KKA, KKU, KKL), KKA, KKU, KKL)
PRED2THR3(:,:,IKB)=PRED2THR3(:,:,IKB+KKL)
!
ELSE ! dry 3D case in a 2D model
PRED2TH3(:,:,:) = PREDTH1(:,:,:)**2 + XCTV**2*PBLL_O_E(:,:,:)**2 * &
MZM(GX_M_M(PTHLM,PDXX,PDZZ,PDZX, KKA, KKU, KKL)**2, KKA, KKU, KKL)
PRED2TH3(:,:,IKB)=PRED2TH3(:,:,IKB+KKL)
!
PRED2R3(:,:,:) = 0.
!
PRED2THR3(:,:,:) = 0.
!
END IF
!
ELSE ! 3D case in a 3D model
!
IF (KRR /= 0) THEN ! moist 3D case
PRED2TH3(:,:,:)= PREDTH1(:,:,:)**2 + ( XCTV*PBLL_O_E(:,:,:)*PETHETA(:,:,:) )**2 * &
MZM(GX_M_M(PTHLM,PDXX,PDZZ,PDZX, KKA, KKU, KKL)**2 &
+ GY_M_M(PTHLM,PDYY,PDZZ,PDZY, KKA, KKU, KKL)**2, KKA, KKU, KKL)
PRED2TH3(:,:,IKB)=PRED2TH3(:,:,IKB+KKL)
!
PRED2R3(:,:,:)= PREDR1(:,:,:)**2 + (XCTV*PBLL_O_E(:,:,:)*PEMOIST(:,:,:))**2 * &
MZM(GX_M_M(PRM(:,:,:,1),PDXX,PDZZ,PDZX, KKA, KKU, KKL)**2 + &
GY_M_M(PRM(:,:,:,1),PDYY,PDZZ,PDZY, KKA, KKU, KKL)**2, KKA, KKU, KKL)
PRED2R3(:,:,IKB)=PRED2R3(:,:,IKB+KKL)
!
PRED2THR3(:,:,:)= PREDR1(:,:,:) * PREDTH1(:,:,:) + XCTV**2*PBLL_O_E(:,:,:)**2 * &
PEMOIST(:,:,:) * PETHETA(:,:,:) * &
MZM(GX_M_M(PRM(:,:,:,1),PDXX,PDZZ,PDZX, KKA, KKU, KKL)* &
GX_M_M(PTHLM,PDXX,PDZZ,PDZX, KKA, KKU, KKL)+ &
GY_M_M(PRM(:,:,:,1),PDYY,PDZZ,PDZY, KKA, KKU, KKL)* &
GY_M_M(PTHLM,PDYY,PDZZ,PDZY, KKA, KKU, KKL), KKA, KKU, KKL)
PRED2THR3(:,:,IKB)=PRED2THR3(:,:,IKB+KKL)
!
ELSE ! dry 3D case in a 3D model
PRED2TH3(:,:,:) = PREDTH1(:,:,:)**2 + XCTV**2*PBLL_O_E(:,:,:)**2 * &
MZM(GX_M_M(PTHLM,PDXX,PDZZ,PDZX, KKA, KKU, KKL)**2 &
+ GY_M_M(PTHLM,PDYY,PDZZ,PDZY, KKA, KKU, KKL)**2, KKA, KKU, KKL)
PRED2TH3(:,:,IKB)=PRED2TH3(:,:,IKB+KKL)
!
PRED2R3(:,:,:) = 0.
!
PRED2THR3(:,:,:) = 0.
!
END IF
!
END IF ! end of the if structure on the turbulence dimensionnality
!
!
!---------------------------------------------------------------------------
!
! 5. Prandtl numbers for scalars
! ---------------------------
DO JSV=1,ISV
!
IF(HTURBDIM=='1DIM') THEN
! 1D case
PRED2THS3(:,:,:,JSV) = PREDS1(:,:,:,JSV) * PREDTH1(:,:,:)
IF (KRR /= 0) THEN
PRED2RS3(:,:,:,JSV) = PREDR1(:,:,:) *PREDS1(:,:,:,JSV)
ELSE
PRED2RS3(:,:,:,JSV) = 0.
END IF
!
ELSE IF (L2D) THEN ! 3D case in a 2D model
!
IF (KRR /= 0) THEN
ZW1 = MZM((XG / PTHVREF * PLM * PLEPS / PTKEM)**2, KKA, KKU, KKL) *PETHETA
ELSE
ZW1 = MZM((XG / PTHVREF * PLM * PLEPS / PTKEM)**2, KKA, KKU, KKL)
END IF
PRED2THS3(:,:,:,JSV) = PREDTH1(:,:,:) * PREDS1(:,:,:,JSV) + &
ZW1* &
MZM(GX_M_M(PSVM(:,:,:,JSV),PDXX,PDZZ,PDZX, KKA, KKU, KKL)* &
GX_M_M(PTHLM,PDXX,PDZZ,PDZX, KKA, KKU, KKL), &
KKA, KKU, KKL)
!
IF (KRR /= 0) THEN
PRED2RS3(:,:,:,JSV) = PREDR1(:,:,:) * PREDS1(:,:,:,JSV) + &
ZW1 * PEMOIST * &
MZM(GX_M_M(PSVM(:,:,:,JSV),PDXX,PDZZ,PDZX, KKA, KKU, KKL)* &
GX_M_M(PRM(:,:,:,1),PDXX,PDZZ,PDZX, KKA, KKU, KKL), &
KKA, KKU, KKL)
ELSE
PRED2RS3(:,:,:,JSV) = 0.
END IF
!
ELSE ! 3D case in a 3D model
!
IF (KRR /= 0) THEN
ZW1 = MZM((XG / PTHVREF * PLM * PLEPS / PTKEM)**2, KKA, KKU, KKL) *PETHETA
ELSE
ZW1 = MZM((XG / PTHVREF * PLM * PLEPS / PTKEM)**2, KKA, KKU, KKL)
END IF
PRED2THS3(:,:,:,JSV) = PREDTH1(:,:,:) * PREDS1(:,:,:,JSV) + &
ZW1* &
MZM(GX_M_M(PSVM(:,:,:,JSV),PDXX,PDZZ,PDZX, KKA, KKU, KKL)* &
GX_M_M(PTHLM,PDXX,PDZZ,PDZX, KKA, KKU, KKL) &
+GY_M_M(PSVM(:,:,:,JSV),PDYY,PDZZ,PDZY, KKA, KKU, KKL)* &
GY_M_M(PTHLM,PDYY,PDZZ,PDZY, KKA, KKU, KKL), &
KKA, KKU, KKL)
!
IF (KRR /= 0) THEN
PRED2RS3(:,:,:,JSV) = PREDR1(:,:,:) * PREDS1(:,:,:,JSV) + &
ZW1 * PEMOIST * &
MZM(GX_M_M(PSVM(:,:,:,JSV),PDXX,PDZZ,PDZX, KKA, KKU, KKL)* &
GX_M_M(PRM(:,:,:,1),PDXX,PDZZ,PDZX, KKA, KKU, KKL) &
+GY_M_M(PSVM(:,:,:,JSV),PDYY,PDZZ,PDZY, KKA, KKU, KKL)* &
GY_M_M(PRM(:,:,:,1),PDYY,PDZZ,PDZY, KKA, KKU, KKL), &
KKA, KKU, KKL)
ELSE
PRED2RS3(:,:,:,JSV) = 0.
END IF
!
END IF ! end of HTURBDIM if-block
!
END DO
!
!---------------------------------------------------------------------------
!
!* 6. SAVES THE REDELSPERGER NUMBERS
! ------------------------------
!
IF ( OTURB_DIAG .AND. TPFILE%LOPENED ) THEN
!
! stores the RED_TH1
TZFIELD%CMNHNAME = 'RED_TH1'
TZFIELD%CSTDNAME = ''
TZFIELD%CLONGNAME = 'RED_TH1'
TZFIELD%CUNITS = '1'
TZFIELD%CDIR = 'XY'
TZFIELD%CCOMMENT = 'X_Y_Z_RED_TH1'
TZFIELD%NGRID = 4
TZFIELD%NTYPE = TYPEREAL
TZFIELD%NDIMS = 3
TZFIELD%LTIMEDEP = .TRUE.
CALL IO_Field_write(TPFILE,TZFIELD,PREDTH1)
!
! stores the RED_R1
TZFIELD%CMNHNAME = 'RED_R1'
TZFIELD%CSTDNAME = ''
TZFIELD%CLONGNAME = 'RED_R1'
TZFIELD%CUNITS = '1'
TZFIELD%CDIR = 'XY'
TZFIELD%CCOMMENT = 'X_Y_Z_RED_R1'
TZFIELD%NGRID = 4
TZFIELD%NTYPE = TYPEREAL
TZFIELD%NDIMS = 3
TZFIELD%LTIMEDEP = .TRUE.
CALL IO_Field_write(TPFILE,TZFIELD,PREDR1)
!
! stores the RED2_TH3
TZFIELD%CMNHNAME = 'RED2_TH3'
TZFIELD%CSTDNAME = ''
TZFIELD%CLONGNAME = 'RED2_TH3'
TZFIELD%CUNITS = '1'
TZFIELD%CDIR = 'XY'
TZFIELD%CCOMMENT = 'X_Y_Z_RED2_TH3'
TZFIELD%NGRID = 4
TZFIELD%NTYPE = TYPEREAL
TZFIELD%NDIMS = 3
TZFIELD%LTIMEDEP = .TRUE.
CALL IO_Field_write(TPFILE,TZFIELD,PRED2TH3)
!
! stores the RED2_R3
TZFIELD%CMNHNAME = 'RED2_R3'
TZFIELD%CSTDNAME = ''
TZFIELD%CLONGNAME = 'RED2_R3'
TZFIELD%CUNITS = '1'
TZFIELD%CDIR = 'XY'
TZFIELD%CCOMMENT = 'X_Y_Z_RED2_R3'
TZFIELD%NGRID = 4
TZFIELD%NTYPE = TYPEREAL
TZFIELD%NDIMS = 3
TZFIELD%LTIMEDEP = .TRUE.
CALL IO_Field_write(TPFILE,TZFIELD,PRED2R3)
!
! stores the RED2_THR3
TZFIELD%CMNHNAME = 'RED2_THR3'
TZFIELD%CSTDNAME = ''
TZFIELD%CLONGNAME = 'RED2_THR3'
TZFIELD%CUNITS = '1'
TZFIELD%CDIR = 'XY'
TZFIELD%CCOMMENT = 'X_Y_Z_RED2_THR3'
TZFIELD%NGRID = 4
TZFIELD%NTYPE = TYPEREAL
TZFIELD%NDIMS = 3
TZFIELD%LTIMEDEP = .TRUE.
CALL IO_Field_write(TPFILE,TZFIELD,PRED2THR3)
!
END IF
!
!---------------------------------------------------------------------------
ENDIF ! (Done only if LHARAT is FALSE)
!
IF (LHOOK) CALL DR_HOOK('PRANDTL',1,ZHOOK_HANDLE)
END SUBROUTINE PRANDTL
!
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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
!
REAL(KIND=JPRB) :: ZHOOK_HANDLE
IF (LHOOK) CALL DR_HOOK('MODE_PRANDTL:PHI3',0,ZHOOK_HANDLE)
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)
!
IF (LHOOK) CALL DR_HOOK('MODE_PRANDTL:PHI3',1,ZHOOK_HANDLE)
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
!
REAL(KIND=JPRB) :: ZHOOK_HANDLE
IF (LHOOK) CALL DR_HOOK('MODE_PRANDTL:PSI_SV',0,ZHOOK_HANDLE)
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
!
IF (LHOOK) CALL DR_HOOK('MODE_PRANDTL:PSI_SV',1,ZHOOK_HANDLE)
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
!
REAL(KIND=JPRB) :: ZHOOK_HANDLE
IF (LHOOK) CALL DR_HOOK('MODE_PRANDTL:D_PHI3DTDZ_O_DDTDZ',0,ZHOOK_HANDLE)
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 JL=1,SIZE(PPHI3,1)
DO JK=1,SIZE(PPHI3,3)
IF ( ABS(PPHI3(JL,1,JK)-XPHI_LIM) < 1.E-12 ) THEN
D_PHI3DTDZ_O_DDTDZ(JL,1,JK)=PPHI3(JL,1,JK)*&
& (1. - PREDTH1(JL,1,JK)*PPHI3(JL,1,JK))
ELSE
D_PHI3DTDZ_O_DDTDZ(JL,1,JK)=PPHI3(JL,1,JK)
ENDIF
ENDDO
ENDDO
END IF
!
!
D_PHI3DTDZ_O_DDTDZ(:,:,IKB-1)=D_PHI3DTDZ_O_DDTDZ(:,:,IKB)
D_PHI3DTDZ_O_DDTDZ(:,:,IKE+1)=D_PHI3DTDZ_O_DDTDZ(:,:,IKE)
!
IF (LHOOK) CALL DR_HOOK('MODE_PRANDTL:D_PHI3DTDZ_O_DDTDZ',1,ZHOOK_HANDLE)
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
!
REAL(KIND=JPRB) :: ZHOOK_HANDLE
IF (LHOOK) CALL DR_HOOK('MODE_PRANDTL:D_PHI3DRDZ_O_DDRDZ',0,ZHOOK_HANDLE)
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
!
!
D_PHI3DRDZ_O_DDRDZ(:,:,IKB-1)=D_PHI3DRDZ_O_DDRDZ(:,:,IKB)
D_PHI3DRDZ_O_DDRDZ(:,:,IKE+1)=D_PHI3DRDZ_O_DDRDZ(:,:,IKE)
!
IF (LHOOK) CALL DR_HOOK('MODE_PRANDTL:D_PHI3DRDZ_O_DDRDZ',1,ZHOOK_HANDLE)
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
!
REAL(KIND=JPRB) :: ZHOOK_HANDLE
IF (LHOOK) CALL DR_HOOK('MODE_PRANDTL:D_PHI3DTDZ2_O_DDTDZ',0,ZHOOK_HANDLE)
IKB = 1+JPVEXT_TURB
IKE = SIZE(PREDTH1,3)-JPVEXT_TURB
!
!
IF (HTURBDIM=='3DIM') THEN
!* 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
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
!
!
D_PHI3DTDZ2_O_DDTDZ(:,:,IKB-1)=D_PHI3DTDZ2_O_DDTDZ(:,:,IKB)
D_PHI3DTDZ2_O_DDTDZ(:,:,IKE+1)=D_PHI3DTDZ2_O_DDTDZ(:,:,IKE)
!
IF (LHOOK) CALL DR_HOOK('MODE_PRANDTL:D_PHI3DTDZ2_O_DDTDZ',1,ZHOOK_HANDLE)
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
!
REAL(KIND=JPRB) :: ZHOOK_HANDLE
IF (LHOOK) CALL DR_HOOK('MODE_PRANDTL:M3_WTH_WTH2',0,ZHOOK_HANDLE)
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)
!
IF (LHOOK) CALL DR_HOOK('MODE_PRANDTL:M3_WTH_WTH2',1,ZHOOK_HANDLE)
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
!
REAL(KIND=JPRB) :: ZHOOK_HANDLE
IF (LHOOK) CALL DR_HOOK('MODE_PRANDTL:D_M3_WTH_WTH2_O_DDTDZ',0,ZHOOK_HANDLE)
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)
!
IF (LHOOK) CALL DR_HOOK('MODE_PRANDTL:D_M3_WTH_WTH2_O_DDTDZ',1,ZHOOK_HANDLE)
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
!
REAL(KIND=JPRB) :: ZHOOK_HANDLE
IF (LHOOK) CALL DR_HOOK('MODE_PRANDTL:M3_WTH_W2TH',0,ZHOOK_HANDLE)
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
M3_WTH_W2TH(:,:,:) = XCSHF*PKEFF*1.5/MZM(PTKE, KKA, KKU, KKL) &
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* (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)
!
IF (LHOOK) CALL DR_HOOK('MODE_PRANDTL:M3_WTH_W2TH',1,ZHOOK_HANDLE)
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
!
REAL(KIND=JPRB) :: ZHOOK_HANDLE
IF (LHOOK) CALL DR_HOOK('MODE_PRANDTL:D_M3_WTH_W2TH_O_DDTDZ',0,ZHOOK_HANDLE)
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
D_M3_WTH_W2TH_O_DDTDZ(:,:,:) = &
- XCSHF*PKEFF*1.5/MZM(PTKE, KKA, KKU, KKL)/(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)
!
IF (LHOOK) CALL DR_HOOK('MODE_PRANDTL:D_M3_WTH_W2TH_O_DDTDZ',1,ZHOOK_HANDLE)
END FUNCTION D_M3_WTH_W2TH_O_DDTDZ
!----------------------------------------------------------------------------
FUNCTION M3_WTH_W2R(KKA,KKU,KKL,PD,PKEFF,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) :: 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
!
REAL(KIND=JPRB) :: ZHOOK_HANDLE
IF (LHOOK) CALL DR_HOOK('MODE_PRANDTL:M3_WTH_W2R',0,ZHOOK_HANDLE)
IKB = 1+JPVEXT_TURB
IKE = SIZE(PD,3)-JPVEXT_TURB
M3_WTH_W2R(:,:,:) = - XCSHF*PKEFF*0.75*XCTV*PBLL_O_E/MZM(PTKE, KKA, KKU, KKL)*PEMOIST*PDTDZ/PD
!
M3_WTH_W2R(:,:,IKB-1)=M3_WTH_W2R(:,:,IKB)
M3_WTH_W2R(:,:,IKE+1)=M3_WTH_W2R(:,:,IKE)
!
IF (LHOOK) CALL DR_HOOK('MODE_PRANDTL:M3_WTH_W2R',1,ZHOOK_HANDLE)
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