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! ##########################
MODULE MODI_LIMA_WARM_NUCL
! ##########################
!
INTERFACE
WAUTELET Philippe
committed
SUBROUTINE LIMA_WARM_NUCL (OACTIT, PTSTEP, KMI, &
PRHODREF, PEXNREF, PPABST, ZT, ZTM, PW_NU, &
PRCM, PRVT, PRCT, PRRT, &
PTHS, PRVS, PRCS, PCCS, PNFS, PNAS )
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!
LOGICAL, INTENT(IN) :: OACTIT ! Switch to activate the
! activation by radiative
! tendency
REAL, INTENT(IN) :: PTSTEP ! Double Time step
! (single if cold start)
INTEGER, INTENT(IN) :: KMI ! Model index
!
REAL, DIMENSION(:,:,:), INTENT(IN) :: PRHODREF ! Reference density
REAL, DIMENSION(:,:,:), INTENT(IN) :: PEXNREF ! Reference Exner function
REAL, DIMENSION(:,:,:), INTENT(IN) :: PPABST ! abs. pressure at time t
REAL, DIMENSION(:,:,:), INTENT(IN) :: ZT ! Temperature
REAL, DIMENSION(:,:,:), INTENT(IN) :: ZTM ! Temperature at time t-dt
!
REAL, DIMENSION(:,:,:), INTENT(IN) :: PW_NU ! updraft velocity used for
! the nucleation param.
!
REAL, DIMENSION(:,:,:), INTENT(IN) :: PRCM ! Cloud water m.r. at t-dt
!
REAL, DIMENSION(:,:,:), INTENT(IN) :: PRVT ! Water vapor m.r. at t
REAL, DIMENSION(:,:,:), INTENT(IN) :: PRCT ! Cloud water m.r. at t
REAL, DIMENSION(:,:,:), INTENT(IN) :: PRRT ! Rain water m.r. at t
!
REAL, DIMENSION(:,:,:), INTENT(INOUT) :: PTHS ! Theta source
REAL, DIMENSION(:,:,:), INTENT(INOUT) :: PRVS ! Water vapor m.r. source
REAL, DIMENSION(:,:,:), INTENT(INOUT) :: PRCS ! Cloud water m.r. source
!
REAL, DIMENSION(:,:,:) , INTENT(INOUT) :: PCCS ! Cloud water C. source
REAL, DIMENSION(:,:,:,:), INTENT(INOUT) :: PNFS ! CCN C. available source
REAL, DIMENSION(:,:,:,:), INTENT(INOUT) :: PNAS ! CCN C. activated source
!
END SUBROUTINE LIMA_WARM_NUCL
END INTERFACE
END MODULE MODI_LIMA_WARM_NUCL
WAUTELET Philippe
committed
! #######################################################################
SUBROUTINE LIMA_WARM_NUCL (OACTIT, PTSTEP, KMI, &
PRHODREF, PEXNREF, PPABST, ZT, ZTM, PW_NU, &
PRCM, PRVT, PRCT, PRRT, &
PTHS, PRVS, PRCS, PCCS, PNFS, PNAS )
! #######################################################################
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!
!!
!! PURPOSE
!! -------
!! The purpose of this routine is to compute the activation of CCN
!! according to Cohard and Pinty, QJRMS, 2000
!!
!!
!!** METHOD
!! ------
!! The activation of CCN is checked for quasi-saturated air parcels
!! to update the cloud droplet number concentration.
!!
!! Computation steps :
!! 1- Check where computations are necessary
!! 2- and 3- Compute the maximum of supersaturation using the iterative
!! Ridder algorithm
!! 4- Compute the nucleation source
!! 5- Deallocate local variables
!!
!! Contains :
!! 6- Functions : Ridder algorithm
!!
!!
!! REFERENCE
!! ---------
!!
!! Cohard, J.-M. and J.-P. Pinty, 2000: A comprehensive two-moment warm
!! microphysical bulk scheme.
!! Part I: Description and tests
!! Part II: 2D experiments with a non-hydrostatic model
!! Accepted for publication in Quart. J. Roy. Meteor. Soc.
!!
!! AUTHOR
!! ------
!! J.-M. Cohard * Laboratoire d'Aerologie*
!! J.-P. Pinty * Laboratoire d'Aerologie*
!! S. Berthet * Laboratoire d'Aerologie*
!! B. Vié * Laboratoire d'Aerologie*
!!
!! MODIFICATIONS
!! -------------
!! Original ??/??/13
!! J. Escobar : 10/2017 , for real*4 use XMNH_EPSILON
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!!
!-------------------------------------------------------------------------------
!
!* 0. DECLARATIONS
! ------------
!
USE MODD_PARAMETERS, ONLY : JPHEXT, JPVEXT
USE MODD_CST
USE MODD_PARAM_LIMA
USE MODD_PARAM_LIMA_WARM
!
USE MODI_GAMMA
USE MODI_LIMA_FUNCTIONS, ONLY : COUNTJV
!
IMPLICIT NONE
!
!* 0.1 Declarations of dummy arguments :
!
LOGICAL, INTENT(IN) :: OACTIT ! Switch to activate the
! activation by radiative
! tendency
REAL, INTENT(IN) :: PTSTEP ! Double Time step
! (single if cold start)
INTEGER, INTENT(IN) :: KMI ! Model index
!
REAL, DIMENSION(:,:,:), INTENT(IN) :: PRHODREF ! Reference density
REAL, DIMENSION(:,:,:), INTENT(IN) :: PEXNREF ! Reference Exner function
REAL, DIMENSION(:,:,:), INTENT(IN) :: PPABST ! abs. pressure at time t
REAL, DIMENSION(:,:,:), INTENT(IN) :: ZT ! Temperature
REAL, DIMENSION(:,:,:), INTENT(IN) :: ZTM ! Temperature at time t-dt
!
REAL, DIMENSION(:,:,:), INTENT(IN) :: PW_NU ! updraft velocity used for
! the nucleation param.
!
REAL, DIMENSION(:,:,:), INTENT(IN) :: PRCM ! Cloud water m.r. at t-dt
!
REAL, DIMENSION(:,:,:), INTENT(IN) :: PRVT ! Water vapor m.r. at t
REAL, DIMENSION(:,:,:), INTENT(IN) :: PRCT ! Cloud water m.r. at t
REAL, DIMENSION(:,:,:), INTENT(IN) :: PRRT ! Rain water m.r. at t
!
REAL, DIMENSION(:,:,:), INTENT(INOUT) :: PTHS ! Theta source
REAL, DIMENSION(:,:,:), INTENT(INOUT) :: PRVS ! Water vapor m.r. source
REAL, DIMENSION(:,:,:), INTENT(INOUT) :: PRCS ! Cloud water m.r. source
!
REAL, DIMENSION(:,:,:) , INTENT(INOUT) :: PCCS ! Cloud water C. source
REAL, DIMENSION(:,:,:,:), INTENT(INOUT) :: PNFS ! CCN C. available source
REAL, DIMENSION(:,:,:,:), INTENT(INOUT) :: PNAS ! CCN C. activated source
!
!
!* 0.1 Declarations of local variables :
!
! Packing variables
LOGICAL, DIMENSION(SIZE(PRHODREF,1),SIZE(PRHODREF,2),SIZE(PRHODREF,3)) :: GNUCT
INTEGER :: INUCT
INTEGER , DIMENSION(SIZE(GNUCT)) :: I1,I2,I3 ! Used to replace the COUNT
INTEGER :: JL ! and PACK intrinsics
!
! Packed micophysical variables
REAL, DIMENSION(:) , ALLOCATABLE :: ZCCS ! cloud conc. source
REAL, DIMENSION(:,:), ALLOCATABLE :: ZNFS ! available nucleus conc. source
REAL, DIMENSION(:,:), ALLOCATABLE :: ZNAS ! activated nucleus conc. source
!
! Other packed variables
REAL, DIMENSION(:) , ALLOCATABLE :: ZRHODREF ! RHO Dry REFerence
REAL, DIMENSION(:) , ALLOCATABLE :: ZEXNREF ! EXNer Pressure REFerence
REAL, DIMENSION(:) , ALLOCATABLE :: ZZT ! Temperature
!
! Work arrays
REAL, DIMENSION(:), ALLOCATABLE :: ZZW1, ZZW2, ZZW3, ZZW4, ZZW5, ZZW6, &
ZCTMIN, &
ZZTDT, & ! dT/dt
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ZSMAX, & ! Maximum supersaturation
ZVEC1
!
REAL, DIMENSION(:,:), ALLOCATABLE :: ZTMP, ZCHEN_MULTI
!
REAL, DIMENSION(SIZE(PRHODREF,1),SIZE(PRHODREF,2),SIZE(PRHODREF,3)) &
:: ZTDT, ZDRC, ZRVSAT, ZW
REAL, DIMENSION(SIZE(PNFS,1),SIZE(PNFS,2),SIZE(PNFS,3)) &
:: ZCONC_TOT ! total CCN C. available
!
INTEGER, DIMENSION(:), ALLOCATABLE :: IVEC1 ! Vectors of indices for
! interpolations
!
!
REAL :: ZEPS ! molar mass ratio
REAL :: ZS1, ZS2, ZXACC
INTEGER :: JMOD
INTEGER :: IIB, IIE, IJB, IJE, IKB, IKE ! Physical domain
!
!-------------------------------------------------------------------------------
!
!
!* 1. PREPARE COMPUTATIONS - PACK
! ---------------------------
!
!
IIB=1+JPHEXT
IIE=SIZE(PRHODREF,1) - JPHEXT
IJB=1+JPHEXT
IJE=SIZE(PRHODREF,2) - JPHEXT
IKB=1+JPVEXT
IKE=SIZE(PRHODREF,3) - JPVEXT
!
!++cb++
!ALLOCATE(ZRTMIN(SIZE(XRTMIN)))
!--cb--
ALLOCATE(ZCTMIN(SIZE(XCTMIN)))
!++cb++
!ZRTMIN(:) = XRTMIN(:) / PTSTEP
!--cb--
ZCTMIN(:) = XCTMIN(:) / PTSTEP
!
! Saturation vapor mixing ratio and radiative tendency
!
ZEPS= XMV / XMD
!
ZRVSAT(:,:,:) = ZEPS / (PPABST(:,:,:) * &
EXP(-XALPW+XBETAW/ZT(:,:,:)+XGAMW*ALOG(ZT(:,:,:))) - 1.0)
ZTDT(:,:,:) = 0.
ZDRC(:,:,:) = 0.
IF (OACTIT) THEN
ZTDT(:,:,:) = (ZT(:,:,:)-ZTM(:,:,:))/PTSTEP ! dT/dt
!!! JPP
!!! JPP
!!! ZDRC(:,:,:) = (PRCT(:,:,:)-PRCM(:,:,:))/PTSTEP ! drc/dt
ZDRC(:,:,:) = PRCS(:,:,:)-(PRCT(:,:,:)/PTSTEP) ! drc/dt
!!! JPP
!!! JPP
!!
!! BV - W and drc/dt effect should not be included in ZTDT (already accounted for in the computations) ?
!!
!! ZTDT(:,:,:) = MIN(0.,ZTDT(:,:,:)+(XG*PW_NU(:,:,:))/XCPD- &
!! (XLVTT+(XCPV-XCL)*(ZT(:,:,:)-XTT))*ZDRC(:,:,:)/XCPD)
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END IF
!
! find locations where CCN are available
!
ZCONC_TOT(:,:,:) = 0.0
DO JMOD = 1, NMOD_CCN
ZCONC_TOT(:,:,:) = ZCONC_TOT(:,:,:) + PNFS(:,:,:,JMOD) ! sum over the free CCN
ENDDO
!
! optimization by looking for locations where
! the updraft velocity is positive!!!
!
GNUCT(:,:,:) = .FALSE.
!
! NEW : -22°C = limit sup for condensation freezing in Fridlin et al., 2007
IF( OACTIT ) THEN
GNUCT(IIB:IIE,IJB:IJE,IKB:IKE) = (PW_NU(IIB:IIE,IJB:IJE,IKB:IKE)>XWMIN .OR. &
ZTDT(IIB:IIE,IJB:IJE,IKB:IKE)<XTMIN) .AND.&
PRVT(IIB:IIE,IJB:IJE,IKB:IKE)>(0.98*ZRVSAT(IIB:IIE,IJB:IJE,IKB:IKE))&
.AND. ZT(IIB:IIE,IJB:IJE,IKB:IKE)>(XTT-22.) &
.AND. ZCONC_TOT(IIB:IIE,IJB:IJE,IKB:IKE)>ZCTMIN(4)
ELSE
GNUCT(IIB:IIE,IJB:IJE,IKB:IKE) = PW_NU(IIB:IIE,IJB:IJE,IKB:IKE)>XWMIN .AND.&
PRVT(IIB:IIE,IJB:IJE,IKB:IKE)>(0.98*ZRVSAT(IIB:IIE,IJB:IJE,IKB:IKE))&
.AND. ZT(IIB:IIE,IJB:IJE,IKB:IKE)>(XTT-22.) &
.AND. ZCONC_TOT(IIB:IIE,IJB:IJE,IKB:IKE)>ZCTMIN(4)
END IF
INUCT = COUNTJV( GNUCT(:,:,:),I1(:),I2(:),I3(:))
!
!
IF( INUCT >= 1 ) THEN
!
ALLOCATE(ZNFS(INUCT,NMOD_CCN))
ALLOCATE(ZNAS(INUCT,NMOD_CCN))
ALLOCATE(ZTMP(INUCT,NMOD_CCN))
ALLOCATE(ZCCS(INUCT))
ALLOCATE(ZZT(INUCT))
ALLOCATE(ZZTDT(INUCT))
ALLOCATE(ZZW1(INUCT))
ALLOCATE(ZZW2(INUCT))
ALLOCATE(ZZW3(INUCT))
ALLOCATE(ZZW4(INUCT))
ALLOCATE(ZZW5(INUCT))
ALLOCATE(ZZW6(INUCT))
ALLOCATE(ZCHEN_MULTI(INUCT,NMOD_CCN))
ALLOCATE(ZVEC1(INUCT))
ALLOCATE(IVEC1(INUCT))
ALLOCATE(ZRHODREF(INUCT))
ALLOCATE(ZEXNREF(INUCT))
DO JL=1,INUCT
ZCCS(JL) = PCCS(I1(JL),I2(JL),I3(JL))
ZZT(JL) = ZT(I1(JL),I2(JL),I3(JL))
ZZW1(JL) = ZRVSAT(I1(JL),I2(JL),I3(JL))
ZZW2(JL) = PW_NU(I1(JL),I2(JL),I3(JL))
ZZTDT(JL) = ZTDT(I1(JL),I2(JL),I3(JL))
ZSW(JL) = PRVT(I1(JL),I2(JL),I3(JL))/ZRVSAT(I1(JL),I2(JL),I3(JL)) - 1.
ZRHODREF(JL) = PRHODREF(I1(JL),I2(JL),I3(JL))
ZEXNREF(JL) = PEXNREF(I1(JL),I2(JL),I3(JL))
DO JMOD = 1,NMOD_CCN
ZNFS(JL,JMOD) = PNFS(I1(JL),I2(JL),I3(JL),JMOD)
ZNAS(JL,JMOD) = PNAS(I1(JL),I2(JL),I3(JL),JMOD)
ZCHEN_MULTI(JL,JMOD) = (ZNFS(JL,JMOD)+ZNAS(JL,JMOD))*PTSTEP*ZRHODREF(JL) &
/ XLIMIT_FACTOR(JMOD)
ENDDO
ENDDO
!
ZZW1(:) = 1.0/ZEPS + 1.0/ZZW1(:) &
+ (((XLVTT+(XCPV-XCL)*(ZZT(:)-XTT))/ZZT(:))**2)/(XCPD*XRV) ! Psi2
!
!
!-------------------------------------------------------------------------------
!
!
!* 2. compute the constant term (ZZW3) relative to smax
! ----------------------------------------------------
!
! Remark : in LIMA's nucleation parameterization, Smax=0.01 for a supersaturation of 1% !
!
!
ZVEC1(:) = MAX( ( 1.0 + 10.0 * XMNH_EPSILON ), MIN( FLOAT(NAHEN)*( 1.0 - 10.0 * XMNH_EPSILON ), &
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XAHENINTP1 * ZZT(:) + XAHENINTP2 ) )
IVEC1(:) = INT( ZVEC1(:) )
ZVEC1(:) = ZVEC1(:) - FLOAT( IVEC1(:) )
ALLOCATE(ZSMAX(INUCT))
!
!
IF (OACTIT) THEN ! including a cooling rate
!
! Compute the tabulation of function of ZZW3 :
!
! (Psi1*w+Psi3*DT/Dt)**1.5
! ZZW3 = XAHENG*(Psi1*w + Psi3*DT/Dt)**1.5 = ------------------------
! 2*pi*rho_l*G**(3/2)
!
!
ZZW4(:)=XPSI1( IVEC1(:)+1)*ZZW2(:)+XPSI3(IVEC1(:)+1)*ZZTDT(:)
ZZW5(:)=XPSI1( IVEC1(:) )*ZZW2(:)+XPSI3(IVEC1(:) )*ZZTDT(:)
WHERE (ZZW4(:) < 0. .OR. ZZW5(:) < 0.)
ZZW4(:) = 0.
ZZW5(:) = 0.
END WHERE
ZZW3(:) = XAHENG( IVEC1(:)+1)*(ZZW4(:)**1.5)* ZVEC1(:) &
- XAHENG( IVEC1(:) )*(ZZW5(:)**1.5)*(ZVEC1(:) - 1.0)
! Cste*((Psi1*w+Psi3*dT/dt)/(G))**1.5
!
!
ELSE ! OACTIT , for clouds
!
!
! Compute the tabulation of function of ZZW3 :
!
! (Psi1 * w)**1.5
! ZZW3 = XAHENG * (Psi1 * w)**1.5 = -------------------------
! 2 pi rho_l * G**(3/2)
!
!
ZZW3(:)=XAHENG(IVEC1(:)+1)*((XPSI1(IVEC1(:)+1)*ZZW2(:))**1.5)* ZVEC1(:) &
-XAHENG(IVEC1(:) )*((XPSI1(IVEC1(:) )*ZZW2(:))**1.5)*(ZVEC1(:)-1.0)
!
END IF ! OACTIT
!
!
! (Psi1*w+Psi3*DT/Dt)**1.5 rho_air
! ZZW3 = ------------------------ * -------
! 2*pi*rho_l*G**(3/2) Psi2
!
ZZW5(:) = 1.
ZZW3(:) = (ZZW3(:)/ZZW1(:))*ZRHODREF(:) ! R.H.S. of Eq 9 of CPB 98 but
! for multiple aerosol modes
WHERE (ZZW3(:) == 0.)
ZZW5(:) = -1.
END WHERE
!
!
!-------------------------------------------------------------------------------
!
!
!* 3. Compute the maximum of supersaturation
! -----------------------------------------
!
!
! estimate S_max for the CPB98 parameterization with SEVERAL aerosols mode
! Reminder : Smax=0.01 for a 1% supersaturation
!
! Interval bounds to tabulate sursaturation Smax
! Check with values used for tabulation in ini_lima_warm.f90
ZS1 = 1.0E-5 ! corresponds to 0.001% supersaturation
ZS2 = 5.0E-2 ! corresponds to 5.0% supersaturation
ZXACC = 1.0E-7 ! Accuracy needed for the search in [NO UNITS]
!
ZSMAX(:) = ZRIDDR(ZS1,ZS2,ZXACC,ZZW3(:),INUCT) ! ZSMAX(:) is in [NO UNITS]
ZSMAX(:) = MIN(MAX(ZSMAX(:), ZSW(:)),ZS2)
!
!
!-------------------------------------------------------------------------------
!
!
!* 4. Compute the nucleus source
! -----------------------------
!
!
! Again : Smax=0.01 for a 1% supersaturation
! Modified values for Beta and C (see in init_aerosol_properties) account for that
!
WHERE (ZZW5(:) > 0. .AND. ZSMAX(:) > 0.)
ZVEC1(:) = MAX( ( 1.0 + 10.0 * XMNH_EPSILON ), MIN( FLOAT(NHYP)*( 1.0 - 10.0 * XMNH_EPSILON ), &
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XHYPINTP1*LOG(ZSMAX(:))+XHYPINTP2 ) )
IVEC1(:) = INT( ZVEC1(:) )
ZVEC1(:) = ZVEC1(:) - FLOAT( IVEC1(:) )
END WHERE
ZZW6(:) = 0. ! initialize the change of cloud droplet concentration
!
ZTMP(:,:)=0.0
!
! Compute the concentration of activable aerosols for each mode
! based on the max of supersaturation ( -> ZTMP )
!
DO JMOD = 1, NMOD_CCN ! iteration on mode number
ZZW1(:) = 0.
ZZW2(:) = 0.
ZZW3(:) = 0.
!
WHERE( ZSMAX(:)>0.0 )
ZZW2(:) = XHYPF12( IVEC1(:)+1,JMOD )* ZVEC1(:) & ! hypergeo function
- XHYPF12( IVEC1(:) ,JMOD )*(ZVEC1(:) - 1.0) ! XHYPF12 is tabulated
!
ZTMP(:,JMOD) = (ZCHEN_MULTI(:,JMOD)/ZRHODREF(:))*ZSMAX(:)**XKHEN_MULTI(JMOD) &
*ZZW2(:)/PTSTEP
ENDWHERE
ENDDO
!
! Compute the concentration of aerosols activated at this time step
! as the difference between ZTMP and the aerosols already activated at t-dt (ZZW1)
!
DO JMOD = 1, NMOD_CCN ! iteration on mode number
ZZW1(:) = 0.
ZZW2(:) = 0.
ZZW3(:) = 0.
!
WHERE( SUM(ZTMP(:,:),DIM=2)*PTSTEP .GT. 25.E6/ZRHODREF(:) )
ZZW1(:) = MIN( ZNFS(:,JMOD),MAX( ZTMP(:,JMOD)- ZNAS(:,JMOD) , 0.0 ) )
ENDWHERE
!
!* update the concentration of activated CCN = Na
!
PNAS(:,:,:,JMOD) = PNAS(:,:,:,JMOD) + &
UNPACK( ZZW1(:), MASK=GNUCT(:,:,:), FIELD=0.0 )
!
!* update the concentration of free CCN = Nf
!
PNFS(:,:,:,JMOD) = PNFS(:,:,:,JMOD) - &
UNPACK( ZZW1(:), MASK=GNUCT(:,:,:), FIELD=0.0 )
!
!* prepare to update the cloud water concentration
!
ZZW6(:) = ZZW6(:) + ZZW1(:)
ENDDO
!
! Update PRVS, PRCS, PCCS, and PTHS
!
ZZW1(:)=0.
WHERE (ZZW5(:)>0.0 .AND. ZSMAX(:)>0.0) ! ZZW1 is computed with ZSMAX [NO UNIT]
ZZW1(:) = MIN(XCSTDCRIT*ZZW6(:)/(((ZZT(:)*ZSMAX(:))**3)*ZRHODREF(:)),1.E-5)
END WHERE
ZW(:,:,:) = MIN( UNPACK( ZZW1(:),MASK=GNUCT(:,:,:),FIELD=0.0 ),PRVS(:,:,:) )
!
PRVS(:,:,:) = PRVS(:,:,:) - ZW(:,:,:)
PRCS(:,:,:) = PRCS(:,:,:) + ZW(:,:,:)
ZW(:,:,:) = ZW(:,:,:) * (XLVTT+(XCPV-XCL)*(ZT(:,:,:)-XTT))/ &
(PEXNREF(:,:,:)*(XCPD+XCPV*PRVT(:,:,:)+XCL*(PRCT(:,:,:)+PRRT(:,:,:))))
PTHS(:,:,:) = PTHS(:,:,:) + ZW(:,:,:)
!
ZW(:,:,:) = PCCS(:,:,:)
PCCS(:,:,:) = UNPACK( ZZW6(:)+ZCCS(:),MASK=GNUCT(:,:,:),FIELD=ZW(:,:,:) )
!
ZW(:,:,:) = UNPACK( 100.0*ZSMAX(:),MASK=GNUCT(:,:,:),FIELD=0.0 )
!
!
!-------------------------------------------------------------------------------
!
!
!* 5. Cleaning
! -----------
!
!
DEALLOCATE(IVEC1)
DEALLOCATE(ZVEC1)
DEALLOCATE(ZNFS)
DEALLOCATE(ZNAS)
DEALLOCATE(ZCCS)
DEALLOCATE(ZZT)
DEALLOCATE(ZSMAX)
DEALLOCATE(ZZW1)
DEALLOCATE(ZZW2)
DEALLOCATE(ZZW3)
DEALLOCATE(ZZW4)
DEALLOCATE(ZZW5)
DEALLOCATE(ZZW6)
DEALLOCATE(ZZTDT)
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DEALLOCATE(ZRHODREF)
DEALLOCATE(ZCHEN_MULTI)
DEALLOCATE(ZEXNREF)
!
END IF ! INUCT
!
!++cb++
DEALLOCATE(ZCTMIN)
!--cb--
!
!
!-------------------------------------------------------------------------------
!
!
!* 6. Functions used to compute the maximum of supersaturation
! -----------------------------------------------------------
!
!
CONTAINS
!------------------------------------------------------------------------------
!
FUNCTION ZRIDDR(PX1,PX2INIT,PXACC,PZZW3,NPTS) RESULT(PZRIDDR)
!
!
!!**** *ZRIDDR* - iterative algorithm to find root of a function
!!
!!
!! PURPOSE
!! -------
!! The purpose of this function is to find the root of a given function
!! the arguments are the brackets bounds (the interval where to find the root)
!! the accuracy needed and the input parameters of the given function.
!! Using Ridders' method, return the root of a function known to lie between
!! PX1 and PX2. The root, returned as PZRIDDR, will be refined to an approximate
!! accuracy PXACC.
!!
!!** METHOD
!! ------
!! Ridders' method
!!
!! EXTERNAL
!! --------
!! FUNCSMAX
!!
!! IMPLICIT ARGUMENTS
!! ------------------
!!
!! REFERENCE
!! ---------
!! NUMERICAL RECIPES IN FORTRAN 77: THE ART OF SCIENTIFIC COMPUTING
!! (ISBN 0-521-43064-X)
!! Copyright (C) 1986-1992 by Cambridge University Press.
!! Programs Copyright (C) 1986-1992 by Numerical Recipes Software.
!!
!! AUTHOR
!! ------
!! Frederick Chosson *CERFACS*
!!
!! MODIFICATIONS
!! -------------
!! Original 12/07/07
!! S.BERTHET 2008 vectorization
!------------------------------------------------------------------------------
!
!* 0. DECLARATIONS
!
!
IMPLICIT NONE
!
!* 0.1 declarations of arguments and result
!
INTEGER, INTENT(IN) :: NPTS
REAL, DIMENSION(:), INTENT(IN) :: PZZW3
REAL, INTENT(IN) :: PX1, PX2INIT, PXACC
REAL, DIMENSION(:), ALLOCATABLE :: PZRIDDR
!
!* 0.2 declarations of local variables
!
!
INTEGER, PARAMETER :: MAXIT=60
REAL, PARAMETER :: UNUSED=0.0 !-1.11e30
REAL, DIMENSION(:), ALLOCATABLE :: fh,fl, fm,fnew
REAL :: s,xh,xl,xm,xnew
REAL :: PX2
INTEGER :: j, JL
!
ALLOCATE( fh(NPTS))
ALLOCATE( fl(NPTS))
ALLOCATE( fm(NPTS))
ALLOCATE(fnew(NPTS))
ALLOCATE(PZRIDDR(NPTS))
!
PZRIDDR(:)= UNUSED
PX2 = PX2INIT
fl(:) = FUNCSMAX(PX1,PZZW3(:),NPTS)
fh(:) = FUNCSMAX(PX2,PZZW3(:),NPTS)
!
DO JL = 1, NPTS
PX2 = PX2INIT
100 if ((fl(JL) > 0.0 .and. fh(JL) < 0.0) .or. (fl(JL) < 0.0 .and. fh(JL) > 0.0)) then
xl = PX1
xh = PX2
do j=1,MAXIT
xm = 0.5*(xl+xh)
fm(JL) = SINGL_FUNCSMAX(xm,PZZW3(JL),JL)
s = sqrt(fm(JL)**2-fl(JL)*fh(JL))
if (s == 0.0) then
GO TO 101
endif
xnew = xm+(xm-xl)*(sign(1.0,fl(JL)-fh(JL))*fm(JL)/s)
if (abs(xnew - PZRIDDR(JL)) <= PXACC) then
GO TO 101
endif
PZRIDDR(JL) = xnew
fnew(JL) = SINGL_FUNCSMAX(PZRIDDR(JL),PZZW3(JL),JL)
if (fnew(JL) == 0.0) then
GO TO 101
endif
if (sign(fm(JL),fnew(JL)) /= fm(JL)) then
xl =xm
fl(JL)=fm(JL)
xh =PZRIDDR(JL)
fh(JL)=fnew(JL)
else if (sign(fl(JL),fnew(JL)) /= fl(JL)) then
xh =PZRIDDR(JL)
fh(JL)=fnew(JL)
else if (sign(fh(JL),fnew(JL)) /= fh(JL)) then
xl =PZRIDDR(JL)
fl(JL)=fnew(JL)
else if (PX2 .lt. 0.05) then
PX2 = PX2 + 1.0E-2
PRINT*, 'PX2 ALWAYS too small, we put a greater one : PX2 =',PX2
fh(JL) = SINGL_FUNCSMAX(PX2,PZZW3(JL),JL)
go to 100
STOP
end if
if (abs(xh-xl) <= PXACC) then
GO TO 101
endif
!!SB
!!$ if (j == MAXIT .and. (abs(xh-xl) > PXACC) ) then
!!$ PZRIDDR(JL)=0.0
!!$ go to 101
!!$ endif
!!SB
end do
STOP
else if (fl(JL) == 0.0) then
PZRIDDR(JL)=PX1
else if (fh(JL) == 0.0) then
PZRIDDR(JL)=PX2
else if (PX2 .lt. 0.05) then
PX2 = PX2 + 1.0E-2
PRINT*, 'PX2 too small, we put a greater one : PX2 =',PX2
fh(JL) = SINGL_FUNCSMAX(PX2,PZZW3(JL),JL)
go to 100
else
!!$ print*, 'PZRIDDR: root must be bracketed'
!!$ print*,'npts ',NPTS,'jl',JL
!!$ print*, 'PX1,PX2,fl,fh',PX1,PX2,fl(JL),fh(JL)
!!$ print*, 'PX2 = 30 % of supersaturation, there is no solution for Smax'
!!$ print*, 'try to put greater PX2 (upper bound for Smax research)'
!!$ STOP
PZRIDDR(JL)=0.0
go to 101
end if
101 ENDDO
!
DEALLOCATE( fh)
DEALLOCATE( fl)
DEALLOCATE( fm)
DEALLOCATE(fnew)
!
END FUNCTION ZRIDDR
!
!------------------------------------------------------------------------------
!
FUNCTION FUNCSMAX(PPZSMAX,PPZZW3,NPTS) RESULT(PFUNCSMAX)
!
!
!!**** *FUNCSMAX* - function describing SMAX function that you want to find the root
!!
!!
!! PURPOSE
!! -------
!! This function describe the equilibrium between Smax and two aerosol mode
!! acting as CCN. This function is derive from eq. (9) of CPB98 but for two
!! aerosols mode described by their respective parameters C, k, Mu, Beta.
!! the arguments are the supersaturation in "no unit" and the r.h.s. of this eq.
!! and the ratio of concentration of injected aerosols on maximum concentration
!! of injected aerosols ever.
!!** METHOD
!! ------
!! This function is called by zriddr.f90
!!
!! EXTERNAL
!! --------
!!
!! IMPLICIT ARGUMENTS
!! ------------------
!! Module MODD_PARAM_LIMA_WARM
!! XHYPF32
!!
!! XHYPINTP1
!! XHYPINTP2
!!
!! Module MODD_PARAM_C2R2
!! XKHEN_MULTI()
!! NMOD_CCN
!!
!! REFERENCE
!! ---------
!! Cohard, J.M., J.P.Pinty, K.Suhre, 2000:"On the parameterization of activation
!! spectra from cloud condensation nuclei microphysical properties",
!! J. Geophys. Res., Vol.105, N0.D9, pp. 11753-11766
!!
!! AUTHOR
!! ------
!! Frederick Chosson *CERFACS*
!!
!! MODIFICATIONS
!! -------------
!! Original 12/07/07
!! S.Berthet 19/03/08 Extension a une population multimodale d aerosols
!
!------------------------------------------------------------------------------
!
!* 0. DECLARATIONS
!
IMPLICIT NONE
!
!* 0.1 declarations of arguments and result
!
INTEGER, INTENT(IN) :: NPTS
REAL, INTENT(IN) :: PPZSMAX ! supersaturation is already in no units
REAL, DIMENSION(:), INTENT(IN) :: PPZZW3 !
REAL, DIMENSION(:), ALLOCATABLE :: PFUNCSMAX !
!
!* 0.2 declarations of local variables
!
REAL :: ZHYPF
!
REAL :: PZVEC1
INTEGER :: PIVEC1
!
ALLOCATE(PFUNCSMAX(NPTS))
!
PFUNCSMAX(:) = 0.
PZVEC1 = MAX( ( 1.0 + 10.0 * XMNH_EPSILON ) ,MIN( FLOAT(NHYP)*( 1.0 - 10.0 * XMNH_EPSILON ) , &
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XHYPINTP1*LOG(PPZSMAX)+XHYPINTP2 ) )
PIVEC1 = INT( PZVEC1 )
PZVEC1 = PZVEC1 - FLOAT( PIVEC1 )
DO JMOD = 1, NMOD_CCN
ZHYPF = 0. ! XHYPF32 is tabulated with ZSMAX in [NO UNITS]
ZHYPF = XHYPF32( PIVEC1+1,JMOD ) * PZVEC1 &
- XHYPF32( PIVEC1 ,JMOD ) *(PZVEC1 - 1.0)
! sum of s**(ki+2) * F32 * Ci * ki * beta(ki/2,3/2)
PFUNCSMAX(:) = PFUNCSMAX(:) + (PPZSMAX)**(XKHEN_MULTI(JMOD) + 2) &
* ZHYPF* XKHEN_MULTI(JMOD) * ZCHEN_MULTI(:,JMOD) &
* GAMMA_X0D( XKHEN_MULTI(JMOD)/2.0)*GAMMA_X0D(3.0/2.0) &
/ GAMMA_X0D((XKHEN_MULTI(JMOD)+3.0)/2.0)
ENDDO
! function l.h.s. minus r.h.s. of eq. (9) of CPB98 but for NMOD_CCN aerosol mode
PFUNCSMAX(:) = PFUNCSMAX(:) - PPZZW3(:)
!
END FUNCTION FUNCSMAX
!
!------------------------------------------------------------------------------
!
FUNCTION SINGL_FUNCSMAX(PPZSMAX,PPZZW3,KINDEX) RESULT(PSINGL_FUNCSMAX)
!
!
!!**** *SINGL_FUNCSMAX* - same function as FUNCSMAX
!!
!!
!! PURPOSE
!! -------
! As for FUNCSMAX but for a scalar
!!
!!** METHOD
!! ------
!! This function is called by zriddr.f90
!!
!------------------------------------------------------------------------------
!
!* 0. DECLARATIONS
!
IMPLICIT NONE
!
!* 0.1 declarations of arguments and result
!
INTEGER, INTENT(IN) :: KINDEX
REAL, INTENT(IN) :: PPZSMAX ! supersaturation is "no unit"
REAL, INTENT(IN) :: PPZZW3 !
REAL :: PSINGL_FUNCSMAX !
!
!* 0.2 declarations of local variables
!
REAL :: ZHYPF
!
REAL :: PZVEC1
INTEGER :: PIVEC1
!
PSINGL_FUNCSMAX = 0.
PZVEC1 = MAX( ( 1.0 + 10.0 * XMNH_EPSILON ),MIN( FLOAT(NHYP)*( 1.0 - 10.0 * XMNH_EPSILON ), &
XHYPINTP1*LOG(PPZSMAX)+XHYPINTP2 ) )
PIVEC1 = INT( PZVEC1 )
PZVEC1 = PZVEC1 - FLOAT( PIVEC1 )
DO JMOD = 1, NMOD_CCN
ZHYPF = 0. ! XHYPF32 is tabulated with ZSMAX in [NO UNITS]
ZHYPF = XHYPF32( PIVEC1+1,JMOD ) * PZVEC1 &
- XHYPF32( PIVEC1 ,JMOD ) *(PZVEC1 - 1.0)
! sum of s**(ki+2) * F32 * Ci * ki * bêta(ki/2,3/2)
PSINGL_FUNCSMAX = PSINGL_FUNCSMAX + (PPZSMAX)**(XKHEN_MULTI(JMOD) + 2) &
* ZHYPF* XKHEN_MULTI(JMOD) * ZCHEN_MULTI(KINDEX,JMOD) &
* GAMMA_X0D( XKHEN_MULTI(JMOD)/2.0)*GAMMA_X0D(3.0/2.0) &
/ GAMMA_X0D((XKHEN_MULTI(JMOD)+3.0)/2.0)
ENDDO
! function l.h.s. minus r.h.s. of eq. (9) of CPB98 but for NMOD_CCN aerosol mode
PSINGL_FUNCSMAX = PSINGL_FUNCSMAX - PPZZW3
!
END FUNCTION SINGL_FUNCSMAX
!
!-----------------------------------------------------------------------------
!
END SUBROUTINE LIMA_WARM_NUCL