source: LMDZ5/trunk/libf/cosp/lidar_simulator.F90 @ 1985

! Copyright (c) 2009, Centre National de la Recherche Scientifique
! All rights reserved.
! 
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! provided that the following conditions are met:
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! IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT 
! OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
      
      SUBROUTINE lidar_simulator(npoints,nlev,npart,nrefl &
                , undef &
                , pres, presf, temp &
                , q_lsliq, q_lsice, q_cvliq, q_cvice &
                , ls_radliq, ls_radice, cv_radliq, cv_radice &
                , frac_out, ice_type &
                , pmol, pnorm, tautot, refl )
!
!---------------------------------------------------------------------------------
! Purpose: To compute lidar signal from model-simulated profiles of cloud water
!          and cloud fraction in each sub-column of each model gridbox.
!
! References: 
! Chepfer H., S. Bony, D. Winker, M. Chiriaco, J.-L. Dufresne, G. Seze (2008),
! Use of CALIPSO lidar observations to evaluate the cloudiness simulated by a 
! climate model, Geophys. Res. Lett., 35, L15704, doi:10.1029/2008GL034207.
!
! Previous references:
! Chiriaco et al, MWR, 2006; Chepfer et al., MWR, 2007
!
! Contacts: Helene Chepfer (chepfer@lmd.polytechnique.fr), Sandrine Bony (bony@lmd.jussieu.fr)
!
! May 2007: ActSim code of M. Chiriaco and H. Chepfer rewritten by S. Bony
!
! May 2008, H. Chepfer:
! - Units of pressure inputs: Pa 
! - Non Spherical particles : LS Ice NS coefficients, CONV Ice NS coefficients
! - New input: ice_type (0=ice-spheres ; 1=ice-non-spherical)
!
! June 2008, A. Bodas-Salcedo:
! - Ported to Fortran 90 and optimisation changes
!
! August 2008, J-L Dufresne:
! - Optimisation changes (sum instructions suppressed)
!
! October 2008, S. Bony,  H. Chepfer and J-L. Dufresne :  
! - Interface with COSP v2.0:
!      cloud fraction removed from inputs
!      in-cloud condensed water now in input (instead of grid-averaged value)
!      depolarisation diagnostic removed
!      parasol (polder) reflectances (for 5 different solar zenith angles) added
!
! December 2008, S. Bony,  H. Chepfer and J-L. Dufresne : 
! - Modification of the integration of the lidar equation.
! - change the cloud detection threshold
!
! April 2008, A. Bodas-Salcedo:
! - Bug fix in computation of pmol and pnorm of upper layer
!
! April 2008, J-L. Dufresne
! - Bug fix in computation of pmol and pnorm, thanks to Masaki Satoh: a factor 2 
! was missing. This affects the ATB values but not the cloud fraction. 
!
!---------------------------------------------------------------------------------
!
! Inputs:
!  npoints  : number of horizontal points
!  nlev : number of vertical levels
!  npart: numberb of cloud meteors (stratiform_liq, stratiform_ice, conv_liq, conv_ice). 
!        Currently npart must be 4
!  nrefl: number of solar zenith angles for parasol reflectances
!  pres : pressure in the middle of atmospheric layers (full levels): Pa
!  presf: pressure in the interface of atmospheric layers (half levels): Pa
!     presf(..,1) : surface pressure ; presf(..,nlev+1)= TOA pressure
!  temp : temperature of atmospheric layers: K
!  q_lsliq: LS sub-column liquid water mixing ratio (kg/kg)
!  q_lsice: LS sub-column ice water mixing ratio (kg/kg)
!  q_cvliq: CONV sub-column liquid water mixing ratio (kg/kg)
!  q_cvice: CONV sub-column ice water mixing ratio (kg/kg)
!  ls_radliq: effective radius of LS liquid particles (meters)
!  ls_radice: effective radius of LS ice particles (meters)
!  cv_radliq: effective radius of CONV liquid particles (meters)
!  cv_radice: effective radius of CONV ice particles (meters)
!  frac_out : cloud cover in each sub-column of the gridbox (output from scops)
!  ice_type : ice particle shape hypothesis (ice_type=0 for spheres, ice_type=1 
!             for non spherical particles)
!
! Outputs:
!  pmol : molecular attenuated backscatter lidar signal power (m^-1.sr^-1)
!  pnorm: total attenuated backscatter lidar signal power (m^-1.sr^-1)
!  tautot: optical thickess integrated from top to level z
!  refl : parasol(polder) reflectance
!
! Version 1.0 (June 2007)
! Version 1.1 (May 2008)
! Version 1.2 (June 2008)
! Version 2.0 (October 2008)
! Version 2.1 (December 2008)
!---------------------------------------------------------------------------------

      IMPLICIT NONE
      REAL :: SRsat
      PARAMETER (SRsat = 0.01) ! threshold full attenuation 

      LOGICAL ok_parasol
      PARAMETER (ok_parasol=.true.)  ! set to .true. if you want to activate parasol reflectances

      INTEGER i, k
      
      INTEGER INDX_LSLIQ,INDX_LSICE,INDX_CVLIQ,INDX_CVICE
      PARAMETER (INDX_LSLIQ=1,INDX_LSICE=2,INDX_CVLIQ=3,INDX_CVICE=4)
! inputs:
      INTEGER npoints,nlev,npart,ice_type
      INTEGER nrefl
      real undef                 ! undefined value
      REAL pres(npoints,nlev)    ! pressure full levels
      REAL presf(npoints,nlev+1) ! pressure half levels
      REAL temp(npoints,nlev)
      REAL q_lsliq(npoints,nlev), q_lsice(npoints,nlev)
      REAL q_cvliq(npoints,nlev), q_cvice(npoints,nlev)
      REAL ls_radliq(npoints,nlev), ls_radice(npoints,nlev)
      REAL cv_radliq(npoints,nlev), cv_radice(npoints,nlev)
      REAL frac_out(npoints,nlev)

! outputs (for each subcolumn):

      REAL pmol(npoints,nlev)  ! molecular backscatter signal power (m^-1.sr^-1)
      REAL pnorm(npoints,nlev) ! total lidar backscatter signal power (m^-1.sr^-1)
      REAL tautot(npoints,nlev)! optical thickess integrated from top
      REAL refl(npoints,nrefl)! parasol reflectance ! parasol

! actsim variables:

      REAL km, rdiffm, Qscat, Cmol
      PARAMETER (Cmol = 6.2446e-32) ! depends on wavelength
      PARAMETER (km = 1.38e-23)     ! Boltzmann constant (J/K)

      PARAMETER (rdiffm = 0.7)      ! multiple scattering correction parameter
      PARAMETER (Qscat = 2.0)       ! particle scattering efficiency at 532 nm

      REAL rholiq, rhoice
      PARAMETER (rholiq=1.0e+03)     ! liquid water (kg/m3)
      PARAMETER (rhoice=0.5e+03)     ! ice (kg/m3)

      REAL pi, rhopart(npart)
      REAL polpart(npart,5)  ! polynomial coefficients derived for spherical and non spherical
                             ! particules

!   grid-box variables:
      REAL rad_part(npoints,nlev,npart)
      REAL rhoair(npoints,nlev), zheight(npoints,nlev+1)
      REAL beta_mol(npoints,nlev), alpha_mol(npoints,nlev)
      REAL kp_part(npoints,nlev,npart)

!   sub-column variables:
      REAL frac_sub(npoints,nlev)
      REAL qpart(npoints,nlev,npart) ! mixing ratio particles in each subcolumn
      REAL alpha_part(npoints,nlev,npart)
      REAL tau_mol_lay(npoints)  ! temporary variable, moL. opt. thickness of layer k
      REAL tau_mol(npoints,nlev) ! optical thickness between TOA and bottom of layer k
      REAL tau_part(npoints,nlev,npart)
      REAL betatot(npoints,nlev)
      REAL tautot_lay(npoints)   ! temporary variable, total opt. thickness of layer k
!     Optical thickness from TOA to surface for Parasol
      REAL tautot_S_liq(npoints),tautot_S_ice(npoints)     ! for liq and ice clouds

! Abderrahmane 8-2-2011
      Logical iflag_testlidar
      PARAMETER (iflag_testlidar=.false.)

!------------------------------------------------------------
!---- 1. Preliminary definitions and calculations :
!------------------------------------------------------------

      if ( npart .ne. 4 ) then
        print *,'Error in lidar_simulator, npart should be 4, not',npart
        stop
      endif

      pi = dacos(-1.D0)

! Polynomial coefficients for spherical liq/ice particles derived from Mie theory.
! Polynomial coefficients for non spherical particles derived from a composite of
! Ray-tracing theory for large particles (e.g. Noel et al., Appl. Opt., 2001)
! and FDTD theory for very small particles (Yang et al., JQSRT, 2003).

! We repeat the same coefficients for LS and CONV cloud to make code more readable
!*     LS Liquid water coefficients:
         polpart(INDX_LSLIQ,1) =  2.6980e-8     
         polpart(INDX_LSLIQ,2) = -3.7701e-6
         polpart(INDX_LSLIQ,3) =  1.6594e-4
         polpart(INDX_LSLIQ,4) = -0.0024
         polpart(INDX_LSLIQ,5) =  0.0626
!*     LS Ice coefficients: 
      if (ice_type.eq.0) then     
         polpart(INDX_LSICE,1) = -1.0176e-8   
         polpart(INDX_LSICE,2) =  1.7615e-6
         polpart(INDX_LSICE,3) = -1.0480e-4
         polpart(INDX_LSICE,4) =  0.0019
         polpart(INDX_LSICE,5) =  0.0460
      endif
!*     LS Ice NS coefficients: 
      if (ice_type.eq.1) then 
         polpart(INDX_LSICE,1) = 1.3615e-8  
         polpart(INDX_LSICE,2) = -2.04206e-6 
         polpart(INDX_LSICE,3) = 7.51799e-5
         polpart(INDX_LSICE,4) = 0.00078213
         polpart(INDX_LSICE,5) = 0.0182131
      endif
!*     CONV Liquid water coefficients:
         polpart(INDX_CVLIQ,1) =  2.6980e-8     
         polpart(INDX_CVLIQ,2) = -3.7701e-6
         polpart(INDX_CVLIQ,3) =  1.6594e-4
         polpart(INDX_CVLIQ,4) = -0.0024
         polpart(INDX_CVLIQ,5) =  0.0626
!*     CONV Ice coefficients: 
      if (ice_type.eq.0) then 
         polpart(INDX_CVICE,1) = -1.0176e-8   
         polpart(INDX_CVICE,2) =  1.7615e-6
         polpart(INDX_CVICE,3) = -1.0480e-4
         polpart(INDX_CVICE,4) =  0.0019
         polpart(INDX_CVICE,5) =  0.0460
      endif
      if (ice_type.eq.1) then
         polpart(INDX_CVICE,1) = 1.3615e-8
         polpart(INDX_CVICE,2) = -2.04206e-6
         polpart(INDX_CVICE,3) = 7.51799e-5
         polpart(INDX_CVICE,4) = 0.00078213
         polpart(INDX_CVICE,5) = 0.0182131
      endif

! density:
!*    clear-sky air:
      rhoair = pres/(287.04*temp)

!*    liquid/ice particules:
      rhopart(INDX_LSLIQ) = rholiq
      rhopart(INDX_LSICE) = rhoice
      rhopart(INDX_CVLIQ) = rholiq
      rhopart(INDX_CVICE) = rhoice

! effective radius particles:
      rad_part(:,:,INDX_LSLIQ) = ls_radliq(:,:)
      rad_part(:,:,INDX_LSICE) = ls_radice(:,:)
      rad_part(:,:,INDX_CVLIQ) = cv_radliq(:,:)
      rad_part(:,:,INDX_CVICE) = cv_radice(:,:)
      rad_part(:,:,:)=MAX(rad_part(:,:,:),0.)
      rad_part(:,:,:)=MIN(rad_part(:,:,:),70.0e-6)
      
! altitude at half pressure levels:
      zheight(:,1) = 0.0
      do k = 2, nlev+1
        zheight(:,k) = zheight(:,k-1) &
                  -(presf(:,k)-presf(:,k-1))/(rhoair(:,k-1)*9.81)
      enddo

! cloud fraction (0 or 1) in each sub-column:
! (if frac_out=1or2 -> frac_sub=1; if frac_out=0 -> frac_sub=0)
      frac_sub = MIN( frac_out, 1.0 )

!------------------------------------------------------------
!---- 2. Molecular alpha and beta:
!------------------------------------------------------------

      beta_mol = pres/km/temp * Cmol
      alpha_mol = 8.0*pi/3.0 * beta_mol

!------------------------------------------------------------
!---- 3. Particles alpha and beta:
!------------------------------------------------------------

! polynomes kp_lidar derived from Mie theory:
      do i = 1, npart
       where ( rad_part(:,:,i).gt.0.0)
         kp_part(:,:,i) = &
            polpart(i,1)*(rad_part(:,:,i)*1e6)**4 &
          + polpart(i,2)*(rad_part(:,:,i)*1e6)**3 &
          + polpart(i,3)*(rad_part(:,:,i)*1e6)**2 &
          + polpart(i,4)*(rad_part(:,:,i)*1e6) &
          + polpart(i,5)
        elsewhere
         kp_part(:,:,i) = 0.
        endwhere
      enddo
      
! mixing ratio particules in each subcolumn:
          qpart(:,:,INDX_LSLIQ) = q_lsliq(:,:) ! oct08
          qpart(:,:,INDX_LSICE) = q_lsice(:,:) ! oct08
          qpart(:,:,INDX_CVLIQ) = q_cvliq(:,:) ! oct08
          qpart(:,:,INDX_CVICE) = q_cvice(:,:) ! oct08

! alpha of particles in each subcolumn:
      do i = 1, npart
        where ( rad_part(:,:,i).gt.0.0)
          alpha_part(:,:,i) = 3.0/4.0 * Qscat &
                 * rhoair(:,:) * qpart(:,:,i) &
                 / (rhopart(i) * rad_part(:,:,i) )
        elsewhere
          alpha_part(:,:,i) = 0.
        endwhere
      enddo

!------------------------------------------------------------
!---- 4. Backscatter signal:
!------------------------------------------------------------

! optical thickness (molecular):
!     opt. thick of each layer
      tau_mol(:,1:nlev) = alpha_mol(:,1:nlev) &
         & *(zheight(:,2:nlev+1)-zheight(:,1:nlev))
!     opt. thick from TOA
      DO k = nlev-1, 1, -1
        tau_mol(:,k) = tau_mol(:,k) + tau_mol(:,k+1)
      ENDDO

! optical thickness (particles):

      tau_part = rdiffm * alpha_part
      DO i = 1, npart
!       opt. thick of each layer
        tau_part(:,:,i) = tau_part(:,:,i) &
           & * (zheight(:,2:nlev+1)-zheight(:,1:nlev) )
!       opt. thick from TOA
        DO k = nlev-1, 1, -1 
          tau_part(:,k,i) = tau_part(:,k,i) + tau_part(:,k+1,i)
        ENDDO
      ENDDO

! molecular signal:
!      Upper layer 
       pmol(:,nlev) = beta_mol(:,nlev) / (2.*tau_mol(:,nlev)) &
            & * (1.-exp(-2.0*tau_mol(:,nlev)))
!      Other layers
       DO k= nlev-1, 1, -1
        tau_mol_lay(:) = tau_mol(:,k)-tau_mol(:,k+1) ! opt. thick. of layer k
        WHERE (tau_mol_lay(:).GT.0.)
          pmol(:,k) = beta_mol(:,k) * EXP(-2.0*tau_mol(:,k+1)) / (2.*tau_mol_lay(:)) &
            & * (1.-exp(-2.0*tau_mol_lay(:)))
        ELSEWHERE
!         This must never happend, but just in case, to avoid div. by 0
          pmol(:,k) = beta_mol(:,k) * EXP(-2.0*tau_mol(:,k+1))
        END WHERE
      END DO
!
! Total signal (molecular + particules):
!
! For performance reason on vector computers, the 2 following lines should not be used
! and should be replace by the later one.
!      betatot(:,:) = beta_mol(:,:) + sum(kp_part*alpha_part,dim=3)
!      tautot(:,:)  = tau_mol(:,:)  + sum(tau_part,dim=3)
      betatot(:,:) = beta_mol(:,:)
      tautot(:,:)  = tau_mol(:,:)
      DO i = 1, npart
           betatot(:,:) = betatot(:,:) + kp_part(:,:,i)*alpha_part(:,:,i)
           tautot(:,:) = tautot(:,:)  + tau_part(:,:,i)
      ENDDO ! i
!
!     Upper layer 
      pnorm(:,nlev) = betatot(:,nlev) / (2.*tautot(:,nlev)) &
            & * (1.-exp(-2.0*tautot(:,nlev)))
!     Other layers
      DO k= nlev-1, 1, -1
        tautot_lay(:) = tautot(:,k)-tautot(:,k+1) ! optical thickness of layer k
        WHERE (tautot_lay(:).GT.0.)
       pnorm(:,k) = betatot(:,k) * EXP(-2.0*tautot(:,k+1)) / (2.*tautot_lay(:)) &
!correc          pnorm(:,k) = betatot(:,k) * EXP(-2.0*tautot(:,k+1)) & ! correc Satoh
!correc               &               / (2.0*tautot_lay(:)) &          ! correc Satoh
               & * (1.-EXP(-2.0*tautot_lay(:)))
        ELSEWHERE
!         This must never happend, but just in case, to avoid div. by 0
          pnorm(:,k) = betatot(:,k) * EXP(-2.0*tautot(:,k+1))
        END WHERE
      END DO

     if (iflag_testlidar) then
!+JLD test 
!     do k=1,nlev
!      print*,'Min val de frac_out=',k,minval(frac_out(:,k))
!      print*,'Max val de frac_out=',k,maxval(frac_out(:,k))
!     enddo
       where ( frac_out(:,:).ge.0.5)
! Correction AI 9 5 11          pnorm(:,:) = pmol(:,:)*10.
       pnorm(:,:) = pmol(:,:)*50.
        elsewhere
          pnorm(:,:) = pmol(:,:)
        endwhere
!-JLD test 
     endif

!-------- End computation Lidar --------------------------

!---------------------------------------------------------
!  Parasol/Polder module
!
!  Purpose : Compute reflectance for one particular viewing direction
!  and 5 solar zenith angles (calculation valid only over ocean)
! ---------------------------------------------------------

! initialization:
    refl(:,:) = 0.0

! activate parasol calculations:
    if (ok_parasol) then

!     Optical thickness from TOA to surface
      tautot_S_liq = 0.
      tautot_S_ice = 0.
      tautot_S_liq(:) = tautot_S_liq(:) &
         + tau_part(:,1,1) + tau_part(:,1,3)
      tautot_S_ice(:) = tautot_S_ice(:) &
         + tau_part(:,1,2) + tau_part(:,1,4)

      call parasol(npoints,nrefl,undef  &
                 ,tautot_S_liq,tautot_S_ice &
                 ,refl)

    endif ! ok_parasol

  END SUBROUTINE lidar_simulator
!
!---------------------------------------------------------------------------------
!
  SUBROUTINE parasol(npoints,nrefl,undef  &
                       ,tautot_S_liq,tautot_S_ice  &
                       ,refl)
!---------------------------------------------------------------------------------
! Purpose: To compute Parasol reflectance signal from model-simulated profiles 
!          of cloud water and cloud fraction in each sub-column of each model 
!          gridbox.
!
!
! December 2008, S. Bony,  H. Chepfer and J-L. Dufresne : 
! - optimization for vectorization
!
! Version 2.0 (October 2008)
! Version 2.1 (December 2008)
!---------------------------------------------------------------------------------

    IMPLICIT NONE

! inputs
    INTEGER npoints              ! Number of horizontal gridpoints
    INTEGER nrefl                ! Number of angles for which the reflectance 
                                 ! is computed. Can not be greater then ntetas
    REAL undef                   ! Undefined value. Currently not used
    REAL tautot_S_liq(npoints)   ! liquid water cloud optical thickness, 
                                   ! integrated from TOA to surface
    REAL tautot_S_ice(npoints)   ! same for ice water clouds only
! outputs
    REAL refl(npoints,nrefl)     ! Parasol reflectances
!
! Local variables
    REAL tautot_S(npoints)       ! cloud optical thickness, from TOA to surface
    REAL frac_taucol_liq(npoints), frac_taucol_ice(npoints)

    REAL pi
!   look up table variables:
    INTEGER ny, it
    INTEGER ntetas, nbtau        ! number of angle and of optical thickness
                                   ! of the look-up table
    PARAMETER (ntetas=5, nbtau=7)
    REAL aa(ntetas,nbtau-1), ab(ntetas,nbtau-1)
    REAL ba(ntetas,nbtau-1), bb(ntetas,nbtau-1)  
    REAL tetas(ntetas),tau(nbtau)                        
    REAL r_norm(ntetas)
    REAL rlumA(ntetas,nbtau), rlumB(ntetas,nbtau)       
    REAL rlumA_mod(npoints,5), rlumB_mod(npoints,5) 

    DATA tau   /0., 1., 5., 10., 20., 50., 100./
    DATA tetas /0., 20., 40., 60., 80./
    
! Look-up table for spherical liquid particles:
    DATA (rlumA(1,ny),ny=1,nbtau) /0.03, 0.090886, 0.283965, &
     0.480587, 0.695235, 0.908229, 1.0 /
    DATA (rlumA(2,ny),ny=1,nbtau) /0.03, 0.072185, 0.252596, &
      0.436401,  0.631352, 0.823924, 0.909013 /
    DATA (rlumA(3,ny),ny=1,nbtau) /0.03, 0.058410, 0.224707, &
      0.367451,  0.509180, 0.648152, 0.709554 /
    DATA (rlumA(4,ny),ny=1,nbtau) /0.03, 0.052498, 0.175844, &
      0.252916,  0.326551, 0.398581, 0.430405 /
    DATA (rlumA(5,ny),ny=1,nbtau) /0.03, 0.034730, 0.064488, &
      0.081667,  0.098215, 0.114411, 0.121567 /

! Look-up table for ice particles:
    DATA (rlumB(1,ny),ny=1,nbtau) /0.03, 0.092170, 0.311941, &
       0.511298, 0.712079 , 0.898243 , 0.976646 /
    DATA (rlumB(2,ny),ny=1,nbtau) /0.03, 0.087082, 0.304293, &
       0.490879,  0.673565, 0.842026, 0.912966 /
    DATA (rlumB(3,ny),ny=1,nbtau) /0.03, 0.083325, 0.285193, &
      0.430266,  0.563747, 0.685773,  0.737154 /
    DATA (rlumB(4,ny),ny=1,nbtau) /0.03, 0.084935, 0.233450, &
      0.312280, 0.382376, 0.446371, 0.473317 /
    DATA (rlumB(5,ny),ny=1,nbtau) /0.03, 0.054157, 0.089911, &
      0.107854, 0.124127, 0.139004, 0.145269 /

!--------------------------------------------------------------------------------
! Lum_norm=f(tetaS,tau_cloud) derived from adding-doubling calculations
!        valid ONLY ABOVE OCEAN (albedo_sfce=5%)
!        valid only in one viewing direction (theta_v=30�, phi_s-phi_v=320�)
!        based on adding-doubling radiative transfer computation
!        for tau values (0 to 100) and for tetas values (0 to 80)
!        for 2 scattering phase functions: liquid spherical, ice non spherical

    IF ( nrefl.GT. ntetas ) THEN
        PRINT *,'Error in lidar_simulator, nrefl should be less then ',ntetas,' not',nrefl
        STOP
    ENDIF

    rlumA_mod=0
    rlumB_mod=0
!
    pi = ACOS(-1.0)
    r_norm(:)=1./ COS(pi/180.*tetas(:))
!
    tautot_S_liq(:)=MAX(tautot_S_liq(:),tau(1))
    tautot_S_ice(:)=MAX(tautot_S_ice(:),tau(1))
    tautot_S(:) = tautot_S_ice(:) + tautot_S_liq(:)
!
! relative fraction of the opt. thick due to liquid or ice clouds
    WHERE (tautot_S(:) .GT. 0.)
        frac_taucol_liq(:) = tautot_S_liq(:) / tautot_S(:)
        frac_taucol_ice(:) = tautot_S_ice(:) / tautot_S(:)
    ELSEWHERE
        frac_taucol_liq(:) = 1.
        frac_taucol_ice(:) = 0.
    END WHERE
    tautot_S(:)=MIN(tautot_S(:),tau(nbtau))
!
! Linear interpolation :

    DO ny=1,nbtau-1
! microphysics A (liquid clouds) 
      aA(:,ny) = (rlumA(:,ny+1)-rlumA(:,ny))/(tau(ny+1)-tau(ny))
      bA(:,ny) = rlumA(:,ny) - aA(:,ny)*tau(ny)
! microphysics B (ice clouds)
      aB(:,ny) = (rlumB(:,ny+1)-rlumB(:,ny))/(tau(ny+1)-tau(ny))
      bB(:,ny) = rlumB(:,ny) - aB(:,ny)*tau(ny)
    ENDDO
!
    DO it=1,ntetas
      DO ny=1,nbtau-1
        WHERE (tautot_S(:).GE.tau(ny).AND.tautot_S(:).LE.tau(ny+1))
            rlumA_mod(:,it) = aA(it,ny)*tautot_S(:) + bA(it,ny)
            rlumB_mod(:,it) = aB(it,ny)*tautot_S(:) + bB(it,ny)
        END WHERE
      END DO
    END DO
!
    DO it=1,ntetas
      refl(:,it) = frac_taucol_liq(:) * rlumA_mod(:,it) &
         + frac_taucol_ice(:) * rlumB_mod(:,it)
! normalized radiance -> reflectance: 
      refl(:,it) = refl(:,it) * r_norm(it)
    ENDDO

    RETURN
  END SUBROUTINE parasol