!
! $Id: aer_sedimnt.F90 3677 2020-05-06 15:18:32Z aborella $
!
SUBROUTINE AER_SEDIMNT(pdtphys, t_seri, pplay, paprs, tr_seri, dens_aer)

!**** *AER_SEDIMNT* -  ROUTINE FOR PARAMETRIZATION OF AEROSOL SEDIMENTATION

!      Christoph Kleinschmitt
!      based on the sedimentation scheme of
!      Olivier Boucher & Jean-Jacques Morcrette 
!      (following the ice sedimentation scheme of Adrian Tompkins)

!**   INTERFACE.
!     ----------
!          *AER_SEDIMNT* IS CALLED FROM *traccoag_mod*.

!-----------------------------------------------------------------------

  USE phys_local_var_mod, ONLY: mdw, budg_sed_part, DENSO4, f_r_wet, vsed_aer
  USE dimphy, ONLY : klon,klev
  USE infotrac_phy
  USE aerophys
  USE YOMCST

IMPLICIT NONE

!-----------------------------------------------------------------------

  ! transfer variables when calling this routine
  REAL,INTENT(IN)                             :: pdtphys ! Pas d'integration pour la physique (seconde)
  REAL,DIMENSION(klon,klev),INTENT(IN)        :: t_seri  ! Temperature
  REAL,DIMENSION(klon,klev),INTENT(IN)        :: pplay   ! pression pour le mileu de chaque couche (en Pa)
  REAL,DIMENSION(klon,klev+1),INTENT(IN)      :: paprs   ! pression pour chaque inter-couche (en Pa)
  REAL,DIMENSION(klon,klev,nbtr),INTENT(INOUT):: tr_seri ! Concentration Traceur [U/KgA]
  REAL,DIMENSION(klon,klev)                   :: dens_aer! density of aerosol particles [kg/m3 aerosol] with default H2SO4 mass

  ! local variables in sedimentation routine
  INTEGER :: JL,JK,nb    
  REAL,DIMENSION(klon,klev)                   :: zvis     ! dynamic viscosity of air [kg/(m*s)]
  REAL,DIMENSION(klon,klev)                   :: zlair    ! mean free path of air [m]
  REAL                                        :: ZRHO     ! air density [kg/m^3]
  REAL                                        :: ZGDP     ! =g/dp=1/(rho*dz)
  REAL                                        :: ZDTGDP   ! =dt/(rho*dz)
  REAL,DIMENSION(klon,nbtr_bin)               :: ZSEDFLX  ! sedimentation flux of tracer [U/(m^2*s)]
  REAL,DIMENSION(nbtr_bin)                    :: ZAERONW  ! tracer concentration at current time step [U/KgA]
  REAL,DIMENSION(klon,nbtr_bin)               :: ZAERONWM1! tracer concentration at preceding time step [U/KgA]
  REAL,DIMENSION(klon,klev,nbtr_bin)          :: ZVAER    ! sedimentation velocity [m/s]
  REAL,DIMENSION(nbtr_bin)                    :: ZSOLAERS ! sedimentation flux arriving from above [U/(m^2*s)]
  REAL,DIMENSION(nbtr_bin)                    :: ZSOLAERB ! sedimentation flux leaving gridbox [U/(m^2*s)]
  REAL,DIMENSION(klon,klev)                   :: m_sulf

! dynamic viscosity of air (Pruppacher and Klett, 1978) [kg/(m*s)]
WHERE (t_seri.GE.273.15)
  zvis=(1.718 + 0.0049*(t_seri-273.15))*1.E-5
  ELSEWHERE
  zvis=(1.718 + 0.0049*(t_seri-273.15)-1.2E-05*(t_seri-273.15)**2)*1.E-5
END WHERE

! mean free path of air (Prupp. Klett) [m]
zlair(:,:) = 0.066 *(1.01325E+5/pplay(:,:))*(t_seri(:,:)/293.15)*1.E-06

!--initialisations of variables carried out from one layer to the next layer
!--actually not needed if (JK>1) test is on
DO JL=1,klon
  DO nb=1,nbtr_bin
    ZSEDFLX(JL,nb)=0.0
    ZAERONWM1(JL,nb)=0.0
  ENDDO
ENDDO

!--from top to bottom (!)
DO JK=klev,1,-1
  DO JL=1,klon
    DO nb=1,nbtr_bin
  !--initialisations
      ZSOLAERS(nb)=0.0
      ZSOLAERB(nb)=0.0
      ZGDP=RG/(paprs(JL,JK)-paprs(JL,JK+1))
      ZDTGDP=pdtphys*ZGDP

  ! source from above
      IF (JK<klev) THEN 
        ZSEDFLX(JL,nb)=ZSEDFLX(JL,nb)*ZAERONWM1(JL,nb)  
        ZSOLAERS(nb)=ZSOLAERS(nb)+ZSEDFLX(JL,nb)*ZDTGDP
      ENDIF

  ! sink to next layer
      ZRHO=pplay(JL,JK)/(RD*t_seri(JL,JK))

      ! stokes-velocity with cunnigham slip- flow correction
      ZVAER(JL,JK,nb) = 2./9.*(DENSO4(JL,JK)*1000.-ZRHO)*RG/zvis(JL,JK)*(f_r_wet(JL,JK)*mdw(nb)/2.)**2.* &
         (1.+ 2.*zlair(JL,JK)/(f_r_wet(JL,JK)*mdw(nb))*(1.257+0.4*EXP(-0.55*f_r_wet(JL,JK)*mdw(nb)/zlair(JL,JK))))

      ZSEDFLX(JL,nb)=ZVAER(JL,JK,nb)*ZRHO
      ZSOLAERB(nb)=ZSOLAERB(nb)+ZDTGDP*ZSEDFLX(JL,nb)

  !---implicit solver
      ZAERONW(nb)=(tr_seri(JL,JK,nb+nbtr_sulgas)+ZSOLAERS(nb))/(1.0+ZSOLAERB(nb))

  !---new time-step AER variable needed for next layer
      ZAERONWM1(JL,nb)=ZAERONW(nb)

      tr_seri(JL,JK,nb+nbtr_sulgas)=ZAERONWM1(JL,nb)
    ENDDO
  ENDDO
ENDDO

!---sedimentation flux to the surface
!---ZAERONWM1 now contains the surface concentration at the new timestep
!---PFLUXAER in unit of xx m-2 s-1 
budg_sed_part(:)=0.0
DO JL=1,klon
  ZRHO=pplay(JL,1)/(RD*t_seri(JL,1))
  DO nb=1,nbtr_bin
    !compute budg_sed_part as sum over bins in kg(S)/m2/s
    budg_sed_part(JL)=budg_sed_part(JL)+ZRHO*ZAERONWM1(JL,nb)*ZVAER(JL,1,nb)*(mSatom/mH2SO4mol) &
                & *dens_aer_dry*4./3.*RPI*(mdw(nb)/2.)**3
  ENDDO
ENDDO

vsed_aer(:,:)=0.0
m_sulf(:,:)=0.0

DO nb=1,nbtr_bin
  !compute mass-weighted mean of sedimentation velocity
  vsed_aer(:,:)=vsed_aer(:,:)+ZVAER(:,:,nb)*(mdw(nb)/2.)**3*MAX(1.e-30, tr_seri(:,:,nb+nbtr_sulgas))
  m_sulf(:,:)=m_sulf(:,:)+(mdw(nb)/2.)**3*MAX(1.e-30, tr_seri(:,:,nb+nbtr_sulgas))
ENDDO

!divide by total aerosol mass in grid cell
vsed_aer(:,:)=vsed_aer(:,:)/m_sulf(:,:)

END SUBROUTINE AER_SEDIMNT