
! $Id: coagulate.F90 5099 2024-07-22 19:29:09Z abarral $

SUBROUTINE COAGULATE(pdtcoag,mdw,tr_seri,t_seri,pplay,dens_aer,is_strato)
  !     -----------------------------------------------------------------------

  !     Author : Christoph Kleinschmitt (with Olivier Boucher)
  !     ------

  !     purpose
  !     -------

  !     interface
  !     ---------
  !      input 
  !       pdtphys        time step duration                 [sec]
  !       tr_seri        tracer mixing ratios               [kg/kg]
  !       mdw             # or mass median diameter          [m]

  !     method
  !     ------

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

  USE dimphy, ONLY : klon,klev
  USE aerophys
  USE infotrac_phy
  USE phys_local_var_mod, ONLY: DENSO4, DENSO4B, f_r_wet, f_r_wetB
  USE strataer_local_var_mod, ONLY: flag_new_strat_compo
  USE lmdz_yomcst
  
  IMPLICIT NONE

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

  ! transfer variables when calling this routine
  REAL,INTENT(IN)                               :: pdtcoag ! Time step in coagulation routine [s]
  REAL,DIMENSION(nbtr_bin),INTENT(IN)           :: mdw     ! aerosol particle diameter in each bin [m]
  REAL,DIMENSION(klon,klev,nbtr),INTENT(INOUT)  :: tr_seri ! Concentration Traceur [U/KgA]
  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)                     :: dens_aer! density of aerosol [kg/m3 aerosol] with default H2SO4 mass
  LOGICAL,DIMENSION(klon,klev),INTENT(IN)       :: is_strato

  ! local variables in coagulation routine
  INTEGER                                       :: i,j,k,nb,ilon,ilev
  REAL, DIMENSION(nbtr_bin)                     :: radiusdry ! dry aerosol particle radius in each bin [m]
  REAL, DIMENSION(nbtr_bin)                     :: radiuswet ! wet aerosol particle radius in each bin [m]
  REAL, DIMENSION(klon,klev,nbtr_bin)           :: tr_t ! Concentration Traceur at time t [U/KgA]
  REAL, DIMENSION(klon,klev,nbtr_bin)           :: tr_tp1 ! Concentration Traceur at time t+1 [U/KgA]
  REAL, DIMENSION(nbtr_bin,nbtr_bin,nbtr_bin)   :: ff   ! Volume fraction of intermediate particles
  REAL, DIMENSION(nbtr_bin)                     :: Vdry ! Volume dry of bins
  REAL, DIMENSION(nbtr_bin)                     :: Vwet ! Volume wet of bins
  REAL, DIMENSION(nbtr_bin,nbtr_bin)            :: Vij  ! Volume sum of i and j
  REAL                                          :: eta  ! Dynamic viscosity of air
  REAL, PARAMETER                               :: mair=4.8097E-26 ! Average mass of an air molecule [kg]
  REAL                                          :: zrho ! Density of air
  REAL                                          :: mnfrpth ! Mean free path of air
  REAL, DIMENSION(nbtr_bin)                     :: Kn   ! Knudsen number of particle i
  REAL, DIMENSION(nbtr_bin)                     :: Di   ! Particle diffusion coefficient
  REAL, DIMENSION(nbtr_bin)                     :: m_par   ! Mass of particle i
  REAL, DIMENSION(nbtr_bin)                     :: thvelpar! Thermal velocity of particle i
  REAL, DIMENSION(nbtr_bin)                     :: mfppar  ! Mean free path of particle i
  REAL, DIMENSION(nbtr_bin)                     :: delta! delta of particle i (from equation 21)
  REAL, DIMENSION(nbtr_bin,nbtr_bin)            :: beta ! Coagulation kernel from Brownian diffusion
  REAL                                          :: beta_const ! Constant coagulation kernel (for comparison)
  REAL                                          :: num
  REAL                                          :: numi
  REAL                                          :: denom

  ! Additional variables for coagulation enhancement factor due to van der Waals forces
  ! Taken from Chan and Mozurkewich, Measurement of the coagulation rate constant for sulfuric acid 
  ! particles as a function of particle size using TDMA, Aerosol Science, 32, 321-339, 2001.
  !--ok_vdw is 0 for no vdW forces, 1 for E(0), 2 for E(infinity)
  INTEGER, PARAMETER                            :: ok_vdw = 0
  REAL, PARAMETER                               :: avdW1 = 0.0757
  REAL, PARAMETER                               :: avdW3 = 0.0015
  REAL, PARAMETER                               :: bvdW0 = 0.0151
  REAL, PARAMETER                               :: bvdW1 = -0.186
  REAL, PARAMETER                               :: bvdW3 = -0.0163
  REAL, PARAMETER                               :: AvdW = 6.4e-20 !Hamaker constant in J = 1e7 erg
  REAL                                          :: AvdWi
  REAL                                          :: xvdW
  REAL                                          :: EvdW

! ff(i,j,k): Volume fraction of Vi,j that is partitioned to each model bin k
! just need to be calculated in model initialization because mdw(:) size is fixed
! no need to recalculate radius, Vdry, Vij, and ff every timestep because it is for  
! dry aerosols
  DO i=1, nbtr_bin
     radiusdry(i)=mdw(i)/2.
     Vdry(i)=radiusdry(i)**3.  !neglecting factor 4*RPI/3
     Vwet(i)=0.0
  ENDDO

  DO j=1, nbtr_bin
     DO i=1, nbtr_bin
        Vij(i,j)= Vdry(i)+Vdry(j)
     ENDDO
  ENDDO
  
!--pre-compute the f(i,j,k) from Jacobson equation 13
  ff=0.0 
  DO k=1, nbtr_bin 
  DO j=1, nbtr_bin
  DO i=1, nbtr_bin
    IF (k==1) THEN
      ff(i,j,k)= 0.0
    ELSEIF (k>1.AND.Vdry(k-1)<Vij(i,j).AND.Vij(i,j)<Vdry(k)) THEN
      ff(i,j,k)= 1.-ff(i,j,k-1)
    ELSEIF (k==nbtr_bin) THEN
      IF (Vij(i,j)>=Vdry(k)) THEN
        ff(i,j,k)= 1.
      ELSE
        ff(i,j,k)= 0.0
      ENDIF
    ELSEIF (k<=(nbtr_bin-1).AND.Vdry(k)<=Vij(i,j).AND.Vij(i,j)<Vdry(k+1)) THEN
      ff(i,j,k)= Vdry(k)/Vij(i,j)*(Vdry(k+1)-Vij(i,j))/(Vdry(k+1)-Vdry(k))
    ENDIF
  ENDDO
  ENDDO
  ENDDO
! End of just need to be calculated at initialization because mdw(:) size is fixed
  
  DO ilon=1, klon
  DO ilev=1, klev 
  !only in the stratosphere
  IF (is_strato(ilon,ilev)) THEN
  !compute actual wet particle radius & volume for every grid box
  IF(flag_new_strat_compo) THEN
     DO i=1, nbtr_bin
        radiuswet(i)=f_r_wetB(ilon,ilev,i)*mdw(i)/2.
        Vwet(i)= radiuswet(i)**3.  !neglecting factor 4*RPI/3
!!      Vwet(i)= Vdry(i)*(f_r_wetB(ilon,ilev,i)**3)
     ENDDO
  ELSE
     DO i=1, nbtr_bin
        radiuswet(i)=f_r_wet(ilon,ilev)*mdw(i)/2.
        Vwet(i)= radiuswet(i)**3.  !neglecting factor 4*RPI/3
!!      Vwet(i)= Vdry(i)*(f_r_wet(ilon,ilev)**3)
     ENDDO
  ENDIF
  
!--Calculations for the coagulation kernel---------------------------------------------------------

  zrho=pplay(ilon,ilev)/t_seri(ilon,ilev)/RD

!--initialize the tracer at time t and convert from [number/KgA] to [number/m3]
  DO i=1, nbtr_bin
  tr_t(ilon,ilev,i) = tr_seri(ilon,ilev,i+nbtr_sulgas) * zrho
  ENDDO

  ! mean free path of air (Pruppacher and Klett, 2010, p.417) [m]
  mnfrpth=6.6E-8*(1.01325E+5/pplay(ilon,ilev))*(t_seri(ilon,ilev)/293.15)
  ! mnfrpth=2.*eta/(zrho*thvelair)
  ! mean free path of air (Prupp. Klett) in [10^-6 m]
  ! ZLAIR = 0.066 *(1.01325E+5/PPLAY)*(T_SERI/293.15)*1.E-06

  ! dynamic viscosity of air (Pruppacher and Klett, 2010, p.417) [kg/(m*s)]
  IF (t_seri(ilon,ilev)>=273.15) THEN
    eta=(1.718+0.0049*(t_seri(ilon,ilev)-273.15))*1.E-5
  ELSE
    eta=(1.718+0.0049*(t_seri(ilon,ilev)-273.15)-1.2E-5*(t_seri(ilon,ilev)-273.15)**2)*1.E-5
  ENDIF

!--pre-compute the particle diffusion coefficient Di(i) from equation 18
  Di=0.0
  DO i=1, nbtr_bin
      Kn(i)=mnfrpth/radiuswet(i)
      Di(i)=RKBOL*t_seri(ilon,ilev)/(6.*RPI*radiuswet(i)*eta)*(1.+Kn(i)*(1.249+0.42*exp(-0.87/Kn(i))))
  ENDDO

!--pre-compute the thermal velocity of a particle thvelpar(i) from equation 20
  thvelpar=0.0
  IF(flag_new_strat_compo) THEN
     DO i=1, nbtr_bin
        m_par(i)=4./3.*RPI*radiuswet(i)**3.*DENSO4B(ilon,ilev,i)*1000.
        thvelpar(i)=sqrt(8.*RKBOL*t_seri(ilon,ilev)/(RPI*m_par(i)))
     ENDDO
  ELSE
     DO i=1, nbtr_bin
        m_par(i)=4./3.*RPI*radiuswet(i)**3.*DENSO4(ilon,ilev)*1000.
        thvelpar(i)=sqrt(8.*RKBOL*t_seri(ilon,ilev)/(RPI*m_par(i)))
     ENDDO
  ENDIF

!--pre-compute the particle mean free path mfppar(i) from equation 22
  mfppar=0.0
  DO i=1, nbtr_bin
   mfppar(i)=8.*Di(i)/(RPI*thvelpar(i))
  ENDDO

!--pre-compute the mean distance delta(i) from the center of a sphere reached by particles 
!--leaving the surface of the sphere and traveling a distance of particle mfppar(i) from equation 21
  delta=0.0
  DO i=1, nbtr_bin
      delta(i)=((2.*radiuswet(i)+mfppar(i))**3.-(4.*radiuswet(i)**2.+mfppar(i)**2.)**1.5)/ &
   (6.*radiuswet(i)*mfppar(i))-2.*radiuswet(i)
  ENDDO

!   beta(i,j): coagulation kernel (rate coefficient) of 2 colliding particles i,j 
!--pre-compute the beta(i,j) from equation 17 in Jacobson
  num=0.0
  DO j=1, nbtr_bin
  DO i=1, nbtr_bin

     num=4.*RPI*(radiuswet(i)+radiuswet(j))*(Di(i)+Di(j))
     denom=(radiuswet(i)+radiuswet(j))/(radiuswet(i)+radiuswet(j)+sqrt(delta(i)**2.+delta(j)**2.))+ &
   4.*(Di(i)+Di(j))/(sqrt(thvelpar(i)**2.+thvelpar(j)**2.)*(radiuswet(i)+radiuswet(j)))
     beta(i,j)=num/denom

!--compute enhancement factor due to van der Waals forces
   IF (ok_vdw == 0) THEN      !--no enhancement factor
      Evdw=1.0
   ELSEIF (ok_vdw == 1) THEN  !--E(0) case
      AvdWi = AvdW/(RKBOL*t_seri(ilon,ilev))*(4.*radiuswet(i)*radiuswet(j))/(radiuswet(i)+radiuswet(j))**2.
      xvdW = LOG(1.+AvdWi)
      EvdW = 1. + avdW1*xvdW + avdW3*xvdW**3
   ELSEIF (ok_vdw == 2) THEN  !--E(infinity) case
      AvdWi = AvdW/(RKBOL*t_seri(ilon,ilev))*(4.*radiuswet(i)*radiuswet(j))/(radiuswet(i)+radiuswet(j))**2.
      xvdW = LOG(1.+AvdWi)
      EvdW = 1. + SQRT(AvdWi/3.)/(1.+bvdW0*SQRT(AvdWi)) + bvdW1*xvdW + bvdW3*xvdW**3.
   ENDIF

   beta(i,j)=beta(i,j)*EvdW

  ENDDO
  ENDDO

!--external loop for equation 14
  DO k=1, nbtr_bin

!--calculating denominator sum 
  denom=0.0
  DO j=1, nbtr_bin
     !    fraction of coagulation of k and j that is not giving k
     denom=denom+(1.-ff(k,j,k))*beta(k,j)*tr_t(ilon,ilev,j)
  ENDDO

  IF (k==1) THEN
!--calculate new concentration of smallest bin
    tr_tp1(ilon,ilev,k)=tr_t(ilon,ilev,k)/(1.+pdtcoag*denom)
    ELSE
!--calculating double sum terms in numerator of eq 14
    num=0.0
    DO j=1, k
       numi=0.0
       DO i=1, k-1

!           see Jacobson: " In order to conserve volume and volume concentration (which
!           coagulation physically does) while giving up some accuracy in number concentration" 

!           Coagulation of i and j giving k
!           with V(i) and then V(j) because it considers i,j and j,i with the double loop

!           BUT WHY WET VOLUME V(i) in old STRATAER? tracers are already dry aerosols and coagulation 
!           kernel beta(i,j) accounts for wet aerosols -> reply below

!             numi=numi+ff(i,j,k)*beta(i,j)*V(i)*tr_tp1(ilon,ilev,i)*tr_t(ilon,ilev,j)
            numi=numi+ff(i,j,k)*beta(i,j)*Vdry(i)*tr_tp1(ilon,ilev,i)*tr_t(ilon,ilev,j)
       ENDDO
       num=num+numi
    ENDDO

!--calculate new concentration of other bins
!      tr_tp1(ilon,ilev,k)=(V(k)*tr_t(ilon,ilev,k)+pdtcoag*num)/( (1.+pdtcoag*denom)*V(k) )
    tr_tp1(ilon,ilev,k)=(Vdry(k)*tr_t(ilon,ilev,k)+pdtcoag*num)/( (1.+pdtcoag*denom)*Vdry(k) )

!       In constant composition (no dependency on aerosol size because no kelvin effect)
!       V(l)= (f_r_wet(ilon,ilev)**3)*((mdw(l)/2.)**3) = (f_r_wet(ilon,ilev)**3)*Vdry(i)
!       so numi and num are proportional (f_r_wet(ilon,ilev)**3)
!       and so 
!        tr_tp1(ilon,ilev,k)=(V(k)*tr_t(ilon,ilev,k)+pdtcoag*num)/( (1.+pdtcoag*denom)*V(k) )
!                     =(Vdry(k)*tr_t(ilon,ilev,k)+pdtcoag*num_dry)/( (1.+pdtcoag*denom)*Vdry(k) ) 
!          with num_dry=...beta(i,j)*Vdry(i)*....
!       so in old STRATAER (.not.flag_new_strat_compo), it was correct
  ENDIF

  ENDDO !--end of loop k

!--convert tracer concentration back from [number/m3] to [number/KgA] and write into tr_seri
  DO i=1, nbtr_bin
     tr_seri(ilon,ilev,i+nbtr_sulgas) = tr_tp1(ilon,ilev,i) / zrho
  ENDDO

  ENDIF ! IF IN STRATOSPHERE
  ENDDO !--end of loop klev
  ENDDO !--end of loop klon
! *********************************************

END SUBROUTINE COAGULATE
