source: LMDZ6/branches/blowing_snow/libf/phylmd/cosp/dsd.F90

!
! $Id: dsd.F90 4131 2022-04-20 15:50:09Z aborella $
!
  subroutine dsd(Q,Re_,Np,D,N,nsizes,dtype,rho_a,tk, &
             dmin,dmax,apm,bpm,rho_c,p1,p2,p3)
  use array_lib
  use math_lib 
  implicit none

! Purpose:
!   Create a discrete drop size distribution
!
!   Starting with Quickbeam V3, this routine now allows input of 
!   both effective radius (Re) and total number concentration (Nt)
!   Roj Marchand July 2010
!
!   The version in Quickbeam v.104 was modified to allow Re but not Nt 
!   This is a significantly modified form for the version      
!
!   Originally Part of QuickBeam v1.03 by John Haynes
!   http://reef.atmos.colostate.edu/haynes/radarsim
!
! Inputs:
!
!   [Q]        hydrometeor mixing ratio (g/kg)
!   [Re]       Optional Effective Radius (microns).  0 = use defaults (p1, p2, p3)
!
!   [D]        array of discrete drop sizes (um) where we desire to know the number concentraiton n(D).
!   [nsizes]   number of elements of [D]
!
!   [dtype]    distribution type
!   [rho_a]    ambient air density (kg m^-3)
!   [tk]       temperature (K)
!   [dmin]     minimum size cutoff (um)
!   [dmax]     maximum size cutoff (um)
!   [rho_c]    alternate constant density (kg m^-3)
!   [p1],[p2],[p3]  distribution parameters
!
! Input/Output:
!   [apm]      a parameter for mass (kg m^[-bpm])
!   [bmp]      b params for mass
!
! Outputs:
!   [N]        discrete concentrations (cm^-3 um^-1)
!              or, for monodisperse, a constant (1/cm^3)
!
! Requires:
!   function infind
!
! Created:
!   11/28/05  John Haynes (haynes@atmos.colostate.edu)
! Modified:
!   01/31/06  Port from IDL to Fortran 90
!   07/07/06  Rewritten for variable DSD's
!   10/02/06  Rewritten using scaling factors (Roger Marchand and JMH), Re added V1.04
!   July 2020 "N Scale factors" (variable fc) removed (Roj Marchand).
 
! ----- INPUTS -----  
  
  integer, intent(in) :: nsizes
  integer, intent(in) :: dtype
  real*8, intent(in)  :: Q,Re_,Np,D(nsizes)
  real*8, intent(in)  :: rho_a,tk,dmin,dmax,rho_c,p1,p2,p3
    
  real*8, intent(inout) :: apm,bpm  
  
! ----- OUTPUTS -----

  real*8, intent(out) :: N(nsizes)
  
! ----- INTERNAL -----
 
   real*8 :: fc(nsizes)

  real*8 :: &
  N0,D0,vu,local_np,dm,ld, &            ! gamma, exponential variables
  dmin_mm,dmax_mm,ahp,bhp, &        ! power law variables
  rg,log_sigma_g, &         ! lognormal variables
  rho_e                 ! particle density (kg m^-3)
  
  real*8 :: tmp1, tmp2
  real*8 :: pi,rc,tc
  real*8 :: Re

  integer k,lidx,uidx

  Re = Re_

  tc = tk - 273.15
  pi = acos(-1.0)
  
  ! // if density is constant, store equivalent values for apm and bpm
  if ((rho_c > 0) .and. (apm < 0)) then
    apm = (pi/6)*rho_c
    bpm = 3.
  endif
  
  ! will preferentially use Re input over Np.
  ! if only Np given then calculate Re
  ! if neigher than use other defaults (p1,p2,p3) following quickbeam documentation
  if(Re==0 .and. Np>0) then
    
        call calc_Re(Q,Np,rho_a, &
             dtype,dmin,dmax,apm,bpm,rho_c,p1,p2,p3, &
             Re)
  endif
 
  
  select case(dtype)
  
! ---------------------------------------------------------!
! // modified gamma                                        !
! ---------------------------------------------------------!
! :: np = total number concentration
! :: D0 = characteristic diameter (um)
! :: dm = mean diameter (um) - first moment over zeroth moment
! :: vu = distribution width parameter

  case(1)  
  
    if( abs(p3+2) < 1E-8) then
  
    if( Np>1E-30) then
    
        ! Morrison scheme with Martin 1994 shape parameter (NOTE: vu = pc +1)
        ! fixed Roj. Dec. 2010 -- after comment by S. Mcfarlane
        vu = (1/(0.2714 + 0.00057145*Np*rho_a*1E-6))**2.0 ! units of Nt = Np*rhoa = #/cm^3
    else
        print *, 'Error: Must specify a value for Np in each volume', &
             ' with Morrison/Martin Scheme.'
            stop    
    endif
    
    elseif (abs(p3+1) > 1E-8) then

      ! vu is fixed in hp structure  
      vu = p3 

    else

      ! vu isn't specified
      
      print *, 'Error: Must specify a value for vu for Modified Gamma distribution'
      stop    
      
    endif
      
      if(Re>0) then

    D0 = 2.0*Re*gamma(vu+2)/gamma(vu+3)
   
        fc = ( &
             ((D*1E-6)**(vu-1)*exp(-1*D/D0)) / &
             (apm*((D0*1E-6)**(vu+bpm))*gamma(vu+bpm)) &
         ) * 1E-12

        N = fc*rho_a*(Q*1E-3)
        
      elseif( p2+1 > 1E-8) then     ! use default value for MEAN diameter
      
        dm = p2
    D0 = gamma(vu)/gamma(vu+1)*dm

        fc = ( &
             ((D*1E-6)**(vu-1)*exp(-1*D/D0)) / &
             (apm*((D0*1E-6)**(vu+bpm))*gamma(vu+bpm)) &
         ) * 1E-12

        N = fc*rho_a*(Q*1E-3)
        
      elseif(abs(p3+1) > 1E-8)  then! use default number concentration
    
        local_np = p1 ! total number concentration / pa check
   
    tmp1 = (Q*1E-3)**(1./bpm)
      
        fc = (D*1E-6 / (gamma(vu)/(apm*local_np*gamma(vu+bpm)))** &
             (1./bpm))**vu
         
        N = ( &
          (rho_a*local_np*fc*(D*1E-6)**(-1.))/(gamma(vu)*tmp1**vu) * &
          exp(-1.*fc**(1./vu)/tmp1) &
      ) * 1E-12

      else
      
        print *, 'Error:  No default value for Dm or Np provided!  '
        stop
        
      endif
    
    
! ---------------------------------------------------------!
! // exponential                                           !
! ---------------------------------------------------------!
! :: N0 = intercept parameter (m^-4)
! :: ld = slope parameter (um)

  case(2)
 
    if(Re>0) then
 
        ld = 1.5/Re   ! units 1/um
        
    fc = (ld*1E6)**(1.+bpm)/(apm*gamma(1+bpm))* &
               exp(-1.*(ld*1E6)*(D*1E-6))*1E-12
     
        N = fc*rho_a*(Q*1E-3)
        
    elseif (abs(p1+1) > 1E-8) then

    ! use N0 default value
    
        N0 = p1

        tmp1 = 1./(1.+bpm)
  
        fc = ((apm*gamma(1.+bpm)*N0)**tmp1)*(D*1E-6)
  
        N = ( &
            N0*exp(-1.*fc*(1./(rho_a*Q*1E-3))**tmp1) &
    ) * 1E-12

    elseif (abs(p2+1) > 1E-8) then

    !     used default value for lambda 
        ld = p2

        fc = (ld*1E6)**(1.+bpm)/(apm*gamma(1+bpm))* &
             exp(-1.*(ld*1E6)*(D*1E-6))*1E-12
     
        N = fc*rho_a*(Q*1E-3)

    else

      !  ld "parameterized" from temperature (carry over from original Quickbeam).
      ld = 1220*10.**(-0.0245*tc)*1E-6
      N0 = ((ld*1E6)**(1+bpm)*Q*1E-3*rho_a)/(apm*gamma(1+bpm))
    
      N = ( &
          N0*exp(-1*ld*D) &
          ) * 1E-12
    
    endif
  
! ---------------------------------------------------------!
! // power law                                             !
! ---------------------------------------------------------!
! :: ahp = Ar parameter (m^-4 mm^-bhp)
! :: bhp = br parameter
! :: dmin_mm = lower bound (mm)
! :: dmax_mm = upper bound (mm)

  case(3)
  
    if(Re>0) then
        print *, 'Variable Re not supported for ', &
         'Power-Law distribution'
    stop
    elseif(Np>0) then
        print *, 'Variable Np not supported for ', &
         'Power-Law distribution'
    stop
    endif

!   :: br parameter
    if (abs(p1+2) < 1E-8) then
!     :: if p1=-2, bhp is parameterized according to Ryan (2000),
!     :: applicatable to cirrus clouds
      if (tc < -30) then
        bhp = -1.75+0.09*((tc+273)-243.16)
      elseif ((tc >= -30) .and. (tc < -9)) then
        bhp = -3.25-0.06*((tc+273)-265.66)
      else
        bhp = -2.15
      endif
    elseif (abs(p1+3) < 1E-8) then      
!     :: if p1=-3, bhp is parameterized according to Ryan (2000),
!     :: applicable to frontal clouds
      if (tc < -35) then
        bhp = -1.75+0.09*((tc+273)-243.16)
      elseif ((tc >= -35) .and. (tc < -17.5)) then
        bhp = -2.65+0.09*((tc+273)-255.66)
      elseif ((tc >= -17.5) .and. (tc < -9)) then
        bhp = -3.25-0.06*((tc+273)-265.66)
      else
        bhp = -2.15
      endif    
    else
!     :: otherwise the specified value is used
      bhp = p1
    endif

!   :: Ar parameter
    dmin_mm = dmin*1E-3
    dmax_mm = dmax*1E-3

!   :: commented lines are original method with constant density
      ! rc = 500.       ! (kg/m^3)
      ! tmp1 = 6*rho_a*(bhp+4)
      ! tmp2 = pi*rc*(dmax_mm**(bhp+4))*(1-(dmin_mm/dmax_mm)**(bhp+4))
      ! ahp = (Q*1E-3)*1E12*tmp1/tmp2

!   :: new method is more consistent with the rest of the distributions
!   :: and allows density to vary with particle size
      tmp1 = rho_a*(Q*1E-3)*(bhp+bpm+1)
      tmp2 = apm*(dmax_mm**bhp*dmax**(bpm+1)-dmin_mm**bhp*dmin**(bpm+1))
      ahp = tmp1/tmp2 * 1E24
      ! ahp = tmp1/tmp2 
 
      lidx = infind(D,dmin)
      uidx = infind(D,dmax)    
      do k=lidx,uidx
 
        N(k) = ( &
        ahp*(D(k)*1E-3)**bhp &
    ) * 1E-12    

      enddo

    ! print *,'test=',ahp,bhp,ahp/(rho_a*Q),D(100),N(100),bpm,dmin_mm,dmax_mm

! ---------------------------------------------------------!
! // monodisperse                                          !
! ---------------------------------------------------------!
! :: D0 = particle diameter (um)

  case(4)
  
    if (Re>0) then
        D0 = Re
    else
        D0 = p1
    endif
    
      rho_e = (6/pi)*apm*(D0*1E-6)**(bpm-3)
      fc(1) = (6./(pi*D0**3*rho_e))*1E12
      N(1) = fc(1)*rho_a*(Q*1E-3)
    
! ---------------------------------------------------------!
! // lognormal                                             !
! ---------------------------------------------------------!
! :: N0 = total number concentration (m^-3)
! :: np = fixed number concentration (kg^-1)
! :: rg = mean radius (um)
! :: log_sigma_g = ln(geometric standard deviation)

  case(5)
    if (abs(p1+1) < 1E-8 .or. Re>0 ) then

!     // rg, log_sigma_g are given
      log_sigma_g = p3
      tmp2 = (bpm*log_sigma_g)**2.
      if(Re.le.0) then 
        rg = p2
      else
    rg =Re*exp(-2.5*(log_sigma_g**2))
      endif
 
         fc = 0.5 * ( &
         (1./((2.*rg*1E-6)**(bpm)*apm*(2.*pi)**(0.5) * &
         log_sigma_g*D*0.5*1E-6)) * &
         exp(-0.5*((log(0.5*D/rg)/log_sigma_g)**2.+tmp2)) &
         ) * 1E-12
                
      N = fc*rho_a*(Q*1E-3)
      
    elseif (abs(p2+1) < 1E-8 .or. Np>0) then

!     // Np, log_sigma_g are given    
      if(Np>0) then
        local_Np=Np
      else
        local_Np = p1
      endif
      
      log_sigma_g = p3
      N0 = local_np*rho_a
      tmp1 = (rho_a*(Q*1E-3))/(2.**bpm*apm*N0)
      tmp2 = exp(0.5*bpm**2.*(log_sigma_g))**2.      
      rg = ((tmp1/tmp2)**(1/bpm))*1E6
      
      N = 0.5*( &
        N0 / ((2.*pi)**(0.5)*log_sigma_g*D*0.5*1E-6) * &
    exp((-0.5*(log(0.5*D/rg)/log_sigma_g)**2.)) &
    ) * 1E-12      
      
    else

      print *, 'Error: Must specify a value for sigma_g'
      stop
    
    endif
    
  end select
  
  end subroutine dsd