/wrfv2_fire/phys/module_mp_wsm5.F

#ifdef _ACCEL
#  include "module_mp_wsm5_accel.F"
#else
#if ( RWORDSIZE == 4 )
#  define VREC vsrec
#  define VSQRT vssqrt
#else
#  define VREC vrec
#  define VSQRT vsqrt
#endif

!Including inline expansion statistical function 
MODULE module_mp_wsm5
!
!
   REAL, PARAMETER, PRIVATE :: dtcldcr     = 120. ! maximum time step for minor loops
   REAL, PARAMETER, PRIVATE :: n0r = 8.e6         ! intercept parameter rain
   REAL, PARAMETER, PRIVATE :: avtr = 841.9       ! a constant for terminal velocity of rain
   REAL, PARAMETER, PRIVATE :: bvtr = 0.8         ! a constant for terminal velocity of rain
   REAL, PARAMETER, PRIVATE :: r0 = .8e-5         ! 8 microm  in contrast to 10 micro m
   REAL, PARAMETER, PRIVATE :: peaut = .55        ! collection efficiency
   REAL, PARAMETER, PRIVATE :: xncr = 3.e8        ! maritime cloud in contrast to 3.e8 in tc80
   REAL, PARAMETER, PRIVATE :: xmyu = 1.718e-5    ! the dynamic viscosity kgm-1s-1
   REAL, PARAMETER, PRIVATE :: avts = 11.72       ! a constant for terminal velocity of snow
   REAL, PARAMETER, PRIVATE :: bvts = .41         ! a constant for terminal velocity of snow
   REAL, PARAMETER, PRIVATE :: n0smax =  1.e11    ! maximum n0s (t=-90C unlimited)
   REAL, PARAMETER, PRIVATE :: lamdarmax = 8.e4   ! limited maximum value for slope parameter of rain
   REAL, PARAMETER, PRIVATE :: lamdasmax = 1.e5   ! limited maximum value for slope parameter of snow
   REAL, PARAMETER, PRIVATE :: lamdagmax = 6.e4   ! limited maximum value for slope parameter of graupel
   REAL, PARAMETER, PRIVATE :: dicon = 11.9       ! constant for the cloud-ice diamter
   REAL, PARAMETER, PRIVATE :: dimax = 500.e-6    ! limited maximum value for the cloud-ice diamter
   REAL, PARAMETER, PRIVATE :: n0s = 2.e6         ! temperature dependent intercept parameter snow
   REAL, PARAMETER, PRIVATE :: alpha = .12        ! .122 exponen factor for n0s
   REAL, PARAMETER, PRIVATE :: pfrz1 = 100.       ! constant in Biggs freezing
   REAL, PARAMETER, PRIVATE :: pfrz2 = 0.66       ! constant in Biggs freezing
   REAL, PARAMETER, PRIVATE :: qcrmin = 1.e-9     ! minimun values for qr, qs, and qg
   REAL, PARAMETER, PRIVATE :: eacrc = 1.0        ! Snow/cloud-water collection efficiency
   REAL, SAVE ::                                      &
             qc0, qck1,bvtr1,bvtr2,bvtr3,bvtr4,g1pbr, &
             g3pbr,g4pbr,g5pbro2,pvtr,eacrr,pacrr,    &
             precr1,precr2,xmmax,roqimax,bvts1,       &
             bvts2,bvts3,bvts4,g1pbs,g3pbs,g4pbs,     &
             g5pbso2,pvts,pacrs,precs1,precs2,pidn0r, &
             pidn0s,xlv1,pacrc,pi,                    &
             rslopermax,rslopesmax,rslopegmax,        &
             rsloperbmax,rslopesbmax,rslopegbmax,     &
             rsloper2max,rslopes2max,rslopeg2max,     &
             rsloper3max,rslopes3max,rslopeg3max
!
! Specifies code-inlining of fpvs function in WSM52D below. JM 20040507
!
CONTAINS
!===================================================================
!
  SUBROUTINE wsm5(th, q, qc, qr, qi, qs                            &
                 ,den, pii, p, delz                                &
                 ,delt,g, cpd, cpv, rd, rv, t0c                    &
                 ,ep1, ep2, qmin                                   &
                 ,XLS, XLV0, XLF0, den0, denr                      &
                 ,cliq,cice,psat                                   &
                 ,rain, rainncv                                    &
                 ,snow, snowncv                                    &
                 ,sr                                               &
                 ,ids,ide, jds,jde, kds,kde                        &
                 ,ims,ime, jms,jme, kms,kme                        &
                 ,its,ite, jts,jte, kts,kte                        &
                                                                   )
!-------------------------------------------------------------------
  IMPLICIT NONE
!-------------------------------------------------------------------
!
  INTEGER,      INTENT(IN   )    ::   ids,ide, jds,jde, kds,kde , &
                                      ims,ime, jms,jme, kms,kme , &
                                      its,ite, jts,jte, kts,kte
  REAL, DIMENSION( ims:ime , kms:kme , jms:jme ),                 &
        INTENT(INOUT) ::                                          &
                                                             th,  &
                                                              q,  &
                                                              qc, &
                                                              qi, &
                                                              qr, &
                                                              qs
  REAL, DIMENSION( ims:ime , kms:kme , jms:jme ),                 &
        INTENT(IN   ) ::                                          &
                                                             den, &
                                                             pii, &
                                                               p, &
                                                            delz
  REAL, INTENT(IN   ) ::                                    delt, &
                                                               g, &
                                                              rd, &
                                                              rv, &
                                                             t0c, &
                                                            den0, &
                                                             cpd, &
                                                             cpv, &
                                                             ep1, &
                                                             ep2, &
                                                            qmin, &
                                                             XLS, &
                                                            XLV0, &
                                                            XLF0, &
                                                            cliq, &
                                                            cice, &
                                                            psat, &
                                                            denr
  REAL, DIMENSION( ims:ime , jms:jme ),                           &
        INTENT(INOUT) ::                                    rain, &
                                                         rainncv, &
                                                              sr
  REAL, DIMENSION( ims:ime , jms:jme ), OPTIONAL,                 &
        INTENT(INOUT) ::                                    snow, &
                                                         snowncv
! LOCAL VAR
  REAL, DIMENSION( its:ite , kts:kte ) ::   t
  REAL, DIMENSION( its:ite , kts:kte, 2 ) ::   qci, qrs
  CHARACTER*256 :: emess
  INTEGER :: mkx_test
  INTEGER ::               i,j,k
!-------------------------------------------------------------------

#ifndef RUN_ON_GPU
      DO j=jts,jte
         DO k=kts,kte
         DO i=its,ite
            t(i,k)=th(i,k,j)*pii(i,k,j)
            qci(i,k,1) = qc(i,k,j)
            qci(i,k,2) = qi(i,k,j)
            qrs(i,k,1) = qr(i,k,j)
            qrs(i,k,2) = qs(i,k,j)
         ENDDO
         ENDDO
         !  Sending array starting locations of optional variables may cause
         !  troubles, so we explicitly change the call.
         CALL wsm52D(t, q(ims,kms,j), qci, qrs                     &
                    ,den(ims,kms,j)                                &
                    ,p(ims,kms,j), delz(ims,kms,j)                 &
                    ,delt,g, cpd, cpv, rd, rv, t0c                 &
                    ,ep1, ep2, qmin                                &
                    ,XLS, XLV0, XLF0, den0, denr                   &
                    ,cliq,cice,psat                                &
                    ,j                                             &
                    ,rain(ims,j),rainncv(ims,j)                    &
                    ,sr(ims,j)                                     &
                    ,ids,ide, jds,jde, kds,kde                     &
                    ,ims,ime, jms,jme, kms,kme                     &
                    ,its,ite, jts,jte, kts,kte                     &
                    ,snow,snowncv                                  &
                                                                   )
         DO K=kts,kte
         DO I=its,ite
            th(i,k,j)=t(i,k)/pii(i,k,j)
            qc(i,k,j) = qci(i,k,1)
            qi(i,k,j) = qci(i,k,2)
            qr(i,k,j) = qrs(i,k,1)
            qs(i,k,j) = qrs(i,k,2)
         ENDDO
         ENDDO
      ENDDO
#else
      CALL get_wsm5_gpu_levels ( mkx_test )
      IF ( mkx_test .LT. kte ) THEN
        WRITE(emess,*)'Number of levels compiled for GPU WSM5 too small. ',      &
                      mkx_test,' < ',kte
        CALL wrf_error_fatal(emess)
      ENDIF
      CALL wsm5_host (                                                           &
                    th(its:ite,kts:kte,jts:jte), pii(its:ite,kts:kte,jts:jte)    &
                   ,q(its:ite,kts:kte,jts:jte), qc(its:ite,kts:kte,jts:jte)      &
                   ,qi(its:ite,kts:kte,jts:jte), qr(its:ite,kts:kte,jts:jte)     &
                   ,qs(its:ite,kts:kte,jts:jte), den(its:ite,kts:kte,jts:jte)    &
                   ,p(its:ite,kts:kte,jts:jte), delz(its:ite,kts:kte,jts:jte)    &
                   ,delt                                                         &
                   ,rain(its:ite,jts:jte),rainncv(its:ite,jts:jte)               &
                   ,snow(its:ite,jts:jte),snowncv(its:ite,jts:jte)               &
                   ,sr(its:ite,jts:jte)                                          &
                   ,its, ite,  jts, jte,  kts, kte                               &
                   ,its, ite,  jts, jte,  kts, kte                               &
                   ,its, ite,  jts, jte,  kts, kte                               &
          )
#endif

  END SUBROUTINE wsm5
!===================================================================
!
  SUBROUTINE wsm52D(t, q                                          & 
                   ,qci, qrs, den, p, delz                        &
                   ,delt,g, cpd, cpv, rd, rv, t0c                 &
                   ,ep1, ep2, qmin                                &
                   ,XLS, XLV0, XLF0, den0, denr                   &
                   ,cliq,cice,psat                                &
                   ,lat                                           &
                   ,rain,rainncv                                  &
                   ,sr                                            &
                   ,ids,ide, jds,jde, kds,kde                     &
                   ,ims,ime, jms,jme, kms,kme                     &
                   ,its,ite, jts,jte, kts,kte                     &
                   ,snow,snowncv                                  &
                                                                  )
!-------------------------------------------------------------------
  IMPLICIT NONE
!-------------------------------------------------------------------
!
!  This code is a 5-class mixed ice microphyiscs scheme (WSM5) of the 
!  Single-Moment MicroPhyiscs (WSMMP). The WSMMP assumes that ice nuclei
!  number concentration is a function of temperature, and seperate assumption
!  is developed, in which ice crystal number concentration is a function
!  of ice amount. A theoretical background of the ice-microphysics and related
!  processes in the WSMMPs are described in Hong et al. (2004).
!  Production terms in the WSM6 scheme are described in Hong and Lim (2006).
!  All units are in m.k.s. and source/sink terms in kgkg-1s-1.
!
!  WSM5 cloud scheme
!
!  Coded by Song-You Hong (Yonsei Univ.)
!             Jimy Dudhia (NCAR) and Shu-Hua Chen (UC Davis)
!             Summer 2002
!
!  Implemented by Song-You Hong (Yonsei Univ.) and Jimy Dudhia (NCAR)
!             Summer 2003
!
!  Reference) Hong, Dudhia, Chen (HDC, 2004) Mon. Wea. Rev.
!             Rutledge, Hobbs (RH83, 1983) J. Atmos. Sci.
!             Hong and Lim (HL, 2006) J. Korean Meteor. Soc.
!
  INTEGER,      INTENT(IN   )    ::   ids,ide, jds,jde, kds,kde , &
                                      ims,ime, jms,jme, kms,kme , &
                                      its,ite, jts,jte, kts,kte,  &
                                      lat
  REAL, DIMENSION( its:ite , kts:kte ),                           &
        INTENT(INOUT) ::                                          &
                                                              t
  REAL, DIMENSION( its:ite , kts:kte, 2 ),                        &
        INTENT(INOUT) ::                                          &
                                                             qci, &
                                                             qrs
  REAL, DIMENSION( ims:ime , kms:kme ),                           &
        INTENT(INOUT) ::                                          &
                                                               q
  REAL, DIMENSION( ims:ime , kms:kme ),                           &
        INTENT(IN   ) ::                                          &
                                                             den, &
                                                               p, &
                                                            delz
  REAL, INTENT(IN   ) ::                                    delt, &
                                                               g, &
                                                             cpd, &
                                                             cpv, &
                                                             t0c, &
                                                            den0, &
                                                              rd, &
                                                              rv, &
                                                             ep1, &
                                                             ep2, &
                                                            qmin, &
                                                             XLS, &
                                                            XLV0, &
                                                            XLF0, &
                                                            cliq, &
                                                            cice, &
                                                            psat, &
                                                            denr
  REAL, DIMENSION( ims:ime ),                                     &
        INTENT(INOUT) ::                                    rain, &
                                                         rainncv, &
                                                              sr
  REAL, DIMENSION( ims:ime, jms:jme ),     OPTIONAL,              &
        INTENT(INOUT) ::                                    snow, &
                                                         snowncv
! LOCAL VAR
  REAL, DIMENSION( its:ite , kts:kte , 2) ::                      &
                                                              rh, &
                                                              qs, &
                                                          rslope, &
                                                         rslope2, &
                                                         rslope3, &
                                                         rslopeb, &
                                                         qrs_tmp, &
                                                            falk, &
                                                            fall, &
                                                           work1
  REAL, DIMENSION( its:ite , kts:kte ) ::                         &
                                                           falkc, &
                                                           fallc, &
                                                              xl, &
                                                             cpm, &
                                                          denfac, &
                                                             xni, &
                                                         denqrs1, &
                                                         denqrs2, &
                                                          denqci, &
                                                          n0sfac, &
                                                           work2, &
                                                           workr, &
                                                           works, &
                                                          work1c, &
                                                          work2c
  REAL, DIMENSION( its:ite , kts:kte ) ::                         &
                                                         den_tmp, &
                                                        delz_tmp
  REAL, DIMENSION( its:ite ) ::                                   &
                                                         delqrs1, &
                                                         delqrs2, &
                                                           delqi
  REAL, DIMENSION( its:ite , kts:kte ) ::                         &
                                                           pigen, &
                                                           pidep, &
                                                           psdep, &
                                                           praut, &
                                                           psaut, &
                                                           prevp, &
                                                           psevp, &
                                                           pracw, &
                                                           psacw, &
                                                           psaci, &
                                                           pcond, &
                                                           psmlt
  INTEGER, DIMENSION( its:ite ) ::                                &
                                                           mstep, &
                                                           numdt
  REAL, DIMENSION(its:ite) ::                             tstepsnow
  REAL, DIMENSION(its:ite) ::                             rmstep
  REAL dtcldden, rdelz, rdtcld
  LOGICAL, DIMENSION( its:ite ) ::                        flgcld
#define WSM_NO_CONDITIONAL_IN_VECTOR
#ifdef WSM_NO_CONDITIONAL_IN_VECTOR
  REAL, DIMENSION(its:ite) :: xal, xbl
#endif
  REAL  ::                                                        &
            cpmcal, xlcal, diffus,                                &
            viscos, xka, venfac, conden, diffac,                  &
            x, y, z, a, b, c, d, e,                               &
            qdt, holdrr, holdrs, supcol, supcolt, pvt,            &
            coeres, supsat, dtcld, xmi, eacrs, satdt,             &
            vt2i,vt2s,acrfac,                                     &
            qimax, diameter, xni0, roqi0,                         &
            fallsum, fallsum_qsi, xlwork2, factor, source,        &
            value, xlf, pfrzdtc, pfrzdtr, supice,  holdc, holdci
! variables for optimization
  REAL, DIMENSION( its:ite )           ::                    tvec1
  REAL ::                                                    temp 
  INTEGER :: i, j, k, mstepmax,                                   &
            iprt, latd, lond, loop, loops, ifsat, n, idim, kdim
! Temporaries used for inlining fpvs function
  REAL  :: dldti, xb, xai, tr, xbi, xa, hvap, cvap, hsub, dldt, ttp
  REAL  :: logtr
!
!=================================================================
!   compute internal functions
!
      cpmcal(x) = cpd*(1.-max(x,qmin))+max(x,qmin)*cpv
      xlcal(x) = xlv0-xlv1*(x-t0c)
!----------------------------------------------------------------
!     diffus: diffusion coefficient of the water vapor
!     viscos: kinematic viscosity(m2s-1)
!     diffus(x,y) = 8.794e-5 * exp(log(x)*(1.81)) / y        ! 8.794e-5*x**1.81/y
!     viscos(x,y) = 1.496e-6 * (x*sqrt(x)) /(x+120.)/y  ! 1.496e-6*x**1.5/(x+120.)/y
!     xka(x,y) = 1.414e3*viscos(x,y)*y
!     diffac(a,b,c,d,e) = d*a*a/(xka(c,d)*rv*c*c)+1./(e*diffus(c,b))
!     venfac(a,b,c) = exp(log((viscos(b,c)/diffus(b,a)))*((.3333333)))         &
!                    /sqrt(viscos(b,c))*sqrt(sqrt(den0/c))
!     conden(a,b,c,d,e) = (max(b,qmin)-c)/(1.+d*d/(rv*e)*c/(a*a))
!
!----------------------------------------------------------------
      idim = ite-its+1
      kdim = kte-kts+1
!
!----------------------------------------------------------------
!     paddint 0 for negative values generated by dynamics
!
      do k = kts, kte
        do i = its, ite
          qci(i,k,1) = max(qci(i,k,1),0.0)
          qrs(i,k,1) = max(qrs(i,k,1),0.0)
          qci(i,k,2) = max(qci(i,k,2),0.0)
          qrs(i,k,2) = max(qrs(i,k,2),0.0)
        enddo
      enddo
!
!----------------------------------------------------------------
!     latent heat for phase changes and heat capacity. neglect the
!     changes during microphysical process calculation
!     emanuel(1994)
!
      do k = kts, kte
        do i = its, ite
          cpm(i,k) = cpmcal(q(i,k))
          xl(i,k) = xlcal(t(i,k))
        enddo
      enddo
      do k = kts, kte
        do i = its, ite
          delz_tmp(i,k) = delz(i,k)
          den_tmp(i,k) = den(i,k)
        enddo
      enddo
!
!----------------------------------------------------------------
!    initialize the surface rain, snow
!
      do i = its, ite
        rainncv(i) = 0.
        if(PRESENT (snowncv) .AND. PRESENT (snow)) snowncv(i,lat) = 0.
        sr(i) = 0.
! new local array to catch step snow
        tstepsnow(i) = 0.
      enddo
!
!----------------------------------------------------------------
!     compute the minor time steps.
!
      loops = max(nint(delt/dtcldcr),1)
      dtcld = delt/loops
      if(delt.le.dtcldcr) dtcld = delt
!
      do loop = 1,loops
!
!----------------------------------------------------------------
!     initialize the large scale variables
!
      do i = its, ite
        mstep(i) = 1
        flgcld(i) = .true.
      enddo
!
!     do k = kts, kte
!       do i = its, ite
!         denfac(i,k) = sqrt(den0/den(i,k))
!       enddo
!     enddo
      do k = kts, kte
        CALL VREC( tvec1(its), den(its,k), ite-its+1)
        do i = its, ite
          tvec1(i) = tvec1(i)*den0
        enddo
        CALL VSQRT( denfac(its,k), tvec1(its), ite-its+1)
      enddo
!
! Inline expansion for fpvs
!         qs(i,k,1) = fpvs(t(i,k),0,rd,rv,cpv,cliq,cice,xlv0,xls,psat,t0c)
!         qs(i,k,2) = fpvs(t(i,k),1,rd,rv,cpv,cliq,cice,xlv0,xls,psat,t0c)
      hsub = xls
      hvap = xlv0
      cvap = cpv
      ttp=t0c+0.01
      dldt=cvap-cliq
      xa=-dldt/rv
      xb=xa+hvap/(rv*ttp)
      dldti=cvap-cice
      xai=-dldti/rv
      xbi=xai+hsub/(rv*ttp)
! this is for compilers where the conditional inhibits vectorization
#ifdef WSM_NO_CONDITIONAL_IN_VECTOR
      do k = kts, kte
        do i = its, ite
          if(t(i,k).lt.ttp) then
            xal(i) = xai
            xbl(i) = xbi
          else
            xal(i) = xa
            xbl(i) = xb
          endif
        enddo
        do i = its, ite
          tr=ttp/t(i,k)
          logtr=log(tr)
          qs(i,k,1)=psat*exp(logtr*(xa)+xb*(1.-tr))
          qs(i,k,1) = min(qs(i,k,1),0.99*p(i,k))
          qs(i,k,1) = ep2 * qs(i,k,1) / (p(i,k) - qs(i,k,1))
          qs(i,k,1) = max(qs(i,k,1),qmin)
          rh(i,k,1) = max(q(i,k) / qs(i,k,1),qmin)
          qs(i,k,2)=psat*exp(logtr*(xal(i))+xbl(i)*(1.-tr))
          qs(i,k,2) = min(qs(i,k,2),0.99*p(i,k))
          qs(i,k,2) = ep2 * qs(i,k,2) / (p(i,k) - qs(i,k,2))
          qs(i,k,2) = max(qs(i,k,2),qmin)
          rh(i,k,2) = max(q(i,k) / qs(i,k,2),qmin)
#else
      do k = kts, kte
        do i = its, ite
          tr=ttp/t(i,k)
          logtr=log(tr)
          qs(i,k,1)=psat*exp(logtr*(xa)+xb*(1.-tr))
          qs(i,k,1) = min(qs(i,k,1),0.99*p(i,k))
          qs(i,k,1) = ep2 * qs(i,k,1) / (p(i,k) - qs(i,k,1))
          qs(i,k,1) = max(qs(i,k,1),qmin)
          rh(i,k,1) = max(q(i,k) / qs(i,k,1),qmin)
          if(t(i,k).lt.ttp) then
            qs(i,k,2)=psat*exp(logtr*(xai)+xbi*(1.-tr))
          else
            qs(i,k,2)=psat*exp(logtr*(xa)+xb*(1.-tr))
          endif
          qs(i,k,2) = min(qs(i,k,2),0.99*p(i,k))
          qs(i,k,2) = ep2 * qs(i,k,2) / (p(i,k) - qs(i,k,2))
          qs(i,k,2) = max(qs(i,k,2),qmin)
          rh(i,k,2) = max(q(i,k) / qs(i,k,2),qmin)
        enddo
      enddo
#endif
        enddo
      enddo
!
!----------------------------------------------------------------
!     initialize the variables for microphysical physics
!
!
      do k = kts, kte
        do i = its, ite
          prevp(i,k) = 0.
          psdep(i,k) = 0.
          praut(i,k) = 0.
          psaut(i,k) = 0.
          pracw(i,k) = 0.
          psaci(i,k) = 0.
          psacw(i,k) = 0.
          pigen(i,k) = 0.
          pidep(i,k) = 0.
          pcond(i,k) = 0.
          psmlt(i,k) = 0.
          psevp(i,k) = 0.
          falk(i,k,1) = 0.
          falk(i,k,2) = 0.
          fall(i,k,1) = 0.
          fall(i,k,2) = 0.
          fallc(i,k) = 0.
          falkc(i,k) = 0.
          xni(i,k) = 1.e3
        enddo
      enddo
!-------------------------------------------------------------
! Ni: ice crystal number concentraiton   [HDC 5c]
!-------------------------------------------------------------
      do k = kts, kte
        do i = its, ite
          temp = (den(i,k)*max(qci(i,k,2),qmin))
          temp = sqrt(sqrt(temp*temp*temp))
          xni(i,k) = min(max(5.38e7*temp,1.e3),1.e6)
        enddo
      enddo
!
!----------------------------------------------------------------
!     compute the fallout term:
!     first, vertical terminal velosity for minor loops
!----------------------------------------------------------------
      do k = kts, kte
        do i = its, ite
          qrs_tmp(i,k,1) = qrs(i,k,1)
          qrs_tmp(i,k,2) = qrs(i,k,2)
        enddo
      enddo
      call slope_wsm5(qrs_tmp,den_tmp,denfac,t,rslope,rslopeb,rslope2,rslope3, &
                     work1,its,ite,kts,kte)
!
      do k = kte, kts, -1
        do i = its, ite
          workr(i,k) = work1(i,k,1) 
          works(i,k) = work1(i,k,2) 
          denqrs1(i,k) = den(i,k)*qrs(i,k,1)
          denqrs2(i,k) = den(i,k)*qrs(i,k,2)
          if(qrs(i,k,1).le.0.0) workr(i,k) = 0.0
          if(qrs(i,k,2).le.0.0) works(i,k) = 0.0
        enddo
      enddo
      call nislfv_rain_plm(idim,kdim,den_tmp,denfac,t,delz_tmp,workr,denqrs1,  &
                           delqrs1,dtcld,1,1)
      call nislfv_rain_plm(idim,kdim,den_tmp,denfac,t,delz_tmp,works,denqrs2,  &
                           delqrs2,dtcld,2,1)
      do k = kts, kte
        do i = its, ite
          qrs(i,k,1) = max(denqrs1(i,k)/den(i,k),0.)
          qrs(i,k,2) = max(denqrs2(i,k)/den(i,k),0.)
          fall(i,k,1) = denqrs1(i,k)*workr(i,k)/delz(i,k)
          fall(i,k,2) = denqrs2(i,k)*works(i,k)/delz(i,k)
        enddo
      enddo
      do i = its, ite
        fall(i,1,1) = delqrs1(i)/delz(i,1)/dtcld
        fall(i,1,2) = delqrs2(i)/delz(i,1)/dtcld
      enddo
      do k = kts, kte
        do i = its, ite
          qrs_tmp(i,k,1) = qrs(i,k,1)
          qrs_tmp(i,k,2) = qrs(i,k,2)
        enddo
      enddo
      call slope_wsm5(qrs_tmp,den_tmp,denfac,t,rslope,rslopeb,rslope2,rslope3, &
                     work1,its,ite,kts,kte)
      do k = kte, kts, -1
        do i = its, ite
          supcol = t0c-t(i,k)
          n0sfac(i,k) = max(min(exp(alpha*supcol),n0smax/n0s),1.)
          if(t(i,k).gt.t0c.and.qrs(i,k,2).gt.0.) then
!----------------------------------------------------------------
! psmlt: melting of snow [HL A33] [RH83 A25]
!       (T>T0: S->R)
!----------------------------------------------------------------
            xlf = xlf0
!           work2(i,k)= venfac(p(i,k),t(i,k),den(i,k))
            work2(i,k)= (exp(log(((1.496e-6*((t(i,k))*sqrt(t(i,k)))        &
                        /((t(i,k))+120.)/(den(i,k)))/(8.794e-5             &
                        *exp(log(t(i,k))*(1.81))/p(i,k))))                 &
                        *((.3333333)))/sqrt((1.496e-6*((t(i,k))            &
                        *sqrt(t(i,k)))/((t(i,k))+120.)/(den(i,k))))        &
                        *sqrt(sqrt(den0/(den(i,k)))))
            coeres = rslope2(i,k,2)*sqrt(rslope(i,k,2)*rslopeb(i,k,2))
            psmlt(i,k) = (1.414e3*(1.496e-6*((t(i,k))*sqrt(t(i,k)))        &
                        /((t(i,k))+120.)/(den(i,k)) )*(den(i,k)))          &
                        /xlf*(t0c-t(i,k))*pi/2.                            &
                        *n0sfac(i,k)*(precs1*rslope2(i,k,2)+precs2         &
                        *work2(i,k)*coeres)
            psmlt(i,k) = min(max(psmlt(i,k)*dtcld/mstep(i),                &
                        -qrs(i,k,2)/mstep(i)),0.)
            qrs(i,k,2) = qrs(i,k,2) + psmlt(i,k)
            qrs(i,k,1) = qrs(i,k,1) - psmlt(i,k)
            t(i,k) = t(i,k) + xlf/cpm(i,k)*psmlt(i,k)
          endif
        enddo
      enddo
!---------------------------------------------------------------
! Vice [ms-1] : fallout of ice crystal [HDC 5a]
!---------------------------------------------------------------
      do k = kte, kts, -1
        do i = its, ite
          if(qci(i,k,2).le.0.) then
            work1c(i,k) = 0.
          else
            xmi = den(i,k)*qci(i,k,2)/xni(i,k)
            diameter  = max(min(dicon * sqrt(xmi),dimax), 1.e-25)
            work1c(i,k) = 1.49e4*exp(log(diameter)*(1.31))
          endif
        enddo
      enddo
!
!  forward semi-laglangian scheme (JH), PCM (piecewise constant),  (linear)
!
      do k = kte, kts, -1
        do i = its, ite
          denqci(i,k) = den(i,k)*qci(i,k,2)
        enddo
      enddo
      call nislfv_rain_plm(idim,kdim,den_tmp,denfac,t,delz_tmp,work1c,denqci,  &
                           delqi,dtcld,1,0)
      do k = kts, kte
        do i = its, ite
          qci(i,k,2) = max(denqci(i,k)/den(i,k),0.)
        enddo
      enddo
      do i = its, ite
        fallc(i,1) = delqi(i)/delz(i,1)/dtcld
      enddo
!
!----------------------------------------------------------------
!      rain (unit is mm/sec;kgm-2s-1: /1000*delt ===> m)==> mm for wrf
!
      do i = its, ite
        fallsum = fall(i,1,1)+fall(i,1,2)+fallc(i,1)
        fallsum_qsi = fall(i,1,2)+fallc(i,1)
        if(fallsum.gt.0.) then
          rainncv(i) = fallsum*delz(i,1)/denr*dtcld*1000. + rainncv(i)
          rain(i) = fallsum*delz(i,1)/denr*dtcld*1000. + rain(i)
        endif
        if(fallsum_qsi.gt.0.) then
          tstepsnow(i)   = fallsum_qsi*delz(i,kts)/denr*dtcld*1000.            &
                           +tstepsnow(i) 
        IF ( PRESENT (snowncv) .AND. PRESENT (snow)) THEN
          snowncv(i,lat) = fallsum_qsi*delz(i,kts)/denr*dtcld*1000.            & 
                           +snowncv(i,lat)    
          snow(i,lat) = fallsum_qsi*delz(i,kts)/denr*dtcld*1000. + snow(i,lat)
        ENDIF
        endif
!       if(fallsum.gt.0.)sr(i)=snowncv(i,lat)/(rainncv(i)+1.e-12)
        if(fallsum.gt.0.)sr(i)=tstepsnow(i)/(rainncv(i)+1.e-12)
      enddo
!
!---------------------------------------------------------------
! pimlt: instantaneous melting of cloud ice [HL A47] [RH83 A28]
!       (T>T0: I->C)
!---------------------------------------------------------------
      do k = kts, kte
        do i = its, ite
          supcol = t0c-t(i,k)
          xlf = xls-xl(i,k)
          if(supcol.lt.0.) xlf = xlf0
          if(supcol.lt.0.and.qci(i,k,2).gt.0.) then
            qci(i,k,1) = qci(i,k,1) + qci(i,k,2)
            t(i,k) = t(i,k) - xlf/cpm(i,k)*qci(i,k,2)
            qci(i,k,2) = 0.
          endif
!---------------------------------------------------------------
! pihmf: homogeneous freezing of cloud water below -40c [HL A45]
!        (T<-40C: C->I)
!---------------------------------------------------------------
          if(supcol.gt.40..and.qci(i,k,1).gt.0.) then
            qci(i,k,2) = qci(i,k,2) + qci(i,k,1)
            t(i,k) = t(i,k) + xlf/cpm(i,k)*qci(i,k,1)
            qci(i,k,1) = 0.
          endif
!---------------------------------------------------------------
! pihtf: heterogeneous freezing of cloud water [HL A44]
!        (T0>T>-40C: C->I)
!---------------------------------------------------------------
          if(supcol.gt.0..and.qci(i,k,1).gt.0.) then
            supcolt=min(supcol,50.)
!           pfrzdtc = min(pfrz1*(exp(pfrz2*supcol)-1.)                         &
!              *den(i,k)/denr/xncr*qci(i,k,1)**2*dtcld,qci(i,k,1))
            pfrzdtc = min(pfrz1*(exp(pfrz2*supcolt)-1.)                        &
            *den(i,k)/denr/xncr*qci(i,k,1)*qci(i,k,1)*dtcld,qci(i,k,1))
            qci(i,k,2) = qci(i,k,2) + pfrzdtc
            t(i,k) = t(i,k) + xlf/cpm(i,k)*pfrzdtc
            qci(i,k,1) = qci(i,k,1)-pfrzdtc
          endif
!---------------------------------------------------------------
! psfrz: freezing of rain water [HL A20] [LFO 45]
!        (T<T0, R->S)
!---------------------------------------------------------------
          if(supcol.gt.0..and.qrs(i,k,1).gt.0.) then
            supcolt=min(supcol,50.)
!           pfrzdtr = min(20.*pi**2*pfrz1*n0r*denr/den(i,k)                    &
!                 *(exp(pfrz2*supcol)-1.)*rslope(i,k,1)**7*dtcld,              &
!                 qrs(i,k,1))
            temp = rslope(i,k,1)
            temp = temp*temp*temp*temp*temp*temp*temp
            pfrzdtr = min(20.*(pi*pi)*pfrz1*n0r*denr/den(i,k)                  &
                  *(exp(pfrz2*supcolt)-1.)*temp*dtcld,                         &
                  qrs(i,k,1))
            qrs(i,k,2) = qrs(i,k,2) + pfrzdtr
            t(i,k) = t(i,k) + xlf/cpm(i,k)*pfrzdtr
            qrs(i,k,1) = qrs(i,k,1)-pfrzdtr
          endif
        enddo
      enddo
!
!----------------------------------------------------------------
!     update the slope parameters for microphysics computation
!
      do k = kts, kte
        do i = its, ite
          qrs_tmp(i,k,1) = qrs(i,k,1)
          qrs_tmp(i,k,2) = qrs(i,k,2)
        enddo
      enddo
      call slope_wsm5(qrs_tmp,den_tmp,denfac,t,rslope,rslopeb,rslope2,rslope3, &
                     work1,its,ite,kts,kte)
!------------------------------------------------------------------
!     work1:  the thermodynamic term in the denominator associated with
!             heat conduction and vapor diffusion
!             (ry88, y93, h85)
!     work2: parameter associated with the ventilation effects(y93)
!
      do k = kts, kte
        do i = its, ite
!         work1(i,k,1) = diffac(xl(i,k),p(i,k),t(i,k),den(i,k),qs(i,k,1))
          work1(i,k,1) = ((((den(i,k))*(xl(i,k))*(xl(i,k)))*((t(i,k))+120.)    &
                       *(den(i,k)))/(1.414e3*(1.496e-6*((t(i,k))*sqrt(t(i,k))))&
                       *(den(i,k))*(rv*(t(i,k))*(t(i,k)))))                    &
                      +  p(i,k)/((qs(i,k,1))*(8.794e-5*exp(log(t(i,k))*(1.81))))
!         work1(i,k,2) = diffac(xls,p(i,k),t(i,k),den(i,k),qs(i,k,2))
          work1(i,k,2) = ((((den(i,k))*(xls)*(xls))*((t(i,k))+120.)*(den(i,k)))&
                       /(1.414e3*(1.496e-6*((t(i,k))*sqrt(t(i,k))))*(den(i,k)) &
                       *(rv*(t(i,k))*(t(i,k))))                                &
                      + p(i,k)/(qs(i,k,2)*(8.794e-5*exp(log(t(i,k))*(1.81)))))
!         work2(i,k) = venfac(p(i,k),t(i,k),den(i,k))
          work2(i,k) = (exp(.3333333*log(((1.496e-6 * ((t(i,k))*sqrt(t(i,k)))) &
                     *p(i,k))/(((t(i,k))+120.)*den(i,k)*(8.794e-5              &
                     *exp(log(t(i,k))*(1.81))))))*sqrt(sqrt(den0/(den(i,k))))) &
                      /sqrt((1.496e-6*((t(i,k))*sqrt(t(i,k))))                 &
                      /(((t(i,k))+120.)*den(i,k)))
        enddo 
      enddo 
!
!===============================================================
!
! warm rain processes
!
! - follows the processes in RH83 and LFO except for autoconcersion
!
!===============================================================
!
      do k = kts, kte
        do i = its, ite
          supsat = max(q(i,k),qmin)-qs(i,k,1)
          satdt = supsat/dtcld
!---------------------------------------------------------------
! praut: auto conversion rate from cloud to rain [HDC 16]
!        (C->R)
!---------------------------------------------------------------
          if(qci(i,k,1).gt.qc0) then
            praut(i,k) = qck1*exp(log(qci(i,k,1))*((7./3.)))
            praut(i,k) = min(praut(i,k),qci(i,k,1)/dtcld)
          endif
!---------------------------------------------------------------
! pracw: accretion of cloud water by rain [HL A40] [LFO 51]
!        (C->R)
!---------------------------------------------------------------
          if(qrs(i,k,1).gt.qcrmin.and.qci(i,k,1).gt.qmin) then
            pracw(i,k) = min(pacrr*rslope3(i,k,1)*rslopeb(i,k,1)               & 
                         *qci(i,k,1)*denfac(i,k),qci(i,k,1)/dtcld)
          endif
!---------------------------------------------------------------
! prevp: evaporation/condensation rate of rain [HDC 14]
!        (V->R or R->V)
!---------------------------------------------------------------
          if(qrs(i,k,1).gt.0.) then
            coeres = rslope2(i,k,1)*sqrt(rslope(i,k,1)*rslopeb(i,k,1))
            prevp(i,k) = (rh(i,k,1)-1.)*(precr1*rslope2(i,k,1)                 &
                         +precr2*work2(i,k)*coeres)/work1(i,k,1)
            if(prevp(i,k).lt.0.) then
              prevp(i,k) = max(prevp(i,k),-qrs(i,k,1)/dtcld)
              prevp(i,k) = max(prevp(i,k),satdt/2)
            else
              prevp(i,k) = min(prevp(i,k),satdt/2)
            endif
          endif
        enddo
      enddo
!
!===============================================================
!
! cold rain processes
!
! - follows the revised ice microphysics processes in HDC
! - the processes same as in RH83 and RH84  and LFO behave
!   following ice crystal hapits defined in HDC, inclduing
!   intercept parameter for snow (n0s), ice crystal number
!   concentration (ni), ice nuclei number concentration
!   (n0i), ice diameter (d)
!
!===============================================================
!
      rdtcld = 1./dtcld
      do k = kts, kte
        do i = its, ite
          supcol = t0c-t(i,k)
          n0sfac(i,k) = max(min(exp(alpha*supcol),n0smax/n0s),1.)
          supsat = max(q(i,k),qmin)-qs(i,k,2)
          satdt = supsat/dtcld
          ifsat = 0
!-------------------------------------------------------------
! Ni: ice crystal number concentraiton   [HDC 5c]
!-------------------------------------------------------------
!         xni(i,k) = min(max(5.38e7*(den(i,k)                                  &
!                      *max(qci(i,k,2),qmin))**0.75,1.e3),1.e6)
          temp = (den(i,k)*max(qci(i,k,2),qmin))
          temp = sqrt(sqrt(temp*temp*temp))
          xni(i,k) = min(max(5.38e7*temp,1.e3),1.e6)
          eacrs = exp(0.07*(-supcol))
!
          if(supcol.gt.0) then
            if(qrs(i,k,2).gt.qcrmin.and.qci(i,k,2).gt.qmin) then
              xmi = den(i,k)*qci(i,k,2)/xni(i,k)
              diameter  = min(dicon * sqrt(xmi),dimax)
              vt2i = 1.49e4*diameter**1.31
              vt2s = pvts*rslopeb(i,k,2)*denfac(i,k)
!-------------------------------------------------------------
! psaci: Accretion of cloud ice by rain [HDC 10]
!        (T<T0: I->S)
!-------------------------------------------------------------
              acrfac = 2.*rslope3(i,k,2)+2.*diameter*rslope2(i,k,2)            &
                      +diameter**2*rslope(i,k,2)
              psaci(i,k) = pi*qci(i,k,2)*eacrs*n0s*n0sfac(i,k)                 &
                           *abs(vt2s-vt2i)*acrfac/4.
            endif
          endif
!-------------------------------------------------------------
! psacw: Accretion of cloud water by snow  [HL A7] [LFO 24]
!        (T<T0: C->S, and T>=T0: C->R)
!-------------------------------------------------------------
          if(qrs(i,k,2).gt.qcrmin.and.qci(i,k,1).gt.qmin) then
            psacw(i,k) = min(pacrc*n0sfac(i,k)*rslope3(i,k,2)                  &
                           *rslopeb(i,k,2)*qci(i,k,1)*denfac(i,k)              &
!                          ,qci(i,k,1)/dtcld)
                           ,qci(i,k,1)*rdtcld)
          endif
          if(supcol .gt. 0) then
!-------------------------------------------------------------
! pidep: Deposition/Sublimation rate of ice [HDC 9]
!       (T<T0: V->I or I->V)
!-------------------------------------------------------------
            if(qci(i,k,2).gt.0.and.ifsat.ne.1) then
              xmi = den(i,k)*qci(i,k,2)/xni(i,k)
              diameter = dicon * sqrt(xmi)
              pidep(i,k) = 4.*diameter*xni(i,k)*(rh(i,k,2)-1.)/work1(i,k,2)
              supice = satdt-prevp(i,k)
              if(pidep(i,k).lt.0.) then
!               pidep(i,k) = max(max(pidep(i,k),satdt/2),supice)
!               pidep(i,k) = max(pidep(i,k),-qci(i,k,2)/dtcld)
                pidep(i,k) = max(max(pidep(i,k),satdt*.5),supice)
                pidep(i,k) = max(pidep(i,k),-qci(i,k,2)*rdtcld)
              else
!               pidep(i,k) = min(min(pidep(i,k),satdt/2),supice)
                pidep(i,k) = min(min(pidep(i,k),satdt*.5),supice)
              endif
              if(abs(prevp(i,k)+pidep(i,k)).ge.abs(satdt)) ifsat = 1
            endif
!-------------------------------------------------------------
! psdep: deposition/sublimation rate of snow [HDC 14]
!        (V->S or S->V)
!-------------------------------------------------------------
            if(qrs(i,k,2).gt.0..and.ifsat.ne.1) then
              coeres = rslope2(i,k,2)*sqrt(rslope(i,k,2)*rslopeb(i,k,2))
              psdep(i,k) = (rh(i,k,2)-1.)*n0sfac(i,k)                          &
                           *(precs1*rslope2(i,k,2)+precs2                      &
                           *work2(i,k)*coeres)/work1(i,k,2)
              supice = satdt-prevp(i,k)-pidep(i,k)
              if(psdep(i,k).lt.0.) then
!               psdep(i,k) = max(psdep(i,k),-qrs(i,k,2)/dtcld)
!               psdep(i,k) = max(max(psdep(i,k),satdt/2),supice)
                psdep(i,k) = max(psdep(i,k),-qrs(i,k,2)*rdtcld)
                psdep(i,k) = max(max(psdep(i,k),satdt*.5),supice)
              else
!             psdep(i,k) = min(min(psdep(i,k),satdt/2),supice)
                psdep(i,k) = min(min(psdep(i,k),satdt*.5),supice)
              endif
              if(abs(prevp(i,k)+pidep(i,k)+psdep(i,k)).ge.abs(satdt))          &
                ifsat = 1
            endif
!-------------------------------------------------------------
! pigen: generation(nucleation) of ice from vapor [HL A50] [HDC 7-8]
!       (T<T0: V->I)
!-------------------------------------------------------------
            if(supsat.gt.0.and.ifsat.ne.1) then
              supice = satdt-prevp(i,k)-pidep(i,k)-psdep(i,k)
              xni0 = 1.e3*exp(0.1*supcol)
              roqi0 = 4.92e-11*exp(log(xni0)*(1.33))
              pigen(i,k) = max(0.,(roqi0/den(i,k)-max(qci(i,k,2),0.))          &
!                        /dtcld)
                         *rdtcld)
              pigen(i,k) = min(min(pigen(i,k),satdt),supice)
            endif
!
!-------------------------------------------------------------
! psaut: conversion(aggregation) of ice to snow [HDC 12]
!       (T<T0: I->S)
!-------------------------------------------------------------
            if(qci(i,k,2).gt.0.) then
              qimax = roqimax/den(i,k)
!             psaut(i,k) = max(0.,(qci(i,k,2)-qimax)/dtcld)
              psaut(i,k) = max(0.,(qci(i,k,2)-qimax)*rdtcld)
            endif
          endif
!-------------------------------------------------------------
! psevp: Evaporation of melting snow [HL A35] [RH83 A27]
!       (T>T0: S->V)
!-------------------------------------------------------------
          if(supcol.lt.0.) then
            if(qrs(i,k,2).gt.0..and.rh(i,k,1).lt.1.)                           &
              psevp(i,k) = psdep(i,k)*work1(i,k,2)/work1(i,k,1)
!              psevp(i,k) = min(max(psevp(i,k),-qrs(i,k,2)/dtcld),0.)
              psevp(i,k) = min(max(psevp(i,k),-qrs(i,k,2)*rdtcld),0.)
          endif
        enddo
      enddo
!
!
!----------------------------------------------------------------
!     check mass conservation of generation terms and feedback to the
!     large scale
!
      do k = kts, kte
        do i = its, ite
          if(t(i,k).le.t0c) then
!
!     cloud water
!
            value = max(qmin,qci(i,k,1))
            source = (praut(i,k)+pracw(i,k)+psacw(i,k))*dtcld
            if (source.gt.value) then
              factor = value/source
              praut(i,k) = praut(i,k)*factor
              pracw(i,k) = pracw(i,k)*factor
              psacw(i,k) = psacw(i,k)*factor
            endif
!
!     cloud ice
!
            value = max(qmin,qci(i,k,2))
            source = (psaut(i,k)+psaci(i,k)-pigen(i,k)-pidep(i,k))*dtcld
            if (source.gt.value) then
              factor = value/source
              psaut(i,k) = psaut(i,k)*factor
              psaci(i,k) = psaci(i,k)*factor
              pigen(i,k) = pigen(i,k)*factor
              pidep(i,k) = pidep(i,k)*factor
            endif
!
!     rain
!
!
            value = max(qmin,qrs(i,k,1))
            source = (-praut(i,k)-pracw(i,k)-prevp(i,k))*dtcld
            if (source.gt.value) then
              factor = value/source
              praut(i,k) = praut(i,k)*factor
              pracw(i,k) = pracw(i,k)*factor
              prevp(i,k) = prevp(i,k)*factor
            endif
!
!    snow
!
            value = max(qmin,qrs(i,k,2))
            source = (-psdep(i,k)-psaut(i,k)-psaci(i,k)-psacw(i,k))*dtcld  
            if (source.gt.value) then
              factor = value/source
              psdep(i,k) = psdep(i,k)*factor
              psaut(i,k) = psaut(i,k)*factor
              psaci(i,k) = psaci(i,k)*factor
              psacw(i,k) = psacw(i,k)*factor
            endif
!
            work2(i,k)=-(prevp(i,k)+psdep(i,k)+pigen(i,k)+pidep(i,k))
!     update
            q(i,k) = q(i,k)+work2(i,k)*dtcld
            qci(i,k,1) = max(qci(i,k,1)-(praut(i,k)+pracw(i,k)                 &
                        +psacw(i,k))*dtcld,0.)
            qrs(i,k,1) = max(qrs(i,k,1)+(praut(i,k)+pracw(i,k)                 &
                        +prevp(i,k))*dtcld,0.)
            qci(i,k,2) = max(qci(i,k,2)-(psaut(i,k)+psaci(i,k)                 &
                        -pigen(i,k)-pidep(i,k))*dtcld,0.)
            qrs(i,k,2) = max(qrs(i,k,2)+(psdep(i,k)+psaut(i,k)                 &
                        +psaci(i,k)+psacw(i,k))*dtcld,0.)
            xlf = xls-xl(i,k)
            xlwork2 = -xls*(psdep(i,k)+pidep(i,k)+pigen(i,k))                  &
                      -xl(i,k)*prevp(i,k)-xlf*psacw(i,k)
            t(i,k) = t(i,k)-xlwork2/cpm(i,k)*dtcld
          else
!
!     cloud water
!
            value = max(qmin,qci(i,k,1))
            source=(praut(i,k)+pracw(i,k)+psacw(i,k))*dtcld
            if (source.gt.value) then
              factor = value/source
              praut(i,k) = praut(i,k)*factor
              pracw(i,k) = pracw(i,k)*factor
              psacw(i,k) = psacw(i,k)*factor
            endif
!
!     rain
!
            value = max(qmin,qrs(i,k,1))
            source = (-praut(i,k)-pracw(i,k)-prevp(i,k)-psacw(i,k))*dtcld
            if (source.gt.value) then
              factor = value/source
              praut(i,k) = praut(i,k)*factor
              pracw(i,k) = pracw(i,k)*factor
              prevp(i,k) = prevp(i,k)*factor
              psacw(i,k) = psacw(i,k)*factor
            endif  
!
!     snow
!
            value = max(qcrmin,qrs(i,k,2))
            source=(-psevp(i,k))*dtcld
            if (source.gt.value) then
              factor = value/source
              psevp(i,k) = psevp(i,k)*factor
            endif
            work2(i,k)=-(prevp(i,k)+psevp(i,k))
!     update
            q(i,k) = q(i,k)+work2(i,k)*dtcld
            qci(i,k,1) = max(qci(i,k,1)-(praut(i,k)+pracw(i,k)                 &
                        +psacw(i,k))*dtcld,0.)
            qrs(i,k,1) = max(qrs(i,k,1)+(praut(i,k)+pracw(i,k)                 &
                        +prevp(i,k) +psacw(i,k))*dtcld,0.)
            qrs(i,k,2) = max(qrs(i,k,2)+psevp(i,k)*dtcld,0.)
            xlf = xls-xl(i,k)
            xlwork2 = -xl(i,k)*(prevp(i,k)+psevp(i,k))
            t(i,k) = t(i,k)-xlwork2/cpm(i,k)*dtcld
          endif
        enddo
      enddo
!
! Inline expansion for fpvs
!         qs(i,k,1) = fpvs(t(i,k),0,rd,rv,cpv,cliq,cice,xlv0,xls,psat,t0c)
!         qs(i,k,2) = fpvs(t(i,k),1,rd,rv,cpv,cliq,cice,xlv0,xls,psat,t0c)
      hsub = xls
      hvap = xlv0
      cvap = cpv
      ttp=t0c+0.01
      dldt=cvap-cliq
      xa=-dldt/rv
      xb=xa+hvap/(rv*ttp)
      dldti=cvap-cice
      xai=-dldti/rv
      xbi=xai+hsub/(rv*ttp)
      do k = kts, kte
      do i = its, ite
          tr=ttp/t(i,k)
          logtr = log(tr)
          qs(i,k,1)=psat*exp(logtr*(xa)+xb*(1.-tr))
          qs(i,k,1) = min(qs(i,k,1),0.99*p(i,k))
          qs(i,k,1) = ep2 * qs(i,k,1) / (p(i,k) - qs(i,k,1))
          qs(i,k,1) = max(qs(i,k,1),qmin)
        enddo
      enddo
!
!----------------------------------------------------------------
!  pcond: condensational/evaporational rate of cloud water [HL A46] [RH83 A6]
!     if there exists additional water vapor condensated/if
!     evaporation of cloud water is not enough to remove subsaturation
!
      do k = kts, kte
        do i = its, ite
!         work1(i,k,1) = conden(t(i,k),q(i,k),qs(i,k,1),xl(i,k),cpm(i,k))
          work1(i,k,1) = ((max(q(i,k),qmin)-(qs(i,k,1)))/(1.+(xl(i,k))         &   
                        *(xl(i,k))/(rv*(cpm(i,k)))*(qs(i,k,1))                 &
                        /((t(i,k))*(t(i,k)))))
          work2(i,k) = qci(i,k,1)+work1(i,k,1)
          pcond(i,k) = min(max(work1(i,k,1)/dtcld,0.),max(q(i,k),0.)/dtcld)
          if(qci(i,k,1).gt.0..and.work1(i,k,1).lt.0.)                          &
            pcond(i,k) = max(work1(i,k,1),-qci(i,k,1))/dtcld
          q(i,k) = q(i,k)-pcond(i,k)*dtcld
          qci(i,k,1) = max(qci(i,k,1)+pcond(i,k)*dtcld,0.)
          t(i,k) = t(i,k)+pcond(i,k)*xl(i,k)/cpm(i,k)*dtcld
        enddo
      enddo
!
!
!----------------------------------------------------------------
!     padding for small values
!
      do k = kts, kte
        do i = its, ite
          if(qci(i,k,1).le.qmin) qci(i,k,1) = 0.0
          if(qci(i,k,2).le.qmin) qci(i,k,2) = 0.0
        enddo
      enddo
      enddo                  ! big loops
  END SUBROUTINE wsm52d
! ...................................................................
      REAL FUNCTION rgmma(x)
!-------------------------------------------------------------------
  IMPLICIT NONE
!-------------------------------------------------------------------
!     rgmma function:  use infinite product form
      REAL :: euler
      PARAMETER (euler=0.577215664901532)
      REAL :: x, y
      INTEGER :: i
      if(x.eq.1.)then
        rgmma=0.
          else
        rgmma=x*exp(euler*x)
        do i=1,10000
          y=float(i)
          rgmma=rgmma*(1.000+x/y)*exp(-x/y)
        enddo
        rgmma=1./rgmma
      endif
      END FUNCTION rgmma
!
!--------------------------------------------------------------------------
      REAL FUNCTION fpvs(t,ice,rd,rv,cvap,cliq,cice,hvap,hsub,psat,t0c)
!--------------------------------------------------------------------------
      IMPLICIT NONE
!--------------------------------------------------------------------------
      REAL t,rd,rv,cvap,cliq,cice,hvap,hsub,psat,t0c,dldt,xa,xb,dldti,         &
           xai,xbi,ttp,tr
      INTEGER ice
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      ttp=t0c+0.01
      dldt=cvap-cliq
      xa=-dldt/rv
      xb=xa+hvap/(rv*ttp)
      dldti=cvap-cice
      xai=-dldti/rv
      xbi=xai+hsub/(rv*ttp)
      tr=ttp/t
      if(t.lt.ttp.and.ice.eq.1) then
        fpvs=psat*exp(log(tr)*(xai))*exp(xbi*(1.-tr))
      else
        fpvs=psat*exp(log(tr)*(xa))*exp(xb*(1.-tr))
      endif
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      END FUNCTION fpvs
!-------------------------------------------------------------------
  SUBROUTINE wsm5init(den0,denr,dens,cl,cpv,allowed_to_read)
!-------------------------------------------------------------------
  IMPLICIT NONE
!-------------------------------------------------------------------
!.... constants which may not be tunable
   REAL, INTENT(IN) :: den0,denr,dens,cl,cpv
   LOGICAL, INTENT(IN) :: allowed_to_read
!
   pi = 4.*atan(1.)
   xlv1 = cl-cpv
!
   qc0  = 4./3.*pi*denr*r0**3*xncr/den0  ! 0.419e-3 -- .61e-3
   qck1 = .104*9.8*peaut/(xncr*denr)**(1./3.)/xmyu*den0**(4./3.) ! 7.03
!
   bvtr1 = 1.+bvtr
   bvtr2 = 2.5+.5*bvtr
   bvtr3 = 3.+bvtr
   bvtr4 = 4.+bvtr
   g1pbr = rgmma(bvtr1)
   g3pbr = rgmma(bvtr3)
   g4pbr = rgmma(bvtr4)            ! 17.837825
   g5pbro2 = rgmma(bvtr2)          ! 1.8273
   pvtr = avtr*g4pbr/6.
   eacrr = 1.0
   pacrr = pi*n0r*avtr*g3pbr*.25*eacrr
   precr1 = 2.*pi*n0r*.78
   precr2 = 2.*pi*n0r*.31*avtr**.5*g5pbro2
   xmmax = (dimax/dicon)**2
   roqimax = 2.08e22*dimax**8
!
   bvts1 = 1.+bvts
   bvts2 = 2.5+.5*bvts
   bvts3 = 3.+bvts
   bvts4 = 4.+bvts
   g1pbs = rgmma(bvts1)    !.8875
   g3pbs = rgmma(bvts3)
   g4pbs = rgmma(bvts4)    ! 12.0786
   g5pbso2 = rgmma(bvts2)
   pvts = avts*g4pbs/6.
   pacrs = pi*n0s*avts*g3pbs*.25
   precs1 = 4.*n0s*.65
   precs2 = 4.*n0s*.44*avts**.5*g5pbso2
   pidn0r =  pi*denr*n0r
   pidn0s =  pi*dens*n0s
   pacrc = pi*n0s*avts*g3pbs*.25*eacrc
!
   rslopermax = 1./lamdarmax
   rslopesmax = 1./lamdasmax
   rsloperbmax = rslopermax ** bvtr
   rslopesbmax = rslopesmax ** bvts
   rsloper2max = rslopermax * rslopermax
   rslopes2max = rslopesmax * rslopesmax
   rsloper3max = rsloper2max * rslopermax
   rslopes3max = rslopes2max * rslopesmax
!
  END SUBROUTINE wsm5init
!------------------------------------------------------------------------------
      subroutine slope_wsm5(qrs,den,denfac,t,rslope,rslopeb,rslope2,rslope3,   &
                            vt,its,ite,kts,kte)
  IMPLICIT NONE
  INTEGER       ::               its,ite, jts,jte, kts,kte
  REAL, DIMENSION( its:ite , kts:kte,2) ::                                     &
                                                                          qrs, &
                                                                       rslope, &
                                                                      rslopeb, &
                                                                      rslope2, &
                                                                      rslope3, &
                                                                           vt
  REAL, DIMENSION( its:ite , kts:kte) ::                                       &
                                                                          den, &
                                                                       denfac, &
                                                                            t
  REAL, PARAMETER  :: t0c = 273.15
  REAL, DIMENSION( its:ite , kts:kte ) ::                                      &
                                                                       n0sfac
  REAL       ::  lamdar, lamdas,  x, y, z, supcol
  integer :: i, j, k
!----------------------------------------------------------------
!     size distributions: (x=mixing ratio, y=air density):
!     valid for mixing ratio > 1.e-9 kg/kg.
      lamdar(x,y)=   sqrt(sqrt(pidn0r/(x*y)))      ! (pidn0r/(x*y))**.25
      lamdas(x,y,z)= sqrt(sqrt(pidn0s*z/(x*y)))    ! (pidn0s*z/(x*y))**.25
!
      do k = kts, kte
        do i = its, ite
          supcol = t0c-t(i,k)
!---------------------------------------------------------------
! n0s: Intercept parameter for snow [m-4] [HDC 6]
!---------------------------------------------------------------
          n0sfac(i,k) = max(min(exp(alpha*supcol),n0smax/n0s),1.)
          if(qrs(i,k,1).le.qcrmin)then
            rslope(i,k,1) = rslopermax
            rslopeb(i,k,1) = rsloperbmax
            rslope2(i,k,1) = rsloper2max
            rslope3(i,k,1) = rsloper3max
          else
            rslope(i,k,1) = 1./lamdar(qrs(i,k,1),den(i,k))
            rslopeb(i,k,1) = exp(log(rslope(i,k,1))*(bvtr))
            rslope2(i,k,1) = rslope(i,k,1)*rslope(i,k,1)
            rslope3(i,k,1) = rslope2(i,k,1)*rslope(i,k,1)
          endif
          if(qrs(i,k,2).le.qcrmin)then
            rslope(i,k,2) = rslopesmax
            rslopeb(i,k,2) = rslopesbmax
            rslope2(i,k,2) = rslopes2max
            rslope3(i,k,2) = rslopes3max
          else
            rslope(i,k,2) = 1./lamdas(qrs(i,k,2),den(i,k),n0sfac(i,k))
            rslopeb(i,k,2) = exp(log(rslope(i,k,2))*(bvts))
            rslope2(i,k,2) = rslope(i,k,2)*rslope(i,k,2)
            rslope3(i,k,2) = rslope2(i,k,2)*rslope(i,k,2)
          endif
          vt(i,k,1) = pvtr*rslopeb(i,k,1)*denfac(i,k)
          vt(i,k,2) = pvts*rslopeb(i,k,2)*denfac(i,k)
          if(qrs(i,k,1).le.0.0) vt(i,k,1) = 0.0
          if(qrs(i,k,2).le.0.0) vt(i,k,2) = 0.0
        enddo
      enddo
  END subroutine slope_wsm5
!-----------------------------------------------------------------------------
      subroutine slope_rain(qrs,den,denfac,t,rslope,rslopeb,rslope2,rslope3,   &
                            vt,its,ite,kts,kte)
  IMPLICIT NONE
  INTEGER       ::               its,ite, jts,jte, kts,kte
  REAL, DIMENSION( its:ite , kts:kte) ::                                       &
                                                                          qrs, &
                                                                       rslope, &
                                                                      rslopeb, &
                                                                      rslope2, &
                                                                      rslope3, &
                                                                           vt, &
                                                                          den, &
                                                                       denfac, &
                                                                            t
  REAL, PARAMETER  :: t0c = 273.15
  REAL, DIMENSION( its:ite , kts:kte ) ::                                      &
                                                                       n0sfac
  REAL       ::  lamdar, x, y, z, supcol
  integer :: i, j, k
!----------------------------------------------------------------
!     size distributions: (x=mixing ratio, y=air density):
!     valid for mixing ratio > 1.e-9 kg/kg.
      lamdar(x,y)=   sqrt(sqrt(pidn0r/(x*y)))      ! (pidn0r/(x*y))**.25
!
      do k = kts, kte
        do i = its, ite
          if(qrs(i,k).le.qcrmin)then
            rslope(i,k) = rslopermax
            rslopeb(i,k) = rsloperbmax
            rslope2(i,k) = rsloper2max
            rslope3(i,k) = rsloper3max
          else
            rslope(i,k) = 1./lamdar(qrs(i,k),den(i,k))
            rslopeb(i,k) = rslope(i,k)**bvtr
            rslope2(i,k) = rslope(i,k)*rslope(i,k)
            rslope3(i,k) = rslope2(i,k)*rslope(i,k)
          endif
          vt(i,k) = pvtr*rslopeb(i,k)*denfac(i,k)
          if(qrs(i,k).le.0.0) vt(i,k) = 0.0
        enddo
      enddo
  END subroutine slope_rain
!------------------------------------------------------------------------------
      subroutine slope_snow(qrs,den,denfac,t,rslope,rslopeb,rslope2,rslope3,   &
                            vt,its,ite,kts,kte)
  IMPLICIT NONE
  INTEGER       ::               its,ite, jts,jte, kts,kte
  REAL, DIMENSION( its:ite , kts:kte) ::                                       &
                                                                          qrs, &
                                                                       rslope, &
                                                                      rslopeb, &
                                                                      rslope2, &
                                                                      rslope3, &
                                                                           vt, &
                                                                          den, &
                                                                       denfac, &
                                                                            t
  REAL, PARAMETER  :: t0c = 273.15
  REAL, DIMENSION( its:ite , kts:kte ) ::                                      &
                                                                       n0sfac
  REAL       ::  lamdas, x, y, z, supcol
  integer :: i, j, k
!----------------------------------------------------------------
!     size distributions: (x=mixing ratio, y=air density):
!     valid for mixing ratio > 1.e-9 kg/kg.
      lamdas(x,y,z)= sqrt(sqrt(pidn0s*z/(x*y)))    ! (pidn0s*z/(x*y))**.25
!
      do k = kts, kte
        do i = its, ite
          supcol = t0c-t(i,k)
!---------------------------------------------------------------
! n0s: Intercept parameter for snow [m-4] [HDC 6]
!---------------------------------------------------------------
          n0sfac(i,k) = max(min(exp(alpha*supcol),n0smax/n0s),1.)
          if(qrs(i,k).le.qcrmin)then
            rslope(i,k) = rslopesmax
            rslopeb(i,k) = rslopesbmax
            rslope2(i,k) = rslopes2max
            rslope3(i,k) = rslopes3max
          else
            rslope(i,k) = 1./lamdas(qrs(i,k),den(i,k),n0sfac(i,k))
            rslopeb(i,k) = rslope(i,k)**bvts
            rslope2(i,k) = rslope(i,k)*rslope(i,k)
            rslope3(i,k) = rslope2(i,k)*rslope(i,k)
          endif
          vt(i,k) = pvts*rslopeb(i,k)*denfac(i,k)
          if(qrs(i,k).le.0.0) vt(i,k) = 0.0
        enddo
      enddo
  END subroutine slope_snow
!-------------------------------------------------------------------
      SUBROUTINE nislfv_rain_plm(im,km,denl,denfacl,tkl,dzl,wwl,rql,precip,dt,id,iter)
!-------------------------------------------------------------------
!
! for non-iteration semi-Lagrangain forward advection for cloud
! with mass conservation and positive definite advection
! 2nd order interpolation with monotonic piecewise linear method
! this routine is under assumption of decfl < 1 for semi_Lagrangian
!
! dzl    depth of model layer in meter
! wwl    terminal velocity at model layer m/s
! rql    cloud density*mixing ration
! precip precipitation
! dt     time step
! id     kind of precip: 0 test case; 1 raindrop  2: snow
! iter   how many time to guess mean terminal velocity: 0 pure forward.
!        0 : use departure wind for advection
!        1 : use mean wind for advection
!        > 1 : use mean wind after iter-1 iterations
!
! author: hann-ming henry juang <henry.juang@noaa.gov>
!         implemented by song-you hong
!
      implicit none
      integer  im,km,id
      real  dt
      real  dzl(im,km),wwl(im,km),rql(im,km),precip(im)
      real  denl(im,km),denfacl(im,km),tkl(im,km)
!
      integer  i,k,n,m,kk,kb,kt,iter
      real  tl,tl2,qql,dql,qqd
      real  th,th2,qqh,dqh
      real  zsum,qsum,dim,dip,c1,con1,fa1,fa2
      real  allold, allnew, zz, dzamin, cflmax, decfl
      real  dz(km), ww(km), qq(km), wd(km), wa(km), was(km)
      real  den(km), denfac(km), tk(km)
      real  wi(km+1), zi(km+1), za(km+1)
      real  qn(km), qr(km),tmp(km),tmp1(km),tmp2(km),tmp3(km)
      real  dza(km+1), qa(km+1), qmi(km+1), qpi(km+1)
!
      precip(:) = 0.0
!
      i_loop : do i=1,im
! -----------------------------------
      dz(:) = dzl(i,:)
      qq(:) = rql(i,:)
      ww(:) = wwl(i,:)
      den(:) = denl(i,:)
      denfac(:) = denfacl(i,:)
      tk(:) = tkl(i,:)
! skip for no precipitation for all layers
      allold = 0.0
      do k=1,km
        allold = allold + qq(k)
      enddo
      if(allold.le.0.0) then
        cycle i_loop
      endif
!
! compute interface values
      zi(1)=0.0
      do k=1,km
        zi(k+1) = zi(k)+dz(k)
      enddo
!
! save departure wind
      wd(:) = ww(:)
      n=1
 100  continue
! plm is 2nd order, we can use 2nd order wi or 3rd order wi
! 2nd order interpolation to get wi
      wi(1) = ww(1)
      wi(km+1) = ww(km)
      do k=2,km
        wi(k) = (ww(k)*dz(k-1)+ww(k-1)*dz(k))/(dz(k-1)+dz(k))
      enddo
! 3rd order interpolation to get wi
      fa1 = 9./16.
      fa2 = 1./16.
      wi(1) = ww(1)
      wi(2) = 0.5*(ww(2)+ww(1))
      do k=3,km-1
        wi(k) = fa1*(ww(k)+ww(k-1))-fa2*(ww(k+1)+ww(k-2))
      enddo
      wi(km) = 0.5*(ww(km)+ww(km-1))
      wi(km+1) = ww(km)
!
! terminate of top of raingroup
      do k=2,km
        if( ww(k).eq.0.0 ) wi(k)=ww(k-1)
      enddo
!
! diffusivity of wi
      con1 = 0.05
      do k=km,1,-1
        decfl = (wi(k+1)-wi(k))*dt/dz(k)
        if( decfl .gt. con1 ) then
          wi(k) = wi(k+1) - con1*dz(k)/dt
        endif
      enddo
! compute arrival point
      do k=1,km+1
        za(k) = zi(k) - wi(k)*dt
      enddo
!
      do k=1,km
        dza(k) = za(k+1)-za(k)
      enddo
      dza(km+1) = zi(km+1) - za(km+1)
!
! computer deformation at arrival point
      do k=1,km
        qa(k) = qq(k)*dz(k)/dza(k)
        qr(k) = qa(k)/den(k)
      enddo
      qa(km+1) = 0.0
!     call maxmin(km,1,qa,' arrival points ')
!
! compute arrival terminal velocity, and estimate mean terminal velocity
! then back to use mean terminal velocity
      if( n.le.iter ) then
        if (id.eq.1) then
          call slope_rain(qr,den,denfac,tk,tmp,tmp1,tmp2,tmp3,wa,1,1,1,km)
        else
          call slope_snow(qr,den,denfac,tk,tmp,tmp1,tmp2,tmp3,wa,1,1,1,km)
        endif 
        if( n.ge.2 ) wa(1:km)=0.5*(wa(1:km)+was(1:km))
        do k=1,km
!#ifdef DEBUG
!        print*,' slope_wsm3 ',qr(k)*1000.,den(k),denfac(k),tk(k),tmp(k),tmp1(k),tmp2(k),ww(k),wa(k)
!#endif
! mean wind is average of departure and new arrival winds
          ww(k) = 0.5* ( wd(k)+wa(k) )
        enddo
        was(:) = wa(:)
        n=n+1
        go to 100
      endif
!
! estimate values at arrival cell interface with monotone
      do k=2,km
        dip=(qa(k+1)-qa(k))/(dza(k+1)+dza(k))
        dim=(qa(k)-qa(k-1))/(dza(k-1)+dza(k))
        if( dip*dim.le.0.0 ) then
          qmi(k)=qa(k)
          qpi(k)=qa(k)
        else
          qpi(k)=qa(k)+0.5*(dip+dim)*dza(k)
          qmi(k)=2.0*qa(k)-qpi(k)
          if( qpi(k).lt.0.0 .or. qmi(k).lt.0.0 ) then
            qpi(k) = qa(k)
            qmi(k) = qa(k)
          endif
        endif
      enddo
      qpi(1)=qa(1)
      qmi(1)=qa(1)
      qmi(km+1)=qa(km+1)
      qpi(km+1)=qa(km+1)
!
! interpolation to regular point
      qn = 0.0
      kb=1
      kt=1
      intp : do k=1,km
             kb=max(kb-1,1)
             kt=max(kt-1,1)
! find kb and kt
             if( zi(k).ge.za(km+1) ) then
               exit intp
             else
               find_kb : do kk=kb,km
                         if( zi(k).le.za(kk+1) ) then
                           kb = kk
                           exit find_kb
                         else
                           cycle find_kb
                         endif
               enddo find_kb
               find_kt : do kk=kt,km
                         if( zi(k+1).le.za(kk) ) then
                           kt = kk
                           exit find_kt
                         else
                           cycle find_kt
                         endif
               enddo find_kt
               kt = kt - 1
! compute q with piecewise constant method
               if( kt.eq.kb ) then
                 tl=(zi(k)-za(kb))/dza(kb)
                 th=(zi(k+1)-za(kb))/dza(kb)
                 tl2=tl*tl
                 th2=th*th
                 qqd=0.5*(qpi(kb)-qmi(kb))
                 qqh=qqd*th2+qmi(kb)*th
                 qql=qqd*tl2+qmi(kb)*tl
                 qn(k) = (qqh-qql)/(th-tl)
               else if( kt.gt.kb ) then
                 tl=(zi(k)-za(kb))/dza(kb)
                 tl2=tl*tl
                 qqd=0.5*(qpi(kb)-qmi(kb))
                 qql=qqd*tl2+qmi(kb)*tl
                 dql = qa(kb)-qql
                 zsum  = (1.-tl)*dza(kb)
                 qsum  = dql*dza(kb)
                 if( kt-kb.gt.1 ) then
                 do m=kb+1,kt-1
                   zsum = zsum + dza(m)
                   qsum = qsum + qa(m) * dza(m)
                 enddo
                 endif
                 th=(zi(k+1)-za(kt))/dza(kt)
                 th2=th*th
                 qqd=0.5*(qpi(kt)-qmi(kt))
                 dqh=qqd*th2+qmi(kt)*th
                 zsum  = zsum + th*dza(kt)
                 qsum  = qsum + dqh*dza(kt)
                 qn(k) = qsum/zsum
               endif
               cycle intp
             endif
!
       enddo intp
!
! rain out
      sum_precip: do k=1,km
                    if( za(k).lt.0.0 .and. za(k+1).lt.0.0 ) then
                      precip(i) = precip(i) + qa(k)*dza(k)
                      cycle sum_precip
                    else if ( za(k).lt.0.0 .and. za(k+1).ge.0.0 ) then
                      precip(i) = precip(i) + qa(k)*(0.0-za(k))
                      exit sum_precip
                    endif
                    exit sum_precip
      enddo sum_precip
!
! replace the new values
      rql(i,:) = qn(:)
!
! ----------------------------------
      enddo i_loop
!
  END SUBROUTINE nislfv_rain_plm
END MODULE module_mp_wsm5
#endif