source: lmdz_wrf/WRFV3/phys/module_bl_gwdo.F @ 1

! WRf:model_layer:physics
!
!
!
!
!
module module_bl_gwdo
contains
!
!-------------------------------------------------------------------
!
   subroutine gwdo(u3d,v3d,t3d,qv3d,p3d,p3di,pi3d,z, &
                  rublten,rvblten, &
                  dtaux3d,dtauy3d,dusfcg,dvsfcg, &
                  var2d,oc12d,oa2d1,oa2d2,oa2d3,oa2d4,ol2d1,ol2d2,ol2d3,ol2d4, &
                  znu,znw,mut,p_top, &
                  cp,g,rd,rv,ep1,pi, &
                  dt,dx,kpbl2d,itimestep, &
                  ids,ide, jds,jde, kds,kde, &
                  ims,ime, jms,jme, kms,kme, &
                  its,ite, jts,jte, kts,kte)
!-------------------------------------------------------------------
      implicit none
!------------------------------------------------------------------------------
!
!-- u3d 3d u-velocity interpolated to theta points (m/s)
!-- v3d 3d v-velocity interpolated to theta points (m/s)
!-- t3d temperature (k)
!-- qv3d 3d water vapor mixing ratio (kg/kg)
!-- p3d 3d pressure (pa)
!-- p3di 3d pressure (pa) at interface level
!-- pi3d 3d exner function (dimensionless)
!-- rublten u tendency due to
! pbl parameterization (m/s/s)
!-- rvblten v tendency due to
!-- cp heat capacity at constant pressure for dry air (j/kg/k)
!-- g acceleration due to gravity (m/s^2)
!-- rd gas constant for dry air (j/kg/k)
!-- z height above sea level (m)
!-- rv gas constant for water vapor (j/kg/k)
!-- dt time step (s)
!-- dx model grid interval (m)
!-- ep1 constant for virtual temperature (r_v/r_d - 1) (dimensionless)
!-- ids start index for i in domain
!-- ide end index for i in domain
!-- jds start index for j in domain
!-- jde end index for j in domain
!-- kds start index for k in domain
!-- kde end index for k in domain
!-- ims start index for i in memory
!-- ime end index for i in memory
!-- jms start index for j in memory
!-- jme end index for j in memory
!-- kms start index for k in memory
!-- kme end index for k in memory
!-- its start index for i in tile
!-- ite end index for i in tile
!-- jts start index for j in tile
!-- jte end index for j in tile
!-- kts start index for k in tile
!-- kte end index for k in tile
!-------------------------------------------------------------------
!
  integer, intent(in ) :: ids,ide, jds,jde, kds,kde, &
                                     ims,ime, jms,jme, kms,kme, &
                                     its,ite, jts,jte, kts,kte
  integer, intent(in ) :: itimestep
!
  real, intent(in ) :: dt,dx,cp,g,rd,rv,ep1,pi
!
  real, dimension( ims:ime, kms:kme, jms:jme ) , &
            intent(in ) :: qv3d, &
                                                                          p3d, &
                                                                         pi3d, &
                                                                          t3d, &
                                                                             z
  real, dimension( ims:ime, kms:kme, jms:jme ) , &
            intent(in ) :: p3di
!
  real, dimension( ims:ime, kms:kme, jms:jme ) , &
            intent(inout) :: rublten, &
                                                                      rvblten
  real, dimension( ims:ime, kms:kme, jms:jme ) , &
            intent(inout) :: dtaux3d, &
                                                                      dtauy3d
!
  real, dimension( ims:ime, kms:kme, jms:jme ) , &
             intent(in ) :: u3d, &
                                                                          v3d
!
  integer, dimension( ims:ime, jms:jme ) , &
             intent(in ) :: kpbl2d
  real, dimension( ims:ime, jms:jme ) , &
             intent(inout ) :: dusfcg, &
                                                                       dvsfcg
!
  real, dimension( ims:ime, jms:jme ) , &
             intent(in ) :: var2d, &
                                                                        oc12d, &
                                                      oa2d1,oa2d2,oa2d3,oa2d4, &
                                                      ol2d1,ol2d2,ol2d3,ol2d4
!
  real, dimension( ims:ime, jms:jme ) , &
             optional , &
             intent(in ) :: mut
!
  real, dimension( kms:kme ) , &
             optional , &
             intent(in ) :: znu, &
                                                                          znw
!
  real, optional, intent(in ) :: p_top
!
!local
!
  real, dimension( its:ite, kts:kte ) :: delprsi, &
                                                                          pdh
  real, dimension( its:ite, kts:kte+1 ) :: pdhi
  real, dimension( its:ite, 4 ) :: oa4, &
                                                                          ol4
  integer :: i,j,k,kdt
!
   do j = jts,jte
      if(present(mut))then
! For ARW we will replace p and p8w with dry hydrostatic pressure
        do k = kts,kte+1
          do i = its,ite
             if(k.le.kte)pdh(i,k) = mut(i,j)*znu(k) + p_top
             pdhi(i,k) = mut(i,j)*znw(k) + p_top
          enddo
        enddo
      else
        do k = kts,kte+1
          do i = its,ite
             if(k.le.kte)pdh(i,k) = p3d(i,k,j)
             pdhi(i,k) = p3di(i,k,j)
          enddo
        enddo
      endif
!
      do k = kts,kte
        do i = its,ite
          delprsi(i,k) = pdhi(i,k)-pdhi(i,k+1)
        enddo
      enddo
        do i = its,ite
            oa4(i,1) = oa2d1(i,j)
            oa4(i,2) = oa2d2(i,j)
            oa4(i,3) = oa2d3(i,j)
            oa4(i,4) = oa2d4(i,j)
            ol4(i,1) = ol2d1(i,j)
            ol4(i,2) = ol2d2(i,j)
            ol4(i,3) = ol2d3(i,j)
            ol4(i,4) = ol2d4(i,j)
        enddo
      call gwdo2d(dudt=rublten(ims,kms,j),dvdt=rvblten(ims,kms,j) &
              ,dtaux2d=dtaux3d(ims,kms,j),dtauy2d=dtauy3d(ims,kms,j) &
              ,u1=u3d(ims,kms,j),v1=v3d(ims,kms,j) &
              ,t1=t3d(ims,kms,j),q1=qv3d(ims,kms,j) &
              ,prsi=pdhi(its,kts),del=delprsi(its,kts) &
              ,prsl=pdh(its,kts),prslk=pi3d(ims,kms,j) &
              ,zl=z(ims,kms,j),rcl=1.0 &
              ,dusfc=dusfcg(ims,j),dvsfc=dvsfcg(ims,j) &
              ,var=var2d(ims,j),oc1=oc12d(ims,j) &
              ,oa4=oa4,ol4=ol4 &
              ,g=g,cp=cp,rd=rd,rv=rv,fv=ep1,pi=pi &
              ,dxmeter=dx,deltim=dt &
              ,kpbl=kpbl2d(ims,j),kdt=itimestep,lat=j &
              ,ids=ids,ide=ide, jds=jds,jde=jde, kds=kds,kde=kde &
              ,ims=ims,ime=ime, jms=jms,jme=jme, kms=kms,kme=kme &
              ,its=its,ite=ite, jts=jts,jte=jte, kts=kts,kte=kte )
   enddo
!
!
   end subroutine gwdo
!
!-------------------------------------------------------------------
!
!
!
!
   subroutine gwdo2d(dudt,dvdt,dtaux2d,dtauy2d, &
                    u1,v1,t1,q1, &
                    prsi,del,prsl,prslk,zl,rcl, &
                    var,oc1,oa4,ol4,dusfc,dvsfc, &
                    g,cp,rd,rv,fv,pi,dxmeter,deltim,kpbl,kdt,lat, &
                    ids,ide, jds,jde, kds,kde, &
                    ims,ime, jms,jme, kms,kme, &
                    its,ite, jts,jte, kts,kte)
!-------------------------------------------------------------------
!
! this code handles the time tendencies of u v due to the effect of mountain
! induced gravity wave drag from sub-grid scale orography. this routine
! not only treats the traditional upper-level wave breaking due to mountain
! variance (alpert 1988), but also the enhanced lower-tropospheric wave
! breaking due to mountain convexity and asymmetry (kim and arakawa 1995).
! thus, in addition to the terrain height data in a model grid gox,
! additional 10-2d topographic statistics files are needed, including
! orographic standard deviation (var), convexity (oc1), asymmetry (oa4)
! and ol (ol4). these data sets are prepared based on the 30 sec usgs orography
! hong (1999). the current scheme was implmented as in hong et al.(2008)
!
! coded by song-you hong and young-joon kim and implemented by song-you hong
!
! references:
! hong et al. (2008), wea. and forecasting
! kim and arakawa (1995), j. atmos. sci.
! alpet et al. (1988), NWP conference.
! hong (1999), NCEP office note 424.
!
! notice : comparible or lower resolution orography files than model resolution
! are desirable in preprocess (wps) to prevent weakening of the drag
!-------------------------------------------------------------------
!
! input
! dudt (ims:ime,kms:kme) non-lin tendency for u wind component
! dvdt (ims:ime,kms:kme) non-lin tendency for v wind component
! u1(ims:ime,kms:kme) zonal wind / sqrt(rcl) m/sec at t0-dt
! v1(ims:ime,kms:kme) meridional wind / sqrt(rcl) m/sec at t0-dt
! t1(ims:ime,kms:kme) temperature deg k at t0-dt
! q1(ims:ime,kms:kme) specific humidity at t0-dt
!
! rcl a scaling factor = reciprocal of square of cos(lat)
! for mrf gsm. rcl=1 if u1 and v1 are wind components.
! deltim time step secs
! del(kts:kte) positive increment of pressure across layer (pa)
!
! output
! dudt, dvdt wind tendency due to gwdo
!
!-------------------------------------------------------------------
   implicit none
!-------------------------------------------------------------------
   integer :: kdt,lat,latd,lond, &
                            ids,ide, jds,jde, kds,kde, &
                            ims,ime, jms,jme, kms,kme, &
                            its,ite, jts,jte, kts,kte
!
   real :: g,rd,rv,fv,cp,pi,dxmeter,deltim,rcl
   real :: dudt(ims:ime,kms:kme),dvdt(ims:ime,kms:kme), &
                            dtaux2d(ims:ime,kms:kme),dtauy2d(ims:ime,kms:kme), &
                            u1(ims:ime,kms:kme),v1(ims:ime,kms:kme), &
                            t1(ims:ime,kms:kme),q1(ims:ime,kms:kme), &
                            zl(ims:ime,kms:kme),prslk(ims:ime,kms:kme)
   real :: prsl(its:ite,kts:kte),prsi(its:ite,kts:kte+1), &
                            del(its:ite,kts:kte)
   real :: oa4(its:ite,4),ol4(its:ite,4)
!
   integer :: kpbl(ims:ime)
   real :: var(ims:ime),oc1(ims:ime), &
                            dusfc(ims:ime),dvsfc(ims:ime)
! critical richardson number for wave breaking : ! larger drag with larger value
!
   real,parameter :: ric = 0.25
!
   real,parameter :: dw2min = 1.
   real,parameter :: rimin = -100.
   real,parameter :: bnv2min = 1.0e-5
   real,parameter :: efmin = 0.0
   real,parameter :: efmax = 10.0
   real,parameter :: xl = 4.0e4
   real,parameter :: critac = 1.0e-5
   real,parameter :: gmax = 1.
   real,parameter :: veleps = 1.0
   real,parameter :: factop = 0.5
   real,parameter :: frc = 1.0
   real,parameter :: ce = 0.8
   real,parameter :: cg = 0.5
!
! local variables
!
   integer :: i,k,lcap,lcapp1,nwd,idir,kpblmin,kpblmax, &
                            klcap,kp1,ikount,kk
!
   real :: rcs,rclcs,csg,fdir,cleff,cs,rcsks, &
                            wdir,ti,rdz,temp,tem2,dw2,shr2,bvf2,rdelks, &
                            wtkbj,coefm,tem,gfobnv,hd,fro,rim,temc,tem1,efact, &
                            temv,dtaux,dtauy
!
   logical :: ldrag(its:ite),icrilv(its:ite), &
                            flag(its:ite),kloop1(its:ite)
!
   real :: taub(its:ite),taup(its:ite,kts:kte+1), &
                            xn(its:ite),yn(its:ite), &
                            ubar(its:ite),vbar(its:ite), &
                            fr(its:ite),ulow(its:ite), &
                            rulow(its:ite),bnv(its:ite), &
                            oa(its:ite),ol(its:ite), &
                            roll(its:ite),dtfac(its:ite), &
                            brvf(its:ite),xlinv(its:ite), &
                            delks(its:ite),delks1(its:ite), &
                            bnv2(its:ite,kts:kte),usqj(its:ite,kts:kte), &
                            taud(its:ite,kts:kte),ro(its:ite,kts:kte), &
                            vtk(its:ite,kts:kte),vtj(its:ite,kts:kte), &
                            zlowtop(its:ite),velco(its:ite,kts:kte-1)
!
   integer :: kbl(its:ite),klowtop(its:ite), &
                            lowlv(its:ite)
!
   logical :: iope
   integer,parameter :: mdir=8
   integer :: nwdir(mdir)
   data nwdir/6,7,5,8,2,3,1,4/
!
! initialize local variables
!
   kbl=0 ; klowtop=0 ; lowlv=0
!
!---- constants
!
   rcs = sqrt(rcl)
   cs = 1. / sqrt(rcl)
   csg = cs * g
   lcap = kte
   lcapp1 = lcap + 1
   fdir = mdir / (2.0*pi)
!
!
!!!!!!! cleff (subgrid mountain scale ) is highly tunable parameter
!!!!!!! the bigger (smaller) value produce weaker (stronger) wave drag
!
   cleff = max(dxmeter,50.e3)
!
! initialize!!
!
   dtaux = 0.0
   dtauy = 0.0
   do k = kts,kte
     do i = its,ite
       usqj(i,k) = 0.0
       bnv2(i,k) = 0.0
       vtj(i,k) = 0.0
       vtk(i,k) = 0.0
       taup(i,k) = 0.0
       taud(i,k) = 0.0
       dtaux2d(i,k)= 0.0
       dtauy2d(i,k)= 0.0
     enddo
   enddo
   do i = its,ite
     taup(i,kte+1) = 0.0
     xlinv(i) = 1.0/xl
   enddo
!
   do k = kts,kte
     do i = its,ite
       vtj(i,k) = t1(i,k) * (1.+fv*q1(i,k))
       vtk(i,k) = vtj(i,k) / prslk(i,k)
       ro(i,k) = 1./rd * prsl(i,k) / vtj(i,k) ! density kg/m**3
     enddo
   enddo
!
   do i = its,ite
     zlowtop(i) = 2. * var(i)
   enddo
!
!--- determine new reference level > 2*var
!
   do i = its,ite
     kloop1(i) = .true.
   enddo
   do k = kts+1,kte
     do i = its,ite
       if(kloop1(i).and.zl(i,k)-zl(i,1).ge.zlowtop(i)) then
         klowtop(i) = k+1
         kloop1(i) = .false.
       endif
     enddo
   enddo
!
   kpblmax = 2
   do i = its,ite
     kbl(i) = max(2, kpbl(i))
     kbl(i) = max(kbl(i), klowtop(i))
     delks(i) = 1.0 / (prsi(i,1) - prsi(i,kbl(i)))
     ubar (i) = 0.0
     vbar (i) = 0.0
     taup(i,1) = 0.0
     oa(i) = 0.0
     kpblmax = max(kpblmax,kbl(i))
     flag(i) = .true.
     lowlv(i) = 2
   enddo
   kpblmax = min(kpblmax+1,kte-1)
!
! compute low level averages within pbl
!
   do k = kts,kpblmax
     do i = its,ite
       if (k.lt.kbl(i)) then
         rcsks = rcs * del(i,k) * delks(i)
         ubar(i) = ubar(i) + rcsks * u1(i,k) ! pbl u mean
         vbar(i) = vbar(i) + rcsks * v1(i,k) ! pbl v mean
       endif
     enddo
   enddo
!
! figure out low-level horizontal wind direction
!
! nwd 1 2 3 4 5 6 7 8
! wd w s sw nw e n ne se
!
   do i = its,ite
     wdir = atan2(ubar(i),vbar(i)) + pi
     idir = mod(nint(fdir*wdir),mdir) + 1
     nwd = nwdir(idir)
     oa(i) = (1-2*int( (nwd-1)/4 )) * oa4(i,mod(nwd-1,4)+1)
     ol(i) = ol4(i,mod(nwd-1,4)+1)
   enddo
!
   kpblmin = kte
   do i = its,ite
     kpblmin = min(kpblmin, kbl(i))
   enddo
!
   do i = its,ite
     if (oa(i).le.0.0) kbl(i) = kpbl(i) + 1
   enddo
!
   do i = its,ite
     delks(i) = 1.0 / (prsi(i,1) - prsi(i,kbl(i)))
     delks1(i) = 1.0 / (prsl(i,1) - prsl(i,kbl(i)))
   enddo
!
!--- saving richardson number in usqj for migwdi
!
   do k = kts,kte-1
     do i = its,ite
       ti = 2.0 / (t1(i,k)+t1(i,k+1))
       rdz = 1./(zl(i,k+1) - zl(i,k))
       tem1 = u1(i,k) - u1(i,k+1)
       tem2 = v1(i,k) - v1(i,k+1)
       dw2 = rcl*(tem1*tem1 + tem2*tem2)
       shr2 = max(dw2,dw2min) * rdz * rdz
       bvf2 = g*(g/cp+rdz*(vtj(i,k+1)-vtj(i,k))) * ti
       usqj(i,k) = max(bvf2/shr2,rimin)
       bnv2(i,k) = 2*g*rdz*(vtk(i,k+1)-vtk(i,k))/(vtk(i,k+1)+vtk(i,k))
       bnv2(i,k) = max( bnv2(i,k), bnv2min )
     enddo
   enddo
!
!-----initialize arrays
!
   do i = its,ite
     xn(i) = 0.0
     yn(i) = 0.0
     ubar (i) = 0.0
     vbar (i) = 0.0
     roll (i) = 0.0
     taub (i) = 0.0
     ulow (i) = 0.0
     dtfac(i) = 1.0
     ldrag(i) = .false.
     icrilv(i) = .false. ! initialize critical level control vector
   enddo
!
!---- compute low level averages
!---- (u,v)*cos(lat) use uv=(u1,v1) which is wind at t0-1
!---- use rcs=1/cos(lat) to get wind field
!
   do k = 1,kpblmax
     do i = its,ite
       if (k .lt. kbl(i)) then
         rdelks = del(i,k) * delks(i)
         rcsks = rcs * rdelks
         ubar(i) = ubar(i) + rcsks * u1(i,k) ! u mean
         vbar(i) = vbar(i) + rcsks * v1(i,k) ! v mean
         roll(i) = roll(i) + rdelks * ro(i,k) ! ro mean
       endif
     enddo
   enddo
!
!----compute the "low level" or 1/3 wind magnitude (m/s)
!
   do i = its,ite
     ulow(i) = max(sqrt(ubar(i)*ubar(i) + vbar(i)*vbar(i)), 1.0)
     rulow(i) = 1./ulow(i)
   enddo
!
   do k = kts,kte-1
     do i = its,ite
       velco(i,k) = (0.5*rcs) * ((u1(i,k)+u1(i,k+1)) * ubar(i) &
                                + (v1(i,k)+v1(i,k+1)) * vbar(i))
       velco(i,k) = velco(i,k) * rulow(i)
       if ((velco(i,k).lt.veleps) .and. (velco(i,k).gt.0.)) then
         velco(i,k) = veleps
       endif
     enddo
   enddo
!
! no drag when critical level in the base layer
!
   do i = its,ite
     ldrag(i) = velco(i,1).le.0.
   enddo
!
   do k = kts+1,kpblmax-1
     do i = its,ite
       if (k .lt. kbl(i)) ldrag(i) = ldrag(i).or. velco(i,k).le.0.
     enddo
   enddo
!
! no drag when bnv2.lt.0
!
   do k = kts,kpblmax-1
     do i = its,ite
       if (k .lt. kbl(i)) ldrag(i) = ldrag(i).or. bnv2(i,k).lt.0.
     enddo
   enddo
!
!-----the low level weighted average ri is stored in usqj(1,1; im)
!-----the low level weighted average n**2 is stored in bnv2(1,1; im)
!---- this is called bnvl2 in phys_gwd_alpert_sub not bnv2
!---- rdelks (del(k)/delks) vert ave factor so we can * instead of /
!
   do i = its,ite
     wtkbj = (prsl(i,1)-prsl(i,2)) * delks1(i)
     bnv2(i,1) = wtkbj * bnv2(i,1)
     usqj(i,1) = wtkbj * usqj(i,1)
   enddo
!
   do k = kts+1,kpblmax-1
     do i = its,ite
       if (k .lt. kbl(i)) then
         rdelks = (prsl(i,k)-prsl(i,k+1)) * delks1(i)
         bnv2(i,1) = bnv2(i,1) + bnv2(i,k) * rdelks
         usqj(i,1) = usqj(i,1) + usqj(i,k) * rdelks
       endif
     enddo
   enddo
!
   do i = its,ite
     ldrag(i) = ldrag(i) .or. bnv2(i,1).le.0.0
     ldrag(i) = ldrag(i) .or. ulow(i).eq.1.0
     ldrag(i) = ldrag(i) .or. var(i) .le. 0.0
   enddo
!
! ----- set all ri low level values to the low level value
!
   do k = kts+1,kpblmax-1
     do i = its,ite
       if (k .lt. kbl(i)) usqj(i,k) = usqj(i,1)
     enddo
   enddo
!
   do i = its,ite
     if (.not.ldrag(i)) then
       bnv(i) = sqrt( bnv2(i,1) )
       fr(i) = bnv(i) * rulow(i) * var(i)
       xn(i) = ubar(i) * rulow(i)
       yn(i) = vbar(i) * rulow(i)
     endif
   enddo
!
! compute the base level stress and store it in taub
! calculate enhancement factor, number of mountains & aspect
! ratio const. use simplified relationship between standard
! deviation & critical hgt
!
   do i = its,ite
     if (.not. ldrag(i)) then
       efact = (oa(i) + 2.) ** (ce*fr(i)/frc)
       efact = min( max(efact,efmin), efmax )
       coefm = (1. + ol(i)) ** (oa(i)+1.)
       xlinv(i) = coefm / cleff
       tem = fr(i) * fr(i) * oc1(i)
       gfobnv = gmax * tem / ((tem + cg)*bnv(i))
       taub(i) = xlinv(i) * roll(i) * ulow(i) * ulow(i) &
                * ulow(i) * gfobnv * efact
     else
       taub(i) = 0.0
       xn(i) = 0.0
       yn(i) = 0.0
     endif
   enddo
!
! now compute vertical structure of the stress.
!
!----set up bottom values of stress
!
   do k = kts,kpblmax
     do i = its,ite
       if (k .le. kbl(i)) taup(i,k) = taub(i)
     enddo
   enddo
!
   do k = kpblmin, kte-1 ! vertical level k loop!
     kp1 = k + 1
     do i = its,ite
!
!-----unstablelayer if ri < ric
!-----unstable layer if upper air vel comp along surf vel <=0 (crit lay)
!---- at (u-c)=0. crit layer exists and bit vector should be set (.le.)
!
       if (k .ge. kbl(i)) then
         icrilv(i) = icrilv(i) .or. ( usqj(i,k) .lt. ric) &
                               .or. (velco(i,k) .le. 0.0)
         brvf(i) = max(bnv2(i,k),bnv2min) ! brunt-vaisala frequency squared
         brvf(i) = sqrt(brvf(i)) ! brunt-vaisala frequency
       endif
     enddo
!
     do i = its,ite
       if (k .ge. kbl(i) .and. (.not. ldrag(i))) then
         if (.not.icrilv(i) .and. taup(i,k) .gt. 0.0 ) then
           temv = 1.0 / velco(i,k)
           tem1 = xlinv(i)*(ro(i,kp1)+ro(i,k))*brvf(i)*velco(i,k)*0.5
           hd = sqrt(taup(i,k) / tem1)
           fro = brvf(i) * hd * temv
!
! rim is the minimum-richardson number by shutts (1985)
!
           tem2 = sqrt(usqj(i,k))
           tem = 1. + tem2 * fro
           rim = usqj(i,k) * (1.-fro) / (tem * tem)
!
! check stability to employ the 'saturation hypothesis'
! of lindzen (1981) except at tropospheric downstream regions
!
           if (rim .le. ric) then ! saturation hypothesis!
             if ((oa(i) .le. 0. .or. kp1 .ge. lowlv(i) )) then
               temc = 2.0 + 1.0 / tem2
               hd = velco(i,k) * (2.*sqrt(temc)-temc) / brvf(i)
               taup(i,kp1) = tem1 * hd * hd
             endif
           else ! no wavebreaking!
             taup(i,kp1) = taup(i,k)
           endif
         endif
       endif
     enddo
   enddo
!
   if(lcap.lt.kte) then
     do klcap = lcapp1,kte
       do i = its,ite
         taup(i,klcap) = prsi(i,klcap) / prsi(i,lcap) * taup(i,lcap)
       enddo
     enddo
   endif
!
! calculate - (g)*d(tau)/d(pressure) and deceleration terms dtaux, dtauy
!
   do k = kts,kte
     do i = its,ite
       taud(i,k) = 1. * (taup(i,k+1) - taup(i,k)) * csg / del(i,k)
     enddo
   enddo
!
!------limit de-acceleration (momentum deposition ) at top to 1/2 value
!------the idea is some stuff must go out the 'top'
!
   do klcap = lcap,kte
     do i = its,ite
       taud(i,klcap) = taud(i,klcap) * factop
     enddo
   enddo
!
!------if the gravity wave drag would force a critical line
!------in the lower ksmm1 layers during the next deltim timestep,
!------then only apply drag until that critical line is reached.
!
   do k = kts,kpblmax-1
     do i = its,ite
       if (k .le. kbl(i)) then
         if(taud(i,k).ne.0.) &
         dtfac(i) = min(dtfac(i),abs(velco(i,k) &
                   /(deltim*rcs*taud(i,k))))
       endif
     enddo
   enddo
!
   do i = its,ite
     dusfc(i) = 0.
     dvsfc(i) = 0.
   enddo
!
   do k = kts,kte
     do i = its,ite
       taud(i,k) = taud(i,k) * dtfac(i)
       dtaux = taud(i,k) * xn(i)
       dtauy = taud(i,k) * yn(i)
       dtaux2d(i,k) = dtaux
       dtauy2d(i,k) = dtauy
       dudt(i,k) = dtaux + dudt(i,k)
       dvdt(i,k) = dtauy + dvdt(i,k)
       dusfc(i) = dusfc(i) + dtaux * del(i,k)
       dvsfc(i) = dvsfc(i) + dtauy * del(i,k)
     enddo
   enddo
!
   do i = its,ite
     dusfc(i) = (-1./g*rcs) * dusfc(i)
     dvsfc(i) = (-1./g*rcs) * dvsfc(i)
   enddo
!
   return
   end subroutine gwdo2d
!-------------------------------------------------------------------
end module module_bl_gwdo