! WRf:model_layer:physics
!
!
!
!
!
module module_bl_gwdo 1
contains
!
!-------------------------------------------------------------------
!
subroutine gwdo(u3d,v3d,t3d,qv3d,p3d,p3di,pi3d,z, & 1,1
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, & 1
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