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pbl_ysu.f90
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!>------------------------------------------------------------
!! YSU PBL scheme (from WRF)
!!
!!------------------------------------------------------------
!wrf:model_layer:physics
!
!
!
!
module module_bl_ysu
contains
!
!-------------------------------------------------------------------
!
subroutine ysu(u3d,v3d,th3d,t3d,qv3d,qc3d,qi3d,p3d,p3di,pi3d, &
rublten,rvblten,rthblten, &
rqvblten,rqcblten,rqiblten,flag_qi, &
cp,g,rovcp,rd,rovg, &
dz8w,z,xlv,rv,psfc, &
znu,znw,mut,p_top, &
znt,ust,zol,hol,hpbl,psim,psih, &
xland,hfx,qfx,tsk,gz1oz0,wspd,br, &
dt,dtmin,kpbl2d, &
svp1,svp2,svp3,svpt0,ep1,ep2,karman,eomeg,stbolt, &
exch_h, &
u10,v10, &
ids,ide, jds,jde, kds,kde, &
ims,ime, jms,jme, kms,kme, &
its,ite, jts,jte, kts,kte, &
!optional
regime )
!-------------------------------------------------------------------
implicit none
!-------------------------------------------------------------------
!-- u3d 3d u-velocity interpolated to theta points (m/s)
!-- v3d 3d v-velocity interpolated to theta points (m/s)
!-- th3d 3d potential temperature (k)
!-- t3d temperature (k)
!-- qv3d 3d water vapor mixing ratio (kg/kg)
!-- qc3d 3d cloud mixing ratio (kg/kg)
!-- qi3d 3d ice mixing ratio (kg/kg)
! (note: if P_QI<PARAM_FIRST_SCALAR this should be zero filled)
!-- p3d 3d pressure (pa)
!-- p3di 3d pressure (pa) at interface level
!-- pi3d 3d exner function (dimensionless)
!-- rr3d 3d dry air density (kg/m^3)
!-- rublten u tendency due to
! pbl parameterization (m/s/s)
!-- rvblten v tendency due to
! pbl parameterization (m/s/s)
!-- rthblten theta tendency due to
! pbl parameterization (K/s)
!-- rqvblten qv tendency due to
! pbl parameterization (kg/kg/s)
!-- rqcblten qc tendency due to
! pbl parameterization (kg/kg/s)
!-- rqiblten qi tendency due to
! pbl parameterization (kg/kg/s)
!-- cp heat capacity at constant pressure for dry air (j/kg/k)
!-- g acceleration due to gravity (m/s^2)
!-- rovcp r/cp
!-- rd gas constant for dry air (j/kg/k)
!-- rovg r/g
!-- dz8w dz between full levels (m)
!-- z height above sea level (m)
!-- xlv latent heat of vaporization (j/kg)
!-- rv gas constant for water vapor (j/kg/k)
!-- psfc pressure at the surface (pa)
!-- znt roughness length (m)
!-- ust u* in similarity theory (m/s)
!-- zol z/l height over monin-obukhov length
!-- hol pbl height over monin-obukhov length
!-- hpbl pbl height (m)
!-- regime flag indicating pbl regime (stable, unstable, etc.)
!-- psim similarity stability function for momentum
!-- psih similarity stability function for heat
!-- xland land mask (1 for land, 2 for water)
!-- hfx upward heat flux at the surface (w/m^2)
!-- qfx upward moisture flux at the surface (kg/m^2/s)
!-- tsk surface temperature (k)
!-- gz1oz0 log(z/z0) where z0 is roughness length
!-- wspd wind speed at lowest model level (m/s)
!-- u10 u-wind speed at 10 m (m/s)
!-- v10 v-wind speed at 10 m (m/s)
!-- br bulk richardson number in surface layer
!-- dt time step (s)
!-- dtmin time step (minute)
!-- rvovrd r_v divided by r_d (dimensionless)
!-- svp1 constant for saturation vapor pressure (kpa)
!-- svp2 constant for saturation vapor pressure (dimensionless)
!-- svp3 constant for saturation vapor pressure (k)
!-- svpt0 constant for saturation vapor pressure (k)
!-- ep1 constant for virtual temperature (r_v/r_d - 1) (dimensionless)
!-- ep2 constant for specific humidity calculation
!-- karman von karman constant
!-- eomeg angular velocity of earths rotation (rad/s)
!-- stbolt stefan-boltzmann constant (w/m^2/k^4)
!-- 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
!
real, intent(in ) :: dt,dtmin,cp,g,rovcp,rovg,rd,xlv,rv
!
real, intent(in ) :: svp1,svp2,svp3,svpt0
real, intent(in ) :: ep1,ep2,karman,eomeg,stbolt
!
real, dimension( ims:ime, kms:kme, jms:jme ) , &
intent(in ) :: qv3d, &
qc3d, &
qi3d, &
p3d, &
pi3d, &
th3d, &
t3d, &
dz8w, &
z
real, dimension( ims:ime, kms:kme, jms:jme ) , &
intent(in ) :: p3di
!
real, dimension( ims:ime, kms:kme, jms:jme ) , &
intent(inout) :: rublten, &
rvblten, &
rthblten, &
rqvblten, &
rqcblten
!
real, dimension( ims:ime, kms:kme, jms:jme ) , &
intent(inout) :: exch_h
real, dimension( ims:ime, jms:jme ) , &
intent(in ) :: u10, &
v10
!
real, dimension( ims:ime, jms:jme ) , &
intent(in ) :: xland, &
hfx, &
qfx, &
psim, &
psih, &
gz1oz0, &
br, &
psfc, &
tsk
!
real, dimension( ims:ime, jms:jme ) , &
intent(inout) :: hol, &
ust, &
hpbl, &
znt, &
wspd, &
zol
!
real, dimension( ims:ime, kms:kme, jms:jme ) , &
intent(in ) :: u3d, &
v3d
!
integer, dimension( ims:ime, jms:jme ) , &
intent(out ) :: kpbl2d
!
logical, intent(in) :: flag_qi
!optional
real, dimension( ims:ime, jms:jme ) , &
optional , &
intent(inout) :: regime
!
real, dimension( ims:ime, kms:kme, jms:jme ) , &
optional , &
intent(inout) :: rqiblten
!
real, dimension( kms:kme ) , &
optional , &
intent(in ) :: znu, &
znw
!
real, dimension( ims:ime, jms:jme ) , &
optional , &
intent(in ) :: mut
!
real, optional, intent(in ) :: p_top
!
!local
integer :: i,j,k
real, dimension( its:ite, kts:kte ) :: rqibl2dt, &
pdh
real, dimension( its:ite, kts:kte+1 ) :: pdhi
!
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
call ysu2d(J=j,ux=u3d(ims,kms,j),vx=v3d(ims,kms,j) &
,tx=t3d(ims,kms,j) &
,qx=qv3d(ims,kms,j),qcx=qc3d(ims,kms,j) &
,qix=qi3d(ims,kms,j) &
,p2d=pdh(its,kts),p2di=pdhi(its,kts) &
,pi2d=pi3d(ims,kms,j) &
,utnp=rublten(ims,kms,j),vtnp=rvblten(ims,kms,j) &
,ttnp=rthblten(ims,kms,j),qtnp=rqvblten(ims,kms,j) &
,qctnp=rqcblten(ims,kms,j),qitnp=rqibl2dt(its,kts) &
,cp=cp,g=g,rovcp=rovcp,rd=rd,rovg=rovg &
,dz8w2d=dz8w(ims,kms,j),z2d=z(ims,kms,j) &
,xlv=xlv,rv=rv &
,psfcpa=psfc(ims,j),znt=znt(ims,j),ust=ust(ims,j) &
,zol=zol(ims,j),hol=hol(ims,j),hpbl=hpbl(ims,j) &
,regime=regime(ims,j),psim=psim(ims,j) &
,psih=psih(ims,j),xland=xland(ims,j) &
,hfx=hfx(ims,j),qfx=qfx(ims,j) &
,tsk=tsk(ims,j),gz1oz0=gz1oz0(ims,j) &
,wspd=wspd(ims,j),br=br(ims,j) &
,dt=dt,dtmin=dtmin,kpbl1d=kpbl2d(ims,j) &
,svp1=svp1,svp2=svp2,svp3=svp3,svpt0=svpt0 &
,ep1=ep1,ep2=ep2,karman=karman,eomeg=eomeg &
,stbolt=stbolt &
,exch_hx=exch_h(ims,kms,j) &
,u10=u10(ims,j),v10=v10(ims,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 )
do k = kts,kte
do i = its,ite
rthblten(i,k,j) = rthblten(i,k,j)/pi3d(i,k,j)
if(present(rqiblten))rqiblten(i,k,j) = rqibl2dt(i,k)
enddo
enddo
enddo
!
end subroutine ysu
!
!-------------------------------------------------------------------
!
subroutine ysu2d(j,ux,vx,tx,qx,qcx,qix,p2d,p2di,pi2d, &
utnp,vtnp,ttnp, &
qtnp,qctnp,qitnp, &
cp,g,rovcp,rd,rovg, &
dz8w2d,z2d,xlv,rv,psfcpa, &
znt,ust,zol,hol,hpbl,psim,psih, &
xland,hfx,qfx,tsk,gz1oz0,wspd,br, &
dt,dtmin,kpbl1d, &
svp1,svp2,svp3,svpt0,ep1,ep2,karman,eomeg,stbolt, &
exch_hx, &
u10,v10, &
ids,ide, jds,jde, kds,kde, &
ims,ime, jms,jme, kms,kme, &
its,ite, jts,jte, kts,kte, &
!optional
regime )
!-------------------------------------------------------------------
implicit none
!-------------------------------------------------------------------
!
! this code is a revised vertical diffusion package ("ysupbl")
! with a nonlocal turbulent mixing in the pbl after "mrfpbl".
! the ysupbl (hong et al. 2006) is based on the study of noh
! et al.(2003) and accumulated realism of the behavior of the
! troen and mahrt (1986) concept implemented by hong and pan(1996).
! the major ingredient of the ysupbl is the inclusion of an explicit
! treatment of the entrainment processes at the entrainment layer.
! this routine uses an implicit approach for vertical flux
! divergence and does not require "miter" timesteps.
! it includes vertical diffusion in the stable atmosphere
! and moist vertical diffusion in clouds.
!
! mrfpbl:
! coded by song-you hong (ncep), implemented by jimy dudhia (ncar)
! fall 1996
!
! ysupbl:
! coded by song-you hong (yonsei university) and implemented by
! song-you hong (yonsei university) and jimy dudhia (ncar)
! summer 2002
!
! references:
!
! hong, noh, and dudhia (2006), mon. wea. rev.
! hong and pan (1996), mon. wea. rev.
! noh, chun, hong, and raasch (2003), boundary layer met.
! troen and mahrt (1986), boundary layer met.
!
!-------------------------------------------------------------------
!
integer,parameter :: ncloud = 3
real,parameter :: xkzmin = 0.01,xkzmax = 1000.,rimin = -100.
real,parameter :: rlam = 30.,prmin = 0.25,prmax = 4.
real,parameter :: brcr_ub = 0.0,brcr_sb = 0.25,cori = 1.e-4
real,parameter :: afac = 6.8,bfac = 6.8,pfac = 2.0
real,parameter :: phifac = 8.,sfcfrac = 0.1
real,parameter :: d1 = 0.02, d2 = 0.05, d3 = 0.001
real,parameter :: h1 = 0.33333335, h2 = 0.6666667
real,parameter :: ckz = 0.001,zfmin = 1.e-8,aphi5 = 5.,aphi16 = 16.
real,parameter :: tmin=1.e-2
real,parameter :: gamcrt = 3.,gamcrq = 2.e-3
real,parameter :: xka = 2.4e-5
!
integer, intent(in ) :: ids,ide, jds,jde, kds,kde, &
ims,ime, jms,jme, kms,kme, &
its,ite, jts,jte, kts,kte, j
!
real, intent(in ) :: dt,dtmin,cp,g,rovcp,rovg,rd,xlv,rv
!
real, intent(in ) :: svp1,svp2,svp3,svpt0
real, intent(in ) :: ep1,ep2,karman,eomeg,stbolt
!
real, dimension( ims:ime, kms:kme ), &
intent(in) :: dz8w2d, &
z2d
!
real, dimension( ims:ime, kms:kme ) , &
intent(in ) :: tx, &
qx, &
qcx, &
qix, &
pi2d
real, dimension( its:ite, kts:kte+1 ) , &
intent(in ) :: p2di
!
real, dimension( its:ite, kts:kte ) , &
intent(in ) :: p2d
!
real, dimension( its:ite, kts:kte ) , &
intent(inout) :: qitnp
!
real, dimension( ims:ime, kms:kme ) , &
intent(inout) :: utnp, &
vtnp, &
ttnp, &
qtnp, &
qctnp
!
real, dimension( ims:ime ) , &
intent(inout) :: hol, &
ust, &
hpbl, &
znt
real, dimension( ims:ime ) , &
intent(in ) :: xland, &
hfx, &
qfx
!
real, dimension( ims:ime ), intent(inout) :: wspd
real, dimension( ims:ime ), intent(in ) :: br
!
real, dimension( ims:ime ), intent(in ) :: psim, &
psih
real, dimension( ims:ime ), intent(in ) :: gz1oz0
!
real, dimension( ims:ime ), intent(in ) :: psfcpa
real, dimension( ims:ime ), intent(in ) :: tsk
real, dimension( ims:ime ), intent(inout) :: zol
integer, dimension( ims:ime ), intent(out ) :: kpbl1d
!
!
real, dimension( ims:ime, kms:kme ) , &
intent(in ) :: ux, &
vx
!optional
real, dimension( ims:ime ) , &
optional , &
intent(inout) :: regime
!
! local vars
!
real, dimension( its:ite, kts:kte+1 ) :: zq
!
real, dimension( its:ite, kts:kte ) :: &
thx,thvx, &
del, &
dza, &
dzq, &
za, &
tvx, &
uxs,vxs, &
thxs,qxs, &
qcxs,qixs
!
real, dimension( its:ite ) :: qixsv,rhox, &
govrth, &
thxsv, &
uxsv,vxsv, &
qxsv,qcxsv, &
qgh,tgdsa,ps
!
real, dimension( its:ite ) :: &
zl1,thermal, &
wscale,hgamt, &
hgamq,brdn, &
brup,phim, &
phih,cpm, &
dusfc,dvsfc, &
dtsfc,dqsfc, &
thgb,prpbl, &
wspd1
!
real, dimension( its:ite, kts:kte ) :: xkzm,xkzh, &
f1,f2, &
r1,r2, &
ad,au, &
cu, &
al, &
zfac
!
!jdf added exch_hx
real, dimension( ims:ime, kms:kme ) , &
intent(inout) :: exch_hx
!
real, dimension( ims:ime ) , &
intent(in ) :: u10, &
v10
real, dimension( its:ite ) :: &
brcr_sbro
!
real, dimension( its:ite, kts:kte, ncloud) :: r3,f3
!
logical, dimension( its:ite ) :: pblflg, &
sfcflg, &
stable
!
integer :: n,i,k,l,nzol,imvdif,ic
integer :: klpbl
!
integer, dimension( its:ite ) :: kpbl
!
real :: zoln,x,y,tvcon,e1,dtstep,brcr
real :: zl,tskv,dthvdz,dthvm,vconv,rzol
real :: dtthx,psix,dtg,psiq,ustm
real :: dt2,rdt,spdk2,fm,fh,hol1,gamfac,vpert,prnum
real :: xkzo,ss,ri,qmean,tmean,alph,chi,zk,rl2,dk,sri
real :: brint,dtodsd,rdz,dsdzt,dsdzq,dsdz2,ttend,qtend
real :: utend,vtend,qctend,qitend,tgc,dtodsu,govrthv
!
real, dimension( its:ite, kts:kte ) :: wscalek, &
xkzml,xkzhl, &
zfacent,entfac
real, dimension( its:ite ) :: ust3, &
wstar3,wstar, &
hgamu,hgamv, &
wm2, we, &
bfxpbl, &
hfxpbl,qfxpbl, &
ufxpbl,vfxpbl, &
delta,dthvx
real :: prnumfac,bfx0,hfx0,qfx0,delb,dux,dvx, &
dsdzu,dsdzv,wm3,dthx,dqx,wspd10,ross,tem1,dsig
!
!----------------------------------------------------------------------
!
klpbl = kte
!
!-- imvdif imvdif = 1 for moist adiabat vertical diffusion
imvdif = 1
!
!----convert ground temperature to potential temperature:
!
do i = its,ite
tgdsa(i) = tsk(i)
ps(i) = psfcpa(i)/1000. ! ps psfc cb
thgb(i) = tsk(i)*(100./ps(i))**rovcp
enddo
!
do k = kts,kte
do i = its,ite
thx(i,k) = tx(i,k)/pi2d(i,k)
enddo
enddo
!
do i = its,ite
qgh(i) = 0.
cpm(i) = cp
enddo
!
do k = kts,kte
do i = its,ite
tvcon = (1.+ep1*qx(i,k))
thvx(i,k) = thx(i,k)*tvcon
enddo
enddo
!
do i = its,ite
e1 = svp1*exp(svp2*(tgdsa(i)-svpt0)/(tgdsa(i)-svp3))
qgh(i) = ep2*e1/(ps(i)-e1)
cpm(i) = cp*(1.+0.8*qx(i,1))
enddo
!
!-----compute the height of full- and half-sigma levels above ground
! level, and the layer thicknesses.
!
do i = its,ite
zq(i,1) = 0.
rhox(i) = ps(i)*1000./(rd*tx(i,1))
enddo
!
do k = kts,kte
do i = its,ite
zq(i,k+1) = dz8w2d(i,k)+zq(i,k)
enddo
enddo
!
do k = kts,kte
do i = its,ite
za(i,k) = 0.5*(zq(i,k)+zq(i,k+1))
dzq(i,k) = zq(i,k+1)-zq(i,k)
del(i,k) = p2di(i,k)-p2di(i,k+1)
enddo
enddo
!
do i = its,ite
dza(i,1) = za(i,1)
enddo
!
do k = kts+1,kte
do i = its,ite
dza(i,k) = za(i,k)-za(i,k-1)
enddo
enddo
!
do i = its,ite
govrth(i) = g/thx(i,1)
enddo
!
!-----initialize vertical tendencies and
!
do i = its,ite
do k = kts,kte
utnp(i,k) = 0.
vtnp(i,k) = 0.
ttnp(i,k) = 0.
enddo
enddo
!
do k = kts,kte
do i = its,ite
qtnp(i,k) = 0.
enddo
enddo
!
do k = kts,kte
do i = its,ite
qctnp(i,k) = 0.
qitnp(i,k) = 0.
enddo
enddo
!
do i = its,ite
wspd1(i) = sqrt(ux(i,1)*ux(i,1)+vx(i,1)*vx(i,1))+1.e-9
enddo
!
!---- compute vertical diffusion
!
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
! compute preliminary variables
!
dtstep = dt
dt2 = 2.*dtstep
rdt = 1./dt2
!
do i = its,ite
bfxpbl(i) = 0.0
hfxpbl(i) = 0.0
qfxpbl(i) = 0.0
ufxpbl(i) = 0.0
vfxpbl(i) = 0.0
hgamu(i) = 0.0
hgamv(i) = 0.0
delta(i) = 0.0
enddo
!
do k = kts,klpbl
do i = its,ite
wscalek(i,k) = 0.0
enddo
enddo
!
do k = kts,klpbl
do i = its,ite
zfac(i,k) = 0.0
enddo
enddo
!
do i = its,ite
hgamt(i) = 0.
hgamq(i) = 0.
wscale(i) = 0.
kpbl(i) = 1
hpbl(i) = zq(i,1)
zl1(i) = za(i,1)
thermal(i)= thvx(i,1)
pblflg(i) = .true.
sfcflg(i) = .true.
if(br(i).gt.0.0) sfcflg(i) = .false.
enddo
!
! compute the first guess of pbl height
!
do i = its,ite
stable(i) = .false.
brup(i) = br(i)
enddo
!
brcr = brcr_ub
do k = 2,klpbl
do i = its,ite
if(.not.stable(i))then
brdn(i) = brup(i)
spdk2 = max(ux(i,k)**2+vx(i,k)**2,1.)
brup(i) = (thvx(i,k)-thermal(i))*(g*za(i,k)/thvx(i,1))/spdk2
kpbl(i) = k
stable(i) = brup(i).gt.brcr
endif
enddo
enddo
!
do i = its,ite
k = kpbl(i)
if(brdn(i).ge.brcr)then
brint = 0.
elseif(brup(i).le.brcr)then
brint = 1.
else
brint = (brcr-brdn(i))/(brup(i)-brdn(i))
endif
hpbl(i) = za(i,k-1)+brint*(za(i,k)-za(i,k-1))
if(hpbl(i).lt.zq(i,2)) kpbl(i) = 1
if(kpbl(i).le.1) pblflg(i) = .false.
enddo
!
do i = its,ite
fm = gz1oz0(i)-psim(i)
fh = gz1oz0(i)-psih(i)
hol(i) = max(br(i)*fm*fm/fh,rimin)
if(sfcflg(i))then
hol(i) = min(hol(i),-zfmin)
else
hol(i) = max(hol(i),zfmin)
endif
hol1 = hol(i)*hpbl(i)/zl1(i)*sfcfrac
hol(i) = -hol(i)*hpbl(i)/zl1(i)
if(sfcflg(i))then
phim(i) = (1.-aphi16*hol1)**(-1./4.)
phih(i) = (1.-aphi16*hol1)**(-1./2.)
bfx0 = max(hfx(i)/rhox(i)/cpm(i)+ep1*thx(i,1)*qfx(i)/rhox(i),0.)
hfx0 = max(hfx(i)/rhox(i)/cpm(i),0.)
qfx0 = max(ep1*thx(i,1)*qfx(i)/rhox(i),0.)
wstar3(i) = (govrth(i)*bfx0*hpbl(i))
wstar(i) = (wstar3(i))**h1
else
phim(i) = (1.+aphi5*hol1)
phih(i) = phim(i)
wstar(i) = 0.
wstar3(i) = 0.
endif
ust3(i) = ust(i)**3.
wscale(i) = (ust3(i)+phifac*karman*wstar3(i)*0.5)**h1
wscale(i) = min(wscale(i),ust(i)*aphi16)
wscale(i) = max(wscale(i),ust(i)/aphi5)
enddo
!
! compute the surface variables for pbl height estimation
! under unstable conditions
!
do i = its,ite
if(sfcflg(i))then
gamfac = bfac/rhox(i)/wscale(i)
hgamt(i) = min(gamfac*hfx(i)/cpm(i),gamcrt)
hgamq(i) = min(gamfac*qfx(i),gamcrq)
vpert = (hgamt(i)+ep1*thx(i,1)*hgamq(i))/bfac*afac
thermal(i) = thermal(i)+max(vpert,0.)
hgamt(i) = max(hgamt(i),0.0)
hgamq(i) = max(hgamq(i),0.0)
brint = -15.9*ust(i)*ust(i)/wspd(i)*wstar3(i)/(wscale(i)**4.)
hgamu(i) = brint*ux(i,1)
hgamv(i) = brint*vx(i,1)
else
pblflg(i) = .false.
endif
enddo
!
! enhance the pbl height by considering the thermal
!
do i = its,ite
if(pblflg(i))then
kpbl(i) = 1
hpbl(i) = zq(i,1)
endif
enddo
!
do i = its,ite
if(pblflg(i))then
stable(i) = .false.
brup(i) = br(i)
endif
enddo
!
brcr = brcr_ub
do k = 2,klpbl
do i = its,ite
if(.not.stable(i).and.pblflg(i))then
brdn(i) = brup(i)
spdk2 = max(ux(i,k)**2+vx(i,k)**2,1.)
brup(i) = (thvx(i,k)-thermal(i))*(g*za(i,k)/thvx(i,1))/spdk2
kpbl(i) = k
stable(i) = brup(i).gt.brcr
endif
enddo
enddo
!
do i = its,ite
if(pblflg(i)) then
k = kpbl(i)
if(brdn(i).ge.brcr)then
brint = 0.
elseif(brup(i).le.brcr)then
brint = 1.
else
brint = (brcr-brdn(i))/(brup(i)-brdn(i))
endif
hpbl(i) = za(i,k-1)+brint*(za(i,k)-za(i,k-1))
if(hpbl(i).lt.zq(i,2)) kpbl(i) = 1
if(kpbl(i).le.1) pblflg(i) = .false.
endif
enddo
!
! stable boundary layer
!
do i = its,ite
if((.not.sfcflg(i)).and.hpbl(i).lt.zq(i,2)) then
brup(i) = br(i)
stable(i) = .false.
else
stable(i) = .true.
endif
enddo
!
do i = its,ite
if((.not.stable(i)).and.((xland(i)-1.5).ge.0))then
wspd10 = u10(i)*u10(i) + v10(i)*v10(i)
wspd10 = sqrt(wspd10)
ross = wspd10 / (cori*znt(i))
brcr_sbro(i) = min(0.16*(1.e-7*ross)**(-0.18),.3)
endif
enddo
!
do k = 2,klpbl
do i = its,ite
if((xland(i)-1.5).ge.0)then
brcr = brcr_sbro(i)
else
brcr = brcr_sb
endif
if(.not.stable(i))then
brdn(i) = brup(i)
spdk2 = max(ux(i,k)**2+vx(i,k)**2,1.)
brup(i) = (thvx(i,k)-thermal(i))*(g*za(i,k)/thvx(i,1))/spdk2
kpbl(i) = k
stable(i) = brup(i).gt.brcr
endif
enddo
enddo
!
do i = its,ite
if((.not.sfcflg(i)).and.hpbl(i).lt.zq(i,2)) then
if((xland(i)-1.5).ge.0)then
brcr = brcr_sbro(i)
else
brcr = brcr_sb
endif
k = kpbl(i)
if(brdn(i).ge.brcr)then
brint = 0.
elseif(brup(i).le.brcr)then
brint = 1.
else
brint = (brcr-brdn(i))/(brup(i)-brdn(i))
endif
hpbl(i) = za(i,k-1)+brint*(za(i,k)-za(i,k-1))
if(hpbl(i).lt.zq(i,2)) kpbl(i) = 1
if(kpbl(i).le.1) pblflg(i) = .false.
endif
enddo
!
! estimate the entrainment parameters
!
do i = its,ite
if(pblflg(i)) then
k = kpbl(i) - 1
prpbl(i) = 1.0
wm3 = wstar3(i) + 5. * ust3(i)
wm2(i) = wm3**h2
bfxpbl(i) = -0.15*thvx(i,1)/g*wm3/hpbl(i)
dthvx(i) = max(thvx(i,k+1)-thvx(i,k),tmin)
dthx = max(thx(i,k+1)-thx(i,k),tmin)
dqx = min(qx(i,k+1)-qx(i,k),0.0)
we(i) = max(bfxpbl(i)/dthvx(i),-sqrt(wm2(i)))
hfxpbl(i) = we(i)*dthx
qfxpbl(i) = we(i)*dqx
!
dux = ux(i,k+1)-ux(i,k)
dvx = vx(i,k+1)-vx(i,k)
if(dux.gt.tmin) then
ufxpbl(i) = max(prpbl(i)*we(i)*dux,-ust(i)*ust(i))
elseif(dux.lt.-tmin) then
ufxpbl(i) = min(prpbl(i)*we(i)*dux,ust(i)*ust(i))
else
ufxpbl(i) = 0.0
endif
if(dvx.gt.tmin) then
vfxpbl(i) = max(prpbl(i)*we(i)*dvx,-ust(i)*ust(i))
elseif(dvx.lt.-tmin) then
vfxpbl(i) = min(prpbl(i)*we(i)*dvx,ust(i)*ust(i))
else
vfxpbl(i) = 0.0
endif
delb = govrth(i)*d3*hpbl(i)
delta(i) = min(d1*hpbl(i) + d2*wm2(i)/delb,100.)
endif
enddo
!
do k = kts,klpbl
do i = its,ite
if(pblflg(i).and.k.ge.kpbl(i))then
entfac(i,k) = ((zq(i,k+1)-hpbl(i))/delta(i))**2.
else
entfac(i,k) = 1.e30
endif
enddo
enddo
!
! compute diffusion coefficients below pbl
!
do k = kts,klpbl
do i = its,ite
if(k.lt.kpbl(i)) then
zfac(i,k) = min(max((1.-(zq(i,k+1)-zl1(i))/(hpbl(i)-zl1(i))),zfmin),1.)
xkzo = ckz*dza(i,k+1)
zfacent(i,k) = (1.-zfac(i,k))**3.
prnumfac = -3.*(max(zq(i,k+1)-sfcfrac*hpbl(i),0.))**2./hpbl(i)**2.
prnum = (phih(i)/phim(i)+bfac*karman*sfcfrac)
prnum = 1. + (prnum-1.)*exp(prnumfac)
prnum = min(prnum,prmax)
prnum = max(prnum,prmin)
wscalek(i,k) = (ust3(i)+phifac*karman*wstar3(i)*(1.-zfac(i,k)))**h1
xkzm(i,k) = xkzo+wscalek(i,k)*karman*zq(i,k+1)*zfac(i,k)**pfac
xkzh(i,k) = xkzm(i,k)/prnum
xkzm(i,k) = min(xkzm(i,k),xkzmax)
xkzm(i,k) = max(xkzm(i,k),xkzmin)
xkzh(i,k) = min(xkzh(i,k),xkzmax)
xkzh(i,k) = max(xkzh(i,k),xkzmin)
endif
enddo
enddo
!
! compute diffusion coefficients over pbl (free atmosphere)
!
do k = kts,kte-1
do i = its,ite
xkzo = ckz*dza(i,k+1)
if(k.ge.kpbl(i)) then
ss = ((ux(i,k+1)-ux(i,k))*(ux(i,k+1)-ux(i,k)) &
+(vx(i,k+1)-vx(i,k))*(vx(i,k+1)-vx(i,k))) &
/(dza(i,k+1)*dza(i,k+1))+1.e-9
govrthv = g/(0.5*(thvx(i,k+1)+thvx(i,k)))
ri = govrthv*(thvx(i,k+1)-thvx(i,k))/(ss*dza(i,k+1))
if(imvdif.eq.1)then
if((qcx(i,k)+qix(i,k)).gt.0.01e-3.and.(qcx(i,k+1)+ &
qix(i,k+1)).gt.0.01e-3)then
! in cloud
qmean = 0.5*(qx(i,k)+qx(i,k+1))
tmean = 0.5*(tx(i,k)+tx(i,k+1))
alph = xlv*qmean/rd/tmean
chi = xlv*xlv*qmean/cp/rv/tmean/tmean
ri = (1.+alph)*(ri-g*g/ss/tmean/cp*((chi-alph)/(1.+chi)))
endif
endif
zk = karman*zq(i,k+1)
rl2 = (zk*rlam/(rlam+zk))**2
dk = rl2*sqrt(ss)
if(ri.lt.0.)then
! unstable regime
sri = sqrt(-ri)
xkzm(i,k) = xkzo+dk*(1+8.*(-ri)/(1+1.746*sri))
xkzh(i,k) = xkzo+dk*(1+8.*(-ri)/(1+1.286*sri))
else
! stable regime
xkzh(i,k) = xkzo+dk/(1+5.*ri)**2
prnum = 1.0+2.1*ri
prnum = min(prnum,prmax)
xkzm(i,k) = (xkzh(i,k)-xkzo)*prnum+xkzo
endif
!
xkzm(i,k) = min(xkzm(i,k),xkzmax)
xkzm(i,k) = max(xkzm(i,k),xkzmin)
xkzh(i,k) = min(xkzh(i,k),xkzmax)
xkzh(i,k) = max(xkzh(i,k),xkzmin)
xkzml(i,k) = xkzm(i,k)
xkzhl(i,k) = xkzh(i,k)
endif
enddo
enddo
!
! compute tridiagonal matrix elements for heat and moisture, and clouds
!
do k = kts,kte
do i = its,ite
au(i,k) = 0.
al(i,k) = 0.
ad(i,k) = 0.
f1(i,k) = 0.
enddo
enddo
!
do ic = 1,ncloud
do i = its,ite
do k = kts,kte
f3(i,k,ic) = 0.
enddo
enddo
enddo
!
do i = its,ite
ad(i,1) = 1.
f1(i,1) = thx(i,1)-300.+hfx(i)/(rhox(i)*cpm(i))/zq(i,2)*dt2
f3(i,1,1) = qx(i,1)+qfx(i)/(rhox(i))/zq(i,2)*dt2
enddo
!
if(ncloud.ge.2) then
do ic = 2,ncloud
do i = its,ite
if(ic.eq.2) then
f3(i,1,ic) = qcx(i,1)
elseif(ic.eq.3) then
f3(i,1,ic) = qix(i,1)
endif
enddo
enddo
endif
!
do k = kts,kte-1
do i = its,ite
dtodsd = dt2/del(i,k)
dtodsu = dt2/del(i,k+1)
dsig = p2d(i,k)-p2d(i,k+1)
rdz = 1./dza(i,k+1)
tem1 = dsig*xkzh(i,k)*rdz
if(pblflg(i).and.k.lt.kpbl(i)) then
dsdzt = tem1*(-hgamt(i)/hpbl(i)-hfxpbl(i)*zfacent(i,k)/xkzh(i,k))
dsdzq = tem1*(-qfxpbl(i)*zfacent(i,k)/xkzh(i,k))
f1(i,k) = f1(i,k)+dtodsd*dsdzt
f1(i,k+1) = thx(i,k+1)-300.-dtodsu*dsdzt
f3(i,k,1) = f3(i,k,1)+dtodsd*dsdzq
f3(i,k+1,1) = qx(i,k+1)-dtodsu*dsdzq
elseif(pblflg(i).and.k.ge.kpbl(i).and.entfac(i,k).lt.4.6) then
xkzh(i,k) = -we(i)*dza(i,kpbl(i))*exp(-entfac(i,k))
xkzh(i,k) = sqrt(xkzh(i,k)*xkzhl(i,k))
xkzh(i,k) = min(xkzh(i,k),xkzmax)
xkzh(i,k) = max(xkzh(i,k),xkzmin)
f1(i,k+1) = thx(i,k+1)-300.
f3(i,k+1,1) = qx(i,k+1)
else
f1(i,k+1) = thx(i,k+1)-300.
f3(i,k+1,1) = qx(i,k+1)
endif
dsdz2 = tem1*rdz
au(i,k) = -dtodsd*dsdz2
al(i,k) = -dtodsu*dsdz2
ad(i,k) = ad(i,k)-au(i,k)
ad(i,k+1) = 1.-al(i,k)
exch_hx(i,k) = xkzh(i,k)
enddo
enddo