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mxkrt.F90
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#if defined(ROW_LAND)
#define SEA_P .true.
#define SEA_U .true.
#define SEA_V .true.
#elif defined(ROW_ALLSEA)
#define SEA_P allip(j).or.ip(i,j).ne.0
#define SEA_U alliu(j).or.iu(i,j).ne.0
#define SEA_V alliv(j).or.iv(i,j).ne.0
#else
#define SEA_P ip(i,j).ne.0
#define SEA_U iu(i,j).ne.0
#define SEA_V iv(i,j).ne.0
#endif
subroutine mxkrta(m,n)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
implicit none
!
integer m,n
!
! --- hycom version 1.0
! --- original slab mixed layer
!
#if defined(RELO)
real, save, allocatable, dimension(:,:) :: &
#else
real, save, dimension(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy) :: &
#endif
depnew
!
integer i,j
!diag integer k
!diag real totem,tosal,tndcyt,tndcys
!
! --- store 'old' t/s column integral in totem/tosal (diagnostic use only)
!
!diag totem=0.
!diag tosal=0.
!diag do k=1,kk
!diag totem=totem+temp(itest,jtest,k,n)*dp(itest,jtest,k,n)
!diag tosal=tosal+saln(itest,jtest,k,n)*dp(itest,jtest,k,n)
!diag end do
!
103 format (i9,2i6,a/(32x,i3,2f8.2,f8.2,2f8.1))
!diag write (lp,103) nstep,itest+i0,jtest+j0, &
!diag ' entering mxkrt: temp saln dens thkns dpth', &
!diag (k,temp(itest,jtest,k,n),saln(itest,jtest,k,n), &
!diag th3d(itest,jtest,k,n)+thbase,dp(itest,jtest,k,n)*qonem, &
!diag p(itest,jtest,k+1)*qonem,k=1,kk)
#if defined(RELO)
!
if (.not.allocated(depnew)) then
allocate( &
depnew(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy) )
call mem_stat_add( (idm+2*nbdy)*(jdm+2*nbdy) )
depnew = r_init
endif
#endif
! --- ---------------
! --- new mixed layer
! --- ---------------
!
!$OMP PARALLEL DO PRIVATE(j) &
!$OMP SHARED(m,n) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
call mxkrtaaj(m,n, j, depnew)
enddo
!$OMP END PARALLEL DO
!
!diag write (lp,103) nstep,itest,jtest, &
!diag ' exiting mxkrta: temp saln dens thkns dpth', &
!diag (k,temp(itest,jtest,k,n),saln(itest,jtest,k,n), &
!diag th3d(itest,jtest,k,n)+thbase,dp(itest,jtest,k,n)*qonem, &
!diag p(itest,jtest,k+1)*qonem,k=1,kk)
!
! --- compare 'old' with 'new' t/s column integral (diagnostic use only)
!
!diag tndcyt=-totem
!diag tndcys=-tosal
!diag do k=1,kk
!diag tndcyt=tndcyt+temp(itest,jtest,k,n)*dp(itest,jtest,k,n)
!diag tndcys=tndcys+saln(itest,jtest,k,n)*dp(itest,jtest,k,n)
!diag end do
!diag write (lp,'(i9,2i6,3x,a,1p,3e12.4/22x,a,3e12.4)') &
!diag nstep,itest+i0,jtest+j0, &
!diag 'total saln,srf.flux,tndcy:',tosal/g,salflx(itest, &
!diag jtest)*delt1,tndcys/g,'total temp,srf.flux,tndcy:',totem/g, &
!diag surflx(itest,jtest)*delt1,tndcyt*spcifh/g
!
! --- ---------------
! --- momentum mixing
! --- ---------------
!
!$OMP PARALLEL DO PRIVATE(j) &
!$OMP SHARED(m,n) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
call mxkrtabj(m,n, j, depnew)
enddo
!$OMP END PARALLEL DO
!
! --- fill mixed layer arrays
!
!$OMP PARALLEL DO PRIVATE(j,i) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
do i=1,ii
if (SEA_P) then
dpbl( i,j)=dpmixl(i,j, n)
tmix( i,j)=temp(i,j,1,n)
smix( i,j)=saln(i,j,1,n)
thmix(i,j)=th3d(i,j,1,n)
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
!
return
end
subroutine mxkrtaaj(m,n, j, depnew)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
implicit none
!
integer m,n,j
real, dimension (1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy) :: &
depnew
!
! --- hycom version 1.0
! --- single row, part A.
!
integer i,k,ka,k0,k1,ktr
!
real tdp(idm),sdp(idm),dtemp(idm),dsaln(idm)
real dpth,ekminv,obuinv,ex,alf1,alf2,cp1,cp3,ape,cc4,spe, &
thknss,ustar3,buoyfl,dsgdt,tmn,smn,tup,sup, &
dtemp2,q,swfold,thet,alfadt,betads, &
swfrac,sflux1,tmin,tmax,smin,smax,trmin,trmax, &
thkold,thknew,thk1ta,t1,t2,s1,s2,tr1,tr2,dp1,dp2,dtrmax, &
chl
!
real ea1, ea2, em1, em2, em3, em4, em5
data ea1, ea2, em1, em2, em3, em4, em5 &
/0.60,0.30,0.45,2.60,1.90,2.30,0.60/ ! Gaspar coefficients
!
# include "stmt_fns.h"
!
! --- ---------------------
! --- set the vertical grid
! --- ---------------------
!
! --- store in -p- a set of interfaces that depict stratification the way a
! --- "pure" isopycnic model would. -dpmixl- is physical mixed layer depth.
! --- store variables averaged over -dpmixl- in layer 1.
!
do i=1,ii
if (SEA_P) then
!
klist(i,j)=-1
!
! --- start building up integral of t and s over mixed layer depth
tdp(i)=temp(i,j,1,n)*dp(i,j,1,n)
sdp(i)=saln(i,j,1,n)*dp(i,j,1,n)
util1(i,j)=dp(i,j,1,n)
util3(i,j)=th3d(i,j,1,n)
p(i,j,2)=dp(i,j,1,n)
pu(i,j,2)=dp(i,j,1,m)
!
do k=2,kk
p(i,j,k+1)=p(i,j,k)+dp(i,j,k,n)
pu(i,j,k+1)=pu(i,j,k)+dp(i,j,k,m)
!
! --- if mixed layer base is very close to interface, move it there
if (abs(p(i,j,k+1)-dpmixl(i,j,n)).lt. &
max(onecm,.001*dp(i,j,k,n)) ) then
dpmixl(i,j,n)=p(i,j,k+1)
endif
!
! --- watch for density decrease with depth (convective adjustment of
! --- the mixed layer) - convection occurs for both time steps to
! --- prevent mid-time and new mixed layer thicknesses from diverging
if (klist(i,j).le.-1 .and. &
p(i,j,k+1).gt.dpmixl(i,j,n) .and. &
p(i,j,k ).le.dpmixl(i,j,n) ) then
if (locsig) then
tup=tdp(i)/util1(i,j)
sup=sdp(i)/util1(i,j)
alfadt=0.5* &
(dsiglocdt(tup,sup,util1(i,j))+ &
dsiglocdt(temp(i,j,k,n),saln(i,j,k,n),util1(i,j)))* &
(tup-temp(i,j,k,n))
betads=0.5* &
(dsiglocds(tup,sup,util1(i,j))+ &
dsiglocds(temp(i,j,k,n),saln(i,j,k,n),util1(i,j)))* &
(sup-saln(i,j,k,n))
if(alfadt+betads.gt.0.0) then
dpmixl(i,j,n)=p (i,j,k+1)
klist(i,j)=-2
end if
else
th3d(i,j,1,n)=sig(tdp(i)/util1(i,j),sdp(i)/util1(i,j)) &
-thbase
if(th3d(i,j,1,n).gt.th3d(i,j,k,n)) then
dpmixl(i,j,n)=p (i,j,k+1)
klist(i,j)=-2
endif
end if
end if
!
if (p(i,j,k+1).le.dpmixl(i,j,n)) then
tdp(i)=tdp(i)+dp(i,j,k,n)*temp(i,j,k,n)
sdp(i)=sdp(i)+dp(i,j,k,n)*saln(i,j,k,n)
util1(i,j)=util1(i,j)+dp(i,j,k,n)
!
else if (p(i,j,k).lt.dpmixl(i,j,n)) then
klist(i,j)=k
end if
enddo !k
!
temp(i,j,1,n)=tdp(i)/util1(i,j)
saln(i,j,1,n)=sdp(i)/util1(i,j)
th3d(i,j,1,n)=sig(temp(i,j,1,n),saln(i,j,1,n))-thbase
! if (klist(i,j).eq.-2) then
! util3(i,j)=th3d(i,j,1,n)
! do k1=2,kk
! if (p(i,j,k1+1).le.dpmixl(i,j,n)) then
! th3d(i,j,k1,n)=th3d(i,j,1,n)
! endif
! enddo !k1
! end if
!
! --- unmix t, s, and tracer
!
! --- the first guesses for upper sublayer values are the old-time mixed
! --- layer values saved in hybgen plus all changes that have occurred
! --- since then
!
! --- prevent spurious maxima or minima from being generated in the lower
! --- sublayer, then adjust upper sublayer values if necessary to conserve
! --- vertical averages
!
if(klist(i,j).ge.2) then
k=klist(i,j)
k0=min(k+1,kk)
dp1=dpmixl(i,j,n)-p(i,j,k)
dp2=p(i,j,k+1)-dpmixl(i,j,n)
q=-dp1/dp2
if(k.eq.nmlb(i,j,n)) then
t1=t1sav(i,j,n)+temp(i,j,k,n)-tmlb(i,j,n)
s1=s1sav(i,j,n)+saln(i,j,k,n)-smlb(i,j,n)
else
t1=temp(i,j,k-1,n)
s1=saln(i,j,k-1,n)
nmlb(i,j,n)=k
end if
tmin=min(t1,temp(i,j,k,n),temp(i,j,k0,n))
tmax=max(t1,temp(i,j,k,n),temp(i,j,k0,n))
smin=min(s1,saln(i,j,k,n),saln(i,j,k0,n))
smax=max(s1,saln(i,j,k,n),saln(i,j,k0,n))
t2=temp(i,j,k,n)+q*(t1-temp(i,j,k,n))
s2=saln(i,j,k,n)+q*(s1-saln(i,j,k,n))
temp(i,j,k,n)=min(tmax,max(tmin,t2))
saln(i,j,k,n)=min(smax,max(smin,s2))
util4(i,j)=th3d(i,j,k,n)
th3d(i,j,k,n)=sig(temp(i,j,k,n),saln(i,j,k,n))-thbase
t1=t1+(t2-temp(i,j,k,n))*dp2/dp1
s1=s1+(s2-saln(i,j,k,n))*dp2/dp1
tdp(i)=tdp(i)+t1*dp1
sdp(i)=sdp(i)+s1*dp1
temp(i,j,1,n)=tdp(i)/dpmixl(i,j,n)
saln(i,j,1,n)=sdp(i)/dpmixl(i,j,n)
th3d(i,j,1,n)=sig(temp(i,j,1,n),saln(i,j,1,n))-thbase
do ktr= 1,ntracr
tr1=1.0 ! THIS MAY BE WRONG FOR MULTIPLE TRACERS
trmin=min(tr1,tracer(i,j,k,n,ktr),tracer(i,j,k0,n,ktr))
trmax=max(tr1,tracer(i,j,k,n,ktr),tracer(i,j,k0,n,ktr))
tr2=tracer(i,j,k,n,ktr)+q*(tr1-tracer(i,j,k,n,ktr))
tracer(i,j,k,n,ktr)=min(trmax,max(trmin,tr2))
enddo
end if
!
! --- set the new grid
!
do k=1,kk
p(i,j,k+1)=max(dpmixl(i,j,n),p(i,j,k+1))
enddo !k
!
endif !ip
enddo !i
!
! --- ----------------------------------------
! --- slab mixed layer entrainment/detrainment
! --- ----------------------------------------
!
do i=1,ii
if (SEA_P) then
!
! --- determine turb.kin.energy generation due to wind stirring
! --- ustar computed in subr. -thermf-
! --- buoyancy flux (m**2/sec**3), all fluxes into the ocean
! --- note: surface density increases (column is destabilized) if buoyfl < 0
thkold=dpmixl(i,j,n)
ustar3=ustar(i,j)**3
tmn=.5*(temp(i,j,1,m)+temp(i,j,1,n))
smn=.5*(saln(i,j,1,m)+saln(i,j,1,n))
dsgdt=dsigdt(tmn,smn)
buoyfl=-g*svref*(dsigds(tmn,smn)* &
(-wtrflx(i,j)*saln(i,j,1,n)+salflx(i,j))*svref+ &
dsgdt *surflx(i,j) *svref/spcifh)
!
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
!
! --- option 1 : k r a u s - t u r n e r mixed-layer t.k.e. closure
!
!cc em=0.8*exp(-p(i,j,2)/(50.*onem)) ! hadley centre choice (orig.: 1.25)
!cc en=0.15 ! hadley centre choice (orig.: 0.4)
!cc thermg=-0.5*((en+1.)*buoyfl+(en-1.)*abs(buoyfl))
!cc turgen(i,j)=delt1*(2.*em*g*ustar3*rhoref+thkold*thermg)*rhoref**2
!
! --- find monin-obukhov length in case of receding mixed layer (turgen < 0).
! --- the monin-obukhov length is found by stipulating turgen = 0.
!
!cc if (turgen(i,j).lt.0.) then
!cc depnew(i,j)=-2.*em*g*ustar3/min(-epsil,svref*thermg)
!cc else
!cc depnew(i,j)=thkold
!cc end if
!
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
!
! --- option 2 : g a s p a r mixed-layer t.k.e. closure
!
dpth=thkold*qonem
ekminv=1./hekman(i,j)
obuinv=buoyfl/max(epsil,ustar3)
ex=exp(min(50.,dpth*obuinv))
alf1=ea1+ea2*max(1.,2.5*dpth*ekminv)*ex
alf2=ea1+ea2*ex
cp1=((1.-em5)*(alf1/alf2)+.5*em4)*athird
cp3=max(0.,(em4*(em2+em3)-(alf1/alf2)*(em2+em3-em3*em5))*athird)
ape=cp3*ustar3-cp1*dpth*buoyfl
!
if(ape.lt.0.) then ! detrainment
turgen(i,j)=(g*delt1*rhoref**3)*ape
depnew(i,j)=min(thkold,g*cp3/(svref*cp1*max(epsil,obuinv)))
!
else ! entrainment
cc4=2.*em4/(em1*em1) * alf1*alf1
spe=(em2+em3)*ustar3-0.5*dpth*buoyfl
turgen(i,j)=(g*delt1*rhoref**3)*(sqrt((.5*ape-cp1*spe)**2 &
+2.*cc4*ape*spe)-(.5*ape+cp1*spe))/(cc4-cp1)
depnew(i,j)=thkold
end if
!
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
!
! --- util1,util2 are used to evaluate pot.energy changes during entrainment
util1(i,j)=util3(i,j)*dp(i,j,1,n)
util2(i,j)=util3(i,j)*dp(i,j,1,n)**2
pu(i,j,2)=dp(i,j,1,n)
!
! --- find thknew in case of mx.layer deepening (turgen>0). store in -depnew-.
! --- entrain as many layers as needed to deplete -turgen-.
!
do k=2,kk
ka=k-1
pu(i,j,k+1)=pu(i,j,k)+dp(i,j,k,n)
if (k.eq.2) then
thstar(i,j,ka,1)=util3(i,j)
endif
if (locsig) then
alfadt=0.5* &
(dsiglocdt(temp(i,j,ka,n),saln(i,j,ka,n),pu(i,j,k))+ &
dsiglocdt(temp(i,j,k ,n),saln(i,j,k ,n),pu(i,j,k)))* &
(temp(i,j,ka,n)-temp(i,j,k,n))
betads=0.5* &
(dsiglocds(temp(i,j,ka,n),saln(i,j,ka,n),pu(i,j,k))+ &
dsiglocds(temp(i,j,k ,n),saln(i,j,k ,n),pu(i,j,k)))* &
(saln(i,j,ka,n)-saln(i,j,k,n))
thstar(i,j,k,1)=thstar(i,j,ka,1)-alfadt-betads
thet=thstar(i,j,k,1)
else
if (k.ne.klist(i,j)) then
thet=th3d(i,j,k,n)
else
thet=util4(i,j)
endif
endif
thknew=max(dpmixl(i,j,n),min(pu(i,j,k+1), &
(2.0*turgen(i,j)+thet*pu(i,j,k)**2-util2(i,j))/ &
max(epsil,thet*pu(i,j,k) -util1(i,j))))
! --- stop iterating for 'thknew' as soon as thknew < k-th interface pressure
if (thknew.lt.pu(i,j,k)) thknew=depnew(i,j)
! --- substitute 'thknew' for monin-obukhov length if mixed layer is deepening
if (turgen(i,j).ge.0.) then
depnew(i,j)=thknew
endif
!
util1(i,j)=util1(i,j)+thet*(pu(i,j,k+1) -pu(i,j,k) )
util2(i,j)=util2(i,j)+thet*(pu(i,j,k+1)**2-pu(i,j,k)**2)
enddo !k
endif !ip
enddo !i
!
dtrmax = (onem*dtrate/86400.0) * delt1
do i=1,ii
if (SEA_P) then
!
!diag if (i.eq.itest.and.j.eq.jtest) then
!diag if (turgen(i,j).lt.0.) then
!diag write (lp,'(i9,2i6,a,1p,2e13.5)') nstep,i+i0,j+j0, &
!diag ' m-o length (m), turgen:',depnew(i,j)*qonem,turgen(i,j)
!diag else
!diag write (lp,'(i9,2i6,a,1p,2e13.5)') nstep,i+i0,j+j0, &
!diag ' new depth (m), turgen:',depnew(i,j)*qonem,turgen(i,j)
!diag endif
!diag endif
!
! --- don't allow mixed layer to get too deep or too shallow. mixed layer
! --- detrainment rate limited to dtrate m/day
depnew(i,j)=min(p(i,j,kk+1)-onem, &
max(thkmin*onem,pu(i,j,3),dp(i,j,1,n)+onemm, &
depnew(i,j),dpmixl(i,j,n)-dtrmax))
!
do k=2,kk
thknew=depnew(i,j)
! --- integrate t/s over depth range slated for entrainment into mixed layer
tdp(i)=tdp(i)+temp(i,j,k,n)*(min(thknew,p(i,j,k+1)) &
-min(thknew,p(i,j,k )))
sdp(i)=sdp(i)+saln(i,j,k,n)*(min(thknew,p(i,j,k+1)) &
-min(thknew,p(i,j,k )))
enddo !k
!
thkold=p(i,j,2)
thknew=depnew(i,j)
thk1ta=thknew*oneta(i,j,n)
thknss=max(thknew,thkold)
!
!diag if (i.eq.itest.and.j.eq.jtest) write (lp,'(i9,2i6,a,2f10.4)') &
!diag nstep,i+i0,j+j0, &
!diag ' old/new mixed layer depth:',thkold*qonem,thknew*qonem
!
! --- distribute thermohaline forcing over new mixed layer depth
! --- flux positive into ocean
if(pensol) then
! --- penetrating solar radiation
if (jerlv0.le.0) then !KPAR or CHL
chl = akpar(i,j,lk0)*wk0+akpar(i,j,lk1)*wk1 &
+akpar(i,j,lk2)*wk2+akpar(i,j,lk3)*wk3
endif
call swfrml_ij(chl,thknew,p(i,j,kk+1),qonem*oneta(i,j,n), &
jerlov(i,j),swfrac)
sflux1=surflx(i,j)-sswflx(i,j)
dtemp(i)=(sflux1+(1.-swfrac)*sswflx(i,j))* &
delt1*g/(spcifh*thk1ta)
if (epmass.eq.1) then !only actual salt flux
dsaln(i)= salflx(i,j)* &
delt1*g/thk1ta
elseif (epmass.eq.2) then !river only is mass flux
dsaln(i)=(salflx(i,j)- &
(wtrflx(i,j)-rivflx(i,j))*saln(i,j,1,n))* &
delt1*g/thk1ta
else !water flux treated as a virtual salt flux
dsaln(i)=(salflx(i,j)-wtrflx(i,j)*saln(i,j,1,n))* &
delt1*g/thk1ta
endif
!diag if (i.eq.itest.and.j.eq.jtest) then
!diag write(lp,104) nstep,i+i0,j+j0,k,0.,1.-swfrac,dtemp(i),dsaln(i)
!diag endif
104 format(i9,2i6,i4,'absorbup,dn,dtemp,dsaln ',2f6.3,2f10.6)
!
else
!
dtemp(i)=surflx(i,j)* &
delt1*g/(spcifh*thk1ta)
if (epmass.eq.1) then !only actual salt flux
dsaln(i)= salflx(i,j)* &
delt1*g/thk1ta
elseif (epmass.eq.2) then !river only is mass flux
dsaln(i)=(salflx(i,j)- &
(wtrflx(i,j)-rivflx(i,j))*saln(i,j,1,n))* &
delt1*g/thk1ta
else !water flux treated as a virtual salt flux
dsaln(i)=(salflx(i,j)-wtrflx(i,j)*saln(i,j,1,n))* &
delt1*g/thk1ta
endif
!
end if !pensol:else
!
! --- calculate average temp, saln over max(old,new) mixed layer depth
temp(i,j,1,n)=tdp(i)/thknss
saln(i,j,1,n)=sdp(i)/thknss
p(i,j,2)=dp(i,j,1,n)
endif !ip
enddo !i
!
! --- homogenize water mass properties down to max(old,new) mixed layer depth
! --- Asselin time smoothing of mixed layer depth
!
do i=1,ii
if (SEA_P) then
thknss=max(depnew(i,j),dpmixl(i,j,n))
dpmixl(i,j,n)=depnew(i,j)
depnew(i,j)=thknss
dpmixl(i,j,m)=(1.0- ra2fac)* dpmixl(i,j,m)+ &
0.5*ra2fac *(dpmold(i,j) + &
dpmixl(i,j,n) )
!
do k=2,kk
p(i,j,k+1)=p(i,j,k)+dp(i,j,k,n)
q=max(0.,min(1.,(depnew(i,j)-p(i,j,k))/(dp(i,j,k,n)+epsil)))
temp(i,j,k,n)=temp(i,j,k,n)+q*(temp(i,j,1,n)-temp(i,j,k,n))
saln(i,j,k,n)=saln(i,j,k,n)+q*(saln(i,j,1,n)-saln(i,j,k,n))
do ktr= 1,ntracr
tracer(i,j,k,n,ktr)=tracer(i,j,k,n,ktr) &
+q*(tracer(i,j,1,n,ktr)-tracer(i,j,k,n,ktr))
enddo
enddo !k
endif !ip
enddo !i
!
! --- add in surface thermohaline forcing over the new mixed layer depth
! --- add penetrating solar radiation
do i=1,ii
if (SEA_P) then
do k=1,kk
thknss=dpmixl(i,j,n)
q=max(0.,min(1.,(thknss-p(i,j,k))/(dp(i,j,k,n)+epsil)))
if(q.eq.1.) then
temp(i,j,k,n)= temp(i,j,k,n)+dtemp(i)
saln(i,j,k,n)=max(saln(i,j,k,n)+dsaln(i),0.0) !must be non-negative
th3d(i,j,k,n)=sig(temp(i,j,k,n),saln(i,j,k,n))-thbase
else
temp(i,j,k,n)= temp(i,j,k,n)+q*dtemp(i)
saln(i,j,k,n)=max(saln(i,j,k,n)+q*dsaln(i),0.0)
if(pensol) then
!
! --- heat layers beneath mixed layer due to
! --- penetrating solar radiation (all redfac in mixed layer)
if (jerlv0.le.0) then
chl = akpar(i,j,lk0)*wk0+akpar(i,j,lk1)*wk1 &
+akpar(i,j,lk2)*wk2+akpar(i,j,lk3)*wk3
endif
call swfrml_ij(chl,max(thknss,p(i,j,k )), &
p(i,j,kk+1),qonem*oneta(i,j,n), &
jerlov(i,j),swfold)
call swfrml_ij(chl, p(i,j,k+1), &
p(i,j,kk+1),qonem*oneta(i,j,n), &
jerlov(i,j),swfrac)
dtemp2=(swfold-swfrac)*sswflx(i,j)*delt1*g/ &
(spcifh*max(onemm,p(i,j,k+1)-max(thknss,p(i,j,k))))
temp(i,j,k,n)=temp(i,j,k,n)+(1.-q)*dtemp2
!diag if (i.eq.itest.and.j.eq.jtest) write (lp,104) nstep,i,j,1, &
!diag 1.-swfold,1.-swfrac,(1.-q)*dtemp2
end if !pensol
th3d(i,j,k,n)=sig(temp(i,j,k,n),saln(i,j,k,n))-thbase
end if
enddo !k
endif !ip
enddo !i
return
end
subroutine mxkrtabj(m,n, j, depnew)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
implicit none
!
integer m,n,j
real, dimension (1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy) :: &
depnew
!
! --- hycom version 1.0
! --- single row, part B.
!
integer i,k,k1
!
real dp1,dp2,q,uv1,uv2,uvmin,uvmax
!
! --- ---------------
! --- momentum mixing
! --- ---------------
!
! --- homogenize -u- down to max(old,new) mixed layer depth
!
do i=1,ii
if (SEA_U) then
util1(i,j)=min(depthu(i,j)-onem,max(dpu(i,j,1,n),thkmin*onem, &
.5*(depnew(i,j)+depnew(i-1,j))))
!
! --- if mixed layer base is very close to interface, move it there
if (abs(util1(i,j)-dpu(i,j,1,n)).lt..001*dpu(i,j,1,n)) then
util1(i,j)=dpu(i,j,1,n)+onecm
endif
!
uflux(i,j)=u(i,j,1,n)*dpu(i,j,1,n)
util2(i,j)=dpu(i,j,1,n)
pu(i,j,2)=dpu(i,j,1,n)
!
do k=2,kk
pu(i,j,k+1)=pu(i,j,k)+dpu(i,j,k,n)
!
! --- if mixed layer base is very close to interface, move it there
if (abs(pu(i,j,k+1)-util1(i,j)).lt. &
max(onecm,.001*dpu(i,j,k,n)) ) then
util1(i,j)=pu(i,j,k+1)
endif
!
if (pu(i,j,k+1).le.util1(i,j)) then
uflux(i,j)=uflux(i,j)+u(i,j,k,n)*dpu(i,j,k,n)
util2(i,j)=util2(i,j)+ dpu(i,j,k,n)
end if
enddo !k
!
u(i,j,1,n)=uflux(i,j)/util2(i,j)
!
! --- unmix u
! --- first guess for upper sublayer value is the value from the layer
! --- immediately above the one containing the mixed layer base
do k=2,kk
k1=min(k+1,kk)
if (pu(i,j,k ).lt.util1(i,j) .and. &
pu(i,j,k+1).gt.util1(i,j) ) then
if(k.ge.3) then
dp1=util1(i,j)-pu(i,j,k)
dp2=pu(i,j,k+1)-util1(i,j)
uv1=u(i,j,k-1,n)
uvmin=min(uv1,u(i,j,k,n),u(i,j,k1,n))
uvmax=max(uv1,u(i,j,k,n),u(i,j,k1,n))
uv2=u(i,j,k,n)-(uv1-u(i,j,k,n))*dp1/dp2
u(i,j,k,n)=min(uvmax,max(uvmin,uv2))
uv1=uv1+(uv2-u(i,j,k,n))*dp2/dp1
u(i,j,1,n)=(uflux(i,j)+uv1*dp1)/util1(i,j)
end if
end if
enddo !k
!
do k=2,kk
!diag uold=u(i,j,k,n)
q=max(0.,min(1.,(util1(i,j)-pu(i,j,k))/(dpu(i,j,k,n)+epsil)))
u(i,j,k,n)=u(i,j,k,n)+q*(u(i,j,1,n)-u(i,j,k,n))
!diag if (i.eq.itest .and. j.eq.jtest) write &
!diag (lp,'(i9,2i6,i4,a,f9.3,2f8.3)') nstep,i+i0,j+j0,k, &
!diag ' dpu, old/new u ',dpu(i,j,k,n)*qonem,uold,u(i,j,k,n)
enddo !k
endif !iu
enddo !i
!
! --- homogenize -v- down to max(old,new) mixed layer depth
!
do i=1,ii
if (SEA_V) then
util1(i,j)=min(depthv(i,j)-onem,max(dpv(i,j,1,n),thkmin*onem, &
.5*(depnew(i,j)+depnew(i,j-1))))
!
! --- if mixed layer base is very close to interface, move it there
if (abs(util1(i,j)-dpv(i,j,1,n)).lt..001*dpv(i,j,1,n)) then
util1(i,j)=dpv(i,j,1,n)+onecm
endif
!
vflux(i,j)=v(i,j,1,n)*dpv(i,j,1,n)
util2(i,j)=dpv(i,j,1,n)
pv(i,j,2)=dpv(i,j,1,n)
!
do k=2,kk
pv(i,j,k+1)=pv(i,j,k)+dpv(i,j,k,n)
!
! --- if mixed layer base is very close to interface, move it there
if (abs(pv(i,j,k+1)-util1(i,j)).lt. &
max(onecm,.001*dpv(i,j,k,n)) ) then
util1(i,j)=pv(i,j,k+1)
endif
!
if (pv(i,j,k+1).le.util1(i,j)) then
vflux(i,j)=vflux(i,j)+v(i,j,k,n)*dpv(i,j,k,n)
util2(i,j)=util2(i,j)+ dpv(i,j,k,n)
end if
enddo !k
!
v(i,j,1,n)=vflux(i,j)/util2(i,j)
!
! --- unmix v
! --- first guess for upper sublayer value is the value from the layer
! --- immediately above the one containing the mixed layer base
do k=2,kk
k1=min(k+1,kk)
if (pv(i,j,k ).lt.util1(i,j) .and. &
pv(i,j,k+1).gt.util1(i,j) ) then
if(k.ge.3) then
dp1=util1(i,j)-pv(i,j,k)
dp2=pv(i,j,k+1)-util1(i,j)
uv1=v(i,j,k-1,n)
uvmin=min(uv1,v(i,j,k,n),v(i,j,k1,n))
uvmax=max(uv1,v(i,j,k,n),v(i,j,k1,n))
uv2=v(i,j,k,n)-(uv1-v(i,j,k,n))*dp1/dp2
v(i,j,k,n)=min(uvmax,max(uvmin,uv2))
uv1=uv1+(uv2-v(i,j,k,n))*dp2/dp1
v(i,j,1,n)=(vflux(i,j)+uv1*dp1)/util1(i,j)
end if
end if
enddo !k
!
do k=2,kk
!diag vold=v(i,j,k,n)
q=max(0.,min(1.,(util1(i,j)-pv(i,j,k))/(dpv(i,j,k,n)+epsil)))
v(i,j,k,n)=v(i,j,k,n)+q*(v(i,j,1,n)-v(i,j,k,n))
!diag if (i.eq.itest .and. j.eq.jtest) write &
!diag (lp,'(i9,2i6,i4,a,f9.3,2f8.3)') nstep,i+i0,j+j0,k, &
!diag ' dpv, old/new v ',dpv(i,j,k,n)*qonem,vold,v(i,j,k,n)
enddo !k
endif !iv
enddo !i
!
return
end
!
subroutine mxkrtb(m,n)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
implicit none
!
integer m,n
!
! --- hycom version 1.0 -- alternative slab mixed layer model
!
integer j
!
!$OMP PARALLEL DO PRIVATE(j) &
!$OMP SHARED(m,n) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
call mxkrtbaj(m,n, j)
enddo
!$OMP END PARALLEL DO
!
!$OMP PARALLEL DO PRIVATE(j) &
!$OMP SHARED(m,n) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
call mxkrtbbj(m,n, j)
enddo
!$OMP END PARALLEL DO
!
return
end
!
subroutine mxkrtbaj(m,n, j)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
implicit none
!
integer m,n,j
!
! --- hycom version 1.0 -- alternative slab mixed layer model
! --- single row, part A.
!
real dpth,ekminv,obuinv,ex,alf1,alf2,cp1,cp3,ape,cc4,spe, &
ustar3,thkold,thknew,value,q,tdp,sdp,trdp(mxtrcr), &
tem,sal,rho,thet,alfadt,betads, &
ttem(kdm),ssal(kdm),ttrc(kdm,mxtrcr),dens(kdm),densl(kdm), &
pres(kdm+1),delp(kdm),sum1,sum2,buoyfl,dsgdt,tmn,smn
!diag real totem,tosal,tndcyt,tndcys
integer kmxbot
integer i,k,ka,ktr
!
! --- abs.bound (m/day) and rel.bound (percent/day) on detrainment rate:
!cc real bound1, bound2
!cc data bound1, bound2 /200.0, 0.10/
!
real ea1, ea2, em1, em2, em3, em4, em5
data ea1, ea2, em1, em2, em3, em4, em5 &
/0.60,0.30,0.45,2.60,1.90,2.30,0.60/ ! Gaspar coefficients
!
# include "stmt_fns.h"
!
do i=1,ii
if (SEA_P) then
!
! --- extract single column from 3-d fields
pres(1)=p(i,j,1)
do k=1,kk
ttem(k)=temp(i,j,k,n)
ssal(k)=saln(i,j,k,n)
dens(k)=th3d(i,j,k,n)
do ktr= 1,ntracr
ttrc(k,ktr)=tracer(i,j,k,n,ktr)
enddo
delp(k)=dp(i,j,k,n)
pres(k+1)=pres(k)+delp(k)
enddo !k
!
103 format (i9,2i6,a/(33x,i3,2f8.3,f8.3,f8.2,f8.1))
!diag if (i.eq.itest .and. j.eq.jtest) &
!diag write (lp,103) nstep,itest+i0,jtest+j0, &
!diag ' entering mxlayr: temp saln dens thkns dpth',(k, &
!diag ttem(k),ssal(k),dens(k)+thbase,delp(k)*qonem,pres(k+1)*qonem,k=1,kk)
!
! --- store 'old' t/s column integral in totem/tosal (diagnostic use only)
!diag totem=0.
!diag tosal=0.
!diag do k=1,kk
!diag totem=totem+ttem(k)*delp(k)
!diag tosal=tosal+ssal(k)*delp(k)
!diag enddo !k
!
tdp=ttem(1)*delp(1)
sdp=ssal(1)*delp(1)
do ktr= 1,ntracr
trdp(ktr)=delp(1)
enddo !ktr
!
kmxbot=1
do k=2,kk
!
! --- watch for density decrease with depth (convective adjustment)
tem=(tdp+ttem(k)*delp(k))/pres(k+1)
sal=(sdp+ssal(k)*delp(k))/pres(k+1)
rho=sig(tem,sal)-thbase
if (locsig) then
alfadt=0.5*(dsiglocdt(tem,sal,pres(k+1))+ &
dsiglocdt(ttem(k),ssal(k),pres(k+1)))*(tem-ttem(k))
betads=0.5*(dsiglocds(tem,sal,pres(k+1))+ &
dsiglocds(ttem(k),ssal(k),pres(k+1)))*(sal-ssal(k))
if(alfadt+betads.gt.0.0) then
ttem(1)=tem
ssal(1)=sal
dens(1)=rho
tdp=tdp+ttem(k)*delp(k)
sdp=sdp+ssal(k)*delp(k)
do ktr= 1,ntracr
trdp(ktr)=trdp(ktr)+ttrc(k,ktr)*delp(k)
enddo
kmxbot=k
end if
else
if (rho.le.dens(1)) then
ttem(1)=tem
ssal(1)=sal
dens(1)=rho
tdp=tdp+ttem(k)*delp(k)
sdp=sdp+ssal(k)*delp(k)
do ktr= 1,ntracr
trdp(ktr)=trdp(ktr)+ttrc(k,ktr)*delp(k)
enddo
kmxbot=k
end if
endif
if (k.gt.kmxbot) then
exit
endif
enddo !k
!
do k=2,kmxbot
ttem(k)=ttem(1)
ssal(k)=ssal(1)
dens(k)=dens(1)
do ktr= 1,ntracr
ttrc(k,ktr)=ttrc(1,ktr)
enddo !ktr
enddo !k
!
! --- ----------------------------------------
! --- slab mixed layer entrainment/detrainment
! --- ----------------------------------------
!
! --- determine turb.kin.energy generation due to wind stirring
! --- ustar computed in subr. -thermf-
! --- buoyancy flux (m**2/sec**3), all fluxes into the ocean
! --- note: surface density increases (column is destabilized) if buoyfl < 0
thkold=pres(kmxbot+1)
ustar3=ustar(i,j)**3
tmn=.5*(temp(i,j,1,m)+temp(i,j,1,n))
smn=.5*(saln(i,j,1,m)+saln(i,j,1,n))
dsgdt=dsigdt(tmn,smn)
buoyfl=-g*svref*(dsigds(tmn,smn)* &
(-wtrflx(i,j)*saln(i,j,1,n)+salflx(i,j))*svref+ &
dsgdt *surflx(i,j) *svref/spcifh)
!
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
!
! --- option 1 : k r a u s - t u r n e r mixed-layer t.k.e. closure
!
!cc em=0.8*exp(-pres(2)/(50.*onem)) ! hadley centre choice (orig.: 1.25)
!cc en=0.15 ! hadley centre choice (orig.: 0.4)
!cc thermg=0.5*((en+1.)*buoyfl+(en-1.)*abs(buoyfl))
!cc turgen(i,j)=delt1*(2.*em*g*ustar3*rhoref+thkold*thermg)*rhoref**2
!
! --- find monin-obukhov length in case of receding mixed layer (turgen < 0).
! --- the monin-obukhov length is found by stipulating turgen = 0.
!
!cc if (turgen(i,j).lt.0.) then
!cc thknew=-2.*em*g*ustar3/min(-epsil,svref*thermg)
!cc else
!cc thknew=thkold
!cc end if
!
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
!
! --- option 2 : g a s p a r mixed-layer t.k.e. closure
!
dpth=thkold*qonem
ekminv=abs(corio(i,j))/max(epsil,ustar(i,j))
obuinv=buoyfl/max(epsil,ustar3)
ex=exp(min(50.,dpth*obuinv))
alf1=ea1+ea2*max(1.,2.5*dpth*ekminv)*ex
alf2=ea1+ea2*ex
cp1=((1.-em5)*(alf1/alf2)+.5*em4)*athird
cp3=max(0.,(em4*(em2+em3)-(alf1/alf2)*(em2+em3-em3*em5))*athird)
ape=cp3*ustar3+cp1*dpth*buoyfl
!
if(ape.lt.0.) then ! detrainment
turgen(i,j)=(g*delt1*rhoref**3)*ape
thknew=min(thkold,g*cp3/(svref*cp1*max(epsil,obuinv)))
!
else ! entrainment
cc4=2.*em4/(em1*em1) * alf1*alf1
spe=(em2+em3)*ustar3+0.5*dpth*buoyfl
turgen(i,j)=(g*delt1*rhoref**3)*(sqrt((.5*ape-cp1*spe)**2 &
+2.*cc4*ape*spe)-(.5*ape+cp1*spe))/(cc4-cp1)
thknew=thkold
end if
!
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
!
! --- sum1,sum2 are used to evaluate pot.energy changes during entrainment
sum1=dens(1)*thkold
sum2=dens(1)*thkold**2
!
! --- find thknew in case of mx.layer deepening (turgen>0). store in -thknew-.
! --- entrain as many layers as needed to deplete -turgen-.
!
do k=2,kk
ka=k-1
if (locsig) then
if (k.eq.2) then
densl(ka)=dens(ka)
endif
alfadt=0.5* &
(dsiglocdt(ttem(ka),ssal(ka),pres(k))+ &
dsiglocdt(ttem(k ),ssal(k ),pres(k)))*(ttem(ka)-ttem(k))
betads=0.5* &
(dsiglocds(ttem(ka),ssal(ka),pres(k))+ &
dsiglocds(ttem(k ),ssal(k ),pres(k)))*(ssal(ka)-ssal(k))
densl(k)=densl(ka)-alfadt-betads
thet=densl(k)
else
thet=dens (k)
endif
if (pres(k+1).gt.thkold) then
value=(2.*turgen(i,j)+thet*pres(k)**2-sum2)/ &
max(epsil,thet*pres(k) -sum1)
! --- stop iterating for 'thknew' as soon as thknew < k-th interface pressure
if (value.lt.pres(k)) then
value=thknew
endif
! --- substitute 'thknew' for monin-obukhov length if mixed layer is deepening
if (turgen(i,j).ge.0.) then
thknew=value
endif
!
sum1=sum1+thet*(pres(k+1) -max(pres(k),thkold) )
sum2=sum2+thet*(pres(k+1)**2-max(pres(k),thkold)**2)
end if
enddo !k
!
!diag if (i.eq.itest .and. j.eq.jtest .and. turgen(i,j).lt.0.) &
!diag write (lp,'(i9,2i6,a,f8.2,1p,e13.3)') nstep,itest+i0,jtest+j0, &
!diag ' monin-obukhov length (m),turgen:',thknew*qonem,turgen(i,j)
!
! --- don't allow mixed layer to get too deep or too shallow.
!cc q=max(bound1*onem,thkold*bound2)*delt1/86400.
!cc thknew=min(pres(kk+1),max(thkmin*onem,delp(1),thknew,thkold-q))
thknew=min(pres(kk+1),max(thkmin*onem,delp(1),thknew))
!
! --- integrate t/s over new mixed layer depth
!
tdp=ttem(1)*delp(1)
sdp=ssal(1)*delp(1)
!
do k=2,kk
if (pres(k).lt.thknew) then
q=min(thknew,pres(k+1))-min(thknew,pres(k))
tdp=tdp+ttem(k)*q
sdp=sdp+ssal(k)*q
end if
enddo !k
!
!diag if (i.eq.itest.and.j.eq.jtest) write (lp,'(i9,2i6,a,2f9.3)') &
!diag nstep,i+i0,j+j0, &
!diag ' old/new mixed layer depth:',thkold*qonem,thknew*qonem
!
! --- distribute thermohaline forcing over new mixed layer depth
!
ttem(1)=(tdp+surflx(i,j)*delt1*g/spcifh)/thknew
ssal(1)=(sdp+salflx(i,j)*delt1*g )/thknew
dens(1)=sig(ttem(1),ssal(1))-thbase
!
! --- homogenize water mass properties down to new mixed layer depth
!