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mxkrtm.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 mxkrtm(m,n)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
implicit none
!
integer m,n
!
! --- hycom version 1.0 (adapted from micom version 2.8)
!
#if defined(RELO)
real, save, allocatable, dimension(:,:) ::&
#else
real, save, dimension(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy) ::&
#endif
sdot
!
integer i,j,k
real delp,q,thk
!cc integer kmax
!cc real totem,tosal,tndcyt,tndcys,work(3)
#if defined(RELO)
!
if (.not.allocated(sdot)) then
allocate( &
sdot(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy) )
call mem_stat_add( (idm+2*nbdy)*(jdm+2*nbdy) )
sdot = r_init
endif
#endif
!
!$OMP PARALLEL DO PRIVATE(j,k,i) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
do k=1,kk
do i=1,ii
if (SEA_P) then
p(i,j,k+1)=p(i,j,k)+dp(i,j,k,n)
endif !ip
enddo !i
enddo !k
enddo !j
!$OMP END PARALLEL DO
!
103 format (i9,2i6,a/(35x,i3,2f8.3,f8.3,0p,f8.2,f8.1))
!diag if (itest.gt.0 .and. jtest.gt.0) write (lp,103) nstep,itest,jtest, &
!diag ' entering mxlayr: temp saln dens thkns dpth', &
!diag (k,temp(itest,jtest,k,n),saln(itest,jtest,k,n), &
!diag th3d(itest,jtest,k,n)+thbase,dp(itest,jtest,k,n)*qonem, &
!diag p(itest,jtest,k+1)*qonem,k=1,kk)
!
if (thermo .or. sstflg.gt.0 .or. srelax) then
!
! --- -----------------------------------
! --- mixed layer entrainment/detrainment
! --- -----------------------------------
!
!$OMP PARALLEL DO PRIVATE(j) &
!$OMP SHARED(m,n,sdot) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
call mxkrtmaj(m,n, sdot, j)
enddo
!$OMP END PARALLEL DO
!
else !.not.thermo ...
!
!$OMP PARALLEL DO PRIVATE(j,i) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
do i=1,ii
if (SEA_P) then
surflx(i,j)=0.
salflx(i,j)=0.
wtrflx(i,j)=0.
sdot(i,j)=dp(i,j,1,n)
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
!
end if !thermo.or.sstflg.gt.0.or.srelax:else
!
!diag if (itest.gt.0.and.jtest.gt.0.and.turgen(itest,jtest).lt.0.) &
!diag write (lp,'(i9,2i6,a,f8.2)') nstep,itest,jtest, &
!diag ' monin-obukhov length (m):',sdot(itest,jtest)*qonem
!
! --- store 'old' t/s column integral in totem/tosal (diagnostic use only)
!cc totem=0.
!cc tosal=0.
!cc do k=1,kk
!cc if (max(dp(itest,jtest,1,n)+sdot(itest,jtest),thkmin*onem).gt.
!cc . p(itest,jtest,k) .or. max(th3d(itest,jtest,1,m),th3d(itest,
!cc . jtest,1,n)) +sigjmp.ge.th3d(i,j,k,n)) then
!cc kmax=k
!cc totem=totem+temp(itest,jtest,k,n)*dp(itest,jtest,k,n)
!cc tosal=tosal+saln(itest,jtest,k,n)*dp(itest,jtest,k,n)
!cc end if
!cc end do
!
!$OMP PARALLEL DO PRIVATE(j) &
!$OMP SHARED(m,n,sdot) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
call mxkrtmbj(m,n, sdot, j)
enddo
!$OMP END PARALLEL DO
!
! --- compare 'old' with 'new' t/s column integral (diagnostic use only)
!
!cc tndcyt=-totem
!cc tndcys=-tosal
!cc do k=kmax,1,-1
!cc tndcyt=tndcyt+temp(itest,jtest,k,n)*dp(itest,jtest,k,n)
!cc tndcys=tndcys+saln(itest,jtest,k,n)*dp(itest,jtest,k,n)
!cc end do
!cc write (lp,'(i9,2i6,i4,3x,a,1p,3e10.2/27x,a,3e10.2)') nstep,itest,
!cc . jtest,kmax,'total saln,srf.flux,tndcy:',tosal/g,salflx(itest,
!cc . jtest)*delt1,tndcys/g,'total temp,srf.flux,tndcy:',totem/g,
!cc . surflx(itest,jtest)*delt1,tndcyt*spcifh/g
!
! --- store 'old' interface pressures in -pu,pv-
!
!$OMP PARALLEL DO PRIVATE(j,k,i) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
do k=2,kk+1
do i=1,ii
if (SEA_U) then
pu(i,j,k)=min(depthu(i,j),.5*(p(i,j,k)+p(i-1,j,k)))
endif !iu
enddo !i
!
do i=1,ii
if (SEA_V) then
pv(i,j,k)=min(depthv(i,j),.5*(p(i,j,k)+p(i,j-1,k)))
endif !iv
enddo !i
enddo !k
enddo !j
!$OMP END PARALLEL DO
!
! --- store 'new' layer thicknesses in -dpu,dpv-
!
!$OMP PARALLEL DO PRIVATE(j,k,i) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
do k=1,kk
do i=1,ii
if (SEA_P) then
p(i,j,k+1)=p(i,j,k)+dp(i,j,k,n)
endif !ip
enddo !i
enddo !k
enddo !j
!$OMP END PARALLEL DO
!
call dpudpv(dpu(1-nbdy,1-nbdy,1,n), &
dpv(1-nbdy,1-nbdy,1,n), &
p,depthu,depthv, 0,0)
!
! --- redistribute momentum in the vertical.
! --- homogenize (u,v) over depth range defined in -util1,util2-
!
! --- thk>0 activates momentum diffusion across mixed-layer interface
thk=vertmx*onem*delt1
!
!$OMP PARALLEL DO PRIVATE(j,i,k,delp,q) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
!
do i=1,ii
if (SEA_U) then
util1(i,j)=max(dpu(i,j,1,n),pu(i,j,2)+thk)
uflux(i,j)=0.
util3(i,j)=0.
!
do k=1,kk
delp=max(0.,min(util1(i,j),pu(i,j,k+1)) &
-min(util1(i,j),pu(i,j,k )))
uflux(i,j)=uflux(i,j)+u(i,j,k,n)*delp
util3(i,j)=util3(i,j) +delp
enddo !k
!
u(i,j,1,n)=uflux(i,j)/util3(i,j)
endif !iu
enddo !i
!
do i=1,ii
if (SEA_V) then
util2(i,j)=max(dpv(i,j,1,n),pv(i,j,2)+thk)
vflux(i,j)=0.
util4(i,j)=0.
!
do k=1,kk
delp=max(0.,min(util2(i,j),pv(i,j,k+1)) &
-min(util2(i,j),pv(i,j,k )))
vflux(i,j)=vflux(i,j)+v(i,j,k,n)*delp
util4(i,j)=util4(i,j) +delp
enddo !k
!
v(i,j,1,n)=vflux(i,j)/util4(i,j)
endif !iv
enddo !i
!
do k=2,kk
!
do i=1,ii
if (SEA_U) then
pu(i,j,k)=pu(i,j,k-1)+dpu(i,j,k-1,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,1,n)*q+u(i,j,k,n)*(1.-q)
endif !iu
enddo !i
!
do i=1,ii
if (SEA_V) then
pv(i,j,k)=pv(i,j,k-1)+dpv(i,j,k-1,n)
q=max(0.,min(1.,(util2(i,j)-pv(i,j,k))/(dpv(i,j,k,n)+epsil)))
v(i,j,k,n)=v(i,j,1,n)*q+v(i,j,k,n)*(1.-q)
endif !iv
enddo !i
enddo !k
enddo !j
!$OMP END PARALLEL DO
!
!diag if (itest.gt.0 .and. jtest.gt.0) write (lp,103) nstep,itest,jtest, &
!diag ' exiting mxlayr: 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)
return
end
subroutine mxkrtmaj(m,n, sdot, j)
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) :: &
sdot
!
! --- hycom version 1.0 (adapted from micom version 2.8)
!
integer i,k,ka
!
real thknss,ustar3,dpth,ekminv,obuinv,buoyfl,dsgdt,tmn,smn, &
ex,alf1,alf2,cp1,cp3,ape,cc4,spe,pnew,alfadt,betads,thet
!
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"
!
locsig=.true.
!
! --- -----------------------------------
! --- 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
thknss=dp(i,j,1,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=-.5*g*((en+1.)*buoyfl+(en-1.)*abs(buoyfl))*rhoref
!cc turgen(i,j)=delt1*(2.*em*g*ustar3*rhoref+thknss*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.
! --- store temporarily in 'sdot'.
!
!cc if (turgen(i,j).lt.0.) then
!cc sdot(i,j)=-2.*em*g*ustar3/min(-epsil,svref*thermg)
!cc else
!cc sdot(i,j)=thknss
!cc end if
!
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
!
! --- option 2 : g a s p a r mixed-layer t.k.e. closure
!
dpth=thknss*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
sdot(i,j)=max(thkmin*onem,min(thknss,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)
sdot(i,j)=thknss
end if
!
! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
!
! --- util1,util2 are used to evaluate pot.energy changes during entrainment
util1(i,j)=th3d(i,j,1,n)*thknss
util2(i,j)=th3d(i,j,1,n)*thknss**2
!
! --- find pnew in case of mixed layer deepening (turgen > 0). store in 'sdot'.
! --- entrain as many layers as needed to deplete -turgen-.
!
do k=2,kk
ka=k-1
if (k.eq.2) then
thstar(i,j,ka,1)=th3d(i,j,ka,n)
endif
if (locsig) then
alfadt=0.5* &
(dsiglocdt(temp(i,j,ka,n),saln(i,j,ka,n),p(i,j,k))+ &
dsiglocdt(temp(i,j,k ,n),saln(i,j,k ,n),p(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),p(i,j,k))+ &
dsiglocds(temp(i,j,k ,n),saln(i,j,k ,n),p(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
thet=th3d(i,j,k,n)
endif
pnew=(2.*turgen(i,j)+thet*p(i,j,k)**2-util2(i,j))/ &
max(epsil,thet*p(i,j,k) -util1(i,j))
! --- stop iterating for 'pnew' as soon as pnew < k-th interface pressure
if (pnew.lt.p(i,j,k)) pnew=sdot(i,j)
! --- substitute 'pnew' for monin-obukhov length if mixed layer is deepening
if (turgen(i,j).ge.0.) sdot(i,j)=pnew
!
util1(i,j)=util1(i,j)+thet*dp(i,j,k,n)
util2(i,j)=util2(i,j)+thet*(p(i,j,k+1)**2-p(i,j,k)**2)
enddo !k
endif !ip
enddo !i
return
end
subroutine mxkrtmbj(m,n, sdot, j)
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) :: &
sdot
!
! --- hycom version 1.0 (adapted from micom version 2.8)
!
integer i,k,ktr,num
!
real tdp(idm),sdp(idm),vsflx(idm)
real pnew,thknss,t1,s1,tmxl,smxl, &
dpno,sn,tn,dtemp,dsaln,tnew,snew,z,s_up,a,e,b,f,d,c1msig, &
cc0,cc3,cc1,cc2,x
!
real ccubq,ccubr,ccubqr,ccubs1,ccubs2,ccubrl,ccubim,root,root1, &
root2,root3
!
# include "stmt_fns.h"
!
! --- cubic eqn. solver used in mixed-layer detrainment
ccubq(s)=athird*(cc1/cc3-athird*(cc2/cc3)**2)
ccubr(s)=athird*(.5*(cc1*cc2)/(cc3*cc3)-1.5*cc0/cc3) &
-(athird*cc2/cc3)**3
ccubqr(s)=sqrt(abs(ccubq(s)**3+ccubr(s)**2))
ccubs1(s)=sign(abs(ccubr(s)+ccubqr(s))**athird,ccubr(s)+ccubqr(s))
ccubs2(s)=sign(abs(ccubr(s)-ccubqr(s))**athird,ccubr(s)-ccubqr(s))
root(s)=ccubs1(s)+ccubs2(s)-athird*cc2/cc3
ccubrl(s)=sqrt(max(0.,-ccubq(s))) &
*cos(athird*atan2(ccubqr(s),ccubr(s)))
ccubim(s)=sqrt(max(0.,-ccubq(s))) &
*sin(athird*atan2(ccubqr(s),ccubr(s)))
root1(s)=2.*ccubrl(s)-athird*cc2/cc3
root2(s)=-ccubrl(s)+sqrt(3.)*ccubim(s)-athird*cc2/cc3
root3(s)=-ccubrl(s)-sqrt(3.)*ccubim(s)-athird*cc2/cc3
!
do i=1,ii
if (SEA_P) then
if (epmass.eq.1) then !only actual salt flux
vsflx(i)= salflx(i,j)
elseif (epmass.eq.2) then !river only is mass flux
vsflx(i)=(salflx(i,j)- &
(wtrflx(i,j)-rivflx(i,j))*saln(i,j,1,n))
else !water flux treated as a virtual salt flux
vsflx(i)=(salflx(i,j)-wtrflx(i,j)*saln(i,j,1,n))
endif
! --- store (pnew - pold) in 'sdot'.
! --- don't allow mixed layer to get too deep or too shallow.
sdot(i,j)=min(p(i,j,kk+1),max(thkmin*onem,sdot(i,j)))- &
dp(i,j,1,n)
klist(i,j)=2
tdp(i)=0.
sdp(i)=0.
!
do k=2,kk
pnew=dp(i,j,1,n)+sdot(i,j)
! --- 'tdp,sdp' will be needed for temp./salin. mixing during entrainment
tdp(i)=tdp(i)+temp(i,j,k,n)*(min(pnew,p(i,j,k+1)) &
-min(pnew,p(i,j,k )))
sdp(i)=sdp(i)+saln(i,j,k,n)*(min(pnew,p(i,j,k+1)) &
-min(pnew,p(i,j,k )))
!
! --- if sdot > 0, remove water from layers about to be entrained.
dpo(i,j,k,n)=dp(i,j,k,n) ! diapyc.flux
dp( i,j,k,n)=max(p(i,j,k+1),pnew)-max(p(i,j,k),pnew)
diaflx(i,j,k)=diaflx(i,j,k)+(dp(i,j,k,n)-dpo(i,j,k,n)) ! diapyc.flux
if (pnew.ge.p(i,j,k+1)) then
do ktr= 1,ntracr
tracer(i,j,k,n,ktr)=0.
enddo !ktr
endif
!
! --- if sdot < 0, mixed layer water will be detrained into isopycnic layer
! --- defined in -klist-. to prevent odd/even time step decoupling of mixed-
! --- layer depth, determine -klist- from layer one -th3d- at 2 consecutive
! --- time levels
!
if (max(th3d(i,j,1,m),th3d(i,j,1,n))+sigjmp.ge.th3d(i,j,k,n)) &
klist(i,j)=k+1
!
! --- set t/s in massless layers. step 1: copy salinity from layer(s) above
!
saln(i,j,k,n)=(saln(i,j,k,n)*dp(i,j,k,n)+saln(i,j,k-1,n)*epsil)/ &
( dp(i,j,k,n)+ epsil)
enddo !k
!
! --- set t/s in massless layers. step 2: copy salinity from layer(s) below
!
do k=kk-1,2,-1
saln(i,j,k,n)=(saln(i,j,k,n)*dp(i,j,k,n)+saln(i,j,k+1,n)*epsil)/ &
( dp(i,j,k,n)+ epsil)
enddo !k
!
! --- set t/s in massless layers. step 3: increase salinity where water
! --- is too fresh to fit into layer k
!
do k=2,kk
if (saln(i,j,k,n).lt.salmin(k)) then
saln(i,j,k,n)=salmin(k)
temp(i,j,k,n)=tofsig(th3d(i,j,k,n)+thbase,saln(i,j,k,n))
end if
enddo !k
!
! --- redistribute temp. and salin. during both de- and entrainment
!
thknss=dp(i,j,1,n)
pnew=thknss+sdot(i,j)
t1=temp(i,j,1,n)
s1=saln(i,j,1,n)
!
tmxl=t1+surflx(i,j)*delt1*g/(spcifh*thknss)
smxl=s1+ vsflx(i) *delt1*g/ thknss
!
!diag if (i.eq.itest.and.j.eq.jtest) write (lp,'(i9,2i6,a,3f7.3,f8.2)') &
!diag nstep,i,j,' t,s,sig,dp after diab.forcing',tmxl,smxl, &
!diag sig(tmxl,smxl),thknss*qonem
!
if (sdot(i,j).ge.0.) then
!
! --- (mixed layer d e e p e n s)
!
!diag if (i.eq.itest.and.j.eq.jtest) write (lp,'(i9,2i6,a,f9.3,a)') &
!diag nstep,i,j,' entrain',sdot(i,j)*qonem,' m of water'
!
tmxl=(tmxl*thknss+tdp(i))/pnew
smxl=(smxl*thknss+sdp(i))/pnew
dp(i,j,1,n)=pnew
diaflx(i,j,1)=diaflx(i,j,1)+sdot(i,j) ! diapyc.flux
!
else if (sdot(i,j).lt.-onecm.and.surflx(i,j).ge.0.) then ! sdot < 0
!
! --- (mixed layer r e c e d e s)
!
k=klist(i,j)
if (k.gt.kk) go to 27
!
!diag if (i.eq.itest.and.j.eq.jtest) &
!diag write (lp,'(i9,2i6,a,i4,a,3p,2f7.3)') nstep,i,j, &
!diag ' sig\*(1),sig\*(',k,') =',th3d(i,j,1,n)+thbase, &
!diag th3d(i,j,k,n)+thbase
!
dpno=max(dp(i,j,k,n),0.)
sn=saln(i,j,k,n)
tn=temp(i,j,k,n)
!
!diag if (i.eq.itest.and.j.eq.jtest) &
!diag write (lp,'(i9,2i6,i4,a,2f9.4,f8.2)') nstep,i,j,k, &
!diag ' t,s,dp before detrainment',tn,sn,dpno*qonem
!
! --- distribute last time step's heating and freshwater flux over depth range
! --- 'pnew' (monin-obukhov length). split fossil mixed layer (depth= -sdot=
! --- thknss-pnew) into lower part ('lo') of depth z cooled and detrained into
! --- layer k, and an upper part ('up') heated to match temperature rise in
! --- mixed layer. transfer as much salinity as possible from sublayer 'up' to
! --- sublayer 'lo' without creating new maxima/minima in water column.
!
dtemp=delt1*g*surflx(i,j)/(spcifh*pnew)
dsaln=delt1*g* vsflx(i) / pnew
!
tnew= t1+dtemp
snew=max(s1+dsaln,0.0) !must be non-negative
!
if (s1.le.sn .and. t1.gt.tn) then
!
! --- scenario 1: transfer t/s so as to achieve t_lo = t_k, s_lo = s_k
!
z=-sdot(i,j)*min(1.,dtemp/max(epsil,tnew-tn))*qonem
s_up=s1+(s1-sn)*dtemp/max(epsil*dtemp,t1-tn)
! --- is scenario 1 feasible?
if (s_up.ge.min(snew,s1)) go to 24
end if ! s_1 < s_n
!
! --- scenario 2: (t_lo,s_lo) differ from (tn,sn). main problem now is in
! --- maintaining density in layer k during detrainment. This requires solving
! --- 3rd deg. polynomial cc3*z**3 + cc2*z**2 + cc1*z + cc0 = 0 for z.
!
s_up=min(s1,snew)
! --- new (t,s) in layer k will be t=(a*z+b)/(z+d), s=(e*z+f)/(z+d).
a=tnew
e=s_up
b=(tn*dpno+ dtemp*sdot(i,j))*qonem
f=(sn*dpno+(s_up-s1)*sdot(i,j))*qonem
d=dpno*qonem
!
c1msig=c1-(th3d(i,j,k,n)+thbase)
cc0=d*d*(d*c1msig+b*c2+f*c3)+b*(d*f*c5+b*(d*c4+b*c6+f*c7))
cc3= ( c1msig+a*c2+e*c3)+a*( e*c5+a*( c4+a*c6+e*c7))
cc1=d*(3. *d*c1msig+(2.*b +a*d)*c2+(2. *f+d*e)*c3)+b*((2.*a*d &
+b )*c4+3.*a*b*c6+(2.*a*f+b*e)*c7)+(a*d*f+b*(d*e+ f))*c5
cc2= (3. *d*c1msig+(2.*a*d+b )*c2+(2.*d*e+ f)*c3)+a*((2.*b &
+a*d)*c4+3.*a*b*c6+(2.*b*e+a*f)*c7)+(b *e+a*( f+d*e))*c5
! --- bound cc3 away from zero
cc3=sign(max(1.e-6,abs(cc3)),cc3)
!
x=0.0 ! dummy argument that is never used
if (ccubq(x)**3+ccubr(x)**2.gt.0.) then
! --- one real root
num=1
z=root(x)
else
! --- three real roots
num=3
z=root1(x)
end if
!
!diag if (i.eq.itest.and.j.eq.jtest) then
!diag work(1)=z
!diag if (num.eq.3) then
!diag work(2)=root2(x)
!diag work(3)=root3(x)
!diag end if
!diag write (lp,100) nstep,i,j,' t,s,dp( 1)=',tnew,snew, &
!diag thknss*qonem,'sdot,z=',sdot(i,j)*qonem,z,'t,s,dp(',k,')=',tn, &
!diag sn,dpno*qonem,'real root(s):',(work(nu),nu=1,num)
!diag end if
100 format (i9,2i6,a,2f7.3,f8.2,3x,a,2f8.2/20x,a,i4,a,2f7.3,f8.2, &
3x,a,1p3e11.4)
!
! --- does root fall into appropriate range?
if (z.le.0.005) go to 27
!
! --- ready to detrain lowest 'z' meters from mixed layer
!
temp(i,j,k,n)=(a*z+b)/(z+d)
saln(i,j,k,n)=(e*z+f)/(z+d)
!
24 continue
sdot(i,j)=max(sdot(i,j),-z*onem)
dp(i,j,1,n)=thknss+sdot(i,j)
dp(i,j,k,n) =dpno -sdot(i,j)
smxl=(snew*pnew+s_up*(dp(i,j,1,n)-pnew))/dp(i,j,1,n)
tmxl=tnew
diaflx(i,j,1)=diaflx(i,j,1)+sdot(i,j) ! diapyc.flux
diaflx(i,j,k)=diaflx(i,j,k)-sdot(i,j) ! diapyc.flux
!
! --- inject 'ventilation' tracer into layer k
do ktr= 1,ntracr
tracer(i,j,k,n,ktr)=(tracer(i,j,k,n,ktr)*dpno-sdot(i,j)) &
/(dpno-sdot(i,j))
enddo !ktr
!
!diag if (i.eq.itest.and.j.eq.jtest) &
!diag write (lp,'(i9,2i6,i4,a,2f9.4,f8.2)') nstep,i,j,k, &
!diag ' t,s,dp after detrainment',temp(i,j,k,n),saln(i,j,k,n), &
!diag dp(i,j,k,n)*qonem
!
end if ! sdot > or < 0
!
27 continue
temp(i,j,1,n)=tmxl
saln(i,j,1,n)=smxl
th3d(i,j,1,n)=sig(tmxl,smxl)-thbase
do ktr= 1,ntracr
tracer(i,j,1,n,ktr)=1.0
enddo !ktr
!
dpmixl(i,j,n)=dp( i,j,1,n)
dpbl( i,j) =dp( i,j,1,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)
!
!diag if (i.eq.itest.and.j.eq.jtest) write &
!diag (lp,'(i9,2i6,i4,a,2f9.4,f8.2)') nstep,i,j,1, &
!diag ' final mixed-layer t,s,dp ',tmxl,smxl,dp(i,j,1,n)*qonem
!
endif !ip
enddo !i
return
end
!
!
!> Revision history:
!>
!> June 1995 - removed restriction 'klist(i,j) .le. kk'
!> June 1995 - added code for setting t/s in massless layers below mix.layer
!> Oct. 1995 - removed bug created while changing klist (June 1995 revision):
!> 'if (k.gt.kk) go to 26' now reads 'if (k.gt.kk) go to 27'
!> May 1997 - changed -sdot- into local array
!> Mar. 1998 - added -th3d-
!> Nov. 1998 - fixed bug in computing tnew,snew in situations where z < 0.005
!> Dec. 1998 - replaced dsaln by (s_up-s1) in definition of 'f'
!> Feb. 1999 - limited 'tofsig' call in loop 45 to cases where saln < salmin
!> Aug. 2000 - adapted from micom 2.8 to run within hycom 1.0
!> May 2002 - buoyfl (into the ocean), calculated here
!> Aug. 2011 - replaced dpold,dpoldm with dpo
!> May 2014 - use land/sea masks (e.g. ip) to skip land
!> Aug. 2018 - added wtrflx, salflx now only actual salt flux
!> Nov. 2018 - allow for wtrflx in buoyancy flux
!> May 2024 - added epmass=2 for river only mass exchange
!> Feb. 2025 - printout now ok for kdm<1000 and idm,jdm<100,000