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diapfl.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 diapf1(m,n)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
!
! --- hycom version 1.0
! --- KPP-style implicit interior diapycnal mixing
implicit none
!
integer m,n
!
! --------------------
! --- diapycnal mixing
! --------------------
!
! --- interior diapycnal mixing due to three processes:
! --- shear instability
! --- double diffusion
! --- background internal waves
!
! --- this is essentially the k-profile-parameterization (kpp) mixing model
! --- (mxkpp.f) with all surface boundary layer processes removed
!
! --- uses the same tri-diagonal matrix solution of vertical diffusion
! --- equation as mxkpp.f
!
integer j
!
if (mod(nstep, mixfrq).ne.0 .and. &
mod(nstep+1,mixfrq).ne.0 ) then
return ! diapycnal mixing only every mixfrq,mixfrq+1 time steps
endif
!
call xctilr(u(1-nbdy,1-nbdy,1,n),1,kk, 1,1, halo_uv)
call xctilr(v(1-nbdy,1-nbdy,1,n),1,kk, 1,1, halo_vv)
call xctilr(p(1-nbdy,1-nbdy,2 ),1,kk, 1,1, halo_ps)
!
!$OMP PARALLEL DO PRIVATE(j) &
!$OMP SHARED(m,n) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
call diapf1aj(m,n, j)
enddo
!$OMP END PARALLEL DO
!
! --- momentum mixing
!
call xctilr(vcty(1-nbdy,1-nbdy,2),1,kk, 1,1, halo_ps)
!
!$OMP PARALLEL DO PRIVATE(j) &
!$OMP SHARED(m,n) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
call diapf1bj(m,n, j)
enddo
!$OMP END PARALLEL DO
!
return
end
subroutine diapf1aj(m,n, j)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
implicit none
!
integer m,n, j
integer i
!
do i=1,ii
if (SEA_P) then
call diapf1aij(m,n, i,j)
endif !ip
enddo !i
!
return
end
subroutine diapf1bj(m,n, j)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
implicit none
!
integer m,n, j
integer i
!
do i=1,ii
if (SEA_U) then
call diapf1uij(m,n, i,j)
endif !iu
if (SEA_V) then
call diapf1vij(m,n, i,j)
endif !iv
enddo !i
!
return
end
subroutine diapf1aij(m,n, i,j)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
#if defined(STOKES)
use mod_stokes ! HYCOM Stokes drift
#endif
!
! --- hycom version 1.0
! --- KPP-style implicit interior diapycnal mixing
implicit none
!
integer m,n, i,j
!
! -----------------------------------------------
! --- diapycnal mixing, single i,j point (part A)
! -----------------------------------------------
!
! --- interior diapycnal mixing due to three processes:
! --- shear instability
! --- double diffusion
! --- background internal waves
!
! --- this is essentially the k-profile-parameterization (kpp) mixing model
! --- (mxkpp.f) with all surface boundary layer processes removed
!
! --- uses the same tri-diagonal matrix solution of vertical diffusion
! --- equation as mxkpp.f
!
! local variables for kpp mixing
real shsq(kdm+1) ! velocity shear squared
real alfadt(kdm+1) ! t contribution to density jump
real betads(kdm+1) ! s contribution to density jump
real dbloc(kdm+1) ! buoyancy jump across interface
real hwide(kdm) ! layer thicknesses in m
real rrho ! double diffusion parameter
real diffdd ! double diffusion diffusivity scale
real prandtl ! prandtl number
real rigr ! local richardson number
real fri ! function of Rig for KPP shear instability
real dflsiw ! wave diffusivity
real dflmiw ! wave viscosity
real dflbot(kdm+1) ! bottom intensified background viscosity
!
! --- local 1-d arrays for matrix inversion
real t1do(kdm+1),t1dn(kdm+1),s1do(kdm+1),s1dn(kdm+1), &
tr1do(kdm+1,mxtrcr),tr1dn(kdm+1,mxtrcr), &
difft(kdm+1),diffs(kdm+1),difftr(kdm+1), &
zm(kdm+1),hm(kdm),dzb(kdm)
!
! --- tridiagonal matrix solution arrays
real tri(kdm,0:1) ! dt/dz/dz factors in trid. matrix
real tcu(kdm), & ! upper coeff for (k-1) on k line of trid.matrix
tcc(kdm), & ! central ... (k ) ..
tcl(kdm), & ! lower ..... (k-1) ..
rhs(kdm) ! right-hand-side terms
!
real ratio,froglp,q,wq,wt,wz0,wz1,wz2
integer k,k1,ka,kmask,ktr,nlayer,mixflg
real riv_input
!
real, parameter :: difriv = 50.0e-4 !river diffusion
!
# include "stmt_fns.h"
froglp=.5*max(2,mixfrq)
!
! --- internal wave diffusion/viscosity
dflsiw = diws(i,j)
dflmiw = diwm(i,j)
!
! --- locate lowest substantial mass-containing layer. avoid near-zero
! --- thickness layers near the bottom
klist(i,j)=0
kmask=0
!
do k=1,kk
p(i,j,k+1)=p(i,j,k)+dp(i,j,k,n)
if (dp(i,j,k,n).lt.onemm) kmask=1
if (p(i,j,k).lt.p(i,j,kk+1)-onem.and.kmask.eq.0) klist(i,j)=k
enddo
!
! --- dflbot (Prandtl number of one, i.e. diffusion = viscosity)
if (botdiw) then
! --- diffusion coefficent profile is: K = Kb / (1 + h/h0)**2
! --- where diwbot = Kb; diwqh0 = 1/h0 (input as h0, see forfun.f)
! --- Decloedt T. and D.S. Luther, 2009: On a Simple Empirical
! --- Parameterization of Topography-Catalyzed Diapycnal Mixing
! --- in the Abyssal Ocean. JPO, 40, pp 487-508.
! --- use Simpson's rule to estimate the average K across each layer
wz0 = 1.0 / (1.0 + (p(i,j,kk+1)- p(i,j,1) )*diwqh0(i,j))**2
wz1 = 1.0 / (1.0 + (p(i,j,kk+1)-0.5*(p(i,j,1)+ &
p(i,j,2) ))*diwqh0(i,j))**2
wz2 = 1.0 / (1.0 + (p(i,j,kk+1)- p(i,j,2) )*diwqh0(i,j))**2
wq = wz0 + wz2 + 4.0*wz1 !6 times the average value over layer 1
do k= 2,kk
wt = wq
wz0 = wz2
wz1 = 1.0 / (1.0 + (p(i,j,kk+1) - &
0.5*(p(i,j,k) + &
p(i,j,k+1) ))*diwqh0(i,j))**2
wz2 = 1.0 / (1.0 + (p(i,j,kk+1) - &
p(i,j,k+1) )*diwqh0(i,j))**2
wq = wz0 + wz2 + 4.0*wz1 !6 times the average value over layer k
dflbot(k) = (0.5/6.0)*(wt+wq)*diwbot(i,j)
enddo
dflbot(kk+1) = dflbot(kk)
else
do k= 2,kk+1
dflbot(k) = 0.0
enddo
endif !botdiw
!
! --- calculate vertical grid and layer widths
do k=1,kk
if (k.eq.1) then
hwide(k)=dp(i,j,k,n)*qonem
zgrid(i,j,k)=-.5*hwide(k)
elseif (k.lt.klist(i,j)) then
hwide(k)=dp(i,j,k,n)*qonem
zgrid(i,j,k)=zgrid(i,j,k-1)-.5*(hwide(k-1)+hwide(k))
elseif (k.eq.klist(i,j)) then
hwide(k)=dp(i,j,k,n)*qonem
zgrid(i,j,k)=zgrid(i,j,k-1)-.5*(hwide(k-1)+hwide(k))
zgrid(i,j,k+1)=zgrid(i,j,k)-.5*hwide(k)
else
hwide(k)=0.
endif
enddo
!
! --- calculate interface variables required to estimate interior diffusivities
do k=1,kk
k1= k+1
ka=min(k+1,kk)
if (k.le.klist(i,j)) then
#if defined(STOKES)
!DAN==========================================================================
!DAN U and V Stokes Drift Layer Average Velocities addes to Shear calculation
!DAN
shsq(k1)=(u(i,j,k, n)+u(i+1,j,k, n)+usd(i,j,k)+usd(i+1,j,k)- &
u(i,j,ka,n)-usd(i+1,j,ka)-u(i,j,ka,n)-usd(i+1,j,ka))**2+ &
(v(i,j,k, n)+v(i,j+1,k, n)+vsd(i,j,k)+vsd(i,j+1,k)- &
v(i,j,ka,n)-v(i,j+1,ka,n)-vsd(i,j,ka)-vsd(i,j+1,ka))**2
#else
shsq( k1)=(u(i,j,k, n)+u(i+1,j,k, n)- &
u(i,j,ka,n)-u(i+1,j,ka,n))**2+ &
(v(i,j,k, n)+v(i,j+1,k, n)- &
v(i,j,ka,n)-v(i,j+1,ka,n))**2
#endif
if (locsig) then
alfadt(k1)=dsiglocdt(ahalf*(temp(i,j,k ,n)+ &
temp(i,j,ka,n) ), &
ahalf*(saln(i,j,k, n)+ &
saln(i,j,ka,n) ),p(i,j,k1))* &
(temp(i,j,k ,n)- &
temp(i,j,ka,n) )
betads(k1)=dsiglocds(ahalf*(temp(i,j,k ,n)+ &
temp(i,j,ka,n) ), &
ahalf*(saln(i,j,k, n)+ &
saln(i,j,ka,n) ),p(i,j,k1))* &
(saln(i,j,k ,n)- &
saln(i,j,ka,n) )
else
alfadt(k1)=dsigdt(ahalf*(temp(i,j,k ,n)+ &
temp(i,j,ka,n) ), &
ahalf*(saln(i,j,k, n)+ &
saln(i,j,ka,n) ) )* &
(temp(i,j,k ,n)- &
temp(i,j,ka,n) )
betads(k1)=dsigds(ahalf*(temp(i,j,k ,n)+ &
temp(i,j,ka,n) ), &
ahalf*(saln(i,j,k, n)+ &
saln(i,j,ka,n) ) )* &
(saln(i,j,k ,n)- &
saln(i,j,ka,n) )
endif
dbloc(k1)=-g*svref*(alfadt(k1)+betads(k1))
endif
enddo
!
! --- determine interior diffusivity profiles throughout the water column
! --- limit mixing to the stratified interior of the ocean
!
do k=1,kk+1
vcty(i,j,k)=0.
dift(i,j,k)=0.
difs(i,j,k)=0.
enddo
!
! --- shear instability plus background internal wave contributions
do k=2,kk+1
if (k-1.le.klist(i,j) .and. p(i,j,k).gt.dpmixl(i,j,n)) then
if (shinst) then
q =zgrid(i,j,k-1)-zgrid(i,j,k) !0.5*(hwide(k-1)+hwide(k))
rigr=max(0.0,dbloc(k)*q/(shsq(k)+epsil))
ratio=min(rigr*qrinfy,1.0)
fri=(1.0-ratio*ratio)
fri=fri*fri*fri
vcty(i,j,k)=difm0*fri+dflmiw+dflbot(k)
difs(i,j,k)=difs0*fri+dflsiw+dflbot(k)
dift(i,j,k)=difs(i,j,k)
else
vcty(i,j,k)=dflmiw+dflbot(k)
difs(i,j,k)=dflsiw+dflbot(k)
dift(i,j,k)=dflsiw+dflbot(k)
endif
endif
enddo
!
! --- double-diffusion (salt fingering and diffusive convection)
if (dbdiff) then
do k=2,kk+1
if (k-1.le.klist(i,j) .and. p(i,j,k).gt.dpmixl(i,j,n)) then
!
! --- salt fingering case
if (-alfadt(k).gt.betads(k) .and. betads(k).gt.0.) then
rrho= min(-alfadt(k)/betads(k),rrho0)
diffdd=1.-((rrho-1.)/(rrho0-1.))**2
diffdd=dsfmax*diffdd*diffdd*diffdd
dift(i,j,k)=dift(i,j,k)+0.7*diffdd
difs(i,j,k)=difs(i,j,k)+diffdd
!
! --- diffusive convection case
elseif (alfadt(k).gt.0.0 .and. betads(k).lt.0.0 .and. &
-alfadt(k).gt.betads(k)) then
rrho=-alfadt(k)/betads(k)
diffdd=1.5e-6*9.*.101*exp(4.6*exp(-.54*(1./rrho-1.)))
prandtl=.15*rrho
if (rrho.gt..5) prandtl=(1.85-.85/rrho)*rrho
dift(i,j,k)=dift(i,j,k)+diffdd
difs(i,j,k)=difs(i,j,k)+prandtl*diffdd
endif
endif
enddo
endif
!
!diag if (i.eq.itest.and.j.eq.jtest) write (lp,101) &
!diag (nstep,i+i0,j+i0,k, &
!diag hwide(k),1.e4*vcty(i,j,k),1.e4*dift(i,j,k), &
!diag 1.e4*difs(i,j,k),k=1,kk+1)
!
! --- perform the vertical mixing at p points
!
mixflg=0
do k=1,klist(i,j)
if (dift(i,j,k+1).gt.0. .or. &
difs(i,j,k+1).gt.0.) mixflg=mixflg+1
difft( k+1)=froglp*dift(i,j,k+1)
diffs( k+1)=froglp*difs(i,j,k+1)
difftr(k+1)=froglp*difs(i,j,k+1)
t1do(k)=temp(i,j,k,n)
s1do(k)=saln(i,j,k,n)
do ktr= 1,ntracr
tr1do(k,ktr)=tracer(i,j,k,n,ktr)
enddo
hm(k)=hwide(k)
zm(k)=zgrid(i,j,k)
enddo
!
if (mixflg.le.1) return
nlayer=klist(i,j)
k=nlayer+1
ka=min(k,kk)
difft( k)=0.
diffs( k)=0.
difftr(k)=0.
t1do(k)=temp(i,j,ka,n)
s1do(k)=saln(i,j,ka,n)
do ktr= 1,ntracr
tr1do(k,ktr)=tracer(i,j,ka,n,ktr)
enddo
zm(k)=zgrid(i,j,k)
!
! --- do rivers here because difs is also used for tracers.
if(cpl_orivers.and.cpl_irivers) then
riv_input = imp_orivers(i,j,1)+imp_irivers(i,j,1)
else
riv_input = rivers(i,j,1)
endif
if (thkriv.gt.0.0 .and. riv_input.ne.0.0) then
do k=1,nlayer
if (-zm(k)+0.5*hm(k).lt.thkriv) then !interface<thkriv
diffs(k+1) = max(diffs(k+1),froglp*difriv)
endif
enddo !k
endif !river
!
! --- compute factors for coefficients of tridiagonal matrix elements.
! tri(k=1:NZ,0) : dt/hwide(k)/ dzb(k-1)=z(k-1)-z(k)=dzabove)
! tri(k=1:NZ,1) : dt/hwide(k)/(dzb(k )=z(k)-z(k+1)=dzbelow)
!
do k=1,nlayer
dzb(k)=zm(k)-zm(k+1)
enddo
!
tri(1,1)=delt1/(hm(1)*dzb(1))
tri(1,0)=0.
do k=2,nlayer
tri(k,1)=delt1/(hm(k)*dzb(k))
tri(k,0)=delt1/(hm(k)*dzb(k-1))
enddo
!
! --- solve the diffusion equation
!
! --- t solution
call tridcof(difft,tri,nlayer,tcu,tcc,tcl)
do k=1,nlayer
rhs(k)=t1do(k)
enddo
call tridmat(tcu,tcc,tcl,nlayer,hm,rhs,t1do,t1dn,difft, i,j)
if ( tofset.eq.0.0 .or. &
(mod(nstep ,tsofrq).ne.0 .and. &
mod(nstep+1,tsofrq).ne.0 ) ) then
do k=1,nlayer
temp(i,j,k,n)=t1dn(k)
enddo
else !include tofset drift correction
do k=1,nlayer
temp(i,j,k,n)=t1dn(k) + baclin*max(2,tsofrq)*tofset
enddo
endif !without:with tofset
!
! --- t-like tracer solution
do ktr= 1,ntracr
if (trcflg(ktr).eq.2) then
do k=1,nlayer
rhs(k)=tr1do(k,ktr)
enddo
call tridmat(tcu,tcc,tcl,nlayer,hm,rhs,tr1do,tr1dn,difft, i,j)
do k=1,nlayer
tracer(i,j,k,n,ktr)=tr1dn(k,ktr)
enddo
endif
enddo !ktr
!
! --- s solution and th3d reset
call tridcof(diffs,tri,nlayer,tcu,tcc,tcl)
do k=1,nlayer
rhs(k)=s1do(k)
enddo
call tridmat(tcu,tcc,tcl,nlayer,hm,rhs,s1do,s1dn,diffs, i,j)
if ( sofset.eq.0.0 .or. &
(mod(nstep ,tsofrq).ne.0 .and. &
mod(nstep+1,tsofrq).ne.0 ) ) then
do k=1,nlayer
saln(i,j,k,n)=s1dn(k)
th3d(i,j,k,n)=sig(temp(i,j,k,n),saln(i,j,k,n))-thbase
enddo
else !include sofset drift correction
do k=1,nlayer
saln(i,j,k,n)=s1dn(k) + baclin*max(2,tsofrq)*sofset
th3d(i,j,k,n)=sig(temp(i,j,k,n),saln(i,j,k,n))-thbase
enddo
endif !without:with sofset
!
! --- standard tracer solution
if (ntracr.gt.0) then
call tridcof(difftr,tri,nlayer,tcu,tcc,tcl)
endif
do ktr= 1,ntracr
if (trcflg(ktr).ne.2) then
do k=1,nlayer
rhs(k)=tr1do(k,ktr)
enddo
call tridmat(tcu,tcc,tcl,nlayer, &
hm,rhs,tr1do(1,ktr),tr1dn(1,ktr),difftr, i,j)
do k=1,nlayer
tracer(i,j,k,n,ktr)=tr1dn(k,ktr)
enddo
endif
enddo !ktr
!
!diag if (i.eq.itest.and.j.eq.jtest) write (lp,102) &
!diag (nstep,i+i0,j+j0,k, &
!diag difft(k),t1do(k),t1dn(k),t1dn(k)-t1do(k), &
!diag diffs(k),s1do(k),s1dn(k),s1dn(k)-s1do(k),k=1,nlayer)
!
return
!
101 format(28x,' thick viscty t diff s diff ' &
/(i9,2i6,i4,2x,4f10.2))
102 format(25x, &
' diff t t old t new t chng diff s s old s new s chng' &
/(i9,2i6,i4,1x,8f8.3))
end
subroutine diapf1uij(m,n, i,j)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
!
! --- hycom version 1.0
! --- KPP-style implicit interior diapycnal mixing
implicit none
!
integer m,n, i,j
!
! -----------------------------------------------------------------
! --- diapycnal mixing, single i,j point, momentum at u grid points
! -----------------------------------------------------------------
!
! --- local 1-d arrays for matrix inversion
real u1do(kdm+1),u1dn(kdm+1), &
diffm(kdm+1),zm(kdm+1),hm(kdm),dzb(kdm)
!
! --- tridiagonal matrix solution arrays
real tri(kdm,0:1) ! dt/dz/dz factors in trid. matrix
real tcu(kdm), & ! upper coeff for (k-1) on k line of trid.matrix
tcc(kdm), & ! central ... (k ) ..
tcl(kdm), & ! lower ..... (k-1) ..
rhs(kdm) ! right-hand-side terms
!
real presu,froglp
integer k,ka,kmask(idm),nlayer,mixflg
!
froglp=.5*max(2,mixfrq)
!
presu=0.
kmask(1)=0
mixflg=0
do k=1,kk+1
ka=min(k,kk)
if (dpu(i,j,ka,n).lt.tencm.or.k.eq.kk+1) kmask(1)=1
if (presu.lt.depthu(i,j)-tencm.and.kmask(1).eq.0) then
diffm(k+1)=.5*froglp*(vcty(i,j,k+1)+vcty(i-1,j,k+1))
if (diffm(k+1).gt.0.) mixflg=mixflg+1
u1do(k)=u(i,j,k,n)
hm(k)=dpu(i,j,k,n)*qonem
if (k.eq.1) then
zm(k)=-.5*hm(k)
else
zm(k)=zm(k-1)-.5*(hm(k-1)+hm(k))
endif
presu=presu+dpu(i,j,k,n)
nlayer=k
elseif (k.eq.nlayer+1) then
diffm(k)=0.
u1do(k)=u1do(k-1)
zm(k)=zm(k-1)-.5*hm(k-1)
endif
enddo
if (mixflg.le.1) return
!
! --- compute factors for coefficients of tridiagonal matrix elements.
do k=1,nlayer
dzb(k)=zm(k)-zm(k+1)
enddo
!
tri(1,1)=delt1/(hm(1)*dzb(1))
tri(1,0)=0.
do k=2,nlayer
tri(k,1)=delt1/(hm(k)*dzb(k))
tri(k,0)=delt1/(hm(k)*dzb(k-1))
enddo
!
! --- solve the diffusion equation
call tridcof(diffm,tri,nlayer,tcu,tcc,tcl)
do k=1,nlayer
rhs(k)= u1do(k)
enddo
call tridmat(tcu,tcc,tcl,nlayer,hm,rhs,u1do,u1dn,diffm, i,j)
do k=1,nlayer
u(i,j,k,n)=u1dn(k)
enddo
!
!diag if (i.eq.itest.and.j.eq.jtest) write (lp,106) &
!diag (nstep,i+i0,j+j0,k,hm(k),u1do(k),u1dn(k),k=1,nlayer)
!
return
106 format(26x,' thick u old u new'/(i9,2i6,i4,1x,f10.3,2f8.3))
end
subroutine diapf1vij(m,n, i,j)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
!
! --- hycom version 1.0
! --- KPP-style implicit interior diapycnal mixing
implicit none
!
integer m,n, i,j
!
! -----------------------------------------------------------------
! --- diapycnal mixing, single i,j point, momentum at v grid points
! -----------------------------------------------------------------
!
! --- local 1-d arrays for matrix inversion
real v1do(kdm+1),v1dn(kdm+1), &
diffm(kdm+1),zm(kdm+1),hm(kdm),dzb(kdm)
!
! --- tridiagonal matrix solution arrays
real tri(kdm,0:1) ! dt/dz/dz factors in trid. matrix
real tcu(kdm), & ! upper coeff for (k-1) on k line of trid.matrix
tcc(kdm), & ! central ... (k ) ..
tcl(kdm), & ! lower ..... (k-1) ..
rhs(kdm) ! right-hand-side terms
!
real presv,froglp
integer k,ka,kmask(idm),nlayer,mixflg
!
froglp=.5*max(2,mixfrq)
!
presv=0.
kmask(1)=0
mixflg=0
do k=1,kk+1
ka=min(k,kk)
if (dpv(i,j,ka,n).lt.tencm.or.k.eq.kk+1) kmask(1)=1
if (presv.lt.depthv(i,j)-tencm.and.kmask(1).eq.0) then
diffm(k+1)=.5*froglp*(vcty(i,j,k+1)+vcty(i,j-1,k+1))
if (diffm(k+1).gt.0.) mixflg=mixflg+1
v1do(k)=v(i,j,k,n)
hm(k)=dpv(i,j,k,n)*qonem
if (k.eq.1) then
zm(k)=-.5*hm(k)
else
zm(k)=zm(k-1)-.5*(hm(k-1)+hm(k))
endif
presv=presv+dpv(i,j,k,n)
nlayer=k
elseif (k.eq.nlayer+1) then
diffm(k)=0.
v1do(k)=v1do(k-1)
zm(k)=zm(k-1)-.5*hm(k-1)
endif
enddo
if (mixflg.le.1) return
!
! --- compute factors for coefficients of tridiagonal matrix elements.
!
do k=1,nlayer
dzb(k)=zm(k)-zm(k+1)
enddo
!
tri(1,1)=delt1/(hm(1)*dzb(1))
tri(1,0)=0.
do k=2,nlayer
tri(k,1)=delt1/(hm(k)*dzb(k))
tri(k,0)=delt1/(hm(k)*dzb(k-1))
enddo
!
! --- solve the diffusion equation
call tridcof(diffm,tri,nlayer,tcu,tcc,tcl)
do k=1,nlayer
rhs(k)=v1do(k)
enddo
call tridmat(tcu,tcc,tcl,nlayer,hm,rhs,v1do,v1dn,diffm, i,j)
do k=1,nlayer
v(i,j,k,n)=v1dn(k)
enddo
!
!diag if (i.eq.itest.and.j.eq.jtest) write (lp,107) &
!diag (nstep,i+i0,j+j0,k,hm(k),v1do(k),v1dn(k),k=1,nlayer)
!
return
107 format(26x,' thick v old v new'/(i9,2i6,i4,1x,f10.3,2f8.3))
end
!
subroutine diapf2(m,n)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
!
! --- hycom version 1.0
! --- MICOM-style explict interior diapycnal mixing for hybrid coordinates
implicit none
!
integer m,n
!
integer j
!
if (diapyc.eq.0. .or. (mod(nstep ,mixfrq).ne.0 .and. &
mod(nstep+1,mixfrq).ne.0)) return
!diag write (lp,'(i9,3x,a)') nstep,'entering d i a p f l'
!
!$OMP PARALLEL DO PRIVATE(j) &
!$OMP SHARED(m,n) &
!$OMP SCHEDULE(STATIC,jblk)
do 31 j=1,jj
call diapf2j(m,n, j)
31 continue
!$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)
!
!diag write (lp,'(i9,3x,a)') nstep,'exiting d i a p f l'
return
end
subroutine diapf2j(m,n, j)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
implicit none
!
integer m,n, j
!
integer i,k,k1,k2,ka,kmin(idm),kmax(idm),ktr
real flxu(idm,kdm),flxl(idm,kdm),pdot(idm,kdm),flngth(idm,kdm), &
ennsq,alfa,beta,q,qmin,qmax,amount,froglp,delp, &
alfadt1,alfadt2,betads1,betads2,plev, &
trflxu(idm,0:kdm+1,mxtrcr), &
trflxl(idm,0:kdm+1,mxtrcr),cliptr(idm,mxtrcr), &
tflxu(idm,0:kdm+1), tflxl(idm,0:kdm+1),clipt( idm), &
sflxu(idm,0:kdm+1), sflxl(idm,0:kdm+1),clips( idm), &
told(idm,2),sold(idm,2),trold(idm,2,mxtrcr)
! real totem(idm),tosal(idm),tndcyt,tndcys ! col.integrals (diag.use only)
!
real small
parameter (small=1.e-6)
!
# include "stmt_fns.h"
!
! --- -------------------------------
! --- diapycnal mixing, single j-row.
! --- -------------------------------
!
! --- if mixfrq > 1, apply mixing algorithm to both time levels
froglp=max(2,mixfrq)
!
do i=1,ii
if (SEA_P) then
!
! --- t/s conservation diagnostics (optional):
! totem(i)=0.
! tosal(i)=0.
! do k=1,kk
! totem(i)=totem(i)+temp(i,j,k,n)*dp(i,j,k,n)
! tosal(i)=tosal(i)+saln(i,j,k,n)*dp(i,j,k,n)
! enddo
!
do k=1,kk
p(i,j,k+1)=p(i,j,k)+dp(i,j,k,n)
enddo !k
!
sold(i,1)=saln(i,j,kk,n)
told(i,1)=temp(i,j,kk,n)
tflxl(i, 0)=0.
tflxu(i,kk+1)=0.
sflxl(i, 0)=0.
sflxu(i,kk+1)=0.
do ktr= 1,ntracr
trold( i, 1,ktr)=tracer(i,j,kk,n,ktr)
trflxl(i, 0,ktr)=0.
trflxu(i,kk+1,ktr)=0.
enddo !ktr
!
!diag if (i.eq.itest.and.j.eq.jtest) &
!diag write (lp,'(i9,2i6,3x,a/(i36,4f10.3))') nstep,i+i0,j+j0, &
!diag 'before diapf2: thickness salinity temperature density', &
!diag (k,dp(i,j,k,n)*qonem,saln(i,j,k,n), &
!diag temp(i,j,k,n),th3d(i,j,k,n)+thbase,k=1,kk)
!
kmin(i)=kk+1
kmax(i)=1
!
do k=2,kk
!
! --- locate lowest mass-containing layer and upper edge of stratified region
if (p(i,j,k).lt.p(i,j,kk+1)-onemm) then
kmax(i)=k
if (kmin(i).eq.kk+1 .and. &
th3d(i,j,k,n).gt.th3d(i,j,k-1,n)+sigjmp) then
kmin(i)=k
endif
endif
enddo !k
!
!diag if (j.eq.jtest.and.itest.ge.ifp(j,l).and.itest.le.ilp(j,l)) &
!diag write (lp,'(i9,2i6,a,2i4)') &
!diag nstep,itest+i0,j+j0,' kmin,kmax =',kmin(itest),kmax(itest)
!
! --- find buoyancy frequency for each layer
!
do k=2,kk-1
k1=k-1
k2=k+1
!
if (k.gt.kmin(i) .and. k.lt.kmax(i)) then
! --- ennsq = buoy.freq.^2 / g^2
if (locsig) then
alfadt1=dsiglocdt(ahalf*(temp(i,j,k1,n)+ &
temp(i,j,k ,n) ), &
ahalf*(saln(i,j,k1,n)+ &
saln(i,j,k, n) ),p(i,j,k))* &
(temp(i,j,k1,n)- &
temp(i,j,k, n) )
betads1=dsiglocds(ahalf*(temp(i,j,k1,n)+ &
temp(i,j,k ,n) ), &
ahalf*(saln(i,j,k1,n)+ &
saln(i,j,k, n) ),p(i,j,k))* &
(saln(i,j,k1,n)- &
saln(i,j,k, n) )
alfadt2=dsiglocdt(ahalf*(temp(i,j,k ,n)+ &
temp(i,j,k2,n) ), &
ahalf*(saln(i,j,k ,n)+ &
saln(i,j,k2,n) ),p(i,j,k2))* &
(temp(i,j,k, n)- &
temp(i,j,k2,n) )
betads2=dsiglocdt(ahalf*(temp(i,j,k ,n)+ &
temp(i,j,k2,n) ), &
ahalf*(saln(i,j,k ,n)+ &
saln(i,j,k2,n) ),p(i,j,k2))* &
(saln(i,j,k, n)- &
saln(i,j,k2,n) )
ennsq=-min(0.,min(alfadt1+betads1,alfadt2+betads2)) &
/max(p(i,j,k2)-p(i,j,k),onem)
else
ennsq=max(0.,min(th3d(i,j,k2,n)-th3d(i,j,k ,n), &
th3d(i,j,k ,n)-th3d(i,j,k1,n))) &
/max(p(i,j,k2)-p(i,j,k),onem)
endif
! --- store (exch.coeff x buoy.freq.^2 / g x time step) in -flngth-
! --- (dimensions of flngth: length in pressure units)
! -----------------------------------------------------------------------
! --- use the following if exch.coeff. = diapyc / buoyancy frequency
flngth(i,k)=diapyc*sqrt(ennsq) * baclin*froglp * onem
! -----------------------------------------------------------------------
! --- use the following if exch.coeff. = diapyc
!cc flngth(i,k)=diapyc*ennsq*g * baclin*froglp * onem
! -----------------------------------------------------------------------
!
endif
enddo !k
!
! --- find t/s fluxes at the upper and lower interface of each layer
! --- (compute only the part common to t and s fluxes)
!
do k=1,kk
flxu(i,k)=0.
flxl(i,k)=0.
!
if (k.gt.kmin(i) .and. k.lt.kmax(i)) then
!
if (locsig) then
plev=p(i,j,k)+0.5*dp(i,j,k,n)
alfa=-svref*dsiglocdt(temp(i,j,k,n),saln(i,j,k,n),plev)
beta= svref*dsiglocds(temp(i,j,k,n),saln(i,j,k,n),plev)
else
alfa=-svref*dsigdt(temp(i,j,k,n),saln(i,j,k,n))
beta= svref*dsigds(temp(i,j,k,n),saln(i,j,k,n))
endif
!
flxu(i,k)=flngth(i,k)/ &
max(beta*(saln(i,j,k,n)-saln(i,j,k-1,n)) &
-alfa*(temp(i,j,k,n)-temp(i,j,k-1,n)),small)
flxl(i,k)=flngth(i,k)/ &
max(beta*(saln(i,j,k+1,n)-saln(i,j,k,n)) &
-alfa*(temp(i,j,k+1,n)-temp(i,j,k,n)),small)
!
q=min(1.,.5*min(p(i,j,k)-p(i,j,k-1),p(i,j,k+2)-p(i,j,k+1))/ &
max(flxu(i,k),flxl(i,k),epsil))
!
!diag if (q.ne.1.) write (lp,'(i9,2i6,i4,a,1p,2e10.2,0p,2f7.2,f5.2)') &
!diag nstep,i+i0,j+j0,k,' flxu/l,dpu/l,q=',flxu(i,k),flxl(i,k), &
!diag (p(i,j,k)-p(i,j,k-1))*qonem,(p(i,j,k+2)-p(i,j,k+1))*qonem,q
!
flxu(i,k)=flxu(i,k)*q
flxl(i,k)=flxl(i,k)*q
!
endif ! kmin < k < kmax
!
!diag if (i.eq.itest.and.j.eq.jtest.and.k.ge.kmin(i).and.k.le.kmax(i)) &
!diag write (lp,'(i9,2i6,i4,3x,a/22x,f9.3,2f7.3,1p,3e10.3)') &
!diag nstep,i+i0,j+j0,k, &
!diag 'thknss temp saln flngth flxu flxl', &
!diag dp(i,j,k,n)*qonem,temp(i,j,k,n),saln(i,j,k,n),flngth(i,k), &
!diag flxu(i,k)*qonem,flxl(i,k)*qonem
!
enddo !k
!
! --- determine mass flux -pdot- implied by t/s fluxes.
!
do k=1,kk
if (k.gt.kmin(i) .and. k.le.kmax(i)) then
pdot(i,k)=flxu(i,k)-flxl(i,k-1)
else
pdot(i,k)=0.
endif
enddo !k
!
! --- convert flxu,flxl into actual t/s (and tracer) fluxes
!
do k=1,kk
tflxu(i,k)=0.
tflxl(i,k)=0.
sflxu(i,k)=0.
sflxl(i,k)=0.
if (k.gt.kmin(i) .and. k.lt.kmax(i)) then
tflxu(i,k)=flxu(i,k)*temp(i,j,k-1,n)
sflxu(i,k)=flxu(i,k)*saln(i,j,k-1,n)
!
tflxl(i,k)=flxl(i,k)*temp(i,j,k+1,n)
sflxl(i,k)=flxl(i,k)*saln(i,j,k+1,n)
endif
do ktr= 1,ntracr
trflxu(i,k,ktr)=0.
trflxl(i,k,ktr)=0.
if (k.gt.kmin(i) .and. k.lt.kmax(i)) then
trflxu(i,k,ktr)=flxu(i,k)*tracer(i,j,k-1,n,ktr)
trflxl(i,k,ktr)=flxl(i,k)*tracer(i,j,k+1,n,ktr)
endif
enddo !ktr
enddo !k
!
do ktr= 1,ntracr
cliptr(i,ktr)=0.
enddo !ktr
clipt( i)=0.
clips( i)=0.
!
! --- update interface pressure and layer temperature/salinity
do k=kk,1,-1
ka=max(1,k-1)
!
sold(i,2)=sold(i,1)
sold(i,1)=saln(i,j,k,n)
told(i,2)=told(i,1)
told(i,1)=temp(i,j,k,n)
do ktr= 1,ntracr
trold(i,2,ktr)=trold( i,1, ktr)
trold(i,1,ktr)=tracer(i,j,k,n,ktr)
enddo
!
dpo(i,j,k,n)=dp(i,j,k,n)
p(i,j,k)=p(i,j,k)-pdot(i,k)
dp(i,j,k,n)=p(i,j,k+1)-p(i,j,k)
!
if (k.ge.kmin(i) .and. k.le.kmax(i)) then
delp=dp(i,j,k,n)
if (delp.gt.0.) then
amount=temp(i,j,k,n)*dpo(i,j,k,n) &
-(tflxu(i,k+1)-tflxu(i,k)+tflxl(i,k-1)-tflxl(i,k))
q=amount
qmax=max(temp(i,j,ka,n),told(i,1),told(i,2))
qmin=min(temp(i,j,ka,n),told(i,1),told(i,2))
amount=max(qmin*delp,min(amount,qmax*delp))
clipt(i)=clipt(i)+(q-amount)
temp(i,j,k,n)=amount/delp
!
amount=saln(i,j,k,n)*dpo(i,j,k,n) &
-(sflxu(i,k+1)-sflxu(i,k)+sflxl(i,k-1)-sflxl(i,k))
q=amount
qmax=max(saln(i,j,ka,n),sold(i,1),sold(i,2))
qmin=min(saln(i,j,ka,n),sold(i,1),sold(i,2))
amount=max(qmin*delp,min(amount,qmax*delp))
clips(i)=clips(i)+(q-amount)
saln(i,j,k,n)=amount/delp
!
do ktr= 1,ntracr
amount=tracer(i,j,k,n,ktr)*dpo(i,j,k,n) &
-(trflxu(i,k+1,ktr)-trflxu(i,k,ktr)+ &
trflxl(i,k-1,ktr)-trflxl(i,k,ktr))
q=amount
qmax=max(tracer(i,j,ka,n,ktr),trold(i,1,ktr), &
trold(i,2,ktr))
qmin=min(tracer(i,j,ka,n,ktr),trold(i,1,ktr), &
trold(i,2,ktr))
amount=max(qmin*delp,min(amount,qmax*delp))
cliptr(i,ktr)=cliptr(i,ktr)+(q-amount)
tracer(i,j,k,n,ktr)=amount/delp
enddo !ktr
endif
endif
enddo !k
!
clipt(i)=clipt(i)/pbot(i,j) + baclin*froglp*tofset
clips(i)=clips(i)/pbot(i,j) + baclin*froglp*sofset
do ktr= 1,ntracr
cliptr(i,ktr)=cliptr(i,ktr)/pbot(i,j)
enddo !ktr
!
do k=1,kk
!
! --- restore 'clipped' and 'offset' t/s amount to column
temp(i,j,k,n)=temp(i,j,k,n)+clipt(i)
saln(i,j,k,n)=saln(i,j,k,n)+clips(i)
th3d(i,j,k,n)=sig(temp(i,j,k,n),saln(i,j,k,n))-thbase
do ktr= 1,ntracr
tracer(i,j,k,n,ktr)=tracer(i,j,k,n,ktr)+cliptr(i,ktr)
enddo !ktr
!
diaflx(i,j,k)=diaflx(i,j,k)+(dp(i,j,k,n)-dpo(i,j,k,n)) ! diapyc.flx.
! --- make sure p is computed from dp, not the other way around (roundoff!)
p(i,j,k+1)=p(i,j,k)+dp(i,j,k,n)
enddo !k
!
! --- t/s conservation diagnostics (optional):
! tndcyt=-totem(i)
! tndcys=-tosal(i)
! do k=1,kk
! tndcyt=tndcyt+temp(i,j,k,n)*dp(i,j,k,n)
! tndcys=tndcys+saln(i,j,k,n)*dp(i,j,k,n)
! enddo
! if (abs(tndcyt/totem(i)).gt.1.e-11)
! . write (lp,100) i,j,' diapf2 temp.col.intgl.:',totem(i),tndcyt,
! . clipt(i)
! if (abs(tndcys/tosal(i)).gt.1.e-11)
! . write (lp,100)