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mxkprf.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 mxkprf(m,n)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
use mod_pipe ! HYCOM debugging interface
!
! --- hycom version 2.1
implicit none
!
integer m,n
!
! ---------------------------------------------------------
! --- k-profile vertical mixing models
! --- a) large, mc williams, doney kpp vertical diffusion
! --- b) mellor-yamada 2.5 vertical diffusion
! --- c) giss vertical diffusion
! ---------------------------------------------------------
!
logical, parameter :: lpipe_mxkprf =.false.
logical, parameter :: ldebug_dpmixl=.false.
!
real delp,dpmx,hblmax,sigmlj,thsur,thtop,alfadt,betads,zintf, &
thjmp(kdm),thloc(kdm)
integer i,j,k
character text*12
!
# include "stmt_fns.h"
!
if (mxlmy) then
call xctilr(u( 1-nbdy,1-nbdy,1,m),1,kk, 1,1, halo_uv)
call xctilr(u( 1-nbdy,1-nbdy,1,n),1,kk, 1,1, halo_uv)
call xctilr(v( 1-nbdy,1-nbdy,1,m),1,kk, 1,1, halo_vv)
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)
call xctilr(ubavg( 1-nbdy,1-nbdy, m),1, 1, 1,1, halo_uv)
call xctilr(vbavg( 1-nbdy,1-nbdy, m),1, 1, 1,1, halo_vv)
else
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)
endif
!
! --- except for KPP, surface boundary layer is the mixed layer
if (mxlgiss .or. mxlmy) then
hblmax = bldmax*onem
!$OMP PARALLEL DO PRIVATE(j,i) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
do i=1,ii
if (SEA_P) then
dpbl(i,j) = 0.5*(dpmixl(i,j,n)+ &
dpmixl(i,j,m) ) !reduce time splitting
dpbl(i,j) = min( dpbl(i,j), hblmax ) !may not be needed
endif !ip
enddo !i
enddo !j
endif !mxlgiss,mxlmy
!
! --- diffisuvity/viscosity calculation
!
!$OMP PARALLEL DO PRIVATE(j) &
!$OMP SHARED(m,n) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
call mxkprfaj(m,n, j)
enddo
!$OMP END PARALLEL DO
!
! --- optional spatial smoothing of viscosity and diffusivities on interior
! --- interfaces.
!
if (difsmo.gt.0) then
util6(1:ii,1:jj) = klist(1:ii,1:jj)
call xctilr(util6, 1, 1, 2,2, halo_ps)
! --- update halo on all layers for simplicity
call xctilr(dift(1-nbdy,1-nbdy,2),1,kk-1, 2,2, halo_ps)
call xctilr(difs(1-nbdy,1-nbdy,2),1,kk-1, 2,2, halo_ps)
call xctilr(vcty(1-nbdy,1-nbdy,2),1,kk-1, 2,2, halo_ps)
do k=2,min(difsmo+1,kk)
call psmooth_dif(dift(1-nbdy,1-nbdy,k),util6,k,2,0,ip, util1)
call psmooth_dif(difs(1-nbdy,1-nbdy,k),util6,k,2,0,ip, util1)
call psmooth_dif(vcty(1-nbdy,1-nbdy,k),util6,k,2,1,ip, util1)
enddo
call xctilr(vcty(1-nbdy,1-nbdy,kk+1),1, 1, 1,1, halo_ps)
else
call xctilr(vcty(1-nbdy,1-nbdy, 2),1,kk, 1,1, halo_ps)
endif
!
if (lpipe .and. lpipe_mxkprf) then
! --- compare two model runs.
util6(1:ii,1:jj) = klist(1:ii,1:jj)
write (text,'(a12)') 'klist '
call pipe_compare_sym1(util6,ip,text)
if (mxlmy) then
do k= 0,kk+1
write (text,'(a9,i3)') 'q2 k=',k
call pipe_compare_sym1(q2( 1-nbdy,1-nbdy,k,n),ip,text)
write (text,'(a9,i3)') 'q2l k=',k
call pipe_compare_sym1(q2l(1-nbdy,1-nbdy,k,n),ip,text)
write (text,'(a9,i3)') 'difqmy k=',k
call pipe_compare_sym1(difqmy(1-nbdy,1-nbdy,k),ip,text)
write (text,'(a9,i3)') 'diftmy k=',k
call pipe_compare_sym1(diftmy(1-nbdy,1-nbdy,k),ip,text)
write (text,'(a9,i3)') 'vctymy k=',k
call pipe_compare_sym1(vctymy(1-nbdy,1-nbdy,k),ip,text)
enddo
endif
do k= 1,kk+1
write (text,'(a9,i3)') 'dift k=',k
call pipe_compare_sym1(dift(1-nbdy,1-nbdy,k),ip,text)
write (text,'(a9,i3)') 'difs k=',k
call pipe_compare_sym1(difs(1-nbdy,1-nbdy,k),ip,text)
write (text,'(a9,i3)') 'vcty k=',k
call pipe_compare_sym1(vcty(1-nbdy,1-nbdy,k),ip,text)
enddo
endif
!
! --- final mixing of variables at p points
!
!$OMP PARALLEL DO PRIVATE(j) &
!$OMP SHARED(m,n) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
call mxkprfbj(m,n, j)
enddo
!$OMP END PARALLEL DO
!
! --- final velocity mixing at u,v points
!
!$OMP PARALLEL DO PRIVATE(j) &
!$OMP SHARED(m,n) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
call mxkprfcj(m,n, j)
enddo
!$OMP END PARALLEL DO
!
! --- mixed layer diagnostics
!
if (diagno .or. mxlgiss .or. mxlmy) then
!
! --- diagnose new mixed layer depth based on density jump criterion
!$OMP PARALLEL DO PRIVATE(j,i,k, &
!$OMP sigmlj,thsur,thtop,alfadt,betads,zintf, &
!$OMP thjmp,thloc) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
do i=1,ii
if (SEA_P) then
!
! --- depth of mixed layer base set to interpolated depth where
! --- the density jump is equivalent to a tmljmp temperature jump.
! --- this may not vectorize, but is used infrequently.
if (locsig) then
sigmlj = -tmljmp*dsiglocdt(temp(i,j,1,n), &
saln(i,j,1,n),p(i,j,1))
else
sigmlj = -tmljmp*dsigdt(temp(i,j,1,n),saln(i,j,1,n))
endif
sigmlj = max(sigmlj,tmljmp*0.03) !cold-water fix
!
if (ldebug_dpmixl .and. i.eq.itest.and.j.eq.jtest) then
write (lp,'(i9,2i5,i3,a,2f7.4)') &
nstep,i+i0,j+j0,k, &
' sigmlj =', &
-tmljmp*dsigdt(temp(i,j,1,n),saln(i,j,1,n)), &
sigmlj
endif
!
thloc(1)=th3d(i,j,1,n)
do k=2,klist(i,j)
if (locsig) then
alfadt=dsiglocdt(ahalf*(temp(i,j,k-1,n)+ &
temp(i,j,k, n) ), &
ahalf*(saln(i,j,k-1,n)+ &
saln(i,j,k, n) ), &
p(i,j,k) )* &
(temp(i,j,k-1,n)-temp(i,j,k, n))
betads=dsiglocds(ahalf*(temp(i,j,k-1,n)+ &
temp(i,j,k, n) ), &
ahalf*(saln(i,j,k-1,n)+ &
saln(i,j,k, n) ), &
p(i,j,k) )* &
(saln(i,j,k-1,n)-saln(i,j,k, n))
thloc(k)=thloc(k-1)-alfadt-betads
else
thloc(k)=th3d(i,j,k,n)
endif
enddo !k
dpmixl(i,j,n) = -zgrid(i,j,klist(i,j)+1)*onem !bottom
thjmp(1) = 0.0
thsur = thloc(1)
do k=2,klist(i,j)
thsur = min(thloc(k),thsur) !ignore surface inversion
thjmp(k) = max(thloc(k)-thsur, &
thjmp(k-1)) !stable profile simplifies the code
!
if (ldebug_dpmixl .and. i.eq.itest.and.j.eq.jtest) then
write (lp,'(i9,2i5,i3,a,2f7.3,f7.4,f9.2)') &
nstep,i+i0,j+j0,k, &
' th,thsur,jmp,zc =', &
thloc(k),thsur,thjmp(k),-zgrid(i,j,k)
endif
!
if (thjmp(k).ge.sigmlj) then
!
! --- find the density on the interface between layers
! --- k-1 and k, using the same cubic polynominal as PQM
!
if (k.eq.2) then
! --- linear between cell centers
thtop = thjmp(1) + (thjmp(2)-thjmp(1))* &
dp(i,j,1,n)/ &
max( dp(i,j,1,n)+ &
dp(i,j,2,n) , &
onemm )
elseif (k.eq.klist(i,j)) then
! --- linear between cell centers
thtop = thjmp(k) + (thjmp(k-1)-thjmp(k))* &
dp(i,j,k,n)/ &
max( dp(i,j,k, n)+ &
dp(i,j,k-1,n) , &
onemm )
else
thsur = min(thloc(k+1),thsur)
thjmp(k+1) = max(thloc(k+1)-thsur, &
thjmp(k))
zintf = zgrid(i,j,k-1) - 0.5*dp(i,j,k-1,n)*qonem
thtop = thjmp(k-2)* &
((zintf -zgrid(i,j,k-1))* &
(zintf -zgrid(i,j,k ))* &
(zintf -zgrid(i,j,k+1)) )/ &
((zgrid(i,j,k-2)-zgrid(i,j,k-1))* &
(zgrid(i,j,k-2)-zgrid(i,j,k ))* &
(zgrid(i,j,k-2)-zgrid(i,j,k+1)) ) + &
thjmp(k-1)* &
((zintf -zgrid(i,j,k-2))* &
(zintf -zgrid(i,j,k ))* &
(zintf -zgrid(i,j,k+1)) )/ &
((zgrid(i,j,k-1)-zgrid(i,j,k-2))* &
(zgrid(i,j,k-1)-zgrid(i,j,k ))* &
(zgrid(i,j,k-1)-zgrid(i,j,k+1)) ) + &
thjmp(k )* &
((zintf -zgrid(i,j,k-2))* &
(zintf -zgrid(i,j,k-1))* &
(zintf -zgrid(i,j,k+1)) )/ &
((zgrid(i,j,k )-zgrid(i,j,k-2))* &
(zgrid(i,j,k )-zgrid(i,j,k-1))* &
(zgrid(i,j,k )-zgrid(i,j,k+1)) ) + &
thjmp(k+1)* &
((zintf -zgrid(i,j,k-2))* &
(zintf -zgrid(i,j,k-1))* &
(zintf -zgrid(i,j,k )) )/ &
((zgrid(i,j,k+1)-zgrid(i,j,k-2))* &
(zgrid(i,j,k+1)-zgrid(i,j,k-1))* &
(zgrid(i,j,k+1)-zgrid(i,j,k )) )
thtop = max( thjmp(k-1), min( thjmp(k), thtop ) )
!
if (ldebug_dpmixl .and. &
i.eq.itest.and.j.eq.jtest) then
write (lp,'(i9,2i5,i3,a,2f7.3,f7.4,f9.2)') &
nstep,i+i0,j+j0,k, &
' thi,thsur,jmp,zi =', &
thtop,thsur,thjmp(k),-zintf
endif
endif !k.eq.2:k.eq.klist:else
!
if (thtop.ge.sigmlj) then
!
! --- in bottom half of layer k-1
!
dpmixl(i,j,n) = &
-zgrid(i,j,k-1)*onem + &
0.5*dp(i,j,k-1,n)* &
(sigmlj+epsil-thjmp(k-1))/ &
(thtop +epsil-thjmp(k-1))
else
!
! --- in top half of layer k
!
dpmixl(i,j,n) = &
-zgrid(i,j,k)*onem - &
0.5*dp(i,j,k,n)* &
(1.0-(sigmlj +epsil-thtop)/ &
(thjmp(k)+epsil-thtop) )
endif !part of layer
!
if (ldebug_dpmixl .and. &
i.eq.itest.and.j.eq.jtest) then
write (lp,'(i9,2i5,i3,a,f7.3,f7.4,f9.2)') &
nstep,i+i0,j+j0,k, &
' thsur,top,dpmixl =', &
thsur,thtop,dpmixl(i,j,n)*qonem
endif
!
exit !calculated dpmixl
endif !found dpmixl layer
enddo !k
endif !ip
enddo !i
enddo !j
!
!$OMP END PARALLEL DO
!
! --- smooth the mixed layer (might end up below the bottom).
call psmooth(dpmixl(1-nbdy,1-nbdy,n),0,0,ip, util1)
!
if (ldebug_dpmixl) then
call xcsync(flush_lp)
endif
!
endif !diagno .or. mxlgiss .or. mxlmy
!
if (diagno) then
!
! --- calculate bulk mixed layer t, s, theta
!
!$OMP PARALLEL DO PRIVATE(j,i,k,delp) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
do i=1,ii
if (SEA_P) then
dpmixl(i,j,n)=min(dpmixl(i,j,n),p(i,j,kk+1))
dpmixl(i,j,m)= dpmixl(i,j,n)
delp=min(p(i,j,2),dpmixl(i,j,n))
tmix(i,j)=delp*temp(i,j,1,n)
smix(i,j)=delp*saln(i,j,1,n)
do k=2,kk
delp=min(p(i,j,k+1),dpmixl(i,j,n)) &
-min(p(i,j,k ),dpmixl(i,j,n))
tmix(i,j)=tmix(i,j)+delp*temp(i,j,k,n)
smix(i,j)=smix(i,j)+delp*saln(i,j,k,n)
enddo
tmix(i,j)=tmix(i,j)/dpmixl(i,j,n)
smix(i,j)=smix(i,j)/dpmixl(i,j,n)
thmix(i,j)=sig(tmix(i,j),smix(i,j))-thbase
!
if (ldebug_dpmixl .and. &
i.eq.itest.and.j.eq.jtest) then
write (lp,'(i9,2i5,i3,a,f9.2)') &
nstep,i+i0,j+j0,k, &
' dpmixl =', &
dpmixl(i,j,n)*qonem
endif
!
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
!
call xctilr(p( 1-nbdy,1-nbdy,2),1,kk, 1,1, halo_ps)
call xctilr(dpmixl(1-nbdy,1-nbdy,n),1, 1, 1,1, halo_ps)
!
!$OMP PARALLEL DO PRIVATE(j,i,k,delp,dpmx) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
do i=1,ii
!
! --- calculate bulk mixed layer u
!
if (SEA_U) then
dpmx=dpmixl(i,j,n)+dpmixl(i-1,j,n)
delp=min(p(i,j,2)+p(i-1,j,2),dpmx)
umix(i,j)=delp*u(i,j,1,n)
do k=2,kk
delp= min(p(i,j,k+1)+p(i-1,j,k+1),dpmx) &
-min(p(i,j,k )+p(i-1,j,k ),dpmx)
umix(i,j)=umix(i,j)+delp*u(i,j,k,n)
enddo !k
umix(i,j)=umix(i,j)/dpmx
endif !iu
!
! --- calculate bulk mixed layer v
!
if (SEA_V) then
dpmx=dpmixl(i,j,n)+dpmixl(i,j-1,n)
delp=min(p(i,j,2)+p(i,j-1,2),dpmx)
vmix(i,j)=delp*v(i,j,1,n)
do k=2,kk
delp= min(p(i,j,k+1)+p(i,j-1,k+1),dpmx) &
-min(p(i,j,k )+p(i,j-1,k ),dpmx)
vmix(i,j)=vmix(i,j)+delp*v(i,j,k,n)
enddo !k
vmix(i,j)=vmix(i,j)/dpmx
endif !iv
enddo !i
enddo !j
!$OMP END PARALLEL DO
endif ! diagno
!
return
end
subroutine mxkprfaj(m,n, j)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
implicit none
!
integer m,n, j
!
! --- calculate viscosity and diffusivity
!
integer i
!
if (mxlkpp) then
do i=1,ii
if (SEA_P) then
call mxkppaij(m,n, i,j)
endif !ip
enddo !i
else if (mxlmy) then
do i=1,ii
if (SEA_P) then
call mxmyaij(m,n, i,j)
endif !ip
enddo !i
else if (mxlgiss) then
do i=1,ii
if (SEA_P) then
call mxgissaij(m,n, i,j)
endif !ip
enddo !i
endif
!
return
end
subroutine mxkprfbj(m,n, j)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
implicit none
!
integer m,n, j
!
! --- final mixing at p points
!
integer i
!
do i=1,ii
if (SEA_P) then
call mxkprfbij(m,n, i,j)
endif
enddo
!
return
end
subroutine mxkprfcj(m,n, j)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
implicit none
!
integer m,n, j
!
! --- final velocity mixing at u,v points
!
integer i
!
do i=1,ii
if (SEA_U) then
call mxkprfciju(m,n, i,j)
endif !iu
if (SEA_V) then
call mxkprfcijv(m,n, i,j)
endif !iv
enddo !i
!
return
end
!
subroutine mxkppaij(m,n, i,j)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
!
! --- hycom version 1.0
implicit none
!
integer m,n, i,j
!
! -------------------------------------------------------------
! --- kpp vertical diffusion, single j-row (part A)
! --- vertical coordinate is z negative below the ocean surface
!
! --- Large, W.C., J.C. McWilliams, and S.C. Doney, 1994: Oceanic
! --- vertical mixing: a review and a model with a nonlocal
! --- boundary layer paramterization. Rev. Geophys., 32, 363-403.
!
! --- quadratic interpolation and variable Cv from a presentation
! --- at the March 2003 CCSM Ocean Model Working Group Meeting
! --- on KPP Vertical Mixing by Gokhan Danabasoglu and Bill Large
! --- http://www.ccsm.ucar.edu/working_groups/Ocean/agendas/030320.html
! --- quadratic interpolation implemented here by 3-pt collocation,
! --- which is slightly different to the Danabasoglu/Large approach.
! -------------------------------------------------------------
!
real, parameter :: difmax = 9999.0e-4 !maximum diffusion/viscosity
real, parameter :: dp0bbl = 20.0 !truncation dist. for bot. b.l.
real, parameter :: ricrb = 0.45 !critical bulk Ri for bot. b.l.
real, parameter :: cv_max = 2.1 !maximum cv
real, parameter :: cv_min = 1.7 !minimum cv
real, parameter :: cv_bfq = 200.0 !cv scale factor
!
! local variables for kpp mixing
real delta ! fraction hbl lies beteen zgrid neighbors
real zrefmn ! nearsurface reference z, minimum
real zref ! nearsurface reference z
real wref,qwref ! nearsurface reference width,inverse
real uref ! nearsurface reference u
real vref ! nearsurface reference v
real bref ! nearsurface reference buoyancy
real swfrac(kdm+1) ! fractional surface shortwave radiation flux
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 swfrml ! fractional surface sw rad flux at ml base
real ritop(kdm) ! numerator of bulk richardson number
real dbloc(kdm+1) ! buoyancy jump across interface
real dvsq(kdm) ! squared current shear for bulk richardson no.
real zgridb(kdm+1) ! zgrid for bottom boundary layer
real hwide(kdm) ! layer thicknesses in m (minimum 1mm)
real dpmm(kdm) ! max(onemm,dp(i,j,:,n))
real qdpmm(kdm) ! 1.0/max(onemm,dp(i,j,:,n))
real qoneta ! 1.0/(1+eta), scale factor from dp to dp'
real pij(kdm+1) ! local copy of p(i,j,:)
real case ! 1 in case A; =0 in case B
real hbl ! boundary layer depth
real hbbl ! bottom boundary layer depth
real rib(3) ! bulk richardson number
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 stable ! = 1 in stable forcing; =0 in unstable
real dkm1(3) ! boundary layer diffusions at nbl-1 level
real gat1(3) ! shape functions at dnorm=1
real dat1(3) ! derivative of shape functions at dnorm=1
real blmc(kdm+1,3) ! boundary layer mixing coefficients
real bblmc(kdm+1,3) ! boundary layer mixing coefficients
real wm ! momentum velocity scale
real ws ! scalar velocity scale
real dnorm ! normalized depth
real tmn ! time averaged SST
real smn ! time averaged SSS
real dsgdt ! dsigdt(tmn,smn)
real buoyfs ! salinity surface buoyancy (into atmos.)
real buoyfl ! total surface buoyancy (into atmos.)
real buoysw ! shortwave surface buoyancy (into atmos.)
real bfsfc ! surface buoyancy forcing (into atmos.)
real bfbot ! bottom buoyancy forcing
real hekmanb ! bottom ekman layer thickness
real cormn4 ! = 4 x min. coriolis magnitude (at 4N, 4S)
real dflsiw ! internal wave diffusivity
real dflmiw ! internal wave viscosity
real dflbot(kdm+1) ! bottom intensified background viscosity
real bfq ! buoyancy frequency
real cvk ! ratio of buoyancy frequencies
real ahbl,bhbl,chbl,dhbl ! coefficients for quadratic hbl calculation
!
logical lhbl ! safe to use quadratic hbl calculation
!
integer nbl ! layer containing boundary layer base
integer nbbl ! layer containing bottom boundary layer base
integer kup2,kdn2,kup,kdn! bulk richardson number indices
!
! --- local 1-d arrays for matrix solution
real u1do(kdm+1),u1dn(kdm+1),v1do(kdm+1),v1dn(kdm+1),t1do(kdm+1), &
t1dn(kdm+1),s1do(kdm+1),s1dn(kdm+1), &
diffm(kdm+1),difft(kdm+1),diffs(kdm+1), &
ghat(kdm+1),zm(kdm+1),hm(kdm),dzb(kdm)
!
! --- local 1-d arrays for iteration loops
real uold(kdm+1),vold (kdm+1),told (kdm+1), &
sold(kdm+1),thold(kdm+1)
!
! --- 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 dtemp,dsaln,wq,wt,wz0,wz1,wz2,ratio,q,ghatflux, &
dvdzup,dvdzdn,viscp,difsp,diftp,f1,sigg,aa1,aa2,aa3,gm,gs,gt, &
dkmp2,dstar,hblmin,hblmax,sflux1,vtsq, &
vctyh,difsh,difth,zrefo,qspcifh,hbblmin,hbblmax, &
chl, &
x0,x1,x2,y0,y1,y2
!
integer k,k1,ka,kb,nlayer,ksave,iter,jrlv
!
integer iglobal,jglobal
!
# include "stmt_fns.h"
!
cormn4 = 4.0e-5 !4 x min. coriolis magnitude (at 4N, 4S)
!
iglobal=i0+i !for debugging
jglobal=j0+j !for debugging
if (iglobal+jglobal.eq.-99) then
write(lp,*) iglobal,jglobal !prevent optimization
endif
!
! --- internal wave diffusion/viscosity
dflsiw = diws(i,j)
dflmiw = diwm(i,j)
!
! --- locate lowest substantial mass-containing layer.
pij(1)=p(i,j,1)
do k=1,kk
dpmm( k) =max(onemm,dp(i,j,k,n))
qdpmm(k) =1.0/dpmm(k)
pij( k+1)=pij(k)+dp(i,j,k,n)
p(i,j,k+1)=pij(k+1)
enddo
do k=kk,1,-1
if (dpmm(k).gt.tencm) then
exit
endif
enddo
klist(i,j)=max(k,2) !always consider at least 2 layers
!
qoneta = 1.0/oneta(i,j,n)
!
! --- 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 + (pij(kk+1)- pij(1) )*diwqh0(i,j))**2
wz1 = 1.0 / (1.0 + (pij(kk+1)-0.5*(pij(1)+ &
pij(2) ))*diwqh0(i,j))**2
wz2 = 1.0 / (1.0 + (pij(kk+1)- pij(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 + (pij(kk+1)-0.5*(pij(k) + &
pij(k+1) ))*diwqh0(i,j))**2
wz2 = 1.0 / (1.0 + (pij(kk+1)- pij(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
!
! --- forcing of t,s by surface fluxes. flux positive into ocean.
!
qspcifh=1.0/spcifh
!
if (thermo .or. sstflg.gt.0 .or. srelax) then
! --- shortwave flux penetration depends on kpar or chl or jerlov water type.
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 swfrac_ij(chl,pij,klist(i,j)+1,qonem*oneta(i,j,n), &
jerlov(i,j),swfrac)
else
swfrac(1) = 1.0
swfrac(2:) = 0.0
endif
!
do k=1,kk
if (thermo .or. sstflg.gt.0 .or. srelax) then
if (k.eq.1) then
sflux1=surflx(i,j)-sswflx(i,j)
dtemp=(sflux1+(1.-swfrac(k+1))*sswflx(i,j))* &
delt1*g*qspcifh*(qdpmm(k)*qoneta)
if (epmass) then !only actual salt flux
dsaln= salflx(i,j)* &
delt1*g* (qdpmm(k)*qoneta)
else !water flux treated as a virtual salt flux
dsaln=(salflx(i,j)-wtrflx(i,j)*saln(i,j,1,n))* &
delt1*g* (qdpmm(k)*qoneta)
endif
!diag if (i.eq.itest.and.j.eq.jtest) then
!diag write (lp,101) nstep,i+i0,j+j0,k, &
!diag 1.0,swfrac(k+1),dtemp,dsaln
!diag call flush(lp)
!diag endif
elseif (k.le.klist(i,j)) then
dtemp=(swfrac(k)-swfrac(k+1))*sswflx(i,j)* &
delt1*g*qspcifh*(qdpmm(k)*qoneta)
dsaln=0.0
!diag if (i.eq.itest.and.j.eq.jtest) then
!diag write (lp,101) nstep,i+i0,j+j0,k, &
!diag swfrac(k),swfrac(k+1),dtemp
!diag call flush(lp)
!diag endif
else !k.gt.klist(i,j)
dtemp=0.0
dsaln=0.0
endif
else !.not.thermo ...
dtemp=0.0
dsaln=0.0
endif !thermo.or.sstflg.gt.0.or.srelax:else
!
! --- modify t and s; set old value arrays at p points for initial iteration
if (k.le.klist(i,j)) then
temp(i,j,k,n)= temp(i,j,k,n)+dtemp
saln(i,j,k,n)=max(saln(i,j,k,n)+dsaln,0.0) !must be non-negative
th3d(i,j,k,n)=sig(temp(i,j,k,n),saln(i,j,k,n))-thbase
told (k)=temp(i,j,k,n)
sold (k)=saln(i,j,k,n)
if (locsig) then
if (k.eq.1) then
thold(k)=th3d(i,j,k,n)
else
ka=k-1
alfadt(k)=dsiglocdt(ahalf*(told(ka)+told(k)), &
ahalf*(sold(ka)+sold(k)), &
p(i,j,k) )* &
(told(ka)-told(k))
betads(k)=dsiglocds(ahalf*(told(ka)+told(k)), &
ahalf*(sold(ka)+sold(k)), &
p(i,j,k) )* &
(sold(ka)-sold(k))
thold(k)=thold(ka)-alfadt(k)-betads(k)
endif
else
thold(k)=th3d(i,j,k,n)
endif
uold (k)=.5*(u(i,j,k,n)+u(i+1,j ,k,n))
vold (k)=.5*(v(i,j,k,n)+v(i ,j+1,k,n))
endif
enddo !k
!
k=klist(i,j)
ka=k+1
kb=min(ka,kk)
told (ka)=temp(i,j,kb,n)
sold (ka)=saln(i,j,kb,n)
if (locsig) then
alfadt(ka)=dsiglocdt(ahalf*(told(k)+told(ka)), &
ahalf*(sold(k)+sold(ka)), &
p(i,j,ka) )* &
(told(k)-told(ka))
betads(ka)=dsiglocds(ahalf*(told(k)+told(ka)), &
ahalf*(sold(k)+sold(ka)), &
p(i,j,ka) )* &
(sold(k)-sold(ka))
thold(ka)=thold(k)-alfadt(ka)-betads(ka)
else
thold(ka)=th3d(i,j,kb,n)
endif
uold (ka)=.5*(u(i,j,k,n)+u(i+1,j ,k,n))
vold (ka)=.5*(v(i,j,k,n)+v(i ,j+1,k,n))
!
! --- calculate z at vertical grid levels - this array is the z values in m
! --- at the mid-depth of each micom layer except for index klist+1, where it
! --- is the z value of the bottom
!
! --- calculate layer thicknesses in m
do k=1,kk
if (k.eq.1) then
hwide(k)=dpmm(k)*qonem
zgrid(i,j,k)=-.5*hwide(k)
else if (k.lt.klist(i,j)) then
hwide(k)=dpmm(k)*qonem
zgrid(i,j,k)=zgrid(i,j,k-1)-.5*(hwide(k-1)+hwide(k))
else if (k.eq.klist(i,j)) then
hwide(k)=dpmm(k)*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
!
! --- perform niter iterations to execute the semi-implicit solution of the
! --- diffusion equation. at least two iterations are recommended
!
do iter=1,niter
!
! --- calculate layer variables required to estimate bulk richardson number
!
! --- calculate nearsurface reference variables,
! --- averaged over -2*epsilon*zgrid, but no more than 8m.
zrefmn = -4.0
zrefo = 1.0 ! impossible value
do k=1,klist(i,j)
zref=max(epsilon*zgrid(i,j,k),zrefmn) ! nearest to zero
if (zref.ne.zrefo) then ! new zref
wref =-2.0*zref
qwref=1.0/wref
wq=min(hwide(1),wref)*qwref
uref=uold(1)*wq
vref=vold(1)*wq
bref=-g*svref*(thold(1)+thbase)*wq
wt=0.0
do ka=2,k
wt=wt+wq
if (wt.ge.1.0) then
exit
endif
wq=min(1.0-wt,hwide(ka)*qwref)
uref=uref+uold(ka)*wq
vref=vref+vold(ka)*wq
bref=bref-g*svref*(thold(ka)+thbase)*wq
enddo
endif
zrefo=zref
!
ritop(k)=(zref-zgrid(i,j,k))* &
(bref+g*svref*(thold(k)+thbase))
dvsq(k)=(uref-uold(k))**2+(vref-vold(k))**2
!
! if (i.eq.itest.and.j.eq.jtest) then
! if (k.eq.1) then
! write(lp,'(3a)')
! & ' k z zref',
! & ' u uref v vref',
! & ' b bref ritop dvsq'
! endif
! write(lp,'(i2,f9.2,f6.2,4f7.3,2f7.3,f9.4,f7.4)')
! & k,zgrid(i,j,k),zref,
! & uold(k),uref,vold(k),vref,
! & -g*svref*(thold(k)+thbase),bref,
! & ritop(k),dvsq(k)
! call flush(lp)
! endif
!diag if (i.eq.itest.and.j.eq.jtest) then
!diag write (lp,'(i9,2i5,i3,a,f8.2,f8.3)') &
!diag nstep,i+i0,j+j0,k, &
!diag ' z,swfrac =',zgrid(i,j,k),swfrac(k)
!diag call flush(lp)
!diag endif
enddo !k=1,klist
!
! --- calculate interface variables required to estimate interior diffusivities
do k=1,klist(i,j)
k1=k+1
ka=min(k1,kk)
shsq (k1)=(uold(k)-uold(k1))**2+(vold(k)-vold(k1))**2
if (.not.locsig) then
alfadt(k1)=dsigdt(ahalf*(told(k)+told(k1)), &
ahalf*(sold(k)+sold(k1)) )* &
(told(k)-told(k1))
betads(k1)=dsigds(ahalf*(told(k)+told(k1)), &
ahalf*(sold(k)+sold(k1)) )* &
(sold(k)-sold(k1))
dbloc(k1)=-g* svref*(thold(k)-thold(ka))
else
dbloc(k1)=-g*svref*(alfadt(k1)+betads(k1))
endif
enddo
!
! --- zero 1-d arrays for viscosity/diffusivity calculations
!
do k=1,kk+1
vcty (i,j,k) =0.0
dift (i,j,k) =0.0
difs (i,j,k) =0.0
ghats(i,j,k) =0.0
blmc( k,1)=0.0
blmc( k,2)=0.0
blmc( k,3)=0.0
bblmc( k,1)=0.0
bblmc( k,2)=0.0
bblmc( k,3)=0.0
enddo
!
! --- determine interior diffusivity profiles throughout the water column
!
! --- shear instability plus background internal wave contributions
do k=2,klist(i,j)+1
if (shinst) then
q =zgrid(i,j,k-1)-zgrid(i,j,k) !0.5*(hwide(k-1)+hwide(k))
if (zgrid(i,j,k).gt.zgrid(i,j,klist(i,j)+1)-thkbot) then
q =min(q, thkbot) !in the nominal bottom boundary layer
endif
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)=min(difm0*fri+dflmiw+dflbot(k),difmax)
difs(i,j,k)=min(difs0*fri+dflsiw+dflbot(k),difmax)
else
vcty(i,j,k)=dflmiw+dflbot(k)
difs(i,j,k)=dflsiw+dflbot(k)
endif
dift(i,j,k)=difs(i,j,k)
enddo
!
! --- double-diffusion (salt fingering and diffusive convection)
if (dbdiff) then
do k=2,klist(i,j)+1
!
! --- 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
else if ( 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.)))
if (rrho.gt.0.5) then
prandtl=(1.85-.85/rrho)*rrho
else
prandtl=.15*rrho
endif
dift(i,j,k)=dift(i,j,k)+diffdd
difs(i,j,k)=difs(i,j,k)+prandtl*diffdd
endif
enddo
endif
!
!diag if (i.eq.itest.and.j.eq.jtest) then
!diag write (lp,102) (nstep,iter,i+i0,j+j0,k, &
!diag hwide(k),1.e4*vcty(i,j,k),1.e4*dift(i,j,k),1.e4*difs(i,j,k), &
!diag k=1,kk+1)
!diag call flush(lp)
!diag endif
!
! --- calculate boundary layer diffusivity profiles and match these to the
! --- previously-calculated interior diffusivity profiles
!
! --- diffusivities within the surface boundary layer are parameterized
! --- as a function of boundary layer thickness times a depth-dependent
! --- turbulent velocity scale (proportional to ustar) times a third-order
! --- polynomial shape function of depth. boundary layer diffusivities depend
! --- on surface forcing (the magnitude of this forcing and whether it is
! --- stabilizing or de-stabilizing) and the magnitude and gradient of interior
! --- mixing at the boundary layer base. boundary layer diffusivity profiles
! --- are smoothly matched to interior diffusivity profiles at the boundary
! --- layer base (the profiles and their first derivatives are continuous
! --- at z=-hbl). the turbulent boundary layer depth is diagnosed first, the
! --- boundary layer diffusivity profiles are calculated, then the boundary
! --- and interior diffusivity profiles are combined.
!
! --- minimum hbl is top mid-layer + 1 cm or bldmin,
! --- maximum hbl is bottom mid-layer - 1 cm or bldmax.
!
hblmin=max( hwide(1)+0.01,bldmin)
hblmax=min(-zgrid(i,j,klist(i,j))-0.01,bldmax)
!
! --- buoyfl = total buoyancy flux (m**2/sec**3) into atmos.
! --- note: surface density increases (column is destabilized) if buoyfl > 0
! --- buoysw = shortwave radiation buoyancy flux (m**2/sec**3) into atmos.
! --- salflx, sswflx and surflx are positive into the ocean
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)
buoyfs=g*svref*(dsigds(tmn,smn)* &
(-wtrflx(i,j)*saln(i,j,1,n)+salflx(i,j))*svref)
buoyfl=buoyfs+ &
g*svref*(dsgdt *surflx(i,j) *svref/spcifh)
buoysw=g*svref*(dsgdt *sswflx(i,j) *svref/spcifh)
!
! --- diagnose the new boundary layer depth as the depth where a bulk
! --- richardson number exceeds ric
!
! --- initialize hbl and nbl to bottomed out values
kup2=1
kup =2
kdn =3
rib(kup2)=0.0
rib(kup) =0.0
nbl=klist(i,j)
hbl=hblmax
!
! --- diagnose hbl and nbl
do k=2,nbl
case=-zgrid(i,j,k)
bfsfc=buoyfl-swfrac(k)*buoysw
if (bfsfc.le.0.0) then
stable=1.0
dnorm =1.0
else
stable=0.0
dnorm =epsilon
endif
!
! --- compute turbulent velocity scales at dnorm, for
! --- hbl = case = -zgrid(i,j,k)
call wscale(i,j,case,dnorm,bfsfc,wm,ws,1)
!