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mod_barotp.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
module mod_barotp
use mod_xc ! HYCOM communication interface
!
! --- module for barotp and related routines
!
public :: barotp, barotp_init
contains
subroutine barotp(m,n)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
use mod_pipe ! HYCOM debugging interface
use mod_tides ! HYCOM tides
#if defined(STOKES)
use mod_stokes ! HYCOM Stokes Drift
#endif
implicit none
!
integer m,n
!
! --- ------------------------------------------------------------------------
! --- advance barotropic equations.
! --- on entry: -n- is time t-dt, -m- is time t
! --- on exit: -m- is time t, -n- is time t+dt
! --- time level 3 is only used internally (n and m are always 1 or 2).
!
! --- LeapFrog version based on:
! --- Y. Morel, Baraille, R., Pichon A. (2008) "Time splitting and
! --- linear stability of the slow part of the barotropic component",
! --- Ocean Modeling, 23, pp 73-81.
! --- ------------------------------------------------------------------------
!
logical, parameter :: lpipe_barotp=.false. !usually .false.
logical, parameter :: ldebug_barotp=.false. !usually .false.
!
character text*12
!
real q,pbudel,pbvdel,utndcy,vtndcy,wblpf,ramph
real d11,d12,d21,d22,ubp,vbp,z1
real xmin(2)
real sminny(jdm,2)
real*8 sump,timenud
integer i,j,l,lll,ml,nl,mn,lstep1,margin,mbdy,k,ktr,icof,nsclip
! & ,iffstep
logical ldrag
! data iffstep/0/
! save iffstep
!
#if defined(RELO)
real, save, allocatable, dimension(:,:) :: &
pbavo,ubavo,vbavo,displd,gslpr,gtide,pbnud, &
flxloc,flyloc,uflxba,vflxba
!
if (.not.allocated(pbavo)) then
allocate( &
pbavo(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy), &
ubavo(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy), &
vbavo(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy), &
displd(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy), &
gslpr(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy), &
gtide(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy), &
pbnud(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy) )
call mem_stat_add( 7*(idm+2*nbdy)*(jdm+2*nbdy) )
pbavo(:,:) = r_init
ubavo(:,:) = r_init
vbavo(:,:) = r_init
displd(:,:) = r_init
gslpr(:,:) = r_init
gtide(:,:) = r_init
pbnud(:,:) = 0.0 !safe to use if no nudging
if (btrmas) then
allocate( &
flxloc(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy), &
flyloc(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy), &
uflxba(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy), &
vflxba(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy) )
call mem_stat_add( 4*(idm+2*nbdy)*(jdm+2*nbdy) )
flxloc(:,:) = r_init
flyloc(:,:) = r_init
uflxba(:,:) = r_init
vflxba(:,:) = r_init
endif
endif
#else
real, save, dimension(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy) :: &
pbavo,ubavo,vbavo,displd,gslpr,gtide, &
flxloc,flyloc,uflxba,vflxba
#endif
!
mbdy = 6
!
margin = mbdy
! --- atmospheric pressure forcing
!
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (mslprf) then
if (natm.eq.2) then
gslpr(i,j) =( mslprs(i,j,l0)*w0+ &
mslprs(i,j,l1)*w1 )*svref
else
gslpr(i,j) =( mslprs(i,j,l0)*w0+ &
mslprs(i,j,l1)*w1+ &
mslprs(i,j,l2)*w2+ &
mslprs(i,j,l3)*w3 )*svref
endif !natm
else
gslpr(i,j) = 0.0
endif !mslprf
!
if (SEA_P) then
!
! --- tidal body forcing, including Scalar SAL,
! --- SAL should only be applied to the mass anomally, i.e. to
! --- non-steric SSH, so use sshflg>0 except in tides-only cases.
if (tidflg.gt.0 .and. sshflg.eq.0) then !tides
gtide(i,j)=-g*etide(i,j) &
-salfac(i,j)* srfhgt(i,j)
elseif (tidflg.gt.0 .and. sshflg.eq.1) then !tides
gtide(i,j)=-g*etide(i,j) &
-salfac(i,j)*(srfhgt(i,j)-steric(i,j))
elseif (tidflg.gt.0 .and. sshflg.ge.2) then !tides
gtide(i,j)=-g*etide(i,j) &
-salfac(i,j)*(srfhgt(i,j)-montg1(i,j))
else
gtide(i,j)=0.0
endif !tides (sshflg)
endif !ip
enddo !i
enddo !j
!
! --- tidal nudging, if required
if (tidnud.ne.0) then
!
! --- Newtonian relaxation of filtered bottom pressure towards tides
! --- Wang et. al (2021) and Fu et. al. (2021)
!
mn = -lstep !centered in time
call tides_observed(mn) !calculate htide
!
ramph = 0.0
timenud = time_8 + (mn*dlt/86400.d0)
if (timenud.ge.nudg_orig) then
timenud = (timenud-nudg_orig)/nudg_time
ramph = (1.0-exp(-5.0*timenud))
endif
if (ramph.gt.0.0) then !tidal nudging
! --- calculate nudging increment once per call
if (tidnud.eq.2) then
! --- hntide is a 49-hour weighted mean of pbavg
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_P) then
q = ramph*dlt*hnudge(i,j)
pbnud(i,j)= q*( onem*htide(i,j) + hntide(i,j) - &
pbavg(i,j,m) )
endif !ip
enddo !i
enddo !j
endif !tidnud=2
endif !tidal nudging
!
!!!!!! if (.true. .and. &
if (ldebug_barotp .and. &
itest.gt.0 .and. jtest.gt.0) then
i = itest
j = jtest
if (tidnud.eq.2) then
q = pbavg(i,j,m)-hntide(i,j)
endif !tidnud=2
write (lp,'(i9,2i5,3x,a,8g15.6)') &
nstep,i+i0,j+j0, &
'nudge,h,tide =', &
q, &
onem*htide(i,j), &
ramph, &
pbnud(i,j)
endif !debug
call xcsync(flush_lp)
else
ramph = 0.0
endif !nudge:else
!
! --- utotn,vtotn from momtum is time step t-1 to t+1 barotropic tendency
call xctilr(utotn,1, 1, 6,6, halo_uv)
call xctilr(vtotn,1, 1, 6,6, halo_vv)
!
if (lpipe .and. lpipe_barotp) then
! --- compare two model runs.
call pipe_compare_sym2(utotn, iu,'barotp:utotn', &
vtotn, iv,'barotp:vtotn')
call pipe_compare_sym1(pvtrop,iq,'barotp:pvtrp')
endif
!
! --- explicit time integration of barotropic flow (forward-backward scheme)
! --- in order to combine forward-backward scheme with leapfrog treatment of
! --- coriolis term, v-eqn must be solved before u-eqn every other time step
!
if (btrmas) then
uflxba(:,:) = 0.0
vflxba(:,:) = 0.0
flxloc(:,:) = 0.0
flyloc(:,:) = 0.0
endif
!
if (btrlfr) then !always true for btrmas
!
if (delt1.ne.baclin) then !not on very 1st time step
! --- start at time level t-dt and go to t+dt.
lstep1 = lstep + lstep !more stable, but also more expensive
icof = 2
!$OMP PARALLEL DO PRIVATE(j,i) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
do i=1,ii
pbavo(i,j) = pbavg(i,j,n) !save t-1 for RA filter
ubavo(i,j) = ubavg(i,j,n) !save t-1 for RA filter
vbavo(i,j) = vbavg(i,j,n) !save t-1 for RA filter
!
pbavg(i,j,3) = pbavg(i,j,n)
ubavg(i,j,3) = ubavg(i,j,n)
vbavg(i,j,3) = vbavg(i,j,n)
enddo !i
enddo !j
else !1st time step
! --- start at time level t and go to t+dt.
lstep1 = lstep
icof = 1
!$OMP PARALLEL DO PRIVATE(j,i) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
do i=1,ii
pbavo(i,j) = 0.0 !makes correct mean height safe
pbavg(i,j,n) = pbavg(i,j,m)
ubavg(i,j,n) = ubavg(i,j,m)
vbavg(i,j,n) = vbavg(i,j,m)
pbavg(i,j,3) = pbavg(i,j,m)
ubavg(i,j,3) = ubavg(i,j,m)
vbavg(i,j,3) = vbavg(i,j,m)
enddo !i
enddo !j
endif !usual:1st time step
else
! --- start at time level t and go to t+dt.
lstep1 = lstep !original, less stable, method
!$OMP PARALLEL DO PRIVATE(j,i) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
do i=1,ii
pbavo(i,j) = 0.0 !makes correct mean height safe
pbavg(i,j,n) = pbavg(i,j,m)
ubavg(i,j,n) = ubavg(i,j,m)
vbavg(i,j,n) = vbavg(i,j,m)
enddo !i
enddo !j
endif !btrlfr
!
ldrag = tidflg.gt.0 .and. drgscl.ne.0.0 .and. thkdrg.eq.0.0
!
if (ldrag) then
displd(:,:) = 0.0
endif
!
! --- time step loop
!
if (btrlfr) then
wblpf = 0.0 !1st minor time step, lll=1, only
else
wblpf = wbaro
endif
!
do 840 lll=1,lstep1,2
!
call xctilr(pbavg( 1-nbdy,1-nbdy,1 ),1, 3, 6,6, halo_ps)
call xctilr(ubavg( 1-nbdy,1-nbdy,1 ),1, 3, 6,6, halo_uv)
call xctilr(vbavg( 1-nbdy,1-nbdy,1 ),1, 3, 6,6, halo_vv)
!
! --- odd minor time step.
!
ml=n
nl=3
!
if (lpipe .and. lpipe_barotp) then
call pipe_compare_sym1( &
pbavg(1-nbdy,1-nbdy,nl),ip,'barot+:pbavn')
call pipe_compare_sym2( &
ubavg(1-nbdy,1-nbdy,nl),iu,'barot+:ubavn', &
vbavg(1-nbdy,1-nbdy,nl),iv,'barot+:vbavn')
call pipe_compare_sym1( &
pbavg(1-nbdy,1-nbdy,ml),ip,'barot+:pbavm')
call pipe_compare_sym2( &
ubavg(1-nbdy,1-nbdy,ml),iu,'barot+:ubavm', &
vbavg(1-nbdy,1-nbdy,ml),iv,'barot+:vbavm')
endif
!
! --- continuity equation, and tidal drag on p-grid
!
! --- rhs: pbavg, ubavg+, vbavg+
! --- lhs: pbavg
!
if (btrmas) then
!
margin = mbdy
!
!$OMP PARALLEL DO PRIVATE(j,l,i) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_U) then
flxloc(i,j) = ubavg(i,j,ml)*(depthu(i,j)*scuy(i,j))
uflxba(i,j) = uflxba(i,j) + &
coeflx(lll+1,icof)*(1.0+wblpf)*flxloc(i,j)
endif !iu
if (SEA_V) then
flyloc(i,j) = vbavg(i,j,ml)*(depthv(i,j)*scvx(i,j))
vflxba(i,j) = vflxba(i,j) + &
coeflx(lll+1,icof)*(1.0+wblpf)*flyloc(i,j)
endif !iv
enddo !i
do l=1,isu(j) !ok
i=ifu(j,l)-1
if (i.ge.1-margin) then
if (iuopn(i,j).ne.0) then
flxloc(i,j) = ubavg(i,j,ml)*scuy(i,j)* &
max(0.,pbot(i,j))
uflxba(i,j) = uflxba(i,j) + &
coeflx(lll+1,icof)*(1.0+wblpf)*flxloc(i,j)
endif !iuopn
endif !i
i=ilu(j,l)+1
if (i.le.ii+margin) then
if (iuopn(i,j).ne.0) then
flxloc(i,j) = ubavg(i,j,ml)*scuy(i,j)* &
max(0.,pbot(i-1,j))
uflxba(i,j) = uflxba(i,j) + &
coeflx(lll+1,icof)*(1.0+wblpf)*flxloc(i,j)
endif !iuopn
endif !i
enddo !l
enddo !j
!
do i=1-margin,ii+margin
do l=1,jsv(i) !ok
j=jfv(i,l)-1
if (j.ge.1-margin) then
if (ivopn(i,j).ne.0) then
flyloc(i,j) = vbavg(i,j,ml)*scvx(i,j)* &
max(0.,pbot(i,j))
vflxba(i,j) = vflxba(i,j) + &
coeflx(lll+1,icof)*(1.0+wblpf)*flyloc(i,j)
endif !ivopn
endif !j
j=jlv(i,l)+1
if (j.le.jj+margin) then
if (ivopn(i,j).ne.0) then
flyloc(i,j) = vbavg(i,j,ml)*scvx(i,j)* &
max(0.,pbot(i,j-1))
vflxba(i,j) = vflxba(i,j) + &
coeflx(lll+1,icof)*(1.0+wblpf)*flyloc(i,j)
endif !ivopn
endif !j
enddo !l
enddo !i
!
margin = mbdy - 1
!
!$OMP PARALLEL DO PRIVATE(j,l,i,ubp,vbp,d11,d12,d21,d22,q) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_P) then
pbavg(i,j,nl) = &
((1.0-wblpf)*pbavg(i,j,ml)+ &
wblpf *pbavg(i,j,nl) )- &
(1.0+wblpf)*dlt*(flxloc(i+1,j)-flxloc(i,j) + &
flyloc(i,j+1)-flyloc(i,j) )* &
scp2i(i,j) &
+pbnud(i,j)
pbavg(i,j,nl) = max( pbotmin(i,j), pbavg(i,j,nl) )
!
if (ldrag) then
!
! --- tidal drag tensor on p-grid:
! --- ub = ub - (dlt/H)*(t.11*ub + t.12*vb)
! --- vb = vb - (dlt/H)*(t.21*ub + t.22*vb)
! --- scalar drag has t.11=t.22 and t.12=t.21=0.0
! --- solve implicitly by inverting the matrix:
! --- 1+(dlt/H)*t.11 (dlt/H)*t.12
! --- (dlt/H)*t.21 1+(dlt/H)*t.22
! --- use depths (H) rather than onem*pbavg (h) for stability.
!
ubp = 0.5*(ubavg(i+1,j,nl)+ubavg(i,j,nl))
vbp = 0.5*(vbavg(i,j+1,nl)+vbavg(i,j,nl))
d11 = -dlt/depths(i,j) * drgten(1,1,i,j)
d12 = -dlt/depths(i,j) * drgten(1,2,i,j)
d21 = -dlt/depths(i,j) * drgten(2,1,i,j)
d22 = -dlt/depths(i,j) * drgten(2,2,i,j)
q = 1.0/((1.0-d11)*(1.0-d22)-d12*d21)
! --- set util5,util6 to the ubavg,vbavg drag increment
util5(i,j) = q*(ubp*(1.0-d22)+vbp*d12) - ubp
util6(i,j) = q*(vbp*(1.0-d11)+ubp*d21) - vbp
! --- add an explicit antidrag correction
! util5(i,j) = util5(i,j) - (d11*untide(i,j)+
! & d12*vntide(i,j) )
! util6(i,j) = util6(i,j) - (d21*untide(i,j)+
! & d22*vntide(i,j) )
!
! if (ldebug_barotp .and.
! & i.eq.itest.and.j.eq.jtest) then
! write (lp,'(i9,2i5,i3,3x,a,4g15.6)')
! & nstep,i+i0,j+j0,lll,
! & 'ubp,new,vbp,new =',
! & ubp,ubp+util5(i,j),
! & vbp,vbp+util6(i,j)
! endif !debug
else
util5(i,j) = 0.0
util6(i,j) = 0.0
endif !ldrag
endif !ip
enddo !i
enddo !j
!
else !.not.btrmas
!
margin = mbdy - 1
!
!$OMP PARALLEL DO PRIVATE(j,i,pbudel,pbvdel, &
!$OMP ubp,vbp,d11,d12,d21,d22,q) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_P) then
#if defined(STOKES)
!
! Barotropic Stokes flow included here
!
pbudel = (ubavg(i+1,j,ml)+usdbavg(i+1,j))* &
(depthu(i+1,j)*scuy(i+1,j)) &
-(ubavg(i, j,ml)+usdbavg(i, j))* &
(depthu(i, j)*scuy(i, j))
pbvdel = (vbavg(i,j+1,ml)+vsdbavg(i,j+1))* &
(depthv(i,j+1)*scvx(i,j+1)) &
-(vbavg(i,j, ml)+vsdbavg(i,j ))* &
(depthv(i,j )*scvx(i,j ))
#else
pbudel = ubavg(i+1,j,ml)*(depthu(i+1,j)*scuy(i+1,j)) &
-ubavg(i ,j,ml)*(depthu(i ,j)*scuy(i ,j))
pbvdel = vbavg(i,j+1,ml)*(depthv(i,j+1)*scvx(i,j+1)) &
-vbavg(i,j ,ml)*(depthv(i,j )*scvx(i,j ))
#endif
pbavg(i,j,nl) = &
((1.-wblpf)*pbavg(i,j,ml)+ &
wblpf *pbavg(i,j,nl) )- &
(1.+wblpf)*dlt*(pbudel + pbvdel)*scp2i(i,j) &
+pbnud(i,j)
pbavg(i,j,nl) = max( pbotmin(i,j), pbavg(i,j,nl) )
!
if (ldrag) then
!
! --- tidal drag tensor on p-grid:
! --- ub = ub - (dlt/H)*(t.11*ub + t.12*vb)
! --- vb = vb - (dlt/H)*(t.21*ub + t.22*vb)
! --- scalar drag has t.11=t.22 and t.12=t.21=0.0
! --- solve implicitly by inverting the matrix:
! --- 1+(dlt/H)*t.11 (dlt/H)*t.12
! --- (dlt/H)*t.21 1+(dlt/H)*t.22
! --- use depths (H) rather than onem*pbavg (h) for stability.
!
ubp = 0.5*(ubavg(i+1,j,nl)+ubavg(i,j,nl))
vbp = 0.5*(vbavg(i,j+1,nl)+vbavg(i,j,nl))
d11 = -dlt/depths(i,j) * drgten(1,1,i,j)
d12 = -dlt/depths(i,j) * drgten(1,2,i,j)
d21 = -dlt/depths(i,j) * drgten(2,1,i,j)
d22 = -dlt/depths(i,j) * drgten(2,2,i,j)
q = 1.0/((1.0-d11)*(1.0-d22)-d12*d21)
! --- set util5,util6 to the ubavg,vbavg drag increment
util5(i,j) = q*(ubp*(1.0-d22)+vbp*d12) - ubp
util6(i,j) = q*(vbp*(1.0-d11)+ubp*d21) - vbp
! --- add an explicit antidrag correction
! util5(i,j) = util5(i,j) - (d11*untide(i,j)+
! & d12*vntide(i,j) )
! util6(i,j) = util6(i,j) - (d21*untide(i,j)+
! & d22*vntide(i,j) )
! --- dissipation per m^2
displd(i,j) = displd(i,j) + &
(ubp*util5(i,j) + vbp*util6(i,j))* &
depths(i,j)*rhoref/dlt
!
! if (ldebug_barotp .and. i.eq.itest.and.j.eq.jtest) then
! write (lp,'(i9,2i5,i3,3x,a,4g15.6)')
! & nstep,i+i0,j+j0,lll,
! & 'ubp,new,vbp,new =',
! & ubp,ubp+util5(i,j),
! & vbp,vbp+util6(i,j)
! endif !debug
else
util5(i,j) = 0.0
util6(i,j) = 0.0
endif !ldrag
endif !ip
enddo !i
enddo !j
endif !btrmas:else
!
mn=ml
!
! --- u momentum equation, 1st
!
! --- rhs: pbavg+, vbavg+, pvtrop+
! --- lhs: ubavg
!
margin = margin - 1
!
!$OMP PARALLEL DO PRIVATE(j,i,utndcy,q) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_U) then
utndcy=-svref*(pbavg(i,j,nl)-pbavg(i-1,j,nl))*scuxi(i,j)- &
(gtide(i,j) -gtide(i-1,j) )*scuxi(i,j)- &
(gslpr(i,j) -gslpr(i-1,j) )*scuxi(i,j)+ &
((vbavg(i ,j, mn)*depthv(i ,j) &
+vbavg(i ,j+1,mn)*depthv(i ,j+1))+ &
(vbavg(i-1,j, mn)*depthv(i-1,j) &
+vbavg(i-1,j+1,mn)*depthv(i-1,j+1)))* &
(0.125*(pvtrop(i,j)+pvtrop(i,j+1)))
!
ubavg(i,j,nl)= &
((1.-wblpf)*ubavg(i,j,ml)+ &
wblpf *ubavg(i,j,nl) )+ &
(1.+wblpf)*dlt*(utndcy+utotn(i,j))
if (ldrag) then
ubavg(i,j,nl)=ubavg(i,j,nl) + &
0.5*(util5(i,j)+util5(i-1,j))
endif
!
! if (ldebug_barotp .and. i.eq.itest.and.j.eq.jtest) then
! write (lp,'(i9,2i5,i3,3x,a,8g15.6)')
! & nstep,i+i0,j+j0,lll,
! & 'u_old,u_new,p_grad,t_g,m_g,corio,u_star,drag =',
! & ubavg(i,j,ml),ubavg(i,j,nl),
! & -svref*(pbavg(i,j,nl)-pbavg(i-1,j,nl))*scuxi(i,j)*dlt,
! & -(gtide(i,j) -gtide(i-1,j) )*scuxi(i,j)*dlt,
! & -(gslpr(i,j) -gslpr(i-1,j) )*scuxi(i,j)*dlt,
! & (vbavg(i ,j, mn)*depthv(i ,j)
! & +vbavg(i ,j+1,mn)*depthv(i ,j+1)
! & +vbavg(i-1,j, mn)*depthv(i-1,j)
! & +vbavg(i-1,j+1,mn)*depthv(i-1,j+1))
! & *(pvtrop(i,j)+pvtrop(i,j+1))
! & *.125 * dlt,utotn(i,j) * dlt,
! & 0.5*(util5(i,j)+util5(i-1,j))
! endif !debug
endif !iu
enddo !i
enddo !j
!
mn = nl
!
! --- v momentum equation, 2nd
! --- rhs: pbavg+, ubavg+, pvtrop+
! --- lhs: vbavg
!
margin = margin - 1
!
!$OMP PARALLEL DO PRIVATE(j,i,vtndcy,q) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_V) then
vtndcy=-svref*(pbavg(i,j,nl)-pbavg(i,j-1,nl))*scvyi(i,j)- &
(gtide(i,j) -gtide(i,j-1) )*scvyi(i,j)- &
(gslpr(i,j) -gslpr(i,j-1) )*scvyi(i,j)- &
((ubavg(i, j ,mn)*depthu(i, j ) &
+ubavg(i+1,j ,mn)*depthu(i+1,j ))+ &
(ubavg(i, j-1,mn)*depthu(i, j-1) &
+ubavg(i+1,j-1,mn)*depthu(i+1,j-1)))* &
(0.125*(pvtrop(i,j)+pvtrop(i+1,j)))
!
vbavg(i,j,nl)= &
((1.-wblpf)*vbavg(i,j,ml)+ &
wblpf *vbavg(i,j,nl) )+ &
(1.+wblpf)*dlt*(vtndcy+vtotn(i,j))
if (ldrag) then
vbavg(i,j,nl)=vbavg(i,j,nl) + &
0.5*(util6(i,j)+util6(i,j-1))
endif
!
! if (ldebug_barotp .and. i.eq.itest.and.j.eq.jtest) then
! write (lp,'(i9,2i5,i3,3x,a,8g15.6)')
! & nstep,i+i0,j+j0,lll,
! & 'v_old,v_new,p_grad,t_g,m_g,corio,v_star,drag =',
! & vbavg(i,j,ml),vbavg(i,j,nl),
! & -svref*(pbavg(i,j,nl)-pbavg(i,j-1,nl))*scvyi(i,j)*dlt,
! & -(gtide(i,j) -gtide(i,j-1) )*scvyi(i,j)*dlt,
! & -(gslpr(i,j) -gslpr(i,j-1) )*scvyi(i,j)*dlt,
! & -(ubavg(i, j ,mn)*depthu(i,j )
! & +ubavg(i+1,j ,mn)*depthu(i+1,j )
! & +ubavg(i, j-1,mn)*depthu(i,j-1)
! & +ubavg(i+1,j-1,mn)*depthu(i+1,j-1))
! & *(pvtrop(i,j)+pvtrop(i+1,j))
! & *.125 * dlt, vtotn(i,j) * dlt,
! & 0.5*(util6(i,j)+util6(i,j-1))
! endif !debug
endif !iv
enddo !i
enddo !j
!
! if (ldebug_barotp) then
! call xcsync(flush_lp)
! endif
!
#if ! defined(RELO)
if (lbflag.eq.1) then
call latbdp( nl)
elseif (lbflag.eq.3) then
call latbdf( nl,lll)
endif
#endif
if (lbflag.eq.2) then
call latbdt( nl,lll)
elseif (lbflag.eq.4) then
call latbdtf(nl,lll)
endif
!
! --- even minor time step.
!
ml=3
nl=n
wblpf = wbaro !used for all subsequent time steps: lll=2,lstep1
!
if (lpipe .and. lpipe_barotp) then
call pipe_compare_sym1( &
pbavg(1-nbdy,1-nbdy,nl),ip,'barot+:pbavn')
call pipe_compare_sym2( &
ubavg(1-nbdy,1-nbdy,nl),iu,'barot+:ubavn', &
vbavg(1-nbdy,1-nbdy,nl),iv,'barot+:vbavn')
call pipe_compare_sym1( &
pbavg(1-nbdy,1-nbdy,ml),ip,'barot+:pbavm')
call pipe_compare_sym2( &
ubavg(1-nbdy,1-nbdy,ml),iu,'barot+:ubavm', &
vbavg(1-nbdy,1-nbdy,ml),iv,'barot+:vbavm')
endif
!
! --- continuity equation
!
! --- rhs: pbavg, ubavg+, vbavg+
! --- lhs: pbavg
!
if (btrmas) then
!
margin = mbdy
!
!$OMP PARALLEL DO PRIVATE(j,l,i) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_U) then
flxloc(i,j) = ubavg(i,j,ml)*(depthu(i,j)*scuy(i,j))
uflxba(i,j) = uflxba(i,j) + &
coeflx(lll+2,icof)*(1.0+wblpf)*flxloc(i,j)
endif
enddo !i
enddo !j
!
!$OMP PARALLEL DO PRIVATE(j,l,i) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_V) then
flyloc(i,j) = vbavg(i,j,ml)*(depthv(i,j)*scvx(i,j))
vflxba(i,j) = vflxba(i,j) + &
coeflx(lll+2,icof)*(1.0+wblpf)*flyloc(i,j)
endif
enddo !i
enddo !j
!
margin = mbdy - 1
!
!$OMP PARALLEL DO PRIVATE(j,l,i,ubp,vbp,d11,d12,d21,d22,q) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_P) then
pbavg(i,j,nl) = &
((1.0-wblpf)*pbavg(i,j,ml)+ &
wblpf *pbavg(i,j,nl) )- &
(1.0+wblpf)*dlt*(flxloc(i+1,j)-flxloc(i,j) + &
flyloc(i,j+1)-flyloc(i,j) )* &
scp2i(i,j) &
+pbnud(i,j)
pbavg(i,j,nl) = max( pbotmin(i,j), pbavg(i,j,nl) )
!
if (ldrag) then
!
! --- tidal drag tensor on p-grid:
! --- ub = ub - (dlt/H)*(t.11*ub + t.12*vb)
! --- vb = vb - (dlt/H)*(t.21*ub + t.22*vb)
! --- solve implicitly by inverting the matrix:
! --- 1+(dlt/H)*t.11 (dlt/H)*t.12
! --- (dlt/H)*t.21 1+(dlt/H)*t.22
! --- use depths (H) rather than onem*pbavg (h) for stability.
!
ubp = 0.5*(ubavg(i+1,j,nl)+ubavg(i,j,nl))
vbp = 0.5*(vbavg(i,j+1,nl)+vbavg(i,j,nl))
d11 = -dlt/depths(i,j) * drgten(1,1,i,j)
d12 = -dlt/depths(i,j) * drgten(1,2,i,j)
d21 = -dlt/depths(i,j) * drgten(2,1,i,j)
d22 = -dlt/depths(i,j) * drgten(2,2,i,j)
q = 1.0/((1.0-d11)*(1.0-d22)-d12*d21)
! --- set util5,util6 to the ubavg,vbavg drag increment
util5(i,j) = q*(ubp*(1.0-d22)+vbp*d12) - ubp
util6(i,j) = q*(ubp*d21+vbp*(1.0-d12)) - vbp
! --- add an explicit antidrag correction
! util5(i,j) = util5(i,j) - (d11*untide(i,j)+
! & d12*vntide(i,j) )
! util6(i,j) = util6(i,j) - (d21*untide(i,j)+
! & d22*vntide(i,j) )
!
! if (ldebug_barotp .and.
! & i.eq.itest.and.j.eq.jtest) then
! write (lp,'(i9,2i5,i3,3x,a,4g15.6)')
! & nstep,i+i0,j+j0,lll,
! & 'ubp,new,vbp,new =',
! & ubp,ubp+util5(i,j),
! & vbp,vbp+util6(i,j)
! endif !debug
else
util5(i,j) = 0.0
util6(i,j) = 0.0
endif !ldrag
endif !ip
enddo !i
enddo !j
!
if (lpipe .and. lpipe_barotp) then
! --- compare two model runs.
text = 'uflxba.ml '
call pipe_compare_sym1(uflxba,iu,text)
text = 'vflxba.ml '
call pipe_compare_sym1(vflxba,iv,text)
text = 'flxloc.ml '
call pipe_compare_sym1(flxloc,iu,text)
text = 'flyloc.ml '
call pipe_compare_sym1(flyloc,iv,text)
endif !lpipe
!
else !.not.btrmas
!
margin = mbdy - 1
!
!$OMP PARALLEL DO PRIVATE(j,i,pbudel,pbvdel, &
!$OMP ubp,vbp,d11,d12,d21,d22,q) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_P) then
#if defined(STOKES)
!
! Barotropic Stokes flow included here
!
pbudel = (ubavg(i+1,j,ml)+usdbavg(i+1,j))* &
(depthu(i+1,j)*scuy(i+1,j)) &
-(ubavg(i, j,ml)+usdbavg(i, j))* &
(depthu(i ,j)*scuy(i, j))
pbvdel = (vbavg(i,j+1,ml)+vsdbavg(i,j+1))* &
(depthv(i,j+1)*scvx(i,j+1)) &
-(vbavg(i,j, ml)+vsdbavg(i,j ))* &
(depthv(i,j )*scvx(i,j ))
#else
pbudel = ubavg(i+1,j,ml)*(depthu(i+1,j)*scuy(i+1,j)) &
-ubavg(i ,j,ml)*(depthu(i ,j)*scuy(i ,j))
pbvdel = vbavg(i,j+1,ml)*(depthv(i,j+1)*scvx(i,j+1)) &
-vbavg(i,j ,ml)*(depthv(i,j )*scvx(i,j ))
#endif
pbavg(i,j,nl) = &
((1.-wblpf)*pbavg(i,j,ml)+ &
wblpf *pbavg(i,j,nl) )- &
(1.+wblpf)*dlt*(pbudel + pbvdel)*scp2i(i,j) &
+pbnud(i,j)
pbavg(i,j,nl) = max( pbotmin(i,j), pbavg(i,j,nl) )
!
if (ldrag) then
! --- tidal drag tensor on p-grid:
! --- ub = ub - (dlt/H)*(t.11*ub + t.12*vb)
! --- vb = vb - (dlt/H)*(t.21*ub + t.22*vb)
! --- solve implicitly by inverting the matrix:
! --- 1+(dlt/H)*t.11 (dlt/H)*t.12
! --- (dlt/H)*t.21 1+(dlt/H)*t.22
! --- use depths (H) rather than onem*pbavg (h) for stability.
!
ubp = 0.5*(ubavg(i+1,j,nl)+ubavg(i,j,nl))
vbp = 0.5*(vbavg(i,j+1,nl)+vbavg(i,j,nl))
d11 = -dlt/depths(i,j) * drgten(1,1,i,j)
d12 = -dlt/depths(i,j) * drgten(1,2,i,j)
d21 = -dlt/depths(i,j) * drgten(2,1,i,j)
d22 = -dlt/depths(i,j) * drgten(2,2,i,j)
q = 1.0/((1.0-d11)*(1.0-d22)-d12*d21)
! --- set util5,util6 to the ubavg,vbavg drag increment
util5(i,j) = q*(ubp*(1.0-d22)+vbp*d12) - ubp
util6(i,j) = q*(ubp*d21+vbp*(1.0-d11)) - vbp
! --- add an explicit antidrag correction
! util5(i,j) = util5(i,j) - (d11*untide(i,j)+
! & d12*vntide(i,j) )
! util6(i,j) = util6(i,j) - (d21*untide(i,j)+
! & d22*vntide(i,j) )
! --- dissipation per m^2
displd(i,j) = displd(i,j) + &
(ubp*util5(i,j) + vbp*util6(i,j))* &
depths(i,j)*rhoref/dlt
!
! if (ldebug_barotp .and. i.eq.itest.and.j.eq.jtest) then
! write (lp,'(i9,2i5,i3,3x,a,4g15.6)')
! & nstep,i+i0,j+j0,lll+1,
! & 'ubp,new,vbp,new =',
! & ubp,ubp+util5(i,j),
! & vbp,vbp+util6(i,j)
! endif !debug
else
util5(i,j) = 0.0
util6(i,j) = 0.0
endif !ldrag
endif !ip
enddo !i
enddo !j
endif !btrmas:else
!
mn=ml
!
! --- v momentum equation, 1st
!
! --- rhs: pbavg+, ubavg+, pvtrop+
! --- lhs: vbavg
!
margin = margin - 1
!
!$OMP PARALLEL DO PRIVATE(j,i,vtndcy,q) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_V) then
vtndcy=-svref*(pbavg(i,j,nl)-pbavg(i,j-1,nl))*scvyi(i,j)- &
(gtide(i,j) -gtide(i,j-1) )*scvyi(i,j)- &
(gslpr(i,j) -gslpr(i,j-1) )*scvyi(i,j)- &
((ubavg(i, j ,mn)*depthu(i, j ) &
+ubavg(i+1,j ,mn)*depthu(i+1,j ))+ &
(ubavg(i, j-1,mn)*depthu(i, j-1) &
+ubavg(i+1,j-1,mn)*depthu(i+1,j-1)))* &
(0.125*(pvtrop(i,j)+pvtrop(i+1,j)))
!
vbavg(i,j,nl)= &
((1.-wblpf)*vbavg(i,j,ml)+ &
wblpf *vbavg(i,j,nl))+ &
(1.+wblpf)*dlt*(vtndcy+vtotn(i,j))
if (ldrag) then
vbavg(i,j,nl)=vbavg(i,j,nl) + &
0.5*(util6(i,j)+util6(i,j-1))
endif
!
! if (ldebug_barotp .and. i.eq.itest.and.j.eq.jtest) then
! write (lp,'(i9,2i5,i3,3x,a,8g15.6)')
! & nstep,i+i0,j+j0,lll+1,
! & 'v_old,v_new,p_grad,t_g,m_g,corio,v_star,drag =',
! & vbavg(i,j,ml),vbavg(i,j,nl),
! & -svref*(pbavg(i,j,nl)-pbavg(i,j-1,nl))*scvyi(i,j)*dlt,
! & -(gtide(i,j) -gtide(i,j-1) )*scvyi(i,j)*dlt,
! & -(gslpr(i,j) -gslpr(i,j-1) )*scvyi(i,j)*dlt,
! & -(ubavg(i, j ,mn)*depthu(i,j )
! & +ubavg(i+1,j ,mn)*depthu(i+1,j )
! & +ubavg(i, j-1,mn)*depthu(i,j-1)
! & +ubavg(i+1,j-1,mn)*depthu(i+1,j-1))
! & *(pvtrop(i,j)+pvtrop(i+1,j))
! & *.125 * dlt, vtotn(i,j) * dlt,
! & 0.5*(util6(i,j)+util6(i,j-1))
! endif !debug
endif !iv
enddo !i
enddo !j
!
mn=nl
!
! --- u momentum equation, 2nd
!
! --- rhs: pbavg+, vbavg+, pvtrop+
! --- lhs: ubavg
!
margin = margin - 1
!
!$OMP PARALLEL DO PRIVATE(j,i,utndcy,q) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_U) then
utndcy=-svref*(pbavg(i,j,nl)-pbavg(i-1,j,nl))*scuxi(i,j)- &
(gtide(i,j) -gtide(i-1,j) )*scuxi(i,j)- &
(gslpr(i,j) -gslpr(i-1,j) )*scuxi(i,j)+ &
((vbavg(i ,j, mn)*depthv(i ,j) &
+vbavg(i ,j+1,mn)*depthv(i ,j+1))+ &
(vbavg(i-1,j, mn)*depthv(i-1,j) &
+vbavg(i-1,j+1,mn)*depthv(i-1,j+1)))* &
(0.125*(pvtrop(i,j)+pvtrop(i,j+1)))
!
ubavg(i,j,nl)= &
((1.-wblpf)*ubavg(i,j,ml)+ &
wblpf *ubavg(i,j,nl) )+ &
(1.+wblpf)*dlt*(utndcy+utotn(i,j))
if (ldrag) then
ubavg(i,j,nl)=ubavg(i,j,nl) + &
0.5*(util5(i,j)+util5(i-1,j))
endif
!
! if (ldebug_barotp .and. i.eq.itest.and.j.eq.jtest) then
! write (lp,'(i9,2i5,i3,3x,a,7g15.6)')
! & nstep,i+i0,j+j0,lll+1,
! & 'u_old,u_new,p_grad,t_g,m_g,corio,u_star,drag =',
! & ubavg(i,j,ml),ubavg(i,j,nl),
! & -svref*(pbavg(i,j,nl)-pbavg(i-1,j,nl))*scuxi(i,j)*dlt,
! & -(gtide(i,j) -gtide(i-1,j) )*scuxi(i,j)*dlt,
! & -(gslpr(i,j) -gslpr(i-1,j) )*scuxi(i,j)*dlt,
! & (vbavg(i ,j, mn)*depthv(i ,j)
! & +vbavg(i ,j+1,mn)*depthv(i ,j+1)
! & +vbavg(i-1,j, mn)*depthv(i-1,j)
! & +vbavg(i-1,j+1,mn)*depthv(i-1,j+1))
! & *(pvtrop(i,j)+pvtrop(i,j+1))
! & *.125 * dlt,utotn(i,j) * dlt,
! & 0.5*(util5(i,j)+util5(i-1,j))
! endif !debug
endif !iu
enddo !i
enddo !j
!
! if (ldebug_barotp) then
! call xcsync(flush_lp)
! endif
!
#if ! defined(RELO)
if (lbflag.eq.1) then
call latbdp( nl)
elseif (lbflag.eq.3) then
call latbdf( nl,lll+1)
endif
#endif
if (lbflag.eq.2) then
call latbdt( nl,lll+1)
elseif (lbflag.eq.4) then
call latbdtf(nl,lll+1)
endif
!
840 continue ! lll=1,lstep1,2
!
ktr = istrcr(701) !displd_mn
if (ldrag .and. ktr.ne.0) then
!disp_count updated in momtum
stracr(:,:,ktr) = stracr(:,:,ktr) + displd(:,:)/real(lstep1)
endif
!
if (lbflag.eq.1) then
!
! --- correct mean height.
! --- this should not be required - so there may be a bug in the bc.
!
!$OMP PARALLEL DO PRIVATE(j,i) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1,jj
do i=1-margin,ii+margin
if (SEA_P) then
util1(i,j) = pbavg(i,j,n)*scp2(i,j)
endif !ip
enddo !i
enddo !j
call xcsum(sump, util1,ipa)
q = sump/area
!
! --- rhs: pbavg
! --- lhs: pbavg
!
margin = 0
!
!$OMP PARALLEL DO PRIVATE(j,i) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_P) then
pbavo(i,j) = pbavo(i,j) - q