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mod_momtum.F
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#if defined(ROW_LAND)
#define SEA_P .true.
#define SEA_U .true.
#define SEA_V .true.
#define SEA_Q .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
#define SEA_Q alliq(j).or.iq(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
#define SEA_Q iq(i,j).ne.0
#endif
module mod_momtum
use mod_xc ! HYCOM communication interface
implicit none
c
c --- module for momtum and related routines
c
private !! default is private
public :: momtum_hs, momtum, momtum4
c
#if defined(RELO)
real, save, allocatable, dimension(:,:) ::
#else
real, save, dimension(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy) ::
#endif
& stress,stresx,stresy,dpmx,thkbop,oneta_mtm
contains
subroutine momtum_hs(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
c
integer m,n
c
c --- -----------------------------------------
c --- hydrostatic equation (and surface stress)
c --- -----------------------------------------
c
logical, parameter :: lpipe_momtum=.false. !usually .false.
!!Alex real, parameter :: dragw_rho=0.01072d0*1026.0d0 !ice-ocean drag from CICE (2x default)
real, parameter :: dragw_rho=0.00536d0*1026.0d0 !ice-ocean dragfrom CICE (default)
real, parameter :: pairc=1013.0d0*100.0d0 !air pressure (Pa)
real, parameter :: rgas=287.1d0 !gas constant (j/kg/k)
real, parameter :: tzero=273.16d0 !celsius to kelvin offset
c
character text*12
c
real dpdn,dpup,q,samo,simo,uimo,vimo,dpsur,psur,usur,vsur,
& airt,vpmx,wndx,wndy,wind,cdw,pair,rair,
& sumdp,sumth,thksur
integer i,j,k,kl,l,margin,mbdy,hlstep
c &,iffstep
c data iffstep/0/
c save iffstep
c
* real*8 wtime
* external wtime
* real*8 wtime1(10),wtime2(20,kdm),wtimes
c
include 'stmt_fns.h'
c
#if defined(RELO)
if (.not.allocated(stress)) then
allocate(
& stress(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& stresx(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& stresy(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& dpmx(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& thkbop(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& oneta_mtm(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy))
call mem_stat_add( 6*(idm+2*nbdy)*(jdm+2*nbdy) )
stress = r_init
stresx = r_init
stresy = r_init
dpmx = r_init
thkbop = r_init
oneta_mtm = 0.0
endif
#endif
c
mbdy = 6
c
c --- dp has up to date halos from cnuity or mod_hycom
call xctilr(dpmixl(1-nbdy,1-nbdy, m),1, 1, 6,6, halo_ps)
call xctilr(pbavg( 1-nbdy,1-nbdy,1 ),1, 2, 6,6, halo_ps)
call xctilr(saln( 1-nbdy,1-nbdy,1,m),1, kk, 6,6, halo_ps)
call xctilr(temp( 1-nbdy,1-nbdy,1,m),1, kk, 6,6, halo_ps)
call xctilr(th3d( 1-nbdy,1-nbdy,1,m),1, kk, 6,6, halo_ps)
call xctilr(oneta( 1-nbdy,1-nbdy, n),1, 1, 6,6, halo_ps) !!Alex
call xctilr(oneta( 1-nbdy,1-nbdy, m),1, 1, 6,6, halo_ps)
if (windf .and. iceflg.eq.2) then
kl=max(nsigma,1)
call xctilr(u( 1-nbdy,1-nbdy,1,n),1,kl, 1,1, halo_uv)
call xctilr(ubavg( 1-nbdy,1-nbdy, n),1, 1, 1,1, halo_uv)
call xctilr(v( 1-nbdy,1-nbdy,1,n),1,kl, 1,1, halo_vv)
call xctilr(vbavg( 1-nbdy,1-nbdy, n),1, 1, 1,1, halo_vv)
endif
c
c --- tidal forcing
c
if(tidflg.eq.2 .or. tidflg.eq.3) then
hlstep=0
call tides_force(hlstep)
endif
c
c --- hydrostatic equation (and surface stress)
c
* wtime1( 1) = wtime()
c
c --- rhs: th3d.m, temp.m, saln.m, p, pbavg.m
c --- lhs: thstar, p, oneta, montg
c
margin = mbdy
c
!$OMP PARALLEL DO PRIVATE(j,k,i)
!$OMP& SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_P) then
sumdp = 0.0
sumth = 0.0
do k=1,kk
if (kapref.ne.0) then !thermobaric
c
c --- sigma-star is virtual potential density, as defined in
c --- Sun et.al. (1999), 'Inclusion of thermobaricity in
c --- isopycnic-coordinate ocean models', JPO 29 pp 2719-2729.
c
c --- use upper interface pressure in converting sigma to sigma-star.
c --- to avoid density variations in layers intersected by bottom
c
if (kapref.gt.0) then
thstar(i,j,k,1)=th3d(i,j,k,m)
& +kappaf(temp(i,j,k,m),
& saln(i,j,k,m),
& th3d(i,j,k,m)+thbase,
& 0.5*(p(i,j,k)+p(i,j,k+1)), !!!Alex
& kapref)
else
thstar(i,j,k,1)=th3d(i,j,k,m)
& +kappaf(temp(i,j,k,m),
& saln(i,j,k,m),
& th3d(i,j,k,m)+thbase,
& 0.5*(p(i,j,k)+p(i,j,k+1)), !!!Alex
& 2)
thstar(i,j,k,2)=th3d(i,j,k,m)
& +kappaf(temp(i,j,k,m),
& saln(i,j,k,m),
& th3d(i,j,k,m)+thbase,
& 0.5*(p(i,j,k)+p(i,j,k+1)), !!!Alex
& kapi(i,j))
#if defined KEY_SIGMA_TRUE
thstar(i,j,k,2) = qthref - thbase -
& qthref/(1.+(thstar(i,j,k,2)+thbase)*thref)
#endif
endif !kapref
else !non-thermobaric
thstar(i,j,k,1)=th3d(i,j,k,m)
#if defined KEY_SIGMA_TRUE
thstar(i,j,k,1) = qthref - thbase -
& qthref/(1.+(thstar(i,j,k,1)+thbase)*thref)
#endif
endif !thermobaric:else
c
p(i,j,k+1)=p(i,j,k)+dp(i,j,k,m)
c
if (sshflg.ne.0) then
sumth = sumth + dp(i,j,k,m)*th3d(i,j,k,m)
sumdp = sumdp + dp(i,j,k,m)
endif !sshflg
enddo !k
c
if (sshflg.ne.0) then
sumth = sumth / max( sumdp, onemm ) !vertical mean of th3d
sumdp = sumdp*qonem * g !depth(m) * g
steric(i,j) = sshgmn(i,j) +
& (sshgmn(i,j) + sumdp) *
& (thmean(i,j) - sumth) /
& (1000.0+thbase+sumth)
endif !sshflg
c
c --- store (1+eta) (= p_total/p_prime) in -oneta-
! oneta(i,j)=1.+pbavg(i,j,m)/p(i,j,kk+1)
! onetai(i,j)=oneta(i,j)-pbavg(i,j,m)/pbot(i,j)
if (btrmas) then
oneta_mtm(i,j)= oneta(i,j,m)
else
oneta_mtm(i,j)=1.0 !disable oneta_mtm
endif
c
c --- m_prime in lowest layer:
montg(i,j,kk,1)=psikk(i,j,1)+
& ( p(i,j,kk+1)*(thkk(i,j,1)-thstar(i,j,kk,1))
& -pbavg(i,j,m)*thstar(i,j,kk,1) )*thref**2
if (kapref.eq.-1) then
montg(i,j,kk,2)=psikk(i,j,2)+
& ( p(i,j,kk+1)*(thkk(i,j,2)-thstar(i,j,kk,2))
& -pbavg(i,j,m)*thstar(i,j,kk,2) )*thref**2
endif !kapref.eq.-1
c
c --- m_prime in remaining layers:
do k=kk-1,1,-1
montg(i,j,k,1)=montg(i,j,k+1,1)+p(i,j,k+1)
& *oneta_mtm(i,j)
& *(thstar(i,j,k+1,1)-thstar(i,j,k,1))*thref**2
if (kapref.eq.-1) then
montg(i,j,k,2)=montg(i,j,k+1,2)+p(i,j,k+1)
& *oneta_mtm(i,j)
& *(thstar(i,j,k+1,2)-thstar(i,j,k,2))*thref**2
endif !kapref.eq.-1
enddo !k
c
c --- srfhgt (used diagnostically, in mxmyaij and for tidal SAL).
if (kapref.ne.-1) then
montg1(i,j) = montg(i,j,1,1)
else
montg1(i,j) = skap(i,j) *montg(i,j,1,1) +
& (1.0-skap(i,j))*montg(i,j,1,2)
endif !kapref
srfhgt(i,j) = montg1(i,j) + thref*pbavg(i,j,m)
c
cdiag if (sshflg.ne.0) then
cdiag if (itest.gt.0 .and. jtest.gt.0) then
cdiag write (lp,'(i9,2i5,3x,a,2f12.6,f12.2)')
cdiag. nstep,itest+i0,jtest+j0,
cdiag. 'sssh =',
cdiag. steric(i,j),sshgmn(i,j),sumdp
cdiag write (lp,'(i9,2i5,3x,a,3f12.6)')
cdiag. nstep,itest+i0,jtest+j0,
cdiag. 'thmn =',
cdiag. sumth,thmean(i,j),1000.0+thbase+sumth
cdiag write (lp,'(i9,2i5,3x,a,3f12.6)')
cdiag. nstep,itest+i0,jtest+j0,
cdiag. 'ssh =',
cdiag. srfhgt(i,j),steric(i,j),srfhgt(i,j)-steric(i,j)
cdiag endif !test
cdiag endif !sshflg
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
c
if (lpipe .and. lpipe_momtum .and. mslprf) then
c --- compare two model runs.
util4(1:ii,1:jj) = mslprs(1:ii,1:jj,l0)
write (text,'(a9,i3)') 'mslprs l=',l0
call pipe_compare(util4, ip,text)
util4(1:ii,1:jj) = mslprs(1:ii,1:jj,l1)
write (text,'(a9,i3)') 'mslprs l=',l1
call pipe_compare(util4, ip,text)
c
util4(1:ii,1:jj) = mslprs(1:ii,1:jj,l0)-mslprs(1:ii,0:jj-1,l0)
write (text,'(a9,i3)') 'mslprY l=',l0
call pipe_compare(util4, iv,text)
util4(1:ii,1:jj) = mslprs(1:ii,1:jj,l1)-mslprs(1:ii,0:jj-1,l1)
write (text,'(a9,i3)') 'mslprY l=',l1
call pipe_compare(util4, iv,text)
c
util4(1:ii,1:jj) = mslprs(1:ii,1:jj,l0)-mslprs(0:ii-1,1:jj,l0)
write (text,'(a9,i3)') 'mslprX l=',l0
call pipe_compare(util4, iu,text)
util4(1:ii,1:jj) = mslprs(1:ii,1:jj,l1)-mslprs(0:ii-1,1:jj,l1)
write (text,'(a9,i3)') 'mslprX l=',l1
call pipe_compare(util4, iu,text)
endif
c
c call dpudpv(dpu(1-nbdy,1-nbdy,1,m),
c & dpv(1-nbdy,1-nbdy,1,m),
c & p,depthu,depthv, max(0,margin-1))
cCL/RB MPI bug correction 2011-01
c call xctilr(dpu( 1-nbdy,1-nbdy,1,1),1,2*kk, 6,6, halo_us)
c call xctilr(dpv( 1-nbdy,1-nbdy,1,1),1,2*kk, 6,6, halo_vs)
c
c --- account for temporal smoothing of mid-time dpmixl. calculate the vertical
c --- excursions of the coordinates immediately above and below the mixed
c --- layer base, then vertically interpolate this motion to dpmixl(i,j,m)
c
if(hybrid .and. mxlkta) then
c
c --- rhs: dp, dpmixl.m
c --- lhs: util1, util2
c
margin = mbdy
c
!$OMP PARALLEL DO PRIVATE(j,i,k,dpup,dpdn,q)
!$OMP& SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_P) then
util1(i,j)=0.0
util2(i,j)=0.0
do k=1,kk
util1(i,j)=util2(i,j)
util2(i,j)=util2(i,j)+dpo(i,j,k,m)
if (util2(i,j).ge.dpmixl(i,j,m).and.
& util1(i,j).lt.dpmixl(i,j,m) ) then
dpup=p(i,j,k )-util1(i,j)
dpdn=p(i,j,k+1)-util2(i,j)
q=(util2(i,j)-dpmixl(i,j,m))/max(onemm,dpo(i,j,k,m))
dpmixl(i,j,m)=dpmixl(i,j,m)+(dpdn+q*(dpup-dpdn))
endif
enddo !k
endif !ip
enddo !l
enddo !i
!$OMP END PARALLEL DO
endif
c
c --- --------------
c --- surface stress
c --- --------------
c
if (windf) then
margin =0
c
!$OMP PARALLEL DO PRIVATE(j,i,k,
!$OMP& dpsur,psur,usur,vsur,thksur,
!$OMP& airt,vpmx,wndx,wndy,wind,cdw,rair,
!$OMP& uimo,vimo,simo,samo)
!$OMP& SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_P) then
if (wndflg.eq.4 .or. wndflg.eq.5 .or.
& (iceflg.eq.2 .and. si_c(i,j).gt.0.0)) then
c --- average currents over top thkcdw meters
thksur = onem*min( thkcdw, depths(i,j) )
usur = 0.0
vsur = 0.0
psur = 0.0
do k= 1,kk
dpsur = min( dpo(i,j,k,n), max( 0.0, thksur-psur ) )
#if defined(STOKES)
usur = usur + dpsur*(u(i,j,k,n)+u(i+1,j,k,n)+
& usd(i,j,k)+usd(i+1,j,k))
vsur = vsur + dpsur*(v(i,j,k,n)+v(i,j+1,k,n)+
& vsd(i,j,k)+vsd(i,j+1,k))
#else
usur = usur + dpsur*(u(i,j,k,n)+u(i+1,j,k,n))
vsur = vsur + dpsur*(v(i,j,k,n)+v(i,j+1,k,n))
#endif
psur = psur + dpsur
if (psur.ge.thksur) then
exit
endif
enddo !k
usur = 0.5*( usur/psur + ubavg(i, j,n) +
& ubavg(i+1,j,n) )
vsur = 0.5*( vsur/psur + vbavg(i,j, n) +
& vbavg(i,j+1,n) )
endif !usur,vsur
c
if (wndflg.eq.2 .or. wndflg.eq.3) then ! tau on p grid
if (natm.eq.2) then
surtx(i,j) = taux(i,j,l0)*w0+taux(i,j,l1)*w1
surty(i,j) = tauy(i,j,l0)*w0+tauy(i,j,l1)*w1
else
surtx(i,j) = taux(i,j,l0)*w0+taux(i,j,l1)*w1
& +taux(i,j,l2)*w2+taux(i,j,l3)*w3
surty(i,j) = tauy(i,j,l0)*w0+tauy(i,j,l1)*w1
& +tauy(i,j,l2)*w2+tauy(i,j,l3)*w3
endif !natm
elseif (wndflg.eq.1) then ! tau on u&v grids - NOT RECOMMEDED
if (natm.eq.2) then
surtx(i,j) = ( (taux(i,j,l0)+taux(i+1,j,l0))*w0
& +(taux(i,j,l1)+taux(i+1,j,l1))*w1)*0.5
surty(i,j) = ( (tauy(i,j,l0)+tauy(i,j+1,l0))*w0
& +(tauy(i,j,l1)+tauy(i,j+1,l1))*w1)*0.5
else
surtx(i,j) = ( (taux(i,j,l0)+taux(i+1,j,l0))*w0
& +(taux(i,j,l1)+taux(i+1,j,l1))*w1
& +(taux(i,j,l2)+taux(i+1,j,l2))*w2
& +(taux(i,j,l3)+taux(i+1,j,l3))*w3)*0.5
surty(i,j) = ( (tauy(i,j,l0)+tauy(i,j+1,l0))*w0
& +(tauy(i,j,l1)+tauy(i,j+1,l1))*w1
& +(tauy(i,j,l2)+tauy(i,j+1,l2))*w2
& +(tauy(i,j,l3)+tauy(i,j+1,l3))*w3)*0.5
endif !natm
else !wndflg.eq.4,5,6
c --- calculate stress from 10m winds using cd_coare or cd_core2
if (natm.eq.2) then
airt = airtmp(i,j,l0)*w0+airtmp(i,j,l1)*w1
vpmx = vapmix(i,j,l0)*w0+vapmix(i,j,l1)*w1
wndx = taux(i,j,l0)*w0+ taux(i,j,l1)*w1
wndy = tauy(i,j,l0)*w0+ tauy(i,j,l1)*w1
else
airt = airtmp(i,j,l0)*w0+airtmp(i,j,l1)*w1
& +airtmp(i,j,l2)*w2+airtmp(i,j,l3)*w3
vpmx = vapmix(i,j,l0)*w0+vapmix(i,j,l1)*w1
& +vapmix(i,j,l2)*w2+vapmix(i,j,l3)*w3
wndx = taux(i,j,l0)*w0+ taux(i,j,l1)*w1
& +taux(i,j,l2)*w2+ taux(i,j,l3)*w3
wndy = tauy(i,j,l0)*w0+ tauy(i,j,l1)*w1
& +tauy(i,j,l2)*w2+ tauy(i,j,l3)*w3
endif !natm
wind = sqrt( wndx**2 + wndy**2 )
if (mslprf .or. flxflg.eq.6) then
if (natm.eq.2) then
pair = mslprs(i,j,l0)*w0+mslprs(i,j,l1)*w1
& +prsbas
else
pair = mslprs(i,j,l0)*w0+mslprs(i,j,l1)*w1
& +mslprs(i,j,l2)*w2+mslprs(i,j,l3)*w3
& +prsbas
endif !natm
else
pair = pairc
endif
if (flxflg.eq.6) then !use virtual temperature
rair = pair / (rgas * (tzero+airt) * (1.0+0.608*vpmx))
else
rair = pair / (rgas * (tzero+airt))
endif
c
if (wndflg.eq.4 .and. flxflg.eq.6) then
c --- use wind-current in place of wind for everything
samo = sqrt( (wndx-usur)**2 + (wndy-vsur)**2 )
cdw = 1.0e-3*cd_coarep(samo,vpmx,airt,pair,
& temp(i,j,1,n))
surtx( i,j) = rair*cdw*samo*(wndx-usur)
surty( i,j) = rair*cdw*samo*(wndy-vsur)
wndocn(i,j) = samo !save for thermf
elseif (wndflg.eq.4) then
cdw = 1.0e-3*cd_coare(wind,vpmx,airt,
& temp(i,j,1,n))
c --- use wind-current magnitude and direction for stress
samo = sqrt( (wndx-usur)**2 + (wndy-vsur)**2 )
surtx(i,j) = rair*cdw*samo*(wndx-usur)
surty(i,j) = rair*cdw*samo*(wndy-vsur)
else ! wndflg.eq.5
cdw = 1.0e-3*cd_core2(wind,vpmx,airt,
& temp(i,j,1,n))
c --- use wind-current magnitude and direction for stress
samo = sqrt( (wndx-usur)**2 + (wndy-vsur)**2 )
surtx(i,j) = rair*cdw*samo*(wndx-usur)
surty(i,j) = rair*cdw*samo*(wndy-vsur)
endif
endif !wndflg
c
surtx(i,j) = surtx(i,j) + oftaux(i,j)
surty(i,j) = surty(i,j) + oftauy(i,j)
c
if (ishlf(i,j).eq.0) then !under an ice shelf
surtx(i,j) = 0.0
surty(i,j) = 0.0
elseif (iceflg.eq.2 .and. si_c(i,j).gt.0.0) then
c --- allow for ice-ocean stress
uimo = si_u(i,j) - usur
vimo = si_v(i,j) - vsur
simo = sqrt( uimo**2 + vimo**2 )
surtx(i,j) = (1.0-si_c(i,j))*surtx(i,j) +
& si_c(i,j) *dragw_rho*simo*uimo
surty(i,j) = (1.0-si_c(i,j))*surty(i,j) +
& si_c(i,j) *dragw_rho*simo*vimo
endif !ice-ocean stress
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
c
call xctilr(surtx,1,1, 6,6, halo_pv)
call xctilr(surty,1,1, 6,6, halo_pv)
endif !windf
c
return
end subroutine momtum_hs
c
real function cd_coare(wind,vpmx,airt,sst)
implicit none
c
real wind,vpmx,airt,sst
c
c --- Wind stress drag coefficient * 10^3 from an approximation
c --- to the COARE 3.0 bulk algorithm (Fairall et al. 2003).
c
c --- wind = wind speed (m/s)
c --- vpmx = water vapor mixing ratio (kg/kg)
c --- airt = air temperature (C)
c --- sst = sea temperature (C)
c
c --- Ta-Ts
c --- ==============
c --- STABLE: 7 to 0.75 degC
c --- NEUTRAL: 0.75 to -0.75 degC
c --- UNSTABLE: -0.75 to -8 degC
c
c --- Va
c --- ==============
c --- Low: 1 to 5 m/s
c --- High: 5 to 34 m/s
c
c --- vamax of 34 m/s from Sraj et al, 2013 (MWR-D-12-00228.1).
c
real tamts,q,qva,va
c
real, parameter :: vamin= 1.0, vamax=34.0
real, parameter :: tdmin= -8.0, tdmax= 7.0
real, parameter :: tzero=273.16
c
real, parameter ::
& as0_00=-0.06695, as0_10= 0.09966, as0_20=-0.02477,
& as0_01= 0.3133, as0_11=-2.116, as0_21= 0.2726,
& as0_02=-0.001473, as0_12= 4.626, as0_22=-0.5558,
& as0_03=-0.004056, as0_13=-2.680, as0_23= 0.3139
real, parameter ::
& as5_00= 0.55815, as5_10=-0.005593, as5_20= 0.0006024,
& as5_01= 0.08174, as5_11= 0.2096, as5_21=-0.02629,
& as5_02=-0.0004472, as5_12=-8.634, as5_22= 0.2121,
& as5_03= 2.666e-6, as5_13= 18.63, as5_23= 0.7755
real, parameter ::
& au0_00= 1.891, au0_10=-0.006304, au0_20= 0.0004406,
& au0_01=-0.7182, au0_11=-0.3028, au0_21=-0.01769,
& au0_02= 0.1975, au0_12= 0.3120, au0_22= 0.01303,
& au0_03=-0.01790, au0_13=-0.1210, au0_23=-0.003394
real, parameter ::
& au5_00= 0.6497, au5_10= 0.003827, au5_20=-4.83e-5,
& au5_01= 0.06993, au5_11=-0.2756, au5_21= 0.007710,
& au5_02= 3.541e-5, au5_12=-1.091, au5_22=-0.2555,
& au5_03=-3.428e-6, au5_13= 4.946, au5_23= 0.7654
real, parameter ::
& an0_00= 1.057, an5_00= 0.6825,
& an0_01=-0.06949, an5_01= 0.06945,
& an0_02= 0.01271, an5_02=-0.0001029
real, parameter ::
& ap0_10= as0_00 + as0_10*0.75 + as0_20*0.75**2,
& ap0_11= as0_11*0.75 + as0_21*0.75**2,
& ap0_12= as0_12*0.75 + as0_22*0.75**2,
& ap0_13= as0_13*0.75 + as0_23*0.75**2
real, parameter ::
& ap5_10= as5_00 + as5_10*0.75 + as5_20*0.75**2,
& ap5_11= as5_11*0.75 + as5_21*0.75**2,
& ap5_12= as5_12*0.75 + as5_22*0.75**2,
& ap5_13= as5_13*0.75 + as5_23*0.75**2
real, parameter ::
& am0_10= au0_00 - au0_10*0.75 + au0_20*0.75**2,
& am0_11= - au0_11*0.75 + au0_21*0.75**2,
& am0_12= - au0_12*0.75 + au0_22*0.75**2,
& am0_13= - au0_13*0.75 + au0_23*0.75**2
real, parameter ::
& am5_10= au5_00 - au5_10*0.75 + au5_20*0.75**2,
& am5_11= - au5_11*0.75 + au5_21*0.75**2,
& am5_12= - au5_12*0.75 + au5_22*0.75**2,
& am5_13= - au5_13*0.75 + au5_23*0.75**2
c
c --- saturation specific humidity (lowe, j.appl.met., 16, 100-103, 1976)
real qsatur,t
qsatur(t)=.622e-3*(6.107799961e+00+t*(4.436518521e-01
& +t*(1.428945805e-02+t*(2.650648471e-04
& +t*(3.031240396e-06+t*(2.034080948e-08
& +t* 6.136820929e-11))))))
c
c --- correct tamts to 100% humidity
tamts = airt-sst - 0.61*(airt+tzero)*(qsatur(airt)-vpmx)
tamts = min( tdmax, max( tdmin, tamts ) )
va = max( vamin, min( vamax, wind ) )
qva = 1.0/va
if (va.le.5.0) then
if (tamts.ge. 0.75) then
cd_coare =
& (as0_00 + as0_01* va + as0_02* va**2 + as0_03* va**3)
& + (as0_10 + as0_11*qva + as0_12*qva**2 + as0_13*qva**3)
& *tamts
& + (as0_20 + as0_21*qva + as0_22*qva**2 + as0_23*qva**3)
& *tamts**2
elseif (tamts.le.-0.75) then
cd_coare =
& (au0_00 + au0_01* va + au0_02* va**2 + au0_03* va**3)
& + (au0_10 + au0_11*qva + au0_12*qva**2 + au0_13*qva**3)
& *tamts
& + (au0_20 + au0_21*qva + au0_22*qva**2 + au0_23*qva**3)
& *tamts**2
elseif (tamts.ge. -0.098) then
q = (tamts+0.098)/0.848 !linear between 0.75 and -0.098
cd_coare = q*
& ( ( as0_01* va + as0_02* va**2 + as0_03* va**3)
& + (ap0_10 + ap0_11*qva + ap0_12*qva**2 + ap0_13*qva**3)
& ) + (1.0-q)*
& (an0_00 + an0_01* va + an0_02* va**2)
else
q = (-tamts-0.098)/0.652 !linear between -0.75 and -0.098
cd_coare = q*
& ( ( au0_01* va + au0_02* va**2 + au0_03* va**3)
& + (am0_10 + am0_11*qva + am0_12*qva**2 + am0_13*qva**3)
& ) + (1.0-q)*
& (an0_00 + an0_01* va + an0_02* va**2)
endif !tamts
else !va>5
if (tamts.ge. 0.75) then
cd_coare =
& (as5_00 + as5_01* va + as5_02* va**2 + as5_03* va**3)
& + (as5_10 + as5_11*qva + as5_12*qva**2 + as5_13*qva**3)
& *tamts
& + (as5_20 + as5_21*qva + as5_22*qva**2 + as5_23*qva**3)
& *tamts**2
elseif (tamts.le.-0.75) then
cd_coare =
& (au5_00 + au5_01* va + au5_02* va**2 + au5_03* va**3)
& + (au5_10 + au5_11*qva + au5_12*qva**2 + au5_13*qva**3)
& *tamts
& + (au5_20 + au5_21*qva + au5_22*qva**2 + au5_23*qva**3)
& *tamts**2
elseif (tamts.ge. -0.098) then
q = (tamts+0.098)/0.848 !linear between 0.75 and -0.098
cd_coare = q*
& ( ( as5_01* va + as5_02* va**2 + as5_03* va**3)
& + (ap5_10 + ap5_11*qva + ap5_12*qva**2 + ap5_13*qva**3)
& ) + (1.0-q)*
& (an5_00 + an5_01* va + an5_02* va**2)
else
q = (-tamts-0.098)/0.652 !linear between -0.75 and -0.098
cd_coare = q*
& ( ( au5_01* va + au5_02* va**2 + au5_03* va**3)
& + (am5_10 + am5_11*qva + am5_12*qva**2 + am5_13*qva**3)
& ) + (1.0-q)*
& (an5_00 + an5_01* va + an5_02* va**2)
endif !tamts
endif !va
c
end function cd_coare
c
real function cd_coarep(samo,vpmx,airt,pair,sst)
implicit none
c
real samo,vpmx,airt,pair,sst
c
c --- Wind stress drag coefficient * 10^3 from an approximation
c --- to the COARE 3.0 bulk algorithm (Fairall et al. 2003).
c
c --- samo = wind-ocean speed (m/s)
c --- vpmx = water vapor mixing ratio (kg/kg)
c --- airt = air temperature (C)
c --- pair = air pressure (Pa)
c --- sst = sea temperature (C)
c
c --- Ta-Ts
c --- ==============
c --- STABLE: 7 to 0.75 degC
c --- NEUTRAL: 0.75 to -0.75 degC
c --- UNSTABLE: -0.75 to -8 degC
c
c --- Va
c --- ==============
c --- Low: 1 to 5 m/s
c --- High: 5 to 34 m/s
c
c --- vamax of 34 m/s from Sraj et al, 2013 (MWR-D-12-00228.1).
c
real tamts,q,qva,va
c
real, parameter :: vamin= 1.0, vamax=34.0
real, parameter :: tdmin= -8.0, tdmax= 7.0
real, parameter :: tzero=273.16
c
real, parameter ::
& as0_00=-0.06695, as0_10= 0.09966, as0_20=-0.02477,
& as0_01= 0.3133, as0_11=-2.116, as0_21= 0.2726,
& as0_02=-0.001473, as0_12= 4.626, as0_22=-0.5558,
& as0_03=-0.004056, as0_13=-2.680, as0_23= 0.3139
real, parameter ::
& as5_00= 0.55815, as5_10=-0.005593, as5_20= 0.0006024,
& as5_01= 0.08174, as5_11= 0.2096, as5_21=-0.02629,
& as5_02=-0.0004472, as5_12=-8.634, as5_22= 0.2121,
& as5_03= 2.666e-6, as5_13= 18.63, as5_23= 0.7755
real, parameter ::
& au0_00= 1.891, au0_10=-0.006304, au0_20= 0.0004406,
& au0_01=-0.7182, au0_11=-0.3028, au0_21=-0.01769,
& au0_02= 0.1975, au0_12= 0.3120, au0_22= 0.01303,
& au0_03=-0.01790, au0_13=-0.1210, au0_23=-0.003394
real, parameter ::
& au5_00= 0.6497, au5_10= 0.003827, au5_20=-4.83e-5,
& au5_01= 0.06993, au5_11=-0.2756, au5_21= 0.007710,
& au5_02= 3.541e-5, au5_12=-1.091, au5_22=-0.2555,
& au5_03=-3.428e-6, au5_13= 4.946, au5_23= 0.7654
real, parameter ::
& an0_00= 1.057, an5_00= 0.6825,
& an0_01=-0.06949, an5_01= 0.06945,
& an0_02= 0.01271, an5_02=-0.0001029
real, parameter ::
& ap0_10= as0_00 + as0_10*0.75 + as0_20*0.75**2,
& ap0_11= as0_11*0.75 + as0_21*0.75**2,
& ap0_12= as0_12*0.75 + as0_22*0.75**2,
& ap0_13= as0_13*0.75 + as0_23*0.75**2
real, parameter ::
& ap5_10= as5_00 + as5_10*0.75 + as5_20*0.75**2,
& ap5_11= as5_11*0.75 + as5_21*0.75**2,
& ap5_12= as5_12*0.75 + as5_22*0.75**2,
& ap5_13= as5_13*0.75 + as5_23*0.75**2
real, parameter ::
& am0_10= au0_00 - au0_10*0.75 + au0_20*0.75**2,
& am0_11= - au0_11*0.75 + au0_21*0.75**2,
& am0_12= - au0_12*0.75 + au0_22*0.75**2,
& am0_13= - au0_13*0.75 + au0_23*0.75**2
real, parameter ::
& am5_10= au5_00 - au5_10*0.75 + au5_20*0.75**2,
& am5_11= - au5_11*0.75 + au5_21*0.75**2,
& am5_12= - au5_12*0.75 + au5_22*0.75**2,
& am5_13= - au5_13*0.75 + au5_23*0.75**2
c
real satvpr,qsaturp,t,t6,p6
c
c --- saturation vapor pressure (Pa),
c --- from a polynominal approximation (lowe, j.appl.met., 16, 100-103, 1976)
satvpr(t)= 100.0*(6.107799961e+00+t*(4.436518521e-01
& +t*(1.428945805e-02+t*(2.650648471e-04
& +t*(3.031240396e-06+t*(2.034080948e-08
& +t* 6.136820929e-11))))))
c
c --- pressure dependent saturation mixing ratio (kg/kg)
c --- p6 is pressure in Pa
qsaturp(t6,p6)=0.622*(satvpr(t6)/(p6-satvpr(t6)))
c
c --- correct tamts to 100% humidity
tamts = airt-sst -
& 0.608*(airt+tzero)*(qsaturp(airt,pair)-vpmx)
tamts = min( tdmax, max( tdmin, tamts ) )
va = max( vamin, min( vamax, samo ) )
qva = 1.0/va
if (va.le.5.0) then
if (tamts.ge. 0.75) then
cd_coarep =
& (as0_00 + as0_01* va + as0_02* va**2 + as0_03* va**3)
& + (as0_10 + as0_11*qva + as0_12*qva**2 + as0_13*qva**3)
& *tamts
& + (as0_20 + as0_21*qva + as0_22*qva**2 + as0_23*qva**3)
& *tamts**2
elseif (tamts.le.-0.75) then
cd_coarep =
& (au0_00 + au0_01* va + au0_02* va**2 + au0_03* va**3)
& + (au0_10 + au0_11*qva + au0_12*qva**2 + au0_13*qva**3)
& *tamts
& + (au0_20 + au0_21*qva + au0_22*qva**2 + au0_23*qva**3)
& *tamts**2
elseif (tamts.ge. -0.098) then
q = (tamts+0.098)/0.848 !linear between 0.75 and -0.098
cd_coarep = q*
& ( ( as0_01* va + as0_02* va**2 + as0_03* va**3)
& + (ap0_10 + ap0_11*qva + ap0_12*qva**2 + ap0_13*qva**3)
& ) + (1.0-q)*
& (an0_00 + an0_01* va + an0_02* va**2)
else
q = (-tamts-0.098)/0.652 !linear between -0.75 and -0.098
cd_coarep = q*
& ( ( au0_01* va + au0_02* va**2 + au0_03* va**3)
& + (am0_10 + am0_11*qva + am0_12*qva**2 + am0_13*qva**3)
& ) + (1.0-q)*
& (an0_00 + an0_01* va + an0_02* va**2)
endif !tamts
else !va>5
if (tamts.ge. 0.75) then
cd_coarep =
& (as5_00 + as5_01* va + as5_02* va**2 + as5_03* va**3)
& + (as5_10 + as5_11*qva + as5_12*qva**2 + as5_13*qva**3)
& *tamts
& + (as5_20 + as5_21*qva + as5_22*qva**2 + as5_23*qva**3)
& *tamts**2
elseif (tamts.le.-0.75) then
cd_coarep =
& (au5_00 + au5_01* va + au5_02* va**2 + au5_03* va**3)
& + (au5_10 + au5_11*qva + au5_12*qva**2 + au5_13*qva**3)
& *tamts
& + (au5_20 + au5_21*qva + au5_22*qva**2 + au5_23*qva**3)
& *tamts**2
elseif (tamts.ge. -0.098) then
q = (tamts+0.098)/0.848 !linear between 0.75 and -0.098
cd_coarep = q*
& ( ( as5_01* va + as5_02* va**2 + as5_03* va**3)
& + (ap5_10 + ap5_11*qva + ap5_12*qva**2 + ap5_13*qva**3)
& ) + (1.0-q)*
& (an5_00 + an5_01* va + an5_02* va**2)
else
q = (-tamts-0.098)/0.652 !linear between -0.75 and -0.098
cd_coarep = q*
& ( ( au5_01* va + au5_02* va**2 + au5_03* va**3)
& + (am5_10 + am5_11*qva + am5_12*qva**2 + am5_13*qva**3)
& ) + (1.0-q)*
& (an5_00 + an5_01* va + an5_02* va**2)
endif !tamts
endif !va
c
end function cd_coarep
c
real function cd_core2(wind,vpmx,airt,sst)
implicit none
c
real wind,vpmx,airt,sst
c
c --- Wind stress drag coefficient * 10^3 from
c --- the CORE v2 bulk algorithm (Large and Yeager, 2009).
c
c --- wind = wind speed (m/s)
c --- vpmx = water vapor mixing ratio (kg/kg)
c --- airt = air temperature (C)
c --- sst = sea temperature (C)
c
c --- Added to HYCOM by Alexandra Bozec, FSU.
c
integer it_a
real u10,v10,uw10,uw
real cd_n10,cd_n10_rt,ce_n10,ch_n10,cd_rt,stab,
& tv,tstar,qstar,bstar,zeta,x2,x,xx,
& psi_m,psi_h,z0,rair,qrair,zi
real cd10,ce10,ch10,ustar
c
real, parameter :: vonkar= 0.4 !Von Karmann constant
real, parameter :: tzero=273.16 !celsius to kelvin offset
real, parameter :: g= 9.806 !same as HYCOM's g
c
c --- saturation specific humidity
real qsatur5,t,qra
qsatur5(t,qra)= 0.98*qra*6.40380e5*exp(-5107.4/(t+tzero))
c
c --- CORE v2 Large and Yeager 2009 Clim. Dyn.: The global climatology
c --- of an interannually varying air-sea flux dataset.
c --- The bulk formulae effectively transform the problem of specifying
c --- the turbulent surface fluxes (at zi=10m) into one of describing
c --- the near surface atmospheric state (wind, temperature and humidity).
c
* write(6,'(a,1p4g14.5)')
* & ' wind,vpmx,airt,sst =',wind,vpmx,airt,sst
*
rair = 1.22
rair = 1.0/rair
zi = 10.0
tv = (airt+tzero)*(1.0+0.608*vpmx) !in Kelvin
uw = max(wind, 0.5) !0.5 m/s floor on wind (undocumented NCAR)
uw10 = uw !first guess 10m wind
cd_n10 = (2.7/uw10+0.142+0.0764*uw10)*1.0e-3 !L-Y eqn. 6a
* write(6,'(a,1p4g14.5)')
* & 'cd_n10 =',cd_n10,
* & (2.7/uw10)*1.0e-3,0.142*1.0e-3,(0.0764*uw10)*1.0e-3
cd_n10_rt = sqrt(cd_n10)
ce_n10 = 34.6 *cd_n10_rt*1.0e-3 !L-Y eqn. 6b
stab = 0.5 + sign(0.5,airt-sst)
ch_n10 = (18.0*stab+32.7*(1-stab))*cd_n10_rt*1.0e-3 !L-Y eqn. 6c
cd10 = cd_n10 !first guess for exchange coeff's at z
ch10 = ch_n10
ce10 = ce_n10
* write(6,'(a,1p4g14.5)')
* & 'uw10,psi_m,cd_n10,cd10=',uw10,0.0,cd_n10,cd10
*
do it_a= 1,2 !Monin-Obukhov iteration
cd_rt = sqrt(cd10)
ustar = cd_rt*uw !L-Y eqn. 7a
tstar = (ch10/cd_rt)*(airt-sst) !L-Y eqn. 7b
qstar = (ce10/cd_rt)*
& (vpmx-qsatur5(sst,qrair)) !L-Y eqn. 7c
bstar = g*(tstar/tv+qstar/(vpmx+1.0/0.608))
zeta = vonkar*bstar*zi/(ustar*ustar) !L-Y eqn. 8a
zeta = sign( min(abs(zeta),10.0), zeta ) !undocumented NCAR
x2 = sqrt(abs(1.0-16.0*zeta)) !L-Y eqn. 8b
x2 = max(x2, 1.0) !undocumented NCAR
x = sqrt(x2)
if (zeta > 0.0) then
psi_m = -5.0*zeta !L-Y eqn. 8c
psi_h = -5.0*zeta !L-Y eqn. 8c
else
psi_m = log((1.0+2.0*x+x2)*(1.0+x2)/8.0)
& - 2.0*(atan(x)-atan(1.0)) !L-Y eqn. 8d
psi_h = 2.0*log((1.0+x2)/2.0) !L-Y eqn. 8e
end if
uw10 = uw/(1.0+cd_n10_rt*(log(zi/10.0)-psi_m) !L-Y eqn. 9
& /vonkar)
cd_n10 = (2.7/uw10+0.142+0.0764*uw10)*1.0e-3 !L-Y eqn. 6a again
cd_n10_rt = sqrt(cd_n10)
ce_n10 = 34.6*cd_n10_rt*1.0e-3 !L-Y eqn. 6b again
stab = 0.5 + sign(0.5,zeta)
ch_n10 =(18.0*stab+32.7*(1.0-stab))*cd_n10_rt*1.0e-3 !L-Y eqn. 6c again
z0 = 10.0*exp(-vonkar/cd_n10_rt) !diagnostic
c
xx = (log(zi/10.0)-psi_m)/vonkar
cd10 = cd_n10/(1.0+cd_n10_rt*xx)**2 !L-Y 10a
xx = (log(zi/10.0)-psi_h)/vonkar
ch10 = ch_n10/(1.0+ch_n10*xx/cd_n10_rt) *
& sqrt(cd10/cd_n10) !L-Y 10b
ce10 = ce_n10/(1.0+ce_n10*xx/cd_n10_rt) *
& sqrt(cd10/cd_n10) !L-Y 10c
* write(6,'(a,1p4g14.5)')
* & 'uw10,psi_m,cd_n10,cd10=',uw10,psi_m,cd_n10,cd10
enddo
c
cd_core2 = cd10*1.0e3
return
end function cd_core2
c
subroutine momtum(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 ! Stokes Drift Velocity Module
#endif
use mod_nc !Netcdf output
implicit none
c
integer m,n
c
c --- ---------------------------------------------------------
c --- momentum equations (2nd order version)
c
c --- Enstrophy conserving advection scheme (Sadourney, 1975)
c
c --- diffusion is Laplacian and/or biharmonic, both with
c --- "constant" and deformation dependent coefficients.
c
c --- hydrostatic equation and surface stress via momtum_hs
c --- ---------------------------------------------------------
c --- on entry:
c --- saln(:,:,:,m) = time step t with RA time smoothing
c --- saln(:,:,:,n) = time step t+1
c
c --- dp(:,:,:,m) = time step t with RA time smoothing
c --- dp(:,:,:,n) = time step t+1
c
c --- dpo(:,:,:,n) = time step t-1
c --- dpo(:,:,:,m) = time step t
c
c --- dpv(:,:,:,n) = time step t-1
c --- dpv(:,:,:,m) = time step t
c --- dpu(:,:,:,n) = time step t-1
c --- dpu(:,:,:,m) = time step t
c
c --- v(:,:,:,n) = time step t-1
c --- v(:,:,:,m) = time step t
c --- u(:,:,:,n) = time step t-1
c --- u(:,:,:,m) = time step t
c
c --- on exit:
c --- dpv(:,:,:,m) = time step t with RA time smoothing
c --- dpv(:,:,:,n) = time step t+1
c --- dpu(:,:,:,m) = time step t with RA time smoothing
c --- dpu(:,:,:,n) = time step t+1
c
c --- v(:,:,:,m) = time step t with RA time smoothing
c --- v(:,:,:,n) = time step t+1
c --- u(:,:,:,m) = time step t with RA time smoothing
c --- u(:,:,:,n) = time step t+1
c
c --- vtotn(:,:) = time step t-1 to t+1 barotropic tendency
c --- utotn(:,:) = time step t-1 to t+1 barotropic tendency
c --- ---------------------------------------------------------
c
logical, parameter :: lpipe_momtum=.false. !usually .false.
c
#if defined(RELO)
real, save, allocatable, dimension(:,:) ::
& vis2u,vis4u,vis2v,vis4v,vort,
& wgtia,wgtib,wgtja,wgtjb,
& dl2u,dl2uja,dl2ujb,dl2v,dl2via,dl2vib,
& pnk0,pnkp,stresl
#else
real, dimension(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy) ::
& vis2u,vis4u,vis2v,vis4v,vort,
& wgtia,wgtib,wgtja,wgtjb,
& dl2u,dl2uja,dl2ujb,dl2v,dl2via,dl2vib,
& pnk0,pnkp,stresl
common/momtumr4/