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mod_momtum.F90
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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
!
! --- module for momtum and related routines
!
private !! default is private
public :: momtum_hs, momtum, momtum4, momtum_init
!
#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, &
defor1, defor2, & ! deformation components
uflux1,vflux1, & ! mass fluxes
potvor ! potential vorticity
contains
subroutine momtum_init()
implicit none
!
! --- ----------------------------------------------
! --- Initialization of arrays for momentum equation
! --- ----------------------------------------------
!
#if defined(RELO)
allocate( &
defor1(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy), &
defor2(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy), &
uflux1(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy), &
vflux1(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy), &
potvor(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy), &
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) )
call mem_stat_add( 10*(idm+2*nbdy)*(jdm+2*nbdy) )
#endif
stress(:,:) = 0.0
stresx(:,:) = r_init
stresy(:,:) = r_init
dpmx(:,:) = r_init
thkbop(:,:) = r_init
! --- all of these should be zero on land.
defor1(:,:) = 0.0
defor2(:,:) = 0.0
uflux1(:,:) = 0.0
vflux1(:,:) = 0.0
potvor(:,:) = 0.0
return
end subroutine momtum_init
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
!
integer m,n
!
! --- -----------------------------------------
! --- hydrostatic equation (and surface stress)
! --- -----------------------------------------
!
logical, parameter :: lpipe_momtum=.false. !usually .false.
!
#if defined (USE_NUOPC_CESMBETA)
logical, parameter :: cesmbeta =.true.
#else
logical, parameter :: cesmbeta =.false.
#endif
!
real, parameter :: dragw_rho=0.01072d0*1026.0d0 !ice-ocean drag from CICE
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
!
character text*12
!
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
! &,iffstep
! data iffstep/0/
! save iffstep
!
! real*8 wtime
! external wtime
! real*8 wtime1(10),wtime2(20,kdm),wtimes
!
# include "stmt_fns.h"
!
!
mbdy = 6
!
! --- 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)
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
!
! --- tidal forcing
!
if (tidflg.eq.2 .or. tidflg.eq.3) then
hlstep=0
call tides_body(hlstep)
endif
!
! --- tidal velocities
!
if (tidflg.eq.-1) then
hlstep=0
call tides_observed_vel(hlstep)
endif
!
! --- hydrostatic equation (and surface stress)
!
! wtime1( 1) = wtime()
!
! --- rhs: th3d.m, temp.m, saln.m, p, pbavg.m
! --- lhs: thstar, p, oneta, montg
!
margin = mbdy
!
!$OMP PARALLEL DO PRIVATE(j,k,i) &
!$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
!
! --- sigma-star is virtual potential density, as defined in
! --- Sun et.al. (1999), 'Inclusion of thermobaricity in
! --- isopycnic-coordinate ocean models', JPO 29 pp 2719-2729.
!
#if defined(KAPPAF_CENTERED)
! --- use layer centered pressure in converting sigma to sigma-star.
#else
! --- use upper interface pressure in converting sigma to sigma-star.
! --- to avoid density variations in layers intersected by bottom
#endif
!
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, &
#if defined(KAPPAF_CENTERED)
0.5*(p(i,j,k+1)+p(i,j,k)), &
#else
p(i,j,k), &
#endif
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, &
#if defined(KAPPAF_CENTERED)
0.5*(p(i,j,k+1)+p(i,j,k)), &
#else
p(i,j,k), &
#endif
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, &
#if defined(KAPPAF_CENTERED)
0.5*(p(i,j,k+1)+p(i,j,k)), &
#else
p(i,j,k), &
#endif
kapi(i,j))
endif !kapref
else !non-thermobaric
thstar(i,j,k,1)=th3d(i,j,k,m)
endif !thermobaric:else
!
p(i,j,k+1)=p(i,j,k)+dp(i,j,k,m)
!
if (sshflg.eq.1 .or. sshflg.eq.3) then
sumth = sumth + dp(i,j,k,m)*th3d(i,j,k,m)
sumdp = sumdp + dp(i,j,k,m)
endif !sshflg
enddo !k
!
if (sshflg.eq.1 .or. sshflg.eq.3) 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
!
! --- m_prime in lowest layer:
montg(i,j,kk,1)=psikk(i,j,1)+montg_c(i,j)+ &
( p(i,j,kk+1)*(thkk(i,j,1)-thstar(i,j,kk,1)) &
-pbavg(i,j,m)*thstar(i,j,kk,1) )*svref**2
if (kapref.eq.-1) then
montg(i,j,kk,2)=psikk(i,j,2)+montg_c(i,j)+ &
( p(i,j,kk+1)*(thkk(i,j,2)-thstar(i,j,kk,2)) &
-pbavg(i,j,m)*thstar(i,j,kk,2) )*svref**2
endif !kapref.eq.-1
!
! --- 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(i,j,m) &
*(thstar(i,j,k+1,1)-thstar(i,j,k,1))*svref**2
if (kapref.eq.-1) then
montg(i,j,k,2)=montg(i,j,k+1,2)+p(i,j,k+1)*oneta(i,j,m) &
*(thstar(i,j,k+1,2)-thstar(i,j,k,2))*svref**2
endif !kapref.eq.-1
enddo !k
!
! --- 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) + svref*pbavg(i,j,m)
!
!diag if (sshflg.eq.1 .or. sshflg.eq.3) then
!diag if (itest.gt.0 .and. jtest.gt.0) then
!diag write (lp,'(i9,2i6,3x,a,2f12.6,f12.2)') &
!diag nstep,itest+i0,jtest+j0, &
!diag 'sssh =', &
!diag steric(i,j),sshgmn(i,j),sumdp
!diag write (lp,'(i9,2i6,3x,a,3f12.6)') &
!diag nstep,itest+i0,jtest+j0, &
!diag 'thmn =', &
!diag sumth,thmean(i,j),1000.0+thbase+sumth
!diag write (lp,'(i9,2i6,3x,a,3f12.6)') &
!diag nstep,itest+i0,jtest+j0, &
!diag 'ssh =', &
!diag srfhgt(i,j),steric(i,j),srfhgt(i,j)-steric(i,j)
!diag endif !test
!diag endif !sshflg
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
!
if (lpipe .and. lpipe_momtum .and. mslprf) then
! --- compare two model runs.
util4(1:ii,1:jj) = mslprs(1:ii,1:jj,l0)
write (text,'(a9,i3)') 'mslprs l=',l0
call pipe_compare_sym1(util4, ip,text)
util4(1:ii,1:jj) = mslprs(1:ii,1:jj,l1)
write (text,'(a9,i3)') 'mslprs l=',l1
call pipe_compare_sym1(util4, ip,text)
!
util4(1:ii,1:jj) = mslprs(1:ii,1:jj,l0)-mslprs(1:ii,0:jj-1,l0)
write (text,'(a9,i3)') 'mslprY l=',l0
call pipe_compare_sym1(util4, iv,text)
util4(1:ii,1:jj) = mslprs(1:ii,1:jj,l1)-mslprs(1:ii,0:jj-1,l1)
write (text,'(a9,i3)') 'mslprY l=',l1
call pipe_compare_sym1(util4, iv,text)
!
util4(1:ii,1:jj) = mslprs(1:ii,1:jj,l0)-mslprs(0:ii-1,1:jj,l0)
write (text,'(a9,i3)') 'mslprX l=',l0
call pipe_compare_sym1(util4, iu,text)
util4(1:ii,1:jj) = mslprs(1:ii,1:jj,l1)-mslprs(0:ii-1,1:jj,l1)
write (text,'(a9,i3)') 'mslprX l=',l1
call pipe_compare_sym1(util4, iu,text)
endif
!
! --- account for temporal smoothing of mid-time dpmixl. calculate the vertical
! --- excursions of the coordinates immediately above and below the mixed
! --- layer base, then vertically interpolate this motion to dpmixl(i,j,m)
!
if(hybrid .and. mxlkta) then
!
! --- rhs: dp, dpmixl.m
! --- lhs: util1, util2
!
margin = mbdy
!
!$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
!
! --- --------------
! --- surface stress
! --- --------------
!
if (windf) then
margin =0
!$OMP PARALLEL DO PRIVATE(j,i,k, &
!$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 (amoflg.ne.0 .or. &
(iceflg.eq.2 .and. si_c(i,j).gt.0.0)) then
! --- 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 ) )
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))
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
!
if (wndflg.eq.2 .or. wndflg.eq.3) then ! tau on p grid
if (cesmbeta .and. cpl_taux) then
surtx(i,j) = imp_taux(i,j,1)
elseif (natm.eq.2) then
surtx(i,j) = taux(i,j,l0)*w0+taux(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
endif ! cpl_taux
if (cesmbeta .and. cpl_tauy) then
surty(i,j) = imp_tauy(i,j,1)
elseif (natm.eq.2) then
surty(i,j) = tauy(i,j,l0)*w0+tauy(i,j,l1)*w1
else
surty(i,j) = tauy(i,j,l0)*w0+tauy(i,j,l1)*w1 &
+ tauy(i,j,l2)*w2+tauy(i,j,l3)*w3
endif ! cpl_tauy
elseif (wndflg.eq.1) then ! tau on u&v grids - NOT RECOMMEDED
#if defined (USE_NUOPC_CESMBETA) && !defined (DMI_CICE_COUPLED)
if (mnproc.eq.1) then
write(lp,*)
write(lp,*) 'error in momtum - wndflg should be '
write(lp,*) ' eq. to 2 with NUOPC'
endif !1st tile
call xcstop('(momtum)')
stop '(momtum)'
#endif /* USE_NUOPC_CESMBETA and DMI_CICE_COUPLED*/
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
! --- calculate stress from 10m winds using cd_coare or cd_core2
! --- for cd_core2, vpmx (vapmix) is specific humidity
#if defined (USE_NUOPC_CESMBETA) && !defined (DMI_CICE_COUPLED)
if (mnproc.eq.1) then
write(lp,*)
write(lp,*) 'error in momtum - wndflg should be '
write(lp,*) ' eq. to 2 with NUOPC'
endif !1st tile
call xcstop('(momtum)')
stop '(momtum)'
#endif /* DMI_CICE_COUPLED and USE_NUOPC_CESMBETA */
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
!
if (wndflg.eq.4 .and. flxflg.eq.6) then
if (amoflg.ne.0) then
! --- use wind-current in place of wind for everything
! --- set ocnscl to 1.0 for full relative wind
samo = sqrt( (wndx-ocnscl*usur)**2 +&
(wndy-ocnscl*vsur)**2 )
cdw = 1.0e-3*cd_coarep(samo,vpmx,airt,pair, &
temp(i,j,1,n))
surtx( i,j) = rair*cdw*samo*(wndx-ocnscl*usur)
surty( i,j) = rair*cdw*samo*(wndy-ocnscl*vsur)
wndocn(i,j) = samo !save for thermf
else
! --- use wind for everything
cdw = 1.0e-3*cd_coarep(wind,vpmx,airt,pair, &
temp(i,j,1,n))
surtx( i,j) = rair*cdw*wind*wndx
surty( i,j) = rair*cdw*wind*wndy
endif !amoflg
elseif (wndflg.eq.4) then
cdw = 1.0e-3*cd_coare(wind,vpmx,airt, &
temp(i,j,1,n))
if (amoflg.ne.0) then
! --- use wind-current magnitude and direction for stress
! --- set ocnscl to 1.0 for full relative wind
samo = sqrt( (wndx-ocnscl*usur)**2 +&
(wndy-ocnscl*vsur)**2 )
surtx(i,j) = rair*cdw*samo*(wndx-ocnscl*usur)
surty(i,j) = rair*cdw*samo*(wndy-ocnscl*vsur)
else
! --- use wind for everything
surtx(i,j) = rair*cdw*wind*wndx
surty(i,j) = rair*cdw*wind*wndy
endif !amoflg
else ! wndflg.eq.5
! --- vpmx assumed to contain specific humidity
cdw = 1.0e-3*cd_core2(wind,vpmx,airt, &
temp(i,j,1,n))
if (amoflg.ne.0) then
! --- use wind-current magnitude and direction for stress
! --- set ocnscl to 1.0 for full relative wind
samo = sqrt( (wndx-ocnscl*usur)**2 +&
(wndy-ocnscl*vsur)**2 )
surtx(i,j) = rair*cdw*samo*(wndx-ocnscl*usur)
surty(i,j) = rair*cdw*samo*(wndy-ocnscl*vsur)
else
! --- use U10 magnitude and direction for stress
surtx(i,j) = rair*cdw*wind*wndx
surty(i,j) = rair*cdw*wind*wndy
endif !amoflg
endif
endif !wndflg
!
if (stroff) then
surtx(i,j) = surtx(i,j) + oftaux(i,j)
surty(i,j) = surty(i,j) + oftauy(i,j)
endif
!
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
! --- allow for ice-ocean stress
#if defined (DMI_CICE_COUPLED)
surtx(i,j) = (1.0-si_c(i,j))*surtx(i,j) + &
si_c(i,j) *si_tx(i,j)
surty(i,j) = (1.0-si_c(i,j))*surty(i,j) + &
si_c(i,j) *si_ty(i,j)
#elif defined (USE_NUOPC_CESMBETA)
! --- ice-ocean stress already in surtx and surty
#else
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 /* USE_NUOPC_CESMBETA */
endif !ice-ocean stress
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
!
call xctilr(surtx,1,1, 6,6, halo_pv)
call xctilr(surty,1,1, 6,6, halo_pv)
endif !windf
!
return
!
contains
include 'internal_kappaf.h'
end subroutine momtum_hs
!
real function cd_coare(wind,vpmx,airt,sst)
implicit none
!
real wind,vpmx,airt,sst
!
! --- Wind stress drag coefficient * 10^3 from an approximation
! --- to the COARE 3.0 bulk algorithm (Fairall et al. 2003).
!
! --- wind = wind speed (m/s)
! --- vpmx = water vapor mixing ratio (kg/kg)
! --- airt = air temperature (C)
! --- sst = sea temperature (C)
!
! --- Ta-Ts
! --- ==============
! --- STABLE: 7 to 0.75 degC
! --- NEUTRAL: 0.75 to -0.75 degC
! --- UNSTABLE: -0.75 to -8 degC
!
! --- Va
! --- ==============
! --- Low: 1 to 5 m/s
! --- High: 5 to 34 m/s
!
! --- vamax of 34 m/s from Sraj et al, 2013 (MWR-D-12-00228.1).
!
real tamts,q,qva,va
!
real, parameter :: vamin= 1.0, vamax=34.0
real, parameter :: tdmin= -8.0, tdmax= 7.0
real, parameter :: tzero=273.16
!
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
!
! --- 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))))))
!
! --- 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
!
end function cd_coare
!
real function cd_coarep(samo,vpmx,airt,pair,sst)
implicit none
!
real samo,vpmx,airt,pair,sst
!
! --- Wind stress drag coefficient * 10^3 from an approximation
! --- to the COARE 3.0 bulk algorithm (Fairall et al. 2003).
!
! --- samo = wind-ocean speed or absolute wind speed (m/s)
! --- vpmx = water vapor mixing ratio (kg/kg)
! --- airt = air temperature (C)
! --- pair = air pressure (Pa)
! --- sst = sea temperature (C)
!
! --- Ta-Ts
! --- ==============
! --- STABLE: 7 to 0.75 degC
! --- NEUTRAL: 0.75 to -0.75 degC
! --- UNSTABLE: -0.75 to -8 degC
!
! --- Va
! --- ==============
! --- Low: 1 to 5 m/s
! --- High: 5 to 34 m/s
!
! --- vamax of 34 m/s from Sraj et al, 2013 (MWR-D-12-00228.1).
!
real tamts,q,qva,va
!
real, parameter :: vamin= 1.0, vamax=34.0
real, parameter :: tdmin= -8.0, tdmax= 7.0
real, parameter :: tzero=273.16
!
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
!
real satvpr,qsaturp,t,t6,p6
!
! --- saturation vapor pressure (Pa),
! --- 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))))))
!
! --- pressure dependent saturation mixing ratio (kg/kg)
! --- p6 is pressure in Pa
qsaturp(t6,p6)=0.622*(satvpr(t6)/(p6-satvpr(t6)))
!
! --- 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
!
end function cd_coarep
!
real function cd_core2(wind,sphm,airt,sst)
implicit none
!
real wind,sphm,airt,sst
!
! --- Wind stress drag coefficient * 10^3 from
! --- the CORE v2 bulk algorithm (Large and Yeager, 2009).
!
! --- wind = absolute wind speed (m/s)
! --- sphm = specific humidity (kg/kg)
! --- airt = air temperature (C)
! --- sst = sea temperature (C)
!
! --- Added to HYCOM by Alexandra Bozec, FSU.
!
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
!
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
!
! --- saturation specific humidity
real qsatur5,t,qra
qsatur5(t,qra)= 0.98*qra*6.40380e5*exp(-5107.4/(t+tzero))
!
! --- CORE v2 Large and Yeager 2009 Clim. Dyn.: The global climatology
! --- of an interannually varying air-sea flux dataset.
! --- The bulk formulae effectively transform the problem of specifying
! --- the turbulent surface fluxes (at zi=10m) into one of describing
! --- the near surface atmospheric state (wind, temperature and humidity).
!
! write(6,'(a,1p4g14.5)')
! & ' wind,sphm,airt,sst =',wind,sphm,airt,sst
!
rair = 1.22
qrair = 1.0/rair
zi = 10.0
tv = (airt+tzero)*(1.0+0.608*sphm) !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)* &
(sphm-qsatur5(sst,qrair)) !L-Y eqn. 7c
bstar = g*(tstar/tv+qstar/(sphm+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
!
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
!