C $Header: /u/gcmpack/MITgcm/pkg/kpp/kpp_forcing_surf.F,v 1.5 2009/11/21 01:27:07 dimitri Exp $
C $Name: $
#include "KPP_OPTIONS.h"
CBOP
C !ROUTINE: KPP_FORCING_SURF
C !INTERFACE: ==========================================================
SUBROUTINE KPP_FORCING_SURF(
I rhoSurf, surfForcU, surfForcV,
I surfForcT, surfForcS, surfForcTice,
I Qsw,
#ifdef ALLOW_SALT_PLUME
I saltPlumeFlux,
#endif /* ALLOW_SALT_PLUME */
I ttalpha, ssbeta,
O ustar, bo, bosol,
#ifdef ALLOW_SALT_PLUME
O boplume,
#endif /* ALLOW_SALT_PLUME */
O dVsq,
I ikppkey, iMin, iMax, jMin, jMax, bi, bj, myTime, myThid )
C !DESCRIPTION: \bv
C /==========================================================\
C | SUBROUTINE KPP_FORCING_SURF |
C | o Compute all surface related KPP fields: |
C | - friction velocity ustar |
C | - turbulent and radiative surface buoyancy forcing, |
C | bo and bosol, and surface haline buoyancy forcing |
C | boplume |
C | - velocity shear relative to surface squared (this is |
C | not really a surface affected quantity unless it is |
C | computed with respect to some resolution independent |
C | reference level, that is KPP_ESTIMATE_UREF defined ) |
C |==========================================================|
C \==========================================================/
IMPLICIT NONE
c taux / rho = surfForcU (N/m^2)
c tauy / rho = surfForcV (N/m^2)
c ustar = sqrt( sqrt( taux^2 + tauy^2 ) / rho ) (m/s)
c bo = - g * ( alpha*surfForcT +
c beta *surfForcS ) / rho (m^2/s^3)
c bosol = - g * alpha * Qsw * drF(1) / rho (m^2/s^3)
c boplume = g * ( beta *saltPlumeFlux/rhoConst )/rho (m^2/s^3)
c------------------------------------------------------------------------
c \ev
C !USES: ===============================================================
#include "SIZE.h"
#include "EEPARAMS.h"
#include "PARAMS.h"
#include "GRID.h"
#include "DYNVARS.h"
#include "KPP_PARAMS.h"
C !INPUT PARAMETERS: ===================================================
C Routine arguments
C ikppkeyb - key for storing trajectory for adjoint (taf)
c imin, imax, jmin, jmax - array computation indices
C bi, bj - array indices on which to apply calculations
C myTime - Current time in simulation
C myThid - Current thread id
c rhoSurf- density of surface layer (kg/m^3)
C surfForcU units are r_unit.m/s^2 (=m^2/s^2 if r=z)
C surfForcV units are r_unit.m/s^2 (=m^2/s^-2 if r=z)
C surfForcS units are r_unit.psu/s (=psu.m/s if r=z)
C - EmPmR * S_surf plus salinity relaxation*drF(1)
C surfForcT units are r_unit.Kelvin/s (=Kelvin.m/s if r=z)
C - Qnet (+Qsw) plus temp. relaxation*drF(1)
C -> calculate -lambda*(T(model)-T(clim))
C Qnet assumed to be net heat flux including ShortWave rad.
C surfForcTice
C - equivalent Temperature flux in the top level that corresponds
C to the melting or freezing of sea-ice.
C Note that the surface level temperature is modified
C directly by the sea-ice model in order to maintain
C water temperature under sea-ice at the freezing
C point. But we need to keep track of the
C equivalent amount of heat that this surface-level
C temperature change implies because it is used by
C the KPP package (kpp_calc.F and kpp_transport_t.F).
C Units are r_unit.K/s (=Kelvin.m/s if r=z) (>0 for ocean warming).
C
C Qsw - surface shortwave radiation (upwards positive)
C saltPlumeFlux - salt rejected during freezing (downward = positive)
C ttalpha - thermal expansion coefficient without 1/rho factor
C d(rho{k,k})/d(T(k)) (kg/m^3/C)
C ssbeta - salt expansion coefficient without 1/rho factor
C d(rho{k,k})/d(S(k)) (kg/m^3/PSU)
C !OUTPUT PARAMETERS:
C ustar (nx,ny) - surface friction velocity (m/s)
C bo (nx,ny) - surface turbulent buoyancy forcing (m^2/s^3)
C bosol (nx,ny) - surface radiative buoyancy forcing (m^2/s^3)
C boplume(nx,ny) - surface haline buoyancy forcing (m^2/s^3)
C dVsq (nx,ny,Nr) - velocity shear re surface squared
C at grid levels for bldepth (m^2/s^2)
INTEGER ikppkey
INTEGER iMin, iMax, jMin, jMax
INTEGER bi, bj
INTEGER myThid
_RL myTime
_RL rhoSurf (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL surfForcU (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
_RL surfForcV (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
_RL surfForcT (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
_RL surfForcS (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
_RL surfForcTice(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
_RS Qsw (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
_RL TTALPHA (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nrp1)
_RL SSBETA (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nrp1)
_RL ustar ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy )
_RL bo ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy )
_RL bosol ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy )
#ifdef ALLOW_SALT_PLUME
_RL saltPlumeFlux (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
_RL boplume(1-OLx:sNx+OLx, 1-OLy:sNy+OLy )
#endif /* ALLOW_SALT_PLUME */
_RL dVsq ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy, Nr )
C !LOCAL VARIABLES: ====================================================
c Local constants
c minusone, p0, p5, p25, p125, p0625
_RL p0 , p5 , p125
parameter( p0=0.0, p5=0.5, p125=0.125 )
integer i, j, k, im1, ip1, jm1, jp1
_RL tempvar2
_RL work3 ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy )
#ifdef KPP_ESTIMATE_UREF
_RL tempvar1, dBdz1, dBdz2, ustarX, ustarY
_RL z0 ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy )
_RL zRef ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy )
_RL uRef ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy )
_RL vRef ( 1-OLx:sNx+OLx, 1-OLy:sNy+OLy )
#endif
CEOP
c------------------------------------------------------------------------
c friction velocity, turbulent and radiative surface buoyancy forcing
c -------------------------------------------------------------------
c taux / rho = surfForcU (N/m^2)
c tauy / rho = surfForcV (N/m^2)
c ustar = sqrt( sqrt( taux^2 + tauy^2 ) / rho ) (m/s)
c bo = - g * ( alpha*surfForcT +
c beta *surfForcS ) / rho (m^2/s^3)
c bosol = - g * alpha * Qsw * drF(1) / rho (m^2/s^3)
c boplume = g * ( beta *saltPlumeFlux/rhoConst )/rho (m^2/s^3)
c------------------------------------------------------------------------
c initialize arrays to zero
DO j = 1-OLy, sNy+OLy
DO i = 1-OLx, sNx+OLx
ustar(i,j) = p0
bo (I,J) = p0
bosol(I,J) = p0
#ifdef ALLOW_SALT_PLUME
boplume(I,J) = p0
#endif /* ALLOW_SALT_PLUME */
END
DO
END
DO
DO j = jmin, jmax
jp1 = j + 1
DO i = imin, imax
ip1 = i+1
work3(i,j) =
& (surfForcU(i,j,bi,bj) + surfForcU(ip1,j,bi,bj)) *
& (surfForcU(i,j,bi,bj) + surfForcU(ip1,j,bi,bj)) +
& (surfForcV(i,j,bi,bj) + surfForcV(i,jp1,bi,bj)) *
& (surfForcV(i,j,bi,bj) + surfForcV(i,jp1,bi,bj))
END
DO
END
DO
cph(
CADJ store work3 = comlev1_kpp, key = ikppkey
cph)
DO j = jmin, jmax
jp1 = j + 1
DO i = imin, imax
ip1 = i+1
if ( work3(i,j) .lt. (phepsi*phepsi*drF(1)*drF(1)) ) then
ustar(i,j) = SQRT( phepsi * p5 * drF(1) )
else
tempVar2 = SQRT( work3(i,j) ) * p5
ustar(i,j) = SQRT( tempVar2 )
endif
END
DO
END
DO
DO j = jmin, jmax
jp1 = j + 1
DO i = imin, imax
ip1 = i+1
bo(I,J) = - gravity *
& ( TTALPHA(I,J,1) * (surfForcT(i,j,bi,bj)+
& surfForcTice(i,j,bi,bj)) +
& SSBETA(I,J,1) * surfForcS(i,j,bi,bj) )
& / rhoSurf(I,J)
bosol(I,J) = gravity * TTALPHA(I,J,1) * Qsw(i,j,bi,bj) *
& recip_Cp*recip_rhoConst
& / rhoSurf(I,J)
END
DO
END
DO
#ifdef ALLOW_SALT_PLUME
IF ( useSALT_PLUME ) THEN
DO j = jmin, jmax
jp1 = j + 1
DO i = imin, imax
ip1 = i+1
boplume(I,J) = - gravity * SSBETA(I,J,1)
& * saltPlumeFlux(i,j,bi,bj)
& * recip_rhoConst / rhoSurf(I,J)
END
DO
END
DO
ENDIF
#endif /* ALLOW_SALT_PLUME */
cph(
CADJ store ustar = comlev1_kpp, key = ikppkey
cph)
#ifdef ALLOW_DIAGNOSTICS
IF ( useDiagnostics ) THEN
CALL DIAGNOSTICS_FILL(bo ,'KPPbo ',0,1,2,bi,bj,myThid)
CALL DIAGNOSTICS_FILL(bosol ,'KPPbosol',0,1,2,bi,bj,myThid)
#ifdef ALLOW_SALT_PLUME
CALL DIAGNOSTICS_FILL(boplume,'KPPboplm',0,1,2,bi,bj,myThid)
#endif /* ALLOW_SALT_PLUME */
ENDIF
#endif /* ALLOW_DIAGNOSTICS */
c------------------------------------------------------------------------
c velocity shear
c --------------
c Get velocity shear squared, averaged from "u,v-grid"
c onto "t-grid" (in (m/s)**2):
c dVsq(k)=(Uref-U(k))**2+(Vref-V(k))**2 at grid levels
c------------------------------------------------------------------------
c initialize arrays to zero
DO k = 1, Nr
DO j = 1-OLy, sNy+OLy
DO i = 1-OLx, sNx+OLx
dVsq(i,j,k) = p0
END
DO
END
DO
END
DO
c dVsq computation
#ifdef KPP_ESTIMATE_UREF
c Get rid of vertical resolution dependence of dVsq term by
c estimating a surface velocity that is independent of first level
c thickness in the model. First determine mixed layer depth hMix.
c Second zRef = espilon * hMix. Third determine roughness length
c scale z0. Third estimate reference velocity.
DO j = jmin, jmax
jp1 = j + 1
DO i = imin, imax
ip1 = i + 1
c Determine mixed layer depth hMix as the shallowest depth at which
c dB/dz exceeds 5.2e-5 s^-2.
work1(i,j) = nzmax(i,j,bi,bj)
DO k = 1, Nr
IF ( k .LT. nzmax(i,j,bi,bj) .AND.
& maskC(I,J,k,bi,bj) .GT. 0. .AND.
& dbloc(i,j,k) / drC(k+1) .GT. dB_dz )
& work1(i,j) = k
ENDDO
c Linearly interpolate to find hMix.
k = work1(i,j)
IF ( k .EQ. 0 .OR. nzmax(i,j,bi,bj) .EQ. 1 ) THEN
zRef(i,j) = p0
ELSEIF ( k .EQ. 1) THEN
dBdz2 = dbloc(i,j,1) / drC(2)
zRef(i,j) = drF(1) * dB_dz / dBdz2
ELSEIF ( k .LT. nzmax(i,j,bi,bj) ) THEN
dBdz1 = dbloc(i,j,k-1) / drC(k )
dBdz2 = dbloc(i,j,k ) / drC(k+1)
zRef(i,j) = rF(k) + drF(k) * (dB_dz - dBdz1) /
& MAX ( phepsi, dBdz2 - dBdz1 )
ELSE
zRef(i,j) = rF(k+1)
ENDIF
c Compute roughness length scale z0 subject to 0 < z0
tempVar1 = p5 * (
& (uVel(i, j, 1,bi,bj)-uVel(i, j, 2,bi,bj)) *
& (uVel(i, j, 1,bi,bj)-uVel(i, j, 2,bi,bj)) +
& (uVel(ip1,j, 1,bi,bj)-uVel(ip1,j, 2,bi,bj)) *
& (uVel(ip1,j, 1,bi,bj)-uVel(ip1,j, 2,bi,bj)) +
& (vVel(i, j, 1,bi,bj)-vVel(i, j, 2,bi,bj)) *
& (vVel(i, j, 1,bi,bj)-vVel(i, j, 2,bi,bj)) +
& (vVel(i, jp1,1,bi,bj)-vVel(i, jp1,2,bi,bj)) *
& (vVel(i, jp1,1,bi,bj)-vVel(i, jp1,2,bi,bj)) )
IF ( tempVar1 .lt. (epsln*epsln) ) THEN
tempVar2 = epsln
ELSE
tempVar2 = SQRT ( tempVar1 )
ENDIF
z0(i,j) = rF(2) *
& ( rF(3) * LOG ( rF(3) / rF(2) ) /
& ( rF(3) - rF(2) ) -
& tempVar2 * vonK /
& MAX ( ustar(i,j), phepsi ) )
z0(i,j) = MAX ( z0(i,j), phepsi )
c zRef is set to 0.1 * hMix subject to z0 <= zRef <= drF(1)
zRef(i,j) = MAX ( epsilon * zRef(i,j), z0(i,j) )
zRef(i,j) = MIN ( zRef(i,j), drF(1) )
c Estimate reference velocity uRef and vRef.
uRef(i,j) = p5 * ( uVel(i,j,1,bi,bj) + uVel(ip1,j,1,bi,bj) )
vRef(i,j) = p5 * ( vVel(i,j,1,bi,bj) + vVel(i,jp1,1,bi,bj) )
IF ( zRef(i,j) .LT. drF(1) ) THEN
ustarX = ( surfForcU(i, j,bi,bj) +
& surfForcU(ip1,j,bi,bj) ) * p5 *recip_drF(1)
ustarY = ( surfForcV(i,j, bi,bj) +
& surfForcV(i,jp1,bi,bj) ) * p5 *recip_drF(1)
tempVar1 = ustarX * ustarX + ustarY * ustarY
if ( tempVar1 .lt. (epsln*epsln) ) then
tempVar2 = epsln
else
tempVar2 = SQRT ( tempVar1 )
endif
tempVar2 = ustar(i,j) *
& ( LOG ( zRef(i,j) / rF(2) ) +
& z0(i,j) / zRef(i,j) - z0(i,j) / rF(2) ) /
& vonK / tempVar2
uRef(i,j) = uRef(i,j) + ustarX * tempVar2
vRef(i,j) = vRef(i,j) + ustarY * tempVar2
ENDIF
ENDDO
ENDDO
DO k = 1, Nr
DO j = jmin, jmax
jm1 = j - 1
jp1 = j + 1
DO i = imin, imax
im1 = i - 1
ip1 = i + 1
dVsq(i,j,k) = p5 * (
$ (uRef(i,j) - uVel(i, j, k,bi,bj)) *
$ (uRef(i,j) - uVel(i, j, k,bi,bj)) +
$ (uRef(i,j) - uVel(ip1,j, k,bi,bj)) *
$ (uRef(i,j) - uVel(ip1,j, k,bi,bj)) +
$ (vRef(i,j) - vVel(i, j, k,bi,bj)) *
$ (vRef(i,j) - vVel(i, j, k,bi,bj)) +
$ (vRef(i,j) - vVel(i, jp1,k,bi,bj)) *
$ (vRef(i,j) - vVel(i, jp1,k,bi,bj)) )
#ifdef KPP_SMOOTH_DVSQ
dVsq(i,j,k) = p5 * dVsq(i,j,k) + p125 * (
$ (uRef(i,j) - uVel(i, jm1,k,bi,bj)) *
$ (uRef(i,j) - uVel(i, jm1,k,bi,bj)) +
$ (uRef(i,j) - uVel(ip1,jm1,k,bi,bj)) *
$ (uRef(i,j) - uVel(ip1,jm1,k,bi,bj)) +
$ (uRef(i,j) - uVel(i, jp1,k,bi,bj)) *
$ (uRef(i,j) - uVel(i, jp1,k,bi,bj)) +
$ (uRef(i,j) - uVel(ip1,jp1,k,bi,bj)) *
$ (uRef(i,j) - uVel(ip1,jp1,k,bi,bj)) +
$ (vRef(i,j) - vVel(im1,j, k,bi,bj)) *
$ (vRef(i,j) - vVel(im1,j, k,bi,bj)) +
$ (vRef(i,j) - vVel(im1,jp1,k,bi,bj)) *
$ (vRef(i,j) - vVel(im1,jp1,k,bi,bj)) +
$ (vRef(i,j) - vVel(ip1,j, k,bi,bj)) *
$ (vRef(i,j) - vVel(ip1,j, k,bi,bj)) +
$ (vRef(i,j) - vVel(ip1,jp1,k,bi,bj)) *
$ (vRef(i,j) - vVel(ip1,jp1,k,bi,bj)) )
#endif /* KPP_SMOOTH_DVSQ */
ENDDO
ENDDO
ENDDO
#else /* KPP_ESTIMATE_UREF */
DO k = 1, Nr
DO j = jmin, jmax
jm1 = j - 1
jp1 = j + 1
DO i = imin, imax
im1 = i - 1
ip1 = i + 1
dVsq(i,j,k) = p5 * (
$ (uVel(i, j, 1,bi,bj)-uVel(i, j, k,bi,bj)) *
$ (uVel(i, j, 1,bi,bj)-uVel(i, j, k,bi,bj)) +
$ (uVel(ip1,j, 1,bi,bj)-uVel(ip1,j, k,bi,bj)) *
$ (uVel(ip1,j, 1,bi,bj)-uVel(ip1,j, k,bi,bj)) +
$ (vVel(i, j, 1,bi,bj)-vVel(i, j, k,bi,bj)) *
$ (vVel(i, j, 1,bi,bj)-vVel(i, j, k,bi,bj)) +
$ (vVel(i, jp1,1,bi,bj)-vVel(i, jp1,k,bi,bj)) *
$ (vVel(i, jp1,1,bi,bj)-vVel(i, jp1,k,bi,bj)) )
#ifdef KPP_SMOOTH_DVSQ
dVsq(i,j,k) = p5 * dVsq(i,j,k) + p125 * (
$ (uVel(i, jm1,1,bi,bj)-uVel(i, jm1,k,bi,bj)) *
$ (uVel(i, jm1,1,bi,bj)-uVel(i, jm1,k,bi,bj)) +
$ (uVel(ip1,jm1,1,bi,bj)-uVel(ip1,jm1,k,bi,bj)) *
$ (uVel(ip1,jm1,1,bi,bj)-uVel(ip1,jm1,k,bi,bj)) +
$ (uVel(i, jp1,1,bi,bj)-uVel(i, jp1,k,bi,bj)) *
$ (uVel(i, jp1,1,bi,bj)-uVel(i, jp1,k,bi,bj)) +
$ (uVel(ip1,jp1,1,bi,bj)-uVel(ip1,jp1,k,bi,bj)) *
$ (uVel(ip1,jp1,1,bi,bj)-uVel(ip1,jp1,k,bi,bj)) +
$ (vVel(im1,j, 1,bi,bj)-vVel(im1,j, k,bi,bj)) *
$ (vVel(im1,j, 1,bi,bj)-vVel(im1,j, k,bi,bj)) +
$ (vVel(im1,jp1,1,bi,bj)-vVel(im1,jp1,k,bi,bj)) *
$ (vVel(im1,jp1,1,bi,bj)-vVel(im1,jp1,k,bi,bj)) +
$ (vVel(ip1,j, 1,bi,bj)-vVel(ip1,j, k,bi,bj)) *
$ (vVel(ip1,j, 1,bi,bj)-vVel(ip1,j, k,bi,bj)) +
$ (vVel(ip1,jp1,1,bi,bj)-vVel(ip1,jp1,k,bi,bj)) *
$ (vVel(ip1,jp1,1,bi,bj)-vVel(ip1,jp1,k,bi,bj)) )
#endif /* KPP_SMOOTH_DVSQ */
ENDDO
ENDDO
ENDDO
#endif /* KPP_ESTIMATE_UREF */
RETURN
END