!wrf:MODEL_LAYER:DYNAMICS
!
#if (RWORDSIZE == 4)
# define VPOWX vspowx
# define VPOW vspow
#else
# define VPOWX vpowx
# define VPOW vpow
#endif
MODULE module_big_step_utilities_em 8
USE module_model_constants
USE module_state_description, only: p_qg, p_qs, p_qi, gdscheme, tiedtkescheme, kfetascheme, g3scheme, &
gfscheme,p_qv, param_first_scalar, p_qr, p_qc, DFI_FWD
USE module_configure, ONLY : grid_config_rec_type
USE module_wrf_error
CONTAINS
!-------------------------------------------------------------------------------
SUBROUTINE calc_mu_uv ( config_flags, & 1
mu, mub, muu, muv, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
TYPE(grid_config_rec_type ) , INTENT(IN ) :: config_flags
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL, DIMENSION( ims:ime , jms:jme ) , INTENT( OUT) :: muu, muv
REAL, DIMENSION( ims:ime , jms:jme ) , INTENT(IN ) :: mu, mub
! local stuff
INTEGER :: i, j, itf, jtf, im, jm
!<DESCRIPTION>
!
! calc_mu_uv calculates the full column dry-air mass at the staggered
! horizontal velocity points (u,v) and places the results in muu and muv.
! This routine uses the reference state (mub) and perturbation state (mu)
!
!</DESCRIPTION>
itf=ite
jtf=MIN(jte,jde-1)
IF ( ( its .NE. ids ) .AND. ( ite .NE. ide ) ) THEN
DO j=jts,jtf
DO i=its,itf
muu(i,j) = 0.5*(mu(i,j)+mu(i-1,j)+mub(i,j)+mub(i-1,j))
ENDDO
ENDDO
ELSE IF ( ( its .EQ. ids ) .AND. ( ite .NE. ide ) ) THEN
DO j=jts,jtf
DO i=its+1,itf
muu(i,j) = 0.5*(mu(i,j)+mu(i-1,j)+mub(i,j)+mub(i-1,j))
ENDDO
ENDDO
i=its
im = its
if(config_flags%periodic_x) im = its-1
DO j=jts,jtf
! muu(i,j) = mu(i,j) +mub(i,j)
! fix for periodic b.c., 13 march 2004, wcs
muu(i,j) = 0.5*(mu(i,j)+mu(im,j)+mub(i,j)+mub(im,j))
ENDDO
ELSE IF ( ( its .NE. ids ) .AND. ( ite .EQ. ide ) ) THEN
DO j=jts,jtf
DO i=its,itf-1
muu(i,j) = 0.5*(mu(i,j)+mu(i-1,j)+mub(i,j)+mub(i-1,j))
ENDDO
ENDDO
i=ite
im = ite-1
if(config_flags%periodic_x) im = ite
DO j=jts,jtf
! muu(i,j) = mu(i-1,j) +mub(i-1,j)
! fix for periodic b.c., 13 march 2004, wcs
muu(i,j) = 0.5*(mu(i-1,j)+mu(im,j)+mub(i-1,j)+mub(im,j))
ENDDO
ELSE IF ( ( its .EQ. ids ) .AND. ( ite .EQ. ide ) ) THEN
DO j=jts,jtf
DO i=its+1,itf-1
muu(i,j) = 0.5*(mu(i,j)+mu(i-1,j)+mub(i,j)+mub(i-1,j))
ENDDO
ENDDO
i=its
im = its
if(config_flags%periodic_x) im = its-1
DO j=jts,jtf
! muu(i,j) = mu(i,j) +mub(i,j)
! fix for periodic b.c., 13 march 2004, wcs
muu(i,j) = 0.5*(mu(i,j)+mu(im,j)+mub(i,j)+mub(im,j))
ENDDO
i=ite
im = ite-1
if(config_flags%periodic_x) im = ite
DO j=jts,jtf
! muu(i,j) = mu(i-1,j) +mub(i-1,j)
! fix for periodic b.c., 13 march 2004, wcs
muu(i,j) = 0.5*(mu(i-1,j)+mu(im,j)+mub(i-1,j)+mub(im,j))
ENDDO
END IF
itf=MIN(ite,ide-1)
jtf=jte
IF ( ( jts .NE. jds ) .AND. ( jte .NE. jde ) ) THEN
DO j=jts,jtf
DO i=its,itf
muv(i,j) = 0.5*(mu(i,j)+mu(i,j-1)+mub(i,j)+mub(i,j-1))
ENDDO
ENDDO
ELSE IF ( ( jts .EQ. jds ) .AND. ( jte .NE. jde ) ) THEN
DO j=jts+1,jtf
DO i=its,itf
muv(i,j) = 0.5*(mu(i,j)+mu(i,j-1)+mub(i,j)+mub(i,j-1))
ENDDO
ENDDO
j=jts
jm = jts
if(config_flags%periodic_y) jm = jts-1
DO i=its,itf
! muv(i,j) = mu(i,j) +mub(i,j)
! fix for periodic b.c., 13 march 2004, wcs
muv(i,j) = 0.5*(mu(i,j)+mu(i,jm)+mub(i,j)+mub(i,jm))
ENDDO
ELSE IF ( ( jts .NE. jds ) .AND. ( jte .EQ. jde ) ) THEN
DO j=jts,jtf-1
DO i=its,itf
muv(i,j) = 0.5*(mu(i,j)+mu(i,j-1)+mub(i,j)+mub(i,j-1))
ENDDO
ENDDO
j=jte
jm = jte-1
if(config_flags%periodic_y) jm = jte
DO i=its,itf
muv(i,j) = mu(i,j-1) +mub(i,j-1)
! fix for periodic b.c., 13 march 2004, wcs
muv(i,j) = 0.5*(mu(i,j-1)+mu(i,jm)+mub(i,j-1)+mub(i,jm))
ENDDO
ELSE IF ( ( jts .EQ. jds ) .AND. ( jte .EQ. jde ) ) THEN
DO j=jts+1,jtf-1
DO i=its,itf
muv(i,j) = 0.5*(mu(i,j)+mu(i,j-1)+mub(i,j)+mub(i,j-1))
ENDDO
ENDDO
j=jts
jm = jts
if(config_flags%periodic_y) jm = jts-1
DO i=its,itf
! muv(i,j) = mu(i,j) +mub(i,j)
! fix for periodic b.c., 13 march 2004, wcs
muv(i,j) = 0.5*(mu(i,j)+mu(i,jm)+mub(i,j)+mub(i,jm))
ENDDO
j=jte
jm = jte-1
if(config_flags%periodic_y) jm = jte
DO i=its,itf
! muv(i,j) = mu(i,j-1) +mub(i,j-1)
! fix for periodic b.c., 13 march 2004, wcs
muv(i,j) = 0.5*(mu(i,j-1)+mu(i,jm)+mub(i,j-1)+mub(i,jm))
ENDDO
END IF
END SUBROUTINE calc_mu_uv
!-------------------------------------------------------------------------------
SUBROUTINE calc_mu_uv_1 ( config_flags, & 1
mu, muu, muv, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
TYPE(grid_config_rec_type ) , INTENT(IN ) :: config_flags
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL, DIMENSION( ims:ime , jms:jme ) , INTENT( OUT) :: muu, muv
REAL, DIMENSION( ims:ime , jms:jme ) , INTENT(IN ) :: mu
! local stuff
INTEGER :: i, j, itf, jtf, im, jm
!<DESCRIPTION>
!
! calc_mu_uv calculates the full column dry-air mass at the staggered
! horizontal velocity points (u,v) and places the results in muu and muv.
! This routine uses the full state (mu)
!
!</DESCRIPTION>
itf=ite
jtf=MIN(jte,jde-1)
IF ( ( its .NE. ids ) .AND. ( ite .NE. ide ) ) THEN
DO j=jts,jtf
DO i=its,itf
muu(i,j) = 0.5*(mu(i,j)+mu(i-1,j))
ENDDO
ENDDO
ELSE IF ( ( its .EQ. ids ) .AND. ( ite .NE. ide ) ) THEN
DO j=jts,jtf
DO i=its+1,itf
muu(i,j) = 0.5*(mu(i,j)+mu(i-1,j))
ENDDO
ENDDO
i=its
im = its
if(config_flags%periodic_x) im = its-1
DO j=jts,jtf
muu(i,j) = 0.5*(mu(i,j)+mu(im,j))
ENDDO
ELSE IF ( ( its .NE. ids ) .AND. ( ite .EQ. ide ) ) THEN
DO j=jts,jtf
DO i=its,itf-1
muu(i,j) = 0.5*(mu(i,j)+mu(i-1,j))
ENDDO
ENDDO
i=ite
im = ite-1
if(config_flags%periodic_x) im = ite
DO j=jts,jtf
muu(i,j) = 0.5*(mu(i-1,j)+mu(im,j))
ENDDO
ELSE IF ( ( its .EQ. ids ) .AND. ( ite .EQ. ide ) ) THEN
DO j=jts,jtf
DO i=its+1,itf-1
muu(i,j) = 0.5*(mu(i,j)+mu(i-1,j))
ENDDO
ENDDO
i=its
im = its
if(config_flags%periodic_x) im = its-1
DO j=jts,jtf
muu(i,j) = 0.5*(mu(i,j)+mu(im,j))
ENDDO
i=ite
im = ite-1
if(config_flags%periodic_x) im = ite
DO j=jts,jtf
muu(i,j) = 0.5*(mu(i-1,j)+mu(im,j))
ENDDO
END IF
itf=MIN(ite,ide-1)
jtf=jte
IF ( ( jts .NE. jds ) .AND. ( jte .NE. jde ) ) THEN
DO j=jts,jtf
DO i=its,itf
muv(i,j) = 0.5*(mu(i,j)+mu(i,j-1))
ENDDO
ENDDO
ELSE IF ( ( jts .EQ. jds ) .AND. ( jte .NE. jde ) ) THEN
DO j=jts+1,jtf
DO i=its,itf
muv(i,j) = 0.5*(mu(i,j)+mu(i,j-1))
ENDDO
ENDDO
j=jts
jm = jts
if(config_flags%periodic_y) jm = jts-1
DO i=its,itf
muv(i,j) = 0.5*(mu(i,j)+mu(i,jm))
ENDDO
ELSE IF ( ( jts .NE. jds ) .AND. ( jte .EQ. jde ) ) THEN
DO j=jts,jtf-1
DO i=its,itf
muv(i,j) = 0.5*(mu(i,j)+mu(i,j-1))
ENDDO
ENDDO
j=jte
jm = jte-1
if(config_flags%periodic_y) jm = jte
DO i=its,itf
muv(i,j) = 0.5*(mu(i,j-1)+mu(i,jm))
ENDDO
ELSE IF ( ( jts .EQ. jds ) .AND. ( jte .EQ. jde ) ) THEN
DO j=jts+1,jtf-1
DO i=its,itf
muv(i,j) = 0.5*(mu(i,j)+mu(i,j-1))
ENDDO
ENDDO
j=jts
jm = jts
if(config_flags%periodic_y) jm = jts-1
DO i=its,itf
muv(i,j) = 0.5*(mu(i,j)+mu(i,jm))
ENDDO
j=jte
jm = jte-1
if(config_flags%periodic_y) jm = jte
DO i=its,itf
muv(i,j) = 0.5*(mu(i,j-1)+mu(i,jm))
ENDDO
END IF
END SUBROUTINE calc_mu_uv_1
!-------------------------------------------------------------------------------
! Map scale factor comments for this routine:
! Locally not changed, but sent the correct map scale factors
! from module_em (msfuy, msfvx, msfty)
SUBROUTINE couple_momentum ( muu, ru, u, msfu, & 1
muv, rv, v, msfv, msfv_inv, &
mut, rw, w, msft, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT( OUT) :: ru, rv, rw
REAL , DIMENSION( ims:ime , jms:jme ) , INTENT(IN ) :: muu, muv, mut
REAL , DIMENSION( ims:ime , jms:jme ) , INTENT(IN ) :: msfu, msfv, msft, msfv_inv
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(IN ) :: u, v, w
! Local data
INTEGER :: i, j, k, itf, jtf, ktf
!<DESCRIPTION>
!
! couple_momentum couples the velocities to the full column mass and
! the map factors.
!
!</DESCRIPTION>
ktf=MIN(kte,kde-1)
itf=ite
jtf=MIN(jte,jde-1)
DO j=jts,jtf
DO k=kts,ktf
DO i=its,itf
ru(i,k,j)=u(i,k,j)*muu(i,j)/msfu(i,j)
ENDDO
ENDDO
ENDDO
itf=MIN(ite,ide-1)
jtf=jte
DO j=jts,jtf
DO k=kts,ktf
DO i=its,itf
rv(i,k,j)=v(i,k,j)*muv(i,j)*msfv_inv(i,j)
! rv(i,k,j)=v(i,k,j)*muv(i,j)/msfv(i,j)
ENDDO
ENDDO
ENDDO
itf=MIN(ite,ide-1)
jtf=MIN(jte,jde-1)
DO j=jts,jtf
DO k=kts,kte
DO i=its,itf
rw(i,k,j)=w(i,k,j)*mut(i,j)/msft(i,j)
ENDDO
ENDDO
ENDDO
END SUBROUTINE couple_momentum
!-------------------------------------------------------------------
SUBROUTINE calc_mu_staggered ( mu, mub, muu, muv, & 2
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL, DIMENSION( ims:ime , jms:jme ) , INTENT( OUT) :: muu, muv
REAL, DIMENSION( ims:ime , jms:jme ) , INTENT(IN ) :: mu, mub
! local stuff
INTEGER :: i, j, itf, jtf
!<DESCRIPTION>
!
! calc_mu_staggered calculates the full dry air mass at the staggered
! velocity points (u,v).
!
!</DESCRIPTION>
itf=ite
jtf=MIN(jte,jde-1)
IF ( ( its .NE. ids ) .AND. ( ite .NE. ide ) ) THEN
DO j=jts,jtf
DO i=its,itf
muu(i,j) = 0.5*(mu(i,j)+mu(i-1,j)+mub(i,j)+mub(i-1,j))
ENDDO
ENDDO
ELSE IF ( ( its .EQ. ids ) .AND. ( ite .NE. ide ) ) THEN
DO j=jts,jtf
DO i=its+1,itf
muu(i,j) = 0.5*(mu(i,j)+mu(i-1,j)+mub(i,j)+mub(i-1,j))
ENDDO
ENDDO
i=its
DO j=jts,jtf
muu(i,j) = mu(i,j) +mub(i,j)
ENDDO
ELSE IF ( ( its .NE. ids ) .AND. ( ite .EQ. ide ) ) THEN
DO j=jts,jtf
DO i=its,itf-1
muu(i,j) = 0.5*(mu(i,j)+mu(i-1,j)+mub(i,j)+mub(i-1,j))
ENDDO
ENDDO
i=ite
DO j=jts,jtf
muu(i,j) = mu(i-1,j) +mub(i-1,j)
ENDDO
ELSE IF ( ( its .EQ. ids ) .AND. ( ite .EQ. ide ) ) THEN
DO j=jts,jtf
DO i=its+1,itf-1
muu(i,j) = 0.5*(mu(i,j)+mu(i-1,j)+mub(i,j)+mub(i-1,j))
ENDDO
ENDDO
i=its
DO j=jts,jtf
muu(i,j) = mu(i,j) +mub(i,j)
ENDDO
i=ite
DO j=jts,jtf
muu(i,j) = mu(i-1,j) +mub(i-1,j)
ENDDO
END IF
itf=MIN(ite,ide-1)
jtf=jte
IF ( ( jts .NE. jds ) .AND. ( jte .NE. jde ) ) THEN
DO j=jts,jtf
DO i=its,itf
muv(i,j) = 0.5*(mu(i,j)+mu(i,j-1)+mub(i,j)+mub(i,j-1))
ENDDO
ENDDO
ELSE IF ( ( jts .EQ. jds ) .AND. ( jte .NE. jde ) ) THEN
DO j=jts+1,jtf
DO i=its,itf
muv(i,j) = 0.5*(mu(i,j)+mu(i,j-1)+mub(i,j)+mub(i,j-1))
ENDDO
ENDDO
j=jts
DO i=its,itf
muv(i,j) = mu(i,j) +mub(i,j)
ENDDO
ELSE IF ( ( jts .NE. jds ) .AND. ( jte .EQ. jde ) ) THEN
DO j=jts,jtf-1
DO i=its,itf
muv(i,j) = 0.5*(mu(i,j)+mu(i,j-1)+mub(i,j)+mub(i,j-1))
ENDDO
ENDDO
j=jte
DO i=its,itf
muv(i,j) = mu(i,j-1) +mub(i,j-1)
ENDDO
ELSE IF ( ( jts .EQ. jds ) .AND. ( jte .EQ. jde ) ) THEN
DO j=jts+1,jtf-1
DO i=its,itf
muv(i,j) = 0.5*(mu(i,j)+mu(i,j-1)+mub(i,j)+mub(i,j-1))
ENDDO
ENDDO
j=jts
DO i=its,itf
muv(i,j) = mu(i,j) +mub(i,j)
ENDDO
j=jte
DO i=its,itf
muv(i,j) = mu(i,j-1) +mub(i,j-1)
ENDDO
END IF
END SUBROUTINE calc_mu_staggered
!-------------------------------------------------------------------------------
SUBROUTINE couple ( mu, mub, rfield, field, name, & 25,2
msf, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
CHARACTER(LEN=1) , INTENT(IN ) :: name
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT( OUT) :: rfield
REAL , DIMENSION( ims:ime , jms:jme ) , INTENT(IN ) :: mu, mub, msf
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(IN ) :: field
! Local data
INTEGER :: i, j, k, itf, jtf, ktf
REAL , DIMENSION(ims:ime,jms:jme) :: muu , muv
!<DESCRIPTION>
!
! subroutine couple couples the input variable with the dry-air
! column mass (mu).
!
!</DESCRIPTION>
ktf=MIN(kte,kde-1)
IF (name .EQ. 'u')THEN
CALL calc_mu_staggered ( mu, mub, muu, muv, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
itf=ite
jtf=MIN(jte,jde-1)
DO j=jts,jtf
DO k=kts,ktf
DO i=its,itf
rfield(i,k,j)=field(i,k,j)*muu(i,j)/msf(i,j)
ENDDO
ENDDO
ENDDO
ELSE IF (name .EQ. 'v')THEN
CALL calc_mu_staggered ( mu, mub, muu, muv, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
itf=ite
itf=MIN(ite,ide-1)
jtf=jte
DO j=jts,jtf
DO k=kts,ktf
DO i=its,itf
rfield(i,k,j)=field(i,k,j)*muv(i,j)/msf(i,j)
ENDDO
ENDDO
ENDDO
ELSE IF (name .EQ. 'w')THEN
itf=MIN(ite,ide-1)
jtf=MIN(jte,jde-1)
DO j=jts,jtf
DO k=kts,kte
DO i=its,itf
rfield(i,k,j)=field(i,k,j)*(mu(i,j)+mub(i,j))/msf(i,j)
ENDDO
ENDDO
ENDDO
ELSE IF (name .EQ. 'h')THEN
itf=MIN(ite,ide-1)
jtf=MIN(jte,jde-1)
DO j=jts,jtf
DO k=kts,kte
DO i=its,itf
rfield(i,k,j)=field(i,k,j)*(mu(i,j)+mub(i,j))
ENDDO
ENDDO
ENDDO
ELSE
itf=MIN(ite,ide-1)
jtf=MIN(jte,jde-1)
DO j=jts,jtf
DO k=kts,ktf
DO i=its,itf
rfield(i,k,j)=field(i,k,j)*(mu(i,j)+mub(i,j))
ENDDO
ENDDO
ENDDO
ENDIF
END SUBROUTINE couple
!-------------------------------------------------------------------------------
SUBROUTINE calc_ww_cp ( u, v, mup, mub, ww, & 1
rdx, rdy, msftx, msfty, &
msfux, msfuy, msfvx, msfvx_inv, &
msfvy, dnw, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(IN ) :: u, v
REAL , DIMENSION( ims:ime , jms:jme ) , INTENT(IN ) :: mup, mub, &
msftx, msfty, &
msfux, msfuy, &
msfvx, msfvy, &
msfvx_inv
REAL , DIMENSION( kms:kme ) , INTENT(IN ) :: dnw
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(OUT ) :: ww
REAL , INTENT(IN ) :: rdx, rdy
! Local data
INTEGER :: i, j, k, itf, jtf, ktf
REAL , DIMENSION( its:ite ) :: dmdt
REAL , DIMENSION( its:ite, kts:kte ) :: divv
REAL , DIMENSION( its:ite+1, jts:jte+1 ) :: muu, muv
!<DESCRIPTION>
!
! calc_ww calculates omega using the velocities (u,v) and the dry-air
! column mass (mup+mub).
! The algorithm integrates the continuity equation through the column
! followed by a diagnosis of omega.
!
!</DESCRIPTION>
!<DESCRIPTION>
!
! calc_ww_cp calculates omega using the velocities (u,v) and the
! column mass mu.
!
!</DESCRIPTION>
jtf=MIN(jte,jde-1)
ktf=MIN(kte,kde-1)
itf=MIN(ite,ide-1)
! mu coupled with the appropriate map factor
DO j=jts,jtf
DO i=its,min(ite+1,ide)
! u is always coupled with my
muu(i,j) = 0.5*(mup(i,j)+mub(i,j)+mup(i-1,j)+mub(i-1,j))/msfuy(i,j)
ENDDO
ENDDO
DO j=jts,min(jte+1,jde)
DO i=its,itf
! v is always coupled with mx
! muv(i,j) = 0.5*(mup(i,j)+mub(i,j)+mup(i,j-1)+mub(i,j-1))/msfvx(i,j)
muv(i,j) = 0.5*(mup(i,j)+mub(i,j)+mup(i,j-1)+mub(i,j-1))*msfvx_inv(i,j)
ENDDO
ENDDO
DO j=jts,jtf
DO i=its,ite
dmdt(i) = 0.
ww(i,1,j) = 0.
ww(i,kte,j) = 0.
ENDDO
! Comments on the modifications for map scale factors
! ADT eqn 47 / my (putting rho -> 'mu') is:
! (1/my) partial d mu/dt = -mx partial d/dx(mu u/my)
! -mx partial d/dy(mu v/mx)
! -partial d/dz(mu w/my)
!
! Using nu instead of z the last term becomes:
! -partial d/dnu(mu (dnu/dt)/my)
!
! Integrating with respect to nu over ALL levels, with dnu/dt=0 at top
! and bottom, the last term becomes = 0
!
! Integral|bot->top[(1/my) partial d mu/dt]dnu =
! Integral|bot->top[-mx partial d/dx(mu u/my)
! -mx partial d/dy(mu v/mx)]dnu
!
! muu='mu'[on u]/my, muv='mu'[on v]/mx
! (1/my) partial d mu/dt is independent of nu
! => LHS = Integral|bot->top[con]dnu = conservation*(-1) = -dmdt
!
! => dmdt = mx*Integral|bot->top[partial d/dx(mu u/my) +
! partial d/dy(mu v/mx)]dnu
! => dmdt = sum_bot->top[divv]
! where
! divv=mx*[partial d/dx(mu u/my) + partial d/dy(mu v/mx)]*delta nu
DO k=kts,ktf
DO i=its,itf
divv(i,k) = msftx(i,j)*dnw(k)*( rdx*(muu(i+1,j)*u(i+1,k,j)-muu(i,j)*u(i,k,j)) &
+rdy*(muv(i,j+1)*v(i,k,j+1)-muv(i,j)*v(i,k,j)) )
! dmdt(i) = dmdt(i) + dnw(k)* ( rdx*(ru(i+1,k,j)-ru(i,k,j)) &
! +rdy*(rv(i,k,j+1)-rv(i,k,j)) )
dmdt(i) = dmdt(i) + divv(i,k)
ENDDO
ENDDO
! Further map scale factor notes:
! Now integrate from bottom to top, level by level:
! mu dnu/dt/my [k+1] = mu dnu/dt/my [k] + [-(1/my) partial d mu/dt
! -mx partial d/dx(mu u/my)
! -mx partial d/dy(mu v/mx)]*dnu[k->k+1]
! ww [k+1] = ww [k] -(1/my) partial d mu/dt * dnu[k->k+1] - divv[k]
! = ww [k] -dmdt * dnw[k] - divv[k]
DO k=2,ktf
DO i=its,itf
! ww(i,k,j)=ww(i,k-1,j) &
! - dnw(k-1)* ( dmdt(i) &
! +rdx*(ru(i+1,k-1,j)-ru(i,k-1,j)) &
! +rdy*(rv(i,k-1,j+1)-rv(i,k-1,j)) )
ww(i,k,j)=ww(i,k-1,j) - dnw(k-1)*dmdt(i) - divv(i,k-1)
ENDDO
ENDDO
ENDDO
END SUBROUTINE calc_ww_cp
!-------------------------------------------------------------------------------
SUBROUTINE calc_cq ( moist, cqu, cqv, cqw, n_moist, & 1
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
INTEGER , INTENT(IN ) :: n_moist
REAL, DIMENSION( ims:ime, kms:kme , jms:jme , n_moist ), INTENT(IN ) :: moist
REAL, DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT( OUT) :: cqu, cqv, cqw
! Local stuff
! Changes from Larry Meadows, Intel Corp. Improve vectorization of this routine
REAL :: qtot(its:ite)
INTEGER :: i, j, k, itf, jtf, ktf, ispe
!<DESCRIPTION>
!
! calc_cq calculates moist coefficients for the momentum equations.
!
!</DESCRIPTION>
ktf=MIN(kte,kde-1)
IF( n_moist >= PARAM_FIRST_SCALAR ) THEN
itf=ite
jtf=MIN(jte,jde-1)
DO j=jts,jtf
DO k=kts,ktf
qtot = 0.
DO ispe=PARAM_FIRST_SCALAR,n_moist
DO i=its,itf
qtot(i) = qtot(i) + moist(i,k,j,ispe) + moist(i-1,k,j,ispe)
ENDDO
ENDDO
DO i=its,itf
cqu(i,k,j) = 1./(1.+0.5*qtot(i))
ENDDO
ENDDO
ENDDO
itf=MIN(ite,ide-1)
jtf=jte
DO j=jts,jtf
DO k=kts,ktf
qtot = 0.
DO ispe=PARAM_FIRST_SCALAR,n_moist
DO i=its,itf
qtot(i) = qtot(i) + moist(i,k,j,ispe) + moist(i,k,j-1,ispe)
ENDDO
ENDDO
DO i = its,itf
cqv(i,k,j) = 1./(1.+0.5*qtot(i))
ENDDO
ENDDO
ENDDO
itf=MIN(ite,ide-1)
jtf=MIN(jte,jde-1)
DO j=jts,jtf
DO k=kts+1,ktf
qtot = 0.
DO ispe=PARAM_FIRST_SCALAR,n_moist
DO i=its,itf
qtot(i) = qtot(i) + moist(i,k,j,ispe) + moist(i,k-1,j,ispe)
ENDDO
ENDDO
DO i = its,itf
cqw(i,k,j) = 0.5*qtot(i)
ENDDO
ENDDO
ENDDO
ELSE
itf=ite
jtf=MIN(jte,jde-1)
DO j=jts,jtf
DO k=kts,ktf
DO i=its,itf
cqu(i,k,j) = 1.
ENDDO
ENDDO
ENDDO
itf=MIN(ite,ide-1)
jtf=jte
DO j=jts,jtf
DO k=kts,ktf
DO i=its,itf
cqv(i,k,j) = 1.
ENDDO
ENDDO
ENDDO
itf=MIN(ite,ide-1)
jtf=MIN(jte,jde-1)
DO j=jts,jtf
DO k=kts+1,ktf
DO i=its,itf
cqw(i,k,j) = 0.
ENDDO
ENDDO
ENDDO
END IF
END SUBROUTINE calc_cq
!----------------------------------------------------------------------
SUBROUTINE calc_alt ( alt, al, alb, & 1
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL, DIMENSION( ims:ime , kms:kme , jms:jme ), INTENT(IN ) :: alb, al
REAL, DIMENSION( ims:ime , kms:kme , jms:jme ), INTENT( OUT) :: alt
! Local stuff
INTEGER :: i, j, k, itf, jtf, ktf
!<DESCRIPTION>
!
! calc_alt computes the full inverse density
!
!</DESCRIPTION>
itf=MIN(ite,ide-1)
jtf=MIN(jte,jde-1)
ktf=MIN(kte,kde-1)
DO j=jts,jtf
DO k=kts,ktf
DO i=its,itf
alt(i,k,j) = al(i,k,j)+alb(i,k,j)
ENDDO
ENDDO
ENDDO
END SUBROUTINE calc_alt
!----------------------------------------------------------------------
SUBROUTINE calc_p_rho_phi ( moist, n_moist, hypsometric_opt, & 2,2
al, alb, mu, muts, ph, phb, p, pb, &
t, p0, t0, ptop, znu, znw, dnw, rdnw, &
rdn, non_hydrostatic, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
LOGICAL , INTENT(IN ) :: non_hydrostatic
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
INTEGER , INTENT(IN ) :: n_moist
INTEGER , INTENT(IN ) :: hypsometric_opt
REAL, DIMENSION( ims:ime , kms:kme , jms:jme ), INTENT(IN ) :: alb, &
pb, &
t
REAL, DIMENSION( ims:ime , kms:kme , jms:jme, n_moist ), INTENT(IN ) :: moist
REAL, DIMENSION( ims:ime , kms:kme , jms:jme ), INTENT( OUT) :: al, p
REAL, DIMENSION( ims:ime , kms:kme , jms:jme ), INTENT(INOUT) :: ph, phb
REAL, DIMENSION( ims:ime , jms:jme ), INTENT(IN ) :: mu, muts
REAL, DIMENSION( kms:kme ), INTENT(IN ) :: znu, znw, dnw, rdnw, rdn
REAL, INTENT(IN ) :: t0, p0, ptop
! Local stuff
INTEGER :: i, j, k, itf, jtf, ktf, ispe
REAL :: qvf, qtot, qf1, qf2
REAL, DIMENSION( its:ite) :: temp,cpovcv_v
REAL :: pfu, phm, pfd
!<DESCRIPTION>
!
! For the nonhydrostatic option, calc_p_rho_phi calculates the
! diagnostic quantities pressure and (inverse) density from the
! prognostic variables using the equation of state.
!
! For the hydrostatic option, calc_p_rho_phi calculates the
! diagnostic quantities (inverse) density and geopotential from the
! prognostic variables using the equation of state and the hydrostatic
! equation.
!
!</DESCRIPTION>
itf=MIN(ite,ide-1)
jtf=MIN(jte,jde-1)
ktf=MIN(kte,kde-1)
#ifndef INTELMKL
cpovcv_v = cpovcv
#endif
IF (non_hydrostatic) THEN
IF (hypsometric_opt == 1) THEN
DO j=jts,jtf
DO k=kts,ktf
DO i=its,itf
al(i,k,j)=-1./muts(i,j)*(alb(i,k,j)*mu(i,j) + rdnw(k)*(ph(i,k+1,j)-ph(i,k,j)))
END DO
END DO
END DO
ELSE IF (hypsometric_opt == 2) THEN
! The relation used to get specific volume, al, is: al = -dZ/dp,
! where dp = mut * d(eta). The pressure depth, dp, is replaced with
! p*(dp/p) ~ p*LOG((p+0.5dp)/(p-0.5dp)). Difference between dp and p*dLOG(p)
! is as follows: p*dLOG(p) - dp = 1/12*(dp/p)**3 + 1/90*(dp/p)**5 + ...
! Therefore, p*dLOG(p) is always larger than dp and the difference is
! in proportion to dp/p. TKW, 02/16/2010
DO j=jts,jtf
DO k=kts,ktf
DO i=its,itf
pfu = muts(i,j)*znw(k+1)+ptop
pfd = muts(i,j)*znw(k) +ptop
phm = muts(i,j)*znu(k) +ptop
al(i,k,j) = (ph(i,k+1,j)-ph(i,k,j)+phb(i,k+1,j)-phb(i,k,j))/phm/LOG(pfd/pfu)-alb(i,k,j)
END DO
END DO
END DO
ELSE
CALL wrf_error_fatal ( 'calc_p_rho_phi: hypsometric_opt should be 1 or 2' )
END IF
IF (n_moist >= PARAM_FIRST_SCALAR ) THEN
DO j=jts,jtf
DO k=kts,ktf
DO i=its,itf
qvf = 1.+rvovrd*moist(i,k,j,P_QV)
temp(i)=(r_d*(t0+t(i,k,j))*qvf)/(p0*(al(i,k,j)+alb(i,k,j)))
ENDDO
#ifdef INTELMKL
CALL VPOWX ( itf-its+1, temp(its), cpovcv, p(its,k,j) )
#else
! use vector version from libmassv or from compat lib in frame/libmassv.F
CALL VPOW ( p(its,k,j), temp(its), cpovcv_v(its), itf-its+1 )
#endif
DO i=its,itf
p(i,k,j)= p(i,k,j)*p0-pb(i,k,j)
ENDDO
ENDDO
ENDDO
ELSE
DO j=jts,jtf
DO k=kts,ktf
DO i=its,itf
p(i,k,j)=p0*( (r_d*(t0+t(i,k,j)))/ &
(p0*(al(i,k,j)+alb(i,k,j))) )**cpovcv &
-pb(i,k,j)
ENDDO
ENDDO
ENDDO
END IF
ELSE
! hydrostatic pressure, al, and ph1 calc; WCS, 5 sept 2001
IF (n_moist >= PARAM_FIRST_SCALAR ) THEN
DO j=jts,jtf
k=ktf ! top layer
DO i=its,itf
qtot = 0.
DO ispe=PARAM_FIRST_SCALAR,n_moist
qtot = qtot + moist(i,k,j,ispe)
ENDDO
qf2 = 1.
qf1 = qtot*qf2
p(i,k,j) = - 0.5*(mu(i,j)+qf1*muts(i,j))/rdnw(k)/qf2
qvf = 1.+rvovrd*moist(i,k,j,P_QV)
al(i,k,j) = (r_d/p1000mb)*(t(i,k,j)+t0)*qvf* &
(((p(i,k,j)+pb(i,k,j))/p1000mb)**cvpm) - alb(i,k,j)
ENDDO
DO k=ktf-1,kts,-1 ! remaining layers, integrate down
DO i=its,itf
qtot = 0.
DO ispe=PARAM_FIRST_SCALAR,n_moist
qtot = qtot + 0.5*( moist(i,k ,j,ispe) + moist(i,k+1,j,ispe) )
ENDDO
qf2 = 1.
qf1 = qtot*qf2
p(i,k,j) = p(i,k+1,j) - (mu(i,j) + qf1*muts(i,j))/qf2/rdn(k+1)
qvf = 1.+rvovrd*moist(i,k,j,P_QV)
al(i,k,j) = (r_d/p1000mb)*(t(i,k,j)+t0)*qvf* &
(((p(i,k,j)+pb(i,k,j))/p1000mb)**cvpm) - alb(i,k,j)
ENDDO
ENDDO
ENDDO
ELSE
DO j=jts,jtf
k=ktf ! top layer
DO i=its,itf
qtot = 0.
qf2 = 1.
qf1 = qtot*qf2
p(i,k,j) = - 0.5*(mu(i,j)+qf1*muts(i,j))/rdnw(k)/qf2
qvf = 1.
al(i,k,j) = (r_d/p1000mb)*(t(i,k,j)+t0)*qvf* &
(((p(i,k,j)+pb(i,k,j))/p1000mb)**cvpm) - alb(i,k,j)
ENDDO
DO k=ktf-1,kts,-1 ! remaining layers, integrate down
DO i=its,itf
qtot = 0.
qf2 = 1.
qf1 = qtot*qf2
p(i,k,j) = p(i,k+1,j) - (mu(i,j) + qf1*muts(i,j))/qf2/rdn(k+1)
qvf = 1.
al(i,k,j) = (r_d/p1000mb)*(t(i,k,j)+t0)*qvf* &
(((p(i,k,j)+pb(i,k,j))/p1000mb)**cvpm) - alb(i,k,j)
ENDDO
ENDDO
ENDDO
END IF
IF (hypsometric_opt == 1) THEN
DO j=jts,jtf
DO k=2,ktf+1 ! integrate hydrostatic equation for geopotential
DO i=its,itf
ph(i,k,j) = ph(i,k-1,j) - (dnw(k-1))*( &
(muts(i,j))*al(i,k-1,j)+ &
mu(i,j)*alb(i,k-1,j) )
ENDDO
ENDDO
ENDDO
ELSE
! Revised hypsometric eq.: dZ=-al*p*dLOG(p), where p is dry pressure
DO j=jts,jtf
DO i=its,itf
ph(i,kts,j) = phb(i,kts,j)
END DO
DO k=kts+1,ktf+1
DO i=its,itf
pfu = muts(i,j)*znw(k) +ptop
pfd = muts(i,j)*znw(k-1)+ptop
phm = muts(i,j)*znu(k-1)+ptop
ph(i,k,j) = ph(i,k-1,j) + (al(i,k-1,j)+alb(i,k-1,j))*phm*LOG(pfd/pfu)
ENDDO
ENDDO
DO k=kts,ktf+1
DO i=its,itf
ph(i,k,j) = ph(i,k,j) - phb(i,k,j)
END DO
END DO
END DO
END IF
END IF
END SUBROUTINE calc_p_rho_phi
!----------------------------------------------------------------------
SUBROUTINE calc_php ( php, ph, phb, & 1
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL, DIMENSION( ims:ime, kms:kme , jms:jme ), INTENT(IN ) :: phb, ph
REAL, DIMENSION( ims:ime, kms:kme , jms:jme ), INTENT( OUT) :: php
! Local stuff
INTEGER :: i, j, k, itf, jtf, ktf
!<DESCRIPTION>
!
! calc_php calculates the full geopotential from the reference state
! geopotential and the perturbation geopotential (phb_ph).
!
!</DESCRIPTION>
itf=MIN(ite,ide-1)
jtf=MIN(jte,jde-1)
ktf=MIN(kte,kde-1)
DO j=jts,jtf
DO k=kts,ktf
DO i=its,itf
php(i,k,j) = 0.5*(phb(i,k,j)+phb(i,k+1,j)+ph(i,k,j)+ph(i,k+1,j))
ENDDO
ENDDO
ENDDO
END SUBROUTINE calc_php
!-------------------------------------------------------------------------------
SUBROUTINE diagnose_w( ph_tend, ph_new, ph_old, w, mu, dt, & 2
u, v, ht, &
cf1, cf2, cf3, rdx, rdy, &
msftx, msfty, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL, DIMENSION( ims:ime, kms:kme , jms:jme ), INTENT(IN ) :: ph_tend, &
ph_new, &
ph_old, &
u, &
v
REAL, DIMENSION( ims:ime, kms:kme , jms:jme ), INTENT( OUT) :: w
REAL, DIMENSION( ims:ime, jms:jme ), INTENT(IN ) :: mu, ht, msftx, msfty
REAL, INTENT(IN ) :: dt, cf1, cf2, cf3, rdx, rdy
INTEGER :: i, j, k, itf, jtf
itf=MIN(ite,ide-1)
jtf=MIN(jte,jde-1)
!<DESCRIPTION>
!
! diagnose_w diagnoses the vertical velocity from the geopoential equation.
! Used with the hydrostatic option.
!
!</DESCRIPTION>
DO j = jts, jtf
! lower b.c. on w
! Notes on map scale factors:
! Chain rule: if Z=Z(X,Y) [true at the surface] then
! dZ/dt = dZ/dX * dX/dt + dZ/dY * dY/dt, U=dX/dt, V=dY/dt
! Using capitals to denote actual values
! In mapped values, u=U, v=V, z=Z, 1/dX=mx/dx, 1/dY=my/dy
! => w = dz/dt = mx u dz/dx + my v dz/dy
! [where dz/dx is just the surface height change between x
! gridpoints, and dz/dy is the change between y gridpoints]
! [NB: cf1, cf2 and cf3 do vertical weighting of u or v values
! nearest the surface]
! Previously msft multiplied by rdy and rdx terms.
! Now msfty multiplies rdy term, and msftx multiplies msftx term
DO i = its, itf
w(i,1,j)= msfty(i,j)*.5*rdy*( &
(ht(i,j+1)-ht(i,j )) &
*(cf1*v(i,1,j+1)+cf2*v(i,2,j+1)+cf3*v(i,3,j+1)) &
+(ht(i,j )-ht(i,j-1)) &
*(cf1*v(i,1,j )+cf2*v(i,2,j )+cf3*v(i,3,j )) ) &
+msftx(i,j)*.5*rdx*( &
(ht(i+1,j)-ht(i,j )) &
*(cf1*u(i+1,1,j)+cf2*u(i+1,2,j)+cf3*u(i+1,3,j)) &
+(ht(i,j )-ht(i-1,j)) &
*(cf1*u(i ,1,j)+cf2*u(i ,2,j)+cf3*u(i ,3,j)) )
ENDDO
! use geopotential equation to diagnose w
! Further notes on map scale factors
! If ph_tend contains: -mx partial d/dx(mu rho u/my)
! -mx partial d/dy(phi mu v/mx)
! -partial d/dz(phi mu w/my)
! then phi eqn is: partial d/dt(mu phi/my) = ph_tend + mu g w/my
! => w = [my/(mu*g)]*[partial d/dt(mu phi/my) - ph_tend]
DO k = 2, kte
DO i = its, itf
w(i,k,j) = msfty(i,j)*( (ph_new(i,k,j)-ph_old(i,k,j))/dt &
- ph_tend(i,k,j)/mu(i,j) )/g
ENDDO
ENDDO
ENDDO
END SUBROUTINE diagnose_w
!-------------------------------------------------------------------------------
SUBROUTINE rhs_ph( ph_tend, u, v, ww, & 1
ph, ph_old, phb, w, &
mut, muu, muv, &
fnm, fnp, &
rdnw, cfn, cfn1, rdx, rdy, &
msfux, msfuy, msfvx, &
msfvx_inv, msfvy, &
msftx, msfty, &
non_hydrostatic, &
config_flags, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
TYPE(grid_config_rec_type), INTENT(IN ) :: config_flags
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL, DIMENSION( ims:ime, kms:kme , jms:jme ), INTENT(IN ) :: &
u, &
v, &
ww, &
ph, &
ph_old, &
phb, &
w
REAL, DIMENSION( ims:ime, kms:kme , jms:jme ), INTENT(INOUT) :: ph_tend
REAL, DIMENSION( ims:ime, jms:jme ), INTENT(IN ) :: muu, muv, mut, &
msfux, msfuy, &
msfvx, msfvy, &
msftx, msfty, &
msfvx_inv
REAL, DIMENSION( kms:kme ), INTENT(IN ) :: rdnw, fnm, fnp
REAL, INTENT(IN ) :: cfn, cfn1, rdx, rdy
LOGICAL, INTENT(IN ) :: non_hydrostatic
! Local stuff
INTEGER :: i, j, k, itf, jtf, ktf, kz, i_start, j_start
REAL :: ur, ul, ub, vr, vl, vb
REAL, DIMENSION(its:ite,kts:kte) :: wdwn
INTEGER :: advective_order
LOGICAL :: specified
!<DESCRIPTION>
!
! rhs_ph calculates the large-timestep tendency terms for the geopotential
! equation. These terms include the advection and "gw". The geopotential
! equation is cast in advective form, so we don't use the flux form advection
! algorithms here.
!
!</DESCRIPTION>
specified = .false.
if(config_flags%specified .or. config_flags%nested) specified = .true.
advective_order = config_flags%h_sca_adv_order
itf=MIN(ite,ide-1)
jtf=MIN(jte,jde-1)
ktf=MIN(kte,kde-1)
! Notes on map scale factors (WCS, 2 march 2008)
! phi equation is: mu/my d/dt(phi) = -(1/my) mx mu u d/dx(phi)
! -(1/my) my mu v d/dy(phi)
! - omega d/d_eta(phi)
! +mu g w/my
!
! A little further explanation...
! The tendency term we are computing here is for mu/my d/dt(phi). It is advective form
! but it is multiplied be mu/my. It will be decoupled from (mu/my) when the implicit w-phi
! solution is computed in subourine advance_w. The formulation dates from the early
! days of the mass coordinate model when we were testing both a flux and an advective formulation
! for the geopotential equation and different forms of the vertical momentum equation and the
! vertically implicit solver.
! advective form for the geopotential equation
DO j = jts, jtf
DO k = 2, kte
DO i = its, itf
wdwn(i,k) = .5*(ww(i,k,j)+ww(i,k-1,j))*rdnw(k-1) &
*(ph(i,k,j)-ph(i,k-1,j)+phb(i,k,j)-phb(i,k-1,j))
ENDDO
ENDDO
! RHS term 3 is: - omega partial d/dnu(phi)
DO k = 2, kte-1
DO i = its, itf
ph_tend(i,k,j) = ph_tend(i,k,j) &
- (fnm(k)*wdwn(i,k+1)+fnp(k)*wdwn(i,k))
ENDDO
ENDDO
ENDDO
IF (non_hydrostatic) THEN ! add in "gw" term.
DO j = jts, jtf ! in hydrostatic mode, "gw" will be diagnosed
! after the timestep to give us "w"
DO i = its, itf
ph_tend(i,kde,j) = 0.
ENDDO
DO k = 2, kte
DO i = its, itf
! phi equation RHS term 4
ph_tend(i,k,j) = ph_tend(i,k,j) + mut(i,j)*g*w(i,k,j)/msfty(i,j)
ENDDO
ENDDO
ENDDO
END IF
! Notes on map scale factors:
! RHS terms 1 and 2 are: -(1/my) mx u mu partial d/dx(phi)
! -(1/my) my v mu partial d/dy(phi)
IF (advective_order <= 2) THEN
! y (v) advection
i_start = its
j_start = jts
itf=MIN(ite,ide-1)
jtf=MIN(jte,jde-1)
IF ( (config_flags%open_ys .or. specified) .and. jts == jds ) j_start = jts+1
IF ( (config_flags%open_ye .or. specified) .and. jte == jde ) jtf = jtf-2
DO j = j_start, jtf
DO k = 2, kte-1
DO i = i_start, itf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.25*rdy/msfty(i,j))* &
( muv(i,j+1)*(v(i,k,j+1)+v(i,k-1,j+1))*msfvy(i,j+1)* &
(phb(i,k,j+1)-phb(i,k,j )+ph(i,k,j+1)-ph(i,k,j )) &
+muv(i,j )*(v(i,k,j )+v(i,k-1,j ))*msfvy(i,j )* &
(phb(i,k,j )-phb(i,k,j-1)+ph(i,k,j )-ph(i,k,j-1)) )
ENDDO
ENDDO
k = kte
DO i = i_start, itf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.5*rdy/msfty(i,j))* &
( muv(i,j+1)*(cfn*v(i,k-1,j+1)+cfn1*v(i,k-2,j+1))*msfvy(i,j+1)* &
(phb(i,k,j+1)-phb(i,k,j )+ph(i,k,j+1)-ph(i,k,j )) &
+muv(i,j )*(cfn*v(i,k-1,j )+cfn1*v(i,k-2,j ))*msfvy(i,j )* &
(phb(i,k,j )-phb(i,k,j-1)+ph(i,k,j )-ph(i,k,j-1)) )
ENDDO
ENDDO
! x (u) advection
i_start = its
j_start = jts
itf=MIN(ite,ide-1)
jtf=MIN(jte,jde-1)
IF ( (config_flags%open_xs .or. specified) .and. its == ids ) i_start = its+1
IF ( (config_flags%open_xe .or. specified) .and. ite == ide ) itf = itf-2
DO j = j_start, jtf
DO k = 2, kte-1
DO i = i_start, itf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.25*rdx/msfty(i,j))* &
( muu(i+1,j)*(u(i+1,k,j)+u(i+1,k-1,j))*msfux(i+1,j)* &
(phb(i+1,k,j)-phb(i ,k,j)+ph(i+1,k,j)-ph(i ,k,j)) &
+muu(i ,j)*(u(i ,k,j)+u(i ,k-1,j))*msfux(i ,j)* &
(phb(i ,k,j)-phb(i-1,k,j)+ph(i ,k,j)-ph(i-1,k,j)) )
ENDDO
ENDDO
k = kte
DO i = i_start, itf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.5*rdx/msfty(i,j))* &
( muu(i+1,j)*(cfn*u(i+1,k-1,j)+cfn1*u(i+1,k-2,j))*msfux(i+1,j)* &
(phb(i+1,k,j)-phb(i ,k,j)+ph(i+1,k,j)-ph(i ,k,j)) &
+muu(i ,j)*(cfn*u(i ,k-1,j)+cfn1*u(i ,k-2,j))*msfux( i,j)* &
(phb(i ,k,j)-phb(i-1,k,j)+ph(i ,k,j)-ph(i-1,k,j)) )
ENDDO
ENDDO
ELSE IF (advective_order <= 4) THEN
! y (v) advection
i_start = its
j_start = jts
itf=MIN(ite,ide-1)
jtf=MIN(jte,jde-1)
IF ( (config_flags%open_ys .or. specified) .and. jts == jds ) j_start = jts+2
IF ( (config_flags%open_ye .or. specified) .and. jte == jde ) jtf = jtf-3
DO j = j_start, jtf
DO k = 2, kte-1
DO i = i_start, itf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.25*rdy/msfty(i,j))*( &
( muv(i,j+1)*(v(i,k,j+1)+v(i,k-1,j+1))*msfvy(i,j+1) &
+muv(i,j )*(v(i,k,j )+v(i,k-1,j ))*msfvy(i,j ))* (1./12.)*( &
8.*(ph(i,k,j+1)-ph(i,k,j-1)) &
-(ph(i,k,j+2)-ph(i,k,j-2)) &
+8.*(phb(i,k,j+1)-phb(i,k,j-1)) &
-(phb(i,k,j+2)-phb(i,k,j-2)) ) )
ENDDO
ENDDO
k = kte
DO i = i_start, itf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.5*rdy/msfty(i,j))*( &
( muv(i,j+1)*(cfn*v(i,k-1,j+1)+cfn1*v(i,k-2,j+1))*msfvy(i,j+1) &
+muv(i,j )*(cfn*v(i,k-1,j )+cfn1*v(i,k-2,j ))*msfvy(i,j ))* (1./12.)*( &
8.*(ph(i,k,j+1)-ph(i,k,j-1)) &
-(ph(i,k,j+2)-ph(i,k,j-2)) &
+8.*(phb(i,k,j+1)-phb(i,k,j-1)) &
-(phb(i,k,j+2)-phb(i,k,j-2)) ) )
ENDDO
ENDDO
! pick up near boundary rows using 2nd order stencil for open and specified conditions
IF ( (config_flags%open_ys .or. specified) .and. jts <= jds+1 ) THEN
j = jds+1
DO k = 2, kte-1
DO i = i_start, itf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.25*rdy/msfty(i,j))* &
( muv(i,j+1)*(v(i,k,j+1)+v(i,k-1,j+1))*msfvy(i,j+1)* &
(phb(i,k,j+1)-phb(i,k,j )+ph(i,k,j+1)-ph(i,k,j )) &
+muv(i,j )*(v(i,k,j )+v(i,k-1,j ))*msfvy(i,j )* &
(phb(i,k,j )-phb(i,k,j-1)+ph(i,k,j )-ph(i,k,j-1)) )
ENDDO
ENDDO
k = kte
DO i = i_start, itf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.5*rdy/msfty(i,j))* &
( muv(i,j+1)*(cfn*v(i,k-1,j+1)+cfn1*v(i,k-2,j+1))*msfvy(i,j+1)* &
(phb(i,k,j+1)-phb(i,k,j )+ph(i,k,j+1)-ph(i,k,j )) &
+muv(i,j )*(cfn*v(i,k-1,j )+cfn1*v(i,k-2,j ))*msfvy(i,j )* &
(phb(i,k,j )-phb(i,k,j-1)+ph(i,k,j )-ph(i,k,j-1)) )
ENDDO
END IF
IF ( (config_flags%open_ye .or. specified) .and. jte >= jde-2 ) THEN
j = jde-2
DO k = 2, kte-1
DO i = i_start, itf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.25*rdy/msfty(i,j))* &
( muv(i,j+1)*(v(i,k,j+1)+v(i,k-1,j+1))*msfvy(i,j+1)* &
(phb(i,k,j+1)-phb(i,k,j )+ph(i,k,j+1)-ph(i,k,j )) &
+muv(i,j )*(v(i,k,j )+v(i,k-1,j ))*msfvy(i,j )* &
(phb(i,k,j )-phb(i,k,j-1)+ph(i,k,j )-ph(i,k,j-1)) )
ENDDO
ENDDO
k = kte
DO i = i_start, itf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.5*rdy/msfty(i,j))* &
( muv(i,j+1)*(cfn*v(i,k-1,j+1)+cfn1*v(i,k-2,j+1))*msfvy(i,j+1)* &
(phb(i,k,j+1)-phb(i,k,j )+ph(i,k,j+1)-ph(i,k,j )) &
+muv(i,j )*(cfn*v(i,k-1,j )+cfn1*v(i,k-2,j ))*msfvy(i,j )* &
(phb(i,k,j )-phb(i,k,j-1)+ph(i,k,j )-ph(i,k,j-1)) )
ENDDO
END IF
! x (u) advection
i_start = its
j_start = jts
itf=MIN(ite,ide-1)
jtf=MIN(jte,jde-1)
IF ( (config_flags%open_xs) .and. its == ids ) i_start = its+2
IF ( (config_flags%open_xe) .and. ite == ide ) itf = itf-3
DO j = j_start, jtf
DO k = 2, kte-1
DO i = i_start, itf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.25*rdx/msfty(i,j))*( &
( muu(i+1,j)*(u(i+1,k,j)+u(i+1,k-1,j))*msfux(i+1,j) &
+muu(i,j )*(u(i ,k,j)+u(i ,k-1,j))*msfux(i ,j) )* (1./12.)*( &
8.*(ph(i+1,k,j)-ph(i-1,k,j)) &
-(ph(i+2,k,j)-ph(i-2,k,j)) &
+8.*(phb(i+1,k,j)-phb(i-1,k,j)) &
-(phb(i+2,k,j)-phb(i-2,k,j)) ) )
ENDDO
ENDDO
k = kte
DO i = i_start, itf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.5*rdx/msfty(i,j))*( &
( muu(i+1,j)*(cfn*u(i+1,k-1,j)+cfn1*u(i+1,k-2,j))*msfux(i+1,j) &
+muu(i,j )*(cfn*u(i ,k-1,j)+cfn1*u(i ,k-2,j))*msfux(i ,j) )* (1./12.)*( &
8.*(ph(i+1,k,j)-ph(i-1,k,j)) &
-(ph(i+2,k,j)-ph(i-2,k,j)) &
+8.*(phb(i+1,k,j)-phb(i-1,k,j)) &
-(phb(i+2,k,j)-phb(i-2,k,j)) ) )
ENDDO
ENDDO
! pick up near boundary rows using 2nd order stencil for open and specified conditions
IF ( (config_flags%open_xs .or. specified) .and. its <= ids+1 ) THEN
i = ids + 1
DO j = j_start, jtf
DO k = 2, kte-1
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.25*rdx/msfty(i,j))* &
( muu(i+1,j)*(u(i+1,k,j)+u(i+1,k-1,j))*msfux(i+1,j)* &
(phb(i+1,k,j)-phb(i ,k,j)+ph(i+1,k,j)-ph(i ,k,j)) &
+muu(i ,j)*(u(i ,k,j)+u(i ,k-1,j))*msfux(i ,j)* &
(phb(i ,k,j)-phb(i-1,k,j)+ph(i ,k,j)-ph(i-1,k,j)) )
ENDDO
ENDDO
k = kte
DO j = j_start, jtf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.5*rdx/msfty(i,j))* &
( muu(i+1,j)*(cfn*u(i+1,k-1,j)+cfn1*u(i+1,k-2,j))*msfux(i+1,j)* &
(phb(i+1,k,j)-phb(i ,k,j)+ph(i+1,k,j)-ph(i ,k,j)) &
+muu(i ,j)*(cfn*u(i ,k-1,j)+cfn1*u(i ,k-2,j))*msfux( i,j)* &
(phb(i ,k,j)-phb(i-1,k,j)+ph(i ,k,j)-ph(i-1,k,j)) )
ENDDO
END IF
IF ( (config_flags%open_xe .or. specified) .and. ite >= ide-2 ) THEN
i = ide-2
DO j = j_start, jtf
DO k = 2, kte-1
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.25*rdx/msfty(i,j))* &
( muu(i+1,j)*(u(i+1,k,j)+u(i+1,k-1,j))*msfux(i+1,j)* &
(phb(i+1,k,j)-phb(i ,k,j)+ph(i+1,k,j)-ph(i ,k,j)) &
+muu(i ,j)*(u(i ,k,j)+u(i ,k-1,j))*msfux(i ,j)* &
(phb(i ,k,j)-phb(i-1,k,j)+ph(i ,k,j)-ph(i-1,k,j)) )
ENDDO
ENDDO
k = kte
DO j = j_start, jtf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.5*rdx/msfty(i,j))* &
( muu(i+1,j)*(cfn*u(i+1,k-1,j)+cfn1*u(i+1,k-2,j))*msfux(i+1,j)* &
(phb(i+1,k,j)-phb(i ,k,j)+ph(i+1,k,j)-ph(i ,k,j)) &
+muu(i ,j)*(cfn*u(i ,k-1,j)+cfn1*u(i ,k-2,j))*msfux( i,j)* &
(phb(i ,k,j)-phb(i-1,k,j)+ph(i ,k,j)-ph(i-1,k,j)) )
ENDDO
END IF
!--------------------------
ELSE IF (advective_order <= 6) THEN
!!! NOTE: this branch has been looked at and fixed with changes for overdecomposition
!!! the branches covering the other advective_order cases have not. 20090923. JM
! y (v) advection
i_start = its
j_start = jts
itf=MIN(ite,ide-1)
jtf=MIN(jte,jde-1)
IF (config_flags%open_ys .or. specified ) j_start = max(jts,jds+3)
IF (config_flags%open_ye .or. specified ) jtf = min(jtf,jde-4)
DO j = j_start, jtf
DO k = 2, kte-1
DO i = i_start, itf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.25*rdy/msfty(i,j))* ( &
( muv(i,j+1)*(v(i,k,j+1)+v(i,k-1,j+1))*msfvy(i,j+1) &
+muv(i,j )*(v(i,k,j )+v(i,k-1,j ))*msfvy(i,j ) )* (1./60.)*( &
45.*(ph(i,k,j+1)-ph(i,k,j-1)) &
-9.*(ph(i,k,j+2)-ph(i,k,j-2)) &
+(ph(i,k,j+3)-ph(i,k,j-3)) &
+45.*(phb(i,k,j+1)-phb(i,k,j-1)) &
-9.*(phb(i,k,j+2)-phb(i,k,j-2)) &
+(phb(i,k,j+3)-phb(i,k,j-3)) ) )
ENDDO
ENDDO
k = kte
DO i = i_start, itf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.5*rdy/msfty(i,j))* ( &
( muv(i,j+1)*(cfn*v(i,k-1,j+1)+cfn1*v(i,k-2,j+1))*msfvy(i,j+1) &
+muv(i,j )*(cfn*v(i,k-1,j )+cfn1*v(i,k-2,j ))*msfvy(i,j ) )* (1./60.)*( &
45.*(ph(i,k,j+1)-ph(i,k,j-1)) &
-9.*(ph(i,k,j+2)-ph(i,k,j-2)) &
+(ph(i,k,j+3)-ph(i,k,j-3)) &
+45.*(phb(i,k,j+1)-phb(i,k,j-1)) &
-9.*(phb(i,k,j+2)-phb(i,k,j-2)) &
+(phb(i,k,j+3)-phb(i,k,j-3)) ) )
ENDDO
ENDDO
! 4th order stencil for open or specified conditions two in form the boundary
IF ( (config_flags%open_ys .or. specified) .and. jts <= jds+2 .and. jds+2 <= jte ) THEN
j = jds+2
DO k = 2, kte-1
DO i = i_start, itf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.25*rdy/msfty(i,j))* ( &
( muv(i,j+1)*(v(i,k,j+1)+v(i,k-1,j+1))*msfvy(i,j+1) &
+muv(i,j )*(v(i,k,j )+v(i,k-1,j ))*msfvy(i,j ) )* (1./12.)*( &
8.*(ph(i,k,j+1)-ph(i,k,j-1)) &
-(ph(i,k,j+2)-ph(i,k,j-2)) &
+8.*(phb(i,k,j+1)-phb(i,k,j-1)) &
-(phb(i,k,j+2)-phb(i,k,j-2)) ) )
ENDDO
ENDDO
k = kte
DO i = i_start, itf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.5*rdy/msfty(i,j))* ( &
( muv(i,j+1)*(cfn*v(i,k-1,j+1)+cfn1*v(i,k-2,j+1))*msfvy(i,j+1) &
+muv(i,j )*(cfn*v(i,k-1,j )+cfn1*v(i,k-2,j ))*msfvy(i,j) )* (1./12.)*( &
8.*(ph(i,k,j+1)-ph(i,k,j-1)) &
-(ph(i,k,j+2)-ph(i,k,j-2)) &
+8.*(phb(i,k,j+1)-phb(i,k,j-1)) &
-(phb(i,k,j+2)-phb(i,k,j-2)) ) )
ENDDO
END IF
IF ( (config_flags%open_ye .or. specified) .and. jts <= jde-3 .and. jde-3 <= jte ) THEN
j = jde-3
DO k = 2, kte-1
DO i = i_start, itf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.25*rdy/msfty(i,j))* ( &
( muv(i,j+1)*(v(i,k,j+1)+v(i,k-1,j+1))*msfvy(i,j+1) &
+muv(i,j )*(v(i,k,j )+v(i,k-1,j ))*msfvy(i,j) )* (1./12.)*( &
8.*(ph(i,k,j+1)-ph(i,k,j-1)) &
-(ph(i,k,j+2)-ph(i,k,j-2)) &
+8.*(phb(i,k,j+1)-phb(i,k,j-1)) &
-(phb(i,k,j+2)-phb(i,k,j-2)) ) )
ENDDO
ENDDO
k = kte
DO i = i_start, itf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.5*rdy/msfty(i,j))* ( &
( muv(i,j+1)*(cfn*v(i,k-1,j+1)+cfn1*v(i,k-2,j+1))*msfvy(i,j+1) &
+muv(i,j )*(cfn*v(i,k-1,j )+cfn1*v(i,k-2,j ))*msfvy(i,j) )* (1./12.)*( &
8.*(ph(i,k,j+1)-ph(i,k,j-1)) &
-(ph(i,k,j+2)-ph(i,k,j-2)) &
+8.*(phb(i,k,j+1)-phb(i,k,j-1)) &
-(phb(i,k,j+2)-phb(i,k,j-2)) ) )
ENDDO
END IF
! 2nd order stencil for open and specified conditions one row in from boundary
IF ( (config_flags%open_ys .or. specified) .and. jts <= jds+1 .and. jds+1 <= jte ) THEN
j = jds+1
DO k = 2, kte-1
DO i = i_start, itf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.25*rdy/msfty(i,j))* &
( muv(i,j+1)*(v(i,k,j+1)+v(i,k-1,j+1))*msfvy(i,j+1)* &
(phb(i,k,j+1)-phb(i,k,j )+ph(i,k,j+1)-ph(i,k,j )) &
+muv(i,j )*(v(i,k,j )+v(i,k-1,j ))*msfvy(i,j )* &
(phb(i,k,j )-phb(i,k,j-1)+ph(i,k,j )-ph(i,k,j-1)) )
ENDDO
ENDDO
k = kte
DO i = i_start, itf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.5*rdy/msfty(i,j))* &
( muv(i,j+1)*(cfn*v(i,k-1,j+1)+cfn1*v(i,k-2,j+1))*msfvy(i,j+1)* &
(phb(i,k,j+1)-phb(i,k,j )+ph(i,k,j+1)-ph(i,k,j )) &
+muv(i,j )*(cfn*v(i,k-1,j )+cfn1*v(i,k-2,j ))*msfvy(i,j )* &
(phb(i,k,j )-phb(i,k,j-1)+ph(i,k,j )-ph(i,k,j-1)) )
ENDDO
END IF
IF ( (config_flags%open_ye .or. specified) .and. jts <= jde-2 .and. jde-2 <= jte ) THEN
j = jde-2
DO k = 2, kte-1
DO i = i_start, itf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.25*rdy/msfty(i,j))* &
( muv(i,j+1)*(v(i,k,j+1)+v(i,k-1,j+1))*msfvy(i,j+1)* &
(phb(i,k,j+1)-phb(i,k,j )+ph(i,k,j+1)-ph(i,k,j )) &
+muv(i,j )*(v(i,k,j )+v(i,k-1,j ))*msfvy(i,j )* &
(phb(i,k,j )-phb(i,k,j-1)+ph(i,k,j )-ph(i,k,j-1)) )
ENDDO
ENDDO
k = kte
DO i = i_start, itf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.5*rdy/msfty(i,j))* &
( muv(i,j+1)*(cfn*v(i,k-1,j+1)+cfn1*v(i,k-2,j+1))*msfvy(i,j+1)* &
(phb(i,k,j+1)-phb(i,k,j )+ph(i,k,j+1)-ph(i,k,j )) &
+muv(i,j )*(cfn*v(i,k-1,j )+cfn1*v(i,k-2,j ))*msfvy(i,j )* &
(phb(i,k,j )-phb(i,k,j-1)+ph(i,k,j )-ph(i,k,j-1)) )
ENDDO
END IF
! x (u) advection
i_start = its
j_start = jts
itf=MIN(ite,ide-1)
jtf=MIN(jte,jde-1)
IF (config_flags%open_xs .or. specified ) i_start = max(its,ids+3)
IF (config_flags%open_xe .or. specified ) itf = min(itf,ide-4)
DO j = j_start, jtf
DO k = 2, kte-1
DO i = i_start, itf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.25*rdx/msfty(i,j))*( &
( muu(i+1,j)*(u(i+1,k,j)+u(i+1,k-1,j))*msfux(i+1,j) &
+muu(i,j )*(u(i,k,j )+u(i,k-1,j ))*msfux(i,j) )* (1./60.)*( &
45.*(ph(i+1,k,j)-ph(i-1,k,j)) &
-9.*(ph(i+2,k,j)-ph(i-2,k,j)) &
+(ph(i+3,k,j)-ph(i-3,k,j)) &
+45.*(phb(i+1,k,j)-phb(i-1,k,j)) &
-9.*(phb(i+2,k,j)-phb(i-2,k,j)) &
+(phb(i+3,k,j)-phb(i-3,k,j)) ) )
ENDDO
ENDDO
k = kte
DO i = i_start, itf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.5*rdx/msfty(i,j))*( &
( muu(i+1,j)*(cfn*u(i+1,k-1,j)+cfn1*u(i+1,k-2,j))*msfux(i+1,j) &
+muu(i,j )*(cfn*u(i ,k-1,j)+cfn1*u(i,k-2,j))*msfux(i,j) )* (1./60.)*( &
45.*(ph(i+1,k,j)-ph(i-1,k,j)) &
-9.*(ph(i+2,k,j)-ph(i-2,k,j)) &
+(ph(i+3,k,j)-ph(i-3,k,j)) &
+45.*(phb(i+1,k,j)-phb(i-1,k,j)) &
-9.*(phb(i+2,k,j)-phb(i-2,k,j)) &
+(phb(i+3,k,j)-phb(i-3,k,j)) ) )
ENDDO
ENDDO
! 4th order stencil two in from the boundary for open and specified conditions
IF ( (config_flags%open_xs) .and. its <= ids+2 .and. ids+2 <= ite ) THEN
i = ids + 2
DO j = j_start, jtf
DO k = 2, kte-1
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.25*rdx/msfty(i,j))*( &
( muu(i+1,j)*(u(i+1,k,j)+u(i+1,k-1,j))*msfux(i+1,j) &
+muu(i,j )*(u(i,k,j )+u(i,k-1,j ))*msfux(i,j) )* (1./12.)*( &
8.*(ph(i+1,k,j)-ph(i-1,k,j)) &
-(ph(i+2,k,j)-ph(i-2,k,j)) &
+8.*(phb(i+1,k,j)-phb(i-1,k,j)) &
-(phb(i+2,k,j)-phb(i-2,k,j)) ) )
ENDDO
k = kte
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.5*rdx/msfty(i,j))*( &
( muu(i+1,j)*(cfn*u(i+1,k-1,j)+cfn1*u(i+1,k-2,j))*msfux(i+1,j) &
+muu(i,j )*(cfn*u(i ,k-1,j)+cfn1*u(i,k-2,j))*msfux(i,j) )* (1./12.)*( &
8.*(ph(i+1,k,j)-ph(i-1,k,j)) &
-(ph(i+2,k,j)-ph(i-2,k,j)) &
+8.*(phb(i+1,k,j)-phb(i-1,k,j)) &
-(phb(i+2,k,j)-phb(i-2,k,j)) ) )
ENDDO
END IF
IF ( (config_flags%open_xe) .and. its <= ide-3 .and. ide-3 <= ite ) THEN
i = ide-3
DO j = j_start, jtf
DO k = 2, kte-1
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.25*rdx/msfty(i,j))*( &
( muu(i+1,j)*(u(i+1,k,j)+u(i+1,k-1,j))*msfux(i+1,j) &
+muu(i,j )*(u(i,k,j )+u(i,k-1,j ))*msfux(i,j) )* (1./12.)*( &
8.*(ph(i+1,k,j)-ph(i-1,k,j)) &
-(ph(i+2,k,j)-ph(i-2,k,j)) &
+8.*(phb(i+1,k,j)-phb(i-1,k,j)) &
-(phb(i+2,k,j)-phb(i-2,k,j)) ) )
ENDDO
k = kte
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.5*rdx/msfty(i,j))*( &
( muu(i+1,j)*(cfn*u(i+1,k-1,j)+cfn1*u(i+1,k-2,j))*msfux(i+1,j) &
+muu(i,j )*(cfn*u(i ,k-1,j)+cfn1*u(i,k-2,j))*msfux(i,j) )* (1./12.)*( &
8.*(ph(i+1,k,j)-ph(i-1,k,j)) &
-(ph(i+2,k,j)-ph(i-2,k,j)) &
+8.*(phb(i+1,k,j)-phb(i-1,k,j)) &
-(phb(i+2,k,j)-phb(i-2,k,j)) ) )
ENDDO
END IF
! 2nd order stencil for open and specified conditions one in from the boundary
IF ( (config_flags%open_xs .or. specified) .and. its <= ids+1 .and. ids+1 <= ite ) THEN
i = ids + 1
DO j = j_start, jtf
DO k = 2, kte-1
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.25*rdx/msfty(i,j))* &
( muu(i+1,j)*(u(i+1,k,j)+u(i+1,k-1,j))*msfux(i+1,j)* &
(phb(i+1,k,j)-phb(i ,k,j)+ph(i+1,k,j)-ph(i ,k,j)) &
+muu(i ,j)*(u(i ,k,j)+u(i ,k-1,j))*msfux(i ,j)* &
(phb(i ,k,j)-phb(i-1,k,j)+ph(i ,k,j)-ph(i-1,k,j)) )
ENDDO
ENDDO
k = kte
DO j = j_start, jtf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.5*rdx/msfty(i,j))* &
( muu(i+1,j)*(cfn*u(i+1,k-1,j)+cfn1*u(i+1,k-2,j))*msfux(i+1,j)* &
(phb(i+1,k,j)-phb(i ,k,j)+ph(i+1,k,j)-ph(i ,k,j)) &
+muu(i ,j)*(cfn*u(i ,k-1,j)+cfn1*u(i ,k-2,j))*msfux( i,j)* &
(phb(i ,k,j)-phb(i-1,k,j)+ph(i ,k,j)-ph(i-1,k,j)) )
ENDDO
END IF
IF ( (config_flags%open_xe .or. specified) .and. its <= ide-2 .and. ide-2 <= ite ) THEN
i = ide-2
DO j = j_start, jtf
DO k = 2, kte-1
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.25*rdx/msfty(i,j))* &
( muu(i+1,j)*(u(i+1,k,j)+u(i+1,k-1,j))*msfux(i+1,j)* &
(phb(i+1,k,j)-phb(i ,k,j)+ph(i+1,k,j)-ph(i ,k,j)) &
+muu(i ,j)*(u(i ,k,j)+u(i ,k-1,j))*msfux(i ,j)* &
(phb(i ,k,j)-phb(i-1,k,j)+ph(i ,k,j)-ph(i-1,k,j)) )
ENDDO
ENDDO
k = kte
DO j = j_start, jtf
ph_tend(i,k,j)=ph_tend(i,k,j) - (0.5*rdx/msfty(i,j))* &
( muu(i+1,j)*(cfn*u(i+1,k-1,j)+cfn1*u(i+1,k-2,j))*msfux(i+1,j)* &
(phb(i+1,k,j)-phb(i ,k,j)+ph(i+1,k,j)-ph(i ,k,j)) &
+muu(i ,j)*(cfn*u(i ,k-1,j)+cfn1*u(i ,k-2,j))*msfux( i,j)* &
(phb(i ,k,j)-phb(i-1,k,j)+ph(i ,k,j)-ph(i-1,k,j)) )
ENDDO
END IF
END IF ! 6th order advection
! lateral open boundary conditions,
! start with north and south (y) boundaries
i_start = its
itf=MIN(ite,ide-1)
! south
IF ( (config_flags%open_ys) .and. jts == jds ) THEN
j=jts
DO k=2,kde
kz = min(k,kde-1)
DO i = its,itf
vb =.5*( fnm(kz)*(v(i,kz ,j+1)+v(i,kz ,j )) &
+fnp(kz)*(v(i,kz-1,j+1)+v(i,kz-1,j )) )
vl=amin1(vb,0.)
ph_tend(i,k,j)=ph_tend(i,k,j)-rdy*mut(i,j)*( &
+vl*(ph_old(i,k,j+1)-ph_old(i,k,j)))
ENDDO
ENDDO
END IF
! north
IF ( (config_flags%open_ye) .and. jte == jde ) THEN
j=jte-1
DO k=2,kde
kz = min(k,kde-1)
DO i = its,itf
vb=.5*( fnm(kz)*(v(i,kz ,j+1)+v(i,kz ,j)) &
+fnp(kz)*(v(i,kz-1,j+1)+v(i,kz-1,j)) )
vr=amax1(vb,0.)
ph_tend(i,k,j)=ph_tend(i,k,j)-rdy*mut(i,j)*( &
+vr*(ph_old(i,k,j)-ph_old(i,k,j-1)))
ENDDO
ENDDO
END IF
! now the east and west (y) boundaries
j_start = its
jtf=MIN(jte,jde-1)
! west
IF ( (config_flags%open_xs) .and. its == ids ) THEN
i=its
DO j = jts,jtf
DO k=2,kde-1
kz = k
ub =.5*( fnm(kz)*(u(i+1,kz ,j)+u(i ,kz ,j)) &
+fnp(kz)*(u(i+1,kz-1,j)+u(i ,kz-1,j)) )
ul=amin1(ub,0.)
ph_tend(i,k,j)=ph_tend(i,k,j)-(msftx(i,j)/msfty(i,j))*rdx*mut(i,j)*( &
+ul*(ph_old(i+1,k,j)-ph_old(i,k,j)))
ENDDO
k = kde
kz = k
ub =.5*( fnm(kz)*(u(i+1,kz ,j)+u(i ,kz ,j)) &
+fnp(kz)*(u(i+1,kz-1,j)+u(i ,kz-1,j)) )
ul=amin1(ub,0.)
ph_tend(i,k,j)=ph_tend(i,k,j)-(msftx(i,j)/msfty(i,j))*rdx*mut(i,j)*( &
+ul*(ph_old(i+1,k,j)-ph_old(i,k,j)))
ENDDO
END IF
! east
IF ( (config_flags%open_xe) .and. ite == ide ) THEN
i = ite-1
DO j = jts,jtf
DO k=2,kde-1
kz = k
ub=.5*( fnm(kz)*(u(i+1,kz ,j)+u(i,kz ,j)) &
+fnp(kz)*(u(i+1,kz-1,j)+u(i,kz-1,j)) )
ur=amax1(ub,0.)
ph_tend(i,k,j)=ph_tend(i,k,j)-(msftx(i,j)/msfty(i,j))*rdx*mut(i,j)*( &
+ur*(ph_old(i,k,j)-ph_old(i-1,k,j)))
ENDDO
k = kde
kz = k-1
ub=.5*( fnm(kz)*(u(i+1,kz ,j)+u(i,kz ,j)) &
+fnp(kz)*(u(i+1,kz-1,j)+u(i,kz-1,j)) )
ur=amax1(ub,0.)
ph_tend(i,k,j)=ph_tend(i,k,j)-(msftx(i,j)/msfty(i,j))*rdx*mut(i,j)*( &
+ur*(ph_old(i,k,j)-ph_old(i-1,k,j)))
ENDDO
END IF
END SUBROUTINE rhs_ph
!-------------------------------------------------------------------------------
SUBROUTINE horizontal_pressure_gradient( ru_tend,rv_tend, & 1
ph,alt,p,pb,al,php,cqu,cqv, &
muu,muv,mu,fnm,fnp,rdnw, &
cf1,cf2,cf3,rdx,rdy,msfux,msfuy,&
msfvx,msfvy,msftx,msfty, &
config_flags, non_hydrostatic, &
top_lid, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
TYPE(grid_config_rec_type), INTENT(IN ) :: config_flags
LOGICAL, INTENT (IN ) :: non_hydrostatic, top_lid
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL, DIMENSION( ims:ime, kms:kme , jms:jme ), INTENT(IN ) :: &
ph, &
alt, &
al, &
p, &
pb, &
php, &
cqu, &
cqv
REAL, DIMENSION( ims:ime, kms:kme , jms:jme ), INTENT(INOUT) :: &
ru_tend, &
rv_tend
REAL, DIMENSION( ims:ime, jms:jme ), INTENT(IN ) :: muu, muv, mu, &
msfux, msfuy, &
msfvx, msfvy, &
msftx, msfty
REAL, DIMENSION( kms:kme ), INTENT(IN ) :: rdnw, fnm, fnp
REAL, INTENT(IN ) :: rdx, rdy, cf1, cf2, cf3
INTEGER :: i,j,k, itf, jtf, ktf, i_start, j_start
REAL, DIMENSION( ims:ime, kms:kme ) :: dpn
REAL :: dpx, dpy
LOGICAL :: specified
!<DESCRIPTION>
!
! horizontal_pressure_gradient calculates the
! horizontal pressure gradient terms for the large-timestep tendency
! in the horizontal momentum equations (u,v).
!
!</DESCRIPTION>
specified = .false.
if(config_flags%specified .or. config_flags%nested) specified = .true.
! Notes on map scale factors:
! Calculates the pressure gradient terms in ADT eqns 44 and 45
! With upper rho -> 'mu', these are:
! Eqn 30: -mu*(mx/my)*(1/rho)*partial dp/dx
! Eqn 31: -mu*(my/mx)*(1/rho)*partial dp/dy
!
! As we are on nu, rather than height, surfaces:
!
! mu dp/dx = mu alpha partial dp'/dx + (nu mu partial dmubar/dx) alpha'
! + mu partial dphi'/dx + (partial dphi/dx)*(partial dp'/dnu - mu')
!
! mu dp/dy = mu alpha partial dp'/dy + (nu mu partial dmubar/dy) alpha'
! + mu partial dphi'/dy + (partial dphi/dy)*(partial dp'/dnu - mu')
! start with the north-south (y) pressure gradient
itf=MIN(ite,ide-1)
jtf=jte
ktf=MIN(kte,kde-1)
i_start = its
j_start = jts
IF ( (config_flags%open_ys .or. specified .or. &
config_flags%nested .or. config_flags%polar ) .and. jts == jds ) j_start = jts+1
IF ( (config_flags%open_ye .or. specified .or. &
config_flags%nested .or. config_flags%polar ) .and. jte == jde ) jtf = jtf-1
DO j = j_start, jtf
IF ( non_hydrostatic ) THEN
k=1
DO i = i_start, itf
dpn(i,k) = .5*( cf1*(p(i,k ,j-1)+p(i,k ,j)) &
+cf2*(p(i,k+1,j-1)+p(i,k+1,j)) &
+cf3*(p(i,k+2,j-1)+p(i,k+2,j)) )
dpn(i,kde) = 0.
ENDDO
IF (top_lid) THEN
DO i = i_start, itf
dpn(i,kde) = .5*( cf1*(p(i,kde-1,j-1)+p(i,kde-1,j)) &
+cf2*(p(i,kde-2,j-1)+p(i,kde-2,j)) &
+cf3*(p(i,kde-3,j-1)+p(i,kde-3,j)) )
ENDDO
ENDIF
DO k=2,ktf
DO i = i_start, itf
dpn(i,k) = .5*( fnm(k)*(p(i,k ,j-1)+p(i,k ,j)) &
+fnp(k)*(p(i,k-1,j-1)+p(i,k-1,j)) )
END DO
END DO
! ADT eqn 45: -mu*(my/mx)*(1/rho)*partial dp/dy
! [alt, al are 1/rho terms; muv, mu are NOT coupled]
DO K=1,ktf
DO i = i_start, itf
! Here are mu dp/dy terms 1-3
dpy = (msfvy(i,j)/msfvx(i,j))*.5*rdy*muv(i,j)*( &
(ph (i,k+1,j)-ph (i,k+1,j-1) + ph(i,k,j)-ph(i,k,j-1)) &
+(alt(i,k ,j)+alt(i,k ,j-1))*(p (i,k,j)-p (i,k,j-1)) &
+(al (i,k ,j)+al (i,k ,j-1))*(pb(i,k,j)-pb(i,k,j-1)) )
! Here is mu dp/dy term 4
dpy = dpy + (msfvy(i,j)/msfvx(i,j))*rdy*(php(i,k,j)-php(i,k,j-1))* &
(rdnw(k)*(dpn(i,k+1)-dpn(i,k))-.5*(mu(i,j-1)+mu(i,j)))
rv_tend(i,k,j) = rv_tend(i,k,j)-cqv(i,k,j)*dpy
END DO
END DO
ELSE
! ADT eqn 45: -mu*(my/mx)*(1/rho)*partial dp/dy
! [alt, al are 1/rho terms; muv, mu are NOT coupled]
DO K=1,ktf
DO i = i_start, itf
! Here are mu dp/dy terms 1-3; term 4 not needed if hydrostatic
dpy = (msfvy(i,j)/msfvx(i,j))*.5*rdy*muv(i,j)*( &
(ph (i,k+1,j)-ph (i,k+1,j-1) + ph(i,k,j)-ph(i,k,j-1)) &
+(alt(i,k ,j)+alt(i,k ,j-1))*(p (i,k,j)-p (i,k,j-1)) &
+(al (i,k ,j)+al (i,k ,j-1))*(pb(i,k,j)-pb(i,k,j-1)) )
rv_tend(i,k,j) = rv_tend(i,k,j)-cqv(i,k,j)*dpy
END DO
END DO
END IF
ENDDO
! now the east-west (x) pressure gradient
itf=ite
jtf=MIN(jte,jde-1)
ktf=MIN(kte,kde-1)
i_start = its
j_start = jts
IF ( (config_flags%open_xs .or. specified .or. &
config_flags%nested ) .and. its == ids ) i_start = its+1
IF ( (config_flags%open_xe .or. specified .or. &
config_flags%nested ) .and. ite == ide ) itf = itf-1
IF ( config_flags%periodic_x ) i_start = its
IF ( config_flags%periodic_x ) itf=ite
DO j = j_start, jtf
IF ( non_hydrostatic ) THEN
k=1
DO i = i_start, itf
dpn(i,k) = .5*( cf1*(p(i-1,k ,j)+p(i,k ,j)) &
+cf2*(p(i-1,k+1,j)+p(i,k+1,j)) &
+cf3*(p(i-1,k+2,j)+p(i,k+2,j)) )
dpn(i,kde) = 0.
ENDDO
IF (top_lid) THEN
DO i = i_start, itf
dpn(i,kde) = .5*( cf1*(p(i-1,kde-1,j)+p(i,kde-1,j)) &
+cf2*(p(i-1,kde-2,j)+p(i,kde-2,j)) &
+cf3*(p(i-1,kde-3,j)+p(i,kde-3,j)) )
ENDDO
ENDIF
DO k=2,ktf
DO i = i_start, itf
dpn(i,k) = .5*( fnm(k)*(p(i-1,k ,j)+p(i,k ,j)) &
+fnp(k)*(p(i-1,k-1,j)+p(i,k-1,j)) )
END DO
END DO
! ADT eqn 44: -mu*(mx/my)*(1/rho)*partial dp/dx
! [alt, al are 1/rho terms; muu, mu are NOT coupled]
DO K=1,ktf
DO i = i_start, itf
! Here are mu dp/dy terms 1-3
dpx = (msfux(i,j)/msfuy(i,j))*.5*rdx*muu(i,j)*( &
(ph (i,k+1,j)-ph (i-1,k+1,j) + ph(i,k,j)-ph(i-1,k,j)) &
+(alt(i,k ,j)+alt(i-1,k ,j))*(p (i,k,j)-p (i-1,k,j)) &
+(al (i,k ,j)+al (i-1,k ,j))*(pb(i,k,j)-pb(i-1,k,j)) )
! Here is mu dp/dy term 4
dpx = dpx + (msfux(i,j)/msfuy(i,j))*rdx*(php(i,k,j)-php(i-1,k,j))* &
(rdnw(k)*(dpn(i,k+1)-dpn(i,k))-.5*(mu(i-1,j)+mu(i,j)))
ru_tend(i,k,j) = ru_tend(i,k,j)-cqu(i,k,j)*dpx
END DO
END DO
ELSE
! ADT eqn 44: -mu*(mx/my)*(1/rho)*partial dp/dx
! [alt, al are 1/rho terms; muu, mu are NOT coupled]
DO K=1,ktf
DO i = i_start, itf
! Here are mu dp/dy terms 1-3; term 4 not needed if hydrostatic
dpx = (msfux(i,j)/msfuy(i,j))*.5*rdx*muu(i,j)*( &
(ph (i,k+1,j)-ph (i-1,k+1,j) + ph(i,k,j)-ph(i-1,k,j)) &
+(alt(i,k ,j)+alt(i-1,k ,j))*(p (i,k,j)-p (i-1,k,j)) &
+(al (i,k ,j)+al (i-1,k ,j))*(pb(i,k,j)-pb(i-1,k,j)) )
ru_tend(i,k,j) = ru_tend(i,k,j)-cqu(i,k,j)*dpx
END DO
END DO
END IF
ENDDO
END SUBROUTINE horizontal_pressure_gradient
!-------------------------------------------------------------------------------
SUBROUTINE pg_buoy_w( rw_tend, p, cqw, mu, mub, & 1
rdnw, rdn, g, msftx, msfty, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL, DIMENSION( ims:ime, kms:kme , jms:jme ), INTENT(IN ) :: p
REAL, DIMENSION( ims:ime, kms:kme , jms:jme ), INTENT(INOUT) :: cqw
REAL, DIMENSION( ims:ime, kms:kme , jms:jme ), INTENT(INOUT) :: rw_tend
REAL, DIMENSION( ims:ime, jms:jme ), INTENT(IN ) :: mub, mu, msftx, msfty
REAL, DIMENSION( kms:kme ), INTENT(IN ) :: rdnw, rdn
REAL, INTENT(IN ) :: g
INTEGER :: itf, jtf, i, j, k
REAL :: cq1, cq2
!<DESCRIPTION>
!
! pg_buoy_w calculates the
! vertical pressure gradient and buoyancy terms for the large-timestep
! tendency in the vertical momentum equation.
!
!</DESCRIPTION>
! BUOYANCY AND PRESSURE GRADIENT TERM IN W EQUATION AT TIME T
! Map scale factor notes
! ADT eqn 46 RHS terms 6 and 7 (where 7 is "-rho g")
! Dividing by my, and using mu and nu (see Klemp et al. eqns 32, 40)
! term 6: +(g/my) partial dp'/dnu
! term 7: -(g/my) mu'
!
! For moisture-free atmosphere, cq1=1, cq2=0
! => (1./msft(i,j)) * g * [rdn(k)*{p(i,k,j)-p(i,k-1,j)}-mu(i,j)]
itf=MIN(ite,ide-1)
jtf=MIN(jte,jde-1)
DO j = jts,jtf
k=kde
DO i=its,itf
cq1 = 1./(1.+cqw(i,k-1,j))
cq2 = cqw(i,k-1,j)*cq1
rw_tend(i,k,j) = rw_tend(i,k,j)+(1./msfty(i,j))*g*( &
cq1*2.*rdnw(k-1)*( -p(i,k-1,j)) &
-mu(i,j)-cq2*mub(i,j) )
END DO
DO k = 2, kde-1
DO i = its,itf
cq1 = 1./(1.+cqw(i,k,j))
cq2 = cqw(i,k,j)*cq1
cqw(i,k,j) = cq1
rw_tend(i,k,j) = rw_tend(i,k,j)+(1./msfty(i,j))*g*( &
cq1*rdn(k)*(p(i,k,j)-p(i,k-1,j)) &
-mu(i,j)-cq2*mub(i,j) )
END DO
ENDDO
ENDDO
END SUBROUTINE pg_buoy_w
!-------------------------------------------------------------------------------
SUBROUTINE w_damp( rw_tend, max_vert_cfl,max_horiz_cfl, & 1,8
u, v, ww, w, mut, rdnw, &
rdx, rdy, msfux, msfuy, &
msfvx, msfvy, dt, &
config_flags, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
USE module_llxy
IMPLICIT NONE
! Input data
TYPE(grid_config_rec_type ) , INTENT(IN ) :: config_flags
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL, DIMENSION( ims:ime, kms:kme , jms:jme ), INTENT(IN ) :: u, v, ww, w
REAL, DIMENSION( ims:ime, kms:kme , jms:jme ), INTENT(INOUT) :: rw_tend
REAL, INTENT(OUT) :: max_vert_cfl
REAL, INTENT(OUT) :: max_horiz_cfl
REAL :: horiz_cfl
REAL, DIMENSION( ims:ime, jms:jme ), INTENT(IN ) :: mut
REAL, DIMENSION( kms:kme ), INTENT(IN ) :: rdnw
REAL, INTENT(IN) :: dt
REAL, INTENT(IN) :: rdx, rdy
REAL , DIMENSION( ims:ime , jms:jme ) , INTENT(IN ) :: msfux, msfuy
REAL , DIMENSION( ims:ime , jms:jme ) , INTENT(IN ) :: msfvx, msfvy
REAL :: vert_cfl, cf_n, cf_d, maxdub, maxdeta
INTEGER :: itf, jtf, i, j, k, maxi, maxj, maxk
INTEGER :: some
CHARACTER*512 :: temp
CHARACTER (LEN=256) :: time_str
CHARACTER (LEN=256) :: grid_str
integer :: total
REAL :: msfuxt , msfxffl
!<DESCRIPTION>
!
! w_damp computes a damping term for the vertical velocity when the
! vertical Courant number is too large. This was found to be preferable to
! decreasing the timestep or increasing the diffusion in real-data applications
! that produced potentially-unstable large vertical velocities because of
! unphysically large heating rates coming from the cumulus parameterization
! schemes run at moderately high resolutions (dx ~ O(10) km).
!
! Additionally, w_damp returns the maximum cfl values due to vertical motion and
! horizontal motion. These values are returned via the max_vert_cfl and
! max_horiz_cfl variables. (Added by T. Hutchinson, WSI, 3/5/2007)
!
!</DESCRIPTION>
itf=MIN(ite,ide-1)
jtf=MIN(jte,jde-1)
some = 0
max_vert_cfl = 0.
max_horiz_cfl = 0.
total = 0
IF(config_flags%map_proj == PROJ_CASSINI ) then
msfxffl = 1.0/COS(config_flags%fft_filter_lat*degrad)
END IF
IF ( config_flags%w_damping == 1 ) THEN
#ifdef OPTIMIZE_CFL_TEST
! 20121025, L. Meadows vector optimization does not include special case for Cassini
IF(config_flags%map_proj == PROJ_CASSINI ) then
CALL wrf_error_fatal('module_big_step_utilities_em.F: -DOPTIMIZE_CFL_TEST option does not support PROJ_CASSINI')
END IF
#endif
DO j = jts,jtf
DO k = 2, kde-1
DO i = its,itf
#if 1
# ifdef OPTIMIZE_CFL_TEST
! L. Meadows, Intel, MIC optimization, 20121025
msfuxt = msfux(i,j)
vert_cfl = abs(ww(i,k,j)/mut(i,j)*rdnw(k)*dt)
IF ( vert_cfl > max_vert_cfl ) THEN
max_vert_cfl = vert_cfl
ENDIF
# else
IF(config_flags%map_proj == PROJ_CASSINI ) then
msfuxt = MIN(msfux(i,j), msfxffl)
ELSE
msfuxt = msfux(i,j)
END IF
vert_cfl = abs(ww(i,k,j)/mut(i,j)*rdnw(k)*dt)
IF ( vert_cfl > max_vert_cfl ) THEN
max_vert_cfl = vert_cfl ; maxi = i ; maxj = j ; maxk = k
maxdub = w(i,k,j) ; maxdeta = -1./rdnw(k)
ENDIF
# endif
horiz_cfl = max( abs(u(i,k,j) * rdx * msfuxt * dt), &
abs(v(i,k,j) * rdy * msfvy(i,j) * dt) )
if (horiz_cfl > max_horiz_cfl) then
max_horiz_cfl = horiz_cfl
endif
if(vert_cfl .gt. w_beta)then
#else
! restructure to get rid of divide
!
! This had been used for efficiency, but with the addition of returning the cfl values,
! the old version (above) was reinstated. (T. Hutchinson, 3/5/2007)
!
cf_n = abs(ww(i,k,j)*rdnw(k)*dt)
cf_d = abs(mut(i,j))
if(cf_n .gt. cf_d*w_beta )then
#endif
#ifndef OPTIMIZE_CFL_TEST
! This internal write is costly on newer Xeon processors because it breaks
! vectorization. (J. Michalakes for L. Meadows at Intel, 12/13/2012)
WRITE(temp,*)i,j,k,' vert_cfl,w,d(eta)=',vert_cfl,w(i,k,j),-1./rdnw(k)
CALL wrf_debug ( 100 , TRIM(temp) )
#endif
if ( vert_cfl > 2. ) some = some + 1
rw_tend(i,k,j) = rw_tend(i,k,j)-sign(1.,w(i,k,j))*w_alpha*(vert_cfl-w_beta)*mut(i,j)
endif
END DO
ENDDO
ENDDO
ELSE
! just print
DO j = jts,jtf
DO k = 2, kde-1
DO i = its,itf
#if 1
# ifdef OPTIMIZE_CFL_TEST
msfuxt = msfux(i,j)
vert_cfl = abs(ww(i,k,j)/mut(i,j)*rdnw(k)*dt)
IF ( vert_cfl > max_vert_cfl ) THEN
max_vert_cfl = vert_cfl
ENDIF
# else
! L. Meadows MIC optimization, 20121025
IF(config_flags%map_proj == PROJ_CASSINI ) then
msfuxt = MIN(msfux(i,j), msfxffl)
ELSE
msfuxt = msfux(i,j)
END IF
vert_cfl = abs(ww(i,k,j)/mut(i,j)*rdnw(k)*dt)
IF ( vert_cfl > max_vert_cfl ) THEN
max_vert_cfl = vert_cfl ; maxi = i ; maxj = j ; maxk = k
maxdub = w(i,k,j) ; maxdeta = -1./rdnw(k)
ENDIF
# endif
horiz_cfl = max( abs(u(i,k,j) * rdx * msfuxt * dt), &
abs(v(i,k,j) * rdy * msfvy(i,j) * dt) )
if (horiz_cfl > max_horiz_cfl) then
max_horiz_cfl = horiz_cfl
endif
if(vert_cfl .gt. w_beta)then
#else
! restructure to get rid of divide
!
! This had been used for efficiency, but with the addition of returning the cfl values,
! the old version (above) was reinstated. (T. Hutchinson, 3/5/2007)
!
cf_n = abs(ww(i,k,j)*rdnw(k)*dt)
cf_d = abs(mut(i,j))
if(cf_n .gt. cf_d*w_beta )then
#endif
#ifndef OPTIMIZE_CFL_TEST
WRITE(temp,*)i,j,k,' vert_cfl,w,d(eta)=',vert_cfl,w(i,k,j),-1./rdnw(k)
CALL wrf_debug ( 100 , TRIM(temp) )
#endif
if ( vert_cfl > 2. ) some = some + 1
endif
END DO
ENDDO
ENDDO
ENDIF
IF ( some .GT. 0 ) THEN
CALL get_current_time_string( time_str )
CALL get_current_grid_name( grid_str )
WRITE(temp,*)some, &
' points exceeded cfl=2 in domain '//TRIM(grid_str)//' at time '//TRIM(time_str)//' hours'
CALL wrf_debug ( 0 , TRIM(temp) )
#ifndef OPTIMIZE_CFL_TEST
WRITE(temp,*)'MAX AT i,j,k: ',maxi,maxj,maxk,' vert_cfl,w,d(eta)=',max_vert_cfl, &
maxdub,maxdeta
CALL wrf_debug ( 0 , TRIM(temp) )
#endif
ENDIF
END SUBROUTINE w_damp
!-------------------------------------------------------------------------------
SUBROUTINE horizontal_diffusion ( name, field, tendency, mu, & 4
config_flags, &
msfux, msfuy, msfvx, msfvx_inv, &
msfvy, msftx, msfty, &
khdif, xkmhd, rdx, rdy, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
TYPE(grid_config_rec_type), INTENT(IN ) :: config_flags
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
CHARACTER(LEN=1) , INTENT(IN ) :: name
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(IN ) :: field, xkmhd
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(INOUT) :: tendency
REAL , DIMENSION( ims:ime , jms:jme ) , INTENT(IN ) :: mu
REAL , DIMENSION( ims:ime , jms:jme ) , INTENT(IN ) :: msfux, &
msfuy, &
msfvx, &
msfvx_inv, &
msfvy, &
msftx, &
msfty
REAL , INTENT(IN ) :: rdx, &
rdy, &
khdif
! Local data
INTEGER :: i, j, k, itf, jtf, ktf
INTEGER :: i_start, i_end, j_start, j_end
REAL :: mrdx, mkrdxm, mkrdxp, &
mrdy, mkrdym, mkrdyp
LOGICAL :: specified
!<DESCRIPTION>
!
! horizontal_diffusion computes the horizontal diffusion tendency
! on model horizontal coordinate surfaces.
!
!</DESCRIPTION>
specified = .false.
if(config_flags%specified .or. config_flags%nested) specified = .true.
ktf=MIN(kte,kde-1)
IF (name .EQ. 'u') THEN
i_start = its
i_end = ite
j_start = jts
j_end = MIN(jte,jde-1)
IF ( config_flags%open_xs .or. specified ) i_start = MAX(ids+1,its)
IF ( config_flags%open_xe .or. specified ) i_end = MIN(ide-1,ite)
IF ( config_flags%open_ys .or. specified ) j_start = MAX(jds+1,jts)
IF ( config_flags%open_ye .or. specified ) j_end = MIN(jde-2,jte)
IF ( config_flags%periodic_x ) i_start = its
IF ( config_flags%periodic_x ) i_end = ite
DO j = j_start, j_end
DO k=kts,ktf
DO i = i_start, i_end
! The interior is grad: (m_x*d/dx), the exterior is div: (m_x*m_y*d/dx(/m_y))
! setting up different averagings of m^2 partial d/dX and m^2 partial d/dY
mkrdxm=(msftx(i-1,j)/msfty(i-1,j))*mu(i-1,j)*xkmhd(i-1,k,j)*rdx
mkrdxp=(msftx(i,j)/msfty(i,j))*mu(i,j)*xkmhd(i,k,j)*rdx
mrdx=msfux(i,j)*msfuy(i,j)*rdx
mkrdym=( (msfuy(i,j)+msfuy(i,j-1))/(msfux(i,j)+msfux(i,j-1)) )* &
0.25*(mu(i,j)+mu(i,j-1)+mu(i-1,j-1)+mu(i-1,j))* &
0.25*(xkmhd(i,k,j)+xkmhd(i,k,j-1)+xkmhd(i-1,k,j-1)+xkmhd(i-1,k,j))*rdy
mkrdyp=( (msfuy(i,j)+msfuy(i,j+1))/(msfux(i,j)+msfux(i,j+1)) )* &
0.25*(mu(i,j)+mu(i,j+1)+mu(i-1,j+1)+mu(i-1,j))* &
0.25*(xkmhd(i,k,j)+xkmhd(i,k,j+1)+xkmhd(i-1,k,j+1)+xkmhd(i-1,k,j))*rdy
! need to do four-corners (t) for diffusion coefficient as there are
! no values at u,v points
! msfuy - has to be y as part of d/dY
! has to be u as we're at a u point
mrdy=msfux(i,j)*msfuy(i,j)*rdy
! correctly averaged version of rho~ * m^2 *
! [partial d/dX(partial du^/dX) + partial d/dY(partial du^/dY)]
tendency(i,k,j)=tendency(i,k,j)+( &
mrdx*(mkrdxp*(field(i+1,k,j)-field(i ,k,j)) &
-mkrdxm*(field(i ,k,j)-field(i-1,k,j))) &
+mrdy*(mkrdyp*(field(i,k,j+1)-field(i,k,j )) &
-mkrdym*(field(i,k,j )-field(i,k,j-1))))
ENDDO
ENDDO
ENDDO
ELSE IF (name .EQ. 'v')THEN
i_start = its
i_end = MIN(ite,ide-1)
j_start = jts
j_end = jte
IF ( config_flags%open_xs .or. specified ) i_start = MAX(ids+1,its)
IF ( config_flags%open_xe .or. specified ) i_end = MIN(ide-2,ite)
IF ( config_flags%open_ys .or. specified ) j_start = MAX(jds+1,jts)
IF ( config_flags%open_ye .or. specified ) j_end = MIN(jde-1,jte)
IF ( config_flags%periodic_x ) i_start = its
IF ( config_flags%periodic_x ) i_end = MIN(ite,ide-1)
IF ( config_flags%polar ) j_start = MAX(jds+1,jts)
IF ( config_flags%polar ) j_end = MIN(jde-1,jte)
DO j = j_start, j_end
DO k=kts,ktf
DO i = i_start, i_end
mkrdxm=( (msfvx(i,j)+msfvx(i-1,j))/(msfvy(i,j)+msfvy(i-1,j)) )* &
0.25*(mu(i,j)+mu(i,j-1)+mu(i-1,j-1)+mu(i-1,j))* &
0.25*(xkmhd(i,k,j)+xkmhd(i,k,j-1)+xkmhd(i-1,k,j-1)+xkmhd(i-1,k,j))*rdx
mkrdxp=( (msfvx(i,j)+msfvx(i+1,j))/(msfvy(i,j)+msfvy(i+1,j)) )* &
0.25*(mu(i,j)+mu(i,j-1)+mu(i+1,j-1)+mu(i+1,j))* &
0.25*(xkmhd(i,k,j)+xkmhd(i,k,j-1)+xkmhd(i+1,k,j-1)+xkmhd(i+1,k,j))*rdx
mrdx=msfvx(i,j)*msfvy(i,j)*rdx
mkrdym=(msfty(i,j-1)/msftx(i,j-1))*xkmhd(i,k,j-1)*rdy
mkrdyp=(msfty(i,j)/msftx(i,j))*xkmhd(i,k,j)*rdy
mrdy=msfvx(i,j)*msfvy(i,j)*rdy
tendency(i,k,j)=tendency(i,k,j)+( &
mrdx*(mkrdxp*(field(i+1,k,j)-field(i ,k,j)) &
-mkrdxm*(field(i ,k,j)-field(i-1,k,j))) &
+mrdy*(mkrdyp*(field(i,k,j+1)-field(i,k,j )) &
-mkrdym*(field(i,k,j )-field(i,k,j-1))))
ENDDO
ENDDO
ENDDO
ELSE IF (name .EQ. 'w')THEN
i_start = its
i_end = MIN(ite,ide-1)
j_start = jts
j_end = MIN(jte,jde-1)
IF ( config_flags%open_xs .or. specified ) i_start = MAX(ids+1,its)
IF ( config_flags%open_xe .or. specified ) i_end = MIN(ide-2,ite)
IF ( config_flags%open_ys .or. specified ) j_start = MAX(jds+1,jts)
IF ( config_flags%open_ye .or. specified ) j_end = MIN(jde-2,jte)
IF ( config_flags%periodic_x ) i_start = its
IF ( config_flags%periodic_x ) i_end = MIN(ite,ide-1)
DO j = j_start, j_end
DO k=kts+1,ktf
DO i = i_start, i_end
mkrdxm=(msfux(i,j)/msfuy(i,j))* &
0.25*(mu(i,j)+mu(i-1,j)+mu(i,j)+mu(i-1,j))* &
0.25*(xkmhd(i,k,j)+xkmhd(i-1,k,j)+xkmhd(i,k-1,j)+xkmhd(i-1,k-1,j))*rdx
mkrdxp=(msfux(i+1,j)/msfuy(i+1,j))* &
0.25*(mu(i+1,j)+mu(i,j)+mu(i+1,j)+mu(i,j))* &
0.25*(xkmhd(i+1,k,j)+xkmhd(i,k,j)+xkmhd(i+1,k-1,j)+xkmhd(i,k-1,j))*rdx
mrdx=msftx(i,j)*msfty(i,j)*rdx
! mkrdym=(msfvy(i,j)/msfvx(i,j))* &
mkrdym=(msfvy(i,j)*msfvx_inv(i,j))* &
0.25*(mu(i,j)+mu(i,j-1)+mu(i,j)+mu(i,j-1))* &
0.25*(xkmhd(i,k,j)+xkmhd(i,k,j-1)+xkmhd(i,k-1,j)+xkmhd(i,k-1,j-1))*rdy
! mkrdyp=(msfvy(i,j+1)/msfvx(i,j+1))* &
mkrdyp=(msfvy(i,j+1)*msfvx_inv(i,j+1))* &
0.25*(mu(i,j+1)+mu(i,j)+mu(i,j+1)+mu(i,j))* &
0.25*(xkmhd(i,k,j+1)+xkmhd(i,k,j)+xkmhd(i,k-1,j+1)+xkmhd(i,k-1,j))*rdy
mrdy=msftx(i,j)*msfty(i,j)*rdy
tendency(i,k,j)=tendency(i,k,j)+( &
mrdx*(mkrdxp*(field(i+1,k,j)-field(i ,k,j)) &
-mkrdxm*(field(i ,k,j)-field(i-1,k,j))) &
+mrdy*(mkrdyp*(field(i,k,j+1)-field(i,k,j )) &
-mkrdym*(field(i,k,j )-field(i,k,j-1))))
ENDDO
ENDDO
ENDDO
ELSE
i_start = its
i_end = MIN(ite,ide-1)
j_start = jts
j_end = MIN(jte,jde-1)
IF ( config_flags%open_xs .or. specified ) i_start = MAX(ids+1,its)
IF ( config_flags%open_xe .or. specified ) i_end = MIN(ide-2,ite)
IF ( config_flags%open_ys .or. specified ) j_start = MAX(jds+1,jts)
IF ( config_flags%open_ye .or. specified ) j_end = MIN(jde-2,jte)
IF ( config_flags%periodic_x ) i_start = its
IF ( config_flags%periodic_x ) i_end = MIN(ite,ide-1)
DO j = j_start, j_end
DO k=kts,ktf
DO i = i_start, i_end
mkrdxm=(msfux(i,j)/msfuy(i,j))*0.5*(xkmhd(i,k,j)+xkmhd(i-1,k,j))*0.5*(mu(i,j)+mu(i-1,j))*rdx
mkrdxp=(msfux(i+1,j)/msfuy(i+1,j))*0.5*(xkmhd(i+1,k,j)+xkmhd(i,k,j))*0.5*(mu(i+1,j)+mu(i,j))*rdx
mrdx=msftx(i,j)*msfty(i,j)*rdx
! mkrdym=(msfvy(i,j)/msfvx(i,j))*0.5*(xkmhd(i,k,j)+xkmhd(i,k,j-1))*0.5*(mu(i,j)+mu(i,j-1))*rdy
mkrdym=(msfvy(i,j)*msfvx_inv(i,j))*0.5*(xkmhd(i,k,j)+xkmhd(i,k,j-1))*0.5*(mu(i,j)+mu(i,j-1))*rdy
! mkrdyp=(msfvy(i,j+1)/msfvx(i,j+1))*0.5*(xkmhd(i,k,j+1)+xkmhd(i,k,j))*0.5*(mu(i,j+1)+mu(i,j))*rdy
mkrdyp=(msfvy(i,j+1)*msfvx_inv(i,j+1))*0.5*(xkmhd(i,k,j+1)+xkmhd(i,k,j))*0.5*(mu(i,j+1)+mu(i,j))*rdy
mrdy=msftx(i,j)*msfty(i,j)*rdy
tendency(i,k,j)=tendency(i,k,j)+( &
mrdx*(mkrdxp*(field(i+1,k,j)-field(i ,k,j)) &
-mkrdxm*(field(i ,k,j)-field(i-1,k,j))) &
+mrdy*(mkrdyp*(field(i,k,j+1)-field(i,k,j )) &
-mkrdym*(field(i,k,j )-field(i,k,j-1))))
ENDDO
ENDDO
ENDDO
ENDIF
END SUBROUTINE horizontal_diffusion
!-----------------------------------------------------------------------------------------
SUBROUTINE horizontal_diffusion_3dmp ( name, field, tendency, mu, & 1
config_flags, base_3d, &
msfux, msfuy, msfvx, msfvx_inv, &
msfvy, msftx, msfty, &
khdif, xkmhd, rdx, rdy, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
TYPE(grid_config_rec_type), INTENT(IN ) :: config_flags
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
CHARACTER(LEN=1) , INTENT(IN ) :: name
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(IN ) :: field, &
xkmhd, &
base_3d
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(INOUT) :: tendency
REAL , DIMENSION( ims:ime , jms:jme ) , INTENT(IN ) :: mu
REAL , DIMENSION( ims:ime , jms:jme ) , INTENT(IN ) :: msfux, &
msfuy, &
msfvx, &
msfvx_inv, &
msfvy, &
msftx, &
msfty
REAL , INTENT(IN ) :: rdx, &
rdy, &
khdif
! Local data
INTEGER :: i, j, k, itf, jtf, ktf
INTEGER :: i_start, i_end, j_start, j_end
REAL :: mrdx, mkrdxm, mkrdxp, &
mrdy, mkrdym, mkrdyp
LOGICAL :: specified
!<DESCRIPTION>
!
! horizontal_diffusion_3dmp computes the horizontal diffusion tendency
! on model horizontal coordinate surfaces. This routine computes diffusion
! a perturbation scalar (field-base_3d).
!
!</DESCRIPTION>
specified = .false.
if(config_flags%specified .or. config_flags%nested) specified = .true.
ktf=MIN(kte,kde-1)
i_start = its
i_end = MIN(ite,ide-1)
j_start = jts
j_end = MIN(jte,jde-1)
IF ( config_flags%open_xs .or. specified ) i_start = MAX(ids+1,its)
IF ( config_flags%open_xe .or. specified ) i_end = MIN(ide-2,ite)
IF ( config_flags%open_ys .or. specified ) j_start = MAX(jds+1,jts)
IF ( config_flags%open_ye .or. specified ) j_end = MIN(jde-2,jte)
IF ( config_flags%periodic_x ) i_start = its
IF ( config_flags%periodic_x ) i_end = MIN(ite,ide-1)
DO j = j_start, j_end
DO k=kts,ktf
DO i = i_start, i_end
mkrdxm=(msfux(i,j)/msfuy(i,j))*0.5*(xkmhd(i,k,j)+xkmhd(i-1,k,j))*0.5*(mu(i,j)+mu(i-1,j))*rdx
mkrdxp=(msfux(i+1,j)/msfuy(i+1,j))*0.5*(xkmhd(i+1,k,j)+xkmhd(i,k,j))*0.5*(mu(i+1,j)+mu(i,j))*rdx
mrdx=msftx(i,j)*msfty(i,j)*rdx
! mkrdym=(msfvy(i,j)/msfvx(i,j))*0.5*(xkmhd(i,k,j)+xkmhd(i,k,j-1))*0.5*(mu(i,j)+mu(i,j-1))*rdy
! mkrdyp=(msfvy(i,j+1)/msfvx(i,j+1))*0.5*(xkmhd(i,k,j+1)+xkmhd(i,k,j))*0.5*(mu(i,j+1)+mu(i,j))*rdy
mkrdym=(msfvy(i,j)*msfvx_inv(i,j))*0.5*(xkmhd(i,k,j)+xkmhd(i,k,j-1))*0.5*(mu(i,j)+mu(i,j-1))*rdy
mkrdyp=(msfvy(i,j+1)*msfvx_inv(i,j+1))*0.5*(xkmhd(i,k,j+1)+xkmhd(i,k,j))*0.5*(mu(i,j+1)+mu(i,j))*rdy
mrdy=msftx(i,j)*msfty(i,j)*rdy
tendency(i,k,j)=tendency(i,k,j)+( &
mrdx*( mkrdxp*( field(i+1,k,j) -field(i ,k,j) &
-base_3d(i+1,k,j)+base_3d(i ,k,j) ) &
-mkrdxm*( field(i ,k,j) -field(i-1,k,j) &
-base_3d(i ,k,j)+base_3d(i-1,k,j) ) ) &
+mrdy*( mkrdyp*( field(i,k,j+1) -field(i,k,j ) &
-base_3d(i,k,j+1)+base_3d(i,k,j ) ) &
-mkrdym*( field(i,k,j ) -field(i,k,j-1) &
-base_3d(i,k,j )+base_3d(i,k,j-1) ) ) &
)
ENDDO
ENDDO
ENDDO
END SUBROUTINE horizontal_diffusion_3dmp
!-----------------------------------------------------------------------------------------
SUBROUTINE vertical_diffusion ( name, field, tendency, & 2
config_flags, &
alt, mut, rdn, rdnw, kvdif, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
TYPE(grid_config_rec_type), INTENT(IN ) :: config_flags
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
CHARACTER(LEN=1) , INTENT(IN ) :: name
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , &
INTENT(IN ) :: field, &
alt
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(INOUT) :: tendency
REAL , DIMENSION( ims:ime , jms:jme ) , INTENT(IN ) :: mut
REAL , DIMENSION( kms:kme ) , INTENT(IN ) :: rdn, rdnw
REAL , INTENT(IN ) :: kvdif
! Local data
INTEGER :: i, j, k, itf, jtf, ktf
INTEGER :: i_start, i_end, j_start, j_end
REAL , DIMENSION(its:ite, jts:jte) :: vfluxm, vfluxp, zz
REAL , DIMENSION(its:ite, 0:kte+1) :: vflux
REAL :: rdz
LOGICAL :: specified
!<DESCRIPTION>
!
! vertical_diffusion
! computes vertical diffusion tendency.
!
!</DESCRIPTION>
specified = .false.
if(config_flags%specified .or. config_flags%nested) specified = .true.
ktf=MIN(kte,kde-1)
IF (name .EQ. 'w')THEN
i_start = its
i_end = MIN(ite,ide-1)
j_start = jts
j_end = MIN(jte,jde-1)
j_loop_w : DO j = j_start, j_end
DO k=kts,ktf-1
DO i = i_start, i_end
vflux(i,k)= (kvdif/alt(i,k,j))*rdnw(k)*(field(i,k+1,j)-field(i,k,j))
ENDDO
ENDDO
DO i = i_start, i_end
vflux(i,ktf)=0.
ENDDO
DO k=kts+1,ktf
DO i = i_start, i_end
tendency(i,k,j)=tendency(i,k,j) &
+rdn(k)*g*g/mut(i,j)/(0.5*(alt(i,k,j)+alt(i,k-1,j))) &
*(vflux(i,k)-vflux(i,k-1))
ENDDO
ENDDO
ENDDO j_loop_w
ELSE IF(name .EQ. 'm')THEN
i_start = its
i_end = MIN(ite,ide-1)
j_start = jts
j_end = MIN(jte,jde-1)
j_loop_s : DO j = j_start, j_end
DO k=kts,ktf-1
DO i = i_start, i_end
vflux(i,k)=kvdif*rdn(k+1)/(0.5*(alt(i,k,j)+alt(i,k+1,j))) &
*(field(i,k+1,j)-field(i,k,j))
ENDDO
ENDDO
DO i = i_start, i_end
vflux(i,0)=vflux(i,1)
ENDDO
DO i = i_start, i_end
vflux(i,ktf)=0.
ENDDO
DO k=kts,ktf
DO i = i_start, i_end
tendency(i,k,j)=tendency(i,k,j)+g*g/mut(i,j)/alt(i,k,j) &
*rdnw(k)*(vflux(i,k)-vflux(i,k-1))
ENDDO
ENDDO
ENDDO j_loop_s
ENDIF
END SUBROUTINE vertical_diffusion
!-------------------------------------------------------------------------------
SUBROUTINE vertical_diffusion_mp ( field, tendency, config_flags, & 1
base, &
alt, mut, rdn, rdnw, kvdif, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
TYPE(grid_config_rec_type), INTENT(IN ) :: config_flags
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , &
INTENT(IN ) :: field, &
alt
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(INOUT) :: tendency
REAL , DIMENSION( ims:ime , jms:jme ) , INTENT(IN ) :: mut
REAL , DIMENSION( kms:kme ) , INTENT(IN ) :: rdn, &
rdnw, &
base
REAL , INTENT(IN ) :: kvdif
! Local data
INTEGER :: i, j, k, itf, jtf, ktf
INTEGER :: i_start, i_end, j_start, j_end
REAL , DIMENSION(its:ite, 0:kte+1) :: vflux
REAL :: rdz
LOGICAL :: specified
!<DESCRIPTION>
!
! vertical_diffusion_mp
! computes vertical diffusion tendency of a perturbation variable
! (field-base). Note that base as a 1D (k) field.
!
!</DESCRIPTION>
specified = .false.
if(config_flags%specified .or. config_flags%nested) specified = .true.
ktf=MIN(kte,kde-1)
i_start = its
i_end = MIN(ite,ide-1)
j_start = jts
j_end = MIN(jte,jde-1)
j_loop_s : DO j = j_start, j_end
DO k=kts,ktf-1
DO i = i_start, i_end
vflux(i,k)=kvdif*rdn(k+1)/(0.5*(alt(i,k,j)+alt(i,k+1,j))) &
*(field(i,k+1,j)-field(i,k,j)-base(k+1)+base(k))
ENDDO
ENDDO
DO i = i_start, i_end
vflux(i,0)=vflux(i,1)
ENDDO
DO i = i_start, i_end
vflux(i,ktf)=0.
ENDDO
DO k=kts,ktf
DO i = i_start, i_end
tendency(i,k,j)=tendency(i,k,j)+g*g/mut(i,j)/alt(i,k,j) &
*rdnw(k)*(vflux(i,k)-vflux(i,k-1))
ENDDO
ENDDO
ENDDO j_loop_s
END SUBROUTINE vertical_diffusion_mp
!-------------------------------------------------------------------------------
SUBROUTINE vertical_diffusion_3dmp ( field, tendency, config_flags, & 1
base_3d, &
alt, mut, rdn, rdnw, kvdif, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
TYPE(grid_config_rec_type), INTENT(IN ) :: config_flags
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , &
INTENT(IN ) :: field, &
alt, &
base_3d
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(INOUT) :: tendency
REAL , DIMENSION( ims:ime , jms:jme ) , INTENT(IN ) :: mut
REAL , DIMENSION( kms:kme ) , INTENT(IN ) :: rdn, &
rdnw
REAL , INTENT(IN ) :: kvdif
! Local data
INTEGER :: i, j, k, itf, jtf, ktf
INTEGER :: i_start, i_end, j_start, j_end
REAL , DIMENSION(its:ite, 0:kte+1) :: vflux
REAL :: rdz
LOGICAL :: specified
!<DESCRIPTION>
!
! vertical_diffusion_3dmp
! computes vertical diffusion tendency of a perturbation variable
! (field-base_3d).
!
!</DESCRIPTION>
specified = .false.
if(config_flags%specified .or. config_flags%nested) specified = .true.
ktf=MIN(kte,kde-1)
i_start = its
i_end = MIN(ite,ide-1)
j_start = jts
j_end = MIN(jte,jde-1)
j_loop_s : DO j = j_start, j_end
DO k=kts,ktf-1
DO i = i_start, i_end
vflux(i,k)=kvdif*rdn(k+1)/(0.5*(alt(i,k,j)+alt(i,k+1,j))) &
*( field(i,k+1,j) -field(i,k,j) &
-base_3d(i,k+1,j)+base_3d(i,k,j) )
ENDDO
ENDDO
DO i = i_start, i_end
vflux(i,0)=vflux(i,1)
ENDDO
DO i = i_start, i_end
vflux(i,ktf)=0.
ENDDO
DO k=kts,ktf
DO i = i_start, i_end
tendency(i,k,j)=tendency(i,k,j)+g*g/mut(i,j)/alt(i,k,j) &
*rdnw(k)*(vflux(i,k)-vflux(i,k-1))
ENDDO
ENDDO
ENDDO j_loop_s
END SUBROUTINE vertical_diffusion_3dmp
!-------------------------------------------------------------------------------
SUBROUTINE vertical_diffusion_u ( field, tendency, & 1
config_flags, u_base, &
alt, muu, rdn, rdnw, kvdif, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
TYPE(grid_config_rec_type), INTENT(IN ) :: config_flags
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , &
INTENT(IN ) :: field, &
alt
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(INOUT) :: tendency
REAL , DIMENSION( ims:ime , jms:jme ) , INTENT(IN ) :: muu
REAL , DIMENSION( kms:kme ) , INTENT(IN ) :: rdn, rdnw, u_base
REAL , INTENT(IN ) :: kvdif
! Local data
INTEGER :: i, j, k, itf, jtf, ktf
INTEGER :: i_start, i_end, j_start, j_end
REAL , DIMENSION(its:ite, 0:kte+1) :: vflux
REAL :: rdz, zz
LOGICAL :: specified
!<DESCRIPTION>
!
! vertical_diffusion_u computes vertical diffusion tendency for
! the u momentum equation. This routine assumes a constant eddy
! viscosity kvdif.
!
!</DESCRIPTION>
specified = .false.
if(config_flags%specified .or. config_flags%nested) specified = .true.
ktf=MIN(kte,kde-1)
i_start = its
i_end = ite
j_start = jts
j_end = MIN(jte,jde-1)
IF ( config_flags%open_xs .or. specified ) i_start = MAX(ids+1,its)
IF ( config_flags%open_xe .or. specified ) i_end = MIN(ide-1,ite)
IF ( config_flags%periodic_x ) i_start = its
IF ( config_flags%periodic_x ) i_end = ite
j_loop_u : DO j = j_start, j_end
DO k=kts,ktf-1
DO i = i_start, i_end
vflux(i,k)=kvdif*rdn(k+1)/(0.25*( alt(i ,k ,j) &
+alt(i-1,k ,j) &
+alt(i ,k+1,j) &
+alt(i-1,k+1,j) ) ) &
*(field(i,k+1,j)-field(i,k,j) &
-u_base(k+1) +u_base(k) )
ENDDO
ENDDO
DO i = i_start, i_end
vflux(i,0)=vflux(i,1)
ENDDO
DO i = i_start, i_end
vflux(i,ktf)=0.
ENDDO
DO k=kts,ktf-1
DO i = i_start, i_end
tendency(i,k,j)=tendency(i,k,j)+ &
g*g*rdnw(k)/muu(i,j)/(0.5*(alt(i-1,k,j)+alt(i,k,j)))* &
(vflux(i,k)-vflux(i,k-1))
ENDDO
ENDDO
ENDDO j_loop_u
END SUBROUTINE vertical_diffusion_u
!-------------------------------------------------------------------------------
SUBROUTINE vertical_diffusion_v ( field, tendency, & 1
config_flags, v_base, &
alt, muv, rdn, rdnw, kvdif, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
TYPE(grid_config_rec_type), INTENT(IN ) :: config_flags
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , &
INTENT(IN ) :: field, &
alt
REAL , DIMENSION( kms:kme ) , INTENT(IN ) :: rdn, rdnw, v_base
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(INOUT) :: tendency
REAL , DIMENSION( ims:ime , jms:jme ) , INTENT(IN ) :: muv
REAL , INTENT(IN ) :: kvdif
! Local data
INTEGER :: i, j, k, itf, jtf, ktf, jm1
INTEGER :: i_start, i_end, j_start, j_end
REAL , DIMENSION(its:ite, 0:kte+1) :: vflux
REAL :: rdz, zz
LOGICAL :: specified
!<DESCRIPTION>
!
! vertical_diffusion_v computes vertical diffusion tendency for
! the v momentum equation. This routine assumes a constant eddy
! viscosity kvdif.
!
!</DESCRIPTION>
specified = .false.
if(config_flags%specified .or. config_flags%nested) specified = .true.
ktf=MIN(kte,kde-1)
i_start = its
i_end = MIN(ite,ide-1)
j_start = jts
j_end = MIN(jte,jde-1)
IF ( config_flags%open_ys .or. specified ) j_start = MAX(jds+1,jts)
IF ( config_flags%open_ye .or. specified ) j_end = MIN(jde-1,jte)
j_loop_v : DO j = j_start, j_end
! jm1 = max(j-1,1)
jm1 = j-1
DO k=kts,ktf-1
DO i = i_start, i_end
vflux(i,k)=kvdif*rdn(k+1)/(0.25*( alt(i,k ,j ) &
+alt(i,k ,jm1) &
+alt(i,k+1,j ) &
+alt(i,k+1,jm1) ) ) &
*(field(i,k+1,j)-field(i,k,j) &
-v_base(k+1) +v_base(k) )
ENDDO
ENDDO
DO i = i_start, i_end
vflux(i,0)=vflux(i,1)
ENDDO
DO i = i_start, i_end
vflux(i,ktf)=0.
ENDDO
DO k=kts,ktf-1
DO i = i_start, i_end
tendency(i,k,j)=tendency(i,k,j)+ &
g*g*rdnw(k)/muv(i,j)/(0.5*(alt(i,k,jm1)+alt(i,k,j)))* &
(vflux(i,k)-vflux(i,k-1))
ENDDO
ENDDO
ENDDO j_loop_v
END SUBROUTINE vertical_diffusion_v
!*************** end new mass coordinate routines
!-------------------------------------------------------------------------------
SUBROUTINE calculate_full ( rfield, rfieldb, rfieldp, & 1
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(IN ) :: rfieldb, &
rfieldp
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(OUT ) :: rfield
! Local indices.
INTEGER :: i, j, k, itf, jtf, ktf
!<DESCRIPTION>
!
! calculate_full
! calculates full 3D field from pertubation and base field.
!
!</DESCRIPTION>
itf=MIN(ite,ide-1)
jtf=MIN(jte,jde-1)
ktf=MIN(kte,kde-1)
DO j=jts,jtf
DO k=kts,ktf
DO i=its,itf
rfield(i,k,j)=rfieldb(i,k,j)+rfieldp(i,k,j)
ENDDO
ENDDO
ENDDO
END SUBROUTINE calculate_full
!------------------------------------------------------------------------------
SUBROUTINE coriolis ( ru, rv, rw, ru_tend, rv_tend, rw_tend, & 1
config_flags, &
msftx, msfty, msfux, msfuy, &
msfvx, msfvy, &
f, e, sina, cosa, fzm, fzp, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
TYPE(grid_config_rec_type) , INTENT(IN ) :: config_flags
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(INOUT) :: ru_tend, &
rv_tend, &
rw_tend
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(IN ) :: ru, &
rv, &
rw
REAL , DIMENSION( ims:ime , jms:jme ) , INTENT(IN ) :: msfux, &
msfuy, &
msfvx, &
msfvy, &
msftx, &
msfty
REAL , DIMENSION( ims:ime , jms:jme ) , INTENT(IN ) :: f, &
e, &
sina, &
cosa
REAL , DIMENSION( kms:kme ) , INTENT(IN ) :: fzm, &
fzp
! Local indices.
INTEGER :: i, j , k, ktf
INTEGER :: i_start, i_end, j_start, j_end
LOGICAL :: specified
!<DESCRIPTION>
!
! coriolis calculates the large timestep tendency terms in the
! u, v, and w momentum equations arise from the coriolis force.
!
!</DESCRIPTION>
specified = .false.
if(config_flags%specified .or. config_flags%nested) specified = .true.
ktf=MIN(kte,kde-1)
! coriolis for u-momentum equation
! Notes on map scale factor
! cosa, sina are related to rotating the coordinate frame if desired
! generally sina=0, cosa=1
! ADT eqn 44, RHS terms 6 and 7: -2 mu w omega cos(lat)/my
! + 2 mu v omega sin(lat)/my
! Define f=2 omega sin(lat), e=2 omega cos(lat)
! => terms are: -e mu w / my + f mu v / my
! rv = mu v / mx ; rw = mu w / my
! => terms are: -e rw + f rv *mx / my
i_start = its
i_end = ite
IF ( config_flags%open_xs .or. specified .or. &
config_flags%nested) i_start = MAX(ids+1,its)
IF ( config_flags%open_xe .or. specified .or. &
config_flags%nested) i_end = MIN(ide-1,ite)
IF ( config_flags%periodic_x ) i_start = its
IF ( config_flags%periodic_x ) i_end = ite
DO j = jts, MIN(jte,jde-1)
DO k=kts,ktf
DO i = i_start, i_end
ru_tend(i,k,j)=ru_tend(i,k,j) + (msfux(i,j)/msfuy(i,j))*0.5*(f(i,j)+f(i-1,j)) &
*0.25*(rv(i-1,k,j+1)+rv(i,k,j+1)+rv(i-1,k,j)+rv(i,k,j)) &
- 0.5*(e(i,j)+e(i-1,j))*0.5*(cosa(i,j)+cosa(i-1,j)) &
*0.25*(rw(i-1,k+1,j)+rw(i-1,k,j)+rw(i,k+1,j)+rw(i,k,j))
ENDDO
ENDDO
! boundary loops for coriolis not needed for open bdy (commented out 20100611 JD)
! IF ( (config_flags%open_xs) .and. (its == ids) ) THEN
! DO k=kts,ktf
!
! ru_tend(its,k,j)=ru_tend(its,k,j) + (msfux(its,j)/msfuy(its,j))*0.5*(f(its,j)+f(its,j)) &
! *0.25*(rv(its,k,j+1)+rv(its,k,j+1)+rv(its,k,j)+rv(its,k,j)) &
! - 0.5*(e(its,j)+e(its,j))*0.5*(cosa(its,j)+cosa(its,j)) &
! *0.25*(rw(its,k+1,j)+rw(its,k,j)+rw(its,k+1,j)+rw(its,k,j))
! ENDDO
! ENDIF
! IF ( (config_flags%open_xe) .and. (ite == ide) ) THEN
! DO k=kts,ktf
!
! ru_tend(ite,k,j)=ru_tend(ite,k,j) + (msfux(ite,j)/msfuy(ite,j))*0.5*(f(ite-1,j)+f(ite-1,j)) &
! *0.25*(rv(ite-1,k,j+1)+rv(ite-1,k,j+1)+rv(ite-1,k,j)+rv(ite-1,k,j)) &
! - 0.5*(e(ite-1,j)+e(ite-1,j))*0.5*(cosa(ite-1,j)+cosa(ite-1,j)) &
! *0.25*(rw(ite-1,k+1,j)+rw(ite-1,k,j)+rw(ite-1,k+1,j)+rw(ite-1,k,j))
! ENDDO
! ENDIF
ENDDO
! coriolis term for v-momentum equation
! Notes on map scale factors
! ADT eqn 45, RHS terms 6 and 6b [0 for sina=0]: -2 mu u omega sin(lat)/mx + ?
! Define f=2 omega sin(lat), e=2 omega cos(lat)
! => terms are: -f mu u / mx
! ru = mu u / my ; rw = mu w / my
! => terms are: -f ru *my / mx + ?
j_start = jts
j_end = jte
IF ( config_flags%open_ys .or. specified .or. &
config_flags%nested .or. config_flags%polar) j_start = MAX(jds+1,jts)
IF ( config_flags%open_ye .or. specified .or. &
config_flags%nested .or. config_flags%polar) j_end = MIN(jde-1,jte)
! boundary loops for coriolis not needed for open bdy (commented out 20100611 JD)
! IF ( (config_flags%open_ys) .and. (jts == jds) ) THEN
! DO k=kts,ktf
! DO i=its,MIN(ide-1,ite)
!
! rv_tend(i,k,jts)=rv_tend(i,k,jts) - (msfvy(i,jts)/msfvx(i,jts))*0.5*(f(i,jts)+f(i,jts)) &
! *0.25*(ru(i,k,jts)+ru(i+1,k,jts)+ru(i,k,jts)+ru(i+1,k,jts)) &
! + (msfvy(i,jts)/msfvx(i,jts))*0.5*(e(i,jts)+e(i,jts))*0.5*(sina(i,jts)+sina(i,jts)) &
! *0.25*(rw(i,k+1,jts)+rw(i,k,jts)+rw(i,k+1,jts)+rw(i,k,jts))
! ENDDO
! ENDDO
! ENDIF
DO j=j_start, j_end
DO k=kts,ktf
DO i=its,MIN(ide-1,ite)
rv_tend(i,k,j)=rv_tend(i,k,j) - (msfvy(i,j)/msfvx(i,j))*0.5*(f(i,j)+f(i,j-1)) &
*0.25*(ru(i,k,j)+ru(i+1,k,j)+ru(i,k,j-1)+ru(i+1,k,j-1)) &
+ (msfvy(i,j)/msfvx(i,j))*0.5*(e(i,j)+e(i,j-1))*0.5*(sina(i,j)+sina(i,j-1)) &
*0.25*(rw(i,k+1,j-1)+rw(i,k,j-1)+rw(i,k+1,j)+rw(i,k,j))
ENDDO
ENDDO
ENDDO
! boundary loops for coriolis not needed for open bdy (commented out 20100611 JD)
! IF ( (config_flags%open_ye) .and. (jte == jde) ) THEN
! DO k=kts,ktf
! DO i=its,MIN(ide-1,ite)
!
! rv_tend(i,k,jte)=rv_tend(i,k,jte) - (msfvy(i,jte)/msfvx(i,jte))*0.5*(f(i,jte-1)+f(i,jte-1)) &
! *0.25*(ru(i,k,jte-1)+ru(i+1,k,jte-1)+ru(i,k,jte-1)+ru(i+1,k,jte-1)) &
! + (msfvy(i,jte)/msfvx(i,jte))*0.5*(e(i,jte-1)+e(i,jte-1))*0.5*(sina(i,jte-1)+sina(i,jte-1)) &
! *0.25*(rw(i,k+1,jte-1)+rw(i,k,jte-1)+rw(i,k+1,jte-1)+rw(i,k,jte-1))
! ENDDO
! ENDDO
! ENDIF
! coriolis term for w-mometum
! Notes on map scale factors
! ADT eqn 46/my, RHS terms 5 and 5b [0 for sina=0]: 2 mu u omega cos(lat)/my +?
! Define e=2 omega cos(lat)
! => terms are: e mu u / my + ???
! ru = mu u / my ; ru = mu v / mx
! => terms are: e ru + ???
DO j=jts,MIN(jte, jde-1)
DO k=kts+1,ktf
DO i=its,MIN(ite, ide-1)
rw_tend(i,k,j)=rw_tend(i,k,j) + e(i,j)* &
(cosa(i,j)*0.5*(fzm(k)*(ru(i,k,j)+ru(i+1,k,j)) &
+fzp(k)*(ru(i,k-1,j)+ru(i+1,k-1,j))) &
-(msftx(i,j)/msfty(i,j))* &
sina(i,j)*0.5*(fzm(k)*(rv(i,k,j)+rv(i,k,j+1)) &
+fzp(k)*(rv(i,k-1,j)+rv(i,k-1,j+1))))
ENDDO
ENDDO
ENDDO
END SUBROUTINE coriolis
!------------------------------------------------------------------------------
SUBROUTINE perturbation_coriolis ( ru_in, rv_in, rw, ru_tend, rv_tend, rw_tend, & 1
config_flags, &
u_base, v_base, z_base, &
muu, muv, phb, ph, &
msftx, msfty, msfux, msfuy, msfvx, msfvy, &
f, e, sina, cosa, fzm, fzp, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
TYPE(grid_config_rec_type) , INTENT(IN ) :: config_flags
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(INOUT) :: ru_tend, &
rv_tend, &
rw_tend
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(IN ) :: ru_in, &
rv_in, &
rw, &
ph, &
phb
REAL , DIMENSION( ims:ime , jms:jme ) , INTENT(IN ) :: msfux, &
msfuy, &
msfvx, &
msfvy, &
msftx, &
msfty
REAL , DIMENSION( ims:ime , jms:jme ) , INTENT(IN ) :: f, &
e, &
sina, &
cosa
REAL , DIMENSION( ims:ime , jms:jme ) , INTENT(IN ) :: muu, &
muv
REAL , DIMENSION( kms:kme ) , INTENT(IN ) :: fzm, &
fzp
REAL , DIMENSION( kms:kme ) , INTENT(IN ) :: u_base, &
v_base, &
z_base
! Local storage
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) :: ru, &
rv
REAL :: z_at_u, z_at_v, wkp1, wk, wkm1
! Local indices.
INTEGER :: i, j , k, ktf
INTEGER :: i_start, i_end, j_start, j_end
LOGICAL :: specified
!<DESCRIPTION>
!
! perturbation_coriolis calculates the large timestep tendency terms in the
! u, v, and w momentum equations arise from the coriolis force. This version
! subtracts off the horizontal velocities from the initial sounding when
! computing the forcing terms, hence "perturbation" coriolis.
!
!</DESCRIPTION>
specified = .false.
if(config_flags%specified .or. config_flags%nested) specified = .true.
ktf=MIN(kte,kde-1)
! coriolis for u-momentum equation
i_start = its
i_end = ite
IF ( config_flags%open_xs .or. specified .or. &
config_flags%nested) i_start = MAX(ids+1,its)
IF ( config_flags%open_xe .or. specified .or. &
config_flags%nested) i_end = MIN(ide-1,ite)
IF ( config_flags%periodic_x ) i_start = its
IF ( config_flags%periodic_x ) i_end = ite
! compute perturbation mu*v for use in u momentum equation
DO j = jts, MIN(jte,jde-1)+1
DO k=kts+1,ktf-1
DO i = i_start-1, i_end
z_at_v = 0.25*( phb(i,k,j )+phb(i,k+1,j ) &
+phb(i,k,j-1)+phb(i,k+1,j-1) &
+ph(i,k,j )+ph(i,k+1,j ) &
+ph(i,k,j-1)+ph(i,k+1,j-1))/g
wkp1 = min(1.,max(0.,z_at_v-z_base(k))/(z_base(k+1)-z_base(k)))
wkm1 = min(1.,max(0.,z_base(k)-z_at_v)/(z_base(k)-z_base(k-1)))
wk = 1.-wkp1-wkm1
rv(i,k,j) = rv_in(i,k,j) - muv(i,j)*( &
wkm1*v_base(k-1) &
+wk *v_base(k ) &
+wkp1*v_base(k+1) )
ENDDO
ENDDO
ENDDO
! pick up top and bottom v
DO j = jts, MIN(jte,jde-1)+1
DO i = i_start-1, i_end
k = kts
z_at_v = 0.25*( phb(i,k,j )+phb(i,k+1,j ) &
+phb(i,k,j-1)+phb(i,k+1,j-1) &
+ph(i,k,j )+ph(i,k+1,j ) &
+ph(i,k,j-1)+ph(i,k+1,j-1))/g
wkp1 = min(1.,max(0.,z_at_v-z_base(k))/(z_base(k+1)-z_base(k)))
wk = 1.-wkp1
rv(i,k,j) = rv_in(i,k,j) - muv(i,j)*( &
+wk *v_base(k ) &
+wkp1*v_base(k+1) )
k = ktf
z_at_v = 0.25*( phb(i,k,j )+phb(i,k+1,j ) &
+phb(i,k,j-1)+phb(i,k+1,j-1) &
+ph(i,k,j )+ph(i,k+1,j ) &
+ph(i,k,j-1)+ph(i,k+1,j-1))/g
wkm1 = min(1.,max(0.,z_base(k)-z_at_v)/(z_base(k)-z_base(k-1)))
wk = 1.-wkm1
rv(i,k,j) = rv_in(i,k,j) - muv(i,j)*( &
wkm1*v_base(k-1) &
+wk *v_base(k ) )
ENDDO
ENDDO
! compute coriolis forcing for u
! Map scale factors: see comments above for Coriolis
DO j = jts, MIN(jte,jde-1)
DO k=kts,ktf
DO i = i_start, i_end
ru_tend(i,k,j)=ru_tend(i,k,j) + (msfux(i,j)/msfuy(i,j))*0.5*(f(i,j)+f(i-1,j)) &
*0.25*(rv(i-1,k,j+1)+rv(i,k,j+1)+rv(i-1,k,j)+rv(i,k,j)) &
- 0.5*(e(i,j)+e(i-1,j))*0.5*(cosa(i,j)+cosa(i-1,j)) &
*0.25*(rw(i-1,k+1,j)+rw(i-1,k,j)+rw(i,k+1,j)+rw(i,k,j))
ENDDO
ENDDO
! boundary loops for perturbation coriolis is needed for open bdy (20110225 JD)
IF ( (config_flags%open_xs) .and. (its == ids) ) THEN
DO k=kts,ktf
ru_tend(its,k,j)=ru_tend(its,k,j) + (msfux(its,j)/msfuy(its,j))*0.5*(f(its,j)+f(its,j)) &
*0.25*(rv(its,k,j+1)+rv(its,k,j+1)+rv(its,k,j)+rv(its,k,j)) &
- 0.5*(e(its,j)+e(its,j))*0.5*(cosa(its,j)+cosa(its,j)) &
*0.25*(rw(its,k+1,j)+rw(its,k,j)+rw(its,k+1,j)+rw(its,k,j))
ENDDO
ENDIF
IF ( (config_flags%open_xe) .and. (ite == ide) ) THEN
DO k=kts,ktf
ru_tend(ite,k,j)=ru_tend(ite,k,j) + (msfux(ite,j)/msfuy(ite,j))*0.5*(f(ite-1,j)+f(ite-1,j)) &
*0.25*(rv(ite-1,k,j+1)+rv(ite-1,k,j+1)+rv(ite-1,k,j)+rv(ite-1,k,j)) &
- 0.5*(e(ite-1,j)+e(ite-1,j))*0.5*(cosa(ite-1,j)+cosa(ite-1,j)) &
*0.25*(rw(ite-1,k+1,j)+rw(ite-1,k,j)+rw(ite-1,k+1,j)+rw(ite-1,k,j))
ENDDO
ENDIF
ENDDO
! coriolis term for v-momentum equation
! Map scale factors: see comments above for Coriolis
j_start = jts
j_end = jte
IF ( config_flags%open_ys .or. specified .or. &
config_flags%nested .or. config_flags%polar) j_start = MAX(jds+1,jts)
IF ( config_flags%open_ye .or. specified .or. &
config_flags%nested .or. config_flags%polar) j_end = MIN(jde-1,jte)
! compute perturbation mu*u for use in v momentum equation
DO j = j_start-1,j_end
DO k=kts+1,ktf-1
DO i = its, MIN(ite,ide-1)+1
z_at_u = 0.25*( phb(i ,k,j)+phb(i ,k+1,j) &
+phb(i-1,k,j)+phb(i-1,k+1,j) &
+ph(i ,k,j)+ph(i ,k+1,j) &
+ph(i-1,k,j)+ph(i-1,k+1,j))/g
wkp1 = min(1.,max(0.,z_at_u-z_base(k))/(z_base(k+1)-z_base(k)))
wkm1 = min(1.,max(0.,z_base(k)-z_at_u)/(z_base(k)-z_base(k-1)))
wk = 1.-wkp1-wkm1
ru(i,k,j) = ru_in(i,k,j) - muu(i,j)*( &
wkm1*u_base(k-1) &
+wk *u_base(k ) &
+wkp1*u_base(k+1) )
ENDDO
ENDDO
ENDDO
! pick up top and bottom u
DO j = j_start-1,j_end
DO i = its, MIN(ite,ide-1)+1
k = kts
z_at_u = 0.25*( phb(i ,k,j)+phb(i ,k+1,j) &
+phb(i-1,k,j)+phb(i-1,k+1,j) &
+ph(i ,k,j)+ph(i ,k+1,j) &
+ph(i-1,k,j)+ph(i-1,k+1,j))/g
wkp1 = min(1.,max(0.,z_at_u-z_base(k))/(z_base(k+1)-z_base(k)))
wk = 1.-wkp1
ru(i,k,j) = ru_in(i,k,j) - muu(i,j)*( &
+wk *u_base(k ) &
+wkp1*u_base(k+1) )
k = ktf
z_at_u = 0.25*( phb(i ,k,j)+phb(i ,k+1,j) &
+phb(i-1,k,j)+phb(i-1,k+1,j) &
+ph(i ,k,j)+ph(i ,k+1,j) &
+ph(i-1,k,j)+ph(i-1,k+1,j))/g
wkm1 = min(1.,max(0.,z_base(k)-z_at_u)/(z_base(k)-z_base(k-1)))
wk = 1.-wkm1
ru(i,k,j) = ru_in(i,k,j) - muu(i,j)*( &
wkm1*u_base(k-1) &
+wk *u_base(k ) )
ENDDO
ENDDO
! compute coriolis forcing for v momentum equation
! Map scale factors: see comments above for Coriolis
! boundary loops for perturbation coriolis is needed for open bdy (20110225 JD)
IF ( (config_flags%open_ys) .and. (jts == jds) ) THEN
DO k=kts,ktf
DO i=its,MIN(ide-1,ite)
rv_tend(i,k,jts)=rv_tend(i,k,jts) - (msfvy(i,jts)/msfvx(i,jts))*0.5*(f(i,jts)+f(i,jts)) &
*0.25*(ru(i,k,jts)+ru(i+1,k,jts)+ru(i,k,jts)+ru(i+1,k,jts)) &
+ (msfvy(i,jts)/msfvx(i,jts))*0.5*(e(i,jts)+e(i,jts))*0.5*(sina(i,jts)+sina(i,jts)) &
*0.25*(rw(i,k+1,jts)+rw(i,k,jts)+rw(i,k+1,jts)+rw(i,k,jts))
ENDDO
ENDDO
ENDIF
DO j=j_start, j_end
DO k=kts,ktf
DO i=its,MIN(ide-1,ite)
rv_tend(i,k,j)=rv_tend(i,k,j) - (msfvy(i,j)/msfvx(i,j))*0.5*(f(i,j)+f(i,j-1)) &
*0.25*(ru(i,k,j)+ru(i+1,k,j)+ru(i,k,j-1)+ru(i+1,k,j-1)) &
+ (msfvy(i,j)/msfvx(i,j))*0.5*(e(i,j)+e(i,j-1))*0.5*(sina(i,j)+sina(i,j-1)) &
*0.25*(rw(i,k+1,j-1)+rw(i,k,j-1)+rw(i,k+1,j)+rw(i,k,j))
ENDDO
ENDDO
ENDDO
! boundary loops for perturbation coriolis is needed for open bdy (20110225 JD)
IF ( (config_flags%open_ye) .and. (jte == jde) ) THEN
DO k=kts,ktf
DO i=its,MIN(ide-1,ite)
rv_tend(i,k,jte)=rv_tend(i,k,jte) - (msfvy(i,jte)/msfvx(i,jte))*0.5*(f(i,jte-1)+f(i,jte-1)) &
*0.25*(ru(i,k,jte-1)+ru(i+1,k,jte-1)+ru(i,k,jte-1)+ru(i+1,k,jte-1)) &
+ (msfvy(i,jte)/msfvx(i,jte))*0.5*(e(i,jte-1)+e(i,jte-1))*0.5*(sina(i,jte-1)+sina(i,jte-1)) &
*0.25*(rw(i,k+1,jte-1)+rw(i,k,jte-1)+rw(i,k+1,jte-1)+rw(i,k,jte-1))
ENDDO
ENDDO
ENDIF
! coriolis term for w-mometum
! Map scale factors: see comments above for Coriolis
DO j=jts,MIN(jte, jde-1)
DO k=kts+1,ktf
DO i=its,MIN(ite, ide-1)
rw_tend(i,k,j)=rw_tend(i,k,j) + e(i,j)* &
(cosa(i,j)*0.5*(fzm(k)*(ru(i,k,j)+ru(i+1,k,j)) &
+fzp(k)*(ru(i,k-1,j)+ru(i+1,k-1,j))) &
-(msftx(i,j)/msfty(i,j))*sina(i,j)*0.5*(fzm(k)*(rv(i,k,j)+rv(i,k,j+1)) &
+fzp(k)*(rv(i,k-1,j)+rv(i,k-1,j+1))))
ENDDO
ENDDO
ENDDO
END SUBROUTINE perturbation_coriolis
!------------------------------------------------------------------------------
SUBROUTINE curvature ( ru, rv, rw, u, v, w, ru_tend, rv_tend, rw_tend, & 1
config_flags, &
msfux, msfuy, msfvx, msfvy, msftx, msfty, &
xlat, fzm, fzp, rdx, rdy, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
TYPE(grid_config_rec_type) , INTENT(IN ) :: config_flags
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , &
INTENT(INOUT) :: ru_tend, &
rv_tend, &
rw_tend
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , &
INTENT(IN ) :: ru, &
rv, &
rw, &
u, &
v, &
w
REAL , DIMENSION( ims:ime , jms:jme ) , INTENT(IN ) :: msfux, &
msfuy, &
msfvx, &
msfvy, &
msftx, &
msfty, &
xlat
REAL , DIMENSION( kms:kme ) , INTENT(IN ) :: fzm, &
fzp
REAL , INTENT(IN ) :: rdx, &
rdy
! Local data
! INTEGER :: i, j, k, itf, jtf, ktf, kp1, im, ip, jm, jp
INTEGER :: i, j, k, itf, jtf, ktf
INTEGER :: i_start, i_end, j_start, j_end
! INTEGER :: irmin, irmax, jrmin, jrmax
REAL , DIMENSION( its-1:ite , kts:kte, jts-1:jte ) :: vxgm
LOGICAL :: specified
!<DESCRIPTION>
!
! curvature calculates the large timestep tendency terms in the
! u, v, and w momentum equations arise from the curvature terms.
!
!</DESCRIPTION>
specified = .false.
if(config_flags%specified .or. config_flags%nested) specified = .true.
itf=MIN(ite,ide-1)
jtf=MIN(jte,jde-1)
ktf=MIN(kte,kde-1)
! irmin = ims
! irmax = ime
! jrmin = jms
! jrmax = jme
! IF ( config_flags%open_xs ) irmin = ids
! IF ( config_flags%open_xe ) irmax = ide-1
! IF ( config_flags%open_ys ) jrmin = jds
! IF ( config_flags%open_ye ) jrmax = jde-1
! Define v cross grad m at scalar points - vxgm(i,j)
i_start = its-1
i_end = ite
j_start = jts-1
j_end = jte
IF ( ( config_flags%open_xs .or. specified .or. &
config_flags%nested) .and. (its == ids) ) i_start = its
IF ( ( config_flags%open_xe .or. specified .or. &
config_flags%nested) .and. (ite == ide) ) i_end = ite-1
IF ( ( config_flags%open_ys .or. specified .or. &
config_flags%nested .or. config_flags%polar) .and. (jts == jds) ) j_start = jts
IF ( ( config_flags%open_ye .or. specified .or. &
config_flags%nested .or. config_flags%polar) .and. (jte == jde) ) j_end = jte-1
IF ( config_flags%periodic_x ) i_start = its-1
IF ( config_flags%periodic_x ) i_end = ite
DO j=j_start, j_end
DO k=kts,ktf
DO i=i_start, i_end
! Map scale factor notes:
! msf...y is constant everywhere for cylindrical map projection
! msf...x varies with y only
! But we know that this is not = 0 for cylindrical,
! therefore use msfvX in 1st line
! which => by symmetry use msfuY in 2nd line - ???
vxgm(i,k,j)=0.5*(u(i,k,j)+u(i+1,k,j))*(msfvx(i,j+1)-msfvx(i,j))*rdy - &
0.5*(v(i,k,j)+v(i,k,j+1))*(msfuy(i+1,j)-msfuy(i,j))*rdx
ENDDO
ENDDO
ENDDO
! Pick up the boundary rows for open (radiation) lateral b.c.
! Rather crude at present, we are assuming there is no
! variation in this term at the boundary.
IF ( ( config_flags%open_xs .or. (specified .AND. .NOT. config_flags%periodic_x) .or. &
config_flags%nested) .and. (its == ids) ) THEN
DO j = jts, jte-1
DO k = kts, ktf
vxgm(its-1,k,j) = vxgm(its,k,j)
ENDDO
ENDDO
ENDIF
IF ( ( config_flags%open_xe .or. (specified .AND. .NOT. config_flags%periodic_x) .or. &
config_flags%nested) .and. (ite == ide) ) THEN
DO j = jts, jte-1
DO k = kts, ktf
vxgm(ite,k,j) = vxgm(ite-1,k,j)
ENDDO
ENDDO
ENDIF
! Polar boundary condition:
! The following change is needed in case one tries using the vxgm route with
! polar B.C.'s in the future, but not needed if 'tan' used
IF ( ( config_flags%open_ys .or. specified .or. &
config_flags%nested .or. config_flags%polar) .and. (jts == jds) ) THEN
DO k = kts, ktf
DO i = its-1, ite
vxgm(i,k,jts-1) = vxgm(i,k,jts)
ENDDO
ENDDO
ENDIF
! Polar boundary condition:
! The following change is needed in case one tries using the vxgm route with
! polar B.C.'s in the future, but not needed if 'tan' used
IF ( ( config_flags%open_ye .or. specified .or. &
config_flags%nested .or. config_flags%polar) .and. (jte == jde) ) THEN
DO k = kts, ktf
DO i = its-1, ite
vxgm(i,k,jte) = vxgm(i,k,jte-1)
ENDDO
ENDDO
ENDIF
! curvature term for u momentum eqn.
! Map scale factor notes:
! ADT eqn 44, RHS terms 4 and 5, in cylindrical: mu u v tan(lat)/(a my)
! - mu u w /(a my)
! ru = mu u / my ; rw = mu w / my ; rv = mu v / mx
! => terms are:
! (mx/my)*u rv tan(lat) / a - u rw / a = (u/a)*[(mx/my) rv tan(lat) - rw]
! ru v tan(lat) / a - u rw / a
! xlat defined with end points half grid space from pole,
! hence are on u latitude points
i_start = its
IF ( config_flags%open_xs .or. specified .or. &
config_flags%nested) i_start = MAX ( ids+1 , its )
IF ( config_flags%open_xe .or. specified .or. &
config_flags%nested) i_end = MIN ( ide-1 , ite )
IF ( config_flags%periodic_x ) i_start = its
IF ( config_flags%periodic_x ) i_end = ite
! Polar boundary condition
IF ((config_flags%map_proj == 6) .OR. (config_flags%polar)) THEN
DO j=jts,MIN(jde-1,jte)
DO k=kts,ktf
DO i=i_start,i_end
ru_tend(i,k,j)=ru_tend(i,k,j) + u(i,k,j)*reradius* ( &
(msfux(i,j)/msfuy(i,j))*0.25*(rv(i-1,k,j+1)+rv(i,k,j+1)+ &
rv(i-1,k,j)+rv(i,k,j))*tan(xlat(i,j)*degrad) &
- 0.25*(rw(i-1,k+1,j)+rw(i-1,k,j)+rw(i,k+1,j)+rw(i,k,j)) )
ENDDO
ENDDO
ENDDO
ELSE ! normal code
DO j=jts,MIN(jde-1,jte)
DO k=kts,ktf
DO i=i_start,i_end
ru_tend(i,k,j)=ru_tend(i,k,j) + 0.5*(vxgm(i,k,j)+vxgm(i-1,k,j)) &
*0.25*(rv(i-1,k,j+1)+rv(i,k,j+1)+rv(i-1,k,j)+rv(i,k,j)) &
- u(i,k,j)*reradius &
*0.25*(rw(i-1,k+1,j)+rw(i-1,k,j)+rw(i,k+1,j)+rw(i,k,j))
ENDDO
ENDDO
ENDDO
END IF
! curvature term for v momentum eqn.
! Map scale factor notes
! ADT eqn 45, RHS terms 4 and 5, in cylindrical: - mu u*u tan(lat)/(a mx)
! - mu v w /(a mx)
! ru = mu u / my ; rw = mu w / my ; rv = mu v / mx
! terms are:
! - (my/mx)*u ru tan(lat) / a - (my/mx)*v rw / a
! = - [my/(mx*a)]*[u ru tan(lat) + v rw]
! - (1/a)*[(my/mx)*u ru tan(lat) + w rv]
! xlat defined with end points half grid space from pole, hence are on
! u latitude points => av here
!
! in original wrf, there was a sign error for the rw contribution
j_start = jts
IF ( config_flags%open_ys .or. specified .or. &
config_flags%nested .or. config_flags%polar) j_start = MAX ( jds+1 , jts )
IF ( config_flags%open_ye .or. specified .or. &
config_flags%nested .or. config_flags%polar) j_end = MIN ( jde-1 , jte )
IF ((config_flags%map_proj == 6) .OR. (config_flags%polar)) THEN
DO j=j_start,j_end
DO k=kts,ktf
DO i=its,MIN(ite,ide-1)
rv_tend(i,k,j)=rv_tend(i,k,j) - (msfvy(i,j)/msfvx(i,j))*reradius* ( &
0.25*(u(i,k,j)+u(i+1,k,j)+u(i,k,j-1)+u(i+1,k,j-1))* &
tan((xlat(i,j)+xlat(i,j-1))*0.5*degrad)* &
0.25*(ru(i,k,j)+ru(i+1,k,j)+ru(i,k,j-1)+ru(i+1,k,j-1)) &
+ v(i,k,j)*0.25*(rw(i,k+1,j-1)+rw(i,k,j-1)+ &
rw(i,k+1,j)+rw(i,k,j)) )
ENDDO
ENDDO
ENDDO
ELSE ! normal code
DO j=j_start,j_end
DO k=kts,ktf
DO i=its,MIN(ite,ide-1)
rv_tend(i,k,j)=rv_tend(i,k,j) - 0.5*(vxgm(i,k,j)+vxgm(i,k,j-1)) &
*0.25*(ru(i,k,j)+ru(i+1,k,j)+ru(i,k,j-1)+ru(i+1,k,j-1)) &
- (msfvy(i,j)/msfvx(i,j))*v(i,k,j)*reradius &
*0.25*(rw(i,k+1,j-1)+rw(i,k,j-1)+rw(i,k+1,j)+rw(i,k,j))
ENDDO
ENDDO
ENDDO
END IF
! curvature term for vertical momentum eqn.
! Notes on map scale factors:
! ADT eqn 46, RHS term 4: [mu/(a my)]*[u*u + v*v]
! ru = mu u / my ; rw = mu w / my ; rv = mu v / mx
! terms are: u ru / a + (mx/my)v rv / a
DO j=jts,MIN(jte,jde-1)
DO k=MAX(2,kts),ktf
DO i=its,MIN(ite,ide-1)
rw_tend(i,k,j)=rw_tend(i,k,j) + reradius* &
(0.5*(fzm(k)*(ru(i,k,j)+ru(i+1,k,j))+fzp(k)*(ru(i,k-1,j)+ru(i+1,k-1,j))) &
*0.5*(fzm(k)*( u(i,k,j) +u(i+1,k,j))+fzp(k)*( u(i,k-1,j) +u(i+1,k-1,j))) &
+(msftx(i,j)/msfty(i,j))*0.5*(fzm(k)*(rv(i,k,j)+rv(i,k,j+1))+fzp(k)*(rv(i,k-1,j)+rv(i,k-1,j+1))) &
*0.5*(fzm(k)*( v(i,k,j) +v(i,k,j+1))+fzp(k)*( v(i,k-1,j) +v(i,k-1,j+1))))
ENDDO
ENDDO
ENDDO
END SUBROUTINE curvature
!------------------------------------------------------------------------------
SUBROUTINE decouple ( rr, rfield, field, name, config_flags, &
fzm, fzp, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
TYPE(grid_config_rec_type) , INTENT(IN ) :: config_flags
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
CHARACTER(LEN=1) , INTENT(IN ) :: name
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(IN ) :: rfield
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(IN ) :: rr
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(OUT ) :: field
REAL , DIMENSION( kms:kme ) , INTENT(IN ) :: fzm, fzp
! Local data
INTEGER :: i, j, k, itf, jtf, ktf
!<DESCRIPTION>
!
! decouple decouples a variable from the column dry-air mass.
!
!</DESCRIPTION>
ktf=MIN(kte,kde-1)
IF (name .EQ. 'u')THEN
itf=ite
jtf=MIN(jte,jde-1)
DO j=jts,jtf
DO k=kts,ktf
DO i=its,itf
field(i,k,j)=rfield(i,k,j)/(0.5*(rr(i,k,j)+rr(i-1,k,j)))
ENDDO
ENDDO
ENDDO
ELSE IF (name .EQ. 'v')THEN
itf=MIN(ite,ide-1)
jtf=jte
DO j=jts,jtf
DO k=kts,ktf
DO i=its,itf
field(i,k,j)=rfield(i,k,j)/(0.5*(rr(i,k,j)+rr(i,k,j-1)))
ENDDO
ENDDO
ENDDO
ELSE IF (name .EQ. 'w')THEN
itf=MIN(ite,ide-1)
jtf=MIN(jte,jde-1)
DO j=jts,jtf
DO k=kts+1,ktf
DO i=its,itf
field(i,k,j)=rfield(i,k,j)/(fzm(k)*rr(i,k,j)+fzp(k)*rr(i,k-1,j))
ENDDO
ENDDO
ENDDO
DO j=jts,jtf
DO i=its,itf
field(i,kte,j) = 0.
ENDDO
ENDDO
ELSE
itf=MIN(ite,ide-1)
jtf=MIN(jte,jde-1)
! For theta we will decouple tb and tp and add them to give t afterwards
DO j=jts,jtf
DO k=kts,ktf
DO i=its,itf
field(i,k,j)=rfield(i,k,j)/rr(i,k,j)
ENDDO
ENDDO
ENDDO
ENDIF
END SUBROUTINE decouple
!-------------------------------------------------------------------------------
SUBROUTINE zero_tend ( tendency, & 23
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(INOUT) :: tendency
! Local data
INTEGER :: i, j, k, itf, jtf, ktf
!<DESCRIPTION>
!
! zero_tend sets the input tendency array to zero.
!
!</DESCRIPTION>
DO j = jts, jte
DO k = kts, kte
DO i = its, ite
tendency(i,k,j) = 0.
ENDDO
ENDDO
ENDDO
END SUBROUTINE zero_tend
!-------------------------------------------------------------------------------
SUBROUTINE zero_tend2d( tendency, & 3
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL , DIMENSION( ims:ime , jms:jme ) , INTENT(INOUT) :: tendency
! Local data
INTEGER :: i, j, k, itf, jtf, ktf
!<DESCRIPTION>
!
! zero_tend sets the input tendency array to zero.
!
!</DESCRIPTION>
DO j = jts, jte
DO i = its, ite
tendency(i,j) = 0.
ENDDO
ENDDO
END SUBROUTINE zero_tend2d
!-------------------------------------------------------------------------------
! Sets the an array on the polar v point(s) to zero
SUBROUTINE zero_pole ( field, & 2
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(INOUT) :: field
! Local data
INTEGER :: i, k
IF (jts == jds) THEN
DO k = kts, kte
DO i = its-1, ite+1
field(i,k,jts) = 0.
END DO
END DO
END IF
IF (jte == jde) THEN
DO k = kts, kte
DO i = its-1, ite+1
field(i,k,jte) = 0.
END DO
END DO
END IF
END SUBROUTINE zero_pole
!-------------------------------------------------------------------------------
! Sets the an array on the polar v point(s)
SUBROUTINE pole_point_bc ( field, & 2
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(INOUT) :: field
! Local data
INTEGER :: i, k
IF (jts == jds) THEN
DO k = kts, kte
DO i = its, ite
! field(i,k,jts) = 2*field(i,k,jts+1) - field(i,k,jts+2)
field(i,k,jts) = field(i,k,jts+1)
END DO
END DO
END IF
IF (jte == jde) THEN
DO k = kts, kte
DO i = its, ite
! field(i,k,jte) = 2*field(i,k,jte-1) - field(i,k,jte-2)
field(i,k,jte) = field(i,k,jte-1)
END DO
END DO
END IF
END SUBROUTINE pole_point_bc
!======================================================================
! physics prep routines
!======================================================================
SUBROUTINE phy_prep ( config_flags, & ! input 1
mu, muu, muv, u, v, p, pb, alt, ph, & ! input
phb, t, tsk, moist, n_moist, & ! input
rho, th_phy, p_phy , pi_phy , & ! output
u_phy, v_phy, p8w, t_phy, t8w, & ! output
z, z_at_w, dz8w, & ! output
p_hyd, p_hyd_w, dnw, & ! output
fzm, fzp, znw, p_top, & ! params
RTHRATEN, &
RTHBLTEN, RUBLTEN, RVBLTEN, &
RQVBLTEN, RQCBLTEN, RQIBLTEN, &
RUCUTEN, RVCUTEN, RTHCUTEN, &
RQVCUTEN, RQCCUTEN, RQRCUTEN, &
RQICUTEN, RQSCUTEN, &
RUSHTEN, RVSHTEN, RTHSHTEN, &
RQVSHTEN, RQCSHTEN, RQRSHTEN, &
RQISHTEN, RQSSHTEN, RQGSHTEN, &
RTHFTEN, RQVFTEN, &
RUNDGDTEN, RVNDGDTEN, RTHNDGDTEN, &
RPHNDGDTEN,RQVNDGDTEN, RMUNDGDTEN, &
!jdf
landmask, xland, &
!jdf
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
!----------------------------------------------------------------------
IMPLICIT NONE
!----------------------------------------------------------------------
TYPE(grid_config_rec_type) , INTENT(IN ) :: config_flags
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
INTEGER , INTENT(IN ) :: n_moist
REAL, DIMENSION( ims:ime, kms:kme , jms:jme , n_moist ), INTENT(IN) :: moist
REAL , DIMENSION( ims:ime, jms:jme ), INTENT(IN ) :: TSK, mu, muu, muv
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , &
INTENT( OUT) :: u_phy, &
v_phy, &
pi_phy, &
p_phy, &
p8w, &
t_phy, &
th_phy, &
t8w, &
rho, &
z, &
dz8w, &
z_at_w
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , &
INTENT( OUT) :: p_hyd, &
p_hyd_w
REAL , INTENT(IN ) :: p_top
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , &
INTENT(IN ) :: pb, &
p, &
u, &
v, &
alt, &
ph, &
phb, &
t
REAL , DIMENSION( kms:kme ) , INTENT(IN ) :: fzm, &
fzp
REAL , DIMENSION( kms:kme ) , INTENT(IN ) :: znw, &
dnw
REAL, DIMENSION( ims:ime , kms:kme, jms:jme ), &
INTENT(INOUT) :: RTHRATEN
REAL, DIMENSION( ims:ime , kms:kme, jms:jme ), &
INTENT(INOUT) :: RUCUTEN, &
RVCUTEN, &
RTHCUTEN, &
RQVCUTEN, &
RQCCUTEN, &
RQRCUTEN, &
RQICUTEN, &
RQSCUTEN, &
RUSHTEN, &
RVSHTEN, &
RTHSHTEN, &
RQVSHTEN, &
RQCSHTEN, &
RQRSHTEN, &
RQISHTEN, &
RQSSHTEN, &
RQGSHTEN
REAL, DIMENSION( ims:ime, kms:kme, jms:jme ) , &
INTENT(INOUT) :: RUBLTEN, &
RVBLTEN, &
RTHBLTEN, &
RQVBLTEN, &
RQCBLTEN, &
RQIBLTEN
REAL, DIMENSION( ims:ime, kms:kme, jms:jme ) , &
INTENT(INOUT) :: RTHFTEN, &
RQVFTEN
REAL, DIMENSION( ims:ime, kms:kme, jms:jme ) , &
INTENT(INOUT) :: RUNDGDTEN, &
RVNDGDTEN, &
RTHNDGDTEN, &
RPHNDGDTEN, &
RQVNDGDTEN
REAL, DIMENSION( ims:ime, jms:jme ) , &
INTENT(INOUT) :: RMUNDGDTEN
!jdf
REAL, DIMENSION( ims:ime, jms:jme ) , &
INTENT(INOUT) :: landmask, &
xland
!jdf
INTEGER :: i_start, i_end, j_start, j_end, k_start, k_end, i_startu, j_startv
INTEGER :: i, j, k
REAL :: w1, w2, z0, z1, z2
REAL :: qtot
INTEGER :: n
!-----------------------------------------------------------------------
!<DESCRIPTION>
!
! phys_prep calculates a number of diagnostic quantities needed by
! the physics routines. It also decouples the physics tendencies from
! the column dry-air mass (the physics routines expect to see/update the
! uncoupled tendencies).
!
!</DESCRIPTION>
! set up loop bounds for this grid's boundary conditions
i_start = its
i_end = min( ite,ide-1 )
j_start = jts
j_end = min( jte,jde-1 )
k_start = kts
k_end = min( kte, kde-1 )
!jdf
do j = j_start,j_end
do i = i_start, i_end
if(landmask(i,j).lt.0.5) xland(i,j)=2.0
enddo
enddo
!jdf
! compute thermodynamics and velocities at pressure points (or half levels)
do j = j_start,j_end
do k = k_start, k_end
do i = i_start, i_end
th_phy(i,k,j) = t(i,k,j) + t0
p_phy(i,k,j) = p(i,k,j) + pb(i,k,j)
pi_phy(i,k,j) = (p_phy(i,k,j)/p1000mb)**rcp
t_phy(i,k,j) = th_phy(i,k,j)*pi_phy(i,k,j)
rho(i,k,j) = 1./alt(i,k,j)*(1.+moist(i,k,j,P_QV))
u_phy(i,k,j) = 0.5*(u(i,k,j)+u(i+1,k,j))
v_phy(i,k,j) = 0.5*(v(i,k,j)+v(i,k,j+1))
enddo
enddo
enddo
! compute z at w points
do j = j_start,j_end
do k = k_start, kte
do i = i_start, i_end
z_at_w(i,k,j) = (phb(i,k,j)+ph(i,k,j))/g
enddo
enddo
enddo
do j = j_start,j_end
do k = k_start, kte-1
do i = i_start, i_end
dz8w(i,k,j) = z_at_w(i,k+1,j)-z_at_w(i,k,j)
enddo
enddo
enddo
do j = j_start,j_end
do i = i_start, i_end
dz8w(i,kte,j) = 0.
enddo
enddo
! compute z at p points or half levels (average of z at full levels)
do j = j_start,j_end
do k = k_start, k_end
do i = i_start, i_end
z(i,k,j) = 0.5*(z_at_w(i,k,j) +z_at_w(i,k+1,j) )
enddo
enddo
enddo
! interp t and p to full levels
do j = j_start,j_end
do k = 2, k_end
do i = i_start, i_end
p8w(i,k,j) = fzm(k)*p_phy(i,k,j)+fzp(k)*p_phy(i,k-1,j)
t8w(i,k,j) = fzm(k)*t_phy(i,k,j)+fzp(k)*t_phy(i,k-1,j)
enddo
enddo
enddo
! extrapolate p and t to surface and top.
! we'll use an extrapolation in z for now
do j = j_start,j_end
do i = i_start, i_end
! bottom
z0 = z_at_w(i,1,j)
z1 = z(i,1,j)
z2 = z(i,2,j)
w1 = (z0 - z2)/(z1 - z2)
w2 = 1. - w1
p8w(i,1,j) = w1*p_phy(i,1,j)+w2*p_phy(i,2,j)
t8w(i,1,j) = w1*t_phy(i,1,j)+w2*t_phy(i,2,j)
! top
z0 = z_at_w(i,kte,j)
z1 = z(i,k_end,j)
z2 = z(i,k_end-1,j)
w1 = (z0 - z2)/(z1 - z2)
w2 = 1. - w1
! p8w(i,kde,j) = w1*p_phy(i,kde-1,j)+w2*p_phy(i,kde-2,j)
!!! bug fix extrapolate ln(p) so p is positive definite
p8w(i,kde,j) = exp(w1*log(p_phy(i,kde-1,j))+w2*log(p_phy(i,kde-2,j)))
t8w(i,kde,j) = w1*t_phy(i,kde-1,j)+w2*t_phy(i,kde-2,j)
enddo
enddo
! calculate hydrostatic pressure at both full and half levels
! first, full level p: assuming dry over model top
do j = j_start,j_end
do i = i_start, i_end
p_hyd_w(i,kte,j) = p_top
enddo
enddo
do j = j_start,j_end
do k = kte-1, k_start, -1
do i = i_start, i_end
qtot = 0.
do n = PARAM_FIRST_SCALAR,n_moist
qtot = qtot + moist(i,k,j,n)
enddo
p_hyd_w(i,k,j) = p_hyd_w(i,k+1,j) - (1.+qtot)*mu(i,j)*dnw(k)
! p_hyd_w(i,k,j) = p_hyd_w(i,k+1,j)+1./alt(i,k,j)*(1.+moist(i,k,j,P_QV))*g*dz8w(i,k,j)
enddo
enddo
enddo
! now calculate hydrostatic pressure at half levels
do j = j_start,j_end
do k = k_start, k_end
do i = i_start, i_end
p_hyd(i,k,j) = 0.5*(p_hyd_w(i,k,j)+p_hyd_w(i,k+1,j))
enddo
enddo
enddo
! decouple all physics tendencies
IF (config_flags%ra_lw_physics .gt. 0 .or. config_flags%ra_sw_physics .gt. 0) THEN
DO J=j_start,j_end
DO K=k_start,k_end
DO I=i_start,i_end
RTHRATEN(I,K,J)=RTHRATEN(I,K,J)/mu(I,J)
ENDDO
ENDDO
ENDDO
ENDIF
IF (config_flags%cu_physics .gt. 0) THEN
DO J=j_start,j_end
DO I=i_start,i_end
DO K=k_start,k_end
RUCUTEN(I,K,J) =RUCUTEN(I,K,J)/mu(I,J)
RVCUTEN(I,K,J) =RVCUTEN(I,K,J)/mu(I,J)
RTHCUTEN(I,K,J)=RTHCUTEN(I,K,J)/mu(I,J)
ENDDO
ENDDO
ENDDO
IF (P_QV .ge. PARAM_FIRST_SCALAR)THEN
DO J=j_start,j_end
DO I=i_start,i_end
DO K=k_start,k_end
RQVCUTEN(I,K,J)=RQVCUTEN(I,K,J)/mu(I,J)
ENDDO
ENDDO
ENDDO
ENDIF
IF (P_QC .ge. PARAM_FIRST_SCALAR)THEN
DO J=j_start,j_end
DO I=i_start,i_end
DO K=k_start,k_end
RQCCUTEN(I,K,J)=RQCCUTEN(I,K,J)/mu(I,J)
ENDDO
ENDDO
ENDDO
ENDIF
IF (P_QR .ge. PARAM_FIRST_SCALAR)THEN
DO J=j_start,j_end
DO I=i_start,i_end
DO K=k_start,k_end
RQRCUTEN(I,K,J)=RQRCUTEN(I,K,J)/mu(I,J)
ENDDO
ENDDO
ENDDO
ENDIF
IF (P_QI .ge. PARAM_FIRST_SCALAR)THEN
DO J=j_start,j_end
DO I=i_start,i_end
DO K=k_start,k_end
RQICUTEN(I,K,J)=RQICUTEN(I,K,J)/mu(I,J)
ENDDO
ENDDO
ENDDO
ENDIF
IF(P_QS .ge. PARAM_FIRST_SCALAR)THEN
DO J=j_start,j_end
DO I=i_start,i_end
DO K=k_start,k_end
RQSCUTEN(I,K,J)=RQSCUTEN(I,K,J)/mu(I,J)
ENDDO
ENDDO
ENDDO
ENDIF
ENDIF
IF (config_flags%shcu_physics .gt. 0) THEN
DO J=j_start,j_end
DO I=i_start,i_end
DO K=k_start,k_end
RUSHTEN(I,K,J) =RUSHTEN(I,K,J)/mu(I,J)
RVSHTEN(I,K,J) =RVSHTEN(I,K,J)/mu(I,J)
RTHSHTEN(I,K,J)=RTHSHTEN(I,K,J)/mu(I,J)
ENDDO
ENDDO
ENDDO
IF (P_QV .ge. PARAM_FIRST_SCALAR)THEN
DO J=j_start,j_end
DO I=i_start,i_end
DO K=k_start,k_end
RQVSHTEN(I,K,J)=RQVSHTEN(I,K,J)/mu(I,J)
ENDDO
ENDDO
ENDDO
ENDIF
IF (P_QC .ge. PARAM_FIRST_SCALAR)THEN
DO J=j_start,j_end
DO I=i_start,i_end
DO K=k_start,k_end
RQCSHTEN(I,K,J)=RQCSHTEN(I,K,J)/mu(I,J)
ENDDO
ENDDO
ENDDO
ENDIF
IF (P_QR .ge. PARAM_FIRST_SCALAR)THEN
DO J=j_start,j_end
DO I=i_start,i_end
DO K=k_start,k_end
RQRSHTEN(I,K,J)=RQRSHTEN(I,K,J)/mu(I,J)
ENDDO
ENDDO
ENDDO
ENDIF
IF (P_QI .ge. PARAM_FIRST_SCALAR)THEN
DO J=j_start,j_end
DO I=i_start,i_end
DO K=k_start,k_end
RQISHTEN(I,K,J)=RQISHTEN(I,K,J)/mu(I,J)
ENDDO
ENDDO
ENDDO
ENDIF
IF(P_QS .ge. PARAM_FIRST_SCALAR)THEN
DO J=j_start,j_end
DO I=i_start,i_end
DO K=k_start,k_end
RQSSHTEN(I,K,J)=RQSSHTEN(I,K,J)/mu(I,J)
ENDDO
ENDDO
ENDDO
ENDIF
IF(P_QG .ge. PARAM_FIRST_SCALAR)THEN
DO J=j_start,j_end
DO I=i_start,i_end
DO K=k_start,k_end
RQGSHTEN(I,K,J)=RQGSHTEN(I,K,J)/mu(I,J)
ENDDO
ENDDO
ENDDO
ENDIF
ENDIF
IF (config_flags%bl_pbl_physics .gt. 0) THEN
DO J=j_start,j_end
DO K=k_start,k_end
DO I=i_start,i_end
RUBLTEN(I,K,J) =RUBLTEN(I,K,J)/mu(I,J)
RVBLTEN(I,K,J) =RVBLTEN(I,K,J)/mu(I,J)
RTHBLTEN(I,K,J)=RTHBLTEN(I,K,J)/mu(I,J)
ENDDO
ENDDO
ENDDO
IF (P_QV .ge. PARAM_FIRST_SCALAR) THEN
DO J=j_start,j_end
DO K=k_start,k_end
DO I=i_start,i_end
RQVBLTEN(I,K,J)=RQVBLTEN(I,K,J)/mu(I,J)
ENDDO
ENDDO
ENDDO
ENDIF
IF (P_QC .ge. PARAM_FIRST_SCALAR) THEN
DO J=j_start,j_end
DO K=k_start,k_end
DO I=i_start,i_end
RQCBLTEN(I,K,J)=RQCBLTEN(I,K,J)/mu(I,J)
ENDDO
ENDDO
ENDDO
ENDIF
IF (P_QI .ge. PARAM_FIRST_SCALAR) THEN
DO J=j_start,j_end
DO K=k_start,k_end
DO I=i_start,i_end
RQIBLTEN(I,K,J)=RQIBLTEN(I,K,J)/mu(I,J)
ENDDO
ENDDO
ENDDO
ENDIF
ENDIF
! decouple advective forcing required by Grell-Devenyi scheme
if(( config_flags%cu_physics == GDSCHEME ) .OR. &
( config_flags%cu_physics == GFSCHEME ) .OR. &
( config_flags%cu_physics == G3SCHEME ) .OR. &
( config_flags%cu_physics == KFETASCHEME ) .OR. &
( config_flags%cu_physics == TIEDTKESCHEME ) ) then ! Tiedtke ZCX&YQW
DO J=j_start,j_end
DO I=i_start,i_end
DO K=k_start,k_end
RTHFTEN(I,K,J)=RTHFTEN(I,K,J)/mu(I,J)
ENDDO
ENDDO
ENDDO
IF (P_QV .ge. PARAM_FIRST_SCALAR)THEN
DO J=j_start,j_end
DO I=i_start,i_end
DO K=k_start,k_end
RQVFTEN(I,K,J)=RQVFTEN(I,K,J)/mu(I,J)
ENDDO
ENDDO
ENDDO
ENDIF
END IF
! fdda
! note fdda u and v tendencies are staggered, also only interior points have muu/muv,
! so only decouple those
IF (config_flags%grid_fdda .gt. 0) THEN
i_startu=MAX(its,ids+1)
j_startv=MAX(jts,jds+1)
DO J=j_start,j_end
DO K=k_start,k_end
DO I=i_startu,i_end
RUNDGDTEN(I,K,J) =RUNDGDTEN(I,K,J)/muu(I,J)
ENDDO
ENDDO
ENDDO
DO J=j_startv,j_end
DO K=k_start,k_end
DO I=i_start,i_end
RVNDGDTEN(I,K,J) =RVNDGDTEN(I,K,J)/muv(I,J)
ENDDO
ENDDO
ENDDO
DO J=j_start,j_end
DO K=k_start,k_end
DO I=i_start,i_end
RTHNDGDTEN(I,K,J)=RTHNDGDTEN(I,K,J)/mu(I,J)
! RMUNDGDTEN(I,J) - no coupling
ENDDO
ENDDO
ENDDO
IF (config_flags%grid_fdda .EQ. 2) THEN
DO J=j_start,j_end
DO K=k_start,kte
DO I=i_start,i_end
RPHNDGDTEN(I,K,J)=RPHNDGDTEN(I,K,J)/mu(I,J)
ENDDO
ENDDO
ENDDO
ELSE IF (config_flags%grid_fdda .EQ. 1) THEN
IF (P_QV .ge. PARAM_FIRST_SCALAR) THEN
DO J=j_start,j_end
DO K=k_start,k_end
DO I=i_start,i_end
RQVNDGDTEN(I,K,J)=RQVNDGDTEN(I,K,J)/mu(I,J)
ENDDO
ENDDO
ENDDO
ENDIF
ENDIF
ENDIF
END SUBROUTINE phy_prep
!------------------------------------------------------------
SUBROUTINE moist_physics_prep_em( t_new, t_old, t0, rho, al, alb, & 1
p, p8w, p0, pb, ph, phb, &
th_phy, pii, pf, &
z, z_at_w, dz8w, &
dt,h_diabatic, &
config_flags,fzm, fzp, &
ids,ide, jds,jde, kds,kde, &
ims,ime, jms,jme, kms,kme, &
its,ite, jts,jte, kts,kte )
IMPLICIT NONE
! Here we construct full fields
! needed by the microphysics
TYPE(grid_config_rec_type), INTENT(IN ) :: config_flags
INTEGER, INTENT(IN ) :: ids,ide, jds,jde, kds,kde
INTEGER, INTENT(IN ) :: ims,ime, jms,jme, kms,kme
INTEGER, INTENT(IN ) :: its,ite, jts,jte, kts,kte
REAL, INTENT(IN ) :: dt
REAL, DIMENSION( ims:ime , kms:kme, jms:jme ), &
INTENT(IN ) :: al, &
alb, &
p, &
pb, &
ph, &
phb
REAL , DIMENSION( kms:kme ) , INTENT(IN ) :: fzm, &
fzp
REAL, DIMENSION( ims:ime , kms:kme, jms:jme ), &
INTENT( OUT) :: rho, &
th_phy, &
pii, &
pf, &
z, &
z_at_w, &
dz8w, &
p8w
REAL, DIMENSION( ims:ime , kms:kme, jms:jme ), &
INTENT(INOUT) :: h_diabatic
REAL, DIMENSION( ims:ime , kms:kme, jms:jme ), &
INTENT(INOUT) :: t_new, &
t_old
REAL, INTENT(IN ) :: t0, p0
REAL :: z0,z1,z2,w1,w2
INTEGER :: i_start, i_end, j_start, j_end, k_start, k_end
INTEGER :: i, j, k
!--------------------------------------------------------------------
!<DESCRIPTION>
!
! moist_phys_prep_em calculates a number of diagnostic quantities needed by
! the microphysics routines.
!
!</DESCRIPTION>
! set up loop bounds for this grid's boundary conditions
i_start = its
i_end = min( ite,ide-1 )
j_start = jts
j_end = min( jte,jde-1 )
k_start = kts
k_end = min( kte, kde-1 )
DO j = j_start, j_end
DO k = k_start, kte
DO i = i_start, i_end
z_at_w(i,k,j) = (ph(i,k,j)+phb(i,k,j))/g
ENDDO
ENDDO
ENDDO
do j = j_start,j_end
do k = k_start, kte-1
do i = i_start, i_end
dz8w(i,k,j) = z_at_w(i,k+1,j)-z_at_w(i,k,j)
enddo
enddo
enddo
do j = j_start,j_end
do i = i_start, i_end
dz8w(i,kte,j) = 0.
enddo
enddo
! compute full pii, rho, and z at the new time-level
! (needed for physics).
! convert perturbation theta to full theta (th_phy)
! use h_diabatic to temporarily save pre-microphysics full theta
DO j = j_start, j_end
DO k = k_start, k_end
DO i = i_start, i_end
#ifdef REVERT
t_new(i,k,j) = t_new(i,k,j)-h_diabatic(i,k,j)*dt
#endif
th_phy(i,k,j) = t_new(i,k,j) + t0
h_diabatic(i,k,j) = th_phy(i,k,j)
rho(i,k,j) = 1./(al(i,k,j)+alb(i,k,j))
pii(i,k,j) = ((p(i,k,j)+pb(i,k,j))/p0)**rcp
z(i,k,j) = 0.5*(z_at_w(i,k,j) +z_at_w(i,k+1,j) )
pf(i,k,j) = p(i,k,j)+pb(i,k,j)
ENDDO
ENDDO
ENDDO
! interp t and p at w points
do j = j_start,j_end
do k = 2, k_end
do i = i_start, i_end
p8w(i,k,j) = fzm(k)*pf(i,k,j)+fzp(k)*pf(i,k-1,j)
enddo
enddo
enddo
! extrapolate p and t to surface and top.
! we'll use an extrapolation in z for now
do j = j_start,j_end
do i = i_start, i_end
! bottom
z0 = z_at_w(i,1,j)
z1 = z(i,1,j)
z2 = z(i,2,j)
w1 = (z0 - z2)/(z1 - z2)
w2 = 1. - w1
p8w(i,1,j) = w1*pf(i,1,j)+w2*pf(i,2,j)
! top
z0 = z_at_w(i,kte,j)
z1 = z(i,k_end,j)
z2 = z(i,k_end-1,j)
w1 = (z0 - z2)/(z1 - z2)
w2 = 1. - w1
! p8w(i,kde,j) = w1*pf(i,kde-1,j)+w2*pf(i,kde-2,j)
p8w(i,kde,j) = exp(w1*log(pf(i,kde-1,j))+w2*log(pf(i,kde-2,j)))
enddo
enddo
END SUBROUTINE moist_physics_prep_em
!------------------------------------------------------------------------------
SUBROUTINE moist_physics_finish_em( t_new, t_old, t0, mut, & 1,1
th_phy, h_diabatic, dt, &
config_flags, &
#if ( WRF_DFI_RADAR == 1 )
dfi_tten_rad,dfi_stage, &
#endif
ids,ide, jds,jde, kds,kde, &
ims,ime, jms,jme, kms,kme, &
its,ite, jts,jte, kts,kte )
IMPLICIT NONE
! Here we construct full fields
! needed by the microphysics
TYPE(grid_config_rec_type), INTENT(IN ) :: config_flags
INTEGER, INTENT(IN ) :: ids,ide, jds,jde, kds,kde
INTEGER, INTENT(IN ) :: ims,ime, jms,jme, kms,kme
INTEGER, INTENT(IN ) :: its,ite, jts,jte, kts,kte
REAL, DIMENSION( ims:ime , kms:kme, jms:jme ), &
INTENT(INOUT) :: t_new, &
t_old, &
th_phy, &
h_diabatic
#if ( WRF_DFI_RADAR == 1 )
REAL, DIMENSION( ims:ime , kms:kme, jms:jme ), &
INTENT(IN), OPTIONAL :: dfi_tten_rad
INTEGER, INTENT(IN ) ,OPTIONAL :: dfi_stage
REAL :: dfi_tten_max, old_max
#endif
REAL mpten, mptenmax, mptenmin
REAL, DIMENSION( ims:ime , jms:jme ), INTENT(INOUT) :: mut
REAL, INTENT(IN ) :: t0, dt
INTEGER :: i_start, i_end, j_start, j_end, k_start, k_end
INTEGER :: i, j, k, imax, jmax, imin, jmin
!--------------------------------------------------------------------
!<DESCRIPTION>
!
! moist_phys_finish_em resets theta to its perturbation value and
! computes and stores the microphysics diabatic heating term.
!
!</DESCRIPTION>
! set up loop bounds for this grid's boundary conditions
i_start = its
i_end = min( ite,ide-1 )
j_start = jts
j_end = min( jte,jde-1 )
! i_start=max(its,ids+4)
! i_end=min(ite,ide-5)
! j_start=max(jts,jds+4)
! j_end=min(jte,jde-5)
k_start = kts
k_end = min( kte, kde-1 )
#if ( WRF_DFI_RADAR == 1 )
IF ( PRESENT(dfi_stage) .and. PRESENT(dfi_tten_rad) ) THEN
IF ( dfi_stage ==DFI_FWD ) THEN
WRITE(wrf_err_message,*)'Add radar tendency: i_start,j_start: ', i_start, j_start
CALL wrf_debug ( 100 , TRIM(wrf_err_message) )
ENDIF
ENDIF
dfi_tten_max=-999
old_max=-999
#endif
! add microphysics theta diff to perturbation theta, set h_diabatic
IF ( config_flags%no_mp_heating .eq. 0 ) THEN
mptenmax = 0.
mptenmin = 999.
DO j = j_start, j_end
DO k = k_start, k_end
DO i = i_start, i_end
mpten = th_phy(i,k,j)-h_diabatic(i,k,j)
if(mpten.gt.mptenmax) then
mptenmax=mpten
imax=i
jmax=j
endif
if(mpten.lt.mptenmin) then
mptenmin=mpten
imin=i
jmin=j
endif
mpten=min(config_flags%mp_tend_lim*dt, mpten)
mpten=max(-config_flags%mp_tend_lim*dt, mpten)
#if ( WRF_DFI_RADAR == 1 )
if(k < k_end ) then
if(dfi_tten_max < dfi_tten_rad(i,k,j) ) dfi_tten_max = dfi_tten_rad(i,k,j)
if(old_max < (th_phy(i,k,j)-h_diabatic(i,k,j)) ) old_max=th_phy(i,k,j)-h_diabatic(i,k,j)
endif
IF ( PRESENT(dfi_stage) .and. PRESENT(dfi_tten_rad) ) THEN
IF ( dfi_stage == DFI_FWD .and. dfi_tten_rad(i,k,j) >= -0.1 .and. &
dfi_tten_rad(i,k,j) <= 0.1 .and. k < k_end ) THEN
! add radar temp tendency
! there is radar coverage
t_new(i,k,j) = t_new(i,k,j) + (dfi_tten_rad(i,k,j))*dt
ELSE
! no radar coverage
t_new(i,k,j) = t_new(i,k,j) + mpten
ENDIF
ENDIF
#else
t_new(i,k,j) = t_new(i,k,j) + mpten
#endif
h_diabatic(i,k,j) = mpten/dt
ENDDO
ENDDO
ENDDO
ELSE
DO j = j_start, j_end
DO k = k_start, k_end
DO i = i_start, i_end
! t_new(i,k,j) = t_new(i,k,j)
h_diabatic(i,k,j) = 0.
ENDDO
ENDDO
ENDDO
ENDIF
END SUBROUTINE moist_physics_finish_em
!----------------------------------------------------------------
SUBROUTINE init_module_big_step
END SUBROUTINE init_module_big_step
SUBROUTINE set_tend ( field, field_adv_tend, msf, & 2
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE
! Input data
INTEGER , INTENT(IN ) :: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(OUT) :: field
REAL , DIMENSION( ims:ime , kms:kme , jms:jme ) , INTENT(IN) :: field_adv_tend
REAL , DIMENSION( ims:ime , jms:jme ) , INTENT(IN) :: msf
! Local data
INTEGER :: i, j, k, itf, jtf, ktf
!<DESCRIPTION>
!
! set_tend copies the advective tendency array into the tendency array.
!
!</DESCRIPTION>
jtf = MIN(jte,jde-1)
ktf = MIN(kte,kde-1)
itf = MIN(ite,ide-1)
DO j = jts, jtf
DO k = kts, ktf
DO i = its, itf
field(i,k,j) = field_adv_tend(i,k,j)*msf(i,j)
ENDDO
ENDDO
ENDDO
END SUBROUTINE set_tend
!------------------------------------------------------------------------------
SUBROUTINE rk_rayleigh_damp( ru_tendf, rv_tendf, & 1
rw_tendf, t_tendf, &
u, v, w, t, t_init, &
mut, muu, muv, ph, phb, &
u_base, v_base, t_base, z_base, &
dampcoef, zdamp, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
! History: Apr 2005 Modifications by George Bryan, NCAR:
! - Generalized the code in a way that allows for
! simulations with steep terrain.
!
! Jul 2004 Modifications by George Bryan, NCAR:
! - Modified the code to use u_base, v_base, and t_base
! arrays for the background state. Removed the hard-wired
! base-state values.
! - Modified the code to use dampcoef, zdamp, and damp_opt,
! i.e., the upper-level damper variables in namelist.input.
! Removed the hard-wired variables in the older version.
! This damper is used when damp_opt = 2.
! - Modified the code to account for the movement of the
! model surfaces with time. The code now obtains a base-
! state value by interpolation using the "_base" arrays.
! Nov 2003 Bug fix by Jason Knievel, NCAR
! Aug 2003 Meridional dimension, some comments, and
! changes in layout of the code added by
! Jason Knievel, NCAR
! Jul 2003 Original code by Bill Skamarock, NCAR
! Purpose: This routine applies Rayleigh damping to a layer at top
! of the model domain.
!-----------------------------------------------------------------------
! Begin declarations.
IMPLICIT NONE
INTEGER, INTENT( IN ) &
:: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL, DIMENSION( ims:ime, kms:kme, jms:jme ), INTENT( INOUT ) &
:: ru_tendf, rv_tendf, rw_tendf, t_tendf
REAL, DIMENSION( ims:ime, kms:kme, jms:jme ), INTENT( IN ) &
:: u, v, w, t, t_init, ph, phb
REAL, DIMENSION( ims:ime, jms:jme ), INTENT( IN ) &
:: mut, muu, muv
REAL, DIMENSION( kms:kme ) , INTENT(IN ) &
:: u_base, v_base, t_base, z_base
REAL, INTENT(IN ) &
:: dampcoef, zdamp
! Local variables.
INTEGER &
:: i_start, i_end, j_start, j_end, k_start, k_end, i, j, k, ktf, k1, k2
REAL &
:: pii, dcoef, z, ztop
REAL :: wkp1, wk, wkm1
REAL, DIMENSION( kms:kme ) :: z00, u00, v00, t00
! End declarations.
!-----------------------------------------------------------------------
pii = 2.0 * asin(1.0)
ktf = MIN( kte, kde-1 )
!-----------------------------------------------------------------------
! Adjust u to base state.
DO j = jts, MIN( jte, jde-1 )
DO i = its, MIN( ite, ide )
! Get height at top of model
ztop = 0.5*( phb(i ,kde,j)+phb(i-1,kde,j) &
+ph(i ,kde,j)+ph(i-1,kde,j) )/g
! Find bottom of damping layer
k1 = ktf
z = ztop
DO WHILE( z >= (ztop-zdamp) )
z = 0.25*( phb(i ,k1,j)+phb(i ,k1+1,j) &
+phb(i-1,k1,j)+phb(i-1,k1+1,j) &
+ph(i ,k1,j)+ph(i ,k1+1,j) &
+ph(i-1,k1,j)+ph(i-1,k1+1,j))/g
z00(k1) = z
k1 = k1 - 1
ENDDO
k1 = k1 + 2
! Get reference state at model levels
DO k = k1, ktf
k2 = ktf
DO WHILE( z_base(k2) .gt. z00(k) )
k2 = k2 - 1
ENDDO
if(k2+1.gt.ktf)then
u00(k) = u_base(k2) + ( u_base(k2) - u_base(k2-1) ) &
* ( z00(k) - z_base(k2) ) &
/ ( z_base(k2) - z_base(k2-1) )
else
u00(k) = u_base(k2) + ( u_base(k2+1) - u_base(k2) ) &
* ( z00(k) - z_base(k2) ) &
/ ( z_base(k2+1) - z_base(k2) )
endif
ENDDO
! Apply the Rayleigh damper
DO k = k1, ktf
dcoef = 1.0 - MIN( 1.0, ( ztop - z00(k) ) / zdamp )
dcoef = (SIN( 0.5 * pii * dcoef ) )**2
ru_tendf(i,k,j) = ru_tendf(i,k,j) - &
muu(i,j) * ( dcoef * dampcoef ) * &
( u(i,k,j) - u00(k) )
END DO
END DO
END DO
! End adjustment of u.
!-----------------------------------------------------------------------
!-----------------------------------------------------------------------
! Adjust v to base state.
DO j = jts, MIN( jte, jde )
DO i = its, MIN( ite, ide-1 )
! Get height at top of model
ztop = 0.5*( phb(i,kde,j )+phb(i,kde,j-1) &
+ph(i,kde,j )+ph(i,kde,j-1) )/g
! Find bottom of damping layer
k1 = ktf
z = ztop
DO WHILE( z >= (ztop-zdamp) )
z = 0.25*( phb(i,k1,j )+phb(i,k1+1,j ) &
+phb(i,k1,j-1)+phb(i,k1+1,j-1) &
+ph(i,k1,j )+ph(i,k1+1,j ) &
+ph(i,k1,j-1)+ph(i,k1+1,j-1))/g
z00(k1) = z
k1 = k1 - 1
ENDDO
k1 = k1 + 2
! Get reference state at model levels
DO k = k1, ktf
k2 = ktf
DO WHILE( z_base(k2) .gt. z00(k) )
k2 = k2 - 1
ENDDO
if(k2+1.gt.ktf)then
v00(k) = v_base(k2) + ( v_base(k2) - v_base(k2-1) ) &
* ( z00(k) - z_base(k2) ) &
/ ( z_base(k2) - z_base(k2-1) )
else
v00(k) = v_base(k2) + ( v_base(k2+1) - v_base(k2) ) &
* ( z00(k) - z_base(k2) ) &
/ ( z_base(k2+1) - z_base(k2) )
endif
ENDDO
! Apply the Rayleigh damper
DO k = k1, ktf
dcoef = 1.0 - MIN( 1.0, ( ztop - z00(k) ) / zdamp )
dcoef = (SIN( 0.5 * pii * dcoef ) )**2
rv_tendf(i,k,j) = rv_tendf(i,k,j) - &
muv(i,j) * ( dcoef * dampcoef ) * &
( v(i,k,j) - v00(k) )
END DO
END DO
END DO
! End adjustment of v.
!-----------------------------------------------------------------------
!-----------------------------------------------------------------------
! Adjust w to base state.
DO j = jts, MIN( jte, jde-1 )
DO i = its, MIN( ite, ide-1 )
ztop = ( phb(i,kde,j) + ph(i,kde,j) ) / g
DO k = kts, MIN( kte, kde )
z = ( phb(i,k,j) + ph(i,k,j) ) / g
IF ( z >= (ztop-zdamp) ) THEN
dcoef = 1.0 - MIN( 1.0, ( ztop - z ) / zdamp )
dcoef = ( SIN( 0.5 * pii * dcoef ) )**2
rw_tendf(i,k,j) = rw_tendf(i,k,j) - &
mut(i,j) * ( dcoef * dampcoef ) * w(i,k,j)
END IF
END DO
END DO
END DO
! End adjustment of w.
!-----------------------------------------------------------------------
!-----------------------------------------------------------------------
! Adjust potential temperature to base state.
DO j = jts, MIN( jte, jde-1 )
DO i = its, MIN( ite, ide-1 )
! Get height at top of model
ztop = ( phb(i,kde,j) + ph(i,kde,j) ) / g
! Find bottom of damping layer
k1 = ktf
z = ztop
DO WHILE( z >= (ztop-zdamp) )
z = 0.5 * ( phb(i,k1,j) + phb(i,k1+1,j) + &
ph(i,k1,j) + ph(i,k1+1,j) ) / g
z00(k1) = z
k1 = k1 - 1
ENDDO
k1 = k1 + 2
! Get reference state at model levels
DO k = k1, ktf
k2 = ktf
DO WHILE( z_base(k2) .gt. z00(k) )
k2 = k2 - 1
ENDDO
if(k2+1.gt.ktf)then
t00(k) = t_base(k2) + ( t_base(k2) - t_base(k2-1) ) &
* ( z00(k) - z_base(k2) ) &
/ ( z_base(k2) - z_base(k2-1) )
else
t00(k) = t_base(k2) + ( t_base(k2+1) - t_base(k2) ) &
* ( z00(k) - z_base(k2) ) &
/ ( z_base(k2+1) - z_base(k2) )
endif
ENDDO
! Apply the Rayleigh damper
DO k = k1, ktf
dcoef = 1.0 - MIN( 1.0, ( ztop - z00(k) ) / zdamp )
dcoef = (SIN( 0.5 * pii * dcoef ) )**2
t_tendf(i,k,j) = t_tendf(i,k,j) - &
mut(i,j) * ( dcoef * dampcoef ) * &
( t(i,k,j) - t00(k) )
END DO
END DO
END DO
! End adjustment of potential temperature.
!-----------------------------------------------------------------------
END SUBROUTINE rk_rayleigh_damp
!==============================================================================
!==============================================================================
SUBROUTINE theta_relaxation( t_tendf, t, t_init, & 1
mut, ph, phb, &
t_base, z_base, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
! Purpose: Newtonian relaxation on potential temperature. Serves two
! purposes: 1) to mimic atmospheric radiation in a simple
! manner, and 2) to keep the vertical profile of temperature
! close to the initial (base-state) profile, which is useful
! for certain idealized applications.
! Reference: Rotunno and Emanuel, 1987, JAS, p. 546
!-----------------------------------------------------------------------
! Begin declarations.
IMPLICIT NONE
INTEGER, INTENT( IN ) &
:: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
REAL, DIMENSION( ims:ime, kms:kme, jms:jme ), INTENT( INOUT ) &
:: t_tendf
REAL, DIMENSION( ims:ime, kms:kme, jms:jme ), INTENT( IN ) &
:: t, t_init, ph, phb
REAL, DIMENSION( ims:ime, jms:jme ), INTENT( IN ) &
:: mut
REAL, DIMENSION( kms:kme ) , INTENT(IN ) &
:: t_base, z_base
! Local variables.
INTEGER :: i, j, k, ktf, k2
REAL :: tau_r , rmax , rmin , inv_tau_r , inv_g , rterm
REAL, DIMENSION( kms:kme ) :: z00,t00
! End declarations.
!-----------------------------------------------------------------------
! set tau_r to 12 h, following RE87
tau_r = 12.0*3600.0
! limit rterm to +/- 2 K/day
rmax = 2.0/86400.0
rmin = -rmax
ktf = MIN( kte, kde-1 )
inv_tau_r = 1.0/tau_r
inv_g = 1.0/g
!-----------------------------------------------------------------------
! Adjust potential temperature to base state.
DO j = jts, MIN( jte, jde-1 )
DO i = its, MIN( ite, ide-1 )
! Get height of model levels:
DO k = kts, ktf
z00(k) = 0.5 * ( phb(i,k,j) + phb(i,k+1,j) + &
ph(i,k,j) + ph(i,k+1,j) ) * inv_g
ENDDO
! Get reference state:
DO k = kts, ktf
k2 = ktf
DO WHILE( z_base(k2) .gt. z00(k) .and. k2 .gt. 1 )
k2 = k2 - 1
ENDDO
if(k2+1.gt.ktf)then
t00(k) = t_base(k2) + ( t_base(k2) - t_base(k2-1) ) &
* ( z00(k) - z_base(k2) ) &
/ ( z_base(k2) - z_base(k2-1) )
else
t00(k) = t_base(k2) + ( t_base(k2+1) - t_base(k2) ) &
* ( z00(k) - z_base(k2) ) &
/ ( z_base(k2+1) - z_base(k2) )
endif
ENDDO
! Apply the RE87 R term:
DO k = kts, ktf
rterm = -( t(i,k,j) - t00(k) )*inv_tau_r
! limit rterm:
rterm = min( rterm , rmax )
rterm = max( rterm , rmin )
t_tendf(i,k,j) = t_tendf(i,k,j) + mut(i,j)*rterm
END DO
END DO
END DO
END SUBROUTINE theta_relaxation
!==============================================================================
!==============================================================================
SUBROUTINE sixth_order_diffusion( name, field, tendency, mu, dt, & 5
config_flags, &
diff_6th_opt, diff_6th_factor, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
! History: 14 Nov 2006 Name of variable changed by Jason Knievel
! 07 Jun 2006 Revised and generalized by Jason Knievel
! 25 Apr 2005 Original code by Jason Knievel, NCAR
! Purpose: Apply 6th-order, monotonic (flux-limited), numerical
! diffusion to 3-d velocity and to scalars.
! References: Ming Xue (MWR Aug 2000)
! Durran ("Numerical Methods for Wave Equations..." 1999)
! George Bryan (personal communication)
!------------------------------------------------------------------------------
! Begin: Declarations.
IMPLICIT NONE
INTEGER, INTENT(IN) &
:: ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte
TYPE(grid_config_rec_type), INTENT(IN) &
:: config_flags
REAL, DIMENSION( ims:ime, kms:kme, jms:jme ), INTENT(INOUT) &
:: tendency
REAL, DIMENSION( ims:ime, kms:kme, jms:jme ), INTENT(IN) &
:: field
REAL, DIMENSION( ims:ime , jms:jme ), INTENT(IN) &
:: mu
REAL, INTENT(IN) &
:: dt
REAL, INTENT(IN) &
:: diff_6th_factor
INTEGER, INTENT(IN) &
:: diff_6th_opt
CHARACTER(LEN=1) , INTENT(IN) &
:: name
INTEGER &
:: i, j, k, &
i_start, i_end, &
j_start, j_end, &
k_start, k_end, &
ktf
REAL &
:: dflux_x_p0, dflux_y_p0, &
dflux_x_p1, dflux_y_p1, &
tendency_x, tendency_y, &
mu_avg_p0, mu_avg_p1, &
diff_6th_coef
LOGICAL &
:: specified
! End: Declarations.
!------------------------------------------------------------------------------
!------------------------------------------------------------------------------
! Begin: Translate the diffusion factor into a diffusion coefficient. See
! Durran's text, section 2.4.3, then adjust for sixth-order diffusion (not
! fourth) and for diffusion in two dimensions (not one). For reference, a
! factor of 1.0 would mean complete diffusion of a 2dx wave in one time step,
! although application of the flux limiter reduces somewhat the effects of
! diffusion for a given coefficient.
diff_6th_coef = diff_6th_factor * 0.015625 / ( 2.0 * dt )
! End: Translate diffusion factor.
!------------------------------------------------------------------------------
!------------------------------------------------------------------------------
! Begin: Assign limits of spatial loops depending on variable to be diffused.
! The halo regions are already filled with values by the time this subroutine
! is called, which allows the stencil to extend beyond the domains' edges.
ktf = MIN( kte, kde-1 )
IF ( name .EQ. 'u' ) THEN
i_start = its
i_end = ite
j_start = jts
j_end = MIN(jde-1,jte)
k_start = kts
k_end = ktf
ELSE IF ( name .EQ. 'v' ) THEN
i_start = its
i_end = MIN(ide-1,ite)
j_start = jts
j_end = jte
k_start = kts
k_end = ktf
ELSE IF ( name .EQ. 'w' ) THEN
i_start = its
i_end = MIN(ide-1,ite)
j_start = jts
j_end = MIN(jde-1,jte)
k_start = kts+1
k_end = ktf
ELSE
i_start = its
i_end = MIN(ide-1,ite)
j_start = jts
j_end = MIN(jde-1,jte)
k_start = kts
k_end = ktf
ENDIF
! End: Assignment of limits of spatial loops.
!------------------------------------------------------------------------------
!------------------------------------------------------------------------------
! Begin: Loop across spatial dimensions.
DO j = j_start, j_end
DO k = k_start, k_end
DO i = i_start, i_end
!------------------------------------------------------------------------------
! Begin: Diffusion in x (i index).
! Calculate the diffusive flux in x direction (from Xue's eq. 3).
dflux_x_p0 = ( 10.0 * ( field(i, k,j) - field(i-1,k,j) ) &
- 5.0 * ( field(i+1,k,j) - field(i-2,k,j) ) &
+ ( field(i+2,k,j) - field(i-3,k,j) ) )
dflux_x_p1 = ( 10.0 * ( field(i+1,k,j) - field(i ,k,j) ) &
- 5.0 * ( field(i+2,k,j) - field(i-1,k,j) ) &
+ ( field(i+3,k,j) - field(i-2,k,j) ) )
! If requested in the namelist (diff_6th_opt=2), prohibit up-gradient diffusion
! (variation on Xue's eq. 10).
IF ( diff_6th_opt .EQ. 2 ) THEN
IF ( dflux_x_p0 * ( field(i ,k,j)-field(i-1,k,j) ) .LE. 0.0 ) THEN
dflux_x_p0 = 0.0
END IF
IF ( dflux_x_p1 * ( field(i+1,k,j)-field(i ,k,j) ) .LE. 0.0 ) THEN
dflux_x_p1 = 0.0
END IF
END IF
! Apply 6th-order diffusion in x direction.
IF ( name .EQ. 'u' ) THEN
mu_avg_p0 = mu(i-1,j)
mu_avg_p1 = mu(i ,j)
ELSE IF ( name .EQ. 'v' ) THEN
mu_avg_p0 = 0.25 * ( &
mu(i-1,j-1) + &
mu(i ,j-1) + &
mu(i-1,j ) + &
mu(i ,j ) )
mu_avg_p1 = 0.25 * ( &
mu(i ,j-1) + &
mu(i+1,j-1) + &
mu(i ,j ) + &
mu(i+1,j ) )
ELSE
mu_avg_p0 = 0.5 * ( &
mu(i-1,j) + &
mu(i ,j) )
mu_avg_p1 = 0.5 * ( &
mu(i ,j) + &
mu(i+1,j) )
END IF
tendency_x = diff_6th_coef * &
( ( mu_avg_p1 * dflux_x_p1 ) - ( mu_avg_p0 * dflux_x_p0 ) )
! End: Diffusion in x.
!------------------------------------------------------------------------------
!------------------------------------------------------------------------------
! Begin: Diffusion in y (j index).
! Calculate the diffusive flux in y direction (from Xue's eq. 3).
dflux_y_p0 = ( 10.0 * ( field(i,k,j ) - field(i,k,j-1) ) &
- 5.0 * ( field(i,k,j+1) - field(i,k,j-2) ) &
+ ( field(i,k,j+2) - field(i,k,j-3) ) )
dflux_y_p1 = ( 10.0 * ( field(i,k,j+1) - field(i,k,j ) ) &
- 5.0 * ( field(i,k,j+2) - field(i,k,j-1) ) &
+ ( field(i,k,j+3) - field(i,k,j-2) ) )
! If requested in the namelist (diff_6th_opt=2), prohibit up-gradient diffusion
! (variation on Xue's eq. 10).
IF ( diff_6th_opt .EQ. 2 ) THEN
IF ( dflux_y_p0 * ( field(i,k,j )-field(i,k,j-1) ) .LE. 0.0 ) THEN
dflux_y_p0 = 0.0
END IF
IF ( dflux_y_p1 * ( field(i,k,j+1)-field(i,k,j ) ) .LE. 0.0 ) THEN
dflux_y_p1 = 0.0
END IF
END IF
! Apply 6th-order diffusion in y direction.
IF ( name .EQ. 'u' ) THEN
mu_avg_p0 = 0.25 * ( &
mu(i-1,j-1) + &
mu(i ,j-1) + &
mu(i-1,j ) + &
mu(i ,j ) )
mu_avg_p1 = 0.25 * ( &
mu(i-1,j ) + &
mu(i ,j ) + &
mu(i-1,j+1) + &
mu(i ,j+1) )
ELSE IF ( name .EQ. 'v' ) THEN
mu_avg_p0 = mu(i,j-1)
mu_avg_p1 = mu(i,j )
ELSE
mu_avg_p0 = 0.5 * ( &
mu(i,j-1) + &
mu(i,j ) )
mu_avg_p1 = 0.5 * ( &
mu(i,j ) + &
mu(i,j+1) )
END IF
tendency_y = diff_6th_coef * &
( ( mu_avg_p1 * dflux_y_p1 ) - ( mu_avg_p0 * dflux_y_p0 ) )
! End: Diffusion in y.
!------------------------------------------------------------------------------
!------------------------------------------------------------------------------
! Begin: Combine diffusion in x and y.
tendency(i,k,j) = tendency(i,k,j) + tendency_x + tendency_y
! End: Combine diffusion in x and y.
!------------------------------------------------------------------------------
ENDDO
ENDDO
ENDDO
! End: Loop across spatial dimensions.
!------------------------------------------------------------------------------
END SUBROUTINE sixth_order_diffusion
!==============================================================================
!==============================================================================
END MODULE module_big_step_utilities_em