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module_small_step_em.F
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!WRF:MODEL_LAYER:DYNAMICS
!
! SMALL_STEP code for the geometric height coordinate model
!
!---------------------------------------------------------------------------
MODULE module_small_step_em
USE module_configure
USE module_model_constants
CONTAINS
SUBROUTINE small_step_prep( u_1, u_2, v_1, v_2, w_1, w_2, &
t_1, t_2, ph_1, ph_2, &
mub, mu_1, mu_2, &
muu, muus, muv, muvs, &
mut, muts, mudf, &
c1h, c2h, c1f, c2f, &
c3h, c4h, c3f, c4f, &
u_save, v_save, w_save, &
t_save, ph_save, mu_save, &
ww, ww_save, &
c2a, pb, p, alt, &
msfux, msfuy, msfvx, &
msfvx_inv, &
msfvy, msftx, msfty, &
rdx, rdy, &
rk_step, &
ids,ide, jds,jde, kds,kde, &
ims,ime, jms,jme, kms,kme, &
its,ite, jts,jte, kts,kte )
IMPLICIT NONE ! religion first
! declarations for the stuff coming in
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
INTEGER, INTENT(IN ) :: rk_step
REAL, DIMENSION(ims:ime, kms:kme, jms:jme),INTENT(INOUT) :: u_1, &
v_1, &
w_1, &
t_1, &
ph_1
REAL, DIMENSION(ims:ime, kms:kme, jms:jme),INTENT( OUT) :: u_save, &
v_save, &
w_save, &
t_save, &
ph_save
REAL, DIMENSION(ims:ime, kms:kme, jms:jme),INTENT(INOUT) :: u_2, &
v_2, &
w_2, &
t_2, &
ph_2
REAL, DIMENSION(ims:ime, kms:kme, jms:jme), INTENT( OUT) :: c2a, &
ww_save
REAL, DIMENSION(ims:ime, kms:kme, jms:jme), INTENT(IN ) :: pb, &
p, &
alt, &
ww
REAL, DIMENSION(ims:ime, jms:jme) , INTENT(INOUT) :: mu_1,mu_2
REAL, DIMENSION(ims:ime, jms:jme) , INTENT(IN ) :: mub, &
muu, &
muv, &
mut, &
msfux,&
msfuy,&
msfvx,&
msfvx_inv,&
msfvy,&
msftx,&
msfty
REAL, DIMENSION(ims:ime, jms:jme) , INTENT( OUT) :: muus, &
muvs, &
muts, &
mudf
REAL, DIMENSION(ims:ime, jms:jme) , INTENT( OUT) :: mu_save
REAL, INTENT(IN) :: rdx,rdy
REAL, DIMENSION( kms:kme ),INTENT(IN ) :: c1h, c2h, c1f, c2f, &
c3h, c4h, c3f, c4f
! local variables
INTEGER :: i, j, k
INTEGER :: i_start, i_end, j_start, j_end, k_start, k_end
INTEGER :: i_endu, j_endv
!<DESCRIPTION>
!
! small_step_prep prepares the prognostic variables for the small timestep.
! This includes switching time-levels in the arrays and computing coupled
! perturbation variables for the small timestep
! (i.e. mu*u" = mu(t)*u(t)-mu(*)*u(*); mu*u" is advanced during the small
! timesteps
!
!</DESCRIPTION>
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)
i_endu = ite
j_endv = jte
! if this is the first RK step, reset *_1 to *_2
! (we are replacing the t-dt fields with the time t fields)
IF ((rk_step == 1) ) THEN
DO j=j_start, j_end
DO i=i_start, i_end
MU_1(i,j)=MU_2(i,j)
ww_save(i,kde,j) = 0.
ww_save(i,1,j) = 0.
MUDF(i,j) = 0. ! initialize external mode div damp to zero
ENDDO
ENDDO
DO j=j_start, j_end
DO k=k_start, k_end
DO i=i_start, i_endu
u_1(i,k,j) = u_2(i,k,j)
ENDDO
ENDDO
ENDDO
DO j=j_start, j_endv
DO k=k_start, k_end
DO i=i_start, i_end
v_1(i,k,j) = v_2(i,k,j)
ENDDO
ENDDO
ENDDO
DO j=j_start, j_end
DO k=k_start, k_end
DO i=i_start, i_end
t_1(i,k,j) = t_2(i,k,j)
ENDDO
ENDDO
ENDDO
DO j=j_start, j_end
DO k=k_start, min(kde,kte)
DO i=i_start, i_end
w_1(i,k,j) = w_2(i,k,j)
ph_1(i,k,j) = ph_2(i,k,j)
ENDDO
ENDDO
ENDDO
DO j=j_start, j_end
DO i=i_start, i_end
MUTS(i,j)=MUB(i,j)+MU_2(i,j)
ENDDO
DO i=i_start, i_endu
MUUS(i,j) = MUU(i,j)
ENDDO
ENDDO
DO j=j_start, j_endv
DO i=i_start, i_end
MUVS(i,j) = MUV(i,j)
ENDDO
ENDDO
DO j=j_start, j_end
DO i=i_start, i_end
MU_SAVE(i,j)=MU_2(i,j)
MU_2(i,j)=0.
ENDDO
ENDDO
ELSE
DO j=j_start, j_end
DO i=i_start, i_end
MUTS(i,j)=MUB(i,j)+MU_1(i,j)
ENDDO
DO i=i_start, i_endu
MUUS(i,j)=0.5*(MUB(i,j)+MU_1(i,j)+MUB(i-1,j)+MU_1(i-1,j))
ENDDO
ENDDO
DO j=j_start, j_endv
DO i=i_start, i_end
MUVS(i,j)=0.5*(MUB(i,j)+MU_1(i,j)+MUB(i,j-1)+MU_1(i,j-1))
ENDDO
ENDDO
DO j=j_start, j_end
DO i=i_start, i_end
MU_SAVE(i,j)=MU_2(i,j)
MU_2(i,j)=MU_1(i,j)-MU_2(i,j)
ENDDO
ENDDO
END IF
! set up the small timestep variables
DO j=j_start, j_end
DO i=i_start, i_end
ww_save(i,kde,j) = 0.
ww_save(i,1,j) = 0.
ENDDO
ENDDO
DO j=j_start, j_end
DO k=k_start, k_end
DO i=i_start, i_end
c2a(i,k,j) = cpovcv*(pb(i,k,j)+p(i,k,j))/alt(i,k,j)
ENDDO
ENDDO
ENDDO
DO j=j_start, j_end
DO k=k_start, k_end
DO i=i_start, i_endu
u_save(i,k,j) = u_2(i,k,j)
! u coupled with my
u_2(i,k,j) = ((c1h(k)*muus(i,j)+c2h(k))*u_1(i,k,j)-(c1h(k)*muu(i,j)+c2h(k))*u_2(i,k,j))/msfuy(i,j)
ENDDO
ENDDO
ENDDO
DO j=j_start, j_endv
DO k=k_start, k_end
DO i=i_start, i_end
v_save(i,k,j) = v_2(i,k,j)
! v coupled with mx
! v_2(i,k,j) = ((c1h(k)*muvs(i,j)+c2h(k))*v_1(i,k,j)-(c1h(k)*muv(i,j)+c2h(k))*v_2(i,k,j))/msfvx(i,j)
v_2(i,k,j) = ((c1h(k)*muvs(i,j)+c2h(k))*v_1(i,k,j)-(c1h(k)*muv(i,j)+c2h(k))*v_2(i,k,j))*msfvx_inv(i,j)
ENDDO
ENDDO
ENDDO
DO j=j_start, j_end
DO k=k_start, k_end
DO i=i_start, i_end
t_save(i,k,j) = t_2(i,k,j)
t_2(i,k,j) = (c1f(k)*muts(i,j)+c2f(k))*t_1(i,k,j)-(c1f(k)*mut(i,j)+c2f(k))*t_2(i,k,j)
ENDDO
ENDDO
ENDDO
DO j=j_start, j_end
! DO k=k_start, min(kde,kte)
DO k=k_start, kde
DO i=i_start, i_end
w_save(i,k,j) = w_2(i,k,j)
! w coupled with my
w_2(i,k,j) = ((c1f(k)*muts(i,j)+c2f(k))* w_1(i,k,j)-(c1f(k)*mut(i,j)+c2f(k))* w_2(i,k,j))/msfty(i,j)
ph_save(i,k,j) = ph_2(i,k,j)
ph_2(i,k,j) = ph_1(i,k,j)-ph_2(i,k,j)
ENDDO
ENDDO
ENDDO
DO j=j_start, j_end
! DO k=k_start, min(kde,kte)
DO k=k_start, kde
DO i=i_start, i_end
ww_save(i,k,j) = ww(i,k,j)
ENDDO
ENDDO
ENDDO
END SUBROUTINE small_step_prep
!-------------------------------------------------------------------------
SUBROUTINE small_step_finish( u_2, u_1, v_2, v_1, w_2, w_1, &
t_2, t_1, ph_2, ph_1, ww, ww1, &
mu_2, mu_1, &
mut, muts, muu, muus, muv, muvs, &
c1h, c2h, c1f, c2f, &
c3h, c4h, c3f, c4f, &
u_save, v_save, w_save, &
t_save, ph_save, mu_save, &
msfux, msfuy, msfvx, msfvy, &
msftx, msfty, &
h_diabatic, &
number_of_small_timesteps,dts, &
rk_step, rk_order, &
ids,ide, jds,jde, kds,kde, &
ims,ime, jms,jme, kms,kme, &
its,ite, jts,jte, kts,kte )
IMPLICIT NONE ! religion first
! stuff passed in
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
INTEGER, INTENT(IN ) :: number_of_small_timesteps
INTEGER, INTENT(IN ) :: rk_step, rk_order
REAL, INTENT(IN ) :: dts
REAL, DIMENSION(ims:ime, kms:kme, jms:jme), INTENT(IN ) :: u_1, &
v_1, &
w_1, &
t_1, &
ww1, &
ph_1
REAL, DIMENSION(ims:ime, kms:kme, jms:jme), INTENT(INOUT) :: u_2, &
v_2, &
w_2, &
t_2, &
ww, &
ph_2
REAL, DIMENSION(ims:ime, kms:kme, jms:jme),INTENT(IN ) :: u_save, &
v_save, &
w_save, &
t_save, &
ph_save, &
h_diabatic
REAL, DIMENSION(ims:ime, jms:jme), INTENT(INOUT) :: muus, muvs
REAL, DIMENSION(ims:ime, jms:jme), INTENT(INOUT) :: mu_2, mu_1
REAL, DIMENSION(ims:ime, jms:jme), INTENT(INOUT) :: mut, muts, &
muu, muv, mu_save
REAL, DIMENSION(ims:ime, jms:jme), INTENT(IN ) :: msfux, msfuy, &
msfvx, msfvy, &
msftx, msfty
REAL, DIMENSION( kms:kme ),INTENT(IN ) :: c1h, c2h, c1f, c2f, &
c3h, c4h, c3f, c4f
! local stuff
INTEGER :: i,j,k
INTEGER :: i_start, i_end, j_start, j_end, i_endu, j_endv
!<DESCRIPTION>
!
! small_step_finish reconstructs the full uncoupled prognostic variables
! from the coupled perturbation variables used in the small timesteps.
!
!</DESCRIPTION>
i_start = its
i_end = min(ite,ide-1)
j_start = jts
j_end = min(jte,jde-1)
i_endu = ite
j_endv = jte
! addition of time level t back into variables
DO j = j_start, j_endv
DO k = kds, kde-1
DO i = i_start, i_end
! v coupled with mx
v_2(i,k,j) = (msfvx(i,j)*v_2(i,k,j) + v_save(i,k,j)*(c1h(k)*muv(i,j)+c2h(k)))/(c1h(k)*muvs(i,j)+c2h(k))
ENDDO
ENDDO
ENDDO
DO j = j_start, j_end
DO k = kds, kde-1
DO i = i_start, i_endu
! u coupled with my
u_2(i,k,j) = (msfuy(i,j)*u_2(i,k,j) + u_save(i,k,j)*(c1h(k)*muu(i,j)+c2h(k)))/(c1h(k)*muus(i,j)+c2h(k))
ENDDO
ENDDO
ENDDO
DO j = j_start, j_end
DO k = kds, kde
DO i = i_start, i_end
! w coupled with my
w_2(i,k,j) = (msfty(i,j)*w_2(i,k,j) + w_save(i,k,j)*(c1f(k)*mut(i,j)+c2f(k)))/(c1f(k)*muts(i,j)+c2f(k))
ph_2(i,k,j) = ph_2(i,k,j) + ph_save(i,k,j)
ww(i,k,j) = ww(i,k,j) + ww1(i,k,j)
ENDDO
ENDDO
ENDDO
IF ( rk_step < rk_order ) THEN
DO j = j_start, j_end
DO k = kds, kde-1
DO i = i_start, i_end
t_2(i,k,j) = (t_2(i,k,j) + t_save(i,k,j)*(c1f(k)*mut(i,j)+c2f(k)))/(c1f(k)*muts(i,j)+c2f(k))
ENDDO
ENDDO
ENDDO
ELSE
DO j = j_start, j_end
DO k = kds, kde-1
DO i = i_start, i_end
t_2(i,k,j) = (t_2(i,k,j) - dts*number_of_small_timesteps*(c1f(k)*mut(i,j)+c2f(k))*h_diabatic(i,k,j) &
+ t_save(i,k,j)*(c1f(k)*mut(i,j)+c2f(k)))/(c1f(k)*muts(i,j)+c2f(k))
ENDDO
ENDDO
ENDDO
ENDIF
DO j = j_start, j_end
DO i = i_start, i_end
mu_2(i,j) = mu_2(i,j) + mu_save(i,j)
ENDDO
ENDDO
END SUBROUTINE small_step_finish
!-----------------------------------------------------------------------
SUBROUTINE calc_p_rho( al, p, ph, &
alt, t_2, t_1, c2a, pm1, &
mu, mut, &
c1h, c2h, c1f, c2f, &
c3h, c4h, c3f, c4f, &
znu, t0, &
rdnw, dnw, smdiv, &
non_hydrostatic, step, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its,ite, jts,jte, kts,kte )
IMPLICIT NONE ! religion first
! declarations for the stuff coming in
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
INTEGER, INTENT(IN ) :: step
REAL, DIMENSION(ims:ime, kms:kme, jms:jme),INTENT( OUT) :: al, &
p
REAL, DIMENSION(ims:ime, kms:kme, jms:jme),INTENT(IN ) :: alt, &
t_2, &
t_1, &
c2a
REAL, DIMENSION(ims:ime, kms:kme, jms:jme),INTENT(INOUT) :: ph, pm1
REAL, DIMENSION(ims:ime, jms:jme) , INTENT(IN ) :: mu, &
mut
REAL, DIMENSION(kms:kme) , INTENT(IN ) :: dnw, &
rdnw, &
znu
REAL, INTENT(IN ) :: t0, smdiv
REAL, DIMENSION( kms:kme ),INTENT(IN ) :: c1h, c2h, c1f, c2f, &
c3h, c4h, c3f, c4f
LOGICAL, INTENT(IN ) :: non_hydrostatic
! local variables
INTEGER :: i, j, k
INTEGER :: i_start, i_end, j_start, j_end, k_start, k_end
REAL :: ptmp
!<DESCRIPTION>
!
! For the nonhydrostatic option,
! calc_p_rho computes the perturbation inverse density and
! perturbation pressure from the hydrostatic relation and the
! linearized equation of state, respectively.
!
! For the hydrostatic option,
! calc_p_rho computes the perturbation pressure, perturbation density,
! and perturbation geopotential
! from the vertical coordinate definition, linearized equation of state
! and the hydrostatic relation, respectively.
!
! forward weighting of the pressure (divergence damping) is also
! computed here.
!
!</DESCRIPTION>
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)
IF (non_hydrostatic) THEN
DO j=j_start, j_end
DO k=k_start, k_end
DO i=i_start, i_end
! al computation is all dry, so ok with moisture
al(i,k,j)=-1./(c1h(k)*Mut(i,j)+c2h(k))*(alt(i,k,j)*(c1h(k)*mu(i,j)) &
+rdnw(k)*(ph(i,k+1,j)-ph(i,k,j)))
! this is temporally linearized p, no moisture correction needed
p(i,k,j)=c2a(i,k,j)*(alt(i,k,j)*(t_2(i,k,j)-(c1h(k)*mu(i,j))*t_1(i,k,j)) &
/((c1h(k)*Mut(i,j)+c2h(k))*(t0+t_1(i,k,j)))-al (i,k,j))
ENDDO
ENDDO
ENDDO
ELSE ! hydrostatic calculation
DO j=j_start, j_end
DO k=k_start, k_end
DO i=i_start, i_end
p(i,k,j)=MU(i,j)*c3h(k)
al(i,k,j)=alt(i,k,j)*(t_2(i,k,j)-(c1h(k)*mu(i,j))*t_1(i,k,j)) &
/((c1h(k)*Mut(i,j)+c2h(k))*(t0+t_1(i,k,j)))-p(i,k,j)/c2a(i,k,j)
ph(i,k+1,j)=ph(i,k,j)-dnw(k)*((c1h(k)*Mut(i,j)+c2h(k))*al (i,k,j) &
+(c1h(k)*mu(i,j))*alt(i,k,j))
ENDDO
ENDDO
ENDDO
END IF
! divergence damping setup
IF (step == 0) then ! we're initializing small timesteps
DO j=j_start, j_end
DO k=k_start, k_end
DO i=i_start, i_end
pm1(i,k,j)=p(i,k,j)
ENDDO
ENDDO
ENDDO
ELSE ! we're in the small timesteps
DO j=j_start, j_end ! and adding div damping component
DO k=k_start, k_end
DO i=i_start, i_end
ptmp = p(i,k,j)
p(i,k,j) = p(i,k,j) + smdiv*(p(i,k,j)-pm1(i,k,j))
pm1(i,k,j) = ptmp
ENDDO
ENDDO
ENDDO
END IF
END SUBROUTINE calc_p_rho
!----------------------------------------------------------------------
SUBROUTINE calc_coef_w( a,alpha,gamma, &
mut, &
c1h, c2h, c1f, c2f, &
c3h, c4h, c3f, c4f, &
cqw, &
rdn, rdnw, c2a, &
dts, g, epssm, top_lid, &
ids,ide, jds,jde, kds,kde, & ! domain dims
ims,ime, jms,jme, kms,kme, & ! memory dims
its,ite, jts,jte, kts,kte ) ! tile dims
IMPLICIT NONE ! religion first
! passed in through the call
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
LOGICAL, INTENT(IN ) :: top_lid
REAL, DIMENSION(ims:ime, kms:kme, jms:jme), INTENT(IN ) :: c2a, &
cqw
REAL, DIMENSION(ims:ime, kms:kme, jms:jme), INTENT(INOUT) :: alpha, &
gamma, &
a
REAL, DIMENSION(ims:ime, jms:jme), INTENT(IN ) :: mut
REAL, DIMENSION(kms:kme), INTENT(IN ) :: rdn, &
rdnw
REAL, INTENT(IN ) :: epssm, &
dts, &
g
REAL, DIMENSION( kms:kme ),INTENT(IN ) :: c1h, c2h, c1f, c2f, &
c3h, c4h, c3f, c4f
! Local stack data.
REAL, DIMENSION(ims:ime) :: cof
REAL :: b, c
REAL :: muthmutf_kk, muthmutf_km1k, muthmutf_kkp1
INTEGER :: i, j, k, kk, i_start, i_end, j_start, j_end, k_start, k_end
INTEGER :: ij, ijp, ijm, lid_flag
!<DESCRIPTION>
!
! calc_coef_w calculates the coefficients needed for the
! implicit solution of the vertical momentum and geopotential equations.
! This requires solution of a tri-diagonal equation.
!
!</DESCRIPTION>
i_start = its
i_end = min(ite,ide-1)
j_start = jts
j_end = min(jte,jde-1)
k_start = kts
k_end = kte-1
lid_flag=1
IF(top_lid)lid_flag=0
outer_j_loop: DO j = j_start, j_end
k = kde-1
DO i = i_start, i_end
cof(i) = (.5*dts*g*(1.+epssm))**2
a(i, 2 ,j) = 0.
a(i,kde,j) =-2.*cof(i)*rdnw(kde-1)**2*c2a(i,kde-1,j)*lid_flag/((c1h(k)*MUT(i,j)+c2h(k))*(c1f(k)*MUT(i,j)+c2f(k)))
gamma(i,1 ,j) = 0.
ENDDO
DO kk=3,kde-1
k=kk-1
DO i=i_start, i_end
a(i,kk,j) = -cqw(i,kk,j)*cof(i)*rdn(kk)* rdnw(kk-1)*c2a(i,kk-1,j)/((c1h(k)*MUT(i,j)+c2h(k))*(c1f(k)*MUT(i,j)+c2f(k)))
ENDDO
ENDDO
DO k=2,kde-1
DO i=i_start, i_end
b = 1.+cqw(i,k,j)*cof(i)*rdn(k)*(rdnw(k )*c2a(i,k, j)/((c1h(k)*MUT(i,j)+c2h(k))*(c1f(k)*MUT(i,j)+c2f(k))) &
+rdnw(k-1)*c2a(i,k-1,j)/((c1h(k-1)*MUT(i,j)+c2h(k-1))*(c1f(k)*MUT(i,j)+c2f(k))) )
c = -cqw(i,k,j)*cof(i)*rdn(k)*rdnw(k )*c2a(i,k,j )/((c1h(k)*MUT(i,j)+c2h(k))*(c1f(k+1)*MUT(i,j)+c2f(k+1)))
alpha(i,k,j) = 1./(b-a(i,k,j)*gamma(i,k-1,j))
gamma(i,k,j) = c*alpha(i,k,j)
ENDDO
ENDDO
k=kde
DO i=i_start, i_end
b = 1.+2.*cof(i)*rdnw(kde-1)**2*c2a(i,kde-1,j)/((c1h(k-1)*MUT(i,j)+c2h(k-1))*(c1f(k)*MUT(i,j)+c2f(k)))
c = 0.
alpha(i,kde,j) = 1./(b-a(i,kde,j)*gamma(i,kde-1,j))
gamma(i,kde,j) = c*alpha(i,kde,j)
ENDDO
ENDDO outer_j_loop
END SUBROUTINE calc_coef_w
!----------------------------------------------------------------------
SUBROUTINE advance_uv ( u, ru_tend, v, rv_tend, &
p, pb, &
ph, php, alt, al, mu, &
muu, cqu, muv, cqv, mudf, &
c1h, c2h, c1f, c2f, &
c3h, c4h, c3f, c4f, &
msfux, msfuy, msfvx, &
msfvx_inv, msfvy, &
rdx, rdy, dts, &
cf1, cf2, cf3, fnm, fnp, &
emdiv, &
rdnw, config_flags, spec_zone, &
non_hydrostatic, top_lid, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE ! religion first
! stuff coming in
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
INTEGER, INTENT(IN ) :: ims,ime, jms,jme, kms,kme
INTEGER, INTENT(IN ) :: its,ite, jts,jte, kts,kte
INTEGER, INTENT(IN ) :: spec_zone
REAL, DIMENSION( ims:ime , kms:kme, jms:jme ), &
INTENT(INOUT) :: &
u, &
v
REAL, DIMENSION( ims:ime , kms:kme, jms:jme ), &
INTENT(IN ) :: &
ru_tend, &
rv_tend, &
ph, &
php, &
p, &
pb, &
alt, &
al, &
cqu, &
cqv
REAL, DIMENSION( ims:ime , jms:jme ), INTENT(IN ) :: muu, &
muv, &
mu, &
mudf
REAL, DIMENSION( kms:kme ), INTENT(IN ) :: fnm, &
fnp , &
rdnw
REAL, DIMENSION( ims:ime , jms:jme ), INTENT(IN ) :: msfux, &
msfuy, &
msfvx, &
msfvy, &
msfvx_inv
REAL, INTENT(IN ) :: rdx, &
rdy, &
dts, &
cf1, &
cf2, &
cf3, &
emdiv
REAL, DIMENSION( kms:kme ),INTENT(IN ) :: c1h, c2h, c1f, c2f, &
c3h, c4h, c3f, c4f
! Local 3d array from the stack (note tile size)
REAL, DIMENSION (its:ite, kts:kte) :: dpn, dpxy
REAL, DIMENSION (its:ite) :: mudf_xy
REAL :: dx, dy
INTEGER :: i,j,k, i_start, i_end, j_start, j_end, k_start, k_end
INTEGER :: i_endu, j_endv, k_endw
INTEGER :: i_start_up, i_end_up, j_start_up, j_end_up
INTEGER :: i_start_vp, i_end_vp, j_start_vp, j_end_vp
INTEGER :: i_start_u_tend, i_end_u_tend, j_start_v_tend, j_end_v_tend
!<DESCRIPTION>
!
! advance_uv advances the explicit perturbation horizontal momentum
! equations (u,v) by adding in the large-timestep tendency along with
! the small timestep pressure gradient tendency.
!
!</DESCRIPTION>
! now, the real work.
! set the loop bounds taking into account boundary conditions.
IF( config_flags%nested .or. config_flags%specified ) THEN
i_start = max( its,ids+spec_zone )
i_end = min( ite,ide-spec_zone-1 )
j_start = max( jts,jds+spec_zone )
j_end = min( jte,jde-spec_zone-1 )
k_start = kts
k_end = min( kte, kde-1 )
i_endu = min( ite,ide-spec_zone )
j_endv = min( jte,jde-spec_zone )
k_endw = k_end
IF( config_flags%periodic_x) THEN
i_start = its
i_end = min(ite,ide-1)
i_endu = ite
ENDIF
ELSE
i_start = its
i_end = min(ite,ide-1)
j_start = jts
j_end = min(jte,jde-1)
k_start = kts
k_end = kte-1
i_endu = ite
j_endv = jte
k_endw = k_end
ENDIF
i_start_up = i_start
i_end_up = i_endu
j_start_up = j_start
j_end_up = j_end
i_start_vp = i_start
i_end_vp = i_end
j_start_vp = j_start
j_end_vp = j_endv
IF ( (config_flags%open_xs .or. &
config_flags%symmetric_xs ) &
.and. (its == ids) ) &
i_start_up = i_start_up + 1
IF ( (config_flags%open_xe .or. &
config_flags%symmetric_xe ) &
.and. (ite == ide) ) &
i_end_up = i_end_up - 1
IF ( (config_flags%open_ys .or. &
config_flags%symmetric_ys .or. &
config_flags%polar ) &
.and. (jts == jds) ) &
j_start_vp = j_start_vp + 1
IF ( (config_flags%open_ye .or. &
config_flags%symmetric_ye .or. &
config_flags%polar ) &
.and. (jte == jde) ) &
j_end_vp = j_end_vp - 1
i_start_u_tend = i_start
i_end_u_tend = i_endu
j_start_v_tend = j_start
j_end_v_tend = j_endv
IF ( config_flags%symmetric_xs .and. (its == ids) ) &
i_start_u_tend = i_start_u_tend+1
IF ( config_flags%symmetric_xe .and. (ite == ide) ) &
i_end_u_tend = i_end_u_tend-1
IF ( config_flags%symmetric_ys .and. (jts == jds) ) &
j_start_v_tend = j_start_v_tend+1
IF ( config_flags%symmetric_ye .and. (jte == jde) ) &
j_end_v_tend = j_end_v_tend-1
dx = 1./rdx
dy = 1./rdy
! start real calculations.
! first, u
u_outer_j_loop: DO j = j_start, j_end
DO k = k_start, k_end
DO i = i_start_u_tend, i_end_u_tend
u(i,k,j) = u(i,k,j) + dts*ru_tend(i,k,j)
ENDDO
ENDDO
DO i = i_start_up, i_end_up
MUDF_XY(i)= -emdiv*dx*(MUDF(i,j)-MUDF(i-1,j))/msfuy(i,j)
ENDDO
DO k = k_start, k_end
DO i = i_start_up, i_end_up
! Comments on map scale factors:
! x pressure gradient: ADT eqn 44, penultimate term on RHS
! = -(mx/my)*(mu/rho)*partial dp/dx
! [i.e., first rho->mu; 2nd still rho; alpha=1/rho]
! Klemp et al. splits into 2 terms:
! mu alpha partial dp/dx + partial dp/dnu * partial dphi/dx
! then into 4 terms:
! mu alpha partial dp'/dx + nu mu alpha' partial dmubar/dx +
! + mu partial dphi/dx + partial dphi'/dx * (partial dp'/dnu - mu')
!
! first 3 terms:
! ph, alt, p, al, pb not coupled
! since we want tendency to fit ADT eqn 44 (coupled) we need to
! multiply by (mx/my):
!
dpxy(i,k)= (msfux(i,j)/msfuy(i,j))*.5*rdx*(c1h(k)*muu(i,j)+c2h(k))*( &
((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)) )
ENDDO
ENDDO
IF (non_hydrostatic) THEN
DO i = i_start_up, i_end_up
dpn(i,1) = .5*( cf1*(p(i,1,j)+p(i-1,1,j)) &
+cf2*(p(i,2,j)+p(i-1,2,j)) &
+cf3*(p(i,3,j)+p(i-1,3,j)) )
dpn(i,kde) = 0.
ENDDO
IF (top_lid) THEN
DO i = i_start_up, i_end_up
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 = k_start+1, k_end
DO i = i_start_up, i_end_up
dpn(i,k) = .5*( fnm(k)*(p(i,k ,j)+p(i-1,k ,j)) &
+fnp(k)*(p(i,k-1,j)+p(i-1,k-1,j)) )
ENDDO
ENDDO
! Comments on map scale factors:
! 4th term:
! php, dpn, mu not coupled
! since we want tendency to fit ADT eqn 44 (coupled) we need to
! multiply by (mx/my):
DO k = k_start, k_end
DO i = i_start_up, i_end_up
dpxy(i,k)=dpxy(i,k) + (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*((c1h(k)*mu(i-1,j))+(c1h(k)*mu(i,j))))
ENDDO
ENDDO
END IF
DO k = k_start, k_end
DO i = i_start_up, i_end_up
u(i,k,j)=u(i,k,j)-dts*cqu(i,k,j)*dpxy(i,k)+(c1h(k)*mudf_xy(i))
ENDDO
ENDDO
ENDDO u_outer_j_loop
! now v
v_outer_j_loop: DO j = j_start_v_tend, j_end_v_tend
DO k = k_start, k_end
DO i = i_start, i_end
v(i,k,j) = v(i,k,j) + dts*rv_tend(i,k,j)
ENDDO
ENDDO
DO i = i_start, i_end
MUDF_XY(i)= -emdiv*dy*(MUDF(i,j)-MUDF(i,j-1))*msfvx_inv(i,j)
ENDDO
IF ( ( j >= j_start_vp) &
.and.( j <= j_end_vp ) ) THEN
DO k = k_start, k_end
DO i = i_start, i_end
! Comments on map scale factors:
! y pressure gradient: ADT eqn 45, penultimate term on RHS
! = -(my/mx)*(mu/rho)*partial dp/dy
! [i.e., first rho->mu; 2nd still rho; alpha=1/rho]
! Klemp et al. splits into 2 terms:
! mu alpha partial dp/dy + partial dp/dnu * partial dphi/dy
! then into 4 terms:
! mu alpha partial dp'/dy + nu mu alpha' partial dmubar/dy +
! + mu partial dphi/dy + partial dphi'/dy * (partial dp'/dnu - mu')
!
! first 3 terms:
! ph, alt, p, al, pb not coupled
! since we want tendency to fit ADT eqn 45 (coupled) we need to
! multiply by (my/mx):
! mudf_xy is NOT a map scale factor coupling
! it is some sort of divergence damping
dpxy(i,k)= (msfvy(i,j)/msfvx(i,j))*.5*rdy*(c1h(k)*muv(i,j)+c2h(k))*( &
((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)) )
ENDDO
ENDDO
IF (non_hydrostatic) THEN
DO i = i_start, i_end
dpn(i,1) = .5*( cf1*(p(i,1,j)+p(i,1,j-1)) &
+cf2*(p(i,2,j)+p(i,2,j-1)) &
+cf3*(p(i,3,j)+p(i,3,j-1)) )
dpn(i,kde) = 0.
ENDDO
IF (top_lid) THEN
DO i = i_start, i_end
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 = k_start+1, k_end
DO i = i_start, i_end
dpn(i,k) = .5*( fnm(k)*(p(i,k ,j)+p(i,k ,j-1)) &
+fnp(k)*(p(i,k-1,j)+p(i,k-1,j-1)) )
ENDDO
ENDDO
! Comments on map scale factors:
! 4th term:
! php, dpn, mu not coupled
! since we want tendency to fit ADT eqn 45 (coupled) we need to
! multiply by (my/mx):
DO k = k_start, k_end
DO i = i_start, i_end
dpxy(i,k)=dpxy(i,k) + (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*((c1h(k)*mu(i,j-1))+(c1h(k)*mu(i,j))))
ENDDO
ENDDO
END IF
DO k = k_start, k_end
DO i = i_start, i_end
v(i,k,j)=v(i,k,j)-dts*cqv(i,k,j)*dpxy(i,k)+(c1h(k)*mudf_xy(i))
ENDDO
ENDDO
END IF
ENDDO v_outer_j_loop
! The check for j_start_vp and j_end_vp makes sure that the edges in v
! are not updated. Let's add a polar boundary condition check here for
! safety to ensure that v at the poles never gets to be non-zero in the
! small time steps.
IF (config_flags%polar) THEN
IF (jts == jds) THEN
DO k = k_start, k_end
DO i = i_start, i_end
v(i,k,jds) = 0.
ENDDO
ENDDO
END IF
IF (jte == jde) THEN
DO k = k_start, k_end
DO i = i_start, i_end
v(i,k,jde) = 0.
ENDDO
ENDDO
END IF
END IF
END SUBROUTINE advance_uv
!---------------------------------------------------------------------
SUBROUTINE advance_mu_t( ww, ww_1, u, u_1, v, v_1, &
mu, mut, muave, muts, muu, muv, mudf,&
c1h, c2h, c1f, c2f, &
c3h, c4h, c3f, c4f, &
uam, vam, wwam, t, t_1, &
t_ave, ft, mu_tend, &
rdx, rdy, dts, epssm, &
dnw, fnm, fnp, rdnw, &
msfux, msfuy, msfvx, msfvx_inv, &
msfvy, msftx, msfty, &
step, config_flags, &
ids, ide, jds, jde, kds, kde, &
ims, ime, jms, jme, kms, kme, &
its, ite, jts, jte, kts, kte )
IMPLICIT NONE ! religion first
! stuff coming in
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
INTEGER, INTENT(IN ) :: step
REAL, DIMENSION( ims:ime , kms:kme, jms:jme ), &
INTENT(IN ) :: &
u, &
v, &
u_1, &
v_1, &
t_1, &
ft
REAL, DIMENSION( ims:ime , kms:kme, jms:jme ), &
INTENT(INOUT) :: &
ww, &