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nh_utils.F90
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!***********************************************************************
!* GNU Lesser General Public License
!*
!* This file is part of the FV3 dynamical core.
!*
!* The FV3 dynamical core is free software: you can redistribute it
!* and/or modify it under the terms of the
!* GNU Lesser General Public License as published by the
!* Free Software Foundation, either version 3 of the License, or
!* (at your option) any later version.
!*
!* The FV3 dynamical core is distributed in the hope that it will be
!* useful, but WITHOUT ANYWARRANTY; without even the implied warranty
!* of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
!* See the GNU General Public License for more details.
!*
!* You should have received a copy of the GNU Lesser General Public
!* License along with the FV3 dynamical core.
!* If not, see <http://www.gnu.org/licenses/>.
!***********************************************************************
!>@brief The module 'nh_utils' peforms non-hydrostatic computations.
!>@author S. J. Lin, NOAA/GFDL
module nh_utils_mod
! Modules Included:
! <table>
! <tr>
! <th>Module Name</th>
! <th>Functions Included</th>
! </tr>
! <tr>
! <td>constants_mod</td>
! <td>rdgas, cp_air, grav</td>
! </tr>
! <tr>
! <td>fv_arrays_mod</td>
! <td>fv_grid_bounds_type, fv_grid_type</td>
! </tr>
! <tr>
! <tr>
! <td>sw_core_mod</td>
! <td>fill_4corners, del6_vt_flux</td>
! </tr>
! <tr>
! <td>tp_core_mod</td>
! <td>fv_tp_2d</td>
! </tr>
! </table>
#ifdef OVERLOAD_R4
use constantsR4_mod, only: rdgas, cp_air, grav
#else
use constants_mod, only: rdgas, cp_air, grav
#endif
use tp_core_mod, only: fv_tp_2d
use sw_core_mod, only: fill_4corners, del6_vt_flux
use fv_arrays_mod, only: fv_grid_bounds_type, fv_grid_type,fv_nest_BC_type_3d
#ifdef MULTI_GASES
use multi_gases_mod, only: vicpqd, vicvqd
#endif
implicit none
private
public update_dz_c, update_dz_d, nh_bc
public sim_solver, sim1_solver, sim3_solver
public sim3p0_solver, rim_2d
public Riem_Solver_c
real, parameter:: r3 = 1./3.
CONTAINS
subroutine update_dz_c(is, ie, js, je, km, ng, dt, dp0, zs, area, ut, vt, gz, ws, &
npx, npy, sw_corner, se_corner, ne_corner, nw_corner, bd, grid_type, dz_min)
! !INPUT PARAMETERS:
type(fv_grid_bounds_type), intent(IN) :: bd
integer, intent(in):: is, ie, js, je, ng, km, npx, npy, grid_type
logical, intent(IN):: sw_corner, se_corner, ne_corner, nw_corner
real, intent(in):: dt, dz_min
real, intent(in):: dp0(km)
real, intent(in), dimension(is-ng:ie+ng,js-ng:je+ng,km):: ut, vt
real, intent(in), dimension(is-ng:ie+ng,js-ng:je+ng):: area
real, intent(inout):: gz(is-ng:ie+ng,js-ng:je+ng,km+1)
real, intent(in ):: zs(is-ng:ie+ng, js-ng:je+ng)
real, intent( out):: ws(is-ng:ie+ng, js-ng:je+ng)
! Local Work array:
real:: gz2(is-ng:ie+ng,js-ng:je+ng)
real, dimension(is-1:ie+2,js-1:je+1):: xfx, fx
real, dimension(is-1:ie+1,js-1:je+2):: yfx, fy
real, parameter:: r14 = 1./14.
integer i, j, k
integer:: is1, ie1, js1, je1
integer:: ie2, je2
real:: rdt, top_ratio, bot_ratio, int_ratio
!--------------------------------------------------------------------
rdt = 1. / dt
top_ratio = dp0(1 ) / (dp0( 1)+dp0(2 ))
bot_ratio = dp0(km) / (dp0(km-1)+dp0(km))
is1 = is - 1
js1 = js - 1
ie1 = ie + 1
je1 = je + 1
ie2 = ie + 2
je2 = je + 2
!$OMP parallel do default(none) shared(js1,je1,is1,ie2,km,je2,ie1,ut,top_ratio,vt, &
!$OMP bot_ratio,dp0,js,je,ng,is,ie,gz,grid_type, &
!$OMP bd,npx,npy,sw_corner,se_corner,ne_corner, &
!$OMP nw_corner,area) &
!$OMP private(gz2, xfx, yfx, fx, fy, int_ratio)
do 6000 k=1,km+1
if ( k==1 ) then
do j=js1, je1
do i=is1, ie2
xfx(i,j) = ut(i,j,1) + (ut(i,j,1)-ut(i,j,2))*top_ratio
enddo
enddo
do j=js1, je2
do i=is1, ie1
yfx(i,j) = vt(i,j,1) + (vt(i,j,1)-vt(i,j,2))*top_ratio
enddo
enddo
elseif ( k==km+1 ) then
! Bottom extrapolation
do j=js1, je1
do i=is1, ie2
xfx(i,j) = ut(i,j,km) + (ut(i,j,km)-ut(i,j,km-1))*bot_ratio
! xfx(i,j) = r14*(3.*ut(i,j,km-2)-13.*ut(i,j,km-1)+24.*ut(i,j,km))
! if ( xfx(i,j)*ut(i,j,km)<0. ) xfx(i,j) = 0.
enddo
enddo
do j=js1, je2
do i=is1, ie1
yfx(i,j) = vt(i,j,km) + (vt(i,j,km)-vt(i,j,km-1))*bot_ratio
! yfx(i,j) = r14*(3.*vt(i,j,km-2)-13.*vt(i,j,km-1)+24.*vt(i,j,km))
! if ( yfx(i,j)*vt(i,j,km)<0. ) yfx(i,j) = 0.
enddo
enddo
else
int_ratio = 1./(dp0(k-1)+dp0(k))
do j=js1, je1
do i=is1, ie2
xfx(i,j) = (dp0(k)*ut(i,j,k-1)+dp0(k-1)*ut(i,j,k))*int_ratio
enddo
enddo
do j=js1, je2
do i=is1, ie1
yfx(i,j) = (dp0(k)*vt(i,j,k-1)+dp0(k-1)*vt(i,j,k))*int_ratio
enddo
enddo
endif
do j=js-ng, je+ng
do i=is-ng, ie+ng
gz2(i,j) = gz(i,j,k)
enddo
enddo
if (grid_type < 3) call fill_4corners(gz2, 1, bd, npx, npy, sw_corner, se_corner, ne_corner, nw_corner)
do j=js1, je1
do i=is1, ie2
if( xfx(i,j) > 0. ) then
fx(i,j) = gz2(i-1,j)
else
fx(i,j) = gz2(i ,j)
endif
fx(i,j) = xfx(i,j)*fx(i,j)
enddo
enddo
if (grid_type < 3) call fill_4corners(gz2, 2, bd, npx, npy, sw_corner, se_corner, ne_corner, nw_corner)
do j=js1,je2
do i=is1,ie1
if( yfx(i,j) > 0. ) then
fy(i,j) = gz2(i,j-1)
else
fy(i,j) = gz2(i,j)
endif
fy(i,j) = yfx(i,j)*fy(i,j)
enddo
enddo
do j=js1, je1
do i=is1,ie1
gz(i,j,k) = (gz2(i,j)*area(i,j) + fx(i,j)- fx(i+1,j)+ fy(i,j)- fy(i,j+1)) &
/ ( area(i,j) + xfx(i,j)-xfx(i+1,j)+yfx(i,j)-yfx(i,j+1))
enddo
enddo
6000 continue
! Enforce monotonicity of height to prevent blowup
!$OMP parallel do default(none) shared(is1,ie1,js1,je1,ws,zs,gz,rdt,km,dz_min)
do j=js1, je1
do i=is1, ie1
ws(i,j) = ( zs(i,j) - gz(i,j,km+1) ) * rdt
enddo
do k=km, 1, -1
do i=is1, ie1
gz(i,j,k) = max( gz(i,j,k), gz(i,j,k+1) + dz_min )
enddo
enddo
enddo
end subroutine update_dz_c
subroutine update_dz_d(ndif, damp, hord, is, ie, js, je, km, ng, npx, npy, area, rarea, &
dp0, zs, zh, crx, cry, xfx, yfx, ws, rdt, gridstruct, bd, lim_fac, dz_min, psm_bc)
type(fv_grid_bounds_type), intent(IN) :: bd
integer, intent(in):: is, ie, js, je, ng, km, npx, npy
integer, intent(in):: hord, psm_bc
real, intent(in) :: rdt, dz_min
real, intent(in) :: dp0(km)
real, intent(in) :: area(is-ng:ie+ng,js-ng:je+ng)
real, intent(in) :: rarea(is-ng:ie+ng,js-ng:je+ng)
real, intent(inout):: damp(km+1)
integer, intent(inout):: ndif(km+1)
real, intent(in ) :: zs(is-ng:ie+ng,js-ng:je+ng)
real, intent(inout) :: zh(is-ng:ie+ng,js-ng:je+ng,km+1)
real, intent(inout), dimension(is:ie+1,js-ng:je+ng,km):: crx, xfx
real, intent(inout), dimension(is-ng:ie+ng,js:je+1,km):: cry, yfx
real, intent(out) :: ws(is:ie,js:je)
type(fv_grid_type), intent(IN), target :: gridstruct
real, intent(in) :: lim_fac
!-----------------------------------------------------
! Local array:
real, dimension(is: ie+1, js-ng:je+ng,km+1):: crx_adv, xfx_adv
real, dimension(is-ng:ie+ng,js: je+1,km+1 ):: cry_adv, yfx_adv
real, dimension(is:ie+1,js:je ):: fx
real, dimension(is:ie ,js:je+1):: fy
real, dimension(is-ng:ie+ng+1,js-ng:je+ng ):: fx2
real, dimension(is-ng:ie+ng ,js-ng:je+ng+1):: fy2
real, dimension(is-ng:ie+ng ,js-ng:je+ng ):: wk2, z2
real:: ra_x(is:ie,js-ng:je+ng)
real:: ra_y(is-ng:ie+ng,js:je)
!--------------------------------------------------------------------
integer i, j, k, isd, ied, jsd, jed
logical:: uniform_grid
uniform_grid = .false.
damp(km+1) = damp(km)
ndif(km+1) = ndif(km)
isd = is - ng; ied = ie + ng
jsd = js - ng; jed = je + ng
if (psm_bc == 0 ) then
!$OMP parallel do default(none) shared(jsd,jed,crx,xfx,crx_adv,xfx_adv,is,ie,isd,ied, &
!$OMP km,dp0,uniform_grid,js,je,cry,yfx,cry_adv,yfx_adv)
do j=jsd,jed
call edge_profile(crx, xfx, crx_adv, xfx_adv, is, ie+1, jsd, jed, j, km, &
dp0, uniform_grid, 0)
if ( j<=je+1 .and. j>=js ) &
call edge_profile(cry, yfx, cry_adv, yfx_adv, isd, ied, js, je+1, j, km, &
dp0, uniform_grid, 0)
enddo
else
!$OMP parallel do default(none) shared(jsd,jed,crx,xfx,crx_adv,xfx_adv,is,ie,isd,ied, &
!$OMP km,dp0,uniform_grid,js,je,cry,yfx,cry_adv,yfx_adv)
do j=jsd,jed
call edge_profile_0grad(crx, xfx, crx_adv, xfx_adv, is, ie+1, jsd, jed, j, km, &
dp0, uniform_grid, 0)
if ( j<=je+1 .and. j>=js ) &
call edge_profile_0grad(cry, yfx, cry_adv, yfx_adv, isd, ied, js, je+1, j, km, &
dp0, uniform_grid, 0)
enddo
endif
!$OMP parallel do default(none) shared(is,ie,js,je,isd,ied,jsd,jed,km,area,xfx_adv,yfx_adv, &
!$OMP damp,zh,crx_adv,cry_adv,npx,npy,hord,gridstruct,bd, &
!$OMP ndif,rarea,lim_fac) &
!$OMP private(z2, fx2, fy2, ra_x, ra_y, fx, fy,wk2)
do k=1,km+1
do j=jsd,jed
do i=is,ie
ra_x(i,j) = area(i,j) + xfx_adv(i,j,k) - xfx_adv(i+1,j,k)
enddo
enddo
do j=js,je
do i=isd,ied
ra_y(i,j) = area(i,j) + yfx_adv(i,j,k) - yfx_adv(i,j+1,k)
enddo
enddo
if ( damp(k)>1.E-5 ) then
do j=jsd,jed
do i=isd,ied
z2(i,j) = zh(i,j,k)
enddo
enddo
call fv_tp_2d(z2, crx_adv(is,jsd,k), cry_adv(isd,js,k), npx, npy, hord, &
fx, fy, xfx_adv(is,jsd,k), yfx_adv(isd,js,k), gridstruct, bd, ra_x, ra_y, lim_fac)
call del6_vt_flux(ndif(k), npx, npy, damp(k), z2, wk2, fx2, fy2, gridstruct, bd)
do j=js,je
do i=is,ie
zh(i,j,k) = (z2(i,j)*area(i,j)+fx(i,j)-fx(i+1,j)+fy(i,j)-fy(i,j+1)) &
/ (ra_x(i,j)+ra_y(i,j)-area(i,j)) + (fx2(i,j)-fx2(i+1,j)+fy2(i,j)-fy2(i,j+1))*rarea(i,j)
enddo
enddo
else
call fv_tp_2d(zh(isd,jsd,k), crx_adv(is,jsd,k), cry_adv(isd,js,k), npx, npy, hord, &
fx, fy, xfx_adv(is,jsd,k), yfx_adv(isd,js,k), gridstruct, bd, ra_x, ra_y, lim_fac)
do j=js,je
do i=is,ie
zh(i,j,k) = (zh(i,j,k)*area(i,j)+fx(i,j)-fx(i+1,j)+fy(i,j)-fy(i,j+1)) &
/ (ra_x(i,j) + ra_y(i,j) - area(i,j))
! zh(i,j,k) = rarea(i,j)*(fx(i,j)-fx(i+1,j)+fy(i,j)-fy(i,j+1)) &
! + zh(i,j,k)*(3.-rarea(i,j)*(ra_x(i,j) + ra_y(i,j)))
enddo
enddo
endif
enddo
!$OMP parallel do default(none) shared(is,ie,js,je,km,ws,zs,zh,rdt,dz_min)
do j=js, je
do i=is,ie
ws(i,j) = ( zs(i,j) - zh(i,j,km+1) ) * rdt
enddo
do k=km, 1, -1
do i=is, ie
! Enforce monotonicity of height to prevent blowup
zh(i,j,k) = max( zh(i,j,k), zh(i,j,k+1) + dz_min )
enddo
enddo
enddo
end subroutine update_dz_d
subroutine Riem_Solver_c(ms, dt, is, ie, js, je, km, ng, &
akap, cappa, cp, &
#ifdef MULTI_GASES
kapad, &
#endif
ptop, hs, w3, pt, q_con, &
delp, gz, pef, ws, p_fac, a_imp, scale_m)
integer, intent(in):: is, ie, js, je, ng, km
integer, intent(in):: ms
real, intent(in):: dt, akap, cp, ptop, p_fac, a_imp, scale_m
real, intent(in):: ws(is-ng:ie+ng,js-ng:je+ng)
real, intent(in), dimension(is-ng:ie+ng,js-ng:je+ng,km):: pt, delp
real, intent(in), dimension(is-ng:,js-ng:,1:):: q_con, cappa
#ifdef MULTI_GASES
real, intent(in), dimension(is-ng:ie+ng,js-ng:je+ng,km):: kapad
#endif
real, intent(in):: hs(is-ng:ie+ng,js-ng:je+ng)
real, intent(in), dimension(is-ng:ie+ng,js-ng:je+ng,km):: w3
! OUTPUT PARAMETERS
real, intent(inout), dimension(is-ng:ie+ng,js-ng:je+ng,km+1):: gz
real, intent( out), dimension(is-ng:ie+ng,js-ng:je+ng,km+1):: pef
! Local:
real, dimension(is-1:ie+1,km ):: dm, dz2, w2, pm2, gm2, cp2
real, dimension(is-1:ie+1,km+1):: pem, pe2, peg
#ifdef MULTI_GASES
real, dimension(is-1:ie+1,km ):: kapad2
#endif
real gama, rgrav
integer i, j, k
integer is1, ie1
gama = 1./(1.-akap)
rgrav = 1./grav
is1 = is - 1
ie1 = ie + 1
!$OMP parallel do default(none) shared(js,je,is1,ie1,km,delp,pef,ptop,gz,rgrav,w3,pt, &
#ifdef MULTI_GASES
!$OMP a_imp,dt,gama,akap,ws,p_fac,scale_m,ms,hs,q_con,cappa,kapad) &
!$OMP private(cp2,gm2, dm, dz2, w2, pm2, pe2, pem, peg, kapad2)
#else
!$OMP a_imp,dt,gama,akap,ws,p_fac,scale_m,ms,hs,q_con,cappa) &
!$OMP private(cp2,gm2, dm, dz2, w2, pm2, pe2, pem, peg)
#endif
do 2000 j=js-1, je+1
do k=1,km
do i=is1, ie1
dm(i,k) = delp(i,j,k)
enddo
enddo
do i=is1, ie1
pef(i,j,1) = ptop ! full pressure at top
pem(i,1) = ptop
#ifdef USE_COND
peg(i,1) = ptop
#endif
enddo
do k=2,km+1
do i=is1, ie1
pem(i,k) = pem(i,k-1) + dm(i,k-1)
#ifdef USE_COND
! Excluding contribution from condensates:
peg(i,k) = peg(i,k-1) + dm(i,k-1)*(1.-q_con(i,j,k-1))
#endif
enddo
enddo
do k=1,km
do i=is1, ie1
dz2(i,k) = gz(i,j,k+1) - gz(i,j,k)
#ifdef USE_COND
pm2(i,k) = (peg(i,k+1)-peg(i,k))/log(peg(i,k+1)/peg(i,k))
#ifdef MOIST_CAPPA
cp2(i,k) = cappa(i,j,k)
gm2(i,k) = 1. / (1.-cp2(i,k))
#endif
#else
pm2(i,k) = dm(i,k)/log(pem(i,k+1)/pem(i,k))
#endif
#ifdef MULTI_GASES
kapad2(i,k) = kapad(i,j,k)
#endif
dm(i,k) = dm(i,k) * rgrav
w2(i,k) = w3(i,j,k)
enddo
enddo
if ( a_imp < -0.01 ) then
call SIM3p0_solver(dt, is1, ie1, km, rdgas, gama, akap, &
#ifdef MULTI_GASES
kapad2, &
#endif
pe2, dm, &
pem, w2, dz2, pt(is1:ie1,j,1:km), ws(is1,j), p_fac, scale_m)
elseif ( a_imp <= 0.5 ) then
call RIM_2D(ms, dt, is1, ie1, km, rdgas, gama, gm2, &
#ifdef MULTI_GASES
kapad2, &
#endif
pe2, &
dm, pm2, w2, dz2, pt(is1:ie1,j,1:km), ws(is1,j), .true.)
else
call SIM1_solver(dt, is1, ie1, km, rdgas, gama, gm2, cp2, akap, &
#ifdef MULTI_GASES
kapad2, &
#endif
pe2, &
dm, pm2, pem, w2, dz2, pt(is1:ie1,j,1:km), ws(is1,j), p_fac)
endif
do k=2,km+1
do i=is1, ie1
pef(i,j,k) = pe2(i,k) + pem(i,k) ! add hydrostatic full-component
enddo
enddo
! Compute Height * grav (for p-gradient computation)
do i=is1, ie1
gz(i,j,km+1) = hs(i,j)
enddo
do k=km,1,-1
do i=is1, ie1
gz(i,j,k) = gz(i,j,k+1) - dz2(i,k)*grav
enddo
enddo
2000 continue
end subroutine Riem_Solver_c
!>GFDL - This routine will not give absoulte reproducibility when compiled with -fast-transcendentals.
!!GFDL - It is now inside of nh_core.F90 and being compiled without -fast-transcendentals.
subroutine Riem_Solver3test(ms, dt, is, ie, js, je, km, ng, &
isd, ied, jsd, jed, akap, cappa, cp, &
#ifdef MULTI_GASES
kapad, &
#endif
ptop, zs, q_con, w, delz, pt, &
delp, zh, pe, ppe, pk3, pk, peln, &
ws, scale_m, p_fac, a_imp, &
use_logp, last_call, fp_out)
!--------------------------------------------
! !OUTPUT PARAMETERS
! Ouput: gz: grav*height at edges
! pe: full hydrostatic pressure
! ppe: non-hydrostatic pressure perturbation
!--------------------------------------------
integer, intent(in):: ms, is, ie, js, je, km, ng
integer, intent(in):: isd, ied, jsd, jed
real, intent(in):: dt ! the BIG horizontal Lagrangian time step
real, intent(in):: akap, cp, ptop, p_fac, a_imp, scale_m
real, intent(in):: zs(isd:ied,jsd:jed)
logical, intent(in):: last_call, use_logp, fp_out
real, intent(in):: ws(is:ie,js:je)
real, intent(in), dimension(isd:,jsd:,1:):: q_con, cappa
real, intent(in), dimension(isd:ied,jsd:jed,km):: delp, pt
#ifdef MULTI_GASES
real, intent(in), dimension(isd:ied,jsd:jed,km):: kapad
#endif
real, intent(inout), dimension(isd:ied,jsd:jed,km+1):: zh
real, intent(inout), dimension(isd:ied,jsd:jed,km):: w
real, intent(inout):: pe(is-1:ie+1,km+1,js-1:je+1)
real, intent(out):: peln(is:ie,km+1,js:je) ! ln(pe)
real, intent(out), dimension(isd:ied,jsd:jed,km+1):: ppe
real, intent(out):: delz(is:ie,js:je,km)
real, intent(out):: pk(is:ie,js:je,km+1)
real, intent(out):: pk3(isd:ied,jsd:jed,km+1)
! Local:
real, dimension(is:ie,km):: dm, dz2, pm2, w2, gm2, cp2
real, dimension(is:ie,km+1)::pem, pe2, peln2, peg, pelng
#ifdef MULTI_GASES
real, dimension(is:ie,km):: kapad2
#endif
real gama, rgrav, ptk, peln1
integer i, j, k
gama = 1./(1.-akap)
rgrav = 1./grav
peln1 = log(ptop)
ptk = exp(akap*peln1)
!$OMP parallel do default(none) shared(is,ie,js,je,km,delp,ptop,peln1,pk3,ptk,akap,rgrav,zh,pt, &
!$OMP w,a_imp,dt,gama,ws,p_fac,scale_m,ms,delz,last_call, &
#ifdef MULTI_GASES
!$OMP peln,pk,fp_out,ppe,use_logp,zs,pe,cappa,q_con,kapad ) &
!$OMP private(cp2, gm2, dm, dz2, pm2, pem, peg, pelng, pe2, peln2, w2,kapad2)
#else
!$OMP peln,pk,fp_out,ppe,use_logp,zs,pe,cappa,q_con ) &
!$OMP private(cp2, gm2, dm, dz2, pm2, pem, peg, pelng, pe2, peln2, w2)
#endif
do 2000 j=js, je
do k=1,km
do i=is, ie
dm(i,k) = delp(i,j,k)
#ifdef MOIST_CAPPA
cp2(i,k) = cappa(i,j,k)
#endif
#ifdef MULTI_GASES
kapad2(i,k) = kapad(i,j,k)
#endif
enddo
enddo
do i=is,ie
pem(i,1) = ptop
peln2(i,1) = peln1
pk3(i,j,1) = ptk
#ifdef USE_COND
peg(i,1) = ptop
pelng(i,1) = peln1
#endif
enddo
do k=2,km+1
do i=is,ie
pem(i,k) = pem(i,k-1) + dm(i,k-1)
peln2(i,k) = log(pem(i,k))
#ifdef USE_COND
! Excluding contribution from condensates:
! peln used during remap; pk3 used only for p_grad
peg(i,k) = peg(i,k-1) + dm(i,k-1)*(1.-q_con(i,j,k-1))
pelng(i,k) = log(peg(i,k))
#endif
pk3(i,j,k) = exp(akap*peln2(i,k))
enddo
enddo
do k=1,km
do i=is, ie
#ifdef USE_COND
pm2(i,k) = (peg(i,k+1)-peg(i,k))/(pelng(i,k+1)-pelng(i,k))
#ifdef MOIST_CAPPA
gm2(i,k) = 1. / (1.-cp2(i,k))
#endif
#else
pm2(i,k) = dm(i,k)/(peln2(i,k+1)-peln2(i,k))
#endif
dm(i,k) = dm(i,k) * rgrav
dz2(i,k) = zh(i,j,k+1) - zh(i,j,k)
w2(i,k) = w(i,j,k)
enddo
enddo
if ( a_imp < -0.999 ) then
call SIM3p0_solver(dt, is, ie, km, rdgas, gama, akap, &
#ifdef MULTI_GASES
kapad2, &
#endif
pe2, dm, &
pem, w2, dz2, pt(is:ie,j,1:km), ws(is,j), p_fac, scale_m )
elseif ( a_imp < -0.5 ) then
call SIM3_solver(dt, is, ie, km, rdgas, gama, akap, &
#ifdef MULTI_GASES
kapad2, &
#endif
pe2, dm, &
pem, w2, dz2, pt(is:ie,j,1:km), ws(is,j), abs(a_imp), p_fac, scale_m)
elseif ( a_imp <= 0.5 ) then
call RIM_2D(ms, dt, is, ie, km, rdgas, gama, gm2, &
#ifdef MULTI_GASES
kapad2, &
#endif
pe2, &
dm, pm2, w2, dz2, pt(is:ie,j,1:km), ws(is,j), .false.)
elseif ( a_imp > 0.999 ) then
call SIM1_solver(dt, is, ie, km, rdgas, gama, gm2, cp2, akap, &
#ifdef MULTI_GASES
kapad2, &
#endif
pe2, dm, &
pm2, pem, w2, dz2, pt(is:ie,j,1:km), ws(is,j), p_fac)
else
call SIM_solver(dt, is, ie, km, rdgas, gama, gm2, cp2, akap, &
#ifdef MULTI_GASES
kapad2, &
#endif
pe2, dm, &
pm2, pem, w2, dz2, pt(is:ie,j,1:km), ws(is,j), &
a_imp, p_fac, scale_m)
endif
do k=1, km
do i=is, ie
w(i,j,k) = w2(i,k)
delz(i,j,k) = dz2(i,k)
enddo
enddo
if ( last_call ) then
do k=1,km+1
do i=is,ie
peln(i,k,j) = peln2(i,k)
pk(i,j,k) = pk3(i,j,k)
pe(i,k,j) = pem(i,k)
enddo
enddo
endif
if( fp_out ) then
do k=1,km+1
do i=is, ie
ppe(i,j,k) = pe2(i,k) + pem(i,k)
enddo
enddo
else
do k=1,km+1
do i=is, ie
ppe(i,j,k) = pe2(i,k)
enddo
enddo
endif
if ( use_logp ) then
do k=2,km+1
do i=is, ie
pk3(i,j,k) = peln2(i,k)
enddo
enddo
endif
do i=is, ie
zh(i,j,km+1) = zs(i,j)
enddo
do k=km,1,-1
do i=is, ie
zh(i,j,k) = zh(i,j,k+1) - dz2(i,k)
enddo
enddo
2000 continue
end subroutine Riem_Solver3test
subroutine imp_diff_w(j, is, ie, js, je, ng, km, cd, delz, ws, w, w3)
integer, intent(in) :: j, is, ie, js, je, km, ng
real, intent(in) :: cd
real, intent(in) :: delz(is:ie, km) !< delta-height (m)
real, intent(in) :: w(is:ie, km) !< vertical vel. (m/s)
real, intent(in) :: ws(is:ie)
real, intent(out) :: w3(is-ng:ie+ng,js-ng:je+ng,km)
! Local:
real, dimension(is:ie,km):: c, gam, dz, wt
real:: bet(is:ie)
real:: a
integer:: i, k
do k=2,km
do i=is,ie
dz(i,k) = 0.5*(delz(i,k-1)+delz(i,k))
enddo
enddo
do k=1,km-1
do i=is,ie
c(i,k) = -cd/(dz(i,k+1)*delz(i,k))
enddo
enddo
! model top:
do i=is,ie
bet(i) = 1. - c(i,1) ! bet(i) = b
wt(i,1) = w(i,1) / bet(i)
enddo
! Interior:
do k=2,km-1
do i=is,ie
gam(i,k) = c(i,k-1)/bet(i)
a = cd/(dz(i,k)*delz(i,k))
bet(i) = (1.+a-c(i,k)) + a*gam(i,k)
wt(i,k) = (w(i,k) + a*wt(i,k-1)) / bet(i)
enddo
enddo
! Bottom:
do i=is,ie
gam(i,km) = c(i,km-1) / bet(i)
a = cd/(dz(i,km)*delz(i,km))
wt(i,km) = (w(i,km) + 2.*ws(i)*cd/delz(i,km)**2 &
+ a*wt(i,km-1))/(1. + a + (cd+cd)/delz(i,km)**2 + a*gam(i,km))
enddo
do k=km-1,1,-1
do i=is,ie
wt(i,k) = wt(i,k) - gam(i,k+1)*wt(i,k+1)
enddo
enddo
do k=1,km
do i=is,ie
w3(i,j,k) = wt(i,k)
enddo
enddo
end subroutine imp_diff_w
subroutine RIM_2D(ms, bdt, is, ie, km, rgas, gama, gm2, &
#ifdef MULTI_GASES
kapad2, &
#endif
pe2, dm2, pm2, w2, dz2, pt2, ws, c_core )
integer, intent(in):: ms, is, ie, km
real, intent(in):: bdt, gama, rgas
real, intent(in), dimension(is:ie,km):: dm2, pm2, gm2
logical, intent(in):: c_core
real, intent(in ) :: pt2(is:ie,km)
real, intent(in ) :: ws(is:ie)
! IN/OUT:
real, intent(inout):: dz2(is:ie,km)
real, intent(inout):: w2(is:ie,km)
real, intent(out ):: pe2(is:ie,km+1)
#ifdef MULTI_GASES
real, intent(inout), dimension(is:ie,km):: kapad2
#endif
! Local:
real:: ws2(is:ie)
real, dimension(km+1):: m_bot, m_top, r_bot, r_top, pe1, pbar, wbar
real, dimension(km):: r_hi, r_lo, dz, wm, dm, dts
real, dimension(km):: pf1, wc, cm , pp, pt1
real:: dt, rdt, grg, z_frac, ptmp1, rden, pf, time_left
real:: m_surf
#ifdef MULTI_GASES
real gamax
#endif
integer:: i, k, n, ke, kt1, ktop
integer:: ks0, ks1
grg = gama * rgas
rdt = 1. / bdt
dt = bdt / real(ms)
pbar(:) = 0.
wbar(:) = 0.
do i=is,ie
ws2(i) = 2.*ws(i)
enddo
do 6000 i=is,ie
do k=1,km
dz(k) = dz2(i,k)
dm(k) = dm2(i,k)
wm(k) = w2(i,k)*dm(k)
pt1(k) = pt2(i,k)
enddo
pe1(:) = 0.
wbar(km+1) = ws(i)
ks0 = 1
if ( ms > 1 .and. ms < 8 ) then
! Continuity of (pbar, wbar) is maintained
do k=1, km
rden = -rgas*dm(k)/dz(k)
#ifdef MOIST_CAPPA
pf1(k) = exp( gm2(i,k)*log(rden*pt1(k)) )
! dts(k) = -dz(k)/sqrt(gm2(i,k)*rgas*pf1(k)/rden)
dts(k) = -dz(k)/sqrt(grg*pf1(k)/rden)
#else
#ifdef MULTI_GASES
gamax = 1./(1.-kapad2(i,k))
pf1(k) = exp( gamax*log(rden*pt1(k)) )
#else
pf1(k) = exp( gama*log(rden*pt1(k)) )
#endif
dts(k) = -dz(k)/sqrt(grg*pf1(k)/rden)
#endif
if ( bdt > dts(k) ) then
ks0 = k-1
goto 222
endif
enddo
ks0 = km
222 if ( ks0==1 ) goto 244
do k=1, ks0
cm(k) = dm(k) / dts(k)
wc(k) = wm(k) / dts(k)
pp(k) = pf1(k) - pm2(i,k)
enddo
wbar(1) = (wc(1)+pp(1)) / cm(1)
do k=2, ks0
wbar(k) = (wc(k-1)+wc(k) + pp(k)-pp(k-1)) / (cm(k-1)+cm(k))
pbar(k) = bdt*(cm(k-1)*wbar(k) - wc(k-1) + pp(k-1))
pe1(k) = pbar(k)
enddo
if ( ks0 == km ) then
pbar(km+1) = bdt*(cm(km)*wbar(km+1) - wc(km) + pp(km))
if ( c_core ) then
do k=1,km
dz2(i,k) = dz(k) + bdt*(wbar(k+1) - wbar(k))
enddo
else
do k=1,km
dz2(i,k) = dz(k) + bdt*(wbar(k+1) - wbar(k))
w2(i,k) = (wm(k)+pbar(k+1)-pbar(k))/dm(k)
enddo
endif
pe2(i,1) = 0.
do k=2,km+1
pe2(i,k) = pbar(k)*rdt
enddo
goto 6000 ! next i
else
if ( c_core ) then
do k=1, ks0-1
dz2(i,k) = dz(k) + bdt*(wbar(k+1) - wbar(k))
enddo
else
do k=1, ks0-1
dz2(i,k) = dz(k) + bdt*(wbar(k+1) - wbar(k))
w2(i,k) = (wm(k)+pbar(k+1)-pbar(k))/dm(k)
enddo
endif
pbar(ks0) = pbar(ks0) / real(ms)
endif
endif
244 ks1 = ks0
do 5000 n=1, ms
do k=ks1, km
rden = -rgas*dm(k)/dz(k)
#ifdef MOIST_CAPPA
pf = exp( gm2(i,k)*log(rden*pt1(k)) )
! dts(k) = -dz(k) / sqrt( gm2(i,k)*rgas*pf/rden )
dts(k) = -dz(k) / sqrt( grg*pf/rden )
#else
#ifdef MULTI_GASES
gamax = 1./(1.-kapad2(i,k))
pf = exp( gamax*log(rden*pt1(k)) )
#else
pf = exp( gama*log(rden*pt1(k)) )
#endif
dts(k) = -dz(k) / sqrt( grg*pf/rden )
#endif
ptmp1 = dts(k)*(pf - pm2(i,k))
r_lo(k) = wm(k) + ptmp1
r_hi(k) = wm(k) - ptmp1
enddo
ktop = ks1
do k=ks1, km
if( dt > dts(k) ) then
ktop = k-1
goto 333
endif
enddo
ktop = km
333 continue
if ( ktop >= ks1 ) then
do k=ks1, ktop
z_frac = dt/dts(k)
r_bot(k ) = z_frac*r_lo(k)
r_top(k+1) = z_frac*r_hi(k)
m_bot(k ) = z_frac* dm(k)
m_top(k+1) = m_bot(k)
enddo
if ( ktop == km ) goto 666
endif
do k=ktop+2, km+1
m_top(k) = 0.
r_top(k) = 0.
enddo
kt1 = max(1, ktop)
do 444 ke=km+1, ktop+2, -1
time_left = dt
do k=ke-1, kt1, -1
if ( time_left > dts(k) ) then
time_left = time_left - dts(k)
m_top(ke) = m_top(ke) + dm(k)
r_top(ke) = r_top(ke) + r_hi(k)
else
z_frac = time_left/dts(k)
m_top(ke) = m_top(ke) + z_frac*dm(k)
r_top(ke) = r_top(ke) + z_frac*r_hi(k)
go to 444 ! next level
endif
enddo
444 continue
do k=ktop+1, km
m_bot(k) = 0.
r_bot(k) = 0.
enddo
do 4000 ke=ktop+1, km
time_left = dt
do k=ke, km
if ( time_left > dts(k) ) then
time_left = time_left - dts(k)
m_bot(ke) = m_bot(ke) + dm(k)
r_bot(ke) = r_bot(ke) + r_lo(k)
else
z_frac = time_left/dts(k)
m_bot(ke) = m_bot(ke) + z_frac* dm(k)
r_bot(ke) = r_bot(ke) + z_frac*r_lo(k)
go to 4000 ! next interface
endif
enddo
m_surf = m_bot(ke)
do k=km, kt1, -1
if ( time_left > dts(k) ) then
time_left = time_left - dts(k)
m_bot(ke) = m_bot(ke) + dm(k)
r_bot(ke) = r_bot(ke) - r_hi(k)
else
z_frac = time_left/dts(k)
m_bot(ke) = m_bot(ke) + z_frac* dm(k)
r_bot(ke) = r_bot(ke) - z_frac*r_hi(k) + (m_bot(ke)-m_surf)*ws2(i)
go to 4000 ! next interface
endif
enddo
4000 continue
666 if ( ks1==1 ) wbar(1) = r_bot(1) / m_bot(1)
do k=ks1+1, km
wbar(k) = (r_bot(k)+r_top(k)) / (m_top(k)+m_bot(k))
enddo
! pbar here is actually dt*pbar
do k=ks1+1, km+1
pbar(k) = m_top(k)*wbar(k) - r_top(k)
pe1(k) = pe1(k) + pbar(k)
enddo
if ( n==ms ) then
if ( c_core ) then
do k=ks1, km
dz2(i,k) = dz(k) + dt*(wbar(k+1)-wbar(k))
enddo
else
do k=ks1, km
dz2(i,k) = dz(k) + dt*(wbar(k+1)-wbar(k))
w2(i,k) = ( wm(k) + pbar(k+1) - pbar(k) ) / dm(k)
enddo
endif
else
do k=ks1, km