module molec_diff 3,1
!------------------------------------------------------------------------------------------------- !
! Module to compute molecular diffusivity for various constituents !
! !
! Public interfaces : !
! !
! init_molec_diff Initializes time independent coefficients !
! init_timestep_molec_diff Time-step initialization for molecular diffusivity !
! compute_molec_diff Computes constituent-independent terms for moleculuar diffusivity !
! vd_lu_qdecomp Computes constituent-dependent terms for moleculuar diffusivity and !
! updates terms in the triadiagonal matrix used for the implicit !
! solution of the diffusion equation !
! !
!---------------------------Code history---------------------------------------------------------- !
! Modularized : J. McCaa, September 2004 !
! Lastly Arranged : S. Park, January. 2010 !
!------------------------------------------------------------------------------------------------- !
use perf_mod
use cam_logfile
, only : iulog
implicit none
private
save
public init_molec_diff
public init_timestep_molec_diff
public compute_molec_diff
public vd_lu_qdecomp
! ---------- !
! Parameters !
! ---------- !
integer, parameter :: r8 = selected_real_kind(12) ! 8 byte real
real(r8), parameter :: km_fac = 3.55E-7_r8 ! Molecular viscosity constant [ unit ? ]
real(r8), parameter :: pr_num = 1._r8 ! Prandtl number [ no unit ]
real(r8), parameter :: pwr = 2._r8/3._r8 ! Exponentiation factor [ unit ? ]
real(r8), parameter :: d0 = 1.52E20_r8 ! Diffusion factor [ m-1 s-1 ] molec sqrt(kg/kmol/K) [ unit ? ]
! Aerononmy, Part B, Banks and Kockarts (1973), p39
! Note text cites 1.52E18 cm-1 ...
real(r8) :: rair ! Gas constant for dry air
real(r8) :: mw_dry ! Molecular weight of dry air
real(r8) :: n_avog ! Avogadro's number [ molec/kmol ]
real(r8) :: gravit
real(r8) :: cpair
real(r8) :: kbtz ! Boltzman constant
integer :: ntop_molec ! Top interface level to which molecular vertical diffusion is applied ( = 1 )
integer :: nbot_molec ! Bottom interface level to which molecular vertical diffusion is applied ( = pver )
real(r8), allocatable :: mw_fac(:) ! sqrt(1/M_q + 1/M_d) in constituent diffusivity [ unit ? ]
contains
!============================================================================ !
! !
!============================================================================ !
subroutine init_molec_diff( kind, ncnst, rair_in, ntop_molec_in, nbot_molec_in, & 1,3
mw_dry_in, n_avog_in, gravit_in, cpair_in, kbtz_in )
use constituents, only : cnst_mw
use upper_bc, only : ubc_init
integer, intent(in) :: kind ! Kind of reals being passed in
integer, intent(in) :: ncnst ! Number of constituents
integer, intent(in) :: ntop_molec_in ! Top interface level to which molecular vertical diffusion is applied ( = 1 )
integer, intent(in) :: nbot_molec_in ! Bottom interface level to which molecular vertical diffusion is applied.
real(r8), intent(in) :: rair_in
real(r8), intent(in) :: mw_dry_in ! Molecular weight of dry air
real(r8), intent(in) :: n_avog_in ! Avogadro's number [ molec/kmol ]
real(r8), intent(in) :: gravit_in
real(r8), intent(in) :: cpair_in
real(r8), intent(in) :: kbtz_in ! Boltzman constant
integer :: m ! Constituent index
if( kind .ne. r8 ) then
write(iulog,*) 'KIND of reals passed to init_molec_diff -- exiting.'
stop 'init_molec_diff'
endif
rair = rair_in
mw_dry = mw_dry_in
n_avog = n_avog_in
gravit = gravit_in
cpair = cpair_in
kbtz = kbtz_in
ntop_molec = ntop_molec_in
nbot_molec = nbot_molec_in
! Initialize upper boundary condition variables
call ubc_init()
! Molecular weight factor in constitutent diffusivity
! ***** FAKE THIS FOR NOW USING MOLECULAR WEIGHT OF DRY AIR FOR ALL TRACERS ****
allocate(mw_fac(ncnst))
do m = 1, ncnst
mw_fac(m) = d0 * mw_dry * sqrt(1._r8/mw_dry + 1._r8/cnst_mw(m)) / n_avog
end do
end subroutine init_molec_diff
!============================================================================ !
! !
!============================================================================ !
subroutine init_timestep_molec_diff(state) 1,4
!--------------------------- !
! Timestep dependent setting !
!--------------------------- !
use upper_bc, only : ubc_timestep_init
use physics_types,only: physics_state
use ppgrid, only: begchunk, endchunk
type(physics_state), intent(in) :: state(begchunk:endchunk)
call ubc_timestep_init( state)
end subroutine init_timestep_molec_diff
!============================================================================ !
! !
!============================================================================ !
integer function compute_molec_diff( lchnk , & 1,3
pcols , pver , ncnst , ncol , t , pmid , pint , &
zi , ztodt , kvh , kvm , tint , rhoi , tmpi2 , &
kq_scal , ubc_t , ubc_mmr , dse_top , cc_top , cd_top , cnst_mw_out , &
cnst_fixed_ubc_out , mw_fac_out , ntop_molec_out , nbot_molec_out )
use upper_bc, only : ubc_get_vals
use constituents, only : cnst_mw, cnst_fixed_ubc
! --------------------- !
! Input-Output Argument !
! --------------------- !
integer, intent(in) :: pcols
integer, intent(in) :: pver
integer, intent(in) :: ncnst
integer, intent(in) :: ncol ! Number of atmospheric columns
integer, intent(in) :: lchnk ! Chunk identifier
real(r8), intent(in) :: t(pcols,pver) ! Temperature input
real(r8), intent(in) :: pmid(pcols,pver) ! Midpoint pressures
real(r8), intent(in) :: pint(pcols,pver+1) ! Interface pressures
real(r8), intent(in) :: zi(pcols,pver+1) ! Interface heights
real(r8), intent(in) :: ztodt ! 2 delta-t
real(r8), intent(inout) :: kvh(pcols,pver+1) ! Diffusivity for heat
real(r8), intent(inout) :: kvm(pcols,pver+1) ! Viscosity ( diffusivity for momentum )
real(r8), intent(inout) :: tint(pcols,pver+1) ! Interface temperature
real(r8), intent(inout) :: rhoi(pcols,pver+1) ! Density ( rho ) at interfaces
real(r8), intent(inout) :: tmpi2(pcols,pver+1) ! dt*(g*rho)**2/dp at interfaces
real(r8), intent(out) :: kq_scal(pcols,pver+1) ! kq_fac*sqrt(T)*m_d/rho for molecular diffusivity
real(r8), intent(out) :: ubc_mmr(pcols,ncnst) ! Upper boundary mixing ratios [ kg/kg ]
real(r8), intent(out) :: cnst_mw_out(ncnst)
logical, intent(out) :: cnst_fixed_ubc_out(ncnst)
real(r8), intent(out) :: mw_fac_out(ncnst)
real(r8), intent(out) :: dse_top(pcols) ! dse on top boundary
real(r8), intent(out) :: cc_top(pcols) ! Lower diagonal at top interface
real(r8), intent(out) :: cd_top(pcols) ! cc_top * dse ubc value
integer, intent(out) :: ntop_molec_out
integer, intent(out) :: nbot_molec_out
! --------------- !
! Local variables !
! --------------- !
integer :: m ! Constituent index
integer :: i ! Column index
integer :: k ! Level index
real(r8) :: mkvisc ! Molecular kinematic viscosity c*tint**(2/3)/rho
real(r8) :: ubc_t(pcols) ! Upper boundary temperature (K)
! ----------------------- !
! Main Computation Begins !
! ----------------------- !
! Get upper boundary values
call ubc_get_vals( lchnk, ncol, ntop_molec, pint, zi, ubc_t, ubc_mmr )
! Below are already computed, just need to be copied for output
cnst_mw_out(:ncnst) = cnst_mw(:ncnst)
cnst_fixed_ubc_out(:ncnst) = cnst_fixed_ubc(:ncnst)
mw_fac_out(:ncnst) = mw_fac(:ncnst)
ntop_molec_out = ntop_molec
nbot_molec_out = nbot_molec
! Density and related factors for moecular diffusion and ubc.
! Always have a fixed upper boundary T if molecular diffusion is active. Why ?
tint (:ncol,ntop_molec) = ubc_t(:ncol)
rhoi (:ncol,ntop_molec) = pint(:ncol,ntop_molec) / ( rair * tint(:ncol,ntop_molec) )
tmpi2(:ncol,ntop_molec) = ztodt * ( gravit * rhoi(:ncol,ntop_molec))**2 &
/ ( pmid(:ncol,ntop_molec) - pint(:ncol,ntop_molec) )
! Compute molecular kinematic viscosity, heat diffusivity and factor for constituent diffusivity
! This is a key part of the code.
kq_scal(:ncol,1:ntop_molec-1) = 0._r8
do k = ntop_molec, nbot_molec
do i = 1, ncol
mkvisc = km_fac * tint(i,k)**pwr / rhoi(i,k)
kvm(i,k) = kvm(i,k) + mkvisc
kvh(i,k) = kvh(i,k) + mkvisc * pr_num
kq_scal(i,k) = sqrt(tint(i,k)) / rhoi(i,k)
end do
end do
kq_scal(:ncol,nbot_molec+1:pver+1) = 0._r8
! Top boundary condition for dry static energy
dse_top(:ncol) = cpair * tint(:ncol,ntop_molec) + gravit * zi(:ncol,ntop_molec)
! Top value of cc for dry static energy
do i = 1, ncol
cc_top(i) = ztodt * gravit**2 * rhoi(i,ntop_molec) * km_fac * ubc_t(i)**pwr / &
( ( pint(i,2) - pint(i,1) ) * ( pmid(i,1) - pint(i,1) ) )
enddo
cd_top(:ncol) = cc_top(:ncol) * dse_top(:ncol)
compute_molec_diff = 1
return
end function compute_molec_diff
!============================================================================ !
! !
!============================================================================ !
integer function vd_lu_qdecomp( pcols , pver , ncol , fixed_ubc , mw , ubc_mmr , & 1
kv , kq_scal, mw_facm , tmpi , rpdel , &
ca , cc , dnom , ze , rhoi , &
tint , ztodt , ntop_molec , nbot_molec , cd_top )
!------------------------------------------------------------------------------ !
! Add the molecular diffusivity to the turbulent diffusivity for a consitutent. !
! Update the superdiagonal (ca(k)), diagonal (cb(k)) and subdiagonal (cc(k)) !
! coefficients of the tridiagonal diffusion matrix, also ze and denominator. !
!------------------------------------------------------------------------------ !
! ---------------------- !
! Input-Output Arguments !
! ---------------------- !
integer, intent(in) :: pcols
integer, intent(in) :: pver
integer, intent(in) :: ncol ! Number of atmospheric columns
integer, intent(in) :: ntop_molec
integer, intent(in) :: nbot_molec
logical, intent(in) :: fixed_ubc ! Fixed upper boundary condition flag
real(r8), intent(in) :: kv(pcols,pver+1) ! Eddy diffusivity
real(r8), intent(in) :: kq_scal(pcols,pver+1) ! Molecular diffusivity ( kq_fac*sqrt(T)*m_d/rho )
real(r8), intent(in) :: mw ! Molecular weight for this constituent
real(r8), intent(in) :: ubc_mmr(pcols) ! Upper boundary mixing ratios [ kg/kg ]
real(r8), intent(in) :: mw_facm ! sqrt(1/M_q + 1/M_d) for this constituent
real(r8), intent(in) :: tmpi(pcols,pver+1) ! dt*(g/R)**2/dp*pi(k+1)/(.5*(tm(k+1)+tm(k))**2
real(r8), intent(in) :: rpdel(pcols,pver) ! 1./pdel ( thickness bet interfaces )
real(r8), intent(in) :: rhoi(pcols,pver+1) ! Density at interfaces [ kg/m3 ]
real(r8), intent(in) :: tint(pcols,pver+1) ! Interface temperature [ K ]
real(r8), intent(in) :: ztodt ! 2 delta-t [ s ]
real(r8), intent(inout) :: ca(pcols,pver) ! -Upper diagonal
real(r8), intent(inout) :: cc(pcols,pver) ! -Lower diagonal
real(r8), intent(inout) :: dnom(pcols,pver) ! 1./(1. + ca(k) + cc(k) - cc(k)*ze(k-1)) , 1./(b(k) - c(k)*e(k-1))
real(r8), intent(inout) :: ze(pcols,pver) ! Term in tri-diag. matrix system
real(r8), intent(out) :: cd_top(pcols) ! Term for updating top level with ubc
! --------------- !
! Local Variables !
! --------------- !
integer :: i ! Longitude index
integer :: k, kp1 ! Vertical indicies
real(r8) :: rghd(pcols,pver+1) ! (1/H_i - 1/H) * (rho*g)^(-1)
real(r8) :: kmq(ncol) ! Molecular diffusivity for constituent
real(r8) :: wrk0(ncol) ! Work variable
real(r8) :: wrk1(ncol) ! Work variable
real(r8) :: cb(pcols,pver) ! - Diagonal
real(r8) :: kvq(pcols,pver+1) ! Output vertical diffusion coefficient
! ----------------------- !
! Main Computation Begins !
! ----------------------- !
! --------------------------------------------------------------------- !
! Determine superdiagonal (ca(k)) and subdiagonal (cc(k)) coeffs of the !
! tridiagonal diffusion matrix. The diagonal elements (cb=1+ca+cc) are !
! a combination of ca and cc; they are not required by the solver. !
!---------------------------------------------------------------------- !
call t_startf('vd_lu_qdecomp')
kvq(:,:) = 0._r8
cd_top(:) = 0._r8
! Compute difference between scale heights of constituent and dry air
do k = ntop_molec, nbot_molec
do i = 1, ncol
rghd(i,k) = gravit / ( kbtz * n_avog * tint(i,k) ) * ( mw - mw_dry )
rghd(i,k) = ztodt * gravit * rhoi(i,k) * rghd(i,k)
enddo
enddo
!-------------------- !
! Molecular diffusion !
!-------------------- !
do k = nbot_molec - 1, ntop_molec, -1
kp1 = k + 1
kmq(:ncol) = kq_scal(:ncol,kp1) * mw_facm
wrk0(:ncol) = ( kv(:ncol,kp1) + kmq(:ncol) ) * tmpi(:ncol,kp1)
wrk1(:ncol) = kmq(:ncol) * 0.5_r8 * rghd(:ncol,kp1)
! Add species separation term
ca(:ncol,k ) = ( wrk0(:ncol) - wrk1(:ncol) ) * rpdel(:ncol,k)
cc(:ncol,kp1) = ( wrk0(:ncol) + wrk1(:ncol) ) * rpdel(:ncol,kp1)
kvq(:ncol,kp1) = kmq(:ncol)
end do
if( fixed_ubc ) then
cc(:ncol,ntop_molec) = kq_scal(:ncol,ntop_molec) * mw_facm &
* ( tmpi(:ncol,ntop_molec) + rghd(:ncol,ntop_molec) ) &
* rpdel(:ncol,ntop_molec)
end if
! Calculate diagonal elements
do k = nbot_molec - 1, ntop_molec + 1, -1
kp1 = k + 1
cb(:ncol,k) = 1._r8 + ca(:ncol,k) + cc(:ncol,k) &
+ rpdel(:ncol,k) * ( kvq(:ncol,kp1) * rghd(:ncol,kp1) &
- kvq(:ncol,k) * rghd(:ncol,k) )
kvq(:ncol,kp1) = kv(:ncol,kp1) + kvq(:ncol,kp1)
end do
k = ntop_molec
kp1 = k + 1
if( fixed_ubc ) then
cb(:ncol,k) = 1._r8 + ca(:ncol,k) &
+ rpdel(:ncol,k) * kvq(:ncol,kp1) * rghd(:ncol,kp1) &
+ kq_scal(:ncol,ntop_molec) * mw_facm &
* ( tmpi(:ncol,ntop_molec) - rghd(:ncol,ntop_molec) ) &
* rpdel(:ncol,ntop_molec)
else
cb(:ncol,k) = 1._r8 + ca(:ncol,k) &
+ rpdel(:ncol,k) * kvq(:ncol,kp1) * rghd(:ncol,kp1)
end if
k = nbot_molec
cb(:ncol,k) = 1._r8 + cc(:ncol,k) + ca(:ncol,k) &
- rpdel(:ncol,k) * kvq(:ncol,k)*rghd(:ncol,k)
do k = 1, nbot_molec + 1, -1
cb(:ncol,k) = 1._r8 + ca(:ncol,k) + cc(:ncol,k)
end do
! Compute term for updating top level mixing ratio for ubc
if( fixed_ubc ) then
cd_top(:ncol) = cc(:ncol,ntop_molec) * ubc_mmr(:ncol)
end if
!-------------------------------------------------------- !
! Calculate e(k). !
! This term is required in solution of tridiagonal matrix !
! defined by implicit diffusion equation. !
!-------------------------------------------------------- !
do k = nbot_molec, ntop_molec + 1, -1
dnom(:ncol,k) = 1._r8 / ( cb(:ncol,k) - ca(:ncol,k) * ze(:ncol,k+1) )
ze(:ncol,k) = cc(:ncol,k) * dnom(:ncol,k)
end do
k = ntop_molec
dnom(:ncol,k) = 1._r8 / ( cb(:ncol,k) - ca(:ncol,k) * ze(:ncol,k+1) )
vd_lu_qdecomp = 1
call t_stopf('vd_lu_qdecomp')
return
end function vd_lu_qdecomp
end module molec_diff