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advance_xm_wpxp_module.F90
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advance_xm_wpxp_module.F90
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!-----------------------------------------------------------------------
! $Id$
!===============================================================================
module advance_xm_wpxp_module
! Description:
! Contains the CLUBB advance_xm_wpxp_module scheme.
! References:
! None
!-----------------------------------------------------------------------
implicit none
private ! Default scope
public :: advance_xm_wpxp
private :: xm_wpxp_lhs, &
xm_wpxp_rhs, &
xm_wpxp_solve, &
xm_wpxp_clipping_and_stats, &
xm_term_ta_lhs, &
xm_term_ta_lhs_all, &
wpxp_term_tp_lhs, &
wpxp_term_tp_lhs_all, &
wpxp_terms_ac_pr2_lhs, &
wpxp_terms_ac_pr2_lhs_all, &
wpxp_term_pr1_lhs_all, &
wpxp_terms_bp_pr3_rhs, &
wpxp_terms_bp_pr3_rhs_all, &
xm_correction_wpxp_cl, &
damp_coefficient, &
diagnose_upxp, &
error_prints_xm_wpxp
! Parameter Constants
integer, parameter, private :: &
nsub = 2, & ! Number of subdiagonals in the LHS matrix
nsup = 2, & ! Number of superdiagonals in the LHS matrix
xm_wpxp_thlm = 1, & ! Named constant for thlm and wpthlp solving
xm_wpxp_rtm = 2, & ! Named constant for rtm and wprtp solving
xm_wpxp_scalar = 3, & ! Named constant for sclrm and wpsclrp solving
xm_wpxp_um = 4, & ! Named constant for optional um and upwp solving
xm_wpxp_vm = 5 ! Named constant for optional vm and vpwp solving
contains
!=============================================================================
subroutine advance_xm_wpxp( dt, sigma_sqd_w, wm_zm, wm_zt, wp2, &
Lscale, wp3_on_wp2, wp3_on_wp2_zt, Kh_zt, Kh_zm, &
tau_C6_zm, Skw_zm, wp2rtp, rtpthvp, rtm_forcing, &
wprtp_forcing, rtm_ref, wp2thlp, thlpthvp, &
thlm_forcing, wpthlp_forcing, thlm_ref, &
rho_ds_zm, rho_ds_zt, invrs_rho_ds_zm, &
invrs_rho_ds_zt, thv_ds_zm, rtp2, thlp2, &
w_1_zm, w_2_zm, varnce_w_1_zm, varnce_w_2_zm, &
mixt_frac_zm, l_implemented, em, wp2sclrp, &
sclrpthvp, sclrm_forcing, sclrp2, exner, rcm, &
p_in_Pa, thvm, Cx_fnc_Richardson, &
ice_supersat_frac, &
pdf_implicit_coefs_terms, &
um_forcing, vm_forcing, ug, vg, wpthvp, &
fcor, um_ref, vm_ref, up2, vp2, &
uprcp, vprcp, rc_coef, &
l_predict_upwp_vpwp, &
l_diffuse_rtm_and_thlm, &
l_stability_correct_Kh_N2_zm, &
l_upwind_wpxp_ta, &
l_upwind_xm_ma, &
l_uv_nudge, &
l_tke_aniso, &
l_use_C7_Richardson, &
l_brunt_vaisala_freq_moist, &
l_use_thvm_in_bv_freq, &
rtm, wprtp, thlm, wpthlp, &
sclrm, wpsclrp, um, upwp, vm, vpwp )
! Description:
! Advance the mean and flux terms by one timestep.
! References:
! https://arxiv.org/pdf/1711.03675v1.pdf#nameddest=url:wpxp_eqns
!
! Eqn. 16 & 17 on p. 3546 of
! ``A PDF-Based Model for Boundary Layer Clouds. Part I:
! Method and Model Description'' Golaz, et al. (2002)
! JAS, Vol. 59, pp. 3540--3551.
! See Also
! ``Equations for CLUBB'' Section 5:
! /Implicit solutions for the means and fluxes/
!-----------------------------------------------------------------------
use parameters_tunable, only: &
C6rt, & ! Variable(s)
C6rtb, &
C6rtc, &
C6thl, &
C6thlb, &
C6thlc, &
C7, &
C7b, &
C7c, &
c_K6, &
C6rt_Lscale0, &
C6thl_Lscale0, &
C7_Lscale0, &
wpxp_L_thresh
use constants_clubb, only: &
fstderr, & ! Constant
rt_tol, &
thl_tol, &
w_tol, &
w_tol_sqd, &
thl_tol_mfl, &
rt_tol_mfl, &
max_mag_correlation, &
one, &
one_half, &
zero, &
zero_threshold, &
eps, &
ep1
use parameters_model, only: &
sclr_dim, & ! Variable(s)
ts_nudge
use grid_class, only: &
gr, & ! Variable(s)
ddzt ! Procedure(s)
use grid_class, only: &
zm2zt, & ! Procedure(s)
zt2zm
use model_flags, only: &
l_clip_semi_implicit, & ! Variable(s)
l_explicit_turbulent_adv_wpxp
use mono_flux_limiter, only: &
calc_turb_adv_range ! Procedure(s)
use pdf_closure_module, only: &
iiPDF_new, & ! Variable(s)
iiPDF_ADG1, &
iiPDF_type
use pdf_parameter_module, only: &
implicit_coefs_terms ! Variable Type
use turbulent_adv_pdf, only: &
sgn_turbulent_velocity ! Procedure(s)
use clubb_precision, only: &
core_rknd ! Variable(s)
use error_code, only: &
clubb_at_least_debug_level, & ! Procedure
err_code, & ! Error Indicator
clubb_fatal_error ! Constants
use stats_type_utilities, only: &
stat_begin_update, & ! Procedure(s)
stat_end_update, &
stat_update_var
use stats_variables, only: &
stats_zt, & ! Variables
stats_zm, &
irtm_sdmp, &
ithlm_sdmp, &
ium_sdmp, &
ivm_sdmp, &
ium_ndg, &
ivm_ndg, &
ium_ref, &
ivm_ref, &
iC7_Skw_fnc, &
iC6rt_Skw_fnc, &
iC6thl_Skw_fnc, &
l_stats_samp
use sponge_layer_damping, only: &
rtm_sponge_damp_settings, &
thlm_sponge_damp_settings, &
uv_sponge_damp_settings, &
rtm_sponge_damp_profile, &
thlm_sponge_damp_profile, &
uv_sponge_damp_profile, &
sponge_damp_xm ! Procedure(s)
implicit none
! Parameter Constants
logical, parameter :: &
l_iter = .true. ! True when the means and fluxes are prognosed
! -------------------- Input Variables --------------------
real( kind = core_rknd ), intent(in) :: &
dt ! Timestep [s]
real( kind = core_rknd ), intent(in), dimension(gr%nz) :: &
sigma_sqd_w, & ! sigma_sqd_w on momentum levels [-]
wm_zm, & ! w wind component on momentum levels [m/s]
wm_zt, & ! w wind component on thermodynamic levels [m/s]
wp2, & ! w'^2 (momentum levels) [m^2/s^2]
Lscale, & ! Turbulent mixing length [m]
em, & ! Turbulent Kinetic Energy (TKE) [m^2/s^2]
wp3_on_wp2, & ! Smoothed wp3 / wp2 on momentum levels [m/s]
wp3_on_wp2_zt, & ! Smoothed wp3 / wp2 on thermo. levels [m/s]
Kh_zt, & ! Eddy diffusivity on thermodynamic levels [m^2/s]
Kh_zm, & ! Eddy diffusivity on momentum levels
tau_C6_zm, & ! Time-scale tau on momentum levels applied to C6 term [s]
Skw_zm, & ! Skewness of w on momentum levels [-]
wp2rtp, & ! <w'^2 r_t'> (thermodynamic levels) [m^2/s^2 kg/kg]
rtpthvp, & ! r_t'th_v' (momentum levels) [(kg/kg) K]
rtm_forcing, & ! r_t forcing (thermodynamic levels) [(kg/kg)/s]
wprtp_forcing, & ! <w'r_t'> forcing (momentum levels) [(kg/kg)/s^2]
rtm_ref, & ! rtm for nudging [kg/kg]
wp2thlp, & ! <w'^2 th_l'> (thermodynamic levels) [m^2/s^2 K]
thlpthvp, & ! th_l'th_v' (momentum levels) [K^2]
thlm_forcing, & ! th_l forcing (thermodynamic levels) [K/s]
wpthlp_forcing, & ! <w'th_l'> forcing (momentum levels) [K/s^2]
thlm_ref, & ! thlm for nudging [K]
rho_ds_zm, & ! Dry, static density on momentum levels [kg/m^3]
rho_ds_zt, & ! Dry, static density on thermo. levels [kg/m^3]
invrs_rho_ds_zm, & ! Inv. dry, static density @ moment. levs. [m^3/kg]
invrs_rho_ds_zt, & ! Inv. dry, static density @ thermo. levs. [m^3/kg]
thv_ds_zm, & ! Dry, base-state theta_v on moment. levs. [K]
! Added for clipping by Vince Larson 29 Sep 2007
rtp2, & ! r_t'^2 (momentum levels) [(kg/kg)^2]
thlp2, & ! th_l'^2 (momentum levels) [K^2]
! End of Vince Larson's addition.
w_1_zm, & ! Mean w (1st PDF component) [m/s]
w_2_zm, & ! Mean w (2nd PDF component) [m/s]
varnce_w_1_zm, & ! Variance of w (1st PDF component) [m^2/s^2]
varnce_w_2_zm, & ! Variance of w (2nd PDF component) [m^2/s^2]
mixt_frac_zm ! Weight of 1st PDF component (Sk_w dependent) [-]
logical, intent(in) :: &
l_implemented ! Flag for CLUBB being implemented in a larger model.
! Additional variables for passive scalars
real( kind = core_rknd ), intent(in), dimension(gr%nz,sclr_dim) :: &
wp2sclrp, & ! <w'^2 sclr'> (thermodynamic levels) [Units vary]
sclrpthvp, & ! <sclr' th_v'> (momentum levels) [Units vary]
sclrm_forcing, & ! sclrm forcing (thermodynamic levels) [Units vary]
sclrp2 ! For clipping Vince Larson [Units vary]
real( kind = core_rknd ), intent(in), dimension(gr%nz) :: &
exner, & ! Exner function [-]
rcm, & ! cloud water mixing ratio, r_c [kg/kg]
p_in_Pa, & ! Air pressure [Pa]
thvm, & ! Virutal potential temperature [K]
Cx_fnc_Richardson,& ! Cx_fnc computed from Richardson_num [-]
ice_supersat_frac
type(implicit_coefs_terms), intent(in) :: &
pdf_implicit_coefs_terms ! Implicit coefs / explicit terms [units vary]
! Variables used to predict <u> and <u'w'>, as well as <v> and <v'w'>.
real( kind = core_rknd ), dimension(gr%nz), intent(in) :: &
um_forcing, & ! <u> forcing term (thermodynamic levels) [m/s^2]
vm_forcing, & ! <v> forcing term (thermodynamic levels) [m/s^2]
ug, & ! <u> geostrophic wind (thermodynamic levels) [m/s]
vg, & ! <v> geostrophic wind (thermodynamic levels) [m/s]
wpthvp ! <w'thv'> (momentum levels) [m/s K]
real( kind = core_rknd ), dimension(gr%nz), intent(in) :: &
uprcp, & ! < u' r_c' > [(m kg)/(s kg)]
vprcp, & ! < v' r_c' > [(m kg)/(s kg)]
rc_coef ! Coefficient on X'r_c' in X'th_v' equation [K/(kg/kg)]
real( kind = core_rknd ), intent(in) :: &
fcor ! Coriolis parameter [s^-1]
real( kind = core_rknd ), dimension(gr%nz), intent(in) :: &
um_ref, & ! Reference u wind component for nudging [m/s]
vm_ref, & ! Reference v wind component for nudging [m/s]
up2, & ! Variance of the u wind component [m^2/s^2]
vp2 ! Variance of the v wind component [m^2/s^2]
logical, intent(in) :: &
l_predict_upwp_vpwp, & ! Flag to predict <u'w'> and <v'w'> along with <u> and <v>
! alongside the advancement of <rt>, <w'rt'>, <thl>,
! <wpthlp>, <sclr>, and <w'sclr'> in subroutine
! advance_xm_wpxp. Otherwise, <u'w'> and <v'w'> are still
! approximated by eddy diffusivity when <u> and <v> are
! advanced in subroutine advance_windm_edsclrm.
l_diffuse_rtm_and_thlm, & ! This flag determines whether or not we want CLUBB to do
! diffusion on rtm and thlm
l_stability_correct_Kh_N2_zm, & ! This flag determines whether or not we want CLUBB to apply
! a stability correction
l_upwind_wpxp_ta, & ! This flag determines whether we want to use an upwind
! differencing approximation rather than a centered
! differencing for turbulent or mean advection terms.
! It affects wprtp, wpthlp, & wpsclrp.
l_upwind_xm_ma, & ! This flag determines whether we want to use an upwind
! differencing approximation rather than a centered
! differencing for turbulent or mean advection terms.
! It affects rtm, thlm, sclrm, um and vm.
l_uv_nudge, & ! For wind speed nudging
l_tke_aniso, & ! For anisotropic turbulent kinetic energy, i.e. TKE = 1/2
! (u'^2 + v'^2 + w'^2)
l_use_C7_Richardson, & ! Parameterize C7 based on Richardson number
l_brunt_vaisala_freq_moist, & ! Use a different formula for the Brunt-Vaisala frequency in
! saturated atmospheres (from Durran and Klemp, 1982)
l_use_thvm_in_bv_freq ! Use thvm in the calculation of Brunt-Vaisala frequency
! -------------------- Input/Output Variables --------------------
real( kind = core_rknd ), intent(inout), dimension(gr%nz) :: &
rtm, & ! r_t (total water mixing ratio) [kg/kg]
wprtp, & ! w'r_t' [(kg/kg) m/s]
thlm, & ! th_l (liquid water potential temperature) [K]
wpthlp ! w'th_l' [K m/s]
! Input/Output Variables
real( kind = core_rknd ), intent(inout), dimension(gr%nz,sclr_dim) :: &
sclrm, wpsclrp ! [Units vary]
! Variables used to predict <u> and <u'w'>, as well as <v> and <v'w'>.
real( kind = core_rknd ), intent(inout), dimension(gr%nz) :: &
um, & ! <u>: mean west-east horiz. velocity (thermo. levs.) [m/s]
upwp, & ! <u'w'>: momentum flux (momentum levels) [m^2/s^2]
vm, & ! <v>: mean south-north horiz. velocity (thermo. levs.) [m/s]
vpwp ! <v'w'>: momentum flux (momentum levels) [m^2/s^2]
! -------------------- Local Variables --------------------
real( kind = core_rknd ), dimension(gr%nz) :: &
C6rt_Skw_fnc, C6thl_Skw_fnc, C7_Skw_fnc
! Eddy Diffusion for wpthlp and wprtp.
real( kind = core_rknd ), dimension(gr%nz) :: Kw6 ! wpxp eddy diff. [m^2/s]
! Variables used as part of the monotonic turbulent advection scheme.
! Find the lowermost and uppermost grid levels that can have an effect
! on the central thermodynamic level during the course of a time step,
! due to the effects of turbulent advection only.
integer, dimension(gr%nz) :: &
low_lev_effect, & ! Index of the lowest level that has an effect.
high_lev_effect ! Index of the highest level that has an effect.
! Constant parameters as a function of Skw.
integer :: &
nrhs ! Number of RHS vectors
! Saved values of predictive fields, prior to being advanced, for use in
! print statements in case of fatal error.
real( kind = core_rknd ), dimension(gr%nz) :: &
rtm_old, & ! Saved value of r_t [kg/kg]
wprtp_old, & ! Saved value of w'r_t' [(kg/kg) m/s]
thlm_old, & ! Saved value of th_l [K]
wpthlp_old ! Saved value of w'th_l' [K m/s]
! Input/Output Variables
real( kind = core_rknd ), dimension(gr%nz,sclr_dim) :: &
sclrm_old, wpsclrp_old ! [Units vary]
! Variables used to predict <u> and <u'w'>, as well as <v> and <v'w'>.
real( kind = core_rknd ), dimension(gr%nz) :: &
um_old, & ! Saved value of <u> [m/s]
upwp_old, & ! Saved value of <u'w'> [m^2/s^2]
vm_old, & ! Saved value of <v> [m/s]
vpwp_old ! Saved value of <v'w'> [m^2/s^2]
! LHS/RHS terms
real( kind = core_rknd ), dimension(3,gr%nz) :: &
lhs_diff_zm, & ! Diffusion term for w'x'
lhs_diff_zt, & ! Diffusion term for w'x'
lhs_ma_zt, & ! Mean advection contributions to lhs
lhs_ma_zm ! Mean advection contributions to lhs
real( kind = core_rknd ), dimension(3,gr%nz) :: &
lhs_ta_wprtp, & ! w'r_t' turbulent advection contributions to lhs
lhs_ta_wpthlp, & ! w'thl' turbulent advection contributions to lhs
lhs_ta_wpup, & ! w'u' turbulent advection contributions to lhs
lhs_ta_wpvp ! w'v' turbulent advection contributions to lhs
real( kind = core_rknd ), dimension(3,gr%nz,sclr_dim) :: &
lhs_ta_wpsclrp ! w'sclr' turbulent advection contributions to lhs
real( kind = core_rknd ), dimension(gr%nz) :: &
rhs_ta_wprtp, & ! w'r_t' turbulent advection contributions to rhs
rhs_ta_wpthlp, & ! w'thl' turbulent advection contributions to rhs
rhs_ta_wpup, & ! w'u' turbulent advection contributions to rhs
rhs_ta_wpvp ! w'v' turbulent advection contributions to rhs
real( kind = core_rknd ), dimension(gr%nz,sclr_dim) :: &
rhs_ta_wpsclrp ! w'sclr' turbulent advection contributions to rhs
real( kind = core_rknd ), dimension(2,gr%nz) :: &
lhs_tp, & ! Turbulent production terms of w'x'
lhs_ta_xm ! Turbulent advection terms of xm
real( kind = core_rknd ), dimension(gr%nz) :: &
lhs_ac_pr2, & ! Accumulation of w'x' and w'x' pressure term 2
lhs_pr1_wprtp, & ! Pressure term 1 for w'r_t' for all grid levels
lhs_pr1_wpthlp, & ! Pressure term 1 for w'thl' for all grid levels
lhs_pr1_wpsclrp ! Pressure term 1 for w'sclr' for all grid levels
logical :: &
l_scalar_calc ! True if sclr_dim > 0
! -------------------- Begin Code --------------------
! Check whether the passive scalars are present.
if ( sclr_dim > 0 ) then
l_scalar_calc = .true.
else
l_scalar_calc = .false.
end if
if ( l_clip_semi_implicit &
.or. ( ( iiPDF_type == iiPDF_new ) &
.and. ( .not. l_explicit_turbulent_adv_wpxp ) ) ) then
nrhs = 1
else
if ( l_predict_upwp_vpwp ) then
nrhs = 4+sclr_dim
else
nrhs = 2+sclr_dim
endif
endif
! Save values of predictive fields to be printed in case of crash.
rtm_old = rtm
wprtp_old = wprtp
thlm_old = thlm
wpthlp_old = wpthlp
if ( sclr_dim > 0 ) then
sclrm_old = sclrm
wpsclrp_old = wpsclrp
endif ! sclr_dim > 0
if ( l_predict_upwp_vpwp ) then
um_old = um
upwp_old = upwp
vm_old = vm
vpwp_old = vpwp
endif ! l_predict_upwp_vpwp
! Compute C6 and C7 as a function of Skw
! The if...then is just here to save compute time
if ( abs(C6rt-C6rtb) > abs(C6rt+C6rtb)*eps/2 ) then
C6rt_Skw_fnc(1:gr%nz) = C6rtb + (C6rt-C6rtb) &
*EXP( -one_half * (Skw_zm(1:gr%nz)/C6rtc)**2 )
else
C6rt_Skw_fnc(1:gr%nz) = C6rtb
endif
if ( abs(C6thl-C6thlb) > abs(C6thl+C6thlb)*eps/2 ) then
C6thl_Skw_fnc(1:gr%nz) = C6thlb + (C6thl-C6thlb) &
*EXP( -one_half * (Skw_zm(1:gr%nz)/C6thlc)**2 )
else
C6thl_Skw_fnc(1:gr%nz) = C6thlb
endif
! Compute C7_Skw_fnc
if ( l_use_C7_Richardson ) then
! New formulation based on Richardson number
C7_Skw_fnc = Cx_fnc_Richardson
else
if ( abs(C7-C7b) > abs(C7+C7b)*eps/2 ) then
C7_Skw_fnc(1:gr%nz) = C7b + (C7-C7b) &
*EXP( -one_half * (Skw_zm(1:gr%nz)/C7c)**2 )
else
C7_Skw_fnc(1:gr%nz) = C7b
endif
! Damp C7 as a function of Lscale in stably stratified regions
C7_Skw_fnc = damp_coefficient( C7, C7_Skw_fnc, &
C7_Lscale0, wpxp_L_thresh, Lscale )
end if ! l_use_C7_Richardson
! Damp C6 as a function of Lscale in stably stratified regions
C6rt_Skw_fnc = damp_coefficient( C6rt, C6rt_Skw_fnc, &
C6rt_Lscale0, wpxp_L_thresh, Lscale )
C6thl_Skw_fnc = damp_coefficient( C6thl, C6thl_Skw_fnc, &
C6thl_Lscale0, wpxp_L_thresh, Lscale )
! C6rt_Skw_fnc = C6rt
! C6thl_Skw_fnc = C6thl
! C7_Skw_fnc = C7
if ( l_stats_samp ) then
call stat_update_var( iC7_Skw_fnc, C7_Skw_fnc, stats_zm )
call stat_update_var( iC6rt_Skw_fnc, C6rt_Skw_fnc, stats_zm )
call stat_update_var( iC6thl_Skw_fnc, C6thl_Skw_fnc, stats_zm )
end if
if ( clubb_at_least_debug_level( 0 ) ) then
! Assertion check for C7_Skw_fnc
if ( any( C7_Skw_fnc(:) > one ) .or. any( C7_Skw_fnc(:) < zero ) ) then
write(fstderr,*) "The C7_Skw_fnc variable is outside the valid range"
err_code = clubb_fatal_error
return
end if
end if
! Define the Coefficent of Eddy Diffusivity for the wpthlp and wprtp.
! Kw6 is used for wpthlp and wprtp, which are located on momentum levels.
! Kw6 is located on thermodynamic levels.
! Kw6 = c_K6 * Kh_zt
Kw6(1:gr%nz) = c_K6 * Kh_zt(1:gr%nz)
! Find the number of grid levels, both upwards and downwards, that can
! have an effect on the central thermodynamic level during the course of
! one time step due to turbulent advection. This is used as part of the
! monotonic turbulent advection scheme.
call calc_turb_adv_range( dt, w_1_zm, w_2_zm, varnce_w_1_zm, varnce_w_2_zm, & ! In
mixt_frac_zm, & ! In
low_lev_effect, high_lev_effect ) ! Out
! Calculate 1st pressure terms for w'r_t', w'thl', and w'sclr'.
call wpxp_term_pr1_lhs_all( C6rt_Skw_fnc, C6thl_Skw_fnc, C7_Skw_fnc, & ! Intent(in)
tau_C6_zm, l_scalar_calc, & ! Intent(in)
lhs_pr1_wprtp, lhs_pr1_wpthlp, lhs_pr1_wpsclrp ) ! Intent(out)
call calc_xm_wpxp_ta_terms( wprtp, wp2rtp, wpthlp, wp2thlp, wpsclrp, wp2sclrp, &
rho_ds_zt, invrs_rho_ds_zm, rho_ds_zm, &
sigma_sqd_w, wp3_on_wp2, wp3_on_wp2_zt, &
pdf_implicit_coefs_terms, &
l_explicit_turbulent_adv_wpxp, l_predict_upwp_vpwp, &
l_scalar_calc, &
l_upwind_wpxp_ta, &
lhs_ta_wprtp, lhs_ta_wpthlp, lhs_ta_wpup, &
lhs_ta_wpvp, lhs_ta_wpsclrp, &
rhs_ta_wprtp, rhs_ta_wpthlp, rhs_ta_wpup, &
rhs_ta_wpvp, rhs_ta_wpsclrp )
! Calculate various terms that are the same between all LHS matricies
call calc_xm_wpxp_lhs_terms( Kh_zm, wm_zm, wm_zt, wp2, & ! In
Kw6, C7_Skw_fnc, invrs_rho_ds_zt, & ! In
rho_ds_zm, l_implemented, em, & ! In
Lscale, thlm, exner, rtm, rcm, p_in_Pa, thvm, & ! In
ice_supersat_frac, & ! In
l_diffuse_rtm_and_thlm, & ! In
l_stability_correct_Kh_N2_zm, & ! In
l_upwind_xm_ma, & ! In
l_brunt_vaisala_freq_moist, & ! In
l_use_thvm_in_bv_freq, & ! In
lhs_diff_zm, lhs_diff_zt, lhs_ma_zt, lhs_ma_zm, & ! Out
lhs_tp, lhs_ta_xm, lhs_ac_pr2 ) ! Out
! Setup and decompose matrix for each variable.
if ( l_clip_semi_implicit &
.or. ( ( iiPDF_type == iiPDF_new ) &
.and. ( .not. l_explicit_turbulent_adv_wpxp ) ) ) then
! LHS matrices are unique, multiple band solves required
call solve_xm_wpxp_with_multiple_lhs( dt, l_iter, nrhs, wm_zt, wp2, & ! In
l_clip_semi_implicit, & ! In
rtpthvp, rtm_forcing, wprtp_forcing, thlpthvp, & ! In
thlm_forcing, wpthlp_forcing, rho_ds_zm, & ! In
rho_ds_zt, invrs_rho_ds_zm, invrs_rho_ds_zt, & ! In
thv_ds_zm, rtp2, thlp2, l_implemented, & ! In
sclrpthvp, sclrm_forcing, sclrp2, & ! In
low_lev_effect, high_lev_effect, C7_Skw_fnc, & ! In
lhs_diff_zm, lhs_diff_zt, lhs_ma_zt, lhs_ma_zm, & ! In
lhs_ta_wprtp, lhs_ta_wpthlp, lhs_ta_wpsclrp, & ! In
rhs_ta_wprtp, rhs_ta_wpthlp, rhs_ta_wpsclrp, & ! In
lhs_tp, lhs_ta_xm, lhs_ac_pr2, lhs_pr1_wprtp, & ! In
lhs_pr1_wpthlp, lhs_pr1_wpsclrp, & ! In
l_predict_upwp_vpwp, & ! In
l_diffuse_rtm_and_thlm, & ! In
l_upwind_xm_ma, & ! In
l_tke_aniso, & ! In
rtm, wprtp, thlm, wpthlp, sclrm, wpsclrp ) ! Out
else
! LHS matrices are equivalent, only one solve required
call solve_xm_wpxp_with_single_lhs( dt, l_iter, nrhs, wm_zt, wp2, tau_C6_zm, & ! In
rtpthvp, rtm_forcing, wprtp_forcing, thlpthvp, & ! In
thlm_forcing, wpthlp_forcing, rho_ds_zm, & ! In
rho_ds_zt, invrs_rho_ds_zm, invrs_rho_ds_zt, & ! In
thv_ds_zm, rtp2, thlp2, l_implemented, & ! In
sclrpthvp, sclrm_forcing, sclrp2, um_forcing, & ! In
vm_forcing, ug, vg, uprcp, vprcp, rc_coef, fcor, & ! In
up2, vp2, & ! In
low_lev_effect, high_lev_effect, & ! In
C6rt_Skw_fnc, C6thl_Skw_fnc, C7_Skw_fnc, & ! In
lhs_diff_zm, lhs_diff_zt, lhs_ma_zt, lhs_ma_zm, & ! In
lhs_ta_wprtp, & ! In
rhs_ta_wprtp, rhs_ta_wpthlp, rhs_ta_wpup, & ! In
rhs_ta_wpvp, rhs_ta_wpsclrp, & ! In
lhs_tp, lhs_ta_xm, lhs_ac_pr2, lhs_pr1_wprtp, & ! In
lhs_pr1_wpthlp, lhs_pr1_wpsclrp, & ! In
l_predict_upwp_vpwp, & ! In
l_diffuse_rtm_and_thlm, & ! In
l_upwind_xm_ma, & ! In
l_tke_aniso, & ! In
rtm, wprtp, thlm, wpthlp, & ! Out
sclrm, wpsclrp, um, upwp, vm,vpwp ) ! Out
endif ! l_clip_semi_implicit &
! .or. ( ( iiPDF_type == iiPDF_new ) &
! .and. ( .not. l_explicit_turbulent_adv_wpxp ) )
if ( clubb_at_least_debug_level( 0 ) ) then
if ( err_code == clubb_fatal_error ) then
call error_prints_xm_wpxp( dt, sigma_sqd_w, wm_zm, wm_zt, wp2, &
Lscale, wp3_on_wp2, wp3_on_wp2_zt, &
Kh_zt, Kh_zm, tau_C6_zm, Skw_zm, &
wp2rtp, rtpthvp, rtm_forcing, &
wprtp_forcing, rtm_ref, wp2thlp, &
thlpthvp, thlm_forcing, &
wpthlp_forcing, thlm_ref, rho_ds_zm, &
rho_ds_zt, invrs_rho_ds_zm, &
invrs_rho_ds_zt, thv_ds_zm, rtp2, &
thlp2, w_1_zm, w_2_zm, &
varnce_w_1_zm, varnce_w_2_zm, &
mixt_frac_zm, l_implemented, em, &
wp2sclrp, sclrpthvp, sclrm_forcing, &
sclrp2, exner, rcm, p_in_Pa, thvm, &
Cx_fnc_Richardson, &
pdf_implicit_coefs_terms, &
um_forcing, vm_forcing, ug, vg, &
wpthvp, fcor, um_ref, vm_ref, up2, &
vp2, uprcp, vprcp, rc_coef, rtm, &
wprtp, thlm, wpthlp, sclrm, wpsclrp, &
um, upwp, vm, vpwp, rtm_old, &
wprtp_old, thlm_old, wpthlp_old, &
sclrm_old, wpsclrp_old, um_old, &
upwp_old, vm_old, vpwp_old, &
l_predict_upwp_vpwp )
end if
end if
if ( rtm_sponge_damp_settings%l_sponge_damping ) then
if ( l_stats_samp ) then
call stat_begin_update( irtm_sdmp, rtm / dt, stats_zt )
endif
rtm(1:gr%nz) = sponge_damp_xm( dt, gr%zt, rtm_ref(1:gr%nz), &
rtm(1:gr%nz), rtm_sponge_damp_profile )
if ( l_stats_samp ) then
call stat_end_update( irtm_sdmp, rtm / dt, stats_zt )
endif
endif ! rtm_sponge_damp_settings%l_sponge_damping
if ( thlm_sponge_damp_settings%l_sponge_damping ) then
if ( l_stats_samp ) then
call stat_begin_update( ithlm_sdmp, thlm / dt, stats_zt )
endif
thlm(1:gr%nz) = sponge_damp_xm( dt, gr%zt, thlm_ref(1:gr%nz), &
thlm(1:gr%nz), thlm_sponge_damp_profile )
if ( l_stats_samp ) then
call stat_end_update( ithlm_sdmp, thlm / dt, stats_zt )
endif
endif ! thlm_sponge_damp_settings%l_sponge_damping
if ( l_predict_upwp_vpwp ) then
if ( uv_sponge_damp_settings%l_sponge_damping ) then
if ( l_stats_samp ) then
call stat_begin_update( ium_sdmp, um / dt, stats_zt )
call stat_begin_update( ivm_sdmp, vm / dt, stats_zt )
endif
um(1:gr%nz) = sponge_damp_xm( dt, gr%zt, um_ref(1:gr%nz), &
um(1:gr%nz), uv_sponge_damp_profile )
vm(1:gr%nz) = sponge_damp_xm( dt, gr%zt, vm_ref(1:gr%nz), &
vm(1:gr%nz), uv_sponge_damp_profile )
if ( l_stats_samp ) then
call stat_end_update( ium_sdmp, um / dt, stats_zt )
call stat_end_update( ivm_sdmp, vm / dt, stats_zt )
endif
endif ! uv_sponge_damp_settings%l_sponge_damping
! Adjust um and vm if nudging is turned on.
if ( l_uv_nudge ) then
! Reflect nudging in budget
if ( l_stats_samp ) then
call stat_begin_update( ium_ndg, um / dt, stats_zt )
call stat_begin_update( ivm_ndg, vm / dt, stats_zt )
endif
um(1:gr%nz) &
= um(1:gr%nz) - ( ( um(1:gr%nz) - um_ref(1:gr%nz) ) * (dt/ts_nudge) )
vm(1:gr%nz) &
= vm(1:gr%nz) - ( ( vm(1:gr%nz) - vm_ref(1:gr%nz) ) * (dt/ts_nudge) )
! Reflect nudging in budget
if ( l_stats_samp ) then
call stat_end_update( ium_ndg, um / dt, stats_zt )
call stat_end_update( ivm_ndg, vm / dt, stats_zt )
endif
endif ! l_uv_nudge
if ( l_stats_samp ) then
call stat_update_var( ium_ref, um_ref, stats_zt )
call stat_update_var( ivm_ref, vm_ref, stats_zt )
endif
endif ! l_predict_upwp_vpwp
return
end subroutine advance_xm_wpxp
!======================================================================================
subroutine xm_wpxp_lhs( l_iter, dt, wpxp, wm_zt, C7_Skw_fnc, & ! In
invrs_rho_ds_zt, wpxp_upper_lim, wpxp_lower_lim, & ! In
l_implemented, lhs_diff_zm, lhs_diff_zt, & ! In
lhs_ma_zm, lhs_ma_zt, lhs_ta_wpxp, lhs_ta_xm, & ! In
lhs_tp, lhs_pr1, lhs_ac_pr2, & ! In
l_diffuse_rtm_and_thlm, & ! In
lhs ) ! Out
! Description:
! Compute LHS band diagonal matrix for xm and w'x'.
! This subroutine computes the implicit portion of
! the xm and w'x' equations.
!
!
! Notes:
!
! Boundary conditions:
! The turbulent flux (wpxp) use fixed-point boundary conditions at both the
! upper and lower boundaries. Therefore, anything set in the wpxp loop
! at both the upper and lower boundaries would be overwritten here.
! However, the wpxp loop does not extend to the boundary levels. An array
! with a value of 1 at the main diagonal on the left-hand side and with
! values of 0 at all other diagonals on the left-hand side will preserve the
! right-hand side value at that level. The value of xm at level k = 1,
! which is below the model surface, is preserved and then overwritten to
! match the new value of xm at level k = 2.
!
! xm(1) wpxp(1) ... wpxp(nzmax)
! [ 0.0 0.0 0.0 ]
! [ 0.0 0.0 0.0 ]
! [ 1.0 1.0 ... 1.0 ]
! [ 0.0 0.0 0.0 ]
! [ 0.0 0.0 0.0 ]
!
!
! LHS turbulent advection (ta) term:
! An "over-implicit" weighted time step is applied to this term.
! The weight of the implicit portion of this term is controlled by
! the factor gamma_over_implicit_ts (abbreviated "gamma" in the
! equation in order to balance a weight that is not equal to 1,
! such that:
! -y(t) * [ gamma * X(t+1) + ( 1 - gamma ) * X(t) ] + RHS;
! where X is the variable that is being solved for in a predictive
! equation (<w'x'> in this case), y(t) is the linearized portion of
! the term that gets treated implicitly, and RHS is the portion of
! the term that is always treated explicitly. A weight of greater
! than 1 can be applied to make the term more numerically stable.
!
!
! xm: Left-hand side (implicit xm portion of the code).
!
! Thermodynamic subdiagonal (lhs index: t_km1_tdiag)
! [ x xm(k-1,<t+1>) ]
! Momentum subdiagonal (lhs index: t_km1_mdiag)
! [ x wpxp(k-1,<t+1>) ]
! Thermodynamic main diagonal (lhs index: t_k_tdiag)
! [ x xm(k,<t+1>) ]
! Momentum superdiagonal (lhs index: t_k_mdiag)
! [ x wpxp(k,<t+1>) ]
! Thermodynamic superdiagonal (lhs index: t_kp1_tdiag)
! [ x xm(k+1,<t+1>) ]
!
!
! w'x': Left-hand side (implicit w'x' portion of the code).
!
! Momentum subdiagonal (lhs index: m_km1_mdiag)
! [ x wpxp(k-1,<t+1>) ]
! Thermodynamic subdiagonal (lhs index: m_k_tdiag)
! [ x xm(k,<t+1>) ]
! Momentum main diagonal (lhs index: m_k_mdiag)
! [ x wpxp(k,<t+1>) ]
! Thermodynamic superdiagonal (lhs index: m_kp1_tdiag)
! [ x xm(k+1,<t+1>) ]
! Momentum superdiagonal (lhs index: m_kp1_mdiag)
! [ x wpxp(k+1,<t+1>) ]
!
!----------------------------------------------------------------------------------
use grid_class, only: &
gr, & ! Variable(s)
zm2zt, & ! Procedure(s)
ddzt
use constants_clubb, only: &
gamma_over_implicit_ts, & ! Constant(s)
one, &
zero
use model_flags, only: &
l_clip_semi_implicit ! Variable(s)
use clubb_precision, only: &
core_rknd ! Variable(s)
use clip_semi_implicit, only: &
clip_semi_imp_lhs ! Procedure(s)
use stats_variables, only: &
ztscr01, & ! Variable(s)
ztscr02, &
ztscr03, &
ztscr04, &
ztscr05, &
zmscr01, &
zmscr02, &
zmscr03, &
zmscr04, &
zmscr05, &
zmscr06, &
zmscr07, &
zmscr08, &
zmscr09, &
zmscr10, &
zmscr11, &
zmscr12, &
zmscr13, &
zmscr14, &
zmscr15
use stats_variables, only: &
l_stats_samp, &
ithlm_ma, &
ithlm_ta, &
irtm_ma, &
irtm_ta, &
iwpthlp_ma, &
iwpthlp_ta, &
iwpthlp_tp, &
iwpthlp_ac, &
iwpthlp_pr1, &
iwpthlp_pr2, &
iwpthlp_dp1, &
iwpthlp_sicl, &
iwprtp_ma, &
iwprtp_ta, &
iwprtp_tp, &
iwprtp_ac, &
iwprtp_pr1, &
iwprtp_pr2, &
iwprtp_dp1, &
iwprtp_sicl
use advance_helper_module, only: &
set_boundary_conditions_lhs, & ! Procedure(s)
calc_stability_correction
implicit none
! External
intrinsic :: min, max
!------------------- Input Variables -------------------
real( kind = core_rknd ), intent(in) :: &
dt ! Timestep [s]
real( kind = core_rknd ), intent(in), dimension(gr%nz) :: &
wpxp, & ! w'x' (momentum levs) at timestep (t) [un vary]
wm_zt, & ! w wind component on thermo. levels [m/s]
C7_Skw_fnc, & ! C_7 parameter with Sk_w applied [-]
invrs_rho_ds_zt, & ! Inv. dry, static density at t-levs. [m^3/kg]
wpxp_upper_lim, & ! Keeps corrs. from becoming > 1 [un vary]
wpxp_lower_lim ! Keeps corrs. from becoming < -1 [un vary]
logical, intent(in) :: &
l_implemented, & ! Flag for CLUBB being implemented in a larger model.
l_iter
!------------------- Output Variable -------------------
real( kind = core_rknd ), intent(out), dimension(nsup+nsub+1,2*gr%nz) :: &
lhs ! Implicit contributions to wpxp/xm (band diag. matrix) (LAPACK)
!------------------- Local Variables -------------------
! Indices
integer :: k
integer :: k_xm, k_wpxp
logical :: l_upper_thresh, l_lower_thresh ! flags for clip_semi_imp_lhs
real( kind = core_rknd ), dimension(3,gr%nz), intent(in) :: &
lhs_diff_zm, & ! Diffusion term for w'x'
lhs_diff_zt, & ! Diffusion term for xm
lhs_ma_zt, & ! Mean advection contributions to lhs
lhs_ma_zm, & ! Mean advection contributions to lhs
lhs_ta_wpxp ! Turbulent advection contributions to lhs
real( kind = core_rknd ), dimension(2,gr%nz), intent(in) :: &
lhs_tp, & ! Turbulent production terms of w'x'
lhs_ta_xm ! Turbulent advection terms of xm
real( kind = core_rknd ), dimension(gr%nz), intent(in) :: &
lhs_ac_pr2, & ! Accumulation of w'x' and w'x' pressure term 2
lhs_pr1 ! Pressure term 1 for w'x'
logical, intent(in) :: &
l_diffuse_rtm_and_thlm ! This flag determines whether or not we want CLUBB to do diffusion
! on rtm and thlm
real (kind = core_rknd) :: &
invrs_dt
!------------------- Begin Code -------------------
! Initializations/precalculations
invrs_dt = 1.0_core_rknd / dt
! Lower boundary for xm, lhs(:,1)
lhs(1,1) = 0.0_core_rknd
lhs(2,1) = 0.0_core_rknd
lhs(3,1) = 1.0_core_rknd
lhs(4,1) = 0.0_core_rknd
lhs(5,1) = 0.0_core_rknd
! Lower boundary for w'x', lhs(:,2)
lhs(1,2) = 0.0_core_rknd
lhs(2,2) = 0.0_core_rknd
lhs(3,2) = 1.0_core_rknd
lhs(4,2) = 0.0_core_rknd
lhs(5,2) = 0.0_core_rknd
! Combine xm and w'x' terms into LHS
do k = 2, gr%nz
k_xm = 2*k - 1 ! xm at odd index values
k_wpxp = 2*k ! w'x' at even index values
! ---- sum xm terms ----
lhs(1,k_xm) = zero
lhs(2,k_xm) = lhs_ta_xm(1,k)
lhs(3,k_xm) = invrs_dt
lhs(4,k_xm) = lhs_ta_xm(2,k)
lhs(5,k_xm) = zero
! ---- sum w'x' terms ----
lhs(1,k_wpxp) = lhs_ma_zm(1,k) + lhs_diff_zm(1,k) &
+ gamma_over_implicit_ts * lhs_ta_wpxp(1,k)
lhs(2,k_wpxp) = lhs_tp(1,k)
lhs(3,k_wpxp) = lhs_ma_zm(2,k) + lhs_diff_zm(2,k) + lhs_ac_pr2(k) &
+ gamma_over_implicit_ts * ( lhs_ta_wpxp(2,k) + lhs_pr1(k) )
lhs(4,k_wpxp) = lhs_tp(2,k)
lhs(5,k_wpxp) = lhs_ma_zm(3,k) + lhs_diff_zm(3,k) &
+ gamma_over_implicit_ts * lhs_ta_wpxp(3,k)
enddo
! Upper boundary for w'x', , lhs(:,2*gr%nz)
! These were set in the loop above for simplicity, so they must be set properly here
lhs(1,2*gr%nz) = 0.0_core_rknd
lhs(2,2*gr%nz) = 0.0_core_rknd
lhs(3,2*gr%nz) = 1.0_core_rknd
lhs(4,2*gr%nz) = 0.0_core_rknd
lhs(5,2*gr%nz) = 0.0_core_rknd
! LHS time tendency
if ( l_iter ) then
do k = 2, gr%nz-1
k_wpxp = 2*k
lhs(3,k_wpxp) = lhs(3,k_wpxp) + invrs_dt
end do
endif
! Calculate diffusion terms for all thermodynamic grid level
if ( l_diffuse_rtm_and_thlm ) then