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advance_wp2_wp3_module.F90
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advance_wp2_wp3_module.F90
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!------------------------------------------------------------------------
! $Id$
!===============================================================================
module advance_wp2_wp3_module
implicit none
private ! Default Scope
public :: advance_wp2_wp3
private :: wp23_solve, &
wp23_lhs, &
wp23_rhs, &
wp2_term_ta_lhs, &
wp2_terms_ac_pr2_lhs, &
wp2_term_dp1_lhs, &
wp2_term_pr1_lhs, &
wp2_terms_bp_pr2_rhs, &
wp2_term_dp1_rhs, &
wp2_term_pr3_rhs, &
wp2_term_pr1_rhs, &
wp3_term_ta_new_pdf_lhs, &
wp3_term_ta_ADG1_lhs, &
wp3_term_tp_lhs, &
wp3_terms_ac_pr2_lhs, &
wp3_term_pr1_lhs, &
wp3_term_ta_explicit_rhs, &
wp3_terms_bp1_pr2_rhs, &
wp3_term_pr1_rhs, &
wp3_term_bp2_rhs, &
wp2_term_ta_lhs_all, &
wp2_terms_ac_pr2_lhs_all, &
wp2_term_dp1_lhs_all, &
wp2_term_pr1_lhs_all, &
wp2_terms_bp_pr2_rhs_all, &
wp2_term_dp1_rhs_all, &
wp2_term_pr3_rhs_all, &
wp2_term_pr1_rhs_all, &
wp3_term_ta_new_pdf_lhs_all, &
wp3_term_ta_ADG1_lhs_all, &
wp3_term_tp_lhs_all, &
wp3_terms_ac_pr2_lhs_all, &
wp3_term_pr1_lhs_all, &
wp3_term_ta_explicit_rhs_all, &
wp3_terms_bp1_pr2_rhs_all, &
wp3_term_pr1_rhs_all, &
wp3_term_bp2_rhs_all
! Private named constants to avoid string comparisons
integer, parameter, private :: &
clip_wp2 = 12 ! Named constant for wp2 clipping.
! NOTE: This must be the same as the clip_wp2 declared in
! clip_explicit!
contains
!=============================================================================
subroutine advance_wp2_wp3( dt, sfc_elevation, sigma_sqd_w, wm_zm, & ! In
wm_zt, a3, a3_zt, wp3_on_wp2, wp4, & ! In
wpthvp, wp2thvp, um, vm, upwp, vpwp, & ! In
up2, vp2, Kh_zm, Kh_zt, tau_zm, tau_zt, & ! In
tau_C1_zm, Skw_zm, Skw_zt, rho_ds_zm, & ! In
rho_ds_zt, invrs_rho_ds_zm, & ! In
invrs_rho_ds_zt, radf, thv_ds_zm, & ! In
thv_ds_zt, mixt_frac, Cx_fnc_Richardson, & ! In
wp2_splat, wp3_splat, & ! intent(in)
pdf_implicit_coefs_terms, & ! In
wprtp, wpthlp, rtp2, thlp2, & ! In
l_min_wp2_from_corr_wx, & ! In
l_upwind_xm_ma, & ! In
l_tke_aniso, & ! In
l_standard_term_ta, & ! In
l_damp_wp2_using_em, & ! In
l_use_C11_Richardson, & ! In
l_damp_wp3_Skw_squared, & ! In
wp2, wp3, wp3_zm, wp2_zt ) ! Inout
! Description:
! Advance w'^2 and w'^3 one timestep.
! References:
! https://arxiv.org/pdf/1711.03675v1.pdf#nameddest=url:wp2_wp3_eqns
!
! Eqn. 12 & 18 on p. 3545--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 6:
! /Implict solution for the vertical velocity moments/
!------------------------------------------------------------------------
use grid_class, only: &
gr, & ! Variable(s)
zt2zm, & ! Procedure(s)
zm2zt
use parameters_tunable, only: &
C11c, & ! Variable(s)
C11b, &
C11, &
C1c, &
C1b, &
C1, &
c_K1, &
c_K8
use sponge_layer_damping, only: &
wp2_sponge_damp_settings, & ! Variable(s)
wp3_sponge_damp_settings, &
wp2_sponge_damp_profile, &
wp3_sponge_damp_profile, &
sponge_damp_xp2, & ! Procedure(s)
sponge_damp_xp3
use stats_type_utilities, only: &
stat_begin_update, & ! Procedure(s)
stat_end_update, &
stat_update_var
use stats_variables, only: &
iC1_Skw_fnc, & ! Variable(s)
iC11_Skw_fnc, &
iwp2_sdmp, &
iwp3_sdmp, &
stats_zm, &
stats_zt, &
l_stats_samp
use constants_clubb, only: &
fstderr, & ! Variables
one, &
one_half, &
one_third, &
w_tol_sqd, &
eps
use pdf_parameter_module, only: &
implicit_coefs_terms ! Variable Type
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 ! Constant
implicit none
intrinsic :: exp
! Input Variables
real( kind = core_rknd ), intent(in) :: &
dt ! Model timestep [s]
real( kind = core_rknd ), intent(in) :: &
sfc_elevation ! Elevation of ground level [m AMSL]
real( kind = core_rknd ), intent(in), dimension(gr%nz) :: &
sigma_sqd_w, & ! sigma_sqd_w (momentum levels) [-]
wm_zm, & ! w wind component on momentum levels [m/s]
wm_zt, & ! w wind component on thermodynamic levels [m/s]
a3, & ! a_3 (momentum levels); See eqn. 25 in `Equations for CLUBB' [-]
a3_zt, & ! a_3 interpolated to thermodynamic levels [-]
wp3_on_wp2, & ! Smoothed version of wp3 / wp2 [m/s]
wp4, & ! w'^4 (momentum levels) [m^4/s^4]
wpthvp, & ! w'th_v' (momentum levels) [K m/s]
wp2thvp, & ! w'^2th_v' (thermodynamic levels) [K m^2/s^2]
um, & ! u wind component (thermodynamic levels) [m/s]
vm, & ! v wind component (thermodynamic levels) [m/s]
upwp, & ! u'w' (momentum levels) [m^2/s^2]
vpwp, & ! v'w' (momentum levels) [m^2/s^2]
up2, & ! u'^2 (momentum levels) [m^2/s^2]
vp2, & ! v'^2 (momentum levels) [m^2/s^2]
Kh_zm, & ! Eddy diffusivity on momentum levels [m^2/s]
Kh_zt, & ! Eddy diffusivity on thermodynamic levels [m^2/s]
tau_zm, & ! Time-scale tau on momentum levels [s]
tau_zt, & ! Time-scale tau on thermodynamic levels [s]
tau_C1_zm, & ! Tau values used for the C1 (dp1) term in wp2 [s]
Skw_zm, & ! Skewness of w on momentum levels [-]
Skw_zt, & ! Skewness of w on thermodynamic levels [-]
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 @ momentum levs. [m^3/kg]
invrs_rho_ds_zt, & ! Inv. dry, static density @ thermo. levs. [m^3/kg]
radf, & ! Buoyancy production at the CL top [m^2/s^3]
thv_ds_zm, & ! Dry, base-state theta_v on momentum levs. [K]
thv_ds_zt, & ! Dry, base-state theta_v on thermo. levs. [K]
mixt_frac, & ! Weight of 1st normal distribution [-]
wprtp, & ! Flux of total water mixing ratio [m/s kg/kg]
wpthlp, & ! Flux of liquid water potential temp. [m/s K]
rtp2, & ! Variance of rt (overall) [kg^2/kg^2]
thlp2, & ! Variance of thl (overall) [K^2]
Cx_fnc_Richardson, & ! Cx_fnc from Richardson_num [-]
wp2_splat, & ! Tendency of <w'2> due to vertical compression of eddies [m^2/s^3]
wp3_splat ! Tendency of <w'3> due to vertical compression of eddies [m^3/s^4]
type(implicit_coefs_terms), intent(in) :: &
pdf_implicit_coefs_terms ! Implicit coefs / explicit terms [units vary]
logical, intent(in) :: &
l_min_wp2_from_corr_wx, & ! Flag to base the threshold minimum value of wp2 on keeping the
! overall correlation of w and x (w and rt, as well as w and
! theta-l) within the limits of -max_mag_correlation_flux to
! max_mag_correlation_flux.
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_tke_aniso, & ! For anisotropic turbulent kinetic energy, i.e. TKE = 1/2
! (u'^2 + v'^2 + w'^2)
l_standard_term_ta, & ! Use the standard discretization for the turbulent advection
! terms. Setting to .false. means that a_1 and a_3 are pulled
! outside of the derivative in advance_wp2_wp3_module.F90 and in
! advance_xp2_xpyp_module.F90.
l_damp_wp2_using_em, & ! In wp2 equation, use a dissipation formula of -(2/3)*em/tau_zm,
! as in Bougeault (1981)
l_use_C11_Richardson, & ! Parameterize C16 based on Richardson number
l_damp_wp3_Skw_squared ! Set damping on wp3 to use Skw^2 rather than Skw^4
! Input/Output
real( kind = core_rknd ), dimension(gr%nz), intent(inout) :: &
wp2, & ! w'^2 (momentum levels) [m^2/s^2]
wp3, & ! w'^3 (thermodynamic levels) [m^3/s^3]
wp3_zm ! w'^3 interpolated to momentum levels [m^3/s^3]
real( kind = core_rknd ), dimension(gr%nz), intent(inout) :: &
wp2_zt ! w'^2 interpolated to thermodyamic levels [m^2/s^2]
! Local Variables
real( kind = core_rknd ), dimension(gr%nz) :: &
tauw3t ! Currently just tau_zt [s]
! Eddy Diffusion for w'^2 and w'^3.
real( kind = core_rknd ), dimension(gr%nz) :: Kw1 ! w'^2 coef. eddy diff. [m^2/s]
real( kind = core_rknd ), dimension(gr%nz) :: Kw8 ! w'^3 coef. eddy diff. [m^2/s]
! Internal variables for C11 function, Vince Larson 13 Mar 2005
! Brian added C1 function.
real( kind = core_rknd ), dimension(gr%nz) :: &
C1_Skw_fnc, & ! C_1 parameter with Sk_w applied [-]
C11_Skw_fnc, & ! C_11 parameter with Sk_w applied [-]
! End Vince Larson's addition.
C16_fnc ! C_16 parameter [-]
integer :: k ! Array indices
!-----------------------------------------------------------------------
! Define tauw
! tauw3t = tau_zt
! . / ( 1.
! . + 3.0_core_rknd * max(
! . min(1.-(mixt_frac-0.01_core_rknd)/(0.05_core_rknd-0.01_core_rknd)
! . ,1.)
! . ,0.)
! . + 3.0_core_rknd * max(
! . min(1.-(mixt_frac-0.99_core_rknd)/(0.95_core_rknd-0.99_core_rknd)
! . ,1.)
! . ,0.)
! . )
! do k=1,gr%nz
!
! Skw = abs( wp3(k)/max(wp2(k),1.e-8)**1.5_core_rknd )
! Skw = min( 5.0_core_rknd, Skw )
! tauw3t(k) = tau_zt(k) / ( 0.005_core_rknd*Skw**4 + one )
!
! end do
tauw3t = tau_zt
! Vince Larson added code to make C11 function of Skw. 13 Mar 2005
! If this code is used, C11 is no longer relevant, i.e. constants
! are hardwired.
if ( l_use_C11_Richardson ) then
C11_Skw_fnc = Cx_fnc_Richardson
else
! Calculate C_{1} and C_{11} as functions of skewness of w.
! The if..then here is only for computational efficiency -dschanen 2 Sept 08
if ( abs(C11-C11b) > abs(C11+C11b)*eps/2 ) then
C11_Skw_fnc(1:gr%nz) = &
C11b + (C11-C11b)*EXP( -one_half * (Skw_zt(1:gr%nz)/C11c)**2 )
else
C11_Skw_fnc(1:gr%nz) = C11b
end if
end if ! l_use_C11_Richardson
! The if..then here is only for computational efficiency -dschanen 2 Sept 08
if ( abs(C1-C1b) > abs(C1+C1b)*eps/2 ) then
C1_Skw_fnc(1:gr%nz) = &
C1b + (C1-C1b)*EXP( -one_half * (Skw_zm(1:gr%nz)/C1c)**2 )
else
C1_Skw_fnc(1:gr%nz) = C1b
end if
if ( l_damp_wp2_using_em ) then
! Insert 1/3 here to account for the fact that in the dissipation term,
! (2/3)*em = (2/3)*(1/2)*(wp2+up2+vp2). Then we can insert wp2, up2,
! and vp2 directly into the dissipation subroutines without prefixing them by (1/3).
C1_Skw_fnc(1:gr%nz) = one_third * C1_Skw_fnc(1:gr%nz)
end if
!C11_Skw_fnc = C11
!C1_Skw_fnc = C1
! Set C16_fnc based on Richardson_num
C16_fnc = Cx_fnc_Richardson
if ( clubb_at_least_debug_level( 0 ) ) then
! Assertion check for C11_Skw_fnc
if ( any( C11_Skw_fnc(:) > one ) .or. any( C11_Skw_fnc(:) < 0._core_rknd ) ) then
write(fstderr,*) "The C11_Skw_fnc is outside the valid range for this variable"
err_code = clubb_fatal_error
return
end if
if ( any( C16_fnc(:) > one ) .or. any( C16_fnc(:) < 0._core_rknd ) ) then
write(fstderr,*) "The C16_fnc is outside the valid range for this variable"
err_code = clubb_fatal_error
return
end if
end if
if ( l_stats_samp ) then
call stat_update_var( iC11_Skw_fnc, C11_Skw_fnc, stats_zt )
call stat_update_var( iC1_Skw_fnc, C1_Skw_fnc, stats_zm )
endif
! Define the Coefficent of Eddy Diffusivity for the wp2 and wp3.
do k = 1, gr%nz, 1
! Kw1 is used for wp2, which is located on momentum levels.
! Kw1 is located on thermodynamic levels.
! Kw1 = c_K1 * Kh_zt
Kw1(k) = c_K1 * Kh_zt(k)
! Kw8 is used for wp3, which is located on thermodynamic levels.
! Kw8 is located on momentum levels.
! Note: Kw8 is usually defined to be 1/2 of Kh_zm.
! Kw8 = c_K8 * Kh_zm
Kw8(k) = c_K8 * Kh_zm(k)
enddo
! Solve semi-implicitly
call wp23_solve( dt, sfc_elevation, sigma_sqd_w, wm_zm, & ! Intent(in)
wm_zt, a3, a3_zt, wp3_on_wp2, wp4, & ! Intent(in)
wpthvp, wp2thvp, um, vm, upwp, vpwp, & ! Intent(in)
up2, vp2, Kw1, Kw8, Kh_zt, Skw_zt, & ! Intent(in)
tau_zm, tauw3t, tau_C1_zm, C1_Skw_fnc, & ! Intent(in)
C11_Skw_fnc, C16_fnc, rho_ds_zm, & ! Intent(in)
rho_ds_zt, invrs_rho_ds_zm, & ! Intent(in)
invrs_rho_ds_zt, radf, & ! Intent(in)
thv_ds_zm, thv_ds_zt, & ! Intent(in)
wp2_splat, wp3_splat, & ! Intent(in)
pdf_implicit_coefs_terms, & ! Intent(in)
wprtp, wpthlp, rtp2, thlp2, & ! Intent(in)
l_min_wp2_from_corr_wx, & ! Intent(in)
l_upwind_xm_ma, & ! Intent(in)
l_tke_aniso, & ! Intent(in)
l_standard_term_ta, & ! Intent(in)
l_damp_wp2_using_em, & ! Intent(in)
l_damp_wp3_Skw_squared, & ! Intent(in)
wp2, wp3, wp3_zm, wp2_zt ) ! Intent(inout)
! When selected, apply sponge damping after wp2 and wp3 have been advanced.
if ( wp2_sponge_damp_settings%l_sponge_damping ) then
if ( l_stats_samp ) then
call stat_begin_update( iwp2_sdmp, wp2 / dt, stats_zm )
endif
wp2 = sponge_damp_xp2( dt, gr%zm, wp2, w_tol_sqd, &
wp2_sponge_damp_profile )
if ( l_stats_samp ) then
call stat_end_update( iwp2_sdmp, wp2 / dt, stats_zm )
endif
endif ! wp2_sponge_damp_settings%l_sponge_damping
if ( wp3_sponge_damp_settings%l_sponge_damping ) then
if ( l_stats_samp ) then
call stat_begin_update( iwp3_sdmp, wp3 / dt, stats_zt )
endif
wp3 = sponge_damp_xp3( dt, gr%zt, wp3, wp3_sponge_damp_profile )
if ( l_stats_samp ) then
call stat_end_update( iwp3_sdmp, wp3 / dt, stats_zt )
endif
endif ! wp3_sponge_damp_settings%l_sponge_damping
if ( clubb_at_least_debug_level( 0 ) ) then
if ( err_code == clubb_fatal_error ) then
write(fstderr,*) "Error in advance_wp2_wp3"
write(fstderr,*) "Intent(in)"
write(fstderr,*) "gr%zt = ", gr%zt, new_line('c')
write(fstderr,*) "dt = ", dt, new_line('c')
write(fstderr,*) "sfc_elevation = ", sfc_elevation, new_line('c')
write(fstderr,*) "sigma_sqd_w = ", sigma_sqd_w, new_line('c')
write(fstderr,*) "wm_zm = ", wm_zm, new_line('c')
write(fstderr,*) "wm_zt = ", wm_zt, new_line('c')
write(fstderr,*) "wp4 = ", wp4, new_line('c')
write(fstderr,*) "wpthvp = ", wpthvp, new_line('c')
write(fstderr,*) "wp2thvp = ", wp2thvp, new_line('c')
write(fstderr,*) "um = ", um, new_line('c')
write(fstderr,*) "vm = ", vm, new_line('c')
write(fstderr,*) "upwp = ", upwp, new_line('c')
write(fstderr,*) "vpwp = ", vpwp, new_line('c')
write(fstderr,*) "up2 = ", up2, new_line('c')
write(fstderr,*) "vp2 = ", vp2, new_line('c')
write(fstderr,*) "Kh_zm = ", Kh_zm, new_line('c')
write(fstderr,*) "Kh_zt = ", Kh_zt, new_line('c')
write(fstderr,*) "tau_zm = ", tau_zm, new_line('c')
write(fstderr,*) "tau_zt = ", tau_zt, new_line('c')
write(fstderr,*) "Skw_zm = ", Skw_zm, new_line('c')
write(fstderr,*) "Skw_zt = ", Skw_zt, new_line('c')
write(fstderr,*) "mixt_frac = ", mixt_frac, new_line('c')
write(fstderr,*) "a3 = ", a3, new_line('c')
write(fstderr,*) "a3_zt = ", a3_zt, new_line('c')
write(fstderr,*) "wp3_on_wp2 = ", wp3_on_wp2, new_line('c')
write(fstderr,*) "tau_C1_zm = ", tau_C1_zm, new_line('c')
write(fstderr,*) "rho_ds_zm = ", rho_ds_zm, new_line('c')
write(fstderr,*) "rho_ds_zt = ", rho_ds_zt, new_line('c')
write(fstderr,*) "invrs_rho_ds_zm = ", invrs_rho_ds_zm, new_line('c')
write(fstderr,*) "invrs_rho_ds_zt = ", invrs_rho_ds_zt, new_line('c')
write(fstderr,*) "radf = ", radf, new_line('c')
write(fstderr,*) "thv_ds_zm = ", thv_ds_zm, new_line('c')
write(fstderr,*) "thv_ds_zt = ", thv_ds_zt, new_line('c')
write(fstderr,*) "Cx_fnc_Richardson = ", Cx_fnc_Richardson, new_line('c')
write(fstderr,*) "pdf_implicit_coefs_terms%coef_wp4_implicit = ", &
pdf_implicit_coefs_terms%coef_wp4_implicit
write(fstderr,*) new_line('c')
write(fstderr,*) "Intent(in/out)"
write(fstderr,*) "wp2_zt = ", wp2_zt, new_line('c')
write(fstderr,*) "wp3_zm = ", wp3_zm, new_line('c')
write(fstderr,*) "wp2 = ", wp2, new_line('c')
write(fstderr,*) "wp3 = ", wp3, new_line('c')
end if ! fatal error
end if
return
end subroutine advance_wp2_wp3
!=============================================================================
subroutine wp23_solve( dt, sfc_elevation, sigma_sqd_w, wm_zm, & ! Intent(in)
wm_zt, a3, a3_zt, wp3_on_wp2, wp4, & ! Intent(in)
wpthvp, wp2thvp, um, vm, upwp, vpwp, & ! Intent(in)
up2, vp2, Kw1, Kw8, Kh_zt, Skw_zt, & ! Intent(in)
tau1m, tauw3t, tau_C1_zm, C1_Skw_fnc, & ! Intent(in)
C11_Skw_fnc, C16_fnc, rho_ds_zm, & ! Intent(in)
rho_ds_zt, invrs_rho_ds_zm, & ! Intent(in)
invrs_rho_ds_zt, radf, & ! Intent(in)
thv_ds_zm, thv_ds_zt, & ! Intent(in)
wp2_splat, wp3_splat, & ! Intent(in)
pdf_implicit_coefs_terms, & ! Intent(in)
wprtp, wpthlp, rtp2, thlp2, & ! Intent(in)
l_min_wp2_from_corr_wx, & ! Intent(in)
l_upwind_xm_ma, & ! Intent(in)
l_tke_aniso, & ! Intent(in)
l_standard_term_ta, & ! Intent(in)
l_damp_wp2_using_em, & ! Intent(in)
l_damp_wp3_Skw_squared, & ! Intent(in)
wp2, wp3, wp3_zm, wp2_zt ) ! Intent(inout)
! Description:
! Decompose, and back substitute the matrix for wp2/wp3
! References:
! _Equations for CLUBB_ section 6.3
!------------------------------------------------------------------------
use grid_class, only: &
gr ! Variable(s)
use grid_class, only: &
zm2zt, & ! Function(s)
zt2zm, &
ddzt
use constants_clubb, only: &
w_tol_sqd, & ! Variables(s)
max_mag_correlation_flux, &
one, &
zero, &
zero_threshold, &
fstderr
use error_code, only: &
clubb_at_least_debug_level, & ! Procedure
err_code, & ! Error Indicator
clubb_fatal_error ! Constants
use model_flags, only: &
l_hole_fill, & ! Variable(s)
l_explicit_turbulent_adv_wp3
use clubb_precision, only: &
core_rknd ! Variable(s)
use lapack_wrap, only: &
band_solve, & ! Procedure(s)
band_solvex
use fill_holes, only: &
fill_holes_vertical
use clip_explicit, only: &
clip_variance, & ! Procedure(s)
clip_variance_level, &
clip_skewness
use pdf_closure_module, only: &
iiPDF_ADG1, & ! Variable(s)
iiPDF_new, &
iiPDF_new_hybrid, &
iiPDF_type
use pdf_parameter_module, only: &
implicit_coefs_terms ! Variable Type
use stats_type_utilities, only: &
stat_begin_update, & ! Procedure(s)
stat_update_var, &
stat_update_var_pt, &
stat_end_update, &
stat_end_update_pt
use stats_variables, only: &
stats_zm, & ! Variable(s)
stats_zt, &
stats_sfc, &
l_stats_samp, &
icoef_wp4_implicit, &
iwp2_ta, &
iwp2_ma, &
iwp2_pd, &
iwp2_ac, &
iwp2_dp1, &
iwp2_dp2, &
iwp2_pr1, &
iwp2_pr2, &
iwp3_ta, &
iwp3_ma, &
iwp3_tp, &
iwp3_ac, &
iwp3_dp1, &
iwp3_pr1, &
iwp3_pr2, &
iwp3_pr3, &
iwp23_matrix_condt_num
use stats_variables, only: &
zmscr01, &
zmscr02, &
zmscr03, &
zmscr04, &
zmscr05, &
zmscr06, &
zmscr07, &
zmscr08, &
zmscr09, &
zmscr10, &
zmscr11, &
zmscr12, &
ztscr01, &
ztscr02
use stats_variables, only: &
ztscr03, &
ztscr04, &
ztscr05, &
ztscr06, &
ztscr07, &
ztscr08, &
ztscr09, &
ztscr10, &
ztscr11, &
ztscr12, &
ztscr13, &
ztscr14, &
ztscr15, &
ztscr16
implicit none
! External
intrinsic :: max, min, sqrt
! Parameter Constants
integer, parameter :: &
nrhs = 1 ! Number of RHS vectors
! Input Variables
real( kind = core_rknd ), intent(in) :: &
dt ! Timestep [s]
real( kind = core_rknd ), intent(in) :: &
sfc_elevation ! Elevation of ground level [m AMSL]
real( kind = core_rknd ), intent(in), dimension(gr%nz) :: &
sigma_sqd_w, & ! sigma_sqd_w (momentum levels) [-]
wm_zm, & ! w wind component on momentum levels [m/s]
wm_zt, & ! w wind component on thermodynamic levels [m/s]
a3, & ! a_3 (momentum levels); See eqn. 25 in `Equations for CLUBB' [-]
a3_zt, & ! a_3 interpolated to thermodynamic levels [-]
wp3_on_wp2, & ! Smoothed version of wp3 / wp2 [m/s]
wp4, & ! w'^4 (momentum levels) [m^4/s^4]
wpthvp, & ! w'th_v' (momentum levels) [K m/s]
wp2thvp, & ! w'^2th_v' (thermodynamic levels) [K m^2/s^2]
um, & ! u wind component (thermodynamic levels) [m/s]
vm, & ! v wind component (thermodynamic levels) [m/s]
upwp, & ! u'w' (momentum levels) [m^2/s^2]
vpwp, & ! v'w' (momentum levels) [m^2/s^2]
up2, & ! u'^2 (momentum levels) [m^2/s^2]
vp2, & ! v'^2 (momentum levels) [m^2/s^2]
Kw1, & ! Coefficient of eddy diffusivity for w'^2 [m^2/s]
Kw8, & ! Coefficient of eddy diffusivity for w'^3 [m^2/s]
Kh_zt, & ! Eddy diffusivity on thermodynamic levels [m^2/s]
Skw_zt, & ! Skewness of w on thermodynamic levels [-]
tau1m, & ! Time-scale tau on momentum levels [s]
tauw3t, & ! Time-scale tau on thermodynamic levels [s]
tau_C1_zm, & ! Tau values used for the C1 (dp1) term in wp2 [s]
C1_Skw_fnc, & ! C_1 parameter with Sk_w applied [-]
C11_Skw_fnc, & ! C_11 parameter with Sk_w applied [-]
C16_fnc, & ! C_16 parameter [-]
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 @ momentum levs. [m^3/kg]
invrs_rho_ds_zt, & ! Inv. dry, static density @ thermo. levs. [m^3/kg]
radf, & ! Buoyancy production at CL top [m^2/s^3]
thv_ds_zm, & ! Dry, base-state theta_v on momentum levs. [K]
thv_ds_zt, & ! Dry, base-state theta_v on thermo. levs. [K]
wprtp, & ! Flux of total water mixing ratio [m/s kg/kg]
wpthlp, & ! Flux of liquid water potential temp. [m/s K]
rtp2, & ! Variance of rt (overall) [kg^2/kg^2]
thlp2, & ! Variance of thl (overall) [K^2]
wp2_splat, & ! Tendency of <w'2> due to vertical compression of eddies [m^2/s^3]
wp3_splat ! Tendency of <w'3> due to vertical compression of eddies [m^3/s^4]
type(implicit_coefs_terms), intent(in) :: &
pdf_implicit_coefs_terms ! Implicit coefs / explicit terms [units vary]
logical, intent(in) :: &
l_min_wp2_from_corr_wx, & ! Flag to base the threshold minimum value of wp2 on keeping the
! overall correlation of w and x (w and rt, as well as w and
! theta-l) within the limits of -max_mag_correlation_flux to
! max_mag_correlation_flux.
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_tke_aniso, & ! For anisotropic turbulent kinetic energy, i.e. TKE = 1/2
! (u'^2 + v'^2 + w'^2)
l_standard_term_ta, & ! Use the standard discretization for the turbulent advection
! terms. Setting to .false. means that a_1 and a_3 are pulled
! outside of the derivative in advance_wp2_wp3_module.F90 and in
! advance_xp2_xpyp_module.F90.
l_damp_wp2_using_em, & ! In wp2 equation, use a dissipation formula of -(2/3)*em/tau_zm,
! as in Bougeault (1981)
l_damp_wp3_Skw_squared ! Set damping on wp3 to use Skw^2 rather than Skw^4
! Input/Output Variables
real( kind = core_rknd ), dimension(gr%nz), intent(inout) :: &
wp2, & ! w'^2 (momentum levels) [m^2/s^2]
wp3, & ! w'^3 (thermodynamic levels) [m^3/s^3]
wp3_zm ! w'^3 interpolated to momentum levels [m^3/s^3]
real( kind = core_rknd ), dimension(gr%nz), intent(inout) :: &
wp2_zt ! w'^2 interpolated to thermodyamic levels [m^2/s^2]
! Local Variables
real( kind = core_rknd ), dimension(5,2*gr%nz) :: &
lhs ! Implicit contributions to wp2/wp3 (band diag. matrix)
real( kind = core_rknd ), dimension(2*gr%nz) :: &
rhs, & ! RHS of band matrix
rhs_save ! Saved RHS of band matrix
! real, target, dimension(2*gr%nz) ::
real( kind = core_rknd ), dimension(2*gr%nz) :: &
solut ! Solution to band diagonal system.
real( kind = core_rknd ), dimension(gr%nz) :: &
coef_wp4_implicit_zt, & ! <w'^4>|_zt=coef_wp4_implicit_zt*<w'^2>|_zt^2 [-]
coef_wp4_implicit ! <w'^4> = coef_wp4_implicit * <w'^2>^2 [-]
real( kind = core_rknd ), dimension(gr%nz) :: &
a1, & ! a_1 (momentum levels); See eqn. 23 in `Equations for CLUBB' [-]
a1_zt ! a_1 interpolated to thermodynamic levels [-]
! real, dimension(gr%nz) :: &
! wp2_n ! w'^2 at the previous timestep [m^2/s^2]
real( kind = core_rknd ) :: &
rcond ! Est. of the reciprocal of the condition #
real( kind = core_rknd ), dimension(gr%nz,5) :: &
wp3_pr3_lhs ! wp3_pr3 (implicit) contribution to lhs
real( kind = core_rknd ) :: &
threshold ! Minimum value for wp2 [m^2/s^2]
! Array indices
integer :: k, km1, kp1, k_wp2, k_wp3
! Set logical to true for Crank-Nicholson diffusion scheme
! or to false for completely implicit diffusion scheme.
! Note: Although Crank-Nicholson diffusion has usually been used for wp2
! and wp3 in the past, we found that using completely implicit
! diffusion stabilized the deep convective cases more while having
! almost no effect on the boundary layer cases. Brian; 1/4/2008.
! logical, parameter :: l_crank_nich_diff = .true.
logical, parameter :: l_crank_nich_diff = .false.
!-----------------------------------------------------------------------
!----- Begin Code -----
if ( .not. l_explicit_turbulent_adv_wp3 ) then
if ( iiPDF_type == iiPDF_new .or. iiPDF_type == iiPDF_new_hybrid ) then
! Unpack coef_wp4_implicit from pdf_implicit_coefs_terms.
! Since PDF parameters and the resulting implicit coefficients and
! explicit terms are calculated on thermodynamic levels, the <w'^4>
! implicit coefficient needs to be unpacked as coef_wp4_implicit_zt.
coef_wp4_implicit_zt = pdf_implicit_coefs_terms%coef_wp4_implicit
! The values of <w'^4> are located on momentum levels. Interpolate
! coef_wp4_implicit_zt to momentum levels as coef_wp4_implicit. The
! discretization diagram is found in the description section of
! function wp3_term_ta_new_pdf_lhs below. These values are always
! positive.
coef_wp4_implicit = max( zt2zm( coef_wp4_implicit_zt ), &
zero_threshold )
! Set the value of coef_wp4_implicit to 0 at the lower boundary and at
! the upper boundary. This sets the value of <w'^4> to 0 at the lower
! and upper boundaries.
coef_wp4_implicit(1) = zero
coef_wp4_implicit(gr%nz) = zero
if ( l_stats_samp ) then
call stat_update_var( icoef_wp4_implicit, coef_wp4_implicit, &
stats_zm )
endif ! l_stats_samp
elseif ( iiPDF_type == iiPDF_ADG1 ) then
! Define a_1 and a_3 (both are located on momentum levels).
! They are variables that are both functions of sigma_sqd_w (where
! sigma_sqd_w is located on momentum levels).
a1 = one / ( one - sigma_sqd_w )
! Interpolate a_1 from momentum levels to thermodynamic levels. This
! will be used for the w'^3 turbulent advection (ta) term.
a1_zt = max( zm2zt( a1 ), zero_threshold ) ! Positive def. quantity
endif ! iiPDF_type
endif ! .not. l_explicit_turbulent_adv_wp3
! Compute the explicit portion of the w'^2 and w'^3 equations.
! Build the right-hand side vector.
call wp23_rhs( dt, wp2, wp3, a1, a1_zt, a3, a3_zt, wp3_on_wp2, & ! intent(in)
coef_wp4_implicit, wp4, wpthvp, wp2thvp, um, vm, & ! intent(in)
upwp, vpwp, up2, vp2, Kw1, Kw8, Kh_zt, & ! intent(in)
Skw_zt, tau1m, tauw3t, tau_C1_zm, C1_Skw_fnc, & ! intent(in)
C11_Skw_fnc, C16_fnc, rho_ds_zm, invrs_rho_ds_zt, radf, & ! intent(in)
thv_ds_zm, thv_ds_zt, wp2_splat, wp3_splat, & ! intent(in)
l_crank_nich_diff, & ! intent(in)
l_tke_aniso, & ! intent(in)
l_standard_term_ta, & ! intent(in)
l_damp_wp2_using_em, & ! intent(in)
l_damp_wp3_Skw_squared, & ! intent(in)
rhs ) ! intent(out)
! Save the value of rhs, which will be overwritten with the solution as
! part of the solving routine.
rhs_save = rhs
! Compute the implicit portion of the w'^2 and w'^3 equations.
! Build the left-hand side matrix.
call wp23_lhs( dt, wp2, wm_zm, wm_zt, a1, a1_zt, a3, a3_zt, &
wp3_on_wp2, coef_wp4_implicit, &
Kw1, Kw8, Skw_zt, tau1m, tauw3t, tau_C1_zm, C1_Skw_fnc, &
C11_Skw_fnc, C16_fnc, rho_ds_zm, rho_ds_zt, &
invrs_rho_ds_zm, invrs_rho_ds_zt, l_crank_nich_diff, &
l_upwind_xm_ma, &
l_tke_aniso, &
l_standard_term_ta, &
l_damp_wp3_Skw_squared, &
lhs, wp3_pr3_lhs )
! Solve the system with LAPACK
if ( l_stats_samp .and. iwp23_matrix_condt_num > 0 ) then
! Perform LU decomp and solve system (LAPACK with diagnostics)
! Note that this can change the answer slightly
call band_solvex( "wp2_wp3", 2, 2, 2*gr%nz, nrhs, &
lhs, rhs, solut, rcond )
if ( clubb_at_least_debug_level( 0 ) ) then
if ( err_code == clubb_fatal_error ) then
write(fstderr,*) "Error in wp23_solve calling band_solvex for wp2_wp3"
write(fstderr,*) "wp2 & wp3 LU decomp. failed"
write(fstderr,*) "wp2 and wp3 LHS"
do k = 1, gr%nz
write(fstderr,*) "zt level = ", k, "height [m] = ", &
gr%zt(k), "LHS = ", lhs(1:5,2*k-1)
write(fstderr,*) "zm level = ", k, "height [m] = ", &
gr%zm(k), "LHS = ", lhs(1:5,2*k)
enddo ! k = 1, gr%nz
write(fstderr,*) "wp2 and wp3 RHS"
do k = 1, gr%nz
write(fstderr,*) "zt level = ", k, "height [m] = ", &
gr%zt(k), "RHS = ", rhs_save(2*k-1)
write(fstderr,*) "zm level = ", k, "height [m] = ", &
gr%zm(k), "RHS = ", rhs_save(2*k)
enddo ! k = 1, gr%nz
return
endif
endif
! Est. of the condition number of the w'^2/w^3 LHS matrix
call stat_update_var_pt( iwp23_matrix_condt_num, 1, one / rcond, stats_sfc )
else
! Perform LU decomp and solve system (LAPACK)
call band_solve( "wp2_wp3", 2, 2, 2*gr%nz, nrhs, &
lhs, rhs, solut )
if ( clubb_at_least_debug_level( 0 ) ) then
if ( err_code == clubb_fatal_error ) then
write(fstderr,*) "Error in wp23_solve calling band_solve for wp2_wp3"
write(fstderr,*) "wp2 & wp3 LU decomp. failed"
write(fstderr,*) "wp2 and wp3 LHS"
do k = 1, gr%nz
write(fstderr,*) "zt level = ", k, "height [m] = ", &
gr%zt(k), "LHS = ", lhs(1:5,2*k-1)
write(fstderr,*) "zm level = ", k, "height [m] = ", &
gr%zm(k), "LHS = ", lhs(1:5,2*k)
enddo ! k = 1, gr%nz
write(fstderr,*) "wp2 and wp3 RHS"
do k = 1, gr%nz
write(fstderr,*) "zt level = ", k, "height [m] = ", &
gr%zt(k), "RHS = ", rhs_save(2*k-1)
write(fstderr,*) "zm level = ", k, "height [m] = ", &
gr%zm(k), "RHS = ", rhs_save(2*k)
enddo ! k = 1, gr%nz
return
endif
endif
endif
! Copy result into output arrays and clip
do k = 1, gr%nz
km1 = max( k-1, 1 )
kp1 = min( k+1, gr%nz )
k_wp3 = 2*k - 1
k_wp2 = 2*k
! wp2_n(k) = wp2(k) ! For the positive definite scheme
wp2(k) = solut(k_wp2)
wp3(k) = solut(k_wp3)
end do
if ( l_stats_samp ) then
! Finalize implicit contributions for wp2
do k = 2, gr%nz-1
km1 = max( k-1, 1 )
kp1 = min( k+1, gr%nz )
! w'^2 term dp1 has both implicit and explicit components;
! call stat_end_update_pt.
call stat_end_update_pt( iwp2_dp1, k, &
zmscr01(k) * wp2(k), stats_zm )
! w'^2 term dp2 has both implicit and explicit components (if the
! Crank-Nicholson scheme is selected); call stat_end_update_pt.
! If Crank-Nicholson diffusion is not selected, then w'^3 term dp1 is
! completely implicit; call stat_update_var_pt.
if ( l_crank_nich_diff ) then
call stat_end_update_pt( iwp2_dp2, k, &
zmscr02(k) * wp2(km1) &
+ zmscr03(k) * wp2(k) &
+ zmscr04(k) * wp2(kp1), stats_zm )
else
call stat_update_var_pt( iwp2_dp2, k, &
zmscr02(k) * wp2(km1) &
+ zmscr03(k) * wp2(k) &
+ zmscr04(k) * wp2(kp1), stats_zm )
endif
! w'^2 term ta is completely implicit; call stat_update_var_pt.
call stat_update_var_pt( iwp2_ta, k, &
zmscr05(k) * wp3(k) &
+ zmscr06(k) * wp3(kp1), stats_zm )
! w'^2 term ma is completely implicit; call stat_update_var_pt.
call stat_update_var_pt( iwp2_ma, k, &
zmscr07(k) * wp2(km1) &
+ zmscr08(k) * wp2(k) &
+ zmscr09(k) * wp2(kp1), stats_zm )
! w'^2 term ac is completely implicit; call stat_update_var_pt.
call stat_update_var_pt( iwp2_ac, k, &
zmscr10(k) * wp2(k), stats_zm )
! w'^2 term pr1 has both implicit and explicit components;
! call stat_end_update_pt.
if ( l_tke_aniso ) then
call stat_end_update_pt( iwp2_pr1, k, &
zmscr12(k) * wp2(k), stats_zm )
endif
! w'^2 term pr2 has both implicit and explicit components;
! call stat_end_update_pt.
call stat_end_update_pt( iwp2_pr2, k, &
zmscr11(k) * wp2(k), stats_zm )
enddo
! Finalize implicit contributions for wp3
do k = 2, gr%nz-1, 1
km1 = max( k-1, 1 )
kp1 = min( k+1, gr%nz )
! w'^3 term pr1 has both implicit and explicit components;
! call stat_end_update_pt.
call stat_end_update_pt( iwp3_pr1, k, &
ztscr01(k) * wp3(k), stats_zt )
! w'^3 term dp1 has both implicit and explicit components (if the
! Crank-Nicholson scheme is selected); call stat_end_update_pt.
! If Crank-Nicholson diffusion is not selected, then w'^3 term dp1 is
! completely implicit; call stat_update_var_pt.
if ( l_crank_nich_diff ) then
call stat_end_update_pt( iwp3_dp1, k, &
ztscr02(k) * wp3(km1) &
+ ztscr03(k) * wp3(k) &
+ ztscr04(k) * wp3(kp1), stats_zt )
else
call stat_update_var_pt( iwp3_dp1, k, &
ztscr02(k) * wp3(km1) &
+ ztscr03(k) * wp3(k) &
+ ztscr04(k) * wp3(kp1), stats_zt )
endif
! w'^3 term ta has both implicit and explicit components;
! call stat_end_update_pt.
call stat_end_update_pt( iwp3_ta, k, &
ztscr05(k) * wp3(km1) &
+ ztscr06(k) * wp2(km1) &
+ ztscr07(k) * wp3(k) &
+ ztscr08(k) * wp2(k) &
+ ztscr09(k) * wp3(kp1), stats_zt )
! w'^3 term tp has both implicit and explicit components;
! call stat_end_update_pt.
call stat_end_update_pt( iwp3_tp, k, &
ztscr10(k) * wp2(km1) &
+ ztscr11(k) * wp2(k), stats_zt )
! w'^3 pressure term 3 (pr3) has both implicit and explicit components;
! call stat_end_update_pt
call stat_end_update_pt( iwp3_pr3, k, &
- wp3_pr3_lhs(k,5) * wp3(km1) &
- wp3_pr3_lhs(k,4) * wp2(km1) &
- wp3_pr3_lhs(k,3) * wp3(k) &