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pdf_closure_module.F90
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pdf_closure_module.F90
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!---------------------------------------------------------------------------
! $Id$
!===============================================================================
module pdf_closure_module
implicit none
public :: pdf_closure, &
calc_wp4_pdf, &
calc_wp2xp_pdf, &
calc_wpxp2_pdf, &
calc_wpxpyp_pdf, &
calc_vert_avg_cf_component
! Options for the two component normal (double Gaussian) PDF type to use for
! the w, rt, and theta-l (or w, chi, and eta) portion of CLUBB's multivariate,
! two-component PDF.
integer, parameter, public :: &
iiPDF_ADG1 = 1, & ! ADG1 PDF
iiPDF_ADG2 = 2, & ! ADG2 PDF
iiPDF_3D_Luhar = 3, & ! 3D Luhar PDF
iiPDF_new = 4, & ! new PDF
iiPDF_TSDADG = 5, & ! new TSDADG PDF
iiPDF_LY93 = 6 ! Lewellen and Yoh (1993)
! Enumerations used for pdf_description
integer, parameter, public :: &
no_cloud = 1, &
all_cloud = 2, &
partly_cloudy = 3, &
delta_at_sat = 4
! The selected two component normal PDF for w, rt, and theta-l.
integer, parameter, public :: &
iiPDF_type = iiPDF_ADG1
private ! Set Default Scope
contains
!------------------------------------------------------------------------
!#######################################################################
!#######################################################################
! If you change the argument list of pdf_closure you also have to
! change the calls to this function in the host models CAM, WRF, SAM
! and GFDL.
!#######################################################################
!#######################################################################
subroutine pdf_closure( hydromet_dim, p_in_Pa, exner, thv_ds, wm, &
wp2, wp3, sigma_sqd_w, &
Skw, Skthl_in, Skrt_in, rtm, rtp2, &
wprtp, thlm, thlp2, &
wpthlp, rtpthlp, sclrm, &
wpsclrp, sclrp2, sclrprtp, &
sclrpthlp, &
#ifdef GFDL
RH_crit, do_liquid_only_in_clubb, & ! h1g, 2010-06-15
#endif
wphydrometp, wp2hmp, &
rtphmp, thlphmp, &
wp4, wprtp2, wp2rtp, &
wpthlp2, wp2thlp, wprtpthlp, &
cloud_frac, ice_supersat_frac, &
rcm, wpthvp, wp2thvp, rtpthvp, &
thlpthvp, wprcp, wp2rcp, rtprcp, &
thlprcp, rcp2, pdf_params, &
pdf_implicit_coefs_terms, &
F_w, F_rt, F_thl, min_F_w, max_F_w, &
min_F_rt, max_F_rt, min_F_thl, max_F_thl, &
wpsclrprtp, wpsclrp2, sclrpthvp, &
wpsclrpthlp, sclrprcp, wp2sclrp, &
rc_coef )
! Description:
! Subroutine that computes pdf parameters analytically.
!
! Based of the original formulation, but with some tweaks
! to remove some of the less realistic assumptions and
! improve transport terms.
! Corrected version that should remove inconsistency
! References:
! The shape of CLUBB's PDF is given by the expression in
! https://arxiv.org/pdf/1711.03675v1.pdf#nameddest=url:clubb_pdf
! Eqn. 29, 30, 31, 32 & 33 on p. 3547 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.
!----------------------------------------------------------------------
use grid_class, only: &
gr ! Variable type(s)
use constants_clubb, only: & ! Constants
three, & ! 3
two, & ! 2
one, & ! 1
one_half, & ! 1/2
zero, & ! 0
Cp, & ! Dry air specific heat at constant p [J/kg/K]
Lv, & ! Latent heat of vaporization [J/kg]
Rd, & ! Dry air gas constant [J/kg/K]
ep, & ! Rd / Rv; ep = 0.622 [-]
ep1, & ! (1.0-ep)/ep; ep1 = 0.61 [-]
ep2, & ! 1.0/ep; ep2 = 1.61 [-]
rt_tol, & ! Tolerance for r_t [kg/kg]
thl_tol, & ! Tolerance for th_l [K]
T_freeze_K, & ! Freezing point of water [K]
fstderr, &
zero_threshold, &
chi_tol, &
eta_tol, &
max_mag_correlation, &
eps, &
w_tol
use parameters_model, only: &
mixt_frac_max_mag, & ! Variable(s)
sclr_dim ! Number of passive scalar variables
use parameters_tunable, only: &
Skw_denom_coef ! Variable(s)
use pdf_parameter_module, only: &
pdf_parameter, & ! Variable Type
implicit_coefs_terms
use new_pdf_main, only: &
new_pdf_driver ! Procedure(s)
use adg1_adg2_3d_luhar_pdf, only: &
ADG1_pdf_driver, & ! Procedure(s)
ADG2_pdf_driver, &
Luhar_3D_pdf_driver
use new_tsdadg_pdf, only: &
tsdadg_pdf_driver ! Procedure(s)
use LY93_pdf, only: &
LY93_driver ! Procedure(s)
use pdf_utilities, only: &
calc_comp_corrs_binormal, & ! Procedure(s)
calc_corr_chi_x, &
calc_corr_eta_x
use array_index, only: &
l_mix_rat_hm ! Variable(s)
use model_flags, only: &
l_explicit_turbulent_adv_wp3, & ! Variable(s)
l_explicit_turbulent_adv_xpyp
use numerical_check, only: &
pdf_closure_check ! Procedure(s)
use saturation, only: &
sat_mixrat_liq, & ! Procedure(s)
sat_mixrat_ice
use stats_variables, only: &
iwp4, & ! Variables
ircp2, &
iwprtp2, &
iwprtpthlp, &
iwpthlp2
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 :: sqrt, exp, min, max, abs, present
! Input Variables
integer, intent(in) :: &
hydromet_dim ! Number of hydrometeor species [#]
real( kind = core_rknd ), dimension(gr%nz), intent(in) :: &
p_in_Pa, & ! Pressure [Pa]
exner, & ! Exner function [-]
thv_ds, & ! Dry, base-state theta_v (ref. th_l here) [K]
wm, & ! mean w-wind component (vertical velocity) [m/s]
wp2, & ! w'^2 [m^2/s^2]
wp3, & ! w'^3 [m^3/s^3]
Skw, & ! Skewness of w [-]
Skthl_in, & ! Skewness of thl [-]
Skrt_in, & ! Skewness of rt [-]
rtm, & ! Mean total water mixing ratio [kg/kg]
rtp2, & ! r_t'^2 [(kg/kg)^2]
wprtp, & ! w'r_t' [(kg/kg)(m/s)]
thlm, & ! Mean liquid water potential temperature [K]
thlp2, & ! th_l'^2 [K^2]
wpthlp, & ! w'th_l' [K(m/s)]
rtpthlp ! r_t'th_l' [K(kg/kg)]
real( kind = core_rknd ), dimension(gr%nz, sclr_dim), intent(in) :: &
sclrm, & ! Mean passive scalar [units vary]
wpsclrp, & ! w' sclr' [units vary]
sclrp2, & ! sclr'^2 [units vary]
sclrprtp, & ! sclr' r_t' [units vary]
sclrpthlp ! sclr' th_l' [units vary]
#ifdef GFDL
! critial relative humidity for nucleation
real( kind = core_rknd ), dimension( min(1,sclr_dim), 2 ), intent(in) :: & ! h1g, 2010-06-15
RH_crit ! critical relative humidity for droplet and ice nucleation
! ---> h1g, 2012-06-14
logical, intent(in) :: do_liquid_only_in_clubb
! <--- h1g, 2012-06-14
#endif
real( kind = core_rknd ), dimension(gr%nz, hydromet_dim), intent(in) :: &
wphydrometp, & ! Covariance of w and a hydrometeor [(m/s) <hm units>]
wp2hmp, & ! Third-order moment: < w'^2 hm' > [(m/s)^2 <hm units>]
rtphmp, & ! Covariance of rt and a hydrometeor [(kg/kg) <hm units>]
thlphmp ! Covariance of thl and a hydrometeor [K <hm units>]
real( kind = core_rknd ), dimension(gr%nz), intent(inout) :: &
! If iiPDF_type == iiPDF_ADG2, this gets overwritten. Therefore,
! intent(inout). Otherwise it should be intent(in)
sigma_sqd_w ! Width of individual w plumes [-]
! Output Variables
real( kind = core_rknd ), dimension(gr%nz), intent(out) :: &
wp4, & ! w'^4 [m^4/s^4]
wprtp2, & ! w' r_t' [(m kg)/(s kg)]
wp2rtp, & ! w'^2 r_t' [(m^2 kg)/(s^2 kg)]
wpthlp2, & ! w' th_l'^2 [(m K^2)/s]
wp2thlp, & ! w'^2 th_l' [(m^2 K)/s^2]
cloud_frac, & ! Cloud fraction [-]
ice_supersat_frac, & ! Ice cloud fracion [-]
rcm, & ! Mean liquid water [kg/kg]
wpthvp, & ! Buoyancy flux [(K m)/s]
wp2thvp, & ! w'^2 th_v' [(m^2 K)/s^2]
rtpthvp, & ! r_t' th_v' [(kg K)/kg]
thlpthvp, & ! th_l' th_v' [K^2]
wprcp, & ! w' r_c' [(m kg)/(s kg)]
wp2rcp, & ! w'^2 r_c' [(m^2 kg)/(s^2 kg)]
rtprcp, & ! r_t' r_c' [(kg^2)/(kg^2)]
thlprcp, & ! th_l' r_c' [(K kg)/kg]
rcp2, & ! r_c'^2 [(kg^2)/(kg^2)]
wprtpthlp ! w' r_t' th_l' [(m kg K)/(s kg)]
type(pdf_parameter), dimension(gr%nz), intent(out) :: &
pdf_params ! pdf paramters [units vary]
type(implicit_coefs_terms), dimension(gr%nz), intent(out) :: &
pdf_implicit_coefs_terms ! Implicit coefs / explicit terms [units vary]
! Parameters output only for recording statistics (new PDF).
real( kind = core_rknd ), dimension(gr%nz), intent(out) :: &
F_w, & ! Parameter for the spread of the PDF component means of w [-]
F_rt, & ! Parameter for the spread of the PDF component means of rt [-]
F_thl ! Parameter for the spread of the PDF component means of thl [-]
real( kind = core_rknd ), dimension(gr%nz), intent(out) :: &
min_F_w, & ! Minimum allowable value of parameter F_w [-]
max_F_w, & ! Maximum allowable value of parameter F_w [-]
min_F_rt, & ! Minimum allowable value of parameter F_rt [-]
max_F_rt, & ! Maximum allowable value of parameter F_rt [-]
min_F_thl, & ! Minimum allowable value of parameter F_thl [-]
max_F_thl ! Maximum allowable value of parameter F_thl [-]
! Output (passive scalar variables)
real( kind = core_rknd ), intent(out), dimension(gr%nz, sclr_dim) :: &
sclrpthvp, &
sclrprcp, &
wpsclrp2, &
wpsclrprtp, &
wpsclrpthlp, &
wp2sclrp
! Local Variables
! Variables that are stored in derived data type pdf_params.
real( kind = core_rknd ), dimension(gr%nz) :: &
w_1, & ! Mean of w (1st PDF component) [m/s]
w_2, & ! Mean of w (2nd PDF component) [m/s]
varnce_w_1, & ! Variance of w (1st PDF component) [m^2/s^2]
varnce_w_2, & ! Variance of w (2nd PDF component) [m^2/s^2]
rt_1, & ! Mean of r_t (1st PDF component) [kg/kg]
rt_2, & ! Mean of r_t (2nd PDF component) [kg/kg]
varnce_rt_1, & ! Variance of r_t (1st PDF component) [kg^2/kg^2]
varnce_rt_2, & ! Variance of r_t (2nd PDF component) [kg^2/kg^2]
thl_1, & ! Mean of th_l (1st PDF component) [K]
thl_2, & ! Mean of th_l (2nd PDF component) [K]
varnce_thl_1, & ! Variance of th_l (1st PDF component) [K^2]
varnce_thl_2, & ! Variance of th_l (2nd PDF component) [K^2]
corr_w_rt_1, & ! Correlation of w and r_t (1st PDF component) [-]
corr_w_rt_2, & ! Correlation of w and r_t (2nd PDF component) [-]
corr_w_thl_1, & ! Correlation of w and th_l (1st PDF component) [-]
corr_w_thl_2, & ! Correlation of w and th_l (2nd PDF component) [-]
corr_rt_thl_1, & ! Correlation of r_t and th_l (1st PDF component) [-]
corr_rt_thl_2, & ! Correlation of r_t and th_l (2nd PDF component) [-]
alpha_thl, & ! Factor relating to normalized variance for th_l [-]
alpha_rt, & ! Factor relating to normalized variance for r_t [-]
crt_1, & ! Coef. on r_t in s/t eqns. (1st PDF comp.) [-]
crt_2, & ! Coef. on r_t in s/t eqns. (2nd PDF comp.) [-]
cthl_1, & ! Coef. on th_l in s/t eqns. (1st PDF comp.) [(kg/kg)/K]
cthl_2 ! Coef. on th_l in s/t eqns. (2nd PDF comp.) [(kg/kg)/K]
real( kind = core_rknd ), dimension(gr%nz) :: &
chi_1, & ! Mean of chi (old s) (1st PDF component) [kg/kg]
chi_2, & ! Mean of chi (old s) (2nd PDF component) [kg/kg]
stdev_chi_1, & ! Standard deviation of chi (1st PDF component) [kg/kg]
stdev_chi_2, & ! Standard deviation of chi (2nd PDF component) [kg/kg]
stdev_eta_1, & ! Standard dev. of eta (old t) (1st PDF comp.) [kg/kg]
stdev_eta_2, & ! Standard dev. of eta (old t) (2nd PDF comp.) [kg/kg]
covar_chi_eta_1, & ! Covariance of chi and eta (1st PDF comp.) [kg^2/kg^2]
covar_chi_eta_2, & ! Covariance of chi and eta (2nd PDF comp.) [kg^2/kg^2]
corr_w_chi_1, & ! Correlation of w and chi (1st PDF component) [-]
corr_w_chi_2, & ! Correlation of w and chi (2nd PDF component) [-]
corr_w_eta_1, & ! Correlation of w and eta (1st PDF component) [-]
corr_w_eta_2, & ! Correlation of w and eta (2nd PDF component) [-]
corr_chi_eta_1, & ! Correlation of chi and eta (1st PDF component) [-]
corr_chi_eta_2, & ! Correlation of chi and eta (2nd PDF component) [-]
rsatl_1, & ! Mean of r_sl (1st PDF component) [kg/kg]
rsatl_2, & ! Mean of r_sl (2nd PDF component) [kg/kg]
rc_1, & ! Mean of r_c (1st PDF component) [kg/kg]
rc_2, & ! Mean of r_c (2nd PDF component) [kg/kg]
cloud_frac_1, & ! Cloud fraction (1st PDF component) [-]
cloud_frac_2, & ! Cloud fraction (2nd PDF component) [-]
mixt_frac ! Weight of 1st PDF component (Sk_w dependent) [-]
! Note: alpha coefficients = 0.5 * ( 1 - correlations^2 ).
! These are used to calculate the scalar widths
! varnce_thl_1, varnce_thl_2, varnce_rt_1, and varnce_rt_2 as in
! Eq. (34) of Larson and Golaz (2005)
! Passive scalar local variables
real( kind = core_rknd ), dimension(gr%nz,sclr_dim) :: &
sclr1, sclr2, &
varnce_sclr1, varnce_sclr2, &
alpha_sclr, &
corr_sclr_thl_1, corr_sclr_thl_2, &
corr_sclr_rt_1, corr_sclr_rt_2, &
corr_w_sclr_1, corr_w_sclr_2
logical :: &
l_scalar_calc, & ! True if sclr_dim > 0
l_calc_ice_supersat_frac ! True if we should calculate ice_supersat_frac
! Quantities needed to predict higher order moments
real( kind = core_rknd ), dimension(gr%nz) :: &
tl1, tl2, &
beta1, beta2
real( kind = core_rknd ), dimension(gr%nz) :: &
sqrt_wp2, & ! Square root of wp2 [m/s]
Skthl, & ! Skewness of thl [-]
Skrt ! Skewness of rt [-]
! Thermodynamic quantity
real( kind = core_rknd ), dimension(gr%nz), intent(out) :: &
rc_coef ! Coefficient on X'r_c' in X'th_v' equation [K/(kg/kg)]
real( kind = core_rknd ), dimension(gr%nz) :: &
wprcp_contrib_comp_1, & ! <w'rc'> contrib. (1st PDF comp.) [m/s(kg/kg)]
wprcp_contrib_comp_2, & ! <w'rc'> contrib. (2nd PDF comp.) [m/s(kg/kg)]
wp2rcp_contrib_comp_1, & ! <w'^2rc'> contrib. (1st comp) [m^2/s^2(kg/kg)]
wp2rcp_contrib_comp_2, & ! <w'^2rc'> contrib. (2nd comp) [m^2/s^2(kg/kg)]
rtprcp_contrib_comp_1, & ! <rt'rc'> contrib. (1st PDF comp.) [kg^2/kg^2]
rtprcp_contrib_comp_2, & ! <rt'rc'> contrib. (2nd PDF comp.) [kg^2/kg^2]
thlprcp_contrib_comp_1, & ! <thl'rc'> contrib. (1st PDF comp.) [K(kg/kg)]
thlprcp_contrib_comp_2 ! <thl'rc'> contrib. (2nd PDF comp.) [K(kg/kg)]
real( kind = core_rknd ), dimension(gr%nz) :: &
wp2rxp, & ! Sum total < w'^2 r_x' > for all hm species x [(m/s)^2(kg/kg)]
wprxp, & ! Sum total < w'r_x' > for all hm species x [(m/s)(kg/kg)]
thlprxp, & ! Sum total < th_l'r_x' > for all hm species x [K(kg/kg)]
rtprxp ! Sum total < r_t'r_x' > for all hm species x [(kg/kg)^2]
! variables for computing ice cloud fraction
real( kind = core_rknd), dimension(gr%nz) :: &
ice_supersat_frac_1, & ! Ice supersaturation fraction (1st PDF comp.) [-]
ice_supersat_frac_2, & ! Ice supersaturation fraction (2nd PDF comp.) [-]
rt_at_ice_sat1, rt_at_ice_sat2, &
chi_at_ice_sat1, chi_at_ice_sat2, rc_1_ice, rc_2_ice
! To test pdf parameters
real( kind = core_rknd ), dimension(gr%nz) :: &
wm_clubb_pdf, &
rtm_clubb_pdf, &
thlm_clubb_pdf, &
wp2_clubb_pdf, &
rtp2_clubb_pdf, &
thlp2_clubb_pdf, &
wp3_clubb_pdf, &
rtp3_clubb_pdf, &
thlp3_clubb_pdf, &
Skw_clubb_pdf, &
Skrt_clubb_pdf, &
Skthl_clubb_pdf
real( kind = core_rknd ), dimension(gr%nz) :: &
chi_at_liq_sat ! Value of chi at saturation for liquid water; always 0
logical, parameter :: &
l_liq_ice_loading_test = .false. ! Temp. flag liq./ice water loading test
integer :: k, i, hm_idx ! Indices
integer, dimension(gr%nz,2) :: &
pdf_description ! Discription of chi_1 and chi_2 PDF (all_cloud, no_cloud, etc)
#ifdef GFDL
real ( kind = core_rknd ), parameter :: t1_combined = 273.16, &
t2_combined = 268.16, &
t3_combined = 238.16
#endif
!------------------------ Code Begins ----------------------------------
! The value of chi at the saturation point for liquid water is always 0.
chi_at_liq_sat = zero
! Check whether the passive scalars are present.
if ( sclr_dim > 0 ) then
l_scalar_calc = .true.
else
l_scalar_calc = .false.
end if
! Initialize to default values to prevent a runtime error
if ( ( iiPDF_type /= iiPDF_ADG1 ) .and. ( iiPDF_type /= iiPDF_ADG2 ) ) then
alpha_thl = one_half
alpha_rt = one_half
if ( l_scalar_calc ) then
alpha_sclr = one_half
endif ! l_scalar_calc
endif ! iiPDF_type /= iiPDF_ADG1 and iiPDF /= iiPDF_ADG2
! Initialize to 0 to prevent a runtime error
if ( iiPDF_type /= iiPDF_new ) then
do k = 1, gr%nz
pdf_implicit_coefs_terms(k)%coef_wp4_implicit = zero
pdf_implicit_coefs_terms(k)%coef_wprtp2_implicit = zero
pdf_implicit_coefs_terms(k)%coef_wpthlp2_implicit = zero
pdf_implicit_coefs_terms(k)%coef_wp2rtp_implicit = zero
pdf_implicit_coefs_terms(k)%term_wp2rtp_explicit = zero
pdf_implicit_coefs_terms(k)%coef_wp2thlp_implicit = zero
pdf_implicit_coefs_terms(k)%term_wp2thlp_explicit = zero
pdf_implicit_coefs_terms(k)%coef_wprtpthlp_implicit = zero
pdf_implicit_coefs_terms(k)%term_wprtpthlp_explicit = zero
F_w(k) = zero
F_rt(k) = zero
F_thl(k) = zero
min_F_w(k) = zero
max_F_w(k) = zero
min_F_rt(k) = zero
max_F_rt(k) = zero
min_F_thl(k) = zero
max_F_thl(k) = zero
end do
endif ! iiPDF_type /= iiPDF_new
! This allows for skewness to be clipped locally without passing the updated
! value back out.
Skrt = Skrt_in
Skthl = Skthl_in
! To avoid recomputing
sqrt_wp2 = sqrt( wp2 )
! Select the PDF closure method for the two-component PDF used by CLUBB for
! w, rt, theta-l, and passive scalar variables.
! Calculate the mixture fraction for the multivariate PDF, as well as both
! PDF component means and both PDF component variances for each of w, rt,
! theta-l, and passive scalar variables.
if ( iiPDF_type == iiPDF_ADG1 ) then ! use ADG1
call ADG1_pdf_driver( wm, rtm, thlm, wp2, rtp2, thlp2, & ! In
Skw, wprtp, wpthlp, sqrt_wp2, & ! In
sigma_sqd_w, mixt_frac_max_mag, & ! In
sclrm, sclrp2, wpsclrp, l_scalar_calc, & ! In
w_1, w_2, rt_1, rt_2, thl_1, thl_2, & ! Out
varnce_w_1, varnce_w_2, varnce_rt_1, & ! Out
varnce_rt_2, varnce_thl_1, varnce_thl_2, & ! Out
mixt_frac, alpha_rt, alpha_thl, & ! Out
sclr1, sclr2, varnce_sclr1, & ! Out
varnce_sclr2, alpha_sclr ) ! Out
elseif ( iiPDF_type == iiPDF_ADG2 ) then ! use ADG2
call ADG2_pdf_driver( wm, rtm, thlm, wp2, rtp2, thlp2, & ! In
Skw, wprtp, wpthlp, sqrt_wp2, & ! In
sclrm, sclrp2, wpsclrp, l_scalar_calc, & ! In
w_1, w_2, rt_1, rt_2, thl_1, thl_2, & ! Out
varnce_w_1, varnce_w_2, varnce_rt_1, & ! Out
varnce_rt_2, varnce_thl_1, varnce_thl_2, & ! Out
mixt_frac, alpha_rt, alpha_thl, & ! Out
sigma_sqd_w, sclr1, sclr2, & ! Out
varnce_sclr1, varnce_sclr2, alpha_sclr ) ! Out
elseif ( iiPDF_type == iiPDF_3D_Luhar ) then ! use 3D Luhar
call Luhar_3D_pdf_driver( wm, rtm, thlm, wp2, rtp2, thlp2, & ! In
Skw, Skrt, Skthl, wprtp, wpthlp, & ! In
w_1, w_2, rt_1, rt_2, thl_1, thl_2, & ! Out
varnce_w_1, varnce_w_2, varnce_rt_1, & ! Out
varnce_rt_2, varnce_thl_1, & ! Out
varnce_thl_2, mixt_frac ) ! Out
elseif ( iiPDF_type == iiPDF_new ) then ! use new PDF
call new_pdf_driver( wm, rtm, thlm, wp2, rtp2, thlp2, Skw, & ! In
wprtp, wpthlp, rtpthlp, & ! In
Skrt, Skthl, & ! In/Out
w_1, w_2, rt_1, rt_2, & ! Out
thl_1, thl_2, varnce_w_1, & ! Out
varnce_w_2, varnce_rt_1, & ! Out
varnce_rt_2, varnce_thl_1, & ! Out
varnce_thl_2, mixt_frac, & ! Out
pdf_implicit_coefs_terms, & ! Out
F_w, F_rt, F_thl, min_F_w, max_F_w, & ! Out
min_F_rt, max_F_rt, min_F_thl, max_F_thl ) ! Out
elseif ( iiPDF_type == iiPDF_TSDADG ) then
call tsdadg_pdf_driver( wm, rtm, thlm, wp2, rtp2, thlp2, & ! In
Skw, Skrt, Skthl, wprtp, wpthlp, & ! In
w_1, w_2, rt_1, rt_2, & ! Out
thl_1, thl_2, varnce_w_1, & ! Out
varnce_w_2, varnce_rt_1, & ! Out
varnce_rt_2, varnce_thl_1, & ! Out
varnce_thl_2, mixt_frac ) ! Out
elseif ( iiPDF_type == iiPDF_LY93 ) then ! use LY93
call LY93_driver( wm, rtm, thlm, wp2, rtp2, & ! In
thlp2, Skw, Skrt, Skthl, & ! In
w_1, w_2, rt_1, rt_2, & ! Out
thl_1, thl_2, varnce_w_1, & ! Out
varnce_w_2, varnce_rt_1, & ! Out
varnce_rt_2, varnce_thl_1, & ! Out
varnce_thl_2, mixt_frac ) ! Out
endif ! iiPDF_type
! Calculate the PDF component correlations.
! Calculate the PDF component correlations of rt and thl.
call calc_comp_corrs_binormal( rtpthlp, rtm, thlm, rt_1, rt_2, & ! In
thl_1, thl_2, varnce_rt_1, & ! In
varnce_rt_2, varnce_thl_1, & ! In
varnce_thl_2, mixt_frac, & ! In
corr_rt_thl_1, corr_rt_thl_2 ) ! Out
if ( iiPDF_type == iiPDF_ADG1 .or. iiPDF_type == iiPDF_ADG2 ) then
! ADG1 and ADG2 define corr_w_rt_1, corr_w_rt_2, corr_w_thl_1, and
! corr_w_thl_2 to all have a value of 0, so skip the calculation.
corr_w_rt_1 = zero
corr_w_rt_2 = zero
corr_w_thl_1 = zero
corr_w_thl_2 = zero
else
! Calculate the PDF component correlations of w and rt.
call calc_comp_corrs_binormal( wprtp, wm, rtm, w_1, w_2, & ! In
rt_1, rt_2, varnce_w_1, & ! In
varnce_w_2, varnce_rt_1, & ! In
varnce_rt_2, mixt_frac, & ! In
corr_w_rt_1, corr_w_rt_2 ) ! Out
! Calculate the PDF component correlations of w and thl.
call calc_comp_corrs_binormal( wpthlp, wm, thlm, w_1, w_2, & ! In
thl_1, thl_2, varnce_w_1, & ! In
varnce_w_2, varnce_thl_1, & ! In
varnce_thl_2, mixt_frac, & ! In
corr_w_thl_1, corr_w_thl_2 ) ! Out
endif
if ( l_scalar_calc ) then
do i = 1, sclr_dim
! Calculate the PDF component correlations of a passive scalar and
! thl.
call calc_comp_corrs_binormal( sclrpthlp(:,i), sclrm(:,i), & ! In
thlm, sclr1(:,i), sclr2(:,i), & ! In
thl_1, thl_2, varnce_sclr1(:,i), & ! In
varnce_sclr2(:,i), varnce_thl_1, & ! In
varnce_thl_2, mixt_frac, & ! In
corr_sclr_thl_1(:,i), &! Out
corr_sclr_thl_2(:,i) )! Out
! Calculate the PDF component correlations of a passive scalar and rt.
call calc_comp_corrs_binormal( sclrprtp(:,i), sclrm(:,i), rtm, & ! In
sclr1(:,i), sclr2(:,i), & ! In
rt_1, rt_2, varnce_sclr1(:,i), & ! In
varnce_sclr2(:,i), varnce_rt_1, & ! In
varnce_rt_2, mixt_frac, & ! In
corr_sclr_rt_1(:,i), & ! Out
corr_sclr_rt_2(:,i) ) ! Out
if ( iiPDF_type == iiPDF_ADG1 .or. iiPDF_type == iiPDF_ADG2 ) then
! ADG1 and ADG2 define all PDF component correlations involving w
! to have a value of 0, so skip the calculation.
corr_w_sclr_1(:,i) = zero
corr_w_sclr_2(:,i) = zero
else
! Calculate the PDF component correlations of w and a passive
! scalar.
call calc_comp_corrs_binormal( wpsclrp(:,i), wm, sclrm(:,i), & ! In
w_1, w_2, sclr1(:,i), & ! In
sclr2(:,i), varnce_w_1, & ! In
varnce_w_2, varnce_sclr1(:,i), & ! In
varnce_sclr2(:,i), mixt_frac, & ! In
corr_w_sclr_1(:,i), &! Out
corr_w_sclr_2(:,i) )! Out
endif
enddo ! i = 1, sclr_dim
endif ! l_scalar_calc
! Compute higher order moments (these are interactive)
wp2rtp = calc_wp2xp_pdf( wm, rtm, w_1, w_2, rt_1, rt_2, varnce_w_1, &
varnce_w_2, varnce_rt_1, varnce_rt_2, &
corr_w_rt_1, corr_w_rt_2, mixt_frac )
wp2thlp = calc_wp2xp_pdf( wm, thlm, w_1, w_2, thl_1, thl_2, varnce_w_1, &
varnce_w_2, varnce_thl_1, varnce_thl_2, &
corr_w_thl_1, corr_w_thl_2, mixt_frac )
! Compute higher order moments (these may be interactive)
if ( l_explicit_turbulent_adv_wp3 .or. iwp4 > 0 ) then
wp4 = calc_wp4_pdf( wm, w_1, w_2, varnce_w_1, varnce_w_2, mixt_frac )
endif
if ( l_explicit_turbulent_adv_xpyp .or. iwprtp2 > 0 ) then
wprtp2 = calc_wpxp2_pdf( wm, rtm, w_1, w_2, rt_1, rt_2, varnce_w_1, &
varnce_w_2, varnce_rt_1, varnce_rt_2, &
corr_w_rt_1, corr_w_rt_2, mixt_frac )
endif
if ( l_explicit_turbulent_adv_xpyp .or. iwpthlp2 > 0 ) then
wpthlp2 = calc_wpxp2_pdf( wm, thlm, w_1, w_2, thl_1, thl_2, varnce_w_1, &
varnce_w_2, varnce_thl_1, varnce_thl_2, &
corr_w_thl_1, corr_w_thl_2, mixt_frac )
endif
if ( l_explicit_turbulent_adv_xpyp .or. iwprtpthlp > 0 ) then
wprtpthlp = calc_wpxpyp_pdf( wm, rtm, thlm, w_1, w_2, rt_1, rt_2, &
thl_1, thl_2, varnce_w_1, varnce_w_2, &
varnce_rt_1, varnce_rt_2, varnce_thl_1, &
varnce_thl_2, corr_w_rt_1, corr_w_rt_2, &
corr_w_thl_1, corr_w_thl_2, corr_rt_thl_1, &
corr_rt_thl_2, mixt_frac )
endif
! Scalar Addition to higher order moments
if ( l_scalar_calc ) then
do i = 1, sclr_dim
wp2sclrp(:,i) &
= calc_wp2xp_pdf( wm, sclrm(:,i), w_1, w_2, sclr1(:,i), &
sclr2(:,i), varnce_w_1, varnce_w_2, &
varnce_sclr1(:,i), varnce_sclr2(:,i), &
corr_w_sclr_1(:,i), corr_w_sclr_2(:,i), &
mixt_frac )
wpsclrp2(:,i) &
= calc_wpxp2_pdf( wm, sclrm(:,i), w_1, w_2, sclr1(:,i), &
sclr2(:,i), varnce_w_1, varnce_w_2, &
varnce_sclr1(:,i), varnce_sclr2(:,i), &
corr_w_sclr_1(:,i), corr_w_sclr_2(:,i), &
mixt_frac )
wpsclrprtp(:,i) &
= calc_wpxpyp_pdf( wm, sclrm(:,i), rtm, w_1, w_2, &
sclr1(:,i), sclr2(:,i), rt_1, rt_2, &
varnce_w_1, varnce_w_2, &
varnce_sclr1(:,i), varnce_sclr2(:,i), &
varnce_rt_1, varnce_rt_2, &
corr_w_sclr_1(:,i), corr_w_sclr_2(:,i), &
corr_w_rt_1, corr_w_rt_2, &
corr_sclr_rt_1(:,i), &
corr_sclr_rt_2(:,i), mixt_frac )
wpsclrpthlp(:,i) &
= calc_wpxpyp_pdf( wm, sclrm(:,i), thlm, w_1, w_2, &
sclr1(:,i), sclr2(:,i), thl_1, &
thl_2, varnce_w_1, varnce_w_2, &
varnce_sclr1(:,i), varnce_sclr2(:,i), &
varnce_thl_1, varnce_thl_2, &
corr_w_sclr_1(:,i), &
corr_w_sclr_2(:,i), corr_w_thl_1, &
corr_w_thl_2, corr_sclr_thl_1(:,i), &
corr_sclr_thl_2(:,i), mixt_frac )
enddo ! i = 1, sclr_dim
endif ! l_scalar_calc
! Compute higher order moments that include theta_v.
! First compute some preliminary quantities.
! "1" denotes first Gaussian; "2" denotes 2nd Gaussian
! liq water temp (Sommeria & Deardorff 1977 (SD), eqn. 3)
tl1 = thl_1*exner
tl2 = thl_2*exner
#ifdef GFDL
if ( sclr_dim > 0 .and. (.not. do_liquid_only_in_clubb) ) then ! h1g, 2010-06-16 begin mod
where ( tl1 > t1_combined )
rsatl_1 = sat_mixrat_liq( p_in_Pa, tl1 )
elsewhere ( tl1 > t2_combined )
rsatl_1 = sat_mixrat_liq( p_in_Pa, tl1 ) &
* (tl1 - t2_combined)/(t1_combined - t2_combined) &
+ sat_mixrat_ice( p_in_Pa, tl1 ) &
* (t1_combined - tl1)/(t1_combined - t2_combined)
elsewhere ( tl1 > t3_combined )
rsatl_1 = sat_mixrat_ice( p_in_Pa, tl1 ) &
+ sat_mixrat_ice( p_in_Pa, tl1 ) * (RH_crit(1, 1) -one ) &
* ( t2_combined -tl1)/(t2_combined - t3_combined)
elsewhere
rsatl_1 = sat_mixrat_ice( p_in_Pa, tl1 ) * RH_crit(1, 1)
endwhere
where ( tl2 > t1_combined )
rsatl_2 = sat_mixrat_liq( p_in_Pa, tl2 )
elsewhere ( tl2 > t2_combined )
rsatl_2 = sat_mixrat_liq( p_in_Pa, tl2 ) &
* (tl2 - t2_combined)/(t1_combined - t2_combined) &
+ sat_mixrat_ice( p_in_Pa, tl2 ) &
* (t1_combined - tl2)/(t1_combined - t2_combined)
elsewhere ( tl2 > t3_combined )
rsatl_2 = sat_mixrat_ice( p_in_Pa, tl2 ) &
+ sat_mixrat_ice( p_in_Pa, tl2 )* (RH_crit(1, 2) -one) &
* ( t2_combined -tl2)/(t2_combined - t3_combined)
elsewhere
rsatl_2 = sat_mixrat_ice( p_in_Pa, tl2 ) * RH_crit(1, 2)
endwhere
else ! sclr_dim <= 0 or do_liquid_only_in_clubb = .T.
rsatl_1 = sat_mixrat_liq( p_in_Pa, tl1 )
rsatl_2 = sat_mixrat_liq( p_in_Pa, tl2 )
endif !sclr_dim > 0
#else
rsatl_1 = sat_mixrat_liq( p_in_Pa, tl1 )
rsatl_2 = sat_mixrat_liq( p_in_Pa, tl2 ) ! h1g, 2010-06-16 end mod
#endif
! SD's beta (eqn. 8)
beta1 = ep * ( Lv/(Rd*tl1) ) * ( Lv/(Cp*tl1) )
beta2 = ep * ( Lv/(Rd*tl2) ) * ( Lv/(Cp*tl2) )
! s from Lewellen and Yoh 1993 (LY) eqn. 1
chi_1 = ( rt_1 - rsatl_1 ) / ( one + beta1 * rsatl_1 )
chi_2 = ( rt_2 - rsatl_2 ) / ( one + beta2 * rsatl_2 )
! Coefficients for s'
! For each normal distribution in the sum of two normal distributions,
! s' = crt * rt' + cthl * thl';
! therefore, x's' = crt * x'rt' + cthl * x'thl'.
! Larson et al. May, 2001.
crt_1 = one/( one + beta1*rsatl_1)
crt_2 = one/( one + beta2*rsatl_2)
cthl_1 = ( (one + beta1 * rt_1) / ( one + beta1*rsatl_1)**2 ) &
* ( Cp/Lv ) * beta1 * rsatl_1 * exner
cthl_2 = ( (one + beta2 * rt_2) / ( one + beta2*rsatl_2 )**2 ) &
* ( Cp/Lv ) * beta2 * rsatl_2 * exner
! Standard deviation of chi for each component.
! Include subplume correlation of qt, thl
! Because of round-off error,
! stdev_chi_1 (and probably stdev_chi_2) can become negative when
! corr_rt_thl_1 = 1 (and corr_rt_thl_2 = 1).
! One could also write this as a squared term
! plus a postive correction; this might be a neater format
stdev_chi_1 = sqrt( max( crt_1**2 * varnce_rt_1 &
- two * corr_rt_thl_1 * crt_1 * cthl_1 &
* sqrt( varnce_rt_1 * varnce_thl_1 ) &
+ cthl_1**2 * varnce_thl_1, &
zero_threshold ) )
stdev_chi_2 = sqrt( max( crt_2**2 * varnce_rt_2 &
- two * corr_rt_thl_2 * crt_2 * cthl_2 &
* sqrt( varnce_rt_2 * varnce_thl_2 ) &
+ cthl_2**2 * varnce_thl_2, &
zero_threshold ) )
! We need to introduce a threshold value for the variance of chi
where ( stdev_chi_1 <= chi_tol )
! Treat chi as a delta function in this component.
stdev_chi_1 = zero
endwhere
where ( stdev_chi_2 <= chi_tol )
! Treat chi as a delta function in this component.
stdev_chi_2 = zero
end where
! Standard deviation of eta for each component.
stdev_eta_1 = sqrt( max( crt_1**2 * varnce_rt_1 &
+ two * corr_rt_thl_1 * crt_1 * cthl_1 &
* sqrt( varnce_rt_1 * varnce_thl_1 ) &
+ cthl_1**2 * varnce_thl_1, &
zero_threshold ) )
stdev_eta_2 = sqrt( max( crt_2**2 * varnce_rt_2 &
+ two * corr_rt_thl_2 * crt_2 * cthl_2 &
* sqrt( varnce_rt_2 * varnce_thl_2 ) &
+ cthl_2**2 * varnce_thl_2, &
zero_threshold ) )
! We need to introduce a threshold value for the variance of chi
where ( stdev_eta_1 <= eta_tol )
! Treat eta as a delta function in this component.
stdev_eta_1 = zero
end where
where ( stdev_eta_2 <= eta_tol )
! Treat eta as a delta function in this component.
stdev_eta_2 = zero
end where
! Covariance of chi and eta for each component.
covar_chi_eta_1 = crt_1**2 * varnce_rt_1 - cthl_1**2 * varnce_thl_1
covar_chi_eta_2 = crt_2**2 * varnce_rt_2 - cthl_2**2 * varnce_thl_2
! Correlation of chi and eta for each component.
where ( stdev_chi_1 * stdev_eta_1 > zero )
corr_chi_eta_1 = covar_chi_eta_1 / ( stdev_chi_1 * stdev_eta_1 )
elsewhere
corr_chi_eta_1 = zero
end where
where ( stdev_chi_2 * stdev_eta_2 > zero )
corr_chi_eta_2 = covar_chi_eta_2 / ( stdev_chi_2 * stdev_eta_2 )
elsewhere
corr_chi_eta_2 = zero
end where
corr_chi_eta_1 = min( max_mag_correlation, max( -max_mag_correlation, corr_chi_eta_1 ) )
corr_chi_eta_2 = min( max_mag_correlation, max( -max_mag_correlation, corr_chi_eta_2 ) )
! Correlation of w and chi for each component.
corr_w_chi_1 &
= calc_corr_chi_x( crt_1, cthl_1, sqrt(varnce_rt_1), sqrt(varnce_thl_1), &
stdev_chi_1, corr_w_rt_1, corr_w_thl_1 )
corr_w_chi_2 &
= calc_corr_chi_x( crt_2, cthl_2, sqrt(varnce_rt_2), sqrt(varnce_thl_2), &
stdev_chi_2, corr_w_rt_2, corr_w_thl_2 )
! Correlation of w and eta for each component.
corr_w_eta_1 &
= calc_corr_eta_x( crt_1, cthl_1, sqrt(varnce_rt_1), sqrt(varnce_thl_1), &
stdev_eta_1, corr_w_rt_1, corr_w_thl_1 )
corr_w_eta_2 &
= calc_corr_eta_x( crt_2, cthl_2, sqrt(varnce_rt_2), sqrt(varnce_thl_2), &
stdev_eta_2, corr_w_rt_2, corr_w_thl_2 )
! Determine whether to compute ice_supersat_frac. We do not compute
! ice_supersat_frac for GFDL (unless do_liquid_only_in_clubb is true),
! because liquid and ice are both fed into rtm, ruining the calculation.
#ifdef GFDL
if (do_liquid_only_in_clubb) then
l_calc_ice_supersat_frac = .true.
else
l_calc_ice_supersat_frac = .false.
end if
#else
l_calc_ice_supersat_frac = .true.
#endif
! Calculate cloud_frac_1 and rc_1
call calc_cloud_frac_component( chi_1, stdev_chi_1, chi_at_liq_sat, &
cloud_frac_1, rc_1, &
pdf_description(:,1) )
! Calculate cloud_frac_2 and rc_2
call calc_cloud_frac_component( chi_2, stdev_chi_2, chi_at_liq_sat, &
cloud_frac_2, rc_2, &
pdf_description(:,2) )
! Compute cloud fraction and mean cloud water mixing ratio.
! Reference:
! https://arxiv.org/pdf/1711.03675v1.pdf#nameddest=url:anl_int_cloud_terms
cloud_frac = calc_cloud_frac( cloud_frac_1, cloud_frac_2, mixt_frac )
rcm = mixt_frac * rc_1 + ( one - mixt_frac ) * rc_2
rcm = max( zero_threshold, rcm )
if ( l_calc_ice_supersat_frac ) then
! We must compute chi_at_ice_sat1 and chi_at_ice_sat2
where ( tl1 <= T_freeze_K )
rt_at_ice_sat1 = sat_mixrat_ice( p_in_Pa, tl1 )
chi_at_ice_sat1 = ( rt_at_ice_sat1 - rsatl_1 ) &
/ ( one + beta1 * rsatl_1 )
elsewhere
! If the temperature is warmer than freezing (> 0C) then ice_supersat_frac
! is not defined, so we use chi_at_liq_sat
chi_at_ice_sat1 = chi_at_liq_sat
endwhere
where ( tl2 <= T_freeze_K )
rt_at_ice_sat2 = sat_mixrat_ice( p_in_Pa, tl2 )
chi_at_ice_sat2 = ( rt_at_ice_sat2 - rsatl_2 ) &
/ ( one + beta2 * rsatl_2 )
elsewhere
! If the temperature is warmer than freezing (> 0C) then ice_supersat_frac
! is not defined, so we use chi_at_liq_sat
chi_at_ice_sat2 = chi_at_liq_sat
endwhere
! Calculate ice supersaturation fraction in the 1st PDF component.
call calc_cloud_frac_component( chi_1, stdev_chi_1, chi_at_ice_sat1, &
ice_supersat_frac_1, rc_1_ice )
! Calculate ice supersaturation fraction in the 2nd PDF component.
call calc_cloud_frac_component( chi_2, stdev_chi_2, chi_at_ice_sat2, &
ice_supersat_frac_2, rc_2_ice )
endif
! Compute moments that depend on theta_v
!
! The moments that depend on th_v' are calculated based on an approximated
! and linearized form of the theta_v equation:
!
! theta_v = theta_l + { (R_v/R_d) - 1 } * thv_ds * r_t
! + [ {L_v/(C_p*exner)} - (R_v/R_d) * thv_ds ] * r_c;
!
! and therefore:
!
! th_v' = th_l' + { (R_v/R_d) - 1 } * thv_ds * r_t'
! + [ {L_v/(C_p*exner)} - (R_v/R_d) * thv_ds ] * r_c';
!
! where thv_ds is used as a reference value to approximate theta_l.
!
! Reference:
! https://arxiv.org/pdf/1711.03675v1.pdf#nameddest=url:anl_int_buoy_terms
! Calculate rc_coef, which is the coefficient on <x'rc'> in the <x'thv'>
! equation.
rc_coef = Lv / ( exner * Cp ) - ep2 * thv_ds
! Calculate the precipitation loading term in the <x'thv'> equation.
wp2rxp = zero
wprxp = zero
thlprxp = zero
rtprxp = zero
if ( l_liq_ice_loading_test ) then
do hm_idx = 1, hydromet_dim, 1
if ( l_mix_rat_hm(hm_idx) ) then
wp2rxp = wp2rxp + wp2hmp(:,hm_idx)
wprxp = wprxp + wphydrometp(:,hm_idx)
thlprxp = thlprxp + thlphmp(:,hm_idx)
rtprxp = rtprxp + rtphmp(:,hm_idx)
endif
enddo ! hm_idx = 1, hydromet_dim, 1
endif ! l_liq_ice_loading_test
! Calculate the contributions to <w'rc'>, <w'^2 rc'>, <rt'rc'>, and
! <thl'rc'> from the 1st PDF component.
call calc_xprcp_component( wm, rtm, thlm, rcm, & ! In
w_1, rt_1, thl_1, varnce_w_1, & ! In
chi_1, stdev_chi_1, stdev_eta_1, & ! In
corr_w_chi_1, corr_chi_eta_1, & ! In
crt_1, cthl_1, rc_1, cloud_frac_1, & ! In
pdf_description(:,1), & ! In
wprcp_contrib_comp_1, & ! Out
wp2rcp_contrib_comp_1, & ! Out
rtprcp_contrib_comp_1, & ! Out