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diagnose_correlations_module.F90
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!-----------------------------------------------------------------------
! $Id$
!===============================================================================
module diagnose_correlations_module
use clubb_precision, only: &
core_rknd
implicit none
public :: calc_mean, calc_varnce, calc_w_corr, &
calc_cholesky_corr_mtx_approx, &
cholesky_to_corr_mtx_approx, setup_corr_cholesky_mtx, &
diagnose_correlations
private :: diagnose_corr, rearrange_corr_array, &
corr_array_assertion_checks
private ! Default scope
contains
!-----------------------------------------------------------------------
subroutine diagnose_correlations( pdf_dim, corr_array_pre, & ! Intent(in)
l_calc_w_corr, & ! Intent(in)
corr_array ) ! Intent(out)
! Description:
! This subroutine diagnoses the correlation matrix in order to feed it
! into SILHS microphysics.
! References:
! Larson et al. (2011), J. of Geophysical Research, Vol. 116, D00T02
! (see CLUBB Trac ticket#514)
!-----------------------------------------------------------------------
use clubb_precision, only: &
core_rknd ! Variable(s)
! use array_index, only: &
! iiPDF_w ! Variable(s)
use constants_clubb, only: &
zero
implicit none
intrinsic :: max, sqrt, transpose
! Input Variables
integer, intent(in) :: &
pdf_dim ! number of diagnosed correlations
real( kind = core_rknd ), dimension(pdf_dim, pdf_dim), intent(in) :: &
corr_array_pre ! Prescribed correlations
logical, intent(in) :: &
l_calc_w_corr ! Calculate the correlations between w and the hydrometeors
! Output variables
real( kind = core_rknd ), dimension(pdf_dim, pdf_dim), intent(out) :: &
corr_array
! Local Variables
real( kind = core_rknd ), dimension(pdf_dim, pdf_dim) :: &
corr_array_pre_swapped, &
corr_array_swapped
! We actually don't need this right now
real( kind = core_rknd ), dimension(pdf_dim) :: &
sigma2_on_mu2_ip_array ! Ratios: sigma_x^2/mu_x^2 (ith PDF comp.) ip [-]
integer :: i ! Loop iterator
!-------------------- Begin code --------------------
! Initialize sigma2_on_mu2_ip_array
do i = 1, pdf_dim
sigma2_on_mu2_ip_array(i) = zero
end do
! Swap the w-correlations to the first row for the prescribed correlations
call rearrange_corr_array( pdf_dim, corr_array_pre, & ! Intent(in)
corr_array_pre_swapped) ! Intent(inout)
! diagnose correlations
if ( .not. l_calc_w_corr ) then
corr_array_swapped = corr_array_pre_swapped
endif
call diagnose_corr( pdf_dim, sqrt(sigma2_on_mu2_ip_array), &
corr_array_pre_swapped, &
corr_array_swapped )
! Swap rows back
call rearrange_corr_array( pdf_dim, corr_array_swapped, & ! Intent(in)
corr_array) ! Intent(out)
end subroutine diagnose_correlations
!-----------------------------------------------------------------------
subroutine diagnose_corr( n_variables, sqrt_sigma2_on_mu2_ip, & ! intent(in)
corr_matrix_prescribed, & !intent(in)
corr_matrix_approx ) ! intent(inout)
! Description:
! This subroutine diagnoses the correlation matrix for each timestep.
! References:
! Larson et al. (2011), J. of Geophysical Research, Vol. 116, D00T02
! (see CLUBB Trac ticket#514)
!-----------------------------------------------------------------------
use clubb_precision, only: &
core_rknd ! Variable(s)
! use parameters_tunable, only: &
! alpha_corr ! Constant(s)
use constants_clubb, only: &
max_mag_correlation
implicit none
intrinsic :: &
sqrt, abs, sign
! Input Variables
integer, intent(in) :: &
n_variables ! number of variables in the correlation matrix [-]
real( kind = core_rknd ), dimension(n_variables), intent(in) :: &
sqrt_sigma2_on_mu2_ip ! sqrt of sigma_x^2/mu_x^2 (ith PDF comp.) ip [-]
real( kind = core_rknd ), dimension(n_variables,n_variables), intent(in) :: &
corr_matrix_prescribed ! correlation matrix [-]
! Input/Output Variables
real( kind = core_rknd ), dimension(n_variables,n_variables), intent(inout) :: &
corr_matrix_approx ! correlation matrix [-]
! Local Variables
integer :: i, j ! Loop iterator
real( kind = core_rknd ) :: &
f_ij
! f_ij_o
real( kind = core_rknd ), dimension(n_variables) :: &
s_1j ! s_1j = sqrt(1-c_1j^2)
!-------------------- Begin code --------------------
! Remove compiler warnings about unused variables.
if ( .false. ) then
print *, "sqrt_sigma2_on_mu2_ip = ", sqrt_sigma2_on_mu2_ip
endif
! calculate all square roots
do i = 1, n_variables
s_1j(i) = sqrt(1._core_rknd-corr_matrix_approx(i,1)**2)
end do
! Diagnose the missing correlations (upper triangle)
do j = 2, (n_variables-1)
do i = (j+1), n_variables
! formula (16) in the ref. paper (Larson et al. (2011))
!f_ij = alpha_corr * sqrt_sigma2_on_mu2_ip(i) * sqrt_sigma2_on_mu2_ip(j) &
! * sign(1.0_core_rknd,corr_matrix_approx(1,i)*corr_matrix_approx(1,j))
! If the predicting c1i's are small then cij will be closer to the prescribed value. If
! the c1i's are bigger, then cij will be closer to formular (15) from the ref. paper. See
! clubb:ticket:514:comment:61 for details.
!f_ij = (1-abs(corr_matrix_approx(1,i)*corr_matrix_approx(1,j)))*corr_matrix_prescribed(i,j) &
! + abs(corr_matrix_approx(1,i)*corr_matrix_approx(1,j))*f_ij_o
f_ij = corr_matrix_prescribed(i,j)
! make sure -1 < f_ij < 1
if ( f_ij < -max_mag_correlation ) then
f_ij = -max_mag_correlation
else if ( f_ij > max_mag_correlation ) then
f_ij = max_mag_correlation
end if
! formula (15) in the ref. paper (Larson et al. (2011))
corr_matrix_approx(i,j) = corr_matrix_approx(i,1) * corr_matrix_approx(j,1) &
+ f_ij * s_1j(i) * s_1j(j)
end do ! do j
end do ! do i
end subroutine diagnose_corr
!-----------------------------------------------------------------------
! subroutine approx_w_corr( nz, pdf_dim, pdf_params, & ! Intent(in)
! rrm, Nrm, Ncnm, &
! stdev_w, sigma_rr_1, &
! sigma_Nr_1, sigma_Ncn_1, &
! corr_array) ! Intent(out)
! ! Description:
! ! Approximate the correlations of w with the hydrometeors.
!
! ! References:
! ! clubb:ticket:514
! !-----------------------------------------------------------------------
!
! use clubb_precision, only: &
! core_rknd ! Variable(s)
!
! use pdf_parameter_module, only: &
! pdf_parameter ! Type
!
! use constants_clubb, only: &
! one, & ! Constant(s)
! rr_tol, &
! Nr_tol, &
! Ncn_tol, &
! w_tol, & ! [m/s]
! chi_tol ! [kg/kg]
!
! implicit none
!
! ! Input Variables
! integer, intent(in) :: &
! pdf_dim, & ! Number of diagnosed correlations
! nz ! Number of model vertical grid levels
!
! type(pdf_parameter), dimension(nz), intent(in) :: &
! pdf_params ! PDF parameters [units vary]
!
! real( kind = core_rknd ), dimension(nz), intent(in) :: &
! rrm, & ! Mean rain water mixing ratio, < r_r > [kg/kg]
! Nrm, & ! Mean rain drop concentration, < N_r > [num/kg]
! Ncnm, & ! Mean cloud nuclei conc., < N_cn > [num/kg]
! stdev_w ! Standard deviation of w [m/s]
!
! real( kind = core_rknd ), intent(in) :: &
! sigma_Ncn_1, & ! Standard deviation of Ncn (1st PDF component) [num/kg]
! sigma_Nr_1, & ! Standard deviation of Nr (2nd PDF component) [num/kg]
! sigma_rr_1 ! Standard dev. of ln rr (1st PDF comp.) ip [ln(kg/kg)]
!
! ! Output Variables
! real( kind = core_rknd ), dimension(pdf_dim, pdf_dim, nz), intent(out) :: &
! corr_array
!
! ! Local Variables
! real( kind = core_rknd ), dimension(nz) :: &
! corr_chi_w, & ! Correlation between w and chi(s_mellor) (both components) [-]
! corr_wrr, & ! Correlation between w and rr (both components) [-]
! corr_wNr, & ! Correlation between w and Nr (both components) [-]
! corr_wNcn ! Correlation between w and Ncn (both components) [-]
!
! real( kind = core_rknd ), dimension(nz) :: &
! wpchip_zt, & ! Covariance of chi and w on the zt-grid [(m/s)(kg/kg)]
! wprrp_zt, & ! Covariance of r_r and w on the zt-grid [(m/s)(kg/kg)]
! wpNrp_zt, & ! Covariance of N_r and w on the zt-grid [(m/s)(#/kg)]
! wpNcnp_zt ! Covariance of N_cn and w on the zt-grid [(m/s)(#/kg)]
!
! real( kind = core_rknd ) :: &
! chi_m, & ! Mean of chi (s_mellor) [kg/kg]
! stdev_chi ! Standard deviation of chi (s_mellor) [kg/kg]
!
! integer :: k ! vertical loop iterator
!
! ! ----- Begin Code -----
!
! call approx_w_covar( nz, pdf_params, rrm, Nrm, Ncnm, & ! Intent(in)
! wpchip_zt, wprrp_zt, wpNrp_zt, wpNcnp_zt ) ! Intent(out)
!
! do k = 1, nz
!
! chi_m &
! = calc_mean( pdf_params(k)%mixt_frac, pdf_params(k)%chi_1, &
! pdf_params(k)%chi_2 )
!
! stdev_chi &
! = sqrt( pdf_params(k)%mixt_frac &
! * ( ( pdf_params(k)%chi_1 - chi_m )**2 &
! + pdf_params(k)%stdev_chi_1**2 ) &
! + ( one - pdf_params(k)%mixt_frac ) &
! * ( ( pdf_params(k)%chi_2 - chi_m )**2 &
! + pdf_params(k)%stdev_chi_2**2 ) &
! )
!
! corr_chi_w(k) &
! = calc_w_corr( wpchip_zt(k), stdev_w(k), stdev_chi, &
! w_tol, chi_tol )
!
! corr_wrr(k) &
! = calc_w_corr( wprrp_zt(k), stdev_w(k), sigma_rr_1, w_tol, rr_tol )
!
! corr_wNr(k) &
! = calc_w_corr( wpNrp_zt(k), stdev_w(k), sigma_Nr_1, w_tol, Nr_tol )
!
! corr_wNcn(k) &
! = calc_w_corr( wpNcnp_zt(k), stdev_w(k), sigma_Ncn_1, w_tol, Ncn_tol )
!
! enddo
!
! call set_w_corr( nz, pdf_dim, & ! Intent(in)
! corr_chi_w, corr_wrr, corr_wNr, corr_wNcn, &
! corr_array ) ! Intent(inout)
!
! end subroutine approx_w_corr
!-----------------------------------------------------------------------
! subroutine approx_w_covar( nz, pdf_params, rrm, Nrm, Ncnm, & ! Intent(in)
! wpchip_zt, wprrp_zt, wpNrp_zt, wpNcnp_zt ) ! Intent(out)
! ! Description:
! ! Approximate the covariances of w with the hydrometeors using Eddy
! ! diffusivity.
!
! ! References:
! ! clubb:ticket:514
! !-----------------------------------------------------------------------
!
! use clubb_precision, only: &
! core_rknd ! Variable(s)
!
! use grid_class, only: &
! gr, & ! Variable(s)
! zm2zt, & ! Procedure(s)
! zt2zm
!
! use pdf_parameter_module, only: &
! pdf_parameter ! Type
!
! use parameters_tunable, only: &
! c_K_hm ! Variable(s)
!
! use constants_clubb, only: &
! one ! Constant(s)
!
! use advance_windm_edsclrm_module, only: &
! xpwp_fnc ! Procedure(s)
!
! use variables_diagnostic_module, only: &
! Kh_zm ! Variable(s)
!
! implicit none
!
! ! Input Variables
! integer, intent(in) :: &
! nz ! Number of model vertical grid levels
!
! type(pdf_parameter), dimension(nz), intent(in) :: &
! pdf_params ! PDF parameters [units vary]
!
! real( kind = core_rknd ), dimension(nz), intent(in) :: &
! rrm, & ! Mean rain water mixing ratio, < r_r > [kg/kg]
! Nrm, & ! Mean rain drop concentration, < N_r > [num/kg]
! Ncnm ! Mean cloud nuclei concentration, < N_cn > [num/kg]
!
! ! Output Variables
! real( kind = core_rknd ), dimension(nz), intent(out) :: &
! wpchip_zt, & ! Covariance of chi(s) and w on the zt-grid [(m/s)(kg/kg)]
! wprrp_zt, & ! Covariance of r_r and w on the zt-grid [(m/s)(kg/kg)]
! wpNrp_zt, & ! Covariance of N_r and w on the zt-grid [(m/s)(#/kg)]
! wpNcnp_zt ! Covariance of N_cn and w on the zt-grid [(m/s)(#/kg)]
!
! ! Local Variables
! real( kind = core_rknd ), dimension(nz) :: &
! wpchip_zm, & ! Covariance of chi(s) and w on the zm-grid [(m/s)(kg/kg)]
! wprrp_zm, & ! Covariance of r_r and w on the zm-grid [(m/s)(kg/kg)]
! wpNrp_zm, & ! Covariance of N_r and w on the zm-grid [(m/s)(#/kg)]
! wpNcnp_zm ! Covariance of N_cn and w on the zm-grid [(m/s)(#/kg)]
!
! integer :: k ! vertical loop iterator
!
! ! ----- Begin Code -----
!
! ! calculate the covariances of w with the hydrometeors
! do k = 1, nz
! wpchip_zm(k) = pdf_params(k)%mixt_frac &
! * ( one - pdf_params(k)%mixt_frac ) &
! * ( pdf_params(k)%chi_1 - pdf_params(k)%chi_2 ) &
! * ( pdf_params(k)%w_1 - pdf_params(k)%w_2 )
! enddo
!
!! same for wpNrp
!! wprrp_zm(1:nz-1) &
!! = xpwp_fnc( -c_K_hm * Kh_zm(1:nz-1), &
!! rrm(1:nz-1) / max( precip_frac(1:nz-1), eps ), &
!! rrm(2:nz) / max( precip_frac(2:nz), eps ), &
!! gr%invrs_dzm(1:nz-1) )
!
! wprrp_zm(1:nz-1) &
! = xpwp_fnc( -c_K_hm * Kh_zm(1:nz-1), &
! rrm(1:nz-1), rrm(2:nz), &
! gr%invrs_dzm(1:nz-1) )
!
! wpNrp_zm(1:nz-1) &
! = xpwp_fnc( -c_K_hm * Kh_zm(1:nz-1), &
! Nrm(1:nz-1), Nrm(2:nz), &
! gr%invrs_dzm(1:nz-1) )
!
! wpNcnp_zm(1:nz-1) = xpwp_fnc( -c_K_hm * Kh_zm(1:nz-1), Ncnm(1:nz-1), &
! Ncnm(2:nz), gr%invrs_dzm(1:nz-1) )
!
! ! Boundary conditions; We are assuming constant flux at the top.
! wprrp_zm(nz) = wprrp_zm(nz-1)
! wpNrp_zm(nz) = wpNrp_zm(nz-1)
! wpNcnp_zm(nz) = wpNcnp_zm(nz-1)
!
! ! interpolate back to zt-grid
! wpchip_zt = zm2zt(wpchip_zm)
! wprrp_zt = zm2zt(wprrp_zm)
! wpNrp_zt = zm2zt(wpNrp_zm)
! wpNcnp_zt = zm2zt(wpNcnp_zm)
!
! end subroutine approx_w_covar
!-----------------------------------------------------------------------
function calc_w_corr( wpxp, stdev_w, stdev_x, w_tol, x_tol )
! Description:
! Compute the correlations of w with the hydrometeors.
! References:
! clubb:ticket:514
!-----------------------------------------------------------------------
use clubb_precision, only: &
core_rknd ! Variable(s)
use constants_clubb, only: &
max_mag_correlation
implicit none
intrinsic :: max
! Input Variables
real( kind = core_rknd ), intent(in) :: &
stdev_w, & ! standard deviation of w [m/s]
stdev_x, & ! standard deviation of x [units vary]
wpxp, & ! Covariances of w with the hydrometeors [units vary]
w_tol, & ! tolerance for w [m/s]
x_tol ! tolerance for x [units vary]
real( kind = core_rknd ) :: &
calc_w_corr
! --- Begin Code ---
calc_w_corr = wpxp / ( max(stdev_x, x_tol) * max(stdev_w, w_tol) )
! Make sure the correlation is in [-1,1]
if ( calc_w_corr < -max_mag_correlation ) then
calc_w_corr = -max_mag_correlation
else if ( calc_w_corr > max_mag_correlation ) then
calc_w_corr = max_mag_correlation
end if
end function calc_w_corr
!-----------------------------------------------------------------------
function calc_varnce( mixt_frac, x1, x2, xm, x1p2, x2p2 )
! Description:
! Calculate the variance xp2 from the components x1, x2.
! References:
! Larson et al. (2011), J. of Geophysical Research, Vol. 116, D00T02,
! page 3535
!-----------------------------------------------------------------------
use clubb_precision, only: &
core_rknd ! Variable(s)
implicit none
! Input Variables
real( kind = core_rknd ), intent(in) :: &
mixt_frac, & ! mixing ratio [-]
x1, & ! first component of the double gaussian [units vary]
x2, & ! second component of the double gaussian [units vary]
xm, & ! mean of x [units vary]
x1p2, & ! variance of the first component [units vary]
x2p2 ! variance of the second component [units vary]
! Return Variable
real( kind = core_rknd ) :: &
calc_varnce ! variance of x (both components) [units vary]
! --- Begin Code ---
calc_varnce &
= mixt_frac * ( ( x1 - xm )**2 + x1p2 ) &
+ ( 1.0_core_rknd - mixt_frac ) * ( ( x2 - xm )**2 + x2p2 )
return
end function calc_varnce
!-----------------------------------------------------------------------
function calc_mean( mixt_frac, x1, x2 )
! Description:
! Calculate the mean xm from the components x1, x2.
! References:
! Larson et al. (2011), J. of Geophysical Research, Vol. 116, D00T02,
! page 3535
!-----------------------------------------------------------------------
use clubb_precision, only: &
core_rknd ! Variable(s)
implicit none
! Input Variables
real( kind = core_rknd ), intent(in) :: &
mixt_frac, & ! mixing ratio [-]
x1, & ! first component of the double gaussian [units vary]
x2 ! second component of the double gaussian [units vary]
! Return Variable
real( kind = core_rknd ) :: &
calc_mean ! mean of x (both components) [units vary]
! --- Begin Code ---
calc_mean = mixt_frac * x1 + (1.0_core_rknd - mixt_frac) * x2
return
end function calc_mean
!-----------------------------------------------------------------------
subroutine calc_cholesky_corr_mtx_approx &
( n_variables, corr_matrix, & ! intent(in)
corr_cholesky_mtx, corr_mtx_approx ) ! intent(out)
! Description:
! This subroutine calculates the transposed correlation cholesky matrix
! from the correlation matrix
!
! References:
! 1 Larson et al. (2011), J. of Geophysical Research, Vol. 116, D00T02
! 2 CLUBB Trac ticket#514
!-----------------------------------------------------------------------
use clubb_precision, only: &
core_rknd ! Variable(s)
use constants_clubb, only: &
zero ! Variable(s)
implicit none
! Input Variables
integer, intent(in) :: &
n_variables ! number of variables in the correlation matrix [-]
real( kind = core_rknd ), dimension(n_variables,n_variables), intent(in) :: &
corr_matrix ! correlation matrix [-]
! Output Variables
! correlation cholesky matrix transposed L', C = LL'; see reference 1 formula 10
real( kind = core_rknd ), dimension(n_variables,n_variables), intent(out) :: &
corr_cholesky_mtx, & ! Transposed correlation cholesky matrix [-]
corr_mtx_approx ! Approximated correlation matrix (C = LL') [-]
! Local Variables
integer :: i, j ! Loop iterators
! Swapped means that the w-correlations are swapped to the first row
real( kind = core_rknd ), dimension(n_variables,n_variables) :: &
corr_cholesky_mtx_swap, & ! Swapped correlation cholesky matrix [-]
corr_mtx_approx_swap, & ! Swapped correlation matrix (approx.) [-]
corr_mtx_swap ! Swapped correlation matrix [-]
!-------------------- Begin code --------------------
call rearrange_corr_array( n_variables, corr_matrix, & ! Intent(in)
corr_mtx_swap ) ! Intent(inout)
call setup_corr_cholesky_mtx( n_variables, corr_mtx_swap, & ! intent(in)
corr_cholesky_mtx_swap ) ! intent(out)
call rearrange_corr_array( n_variables, corr_cholesky_mtx_swap, & ! Intent(in)
corr_cholesky_mtx ) ! Intent(inout)
call cholesky_to_corr_mtx_approx( n_variables, corr_cholesky_mtx_swap, & ! intent(in)
corr_mtx_approx_swap ) ! intent(out)
call rearrange_corr_array( n_variables, corr_mtx_approx_swap, & ! Intent(in)
corr_mtx_approx ) ! Intent(inout)
call corr_array_assertion_checks( n_variables, corr_mtx_approx )
! Set lower triangle to zero for conformity
do i = 2, n_variables
do j = 1, i-1
corr_mtx_approx(j,i) = zero
end do
end do
return
end subroutine calc_cholesky_corr_mtx_approx
!-----------------------------------------------------------------------
!-----------------------------------------------------------------------
subroutine setup_corr_cholesky_mtx( n_variables, corr_matrix, & ! intent(in)
corr_cholesky_mtx_t ) ! intent(out)
! Description:
! This subroutine calculates the transposed correlation cholesky matrix
! from the correlation matrix
!
! References:
! 1 Larson et al. (2011), J. of Geophysical Research, Vol. 116, D00T02
! 2 CLUBB Trac ticket#514
!-----------------------------------------------------------------------
use clubb_precision, only: &
core_rknd ! Variable(s)
use constants_clubb, only: &
zero, & ! Variable(s)
one
implicit none
intrinsic :: sqrt
! Input Variables
integer, intent(in) :: &
n_variables ! number of variables in the correlation matrix [-]
real( kind = core_rknd ), dimension(n_variables,n_variables), intent(in) :: &
corr_matrix ! correlation matrix [-]
! Output Variables
! correlation cholesky matrix transposed L', C = LL'; see reference 1 formula 10
real( kind = core_rknd ), dimension(n_variables,n_variables), intent(out) :: &
corr_cholesky_mtx_t ! transposed correlation cholesky matrix [-]
! Local Variables
integer :: i, j, k ! Loop iterators
real( kind = core_rknd ), dimension(n_variables, n_variables) :: &
s ! s(i,j) = sqrt(1-c(i,j)^2); see ref 1
!-------------------- Begin code --------------------
! calculate all necessary square roots
do i = 1, n_variables-1
do j = i+1, n_variables
s(j,i) = sqrt(1._core_rknd - corr_matrix(j,i)**2)
end do
end do
!!! calculate transposed correlation cholesky matrix; ref 1 formula 10
! initialize matrix to zero
do i = 1, n_variables
do j = 1, n_variables
corr_cholesky_mtx_t(j,i) = zero
end do
end do
! initialize upper triangle and diagonal to one
do i = 1, n_variables
do j = i, n_variables
corr_cholesky_mtx_t(j,i) = one
end do
end do
! set diagonal elements
do j = 2, n_variables
do i = 1, j-1
corr_cholesky_mtx_t(j,j) = corr_cholesky_mtx_t(j,j)*s(j,i)
! print *, "s(", j, ",", i, ") = ", s(j,i)
end do
end do
! set first row
do j = 2, n_variables
corr_cholesky_mtx_t(j,1) = corr_matrix(j,1)
end do
! set upper triangle
do i = 2, n_variables-1
do j = i+1, n_variables
do k = 1, i-1
corr_cholesky_mtx_t(j,i) = corr_cholesky_mtx_t(j,i)*s(j,k)
end do
corr_cholesky_mtx_t(j,i) = corr_cholesky_mtx_t(j,i)*corr_matrix(j,i)
end do
end do
return
end subroutine setup_corr_cholesky_mtx
!-----------------------------------------------------------------------
!-----------------------------------------------------------------------
subroutine cholesky_to_corr_mtx_approx( n_variables, corr_cholesky_mtx_t, & ! intent(in)
corr_matrix_approx ) ! intent(out)
! Description:
! This subroutine approximates the correlation matrix from the correlation
! cholesky matrix
!
! References:
! 1 Larson et al. (2011), J. of Geophysical Research, Vol. 116, D00T02
! 2 CLUBB Trac ticket#514
!-----------------------------------------------------------------------
use clubb_precision, only: &
core_rknd ! Variable(s)
implicit none
intrinsic :: matmul, transpose
! Input Variables
integer, intent(in) :: &
n_variables ! number of variables in the correlation matrix [-]
real( kind = core_rknd ), dimension(n_variables,n_variables), intent(in) :: &
corr_cholesky_mtx_t ! transposed correlation cholesky matrix [-]
! Output Variables
real( kind = core_rknd ), dimension(n_variables,n_variables), intent(out) :: &
corr_matrix_approx ! correlation matrix [-]
!-------------------- Begin code --------------------
! approximate the correlation matrix; see ref 1 formula (8)
corr_matrix_approx = matmul(corr_cholesky_mtx_t, transpose(corr_cholesky_mtx_t))
return
end subroutine cholesky_to_corr_mtx_approx
!-----------------------------------------------------------------------
!-----------------------------------------------------------------------
subroutine corr_array_assertion_checks( n_variables, corr_array )
! Description:
! This subroutine does the assertion checks for the corr_array.
! References:
!
!
!-----------------------------------------------------------------------
use clubb_precision, only: &
core_rknd ! Variable(s)
use constants_clubb, only: &
max_mag_correlation ! Variable(s)
use constants_clubb, only: &
one ! Variable(s)
use error_code, only: &
clubb_at_least_debug_level ! Procedure
implicit none
! Input Variables
integer, intent(in) :: &
n_variables ! number of variables in the correlation matrix [-]
real( kind = core_rknd ), dimension(n_variables,n_variables), intent(in) :: &
corr_array ! correlation matrix [-]
! Local Variables
integer :: i, j ! Loop iterator
real( kind = core_rknd ), parameter :: &
tol = 1.e-6_core_rknd ! Maximum acceptable tolerance for the difference of the diagonal
! elements of corr_array to one
!-------------------- Begin code --------------------
if ( clubb_at_least_debug_level( 1 ) ) then
do i = 1, n_variables - 1
do j = i+1, n_variables
! Check if upper and lower triangle values are within the correlation boundaries
if ( ( corr_array(i,j) < -max_mag_correlation ) &
.or. ( corr_array(i,j) > max_mag_correlation ) &
.or. ( corr_array(j,i) < -max_mag_correlation ) &
.or. ( corr_array(j,i) > max_mag_correlation ) ) &
then
stop "Error: A value in the correlation matrix is out of range."
endif
enddo
enddo
endif
if ( clubb_at_least_debug_level( 2 ) ) then
do i = 1, n_variables
! Check if the diagonal elements are one (up to a tolerance)
if ( ( corr_array(i,i) > one + tol ) .or. (corr_array(i,i) < one - tol ) ) then
stop "Error: Diagonal element(s) of the correlation matrix are unequal to one."
endif
enddo
endif
return
end subroutine corr_array_assertion_checks
!-----------------------------------------------------------------------
subroutine rearrange_corr_array( pdf_dim, corr_array, & ! Intent(in)
corr_array_swapped) ! Intent(out)
! Description:
! This subroutine swaps the w-correlations to the first row if the input
! matrix is in the same order as the *_corr_array_cloud.in files. It swaps
! the rows back to the order of the *_corr_array_cloud.in files if the
! input matrix is already swapped (first row w-correlations).
!
! References:
!
!-----------------------------------------------------------------------
use clubb_precision, only: &
core_rknd ! Variable(s)
use array_index, only: &
iiPDF_w ! Variable(s)
implicit none
intrinsic :: max, sqrt, transpose
! Input Variables
integer, intent(in) :: &
pdf_dim ! number of diagnosed correlations
real( kind = core_rknd ), dimension(pdf_dim, pdf_dim), intent(in) :: &
corr_array ! Correlation matrix
! Output variables
real( kind = core_rknd ), dimension(pdf_dim, pdf_dim), intent(out) :: &
corr_array_swapped ! Swapped correlation matrix
! Local Variables
real( kind = core_rknd ), dimension(pdf_dim) :: &
swap_array
!-------------------- Begin code --------------------
! Swap the w-correlations to the first row for the prescribed correlations
corr_array_swapped = corr_array
swap_array = corr_array_swapped (:,1)
corr_array_swapped(1:iiPDF_w, 1) = corr_array_swapped(iiPDF_w, iiPDF_w:1:-1)
corr_array_swapped((iiPDF_w+1):pdf_dim, 1) = corr_array_swapped( &
(iiPDF_w+1):pdf_dim, iiPDF_w)
corr_array_swapped(iiPDF_w, 1:iiPDF_w) = swap_array(iiPDF_w:1:-1)
corr_array_swapped((iiPDF_w+1):pdf_dim, iiPDF_w) = swap_array((iiPDF_w+1):pdf_dim)
return
end subroutine rearrange_corr_array
!-----------------------------------------------------------------------
!-----------------------------------------------------------------------
! subroutine set_w_corr( nz, pdf_dim, & ! Intent(in)
! corr_chi_w, corr_wrr, corr_wNr, corr_wNcn, &
! corr_array ) ! Intent(inout)
!
! ! Description:
! ! Set the first row of corr_array to the according w-correlations.
!
! ! References:
! ! clubb:ticket:514
! !-----------------------------------------------------------------------
!
! use clubb_precision, only: &
! core_rknd ! Variable(s)
!
! use array_index, only: &
! iiPDF_w, & ! Variable(s)
! iiPDF_chi, &
! iiPDF_rr, &
! iiPDF_Nr, &
! iiPDF_Ncn
!
! implicit none
!
! ! Input Variables
! integer, intent(in) :: &
! nz, & ! Number of model vertical grid levels
! pdf_dim ! Number of Variables to be diagnosed
!
! real( kind = core_rknd ), dimension(nz), intent(in) :: &
! corr_chi_w, & ! Correlation between chi (s) & w (both components) [-]
! corr_wrr, & ! Correlation between rr & w (both components) [-]
! corr_wNr, & ! Correlation between Nr & w (both components) [-]
! corr_wNcn ! Correlation between Ncn & w (both components) [-]
!
! ! Input/Output Variables
! real( kind = core_rknd ), dimension(pdf_dim, pdf_dim, nz), &
! intent(inout) :: &
! corr_array
!
! ! ----- Begin Code -----
!
! corr_array(iiPDF_w, iiPDF_chi, :) = corr_chi_w
! corr_array(iiPDF_w, iiPDF_rr, :) = corr_wrr
! corr_array(iiPDF_w, iiPDF_Nr, :) = corr_wNr
! corr_array(iiPDF_w, iiPDF_Ncn, :) = corr_wNcn
!
! end subroutine set_w_corr
!=============================================================================
! subroutine unpack_correlations( pdf_dim, corr_array, & ! Intent(in)
! corr_w_chi, corr_wrr, corr_wNr, corr_wNcn, &
! corr_chi_eta, corr_chi_rr, corr_chi_Nr, corr_chi_Ncn, &
! corr_eta_rr, corr_eta_Nr, corr_eta_Ncn, corr_rrNr )
!
! ! Description:
!
! ! References:
! !-----------------------------------------------------------------------
! use clubb_precision, only: &
! core_rknd ! Variable(s)
! use array_index, only: &
! iiPDF_w, & ! Variable(s)
! iiPDF_chi, &
! iiPDF_eta, &
! iiPDF_rr, &
! iiPDF_Nr, &
! iiPDF_Ncn
! implicit none
! intrinsic :: max, sqrt, transpose
! ! Input Variables
! integer, intent(in) :: &
! pdf_dim ! number of diagnosed correlations
! real( kind = core_rknd ), dimension(pdf_dim, pdf_dim), intent(in) :: &
! corr_array ! Prescribed correlations
! ! Output variables
! real( kind = core_rknd ), intent(out) :: &
! corr_w_chi, & ! Correlation between w and chi(s) (1st PDF component) [-]
! corr_wrr, & ! Correlation between w and rr (1st PDF component) ip [-]
! corr_wNr, & ! Correlation between w and Nr (1st PDF component) ip [-]
! corr_wNcn, & ! Correlation between w and Ncn (1st PDF component) [-]